Angela is riding on a circular Ferris wheel that has a 59-foot radius. After boarding the Ferris wheel, she traveled a distance of 44.3 feet along the arc before the Ferris wheel stopped for the next rider.
a) Make a drawing of the situation and illustrate relevant quantities.
b) The angle that Angela swept out along the arc had a measure of how many radians?
c) The angle that Angela swept out along the arc had a measure of how many degrees?

Answers

Answer 1

a) Drawing of the situation is shown in below figure.

b) 0.75 radians

c) 42.97 degrees

Define the term conversion?

Conversion is the process of changing a value from one unit or system of measurement to another.

a) The situation of the drawing: The center of the Ferris wheel is labeled "O", and its radius is 59 feet. Angela boards the Ferris wheel at point A and travels a distance of 44.3 feet along the arc to point B. The angle that she sweeps out along the arc is labeled θ.

(Drawing of the situation is shown in below figure)

b) The length of an arc of a circle by the formula:  s = rθ

Given, the radius of the circle is 59 feet and the length of the arc that Angela travels is 44.3 feet. So,

θ = s / r

θ = 44.3 / 59

θ ≈ 0.75 radians

Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 0.75 radians.

c) To convert radians to degrees, we use the formula:

θ (in degrees) = θ (in radians) × 180 / π

θ (in degrees) = 0.75 × 180 / π

θ (in degrees) ≈ 42.97 degrees

Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 42.97 degrees.

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Angela Is Riding On A Circular Ferris Wheel That Has A 59-foot Radius. After Boarding The Ferris Wheel,
Answer 2

a) Drawing of the situation is shown in below figure.
b) 0.75 radians
c) 42.97 degrees

Define the term conversion?

Conversion is the process of changing a value from one unit or system of measurement to another.


a) The situation of the drawing: The center of the Ferris wheel is labeled "O", and its radius is 59 feet. Angela boards the Ferris wheel at point A and travels a distance of 44.3 feet along the arc to point B. The angle that she sweeps out along the arc is labeled θ.
(Drawing of the situation is shown in below figure)
b) The length of an arc of a circle by the formula:  s = rθ
Given, the radius of the circle is 59 feet and the length of the arc that Angela travels is 44.3 feet. So,
θ = s / r
θ = 44.3 / 59
θ ≈ 0.75 radians
Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 0.75 radians.
c) To convert radians to degrees, we use the formula:
θ (in degrees) = θ (in radians) × 180 / π
θ (in degrees) = 0.75 × 180 / π
θ (in degrees) ≈ 42.97 degrees
Therefore, the angle that Angela sweeps out along the arc has a measure of approximately 42.97 degrees.

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Angela Is Riding On A Circular Ferris Wheel That Has A 59-foot Radius. After Boarding The Ferris Wheel,

Related Questions

If point c is between points A and B the. __+CB=AB

Answers

AC+ CB=AB is the answer

Help please! I have no idea!!!!

Answers

By shifting the appropriate numbers to the appropriate locations, the equations become true with [tex]f(-6) = 5, f(x) = 3[/tex] , and  [tex]x = -5,[/tex] and  [tex]f(7) = 8[/tex] .

What is equation?

An equation is a claim that two expressions are equivalent in mathematics. Usually, it has one or more factors, which stand in for the unknowable elements we're trying to figure out how to calculate.

Equations can be used to depict actual-world circumstances or to explain relationships between various mathematical things.

For instance, the equation  [tex]"x + 3 = 7"[/tex] indicates that the total of the constant "3" and the variable "x" equals 7. By taking 3 out of both parts of the equation, we can find "x" and get [tex]"x = 4"[/tex] as a result.

Given

To make the equations true, move the right values to the right places in the table below:

[tex]f(-6) = 5[/tex]

[tex]f(x) = 3; x = -5[/tex]

[tex]f(7) = 8[/tex]

By shifting the appropriate numbers to the appropriate locations, the equations become true with  [tex]f(-6) = 5, f(x) = 3,[/tex] and [tex]x = -5[/tex] , and [tex]f(7) = 8[/tex] .

