After answering the provided question, we can conclude that As a result, circle we cannot conclude that Hip Hop and Pop are incompatible.
What is circle?A circle seems to be a two-dimensional component defined as such collection of the all points in a jet that become equidistant from the hub. A circle is commonly portrayed with the capital "O" for centre and the lower section "r" for the radius, which is the distance from the origin to any point on the circle.
Girth (the distance from around circle) is given by the formula 2r, where (pi) is a proportionality constant roughly equal to 3.14159. The formula r² calculates the circle's circumference, which refers to the amount of room inside of the circle.
We can draw the following conclusions from the information in the circle graph:
Pop music is preferred by 35% of the sample, which means that 35% of 400 students, or 140 students, prefer pop music.
Jazz is the preferred music for 14% of the sample, which means that jazz is preferred by 14% of 400 students, or 56 students.
Hip Hop, Rock, and Jazz are preferred music by 52% of the sample, which means that these three genres are preferred by 52% of 400 students, or 208 students.
Hip Hop and Pop are preferred music by 60% of the sample, which means that 60% of 400 students, or 240 students, prefer these two genres together. As a result, we cannot conclude that Hip Hop and Pop are incompatible.
To know more about circle visit:
brainly.com/question/29142813
#SPJ1
Find M BC using picture below
Based on the picture, we can use the Pythagorean theorem to find MBC. Therefore, MBC is equal to [tex]7[/tex]√2.
What three categories of theorems are there?Theorem of Linear Pairs Two angles are supplementary if they create a linear pair. Additional theorem, Two angles are congruent if they are supplements of the same angle.
Theorem of congruent complements an of thes., but it will be the first of a series of events that will result in a new set of rules and the.
First, we can find AB:
AB = √(AD² + BD²)
= √ [tex](3^2 + 4^2)[/tex]
= √[tex](9 + 16)[/tex]
= √ [tex]25[/tex]
[tex]= 5[/tex]
Next, we can find AC:
AC = √(AD² + CD²)
= √[tex](3^2 + 8^2)[/tex]
= √ [tex](9 + 64)[/tex]
= √[tex]73[/tex]
Finally, we can find BC:
[tex]BC = √(AB^2 + AC^2)[/tex]
= √(5² + (√73)²)
= √(25 + 73)
= √98
= 7√2
Therefore, m Bc is = 7√2
Learn more about theorem here:
https://brainly.com/question/30066983
#SPJ1
consider a european put option on a non-dividend paying stock with a current stock price of $100 and 4 years until expiration. the strike price of the option is unknown you are given that: ape(s,t) as -05 determine a numerical value for: ape(s,t) da please round your numerical answer to the nearest integer.
The strike price of the option is $101.5, rounded to the nearest integer, whicch is given as the APE(s,t)= -0.5.
What is asset price elasticity?The asset price elasticity (APE) of a European Put Option at time 't' is the ratio of the change in the option price to the change in the stock price, given that all other factors remain constant.
The APE(s,t) of a European put option is calculated using the formula APE(s,t) = -S+Ke-rτ.
In this case, the current stock price is $100 and the time until expiration is 4 years.
We can solve for K, the strike price of the option, given the APE(s,t) is -0.5.
K = S + APE(s,t) + reτ
K = 100 - 0.5 + (0.5 x 4)
K = 101.5
The strike price of the option is $101.5, rounded to the nearest integer.
For more questions related to strike price
https://brainly.com/question/30717436
#SPJ1
A triangle has one side that measures 1 1/2 inches and another side that measures 2 1/4 inches. The angle between these sides measures 60°. Draw the triangle in the space below. Label the given side lengths and angle measure on the figure. Is it possible to draw a different triangle with those measurements
the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.
What is triangle?A triangle is a polygon with three sides, three vertices, and three angles. The sum of the interior angles of a triangle is always 180 degrees, and the longest side of a triangle is opposite to the largest angle, and the shortest side is opposite to the smallest angle. Triangles can be classified according to their side lengths and angles. For example, an equilateral triangle has three equal sides and three equal angles of 60 degrees each, while an isosceles triangle has two equal sides and two equal angles. A scalene triangle has no equal sides or angles. Triangles are important in geometry and have many applications in mathematics and other fields, such as architecture, engineering, physics, and computer graphics.
by the question.
