Modulus of Rigidity or Shear Modulus (G) The modulus of rigidity or shear modulus is a measure of the rigidity of the material when in "shear' - when it is twisting. It is a ratio of the shear stress and the shear strain of the material: Shear Stress F/ A1 (6.1) Shear Strain Ax/h This formula only works when the material is stressed in its elastic region. דן Polar Moment of Inertia (J) This is an equation that shows the ability of a circular cross-section beam or specimen to resis torsion (twisting). A higher polar moment of inertia shows that the beam or specimen can resist i higher torsion or twisting force. The diameter of the beam determines polar moment of inertia A larger diameter gives a larger polar moment of inertia. #D* J = 32 (6.2) The general equation for the torque in a circular cross-section beam or specimen is: TG (6.3) Where is in radian. Torque The twisting force (torque) at the end of a specimen is the moment of force on the torque arm: T = F x Torque Arm Length (m) (6.4) Shear Stress

Answers

Answer 1

Modulus of rigidity (shear modulus) measures a material's rigidity in shear stress/strain. Polar moment of inertia measures the ability of a circular beam to resist torsion measured with J = 32 / (pi x D^4) , and torque is the twisting force on a specimen measured as  T = G x J x θ.

The modulus of rigidity or shear modulus, represented by G, is a measure of a material's rigidity when subjected to shear stress. Shear stress is the force applied perpendicular to the cross-sectional area of a material, while shear strain is the resulting deformation or twisting of the material.

The equation G = shear stress / shear strain is only valid in the elastic region of a material, where it can return to its original shape after the force is removed.

The polar moment of inertia, J, is a measure of a circular cross-section beam or specimen's resistance to torsion or twisting. A larger diameter of the beam results in a larger polar moment of inertia.

The equation J = 32 / (pi x D^4) is used to calculate the polar moment of inertia, where D is the diameter of the beam.

The torque in a circular cross-section beam or specimen is given by the equation T = G x J x θ, where G is the shear modulus, J is the polar moment of inertia, and theta is the angle of twist in radians.

The torque arm length and the applied force F are used to calculate the twisting force or torque in the specimen.

To know more about modulus of rigidity:

https://brainly.com/question/18793028

#SPJ4


Related Questions

Solve for w.
74=171-w

Answers

Answer:

w = 97

Step-by-step explanation:

Solve for w.

74=171-w

74 = 171 - w

w = 171 - 74

w = 97

----------------------

check

74 = 171 - 97

74 = 74

the answer is good

Help. I dont understand this math question and need help please and thank you.

Answers

Answer:

●B. The numbers -1,0,1 are zeros of multiplicity 1.

Step-by-step explanation:

So first, understand that when you are asked for roots, zeros, solutions, or x-intercepts...all of these, they are essentially asking for the same thing. Roots ARE solutions ARE zeros ARE x-intercepts. Maybe its oversimplifying a little bit; there are tiny nuanced differences to a mathematician but if you are just learning this, go ahead and over simplify. They are all the same. So you set it equal to 0 and solve.

Yes, literally, change y to a 0 and solve. See image.

You can factor out a 2x and then you have a "difference of squares" so factor that too.

see image.

"multiplicity" is a cool word. It just means how many times a number is the answer. It sort of doesn't even apply here. 0, -1, and 1 are the answer just one time each...so multiplicity 1. Also, on the graph, the curve will cross the x-axis like a line, so there's that. (See multiplicity 2 is cooler, because the curve will "bounce" at the x-intercept instead, but that's not happening here)

Anyway, set the problem equal to 0 and solve. Ta-da! You're done! Hope this helps! See image.

In the diagram of right triangle ABC shown below, AB= 14 and AC = 9.

What is the measure of ZA, to the nearest degree?
1) 33
2) 40
3) 50
4) 57

Answers

The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a given a right angle triangle in the picture

It is required to find the measure of angle A

Applying cos ratio to find the measure of the angle A:

cosA = 9/14

cosA = 0.642

A = 49.99 ≈ 50 degree

Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

Learn more about trigonometry here:

https://brainly.com/question/26719838

Use the Pythagorean theorem to find the distance between points P and Q​

Answers

The distance between the points P and Q is 10 units using the Pythagorean theorem.

What is Pythagoras Theorem?

The right-angled triangle's three sides are related in accordance with the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of the other two sides. According to the Pythagoras theorem, if a triangle has a right angle, the hypotenuse's square is equal to the sum of the squares of the other two sides.

The coordinates of the point P and Q are (3, 2) and (9, 10).

Using the Pythagoras theorem:

c² = (x2 - x1)² + (y2 - y1)²

Substitute the values:

c² = (9 - 3)² + (10 - 2)²

c² = 36 + 64

c² = 100

c = 10 units.

Hence, the distance between the points P and Q is 10 units using the Pythagorean theorem.

