Suppose a student organization at a university collected data for a study involving class sizes from different departments. The following table shows the average class size from a random sample of classes in the business school vs. the average class size from a random sample of classes in the engineering school. Data for the sample sizes and standard deviations are also shown. Use this data to complete parts a through c. Business Engineering 39.7 32.2 Sample mean Sample standard deviation 10.4 12.4 Sample size 17 20 a. Perform a hypothesis test using a = 0.10 to determine if the average class size differs between these departments. Assume the population variances for the number of students per class are not equal. Determine the null and alternative hypotheses for the test. H₂H₁ H₂ = 0 H₁ H₁-H₂0 Calculate the appropriate test statistic and interpret the result.

Answer:

20

Step-by-step explanation:

To maximize the enclosed area of two adjacent rectangular corrals with 800 feet of fencing, the dimensions should be 400 feet parallel to the shared side and 133.33 feet perpendicular to the shared side.

I'm glad you reached out for help with this question. To find the dimensions that will result in the maximum enclosed area for two adjacent rectangular corrals using 800 feet of fencing, we can follow these steps:
Let x be the length of the fence parallel to the shared side of the rectangles, and y be the length of the fence perpendicular to the shared side.

The total fencing used will be x + 3y = 800, since there are three y-lengths and one shared x-length.
We can rearrange the equation to solve for x: x = 800 - 3y.
The area of both rectangles combined is A = xy.

We want to maximize this area.

Substitute the equation for x into the area equation: A = (800 - 3y)y = 800y - 3y^2.
To find the maximum area, take the derivative of A with respect to y: dA/dy = 800 - 6y.
Set dA/dy to zero and solve for y: 0 = 800 - 6y => y = 800/6 = 133.33.
Find the value of x using the equation x = 800 - 3y: x = 800 - 3(133.33) = 400.
The dimensions of the corrals should be x = 400 feet and y = 133.33 feet for the maximum enclosed area.
In summary, to maximize the enclosed area of two adjacent rectangular corrals with 800 feet of fencing, the dimensions should be 400 feet parallel to the shared side and 133.33 feet perpendicular to the shared side.

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The sum of the measures of the angle of a triangle is 180 degrees.

The given triangle is a type of triangle and the type of triangle a scalene triangle.

For a scalene triangle, the measure of the three sides are unequal and the sum of the interior angle of a triangle is 180 degrees.

Hence the measure of the angles <A, <B and <C are all less than 90 degrees since they are all acute angles.

We can therefore conclude that:

m<A + m<B + m<C = 180 degrees

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Answer:

2 feet.

Step-by-step explanation:

Since the volume of cube A is 64, we can divide the edge (4) by two because cube B can only hold half as much liquid.

Thus, the edge of cube b is 2 feet.

Hope it helped!

Answer:

the answer might be unlikely

Answer:

Step-by-step explanation:

Answer:

Look at image below

Step-by-step explanation:

I got it incorrect.. here's the answer

Answer:

Step-by-step explanation:

second one

Answer:

middle table

Step-by-step explanation:

The middle table has the same set of ordered pairs as the given set.

Answer:

1. -1/2b

2. 3a/b^2

3. 3b^2/1a^2

4. -1a^2b/2

Step-by-step explanation:

Simplified answers and then the variables cancel out each out as much as they can (That's the best way to explain it)

Answer: -4a/8ab goes with -1/2b

-9b^3/-3a^2b goes with 3a/b^2

3a^4/1a^3b^2 goes with 3b^2/1a^2

5a^4b/-10a^2 goes with-1a^2b/2

Step-by-step explanation:

When ever you do problems with fractions make sure you combine like terms. If you have multiple a’s, in this case you should divide them. When you divide a’s with exponents you always subtract the exponents by each other. Hope this helps!

Answer:

I do not know there is a math app

To find a factorization of n, we can use the Pollard rho algorithm or another algorithm for factorization = 1.

The Rabin-Miller primality test is a probabilistic algorithm for determining whether a given number is prime or composite.

It is based on Fermat's Little Theorem and is widely used in cryptography.
To apply the Rabin-Miller primality test to a number n, we choose a random integer a between 1 and n-1, and then check whether a(n-1) ≡ 1 mod n and whether there exists a non-zero integer j such that a^(2^j * (n-1)) ≡ -1 mod n.