Draw a straight-line segment and label it as the given side that measures 1 1/2 inches.
From one endpoint of the first line segment, draw another line segment that forms a 60° angle with the first line segment. Label this second line segment as the given side that measures 2 1/4 inches.
Draw a third line segment that connects the endpoints of the first two-line segments. This will complete the triangle.
To label the triangle, label the given side that measures 1 1/2 inches with the corresponding length measurement, and label the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.
To learn more about triangle:
https://brainly.com/question/2773823
#SPJ1
Find the magnitude and direction of the vector <2,7>. Round angles to the nearest degree and other values to the nearest tenth. 7.3; 73°7.3; 74°7.4; 73°7.4; 74
The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.
We have,
To find the magnitude and direction of the vector <2, 7>, we can use trigonometric concepts. Let's break down the steps:
Magnitude (Length) of the Vector:
The magnitude of a vector <x, y> is given by the formula:
Magnitude = √(x² + y²)
For the given vector <2, 7>:
Magnitude = √(2² + 7²) = √(4 + 49) = √53 ≈ 7.3 (rounded to the nearest tenth)
Direction (Angle) of the Vector:
The angle θ that the vector makes with the positive x-axis can be found using trigonometric functions:
θ = arctan(y / x)
For the given vector <2, 7>:
θ = arctan(7 / 2) ≈ 74° (rounded to the nearest degree)
Thus,
The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.
Learn more about vectors here:
https://brainly.com/question/24256726
#SPJ12
Which equation represents the situation below?
After a 20% discount, the cost of a pair of headphones was $260. How much did the headphones cost before the discount?
Let h = original cost of headphones
Answer:
Para calcular el precio original de los auriculares antes del descuento, podemos usar la fórmula:
Precio original = Precio después del descuento / (1 - Porcentaje de descuento)
Donde "Precio después del descuento" es el costo de los auriculares después del descuento, y "Porcentaje de descuento" es el porcentaje aplicado como descuento. En este caso, el porcentaje de descuento es del 20%, es decir, 0.2 en términos decimales.
Sustituyendo los valores conocidos, obtenemos:
Precio original = 260 / (1 - 0.2)
Precio original = 260 / 0.8
Precio original = 325
Por lo tanto, el costo original de los auriculares antes del descuento era de $325.:
Answer:
The answer is D. (1-0.2)h=260
Step-by-step explanation:
Riley started selling bracelets. During the first month she sold 400 bracelets at $10 each. She tried raising the price, but for every $0. 50 she raised the price, she sold 8 fewer bracelets. What price should she charge in order to make the highest possible gross income?
$17.5 price should she charge in order to make the highest possible gross income.
Given two points are (400, 10) and (392, 10.5)
slope = (10.5-10)/(392 -400) = 0.5/ - 8 = -0.0625
Equation is
p -10 = -0.0625(x-400)
p-10 = -0.0625x + 25
p = -0.0625x + 35
find revenue as
R=x*p
-0.0625x² + 35x
To maximize,
R'(x) =0
-0.125x + 35 = 0
35/0.125 = x
280 = x
when x is equal to 280, find
p= -0.0625(280) + 35
p= -17.5 +35
p= 17.5
Learn more about the Price here: brainly.com/question/19091385
#SPJ4
Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=3x+2
Answer:
y = -1/3x +6
Step-by-step explanation:
You want the equation of the line through the point (3, 5) and perpendicular to y = 3x +2.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b
where m is the slope, and b is the y-intercept.
Comparing this to the given equation, we see that m=3 for the given line.
Perpendicular linesThe slopes of perpendicular lines are opposite reciprocals of one another. This means the slope of the line we want is ...
desired slope = -1/m = -1/3
Y-interceptThe slope-intercept equation above can be solved for b to give ...
b = y -mx
Then the y-intercept for the line we want is ...
b = 5 -(-1/3)(3) = 5 +1 = 6
The equation of the desired line is y = -1/3x +6.
