Test the claim that the mean GPA of night students is smaller than 2.4 at the .05 significance level. The null and alternative hypothesis would be:
a. H0 : μ = 2.4 Ha : μ > 2.4 b. H0 : p = 0.6 Ha : p < 0.6 c. H0 : p = 0.6 Ha : p ≠ 0.6 d. Η0 : μ = 2.4 Ha :μ ≠ 2.4 e. H0 : p = 0.6 Ha : p > 0.6 f. H0 : μ = 2.4 Ha : μ < 2.4 The test is: a. right-tailed b. left-tailed
c. two-tailed

T=9h

I probably anwserd Late also I was stumped on this to

Answer:

y=90x+2,000

y=mx+b

Answer:If the digit of 0 is allowed, then:

1/(10*9*8)= 1/720

If it is not permitted, then:

1/(9*8*7)= 1/504

I hope this helps you!

Step-by-step explanation:

Answer:

(2, 5 )

Step-by-step explanation:

y = 2x + 1 → (1)

3y = 4x + 7  → (2)

substitute y = 2x + 1 into (2)

3(2x + 1) = 4x + 7 ← distribute parenthesis on left side

6x + 3 = 4x + 7 ( subtract 4x from both sides )

2x + 3 = 7 ( subtract 3 from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

substitute x = 2 into (1) for corresponding value of y

y = 2(2) + 1 = 4 + 1 = 5

solution is (2, 5 )

To make 4 batches of applesauce, 7 cups of apples are needed.

So the number of cups, of apples in one batch is calculated as by taking the ratio as 4:7 to 1:x . Here xis the number of cups for 1 batch.

So, from the expressions, we can see that,

(A) is correct option,

(B) is correct option,

(E) is correct option

(F) is correct option

As these all corresponds to "7/4"

Answer:

4(4x+7)

Step-by-step explanation:

all I did was evaluate the exponent then added all the numbers to then rearrange the terms and the use your common factors

Answer:

Add 8 to both sides

Step-by-step explanation:

Normally after adding 8 to both sides you'd solve for x by then dividing by -5, but they just want u to explain what to do lol.

By evaluating the polynomial, we will see that the sign on the interval [-4, 2] is negative.

Here we have the polynomial:

f(x) = (x - 2)*(x + 4)*(x + 5).

You can see that the roots of the polynomial are at:

x = 2

x = -4

x = -5.

Then, on the interval [-4, 2], the sign of the polynomial don't change. So to get the sign of f(x) on that interval we can just evaluate it in any value of x that belongs to the interval, for example, x = 0.

f(0) = (0 - 2)*(0 + 4)*(0 + 5) = -2*4*5 = -40

With this, we can conclude that the sign of f(x) on the given interval is negative.

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Answer:

always negative

Step-by-step explanation:

a. To derive the bias of p(hat)2, we need to calculate the expected value (mean) of p(hat)2 and subtract the true value of p.

Bias(p(hat)2) = E(p(hat)2) - p

Now, p(hat)2 = (Y+1)/(n+2), and Y has a binomial distribution with parameters n and p. Therefore, the expected value of Y is E(Y) = np.

E(p(hat)2) = E((Y+1)/(n+2))

          = (E(Y) + 1)/(n+2)

          = (np + 1)/(n+2)

The bias of p(hat)2 is given by:

Bias(p(hat)2) = (np + 1)/(n+2) - p

b. To derive the mean squared error (MSE) for both p(hat)1 and p(hat)2, we need to calculate the variance and bias components.

For p(hat)1:

Bias(p(hat)1) = E(p(hat)1) - p = E(Y/n) - p = (1/n)E(Y) - p = (1/n)(np) - p = p - p = 0

Variance(p(hat)1) = Var(Y/n) = (1/n^2)Var(Y) = (1/n^2)(np(1-p))

MSE(p(hat)1) = Variance(p(hat)1) + [Bias(p(hat)1)]^2 = (1/n^2)(np(1-p))

For p(hat)2:

Bias(p(hat)2) = (np + 1)/(n+2) - p (as derived in part a)

Variance(p(hat)2) = Var((Y+1)/(n+2)) = Var(Y/(n+2)) = (1/(n+2)^2)Var(Y) = (1/(n+2)^2)(np(1-p))

MSE(p(hat)2) = Variance(p(hat)2) + [Bias(p(hat)2)]^2 = (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

c. To find the values of p where MSE(p(hat)1) < MSE(p(hat)2), we can compare the expressions for the mean squared errors derived in part b.

(1/n^2)(np(1-p)) < (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

Simplifying this inequality requires a specific value for n. Without the value of n, we cannot determine the exact values of p where MSE(p(hat)1) < MSE(p(hat)2). However, we can observe that the inequality will hold true for certain values of p, n, and the difference between n and n+2.

