Hans stands at the rim of the Grand Canyon and yodels down to the bottom. He hears his yodel echo back from the canyon floor 5.20 s later. Assume that the speed of sound in air is 340.0(m)/(s). How deep is the canyon at this location?

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

D

Step-by-step explanation:

answer is d

Answer:

y=2x-2

Step-by-step explanation:

The slope is 2 and your y intercept is already given as -2.

Slope intercept is basically y=mx+b

plug it in so you get y=2x-2

Answer

789

Step-by-step explanat

the answer is two thirds because math is ez

Answer:

The answer is B

Step-by-step explanation:

t-15+15=76+15

t=91

t-15=76  

I took the test and I got a 100%

Answer:

b

Step-by-step explanation:

According to the discount, the price of the tablet computer after the markup is $610.30.

In this problem, a store offered a 30% discount on a tablet computer that originally sold for $670. We can calculate the discounted price of the tablet computer by finding 30% of its original price and subtracting it from the original price.

Discounted price = Original price - Discount

Discounted price = $670 - 30% of $670

Discounted price = $670 - $201

Discounted price = $469

So, the discounted price of the tablet computer is $469.

The problem then asks us to find the price of the tablet computer after it is marked up by 30%. To do this, we need to add 30% of the discounted price to the discounted price.

Markup price = Discounted price + Markup

Markup price = $469 + 30% of $469

Markup price = $469 + $141.30

Markup price = $610.30

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the following expressions are defined:

b) BC

c) \(B^T\)

d) B-C

e) A+B

f) \(BA^T\)

To determine which of the given expressions are defined, we need to consider the compatibility of matrix dimensions.

a) CA: Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix. In this case, A is a 7x6 matrix and C is an 8x7 matrix. The number of columns in A (6) does not match the number of rows in C (8), so CA is not defined.

b) BC: Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix. Both B and C are 7x6 matrices, so the number of columns in B (6) matches the number of rows in C (6). Therefore, BC is defined.

c) \(B^T\): The transpose of a matrix is defined for any matrix. So, \(B^T\)is defined.

d) B-C: Matrix subtraction is defined when the matrices have the same dimensions. Both B and C are 7x6 matrices, so B-C is defined.

e) A+B: Matrix addition is defined when the matrices have the same dimensions. Both A and B are 7x6 matrices, so A+B is defined.

f) \(BA^T\): Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix. A is a 7x6 matrix, and \(A^T\)is a 6x7 matrix. The number of columns in A (6) matches the number of rows in \(A^T\) (6). Therefore, \(BA^T\) is defined.

So, the following expressions are defined:

b) BC

c) \(B^T\)

d) B-C

e) A+B

f) \(BA^T\)

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Answer:

9. x = 5

10. m∠Y = 34°

Step-by-step explanation:

9.

Remember that congruent sides have congruent angles as well. That means 9x + 1 will be shown up in our equation twice. And as always, all angles in a triangle add up to 180.

2(9x + 1) + 88 = 180

18x + 2 + 88 = 180

18x + 90 = 180

18x = 90

x = 5

10.

The same concept applies here in question 10. Congruent angles and sides match each other. Therefore,

Step 1:

6x - 23 = 4x + 9

2x - 23 = 9

2x = 32

x = 16

Step 2:

Now that you have found x, plug it back into the given equations and find the other angle.

6(16) - 23 = 73

4(16) + 9 = 73

180 - (73)(2) = 34

answer:

153.94cm²

Step-by-step explanation:

<3

Answer:

7

Step-by-step explanation:

Given the following :

7 heart stickers and 14 star stickers :

The greatest number of pages that can be decorated using the stickers above without any left over ;

To get this we obtain the greatest common factor of 7 and 14

Factors of 14

14 : 1, 2, 7, 14

Factors of 7

7 : 1, 7

The greatest factor common in both numbers is 7

Hence, greatest number of pages that can be decorated without any leftover is 7

Step-by-step explanation:

hypotenuse = √3^2+8^2

= 8.5

x= √(8.5)^2-9= 7.9

Answer:

Half a gallon

Step-by-step explanation:

1 quart is 1/4 of a gallon, so if you need a different unit let me know.