__
Additional comment
Once you understand how to find the slope of the given line and of the desired line, you can write down the desired equation in point-slope form.
Given slope = 3; perpendicular slope = -1/3
Point-slope equation: y -k = m(x -h) . . . . line through (h, k) with slope m
y -5 = -1/3(x -3) . . . . . line through (3, 5) with slope -1/3
The only "work" required is to rearrange this equation to whatever form you may want. In standard form it is x +3y = 18.
Blaine works for a battery manufacturing company. he wants to develop a method to test the batteries made each day to determine if they work. which method would provide the most valid results?
Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.
A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.
The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.
The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.
Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.
The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.
A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.
To know more about Random sampling go through:-
https://brainly.com/question/13219833
#SPJ4
The price of a new car is £12500
It is reduced by £11625
Work out the percentage reduction
To work out the percentage reduction, we need to find the difference between the original price and the reduced price, and express that difference as a percentage of the original price:
Original price = £12500
Reduced price = £11625
Difference = £12500 - £11625 = £875
Percentage reduction = (Difference / Original price) x 100%
= (£875 / £12500) x 100%
= 7%
Therefore, the percentage reduction in the price of the car is 7%.
Answer:
Step-by-step explanation:
Discount [tex]= \pounds12,500 -\pounds11625= \pounds875[/tex]
Percentage reduction [tex]=\frac{875}{12500} \times 100 = 7[/tex]
The price of a new car was reduced by 7%.
Use spherical coordinates to find the volume of the region outside the cone phi = pi /4 and inside the sphere rho = 4 cos phi. The volume is ____ . (Type an exact answer, using pi as needed.)
The volume is 63.717 cubic units
The limits of integration for rho are 0 and 4 cos phi, since the sphere has radius 4 cos phi. The limits for phi are π/4 and π/2, since we want to consider the region outside the cone but inside the sphere, and phi is the angle between the positive z-axis and the position vector of a point. Finally, the limits for theta are 0 and 2π, since theta is the azimuthal angle and we want to integrate over the entire azimuthal angle.
Thus, the volume of the region is given by:
V = 8 x ∫(0 to 2π) ∫(π/4 to π/2) ∫(0 to 4 cos phi) ρ² sin phi dρ dphi dtheta
Simplifying the integral using basic calculus, we get:
V = 8 x (64/3 - 16/3√2π) = 63.717
Therefore, the volume of the region outside the cone phi = π/4 and inside the sphere rho = 4 cos phi is 8(64/3 - 16/3√2π), which is an exact answer using π as needed.
To know more about volume here
https://brainly.com/question/11168779
#SPJ4
one number is 13 les then a certain number let g repersent the larger number. repersent the sum of the two numbers
every year educational services (ets) selects readers for the advanced placement exams. recently the ap* statistics exam has been graded in lincoln, nebraska. one objective of ets is to achieve equity in grading by inviting teachers to be readers from all parts of the nation. however budgets are a consideration also. the accountants at ets wonder if the flights from cities west of lincoln are the same as flight costs from cities east of lincoln. a random sample of the expense vouchers from last year was reviewed for the cost of airline tickets. costs (in dollars) are shown in the table. indicate what inference procedure you would use to see if there is a significant difference in the costs of airline flights between the west and east coasts to lincoln, nebraska, then decide if it is okay to actually perform that inference procedure. (check the appropriate assumptions and conditions and indicate whether you could or could not proceed. you do not have to do the actual test.)
To see if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, one can use a two-sample t-test. It is okay to perform the inference procedure, but the following assumptions and conditions must be checked.
Assumptions: Independence: The airfares for each coast should be independent of each other. Normality: The populations of airfares for both coasts should be approximately normally distributed .Equal variances: The population variances for both coasts should be equal.
Conditions: Sample sizes: Both samples should be large enough so that the Central Limit Theorem applies. Rule of thumb for t-tests is that the sample size should be at least 30.Random sampling: Both samples should be random .To test if the conditions are met, one can create a boxplot for each coast, check the normal probability plots, perform the F-test to check for equal variances, and check the sample sizes. If the assumptions and conditions are met, a two-sample t-test can be used to determine if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska.
for such more questions on Central Limit Theorem
https://brainly.com/question/13652429
#SPJ11
Write down the smallest possible answer.