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The complete question is :- Use the table below to drag the correct numbers to their appropriate spots to make the equations true:

(Fill in the blank)

X                                      f(x)

-6                                     8

7                                        3

4                                      -5

3                                      -2

-5                                     12

Standard Error of the Mean =
Confidence Interval Estimate for the Mean
Margin of Error E= Z
= Z. V
±Z
You want to rent a one-bedroom apartment near BCIT for next term. The mean monthly rent for a random sample of 36 apartments advertised for rent on Craigslist is $1,235. Assume that the population standard deviation is $150.
(a) Give the point estimate of the true mean monthly rent for one-bedroom
apartments available for rent near BCIT.
Answer=$
(b) At the 95% confidence level, what is the margin of error on your estimate of the true mean monthly rent for one-bedroom apartments available for rent near
BCIT.
Answer=$
(c) Construct a 95% confidence interval for the true mean monthly rent for one-bedroom apartments.
Lower value=$
Upper value=$
Choose the correct statement to interpret the confidence interval.
• I am totally confident that the population mean belongs to this confidence interval.
• I am 95% confident that the true population mean belongs to this confidence interval.
(d) A friend claims the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300. Based on your confidence interval do you agree?
• Yes
• No
(e) What is the z-score used to construct a 92% confidence interval?
Answer= (Enter a positive value in 2 decimal places)

Answers

"I am 95% convinced that the true population mean corresponds to this confidence interval," is the appropriate sentence to use when interpreting the confidence interval.

What does the statistical term "population" mean?

Each whole group that shares at least one trait is referred to be a population. People do not make up all populations. Individuals, animals, groups, organisations, edifices, edifices, buildings, houses, farms, items, or events can all be considered populations.

As a rough estimate, the true mean monthly rent is $1,235.

At a 95% confidence level, the critical value (Z) for a two-tailed test is 1.96. The margin of error can be calculated as follows:

The 95% confidence interval can be obtained as follows:

CI = 1235 1.96*(150/36) CI = X Z*(n/n)

Lower value: 1.96 * (150/36) * 1235 = $1,175.20

Higher value: $1,294.80 = 1235 + 1.96 * (150/36).

Higher value: $1,294.80; Lower value: $1,175.20

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the measures of the angles in a triangle are in the extended ratio of 1:4:7 find the measures of the angles

Answers

The angles of the triangle measure 15 degrees, 60 degrees, and 105 degrees.

Let the measures of the angles in the triangle be x, 4x, and 7x, where x is a constant.

According to the properties of a triangle, the sum of the angles is 180 degrees. So we have

x + 4x + 7x = 180

Simplifying this equation, we get

12x = 180

Dividing both sides by 12, we get

x = 15

Therefore, the measures of the angles are:

x = 15 degrees

4x = 4 × 15

Multiply the numbers

= 60 degrees

7x = 7 × 15

Multiply the numbers

= 105 degrees

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If An = 4(2)^n-1 , what is Sa?​

Answers

The sum of the geometric progression is the sum S₃ = 32

What is sum of terms of a geometric progression?

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

a = first term ,r = common ratio and n = number of terms

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

a = first term = 4 and r = common ratio = 2

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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How many 3/4 are in 2?

Answers

Answer:

Step-by-step explanation:

Because we want to know how many three-fourths there are, we have to make groups of 3 fourths, or divide the number of fourths we have by 3. So there are (2\times 4)\div 3 = 8\div 3 = 2 \fraction three-fourths in 2.

What is the value of 2/2 exponent -3

Answers

Answer:1

Step-by-step explanation:

2/2=1

1^-3=1

1/1times1times1

Answer:

1

Step-by-step explanation:

[tex]\frac{2}{2}[/tex] = 1

[tex]1^{-3}[/tex] To make a negative exponent positive, put it under one.

[tex]\frac{1}{1^{3} }[/tex] = [tex]\frac{1}{1}[/tex] = 1

Helping in the name of Jesus.

The table below shows a set of dataWhich statement about the table is true?

Answers

The correct option A) There is a cluster, and as x decreases, y increases.

The table represents a set of data containing two variables, x and y. By analyzing the data, we can observe a cluster of values around x = 4 with corresponding y values in the range of 42-45. As we move towards smaller x values, there is a general trend of increasing y values. However, there are a few outliers. Based on these observations, statement A is the most accurate description of the data in the table. It is important to note that the accuracy of the statement is limited to the given data, and further analysis or additional data may reveal a different trend or pattern.

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Complete question:

The table below shows a set of data. Which statement about the table is true?

x: 1.6, 1.9, 2.3, 3.4, 3.8, 4.2, 4.3, 4.6, 4.8.

y: 39, 38, 42, 40, 41, 44, 42, 45, 44

Which statement about the table is true?