Learn more about Pythagoras Theorem here:

https://brainly.com/question/343682

#SPJ1

-4(7j+2) = 10

Urgent question, please! How do I know I start to solve the above by distributing it, and not dividing the -4 from both sides? How do I know?
Please answer! Thank you.

Answers

Answer:

hdjeujnejsjjdjdjjdjd

You would know when to distribute or divide when the numbers seem easy. For example 7/-4 will stay a fraction so it’s a bit harder to solve. Whereas 4/2 is =2 so it’s easier to solve. In this case you should distribute

-4(7j+2)=10
-28j-8=10
-28j=18
J=-18/28

T/F. Research shows that sketch artists almost always produce more-accurate facial images than technicians using other methods.

Answers

The given statement " Research shows that sketch artists almost always produce more-accurate facial images than technicians using other methods." is True. Because sketch artists are able to capture more nuanced details of face

Research suggests that trained sketch artists can produce more accurate facial images compared to other methods such as facial recognition software or composite imaging software. This is because sketch artists can capture more details and variations in the facial features of a suspect or witness.

They can also work with the witness to create a likeness that accurately reflects their memory of the individual. Additionally, sketch artists are able to adjust and refine the image as the witness provides more information or corrections, leading to a more accurate final image.

To know more about facial images:

https://brainly.com/question/26152614

#SPJ4

A joined in a partnership with B after 3 months by investing Rs. 27000. The profit of A is 3/5th of B's share at the end of one year. What was the amount invested by B?

Answers

Thus, A’s share is Rs. 2,40,000 and B’s share is Rs. 2,61,000.

What is profit and loss?

A profit and loss statement (P&L) is a financial statement that summarizes income, expenses, and expenses incurred during a specified period of time.

Along with the balance sheet and cash flow statement, the income statement is one of the three financial statements issued quarterly and annually by all publicly traded companies.

When used together, the Income Statement, Balance Sheet, and Cash Flow Statement provide detailed insight into the company's overall financial performance.

Accounting is created using the cash method or the accrual method of accounting.

Changes over time are more important than the numbers themselves, so it's important to compare income statements from different accounting periods. 

According to our question-

Ratio of their share in profit = Ratio of their investments

Ratio of their share in profit = Ratio of their investments

⇒ 27000 × 5 + 23000 × 15 ∶ 36000 × 9 + 33000 × 6 ∶ 50000 × 6

Thus, ratio of their investments = 480000 ∶ 522000 ∶ 300000 = 480 ∶ 522 ∶ 300 = 80 ∶ 87 ∶ 50

Profit earned after a year = Rs. 6,51,000

A’s share = (80/217) × 651000 = Rs. 240000

B’s share = (87/217) × 651000 = Rs. 261000

Hence, Thus, A’s share is Rs. 2,40,000 and B’s share is Rs. 2,61,000.

learn more about profit and loss click here:

https://brainly.com/question/26483369

#SPJ1

assume tommys taco truck is open from 11:30am to 1;30 how many cusotmers on average are at the truck

Answers

On average I would say it really depends. 200

exercise 2.4.3 in each case, solve the systems of equations by finding the inverse of the coefficient matrix.

Answers

The inverse of the coefficient matrix is A^-1 = [-2 2]. The solution to the system of equations is x = -1 and y = 1/5.

To solve the system of equations:

2x + 2y = 1

2x - 3y = 0

We can write this system in matrix form as:

[2 2] [x] [1]

[2 -3] [y] = [0]

The coefficient matrix is:

[2 2]

[2 -3]

To find the inverse of the coefficient matrix, we can use the following formula:

A^-1 = (1/|A|) adj(A)

where |A| is the determinant of A and adj(A) is the adjugate of A.

The determinant of the coefficient matrix is:

|A| = (2)(-3) - (2)(2) = -10

The adjugate of the coefficient matrix is:

adj(A) = [-3 2]

[-2 2]

Therefore, the inverse of the coefficient matrix is:

A^-1 = (1/-10) [-3 2]

[-2 2]

Multiplying both sides of the matrix equation by A^-1, we get:

[x] 1 [-3 2] [1]

[y] = -10 [-2 2] [0]

Simplifying the right-hand side, we get:

[x] [-1]

[y] = [1/5]

Therefore, the solution to the system of equations is:

x = -1

y = 1/5

To know more about inverse of matrix:

https://brainly.com/question/4017205

#SPJ4

_____The given question is incomplete, the complete question is given below:

solve the systems of equations by finding the inverse of the coefficient matrix. a. 2x+2y=1 2x-3y-0

HELP ME ASAP YOU WILL BE BRAINLIEST!!!

Answers

Answer:

0.2162   (21.62%)

Step-by-step explanation:

Notice the total time of students is 407. (this is 83+79+88+72+85)

So the probability of having a 3 is:

[tex]P(3)= \frac{88}{407} =0.2162[/tex]

This is 21.62%

Use factoring to solve the polynomial equation. Check by substitution or by using a graphing utility and identifying
x-intercepts.
8x4-32x² = 0
Rewrite the equation in factored form.
(Blank)=0


Then what is the solution pair?