Therefore, the 95% confidence interval for the population proportion of disks that are defective is (0.8357, 0.9475). This means that there is a 95% probability that the true population proportion of disks that are defective is between 0.8357 and 0.9475.

The quality-conscious disk manufacturer can use a 95% confidence interval to estimate the fraction of defective disks made by the company. The 95% confidence interval is calculated using the sample data to construct an interval estimate of the population proportion.
Using the given data, the sample proportion of disks that are not defective is 904/1015 = 0.8915.
The 95% confidence interval for the population proportion of disks that are defective is then given by:
Lower limit = 0.8915 – (1.96 x √(0.8915 x (1- 0.8915)/1015))
= 0.8915 – (1.96 x 0.0285)
= 0.8915 – 0.0558
= 0.8357
Upper limit = 0.8915 + (1.96 x √(0.8915 x (1- 0.8915)/1015))
= 0.8915 + (1.96 x 0.0285)
= 0.8915 + 0.0558
= 0.9475
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Outside temperatures over a 24-hour period can be represented by a sinusoidal function. Let's consider the specific scenario where the high temperature reaches 78°F.

A sinusoidal function is a mathematical model that describes periodic phenomena, such as the variation in temperature throughout a day. It follows a sine or cosine wave pattern. In this case, we have a high temperature of 78°F. To create a sinusoidal function, we need to determine the amplitude, period, and phase shift. Outside temperatures over a 24-hour period can be represented by a sinusoidal function. In the specific scenario where the high temperature reaches 78°F, we can use a sinusoidal function to model the temperature variation throughout the day. Now, let's move on to the explanation. To create a sinusoidal function, we consider the amplitude, period, and phase shift. The amplitude represents the maximum deviation from the average temperature. In this case, since we have the high temperature of 78°F, we can assume that the amplitude is half of the difference between the maximum and minimum temperatures. Let's say the average temperature is 60°F, then the amplitude would be (78 - 60) / 2 = 9°F. The period represents the length of one complete cycle of the sinusoidal function. In a 24-hour period, there are 24 cycles, so the period would be 24 hours. The phase shift determines the horizontal shift of the function. If we assume that the maximum temperature occurs at noon (12:00 PM), then there is no phase shift, and the sinusoidal function starts at the maximum temperature. Therefore, with an amplitude of 9°F, a period of 24 hours, and no phase shift, the sinusoidal function that models the outside temperatures over a 24-hour period, with a high temperature of 78°F, can be written as: T(t) = 9*sin(2πt/24) + 60, where T(t) represents the temperature at time t. This function will generate a sinusoidal curve that reaches a maximum temperature of 78°F at noon and has a variation of ±9°F around the average temperature of 60°F throughout the day.

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area = pi x r²

3,14 x r² = 452,16

r² = 144

r = 12

Answer:

92

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

155+33=188-4=184 divided by 2 =92

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The slope is 1/6x

You have to re-arranged the problem

x - 6y = 9 --> 6y = x - 9

6y = x - 9

__   ____    ---->  y = 1/6x - 3/2

6        6

On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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There are 2 students who used none of the above-mentioned means of transportation.

There were 2 students who used none of the above-mentioned means of transportation.

A poll was conducted on 100 students at a commuter campus to determine how they got to school.

The following are the results: 36 people drove alone.

34 people carpooled.30 people used public transportation.

5 people used both carpools and public transportation.8 people used both a carpool and their own car.

7 people used buses and their own cars.

4 people used all three modes of transportation.

Now, let us calculate the number of students who didn't use any of the above means of transportation:

Number of students who drove alone = 36

Number of students who carpooled = 34

Number of students who used public transport = 30

Number of students who used carpool and public transport = 5

Number of students who used carpool and their own car = 8

Number of students who used buses and their own car = 7

Number of students who used all three modes of transportation = 4

Thus, the total number of students who used one or more means of transportation =36+34+30+5+8+7+4 = 124

Now, subtracting the number of students who used one or more means of transportation from the total number of students polled will give us the number of students who used none of the means of transportation.