If either of these conditions is not satisfied, then n is composite. Otherwise, we repeat the test with a different random integer.
(1) For n = 1729 and a = 671:
First, we have n-1 = 26 * 27. We compute:
a(n-1) mod n = 671(26*27) mod 1729 = 1
Next, we look for a value of j such that a(2j * (n-1)) ≡ -1 mod n. We compute:
a(21 * (n-1)) mod n = 671(26*27/21) mod 1729 = 899
a(22 * (n-1)) mod n = 671(26*27/22) mod 1729 = 1
Since we found a value of j such that a(2j * (n-1)) ≡ -1 mod n, we conclude that n is probably prime.
(2) For n = 104513 and a = 3:
First, we have n-1 = 26 * 1633. We compute:
a(n-1) mod n = 3(26*1633) mod 104513 = 1
Next, we look for a value of j such that a(2j * (n-1)) ≡ -1 mod n. We compute:
a(20 * (n-1)) mod n = 3(26*1633/20) mod 104513 = 1
a(21 * (n-1)) mod n = 3(26*1633/21) mod 104513 = 11054
a(23 * (n-1)) mod n = 3(26*1633/23) mod 104513 = 1

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9514 1404 393

Answer:

  (1, 7)

Step-by-step explanation:

Fill in x=1 and do the arithmetic.

  h(1) = 4(1) +3 = 7

The coordinate pair is ...

  (x, h(x)) = (1, h(1)) = (1, 7)

1 math book is 3.33 pounds or 3 1/3

21x3 1/3 or 3.33 = 69.93

The quadratic model for the ball's height as a function of time are given below

Equation 1: t₁²a + t₁b + c = y₁

Equation 2: t₂²a + t₂b + c = y₂

Equation 3: t₃²a + t₃b + c = y₃

To find a quadratic model for the ball's height as a function of time, we can use the given data table to fit a quadratic equation to the points. The general form of a quadratic equation is:

y = ax² + bx + c

Let's use the given data to determine the values of a, b, and c.

Assuming the table contains the time (t) in the first column and the corresponding height (y) in the second column, we can use three data points to form three equations.

Let's say the data points are:

t₁, y₁

t₂, y₂

t₃, y₃

The three equations we can form are:

y₁ = a(t₁)² + b(t₁) + c

y₂ = a(t₂)² + b(t₂) + c

y₃ = a(t₃)² + b(t₃) + c

To solve for a, b, and c, we can rewrite these equations as a system of linear equations:

Equation 1: t₁²a + t₁b + c = y₁

Equation 2: t₂²a + t₂b + c = y₂

Equation 3: t₃²a + t₃b + c = y₃

We have three equations with three unknowns (a, b, and c). Solving this system of equations will give us the quadratic model for the ball's height as a function of time.

Note: Without the specific data points, I cannot provide the exact quadratic model. Please provide the values in the table, and I'll be able to help you find the quadratic equation that models the ball's height.

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Answer:

-17

Step-by-step explanation:

1st step =7-4 X 6

2nd step =7-24

3rd step =-17

Answer:

pi r^2

Step-by-step explanation:

that's the answer for question 13

Answer:

Choice C

Step-by-step explanation:

$80 to 5 hours

Divide both numbers by 5 to find the unit rate:

$16 to 1 hour, or 16 to 1

For x hours, the pay, y, is y = 16x.

Choice A is true.

Look at choice B.

When x = 5, y = 80.

This is correct because we are given that information.

The process is to multiply the hours by 16.

For x hours, y = 16x (from choice A)

For x = 7, y = 7 * 16

Choice B works.

Look at choice C.

We need a proportion. The left side is the ratio 80/5, meaning $80 for 5 hours of work. Notice that the first number in the ratio is dollars, and the second number is hours. Now we need another ratio written in the same order to set up a proportion. x dollars is to 7 hours. This is the ratio x/7. The correct proportion is

80/5 = x/7

Choice C is 80/5 = 7/x

Choice C is incorrect.

Look at choice D.

The graph shows that for 5 hours, the pay is $80, so by looking up x = 7, you can find the correct amount of pay.

Choice D works.

Answer: Choice C

The experimental probability for 20 customers on 25 out of 30 days is,

for fewer than 20 customers on thirty-first day is 0.8333.

for  20 or more customers on thirty-first day is 0.1667.

The experimental probability of having fewer than 20 customers on the thirty-first day ,

Calculate by looking at the frequency of days with fewer than 20 customers out of the total number of days recorded.