Answers

The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2

Using factoring to solve the polynomial equation

To solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:

8x²(x² - 4) = 0

Now we can use the difference of squares identity to factor the quadratic expression:

8x²(x + 2)(x - 2) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.

Therefore, we can set each factor equal to zero and solve for x:

8x² = 0 or x + 2 = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = -2 or x = 2

So the solution set for the equation is {0, -2, 2}.

To check the solution, we can substitute each value into the original equation and verify that it equals zero.

Read more about polynomial at

https://brainly.com/question/4142886

#SPJ1

A sequence has the nth term rule T(n) = 32 - 3n
What is the value of the first negative term in this sequence?

Answers

[tex]T(11) = -1[/tex] represents the initial negative term inside the series.

What do the concepts positive and negative in logic mean?

A phrase that acknowledges a characteristic or trait in anything is said to be positive. Negative terms are those that downplay some aspect or characteristic of something. The positive or negativizes of a phrase is termed its quality.

What does "positive" and "negative" mean?

Positive simply denotes excellent or the polar opposite of negative. For instance, you're less likely to receive favorable feedback on your scorecard if you've a good mindset toward your assignments. It might be difficult to keep track of all the different definitions of the word positive.

T(n) is negative when [tex]32 - 3n < 0[/tex], which can be rearranged as:

[tex]3n > 32[/tex]

[tex]n > 32/3[/tex]

Since [tex]n[/tex] is an integer, the smallest value of n that satisfies this inequality is [tex]n = 11[/tex].

Therefore, the [tex]11th[/tex] term of the sequence is:

[tex]T(11) = 32 - 3(11) = -1[/tex]

So the first negative term in the sequence is [tex]T(11) = -1.[/tex]

To know more about negative term visit:

https://brainly.com/question/21959954

#SPJ1

prove if one pair of opposite sides of a quadrilateral is both congruent and parallel, then it is a parallelogram

Answers

As we have proved that if one pair of opposite sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram.

To prove this, we can use the concept of alternate angles. Alternate angles are angles that are on opposite sides of a transversal line and are congruent (equal). We can draw a line segment AC between points A and C, which divides the quadrilateral into two triangles, namely triangle ABC and triangle ACD.

Since AB and CD are parallel, line segment AC acts as a transversal line, and the angle formed by AB and AC is equal to the angle formed by CD and AC. These angles are alternate angles, and therefore they are equal. Similarly, the angle formed by BC and AC is equal to the angle formed by AD and AC, since they are also alternate angles.

Now, we know that triangle ABC and triangle ACD share a common side AC, and two pairs of angles are equal in both triangles. Therefore, by the angle-angle-side (AAS) theorem, the two triangles are congruent to each other. Congruent triangles have equal corresponding sides, and since AB and CD are equal, we can conclude that BC and AD are also equal in length.

Therefore, we have shown that if one pair of opposite sides of a quadrilateral are equal and parallel, then the other pair of opposite sides are also equal and parallel.

This means that the quadrilateral is a parallelogram. In this case, we can conclude that quadrilateral ABCD is a parallelogram.

To know more about parallelogram here

https://brainly.com/question/29147156

#SPJ4

Given that a randomly chosen card from a standard deck of 52 cards is less
than 7, what is the probability it is the 5 of diamonds? Assume that aces are
low cards.

Answers

The probability that a randomly chosen card that is less than 7 is the 5 of diamonds is 5%.

How to Solve Probability?

There are four suits in a standard deck of 52 cards: diamonds, clubs, hearts, and spades. Each suit has 13 cards, with ranks ranging from 2 (low) to 10, jack, queen, king, and ace (high).

If a randomly chosen card from the deck is less than 7, there are only two possibilities: it is either a 2, 3, 4, 5, or 6 of any suit, or it is the 5 of diamonds.

There are 20 cards that are less than 7 in the deck (4 cards of each of the 5 ranks). Out of these 20 cards, only one is the 5 of diamonds.

Therefore, the probability that a randomly chosen card that is less than 7 is the 5 of diamonds is:

1/20 = 0.05 = 5%

Learn more about probability on:

https://brainly.com/question/25870256

#SPJ1

1. BIRDS A house cat, Sophie, scared away
5 birds when she arrived on the porch.
If 3 birds remain, write and solve an
equation to find how many birds were
on the porch before Sophie arrived.

Answers

5+3=x
x=8
Hope this helps!

Find the closed formula for each of the following sequences by relating them to a well known sequence. Assume the first term given is a1.
(a) 2, 5, 10, 17, 26, . . .
(b) 0, 2, 5, 9, 14, 20, . . .
(c) 8, 12, 17, 23, 30, . . .
(d) 1, 5, 23, 119, 719, . . .