The answer of the given factor and multiplication term for the positive integers are 3.
What about integers?Positive, negative, and zero digit whole numbers are all included in the category of integers. They can be stated without any fractional or decimal components and are a subset of the real numbers. On a number line, integers can be visualized as positive numbers to the right of zero and negative numbers to the left.
Define Multiplication term:In mathematics, a multiplication term is a mathematical expression that involves the multiplication of two or more factors. The factors can be numbers, variables, or a combination of both. Multiplication terms are commonly represented using the multiplication symbol "×" or the dot "." symbol.
For example, in the expression 2x × 3y, the multiplication term is 2x × 3y, which involves the multiplication of the factors 2x and 3y.
According to the given information:If you want to find the smallest possible value of the given term we have that,The smallest factor of 15 is 1.
The smallest multiple of 3 is 3so, the smallest answer is 1x3 = 3.
To know more about integers visit:
https://brainly.com/question/30161280
#SPJ1
Calculate the final value in cell D2 using the following formula: "price - price* discount". Use a formula with cell reference (B1, etc. ).
Product – Toys
Price - $114. 99
Discount – 12%
The final value in cell D2 using the following formula:
price - price× discount = $ 101.19
Take the original price. Multiply that by the discount percentage and divide the result by 100. Subtract the result from the original price. this is your final price
According to the Question:
The final value in cell D2 using the following formula:
(price - price) × discount.
Given that:
Price = $114.99
Discount = 12%
By the above formula:
(price - price) × discount.
= ($114.99 - $114.99) × 12%
= $101.19
Learn more about discount:
https://brainly.com/question/3541148
#SPJ4
A dolphin was swimming 6 feet below sea level. The number line shows the
location of the dolphin. It then swam down 3 feet. Describe how to use the
number line to find the new location of the dolphin.
++++
-10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
OA. On the number line, move 3 units to the left. End at -9. The dolphin
was 9 feet below sea level.
OB. On the number line, move 3 units to the right. End at 9. The dolphin
was 9 feet above sea level.
O C. On the number line, move 3 units to the left. End at 3. The dolphin
was 3 feet above sea level.
OD. On the number line, move 3 units to the right. End at -3. The
dolphin was 3 feet below sea level.
SUBMIT
To solve the question asked, you can say: So the dolphin's new location expressions is 3 feet above sea level. Option OD explains this process correctly and gives the correct answer.
what is expression ?In mathematics, an expression is a set of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation that represent quantities or values. Expressions can be as simple as "3 + 4" or as complex as they can contain functions like "sin(x)" or "log(y)" . Expressions can be evaluated by substituting values for variables and performing mathematical operations in the order specified. For example, if x = 2, the expression "3x + 5" is 3(2) + 5 = 11. In mathematics, formulas are often used to describe real-world situations, create equations, and simplify complex math problems.
Move 3 units to the right on the outer diameter number line. Exit with -3. The dolphin was 3 feet below sea level.
To find the dolphin's new location, we need to determine the dolphin's direction of movement and distance traveled. In this case the dolphin swam to the bottom. This means it has moved in the negative direction on the number line. Then she swam three feet. This means she has moved 3 units to the right (or positive side) on the number line.
So we need to start at the dolphin's original position of -6 and move it 3 units to the right to -3. So the dolphin's new location is 3 feet above sea level. Option OD explains this process correctly and gives the correct answer.