100 - 124 = -24

But, negative values are meaningless in this context.

Hence, the answer is 2.

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Simple Interest is the interest that is accumulated on a loan, savings, investment that is kept in a financial institution at a particular interest rate for a given time period.

The offer that would leave Kevin with more money after 6 years is the offer from Bank B

A = P(1 + rt)

Where:

P = Prinicpal (initial amount saved or invested) = $4,000

r = Interest rate

t = Time in years

A = Amount after time t

P = Prinicpal (initial amount saved or invested) = $4,000

r = Interest rate = 6%

t = Time in years = 6 years

A = Amount after time t = ?

 First, converting R percent to r a decimal

r = R/100

= 6%/100

= 0.06 per year.

Solving our equation:

A = 4000(1 + (0.06 × 6)) = 5440

A = $5,440.00

The amount Kevin will have after 6 years from Bank A is $5,440.00

Step 1: Mifflin Harcourt Publishing Company Bank B offers a special account for new customers that will pay 7% simple interest for 3 years.

P = Prinicpal (initial amount saved or invested) = $4,000

r = Interest rate = 7%

t = Time in years = 3 years

A = Amount after time t = ?

First, converting R percent to r a decimal

r = R/100

= 7%/100

= 0.07 per year.

Solving our equation:

A = 4000(1 + (0.07 × 3)) = 4840

A = $4,840.00

Step 2: After the 3 years, Kevin would have to transfer all his earnings to a regular account that will pay 5% simple interest on the new transferred principal.

Hence, the new principal is $4,840

r = Interest rate = 5%

t = Time in years = 3 years

A = Amount after time t = ?

First, converting R percent to r a decimal

r = R/100

= 5%/100

= 0.05 per year.

Solving our equation:

A = 4840(1 + (0.05 × 3)) = 5566

A = $5,566.00

The amount Kevin will have from Bank B is $5,566.00

Therefore, the offer that would leave Kevin with more money after 6 years is the offer from Bank B

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The solution of the quadratic equation is x = 2. Therefore, \(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)  or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

where

Hence,

a = 1

b = -4

c = 4

Therefore,

\(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\) or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

Finally

x = 2

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Answer:

Options A, D and F

Step-by-step explanation:

From the picture attached,

lines 'l' ad 'm' are the parallel lines and line 't' is a transversal intersecting each line at two different points.

From the angles formed at the points of intersection,

∠5 ≅ ∠8 [Vertical angles]

∠5 ≅ ∠4 [Alternate interior angles]

∠5 ≅ ∠1 [Corresponding angles]

Therefore, Options A, D and F will be the correct options.

Answer:

x - 2 = y OR f(x) = x - 2

remember: f(x) = y

Step-by-step explanation:

f(f^-1(x)) = f^-1(f(x)) = x, we have confirmed that f^-1(x) = (x - 5) / 2 is the correct inverse of f(x) = 2x + 5.

To find the inverse of a function, we switch the x and y variables and solve for y.

Let's say we have the function f(x) = 2x + 5.

Replace f(x) with y: y = 2x + 5.

Switch x and y: x = 2y + 5.

Solve for y:

x = 2y + 5

x - 5 = 2y

(x - 5) / 2 = y

Therefore, the inverse of f(x) = 2x + 5 is f^-1(x) = (x - 5) / 2.

We can verify that this is the correct inverse by composing the two functions and seeing that they cancel each other out:

f(f^-1(x)) = f((x - 5) / 2) = 2((x - 5) / 2) + 5 = x

f^-1(f(x)) = f^-1(2x + 5) = ((2x + 5) - 5) / 2 = x/2

what is variables?

In mathematics, variables are symbols or letters that represent numbers or other values. Variables are used to express mathematical relationships and formulas, and they can take on different values depending on the context in which they are used. For example, in the equation y = mx + b, y and x are variables that represent different quantities, and m and b are constants that have fixed values. Variables can be manipulated using mathematical operations such as addition, subtraction, multiplication, and division, and they are a fundamental concept in algebra and other areas of mathematics.

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Explanation:

Given the functions

f(x) = x-5

G(x) = x^2

We are to find the composite function G(f(x))