Answers

The final closed formula answers for each part,

(a) an = n^2 + 1

(b) an = n(n + 1)(n + 2)/6

(c) an = 2n + 6

(d) an = n! + (n-1)! + ... + 2! + 1!

(a) The given sequence can be seen as the sequence of partial sums of the sequence of odd numbers: 1, 3, 5, 7, 9, . . . . That is, the nth term of the given sequence is the sum of the first n odd numbers, which is n^2. Therefore, the closed formula for the given sequence is an = n^2 + 1.

(b) The given sequence can be seen as the sequence of partial sums of the sequence of triangular numbers: 1, 3, 6, 10, 15, . . . . That is, the nth term of the given sequence is the sum of the first n triangular numbers, which is n(n + 1)(n + 2)/6. Therefore, the closed formula for the given sequence is an = n(n + 1)(n + 2)/6.

(c) The given sequence can be seen as the sequence of differences between consecutive squares: 1, 5, 9, 16, 21, . . . . That is, the nth term of the given sequence is the difference between the (n+1)th square and the nth square, which is (n + 1)^2 - n^2 = 2n + 1. Therefore, the closed formula for the given sequence is an = 2n + 6.

(d) The given sequence can be seen as the sequence of partial sums of the sequence defined recursively by a1 = 1 and an+1 = an(n + 1) for n ≥ 1. That is, the nth term of the given sequence is the sum of the first n terms of the recursive sequence. It can be shown that the nth term of the recursive sequence is n! (n factorial), and therefore the nth term of the given sequence is the sum of the first n factorials. That is, an = 1 + 1! + 2! + ... + (n-1)! + n!. Therefore, the closed formula for the given sequence is an = n! + (n-1)! + ... + 2! + 1!.

Learn more about closed formula here

brainly.com/question/29029062

#SPJ4

AA contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning?
Select ALL of the models that can be used to simulate this event.

A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections
E) a bag of 12 black chips and 60 red chips

Answers

Answer:

Model D) a spinner with 6 equal sections can be used to simulate the contestant's chances of winning.

Step-by-step explanation:

A spinner with 6 equal sections represents the possible outcomes of the game show, where each section represents a possible win or loss. Since the contestant has a 1 in 6 chance of winning, the spinner would have one section representing a win and five sections representing a loss. Each spin of the spinner would represent one try at the game show, and the probability of winning can be determined by calculating the theoretical probability of landing on the win section.

universe gas law state that the volume (VM³) of a given mass of an ideal gas varies directly with it absolute temperature (TK) an inversely with it pressure (pM/ m²). A certain mass of gas at an absolute temperature 275K and pressure 10 N/ m² has volume 0.0224m³. find the formula that connect p, V, and T​

Answers

The formula for the  temperature (T), number of gas molecules (n), volume (V), and pressure (P)  is found as: nR = 0.224 / 275.

Explain about the universe gas law?

While dealing with gas, a popular equation was utilized to relate the various components necessary to solve a gas problem. This same Ideal Gas Equation is the name given to this formula. We have always understood that there is no such thing as an ideal. Two well-known presumptions must have been made in this case in advance:

the particles also had no forces acting among them, and these particles do not start taking up any space, implying their atomic volume is entirely ignored.

Those four gas variables are: temperature (T), number of gas molecules (n), volume (V), and pressure (P) . Last but not least, the following equation's constant, R, or the gas constant, will be covered in more detail later:

PV = nRT

PV/T = nR

Given data:

absolute temperature 275Kpressure 10 N/ m² volume 0.0224 m³

Putting the value;

nR = PV/T

nR = 10*0.0224 / 275

nR = 0.224 / 275

Thus, the formula for the  temperature (T), number of gas molecules (n), volume (V), and pressure (P)  is found as: nR = 0.224 / 275.

Know more about the universe gas law

https://brainly.com/question/27870704

#SPJ1

Find the mass of the solid bounded by the xy-plane, yz-plane, xz-plane, and the plane (x/2)+(y/3)+(z/6)=1, if the density of the solid is given by δ(x,y,z)=x+4y.
mass=?

Answers

The mass of the solid is approximately 17.333 units.

To find the mass of the solid bounded by the given planes, we need to integrate the density function δ(x,y,z) over the volume of the solid. We can express the volume of the solid as the region enclosed by the planes

0 ≤ x ≤ 2, 0 ≤ y ≤ 3, 0 ≤ z ≤ 6-3x-2y

So, the mass of the solid is given by the triple integral

M = ∭ δ(x,y,z) dV

= ∫₀² ∫₀³ ∫₀^(6-3x-2y) (x+4y) dz dy dx

= ∫₀² ∫₀³ [(x+4y)(6-3x-2y)] dy dx

= ∫₀² [(6x-3x²)⁄2 + 8xy - 4y²] dy

= ∫₀² [(6x-3x²)⁄2 + 12x - 36] dx

= [3x³/2 - x⁴/4 + 6x² - 36x]₀²

= (12 - 8/3 + 24 - 72) - (0 - 0 + 0 - 0)

= 17.333 units

Learn more about mass here

brainly.com/question/14864913

#SPJ4

Which of the columns in the table below is categorical data? Name Position Goals Bob Goal 0 Cindy Wing 5 Maurice Center 10 Luke Center 15 A. Name B. Goals C. Position​

Answers

The categorical data in the table is column C, Position.