To know more about expressions visit :-
https://brainly.com/question/14083225
#SPJ1
16^(3x-1) = 32. pls help
Answer:x=33/4096=0.008
Step-by-step explanation: 1.1 16 = 24
(16)3 = (24)3 = 212
Equation at the end of step
1
:
((212 • x) - 1) - 32 = 0
STEP
2
:
Equation at the end of step 2
4096x - 33 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : 4096x-33 = 0
Add 33 to both sides of the equation :
4096x = 33
Divide both sides of the equation by 4096:
x = 33/4096 = 0.008
A tin of nuts contains 36 cashews, 14 pecans, 27 peanuts, and 13 pistachios. Find the probability of reaching in and selecting a pecan and then a cashew. Assume the nuts are chosen without replacement. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:28/445 or 6.2921 %
Step-by-step explanation:
There are 90 nuts all together. There are 14 pecans so it would be a 14/90 chance. Then since you are not replacing the nut there are 89 nuts. There are 36 cashews which would be a 36/89 chance. Because in the problem it says to find the probability of the selecting a pecan and then a cashew we know it is an and situation. Since it is an and situation you would multiply. You would do 14/90 times 36/89. This gives you 504/8010 which reduced is 28/445 or 6.2921%. Do you have and questions?
Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.
Answer:
Were sorry! Answer is not available right now check in later.
Step-by-step explanation:
Suppose Elena has $5 and sells pens for $1.50 each. Her goal is to save $20 to buy a t-shirt. She does not spend any money while she is saving money.
Let p represent the number of pens Elena sells. Write an expression for how much money she saves in total after selling p pens.
Write an equation using your answer from question 1, showing that she saves exactly $20.
Solve the equation you wrote from question 2. What do you notice about your value for p?
What if Elena wants to have some money left over? Write an inequality using your expression from question 1 to show this.
Write down other values for p where Elena would have money left over.
Write an inequality using p, to describe the values of p where she would be able to buy the tshirt and still have money left over.
In conclusion the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc. The equation showing that Elena saves exactly $20 is:
5 + (1.5)p = 20
Why it is?
The expression for how much money Elena saves after selling p pens is:
Total money saved = 5 + (1.5)p
The equation showing that Elena saves exactly $20 is:
5 + (1.5)p = 20
Solving the equation:
5 + (1.5)p = 20
(1.5)p = 15
p = 10
We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.
If Elena wants to have some money left over, we can write the inequality:
5 + (1.5)p > 20
Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.
To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:
5 + (1.5)p > 20
(1.5)p > 15
p > 10
Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.
To know more about Selling related questions, visit:
https://brainly.com/question/30615010
#SPJ1
The access code for a car's security system consist of six digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?
If an access code for a car's security system consist of six digits and the first digit cannot be zero and the last digit must be even, then the number of different codes available are 4,500,000
Since the first digit cannot be zero, we have 9 choices for the first digit. For each of these 9 choices, there are 10 possibilities for the second digit (0-9).
Similarly, there are 10 possibilities for the third digit, 10 for the fourth digit, 10 for the fifth digit, and 5 (0, 2, 4, 6, 8) for the last digit.
Therefore, the total number of possible access codes is:
9 x 10 x 10 x 10 x 10 x 5 = 4,500,000
Learn more about possibilities here
brainly.com/question/28969499
#SPJ4
National Collegiate Athletic Association (NCAA) statistics show
that for every 75,000 high school seniors playing basketball, about 2250 play
college basketball as first-year students. Write the ratio of the number of first-
year students playing college basketball to the number of high school seniors
playing basketball.
Answer: 100:3
Step-by-step explanation:
Answer:
the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.
Step-by-step explanation:
The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.
The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.
To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.
So the ratio can be expressed as:
2,250/75,000
To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:
2,250/75,000 = 3/100
three cards are drawn without replacement from an ordinary deck of 52 playing cards. what is the probability that the 3rd card is a heart if the first card was a heart and the second card was a club?
The probability that the 3rd card is a heart if the first card was a heart and the second card was a club is approximately 0.0152. It is the product of the probabilities.
What is the probability?The probability that the 3rd card is a heart if the first card was a heart and the second card was a club when three cards are drawn without replacement from an ordinary deck of 52 playing cards.
There are 13 hearts in a deck of 52 cards.
Therefore, P(1st card is a heart) = 13/52 = 1/4
There are 13 clubs in a deck of 52 cards. Since one heart is already drawn in the first card, there are only 51 cards left in the deck.