A) There is a cluster, and as x decreases, y increases.

B) There is a cluster, and as x increases, y increases.

C) There is not a cluster, and as x increases, y increases.

D) There is not a cluster, and as x decreases, y increases.

Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=1/38, where 0≤t≤38
Step 1 of 2:
What is the probability that you will wait at least 26 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.
Step 2 of 2:
What is the average waiting time?

Answers

The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.

Step 1:

The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:

P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38

= (38/38) - (26/38) = 12/38 = 0.316

So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.

Step 2:

The average waiting time can be calculated by finding the expected value of the probability density function:

E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt

= [(t²)/(238)] from 0 to 38

= (38²)/(238) = 19

Therefore, the average waiting time is 19 minutes.

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Parallelogram ABCD is a rhombus with measure EBC = 36. What is the measure of DAE?

picture below

Answers

Answer:

54°

Step-by-step explanation:

AB = BC = CD = AD (Because all sides of a rhombus are equal)

Let's consider the triangle DBC:

BC = DC => ∠DBC = 36°

The angle DCB is equal to:

180° - 36*2 = 180° - 72° = 108°

In a parallelogram, opposite angles are equal.

Then the angle DAB = DCB = 108°

Also, we know that the diagonals of a rhombus are the bisectors of the angles from which they come.

So, the angle DAE = EAB = 108° / 2 = 54°

Find the slope of the line that passes through the pair of points.

(5, 4), (8, –1)


Answers

Answer:

m = -5/3

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (5, 4) (8, –1)

We see the y decrease by 5 and the x increase by 3, so the slope is

m = -5/3

There are two coins. One of them is a biased coin such that P (head): P (tail) is 1 : 3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.​

Answers

Answer:

Step-by-step explanation:

Let B be the event that the selected coin is biased, and F be the event that the selected coin is fair. Let H be the event that the coin toss shows a head.

We want to find P(B|H), the probability that the selected coin is biased given that the coin toss shows a head. By Bayes' theorem, we have:

P(B|H) = P(H|B) * P(B) / P(H)

We know that P(H|B) = 1/4 (since the biased coin has a probability of 1/4 of showing a head), and that P(B) = 1/2 (since there are two coins, one of which is biased).

To find P(H), we can use the law of total probability:

P(H) = P(H|B) * P(B) + P(H|F) * P(F)

P(H) = (1/4) * (1/2) + (1/2) * (1/2)

P(H) = 3/8

Putting it all together:

P(B|H) = P(H|B) * P(B) / P(H)

P(B|H) = (1/4) * (1/2) / (3/8)

P(B|H) = 1/3

Therefore, the probability that the selected coin is biased given that the coin toss shows a head is 1/3.

Find the volume of the solid.
3 in
8 in
8 in
7 in
15 in

Answers

Answer:

Volume = length x width x height

3 in x 8 in x 8 in = 192 cubic inches

A cube of sugar is 2cm wide. Calculate the number of cube in a box 720cm³​

Answers

Answer:

90 cubes in the box.

Step-by-step explanation:

To find how many cubes would fit into the box, first we must find the volume of each cube. 2cm x 2cm x 2cm= 8 cubic centimeters. The entire volume of the box is 720 cubic centimeters, so we can divide 720 by 8.

720/8=90

90 cubes can fit into the box.

Answer: 90

Step-by-step explanation:

First, we need to calculate the volume of one cube of sugar:

V = s³, where s is the side length of the cube

V = 2³ = 8 cm³

To find the number of cubes that can fit in a box of 720 cm³, we need to divide the volume of the box by the volume of one cube:

720 cm³ ÷ 8 cm³/cube = 90 cubes

Therefore, 90 cubes of sugar can fit in a box with a volume of 720 cm³.

Find the values of a and b such that 4x^2+12x=4(x+p)^2-q

Answers

Answer: p = 1.5 and q = 9

Step-by-step explanation:

Expand the right side then compare the coefficients of like terms on both sides, that is

4(x + p)² - q ← expand (x + p)² using FOIL

= 4(x² + 2px + p²) - q ← distribute parenthesis

= 4x² + 8px + 4p² - q

Comparing coefficients of like terms on both sides

8p = 12 ( coefficients of x- terms ) ← divide both sides by 8

p = 1.5

4p² - q = 0 ( constant terms ), that is

4(1.5)² - q = 0

9 - q = 0 ( subtract 9 from both sides )