In this case, out of the 30 days recorded, there have been fewer than 20 customers on 25 days.

This implies, the experimental probability of having fewer than 20 customers on the thirty-first day is,

Experimental probability = Number of days with fewer than 20 customers / Total number of days recorded

⇒Experimental probability = 25 / 30

Simplifying the fraction,

⇒Experimental probability = 5 / 6

⇒Experimental probability = 0.8333

The experimental probability of having 20 or more customers on the thirty-first day,

Calculate as the complement of the probability of having fewer than 20 customers.

It is 1 minus the experimental probability of having fewer than 20 customers.

Experimental probability of 20 or more customers = 1 - Experimental probability of fewer than 20 customers

⇒ Experimental probability of 20 or more customers = 1 - (5/6)

Simplifying the expression,

⇒Experimental probability of 20 or more customers = 1/6

Therefore, the experimental probability is,

when there will be fewer than 20 customers on the thirty-first day is 5/6 or approximately 0.8333.

when there will be 20 or more customers on the thirty-first day is 1/6 or approximately 0.1667.

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The above question is incomplete, the complete question is:

For the past 30 days, Rae has been recording the number of customers at her restaurant between 10 A. M. And 11 A. M. During that hour, there have been fewer than 20 customers on 25 out of 30 days

A. What is the experimental probability there will be fewer than 20 customers on the thirty-first day?

B. What is the experimental probability there will be 20 or more customers on the thirty first day?

The median lies in the group "30 < x < 40".

To determine the median, we followed these steps:

Therefore, the median lies in the group "30 < x < 40".

The median is a statistical measure that represents the middle value in a set of numerical data. It is used to describe the central tendency of the data and to determine where the majority of the values lie. To find the median, the data must be arranged in ascending or descending order, and the middle value is taken.

If the number of observations is odd, the median is the middle value. If the number of observations is even, the median is the average of the two middle values. The median is useful for finding the central value of data that may have extreme outliers or skewness, as it is not affected by the presence of such values.

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Answer:

50

Step-by-step explanation:

115 = p

115 = 2m + 15  

-15          -15

100 = 2m

/2      /2

50 = m

If you take away like I did in this method it will get you answer (backwards PEMDAS)

Ok in my own words hmm.

Midpoint to me would be the point in the middle.

I've seen and worked with midpoints on lines and triangles.

So the midpoint would be the point in the middle of a line segment.

Hope this is helpful!

Answer:

It's the center of a line which involves coordinates (x,y) and by defining a line it's made up of multiple coordinates

Step-by-step explanation:

Hope it's helpful

Answer:

57,700.10

Step-by-step explanation:

To solve, we use the equation \(17,600(1.16)^8\)

we set it to the power of 8, since it is compounding quarterly this means it compounds 4 times a year, and since there is 2 years, we get 8 compounds.

please rate and mark as brainlest

The sequence can be described using the formula:

\(a_{n}\) = -64 + (n-1)

∴ \(a_{n}\) represents the nth term in the sequence.

To find the 10th term, we substitute n = 10 in the above formula:

\(a_{10}\) = -64 + (10-1) = -64 + 9 = -55

Therefore, the 10th term in the sequence is -55.

Answer:

see explanation

Step-by-step explanation:

there is a common difference between consecutive terms, that is

- 63 - (- 64) = - 63 + 64 = 1

- 62 - (- 63) = - 62 + 63 = 1

- 61 - (- 62) = - 61 + 62 = 1

this indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = - 64 and d = 1 , then

\(a_{n}\) = - 64 + 1(n - 1) = - 64 + n - 1 = n - 65

use this rule to find the 10th term

a₁₀ = n - 65 = 10 - 65 = - 55

The integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

To determine the values of p for which the integral ∫10x^p * ln(x) dx converges, we need to consider the convergence of the integrand for different values of p. The integral will converge if the integrand is well-behaved and does not exhibit any divergence.

Let's analyze the integrand in two separate cases:

Case 1: p ≠ -1

When p ≠ -1, the integrand is well-defined for all x > 0. We can proceed with evaluating the integral.

∫10x^p * ln(x) dx = [x^(p+1) * ln(x)] / (p+1) + C

To calculate the value of the integral for a specific value of p, we can substitute the limits of integration into the antiderivative expression and evaluate the resulting expression.