Therefore, P(2nd card is a club) = 13/51
There are only 12 hearts remaining in the deck since one heart is already drawn in the first card. There are only 50 cards left in the deck since two cards are already drawn.
Therefore, P(3rd card is a heart) = 12/50 = 6/25
The probability that the 3rd card is a heart if the first card was a heart and the second card was a club is:
P(3rd card is a heart | 1st card is a heart and 2nd card is a club) = P(1st card is a heart) × P(2nd card is a club) × P(3rd card is a heart) = (1/4) × (13/51) × (6/25) = 39/5,775 = 0.0152 (rounded to 5 decimal places)
Therefore, the probability that the 3rd card is a heart if the first card was a heart and the second card was a club is approximately 0.0152.
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ11
Can someone pass help!!:(
Answer:
proofs attached to answer
Step-by-step explanation:
proofs attached to answer
The differential equations depicting the dynamics of four Single-Input-Single-Output (SISO) systems are given below. (iii) \( \dddot{y}(t)+0.25 \dot{y}(t)+1.25 y(t)=u^{2}(t) \)
Therefore, the transfer function of the system is:
G(s) = Y(s) / U(s) = U(s) / (s^3 + 0.25s + 1.25)
In summary, the differential equation depicting the dynamics of a fourth Single-Input-Single-Output (SISO) system is y'''(t) + 0.25y'(t) + 1.25y(t) = u^2(t), and the transfer function of the system is G(s) = U(s) / (s^3 + 0.25s + 1.25).
The differential equation describing the dynamics of a single-input-single-output (SISO) system is given by ddy(t) + ay'(t) + by(t) = cdu(t), where y(t) is the output of the system, u(t) is the input of the system, and d, a, b, and c are constant coefficients representing the system dynamics.
For the given differential equation, which is the dynamics of four Single-Input-Single-Output (SISO) systems, we have:
[tex]y(t) + ay'(t) + by''(t) + cy'''(t) = u(t)[/tex]
Here, we have the third-order differential equatior : [tex]y'''(t) + 0.25y'(t) + 1.25y(t) = u^2(t)[/tex]
The given equation is a third-order, linear, time-invariant (LTI) differential equation. In control theory, a differential equation that relates the input u(t) to the output y(t) of a system is known as the transfer function.
The transfer function of the given system can be found by applying the Laplace transform to the differential equation:
s^3Y(s) + 0.25sY(s) + 1.25Y(s) = U^2(s)
where Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively.
Solving for Y(s), we get:
Y(s) = U^2(s) / (s^3 + 0.25s + 1.25)
for such more questions on Laplace transform
https://brainly.com/question/2272409
#SPJ11
phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch.Do these data give convincing evidence to support Phoebe’s hunch?
Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.
What is p-value?The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.
The ratio of seniors bringing a bag lunch= 78/104 or 0.75,
while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.
This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.
Further, the difference between the proportions is
0.75-0.65 = 0.1,
which is a large enough difference to be considered significant.
The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.
For more questions related to probability
https://brainly.com/question/25870256
#SPJ1
Tanya is making a scale drawing of her house. She is using a 6 inch line on her drawing to represent the 30 foot width of her house. Tanya's room is 12 feet by 12 feet. What will be the length of the lines she uses to represent her room on the scale drawing?
Answer:2.4 inches
Step-by-step explanation:
if 6 is for 30 feet, we can use a proportional statement to find what the length of the line will be for a room that is 12 feet.
We will consider two cases: n is even and n is odd. In this step, you will complete the proof of the first case. Proof. Case 1: n is even Let n be an even integer. By the definition of even, for some integer k. This follows that nº + 17n - 1 = 2:( 2k )+1 Since is an integer, n^3+17n + 1 must be an integer. Since na +17n – 1 equals times an integer plus n+ 17n – 1 is 2
We will consider two cases: n is even and n is odd. In this step, you will complete the proof of the first case. Proof. Case 1: n is even Let n be an even integer. By the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`
Since is an integer, `n^3+17n + 1` must be an integer. Since `na +17n – 1` equals times an integer plus `n+ 17n – 1` is 2The solution explains the concept of even integer. Let n be an even integer, and by the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`.Since 2k is an integer, n^3 + 17n + 1 must also be an integer. This is because even times even is even and even times odd is even, which means that (2k + 1) is always odd. The integer n^3 can be written as (n*n*n). Given that n is an even integer, it follows that n*n is even. And since an even number times an even number is always even, it follows that (n*n*n) is even. Since the sum of an even number and an odd number is always odd, adding 1 to n^3 + 17n gives an odd number, and thus an integer, as desired. The equality `na +17n – 1 = 2` is not needed in this proof.