- q = - 9 ( multiply both sides by - 1 )

q = 9

IF 1 POUND OF RAW SPAGHETTI NOODLES MAKES 5 CUPS OF COOKED SPAGHETTI NOODLES, HOW MANY POUNDS OF RAW SPAGHETTI NOODLES WOULD BE NEEDED TO MAKE 30 CUPS OF COOKED NOODLES

Answers

Answer: 6 pounds

Step-by-step explanation:

If 1 pound of raw spaghetti makes 5 cups of cooked spaghetti, then we can set up a proportion:

1 pound raw spaghetti : 5 cups cooked spaghetti = x pounds raw spaghetti : 30 cups cooked spaghetti

To solve for x, we can cross-multiply and simplify:

1 * 30 = 5 * x

30 = 5x

x = 6

Therefore, 6 pounds of raw spaghetti noodles would be needed to make 30 cups of cooked noodles.

Multiply fraction or mixed number by a whole number 3 x 3/5

Answers

Answer:

To multiply a whole number and a fraction, we can simply multiply the whole number with the numerator of the fraction and keep the denominator the same.

So, 3 x 3/5 = (3 x 3)/5 = 9/5

Therefore, 3 x 3/5 = 9/5.

Answer:

Step-by-step explanation:

9x/5

Individuals who identify as male and female were surveyed
regarding their diets.
Meat-
eater
Male 35
Female 37
Total 72
.
Vegetarian Pescatarian Vegan Total
12
23
35
24
14
38
18
27
45
89
101
190
What is the probability that a randomly selected
person is a pescatarian or vegetarian? Round your
answer to the hundredths place.

Answers

Answer:

The number of individuals who are either pescatarians or vegetarians is 12 + 27 = 39.

The total number of individuals surveyed is 190.

Therefore, the probability of selecting a pescatarian or vegetarian at random from the survey is:

39/190 ≈ 0.21

Rounding to the hundredths place, the probability is approximately 0.21.

Find an equation for a sinusoidal function that has period 47, amplitude 1, and contains the point
(-л, 2).
Write your answer in the form f(x) = Asin (Bx + C) + D, where A, B, C, and D are real numbers.
f(x) =

Answers

The sine function with the desired features is given as follows:

F(x) = sin(3.5π(x + π/2)) + 1.

How to define the sine function?

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are listed as follows:

A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.

The function has an amplitude of 1, hence the parameter A is given as follows:

A = 1.

The period is of 4/7, hence the coefficient B is given as follows:

2π/B = 4/7

4B = 14π

B = 3.5π.

The function contains the point (-π, 2), hence the phase shift and the vertical shift are given as follows:

c = π/2, as the function has it's maximum value at x = π, while the standard function has at x = π/2.d = 1, as the function oscillates between 0 and 2.

Hence the function is:

F(x) = sin(3.5π(x + π/2)) + 1.

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Question 6 (2 points)
A wire costs $3 per foot. How much will 18 inches of wire cost?
$1.50
$3.00
$4.50
$9

Answers

It’s 4 dollars and 50 cents

Answer:

$4.50

Step-by-step explanation:

There are 12 inches in a foot. 18 inches is 1.5 feet.

1 foot of wire is $3.00 and a half of foot should be $1.50.

1.5 feet of wire should cost $4.50

1.5 ft × $3/ft

= $4.50

15. Math. The poissonier receives 30 lb.. 4 oz. of
dressed mahi-mahi. After filleting and skinning.
13 lb.. 12 oz. of fillets were produced. What
is the yield percentage of the fillets? If the
whole dressed mahi-mahi was purchased
for $5.85/b.. what is the per pound cost of
the fillets?

Answers

Answer:

To find the yield percentage of the fillets, we need to divide the weight of the fillets by the weight of the dressed mahi-mahi and then multiply by 100 to get a percentage:

Yield percentage = (Weight of fillets / Weight of dressed mahi-mahi) x 100%

First, we need to convert the weights to a common unit, such as ounces:

Weight of dressed mahi-mahi = 30 lb. 4 oz. = 484 oz.

Weight of fillets = 13 lb. 12 oz. = 220 oz.

Now we can calculate the yield percentage:

Yield percentage = (220 oz. / 484 oz.) x 100% = 45.45%

So the yield percentage of the fillets is 45.45%.

To find the per pound cost of the fillets, we need to divide the total cost of the dressed mahi-mahi by its weight in pounds, and then multiply by the yield percentage to get the cost per pound of fillets:

Total cost of dressed mahi-mahi = 30.25 lb. x $5.85/b. = $176.96

Weight of dressed mahi-mahi in pounds = 30.25 lb.