Case 2: p = -1

When p = -1, the integrand becomes 10x^(-1) * ln(x), which poses a potential issue at x = 0. To determine if the integral converges for this case, we need to examine the behavior of the integrand near x = 0.

As x approaches 0, the expression ln(x) approaches negative infinity, which would cause the integrand to diverge. Therefore, for p = -1, the integral does not converge.

In summary, the integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

Please note that when evaluating the definite integral for specific limits of integration, you should substitute the limits into the antiderivative expression and then calculate the difference of the resulting expressions evaluated at the upper and lower limits.

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Answer:

-4

Step-by-step explanation:

Wehn dealing with order of operations, we can remember the expression PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction.

So, our first step in the above problem is the parentheses:

\(2(3-5)^3+4(-4+7)\\2(-2)^3+4(3)\)

The second step is exponents:

\(2(-2)^3+4(3)\\2(-8)+4(3)\)

The third step is multiplication:

\(2(-8)+4(3)\\-16+12\)

The fourth and final step is addition:

\(-16+12\\-4\)

Answer:

784 students ride the bus

Step-by-step explanation:

80% DO ride the bus

980 x 80%= 784

Six times as much as 9 is equal to 54 and Nine times as much as 6 is equal to 54 are the correct answers for the given multiplication equation. Thus, options b and d are correct.

The given equation is,

9 × 6 = 54 ---------- (equation 1 )

Multiplication equations are equations that perform multiplication operations. A complete multiplication equation will have the values that are being multiplied with each number on one side of the equal symbol.

The correct arrangements of the multiplication equation 9 x 6 = 54 are:

1. Six times as much as 9 is equal to 54.

Mathematically, 6 x 9 = 54.

2. Nine times as much as 6 is equal to 54.

Mathematically, 9 x 6 = 54.

Therefore we can conclude that Six times as much as 9 is equal to 54 and Nine times as much as 6 is equal to 54 are correct answers.

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The complete question is-

What does this multiplication equation mean? Select each correct answer.

9 × 6 = 54

Options:

a. Nine more than 6 is equal to 54.

b. Nine times as much as 6 is equal to 54.

c.  Six more than 9 is equal to 54

d.  Six times as much as 9 is equal to 54.

Answer:

x = 19

Step-by-step explanation:

l, m and n are the parallel lines.

Two transversal lines are intersecting these parallel lines.

By Intercept theorem,

Lengths of intercepts between the parallel lines are proportional.

\(\frac{38}{8}=\frac{x}{4}\)

x = \(\frac{4\times 38}{8}\)

x = 19

Therefore, x = 19 will be the answer.

a. To approximate the given quantity using Taylor polynomials with n=3, we need to use the formula for the Taylor polynomial of degree n:

Pn(x) = f(a) + f'(a)(x-a) + (1/2!)f''(a)(x-a)^2 + (1/3!)f'''(a)(x-a)^3 + ... + (1/n!)f^(n)(a)(x-a)^n
where f(x) = sinh(x), a = 0. The derivatives of sinh(x) are:
f'(x) = cosh(x), f''(x) = sinh(x), f'''(x) = cosh(x), and so on.
Therefore, the Taylor polynomial of degree 3 for sinh(x) centered at a = 0 is:
P3(x) = x + (1/2!)(x)^3
To approximate sinh(0.24), we substitute x = 0.24 into the formula above:
P3(0.24) = 0.24 + (1/2!)(0.24)^3 = 0.240008
b. To compute the absolute error in the approximation assuming the exact value is given by a calculator, we need to subtract the actual value of sinh(0.24) from the approximation we obtained in part a:
Error = |P3(0.24) - sinh(0.24)| = |0.240008 - 0.241663| = 0.001655
Therefore, the absolute error in the approximation is 0.001655.
To approximate sinh(0.17), we use the same formula and substitute x = 0.17:
P3(0.17) = 0.17 + (1/2!)(0.17)^3 = 0.170005
To compute the absolute error in this case, we subtract the actual value of sinh(0.17) from the approximation we obtained:
Error = |P3(0.17) - sinh(0.17)| = |0.170005 - 0.17031| = 0.000305
Therefore, the absolute error in the approximation for sinh(0.17) is 0.000305.

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Answer: 1

Step-by-step explanation:

Answer:

y ⁷

Step-by-step explanation:

y⁵ * y² = y ⁽ ⁵ ⁺ ² ⁾   (adding exponents)

          = y ⁷