What is table?

In mathematics and statistics, a table is a way of presenting data in a structured manner, typically with columns and rows. Tables are commonly used to organize and present large amounts of data in a clear and concise way, making it easier to read and analyze. Tables can be used to display numerical data, as well as categorical data, such as names, dates, and labels. They can also be used to summarize data and display relationships between different variables. Tables are often used in scientific research, business, finance, and other fields where data analysis is important.

Here,

In the table given, the only column that contains categories or groups is the "Position" column. It contains categorical data as it lists the positions of the players - Goal, Wing, and Center. On the other hand, "Name" and "Goals" columns contain individual values and numerical data, respectively, and are not considered categorical data.

To know more about table,

https://brainly.com/question/30244091

#SPJ1

Tara bought 12 yards of fabric to make tote bags. Each bag requires 1.25 yards of fabric. Write an equation that shows how the number of yards or fabric remaining, depends on the number of tote bags Tara sews, x.

Answers

Answer: y = 12 - 1.25x

Step-by-step explanation:

Let y be the number of yards of fabric remaining after Tara sews x tote bags.

Initially, Tara has 12 yards of fabric. For every tote bag she sews, she uses 1.25 yards of fabric. Therefore, the total amount of fabric used after sewing x tote bags is 1.25x yards.

The number of yards of fabric remaining is the difference between the initial amount of fabric and the total amount of fabric used:

y = 12 - 1.25x

This equation shows how the number of yards of fabric remaining depends on the number of tote bags Tara sews, x. As she sews more tote bags, the amount of fabric remaining decreases.

Answer:

5.75 yds left

1.25 yards each bag multiplied by 5 bags is 6.25 yards utilized

Tara's yardage was 12-6.25 = 5.75.

She has 5.75 yards to go.

Step-by-step explanation:

brainliest pls

A candy-store owner held a contest for customers to guess the number of jelly beans in a
large glass jar that was on display. The contest had more than 100 entrants, although none
guessed the exact total of 517 jelly beans. The median guess was 371 jelly beans, and the
interquartile range was 381 jelly beans. The winner guessed 522 jelly beans.
Which is a measure of how much the customers' guesses varied?
371 jelly beans 381 jelly beans 517 jelly beans
522 jelly beans

Answers

In response to the stated question, we may state that The other numbers range - 371 jelly beans, 517 jelly beans, and 522 jelly beans

What is range?

The variable's range is calculated by taking its greatest observed value and subtracting its minimum observed value (minimum). Possible range or variational bounds: a variety of steel costs; a variety of styles; The scope or size of a method or action: perception. The maximum or anticipated range of a weapon's projectile. A list or set's range is the number between the lowest and maximum. Align all of the numbers before determining the region. Next, subtract (reduce) the lowest number from the greatest number. The solution includes the range of the list. The solution specifies the range of the list.

The interquartile range (IQR) indicates how far the consumers' predictions differed. In this instance, the IQR is 381 jelly beans. The IQR is a measure of the spread of predictions around the median since it shows the range of the middle 50% of the guesses.

The other numbers - 371 jelly beans, 517 jelly beans, and 522 jelly beans - are not measurements of how much the consumers' predictions changed, but rather individual data points (the median guess, the actual number of jelly beans, and the winning guess, respectively).

To know more about range visit:

https://brainly.com/question/28135761

#SPJ1

A invested Rs 4500 for 3 years at the rate of 8% annual compound interest and B invested the
same amount for same time at the rate of per month per rupee I paisa simple interest. Calculate
(i) The interest received by A. (ii) The interest received by B.

Answers

The calculation of the interest received by Investor A and Investor B is as follows:

Investor A = $1,168.70 (Compound)Investor B = $1,620 (Simple).

What is the difference between compound and simple interest?

Compound interest is based on the system of charging interest on accumulated interest and principal for each period.

Simple interest is charged on only the principal for each period.

A's Investment at 8% Annual Compound Interest:

N (# of periods) = 3 years

I/Y (Interest per year) = 8%

PV (Present Value) = $4,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $5,668.70

Total Interest = $1,168.70

B's Investment at Paisa 1 per R1.00 Monthly Simple Interest:

N (# of periods) = 3 years

r = 1 paisa per rupee per month

= 1÷100*100 = 1%

Annually rate =1%*12 = 12%

PV (Present Value) = $4,500

Results:

Total Interest = $1,620 (R4,500 x 12% x 3)

Future Value (FV) = $6,120.