Weight of fillets in pounds = 13.75 lb.

Cost per pound of fillets = (Total cost of dressed mahi-mahi / Weight of dressed mahi-mahi) x Yield percentage / 100%

Cost per pound of fillets = ($176.96 / 30.25 lb.) x 45.45% = $3.04/lb.

Therefore, the per pound cost of the fillets is $3.04/lb.

3.4 3.2 3.3 5m 3.142 Radius of semi-circie = 5.5m Area of cir Au 35m YOGA TWEM Define the word Perimeter in this context. Calculate the length of the swimming pool. If the circumference of the semi-circle is 17 3m. Calculate tl. total perimeter of the swimming pool. Calculate the total area of the floor of the swimm You may use the given formu​

Answers

In the context of a semi-circle, the perimeter refers to the total distance around the curved edge of the semi-circle. It is calculated by adding the length of the straight edge (diameter) to half the circumference of the semi-circle.

The total area of the floor of the swimming pool is 23.86 square meters.

How to calculate the value

The diameter of the semi-circle is twice the radius, so the diameter is 2 × 5.5m = 11m.

Therefore, the perimeter of the semi-circle is:

Perimeter = Diameter + Circumference/2

Perimeter = 11m + 17.3m/2

Perimeter = 20.3m

The length of the swimming pool is equal to the perimeter of the semi-circle, which is 20.3 meters.

To calculate the total area of the floor of the swimming pool, we need to find the area of the semi-circle. The formula for the area of a semi-circle is:

Area = πr²/2

where π is a constant approximately equal to 3.14 and r is the radius of the semi-circle.

In this case, the radius is 5.5m, so the area of the semi-circle is:

Area = π(5.5m)²/2

Area = 47.71m²/2

Area = 23.86m²

Therefore, the total area of the floor of the swimming pool is 23.86 square meters.

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Radius of semi-circle = 5.5m Define the word Perimeter in this context. Calculate the length of the swimming pool. If the circumference of the semi-circle is 17 3m.  Calculate the total area of the floor of the swimming pool.

FILL IN THE BLANK.A point that moves on a coordinate line is said to be in simple ___ ___ if its distance d from origin at time t is given by either d=a sinωt or d=a cosωt.

Answers

"A point that moves on a coordinate line is said to be in simple harmonic motion if its distance d from origin at time t is given by either d = a sinωt or d = a cosωt."

Any function which is written in the form 'a sin(ωt+Ф)' and 'a cos(ωt+Ф)' is said to be a simple harmonic motion.

One definition of a periodic motion is a straightforward harmonic motion. The acceleration of the particle at any location is directly proportional to the displacement from the mean position in simple harmonic motion, which is an oscillatory motion.

Simple harmonic motion, or SHM, is a specific type of repeated or periodic motion that describes the motion of the pendulum. The oscillating object's location changes sinusoidally over time.

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Suppose the chance of rain on Saturday is and the chance of rain on Sunday is also. A student wants to run a simulation to estimate the probability that it will rain on both days. (Example 1) Date Go Online You can complete you Part A How can the student model the chance of it raining on each day? Design a simulation.​

Answers

The student can model the chance of it raining on each day through a simulation that is designed with the help of a random number generator.

How to model the situation ?

Use a random number generator to simulate the probability of rain for Saturday and Sunday, using the given probability as the likelihood of rain. For example, if the probability of rain is 0.3, the random number generator can generate a random number between 0 and 1, and if the number is less than 0.3, it is considered as rain, otherwise, it is considered as no rain.

Repeat step 1 a large number of times, say 10,000 or more, to obtain a sample of random outcomes for the probability of rain on each day. Count the number of times it rains on both days in the sample. The student can then divide the number of times it rains on both days by the total number of simulations to estimate the probability of it raining on both days.

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what the answer of this

Answers

The correct option for this question is (d) "No, none of the sides are parallel."

why it is and what is a Quadrilateral?

To determine if quadrilateral CDEF is a trapezoid, we need to check if it has exactly one pair of parallel sides.

We can find the slopes of the line segments CD and EF as follows:

slope of CD = (5 - (-6)) / (-8 - (-1)) = 11 / (-7) = -1.57 (approx.)

slope of EF = (8 - 5) / (3 - 4) = 3 / (-1) = -3

Since the slopes are different, CD and EF are not parallel, and therefore, CDEF is not a trapezoid.