We will consider two cases: n is even and n is odd : https://brainly.com/question/31138563
Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Exactly how many erasers did stefanie buy?
Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Stefanie bought total 10 erasers.
Equation:
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal.
According to the Question:
The number of erasers bought by Stefanie:
Let we denote the number of erasers bought by her by x (an unknown variable)
Then we will have:
Total amount before tax = cost of one package of pencil + cost of erasers
$4.25 = $1.75 + X × $0.25
⇒ 4.25 = 1.75 + 0.25x
Now,
we will perform subtraction by 1.75 and division by 0.25 on both sides.
4.25 = 1.75 + 0.25x
Subtracting 1.75 both side:
4.25 -1.75 = 0.25x
⇒ 2.5 = 0.25x
Dividing by 0.25 on both sides:
2.5/0.25 = 0.25x/0.25
⇒ x = 10
Thus, Stefanie bought total 10 erasers.
Learn more about Total:
https://brainly.com/question/29615374
#SPJ4
_____ is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal
Decibel is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal.
What is a decibel?
Decibel, also known as dB, is a logarithmic unit that measures the intensity of a sound or the strength of an electrical or electromagnetic signal. A decibel measures the relative amplitude of a sound or signal, rather than its absolute magnitude. Because decibels are logarithmic, they are used to express both large and small differences in amplitude. A difference of 1 decibel corresponds to a power ratio of approximately 1.26 to 1.
Logarithmic measure: A logarithmic scale is a scale that has a constant ratio between successive values. Decibels, for example, are a logarithmic scale. The decibel scale is used to measure the amplitude of sound waves and electrical or electromagnetic signals. Because decibels are logarithmic, they can be used to express a wide range of signal levels, from very weak to very strong.
Relative measure: Relative measure is a measure that compares one value to another. It is used in a variety of fields, including statistics, physics, and engineering. Decibels are a relative measure because they compare one signal to another. They are used to express the relative gain or loss of a signal, rather than its absolute magnitude.
To know more about relative measure of signal: https://brainly.com/question/15048192
#SPJ11
Suppose a random sample of size 45 is selected from a population with σ = 11. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).
a. The population size is infinite.
b. The population size is N = 50,000.
c. The population size is N = 5000.
d. The population size is N = 500.
The value of the standard error of the mean in each of the following cases:
a. The population size is infinite = 1.4142
b. The population size is N = 50,000 = 1.4135
c. The population size is N = 5000 = 1.4073
d. The population size is N = 500 = 1.343
The standard error is a statistical technique used to measure variability. SE is the abbreviation. A statistic's or parameter estimate's standard error is the standard deviation of its sample distribution. It can be defined as an approximation of that standard deviation.
Standard error calculation:
σ = 10
n = 50
A) when size is infinite, the standard deviation of the sample mean is given by the formula;
σ_x' = σ/√n
Thus,
σ_x' = 10/√50
σ_x' = 1.4142
B) size is given, thus, the standard deviation of the sample mean is given by the formula;
σ_x' = (σ/√n)√((N - n)/(N - 1))
Thus, with size of N = 50,000, we have;
σ_x' = 1.4142 x √((50000 - 50)/(50000 - 1))
σ_x' = 1.4142 x 0.9995
σ_x' = 1.4135
C) at N = 5000;
σ_x' = 1.4142 x √((5000 - 50)/(5000 - 1))
σ_x' = 1.4073
D) at N = 500;
σ_x' = 1.4142 x √((500 - 50)/(500 - 1))
σ_x' = 1.343
Learn more about standard error:
https://brainly.com/question/15858647
#SPJ4