Thus, while Investor A receives $1,168.70 at the end of 3 years, Investor B receives $1,620.

Learn more about compound and simple interests at https://brainly.com/question/2277782.

#SPJ1

Between 11pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour

URGENT

Answers

a. In this exercise, we are given that Mystery Pizza has an average οf 4.2 teIephοne orders per hour between 11 P.M. and midnight on Thursday night. Nοw using these given vaIues, we wiII caIcuIate the probabiIity that at Ieast 30 minutes wiII eIapse before having the next teIephone οrder.

Hοw can we calculate the probability of the expected time for an event to occur?

Accοrding to probabiIity theory and statistics, the exponentiaI distributiοn is the probabiIity distribution of time between occurrences in the Poissοn distribution. It is a distribution of probabiIities that frequentIy correIates to the amount of time before a specific event takes pIace. It is a prοcess in which events take pIace continuousIy, independentIy, and at an average pace that remains constant throughout the process.

In caIcuIating the area under the curve of its graph (CDF), we wiII have to use the fοIIowing formuIa for the mean and the standard deviation,

Mean and Standard Deviatiοn:

[tex]$\begin{array}{r}{\mu={\frac{1}{\lambda}};}\\ {\sigma={\frac{1}{\lambda}}\,.}\end{array}$[/tex]

where,

x is the randοm variabIeλ is the rate parameter, aIsοthe mean time between the event

First, let us calculate the mean and standard deviation using the given Pοisson mean [tex]$\lambda=4.2.$[/tex] Using the fοrmula, we have,

[tex]$\begin{aligned}\rm{\mu=\sigma={\frac{1}{\lambda}}}\\ {={\frac{1}{4.2}\\{=0.2381}\end{aligned}$[/tex]

Sο we have the mean and the standard deviation of 0.2381 hours.

Nοw, we wiII caIcuIate the probabiIity that at Ieast 30 minutes or 0.50 hοurs wiII eIapse before the next teIephone order. Keep in mind that we are caIcuIating the probabiIity for "more than" the x so we wiII use the right-taiIed formuIa for this which is given by,

Right-tailed area(Mοre than x) :

[tex]$P(X\gt x)=e^{-\lambda x};$[/tex]

where,

x is the randοm variableλ is the rate parameter, alsο the mean time between the events

Using the fοrmula, we have:

[tex]$\begin{array}{r l}{P(X\gt 0.50)=e^{-\lambda x}}\\ {=e^{-42(0.50)}}\\ {=0.1225\,.}\end{array}$[/tex]

Therefοre, we can concIude that there is a 12.25% chance that at Ieast 30 minutes or 0.5 hours wiII eIapse before another teIephone order.

b. Next, we wiII caIcuIate the probabiIity that Iess than 15 minutes wiII eIapse befοre the next teIephone order. Remember that we are caIcuIating the probabiIity of Iess than x. This means that we wiII be using the fοrmuIa for the Ieft-taiIed area which is given by,

Left-tailed area(Less than οr equal to x):

[tex]$P(X\leq x)=1-e^{-\lambda x}$[/tex]

where,

x is the randοm variableλ is the rate parameter, alsο the mean time between the eve

Using the fοrmula, we have:

[tex]$\begin{array}{r l}{P(X\leq0.25)=1-e^{-\lambda x}}\\ {=1-e^{-42(0.25)}}\\ {=1-0.3499}\\ {=0.6501\,.}\end{array}$[/tex]

Therefοre, there is a 65.01% that Iess than 15 minutes wiII eIapse before the next teIephοne caII.

c. In this part, we wiII caIcuIate the probabiity that between 15− 30 minutes wiII eIapse befοre the next teIephone order. MathematicaIIy, we have,

[tex]$P(0.25\lt X\lt 0.5)=P(X\lt 0.50)-P(X\lt 0.25)$[/tex]

Frοm part a, we have the value for P(X>0.50) which is 0.1225. Now using the cοmplement rule, we can get P(X<50}

[tex]$\begin{array}{c}{{P(X\lt 50)=1-P(X\gt 50)}}\\ {{=1-0.1225=0.8775\,.}}\end{array}$[/tex]

We have nοw the value of P(X<0.50) which is 0.8775.

We can nοw get the P(0.25<X<0.50)  by subtracting P(X<0.50) by P(X<0.25) frοm part b.. So we have,

[tex]$\begin{array}{r}{P(0.25\lt X\lt 0.50)=P(X\lt 0.50)-P(X\lt 0.25)}\\ {=0.8775-0.6501}\\ {=0.2274\,.}\end{array}$[/tex]

Sο we have P(0.25<X<0.50)=0.2274. Therefore, we can concIude that there is a 22.74% chance that between 15 and 30 minutes wiII eIapse before having a teIephone order.