Alternatively, we can also find the slopes of the line segments CF and DE as follows:

slope of CF = (-5 - (-6)) / (4 - (-1)) = 1/5

slope of DE = (8 - 5) / (3 - (-8)) = 3/11

Since the slopes are different, CF and DE are not parallel, and therefore, CDEF is not a trapezoid.

Therefore, the answer is option (d) "No, none of the sides are parallel."

A quadrilateral is a geometric shape that has four straight sides and four vertices (corners). It is a two-dimensional polygon with four sides and four angles. The sum of the interior angles of a quadrilateral is always 360 degrees.

There are many types of quadrilaterals, including squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.

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in exploration 4.5.3 question 7, what is the magnitude of the the sum of the forces? (round your answer to the nearest tenth).\

Answers

Because the resultant is the closing side of the triangle according to the triangle law of vector addition, the resultant vector's magnitude would be 13.93 metres.

A vector quantity is what?

The vector quantities are those that include both the direction and the magnitude of the quantities.

The vector quantities include things like force, acceleration, and displacement.

Scalar quantities only have the magnitude of the quantity measured; they do not have information about the direction.

The triangle law of vector addition can be used to calculate the resultant vector.

Using the right-angled triangle's Pythagoras theorem

[tex]Base^{2} + Height^{2} = Resultant^{2}[/tex]

[tex]132 + 52 = Resultant^{2}[/tex]

Outcome 2 = 194

The outcome is 194

=13.93 m

According to the triangle law of vector addition, the resultant vector would have a magnitude of 13.93 metres since it is the triangle's closing side.

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A rain gutter is made of sheets of metal 9 inches wide. The gutters have a 3 inch base and two 3 inch sides, folded up at an angle of . What angle will maximize the cross sectional area of the rain gutter?

Answers

The value of angle that maximizes the cross sectional area is 60°

What is the cross sectional area of a solid?

The cross sectional area of a solid is the two dimensional surface formed when the solid is sectioned by a plane.

The shape of the cross sectional area of the gutter is a trapezoid

Area of a trapezoid = ((Sum of the lengths of the parallel sides)/2) × Height

Let a and b represent the parallel sides of the trapezoid, and let a represent the base of the trapezoid we get;

A = ((a + b)/2) × h

a = 3 inches

b = The longer parallel side

h = The height of the trapezoid

The angle formed by the sides of a trapezium and the horizontal = θ

Therefore;

h = 3 × sin(θ)

b = 3 + 2 × 3·cos(θ)

A(θ) = ((3 + 3 + 2 × 3·cos(θ)) × 3 × sin(θ))/2 = 9·sin(θ)·cos(θ) + 9·sin(θ)

At the extremum value of θ, we get;

A'(θ) = 18·cos²(θ) + 9·cos(θ) - 9 = 0

Solving, we get;

cos(θ) = 0.5 or cos(θ) = -1

Therefore;

θ = arccos(0.5) = 60° and θ = arccos(0.5) = 180°

When θ = 60°, we get;

A(max) = 9·sin(60)·cos(60) + 9·sin(60) ≈ 11.69

The cross sectional area when θ is 60° is about 11.69 square inches which is larger than the 9 square inched when θ = 90°

The angle that maximizes the cross sectional area is θ = 60°

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A candy store owner used a cylindrical wooden log as a bench in their store. The height
of that log was 2
feet. The diameter of its base was 1.25
feet. If it costs $7.20
per square foot to paint that log at every side, how much approximately will it cost the
store owner? The total surface area of the right circular cylinder is 2nrh+2rr2
, where, r
is the radius of the base of the cylinder and, h
is the height of the cylinder

Answers

Answer:

Step-by-step explanation:

its 60

3) ____ is the expression,
which tells the nature of the roots of a quadratic equation of the form
3) ____ is the expression,
which tells the nature of the roots of a quadratic equation of the form

Answers

Answer: The quadratic formula

Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ = 100.0 and a = 15.0. A random sample of 53 people is taken.
Step 1 of 2: What is the probability of a random person on the street having an IQ score of less than 99? Round your answer
to 4 decimal places, if necessary.

Answers

The probability that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.

What is Probability?

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

According to our question-

z= x-a/u

98-100/15

Hence, A chance of a random individual on the street having an IQ below 98 is 0.4470, or 44.70%.

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