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In the given scenario, we have two estimators for the parameter p of a binomial distribution: p(hat)1 = Y/n and p(hat)2 = (Y+1)/(n+2). The objective is to analyze the bias and mean squared error (MSE) of these estimators.

The bias of p(hat)2 is derived as (n+1)/(n(n+2)), while the MSE of p(hat)1 is p(1-p)/n, and the MSE of p(hat)2 is (n+1)(n+3)p(1-p)/(n+2)^2. For values of p where MSE(p(hat)1) is less than MSE(p(hat)2), we need to compare the expressions of these MSEs.

(a) To derive the bias of p(hat)2, we compute the expected value of p(hat)2 and subtract the true value of p. Taking the expectation:

E(p(hat)2) = E[(Y+1)/(n+2)]

          = (1/(n+2)) * E(Y+1)

          = (1/(n+2)) * (E(Y) + 1)

          = (1/(n+2)) * (np + 1)

          = (np + 1)/(n+2)

Subtracting p, the true value of p, we find the bias:

Bias(p(hat)2) = E(p(hat)2) - p

             = (np + 1)/(n+2) - p

             = (np + 1 - p(n+2))/(n+2)

             = (n+1)/(n(n+2))

(b) To derive the MSE of p(hat)1, we use the definition of MSE:

MSE(p(hat)1) = Var(p(hat)1) + [Bias(p(hat)1)]^2

Given that p(hat)1 = Y/n, its variance is:

Var(p(hat)1) = Var(Y/n)

            = (1/n^2) * Var(Y)

            = (1/n^2) * np(1-p)

            = p(1-p)/n

Substituting the bias derived earlier:

MSE(p(hat)1) = p(1-p)/n + [0]^2

            = p(1-p)/n

To derive the MSE of p(hat)2, we follow the same process. The variance of p(hat)2 is:

Var(p(hat)2) = Var((Y+1)/(n+2))

            = (1/(n+2)^2) * Var(Y)

            = (1/(n+2)^2) * np(1-p)

            = (np(1-p))/(n+2)^2

Adding the squared bias:

MSE(p(hat)2) = (np(1-p))/(n+2)^2 + [(n+1)/(n(n+2))]^2

            = (n+1)(n+3)p(1-p)/(n+2)^2

(c) To compare the MSEs, we need to determine when MSE(p(hat)1) < MSE(p(hat)2). Comparing the expressions:

p(1-p)/n < (n+1)(n+3)p(1-p)/(n+2)^2

Simplifying:

(n+2)^2 < n(n+1)(n+3)

Expanding:

n^2 + 4n + 4 < n^3 + 4n^2 + 3n^2

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Answer:

y = -5/2 x - 2

Step-by-step explanation:

The standard form of equation of a line is expressed as;

y = mx+c

m is the slope

c is the yintercept

Given

m = -5/2

c = -2

Substotute into the exoression above

y = -5/2 x + (-2)

y = -5/2 x - 2

Hence the equation in standard form is y = -5/2 x - 2

We can reduce the width of the confidence interval by increasing the sample size, reducing the confidence level and decreasing the mean (A, D, and F)

A confidence interval is an estimate of the interval that has a specified probability of including an unknown population parameter.

The purpose of a confidence interval is to estimate the true value of the population parameter being measured, such as a mean, a standard deviation, or a proportion.

In general, a wider confidence interval indicates more uncertainty about the estimate, while a narrower confidence interval suggests more precision in the estimate.

We want narrower confidence intervals to demonstrate more precision, as this allows us to draw more reliable conclusions about population parameters.

We cannot reduce the width of the confidence interval by increasing the sample size, increasing the confidence level or increasing the mean.

Thus, the correct options are a, d, and f.

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Answer:

The first on is -80,

next one is -60

third one 3

last one is -54

Step-by-step explanation:

The graph of the function y = x²+ 6x + 7 is given in the attachment.

To graph the quadratic function y = x²+ 6x + 7:

Find the vertex using the formula -b/(2a), where a is the coefficient of x²and b is the coefficient of x.

The vertex will be at (-3, -2).

Plot the vertex (-3, -2) on the graph.

Choose additional x-values and calculate the corresponding y-values by substituting them into the equation.

Plot these points on the graph.

Connect the plotted points smoothly to form a U-shaped curve, which represents the parabola.

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The value of expected time ex(b)=1 day approximately if b is the number of days a busy student delays Laundry.

The basic anticipated value formula is (P(x) * n): the probability of an occurrence multiplied by the number of times the event occurs.

The expected value (also known as the expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average in probability theory. The anticipated value is the arithmetic mean of a large number of independently chosen random variable outcomes.

Let b be the number of days a busy student puts off doing laundry.

The given information is tabulated as below:

Days(b)                      1              2

Probability, p(b)       2/3          1/3

The expected time is given as,

E(b)=∑i=1ᵇp(b)

=(1×(2/3))+(2×(1/3))

=4/3

=1.3333

Therefore, the value of ex(b):

1.3333 day ≈ 1 day

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The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

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The amount of concrete required to make 80 pots is 0.24192 cubic meters after adding 5% of the required concrete.