Tο know more about Standard Deviatiοn visit:-

https://brainly.com/question/30364905

#SPJ1

Subtract: ? 5/6 - 4/6​

Answers

Answer:

1/6

Step-by-step explanation:

5/6 - 4/6 = 1/6

Answer:

Step-by-step explanation:

To subtract these fractions, we need to have a common denominator. In this case, the denominators 5 and 6 do not match, so we have to find the least common multiple (LCM) of 5 and 6, which is 30.

Then, we can convert both fractions so that they have a denominator of 30:

5/6 = 25/30

4/6 = 20/30

Now we can subtract the numerators:

25/30 - 20/30 = 5/30

Simplifying the result to its lowest terms, we have:

5/30 = 1/6

Therefore, 5/6 - 4/6 = 1/6.

f the determinant of a matrix is , and the matrix is obtained from by swapping the third and fourth columns, then

Answers

If the determinant of a 5 times 5 matrix A, swapping two columns in a matrix changes the sign of the determinant. Thus, det(C) = -det(A) = -(9) = -9. Determinant of a 4 times 4 matrix A is det (A) = 6, multiplying a column of a matrix by a scalar k multiplies the determinant by k. Thus, det(B) = 5det(A) = 5(6) = 30.

To evaluate det(C) given that det(A) = 9 and C is obtained by swapping the third and fourth columns of A, we can use the fact that swapping two columns of a matrix multiplies its determinant by -1. Thus, det(C) = -det(A) = -9.

To evaluate det(B) given that det(A) = 6 and B is obtained by multiplying the second column of A by 5, we can use the fact that multiplying a column of a matrix by a scalar multiplies its determinant by that scalar. Thus, det(B) = 5(det(A)) = 5(6) = 30.

To know more about determinant:

https://brainly.com/question/4470545

#SPJ4

____The given question is incomplete, the complete question is given below:

If the determinant of a 5 times 5 matrix A is det (A) = 9= and the matrix C is obtained from A by swapping the third and fourth columns, then det C = If the determinant of a 4 times 4 matrix A is det (A) = 6, and the matrix B is obtained from A by multiplying the second column by 5 then det (B) =

For the graph, find the average rate of change on the intervals given

See attached picture b

Answers

We cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function.

Define the term graph?

The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis. The difference between the change in output values and the change in input values is known as the average rate of change of a function over a period.

Let's assume that the function is denoted by f(x). Then, the average rate of change on the interval (a, b) can be calculated as

average rate of change = (f(b) - f(a)) / (b - a)

Using this formula, we can calculate the average rate of change on the given intervals as follows:

For the interval (-3, -2):

average rate of change = [tex]\frac{[f(-2) - f(-3)]}{[-2 - (-3)]}[/tex]

For the interval (1, 3):

average rate of change = [tex]\frac{(f(3) - f(1))}{(3 - 1)}[/tex]

For the interval (-1, 1):

average rate of change = [tex]\frac{(f(1) - f(-1))}{ (1 - (-1))}[/tex]

Note that we cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function. If you provide the function or the graph, I can help you find the actual values of the average rate of change on these intervals.

To know more about plot, visit:

https://brainly.com/question/30195492

#SPJ1

I will mark you brainiest!

If the triangles above are reflections of each other, then BC ≅ to:
A) DE.
B) ED.
C) EF.
D) DF.
E) AC.

Answers

Answer:

D

Step-by-step explanation:

If their reflections are congruent to each other then looking at the diagram we can see a reflection just like a mirror where its flipped on the other side of the dotted line. When flipping it and aligning one triangle to the other we find that BC is congruent to DF

A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. Yoself drank 4 ounces of orange Juice. What percent of the daily recommended amount of Vitamin C is this ? Explain your thinking.

Answers

Step-by-step explanation:

'Yoself'  drank 1/4 of 16 oz so he got 1/4 of 250%  

   1/4 * 250% = 62.5 %

Let f(x) = x? - 6x + 8 and g (x) = x - 5.
Find (f + g) (x) and (f - g) (x) .

Answers

Answer:

(f + g)(x) = x^2 - 5x + 3.

(f - g)(x) = x^2 - 7x + 13

Step by step explanation:

To find (f + g)(x), we add the functions f(x) and g(x) together:

(f + g)(x) = f(x) + g(x) = (x^2 - 6x + 8) + (x - 5)

Combining like terms, we get:

(f + g)(x) = x^2 - 5x + 3

Therefore, (f + g)(x) = x^2 - 5x + 3.

To find (f - g)(x), we subtract the function g(x) from f(x):

(f - g)(x) = f(x) - g(x) = (x^2 - 6x + 8) - (x - 5)

Again, combining like terms, we get:

(f - g)(x) = x^2 - 7x + 13

Therefore, (f - g)(x) = x^2 - 7x + 13.
Other Questions
if the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square. the area of this square will be 40cm^2 greater than the area of the rectangle. Find the area of the rectangle. who is the physicist who invented the electric battery 2. Is the coal seam exposed on both sides of the prominent north-south trending mountain, or just on the east side? What is the lowest eleva- tion at which coal occurs in the map area? Question 14 (2 points)Suppose you flip a coin and then roll a die. You record your result. What is theprobability you flip heads and roll a 6?1/121/41/29/12 The image shows flat sedimentary rock layers in the foreground and angled sedimentary rock layers in the background.Flat sedimentary rock layers in the foreground, and angled sedimentary rock layers in the background.According to the principle of original horizontality, what most likely happened to the rock layers in the background?They cracked at an angle.They were deposited at an angle.They were deposited vertically and then shifted by a geologic event.They were deposited horizontally and then shifted by a geologic event. Angerstein Inc. produces calendars in a two-process, two-department operation. In the Printing Department, calendars are printed and cut. In the Assembly Department, the material received from Printing is assembled into individual calendars and bound. Each department maintains its own Work in Process Inventory, and costs are assigned using weighted average process costing. In Assembly, conversion costs are incurred evenly throughout the process; direct material is added at the end of the process. For September 2013, the following production and cost information is available for the Assembly Department: Beginning WIP Inventory: 5,000 calendars (30 percent complete as to conversion); transferred in cost, $7,550; conversion cost, $1,093Transferred in during September: 80,000 calendarsCurrent period costs: transferred in, $80,000; direct material, $10,270; conversion, $13,991Ending WIP Inventory: 6,000 calendars (80 percent complete as to conversion)For the Assembly Department, compute the following:a. equivalent units of production for each cost componentb. cost per EUP for each cost componentc. cost transferred to Finished Goods Inventoryd. cost of ending WIP Inventory Drag and drop the labels to describe the dose-response curve. Many people sabotage their goals and dreams by unconsciously choosing actions, thoughts, and/or emotions that get them off course from their goals and dreams.True or False shirley, a u.s. citizen, has invented a solar-powered amplifier that can be used in small speakers, such as bluetooth speakers, to increase the volume up to five times. she decides to apply for a patent for this device in the united states. if she receives approval for the patent, what would be the duration of patent protection? Question 24 (2 points)Suppose a race takes place involving 15 participants. In how many different ways canthe top three finishers be arranged?3154552730 All of the following are characteristics of a plantation excepA. Produced one to two cash cropsB. work was done by slave laborersC. operated like a small farmD. operated like a small self-sufficient community the oldest bird fossils date back to around 150 million years ago. the number of different bird species in the fossil record remained small for the next 90 million years. around 65 million years ago, the dinosaurs went extinct. after the extinction, around 60 million years ago, thousands of new bird species began to appear in the fossil record that occupied a variety of habitats. what it is? The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the united states from birth to 17 years, given the households annual income, x. What is the approximate total cost of raising a child from birth to 17 years in a household with an annual income of 80,321 write the overall equation and mechanism for the synthesis of isopentyl acetate. include structures. include all reagents and products but not solvents. g A series of locks manages the water height along a water source used to produce energy. As the locks are opened and closed, the water height between two consecutive locks fluctuates.The height of the water at point B located between two locks is observed. Water height measurements are made every 10 minutes beginning at 8:00 a.m.It is determined that the height of the water at B can be modeled by the function f(x)=11cos(x/48 5/12)+28 , where the height of water is measured in feet and x is measured in minutes.What is the maximum and minimum water height at B, and when do these heights first occur? in a distributor ignition system, what rotates under the distributor cap to send the high voltage to each spark plug wire? a firm's stock is currently selling for $25 per share, the annual dividend is $1.00, and expected earnings are $5.00 per share. what is the firm's dividend payout ratio? How do you calculate working capital investments? art has come out with a new and improved product. as a result, the firm projects an roe of 25%, and it will maintain a plowback ratio of 0.20. its earnings this coming year will be $3 per share. investors expect a 12% rate of return on the stock. what price do you expect art shares to sell for in 4 years? dealignment eraThe party era that lasted from the late 1960s to the early 1990s that was characterized by a gradual reduction in the dominance of the Democratic Party without another party becoming truly dominant.the new deal coalition slowly disintegrated in the 1968 election (in which Nixon was elected) and collapsed in 1980 when Republicans captured the presidency and the Senatewhat emerged was a political era in which republican and democratic parties had relatively equal footingthis change was triggered by three major developments:-the strong support by the democratic party for the civil rights movement caused many white southerners to become Republicans. This also caused African Americans and northeastern republicans to become democrats-democratic support for feminists and gays, and supported their efforts for equal rights and a strict separation of church and state. THis caused religiously conservative Democrats to support the Republican party instead-the democratic party's support for antiwar sentiments gave Republicans the opportunity to become the party that favored a strong national defense. This caused Democrats who supported a strong military and aggressive foreign policy to favor the Republican partyall of these factors caused the democratic party to lose their big advantage in control over local government and decreased their strength in party identification. Democrats also began to lose control in Congress, first in the Senate then the house