Given that:External dimensions of the prism, a = 18 cmHeight of the prism, h = 16 cm Thickness of the walls, t = 3 cmNumber of pots, n = 80Wastage is 5% of the required concreteLet the side of the inner square be 'a1'. Then,a = a1 + 2t⇒ a1 = a - 2t = 18 - 2×3 = 12 cmVolume of the pot = volume of the outer prism - volume of the inner prismVolume of the outer prismVolume of the outer prism = a²hVolume of the outer prism = 18²×16 = 5184 cm³Volume of the inner prismVolume of the inner prism = a1²hVolume of the inner prism = 12²×16 = 2304 cm³Volume of the potVolume of the pot = 5184 - 2304 = 2880 cm³In m³, Volume of the pot = 2880/1000000 m³Volume of 80 such potsVolume of 80 pots = 80 × 2880/1000000 m³= 0.2304 m³Concrete required for the potsConcrete required = volume of 80 pots × (100 + 5)/100Concrete required = 0.2304 × 105/100 m³Concrete required = 0.24192 m³

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The sum of a number and its opposite, or additive inverse, is always zero. Therefore, 23 added to its additive inverse, -23, equals zero.

When two numbers are added together, the result is their sum. In this case, we are adding 23 and -23.

The number 23 is a positive integer, and its opposite or additive inverse is the negative of 23, which is -23. When added to the original number, results in a sum of zero, because of the additive inverse of a number property.

So, when we add 23 to -23, we get:

23 + (-23) = 0

This is because adding a number and its additive inverse always results in a sum of zero.

In general, when we add any number to its additive inverse, we get a sum of zero. This is a fundamental property of addition in mathematics and is known as the additive inverse property.

For example, if we add 10 to its additive inverse, -10, we get:

10 + (-10) = 0

Likewise, if we add -7 to its additive inverse, 7, we get:

-7 + 7 = 0

In fact, we can add any number to its additive inverse and get a sum of zero. This property is used in many mathematical applications, such as solving equations and balancing chemical reactions.

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The Prime Factors of 1352 are: 2, 2, 2, 13, 13.

352 ÷ 2 = 676

676 ÷ 2 = 338

338 ÷ 2 = 169

169 ÷ 13 = 13

13 ÷ 13 = 1

Again, all the prime numbers you used to divide above are the Prime Factors of 1352. Thus, the Prime Factors of 1352 are: 2, 2, 2, 13, 13.

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Answer:

8

Step-by-step explanation:

the table shows the function f(x) = 2x²

Rate of Change:  [f(1) - f(3)] / 1-3

= 2(1²) - 2(3²) / -2

= 2 - 18 / -2

= -16/-2

= 8

Answer:

$115 each

Step-by-step explanation:

(800 - 340)/4 = 115

The average rate of change of a function over the  interval (0, 3) is: 5

We are given the quadratic function as:

r(x) = x² + 2x - 5

The formula for calculating the average rate of change of a function over an interval (a, b) is:

f'(x) = [f(b) - f(a)] / (b - a)

Applying that to our function over the interval (0, 3)

r(0) = 0² + 2(0) - 5 = -5

r(3) = 3² + 2(3) - 5

r(3) = 10

Thus:

r'(x) = (10 - (-5))/(3 - 0)

r'(x) = 15/3

r'(x) = 5

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The trigonometric expression \(\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}\) is equivalent to the trigonometric expression \(\sec \alpha \cdot \csc \alpha + 1\).

In this problem we must prove that one side of the equality is equal to the expression of the other side, requiring the use of algebraic and trigonometric properties. Now we proceed to present the corresponding procedure:

\(\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}\)

\(\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }\)

\(\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}\)

\(\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}\)

\(\frac{\tan^{3}\alpha - 1}{\tan \alpha \cdot (\tan \alpha - 1)}\)

\(\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}\)

\(\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}\)

\(\tan \alpha + 1 + \cot \alpha\)

\(\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1\)

\(\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1\)

\(\frac{1}{\cos \alpha \cdot \sin \alpha} + 1\)

\(\sec \alpha \cdot \csc \alpha + 1\)

The trigonometric expression \(\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}\) is equivalent to the trigonometric expression \(\sec \alpha \cdot \csc \alpha + 1\).

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We need to use the fact that a rectangle with a fixed Dimension will have the largest area when it is a square. Let's assume that the length of the rectangle runs parallel to the river, so we only need to fence the other three sides.

If the width of the rectangle is "x," then the length of the rectangle is (2000 - 2x) because we subtract the length of the two sides parallel to the river.

To find the area, we multiply the length by the width, so the area is A = x(2000 - 2x).

To find the value of x that maximizes the area, we need to take the derivative of A with respect to x and set it equal to zero:

A' = 2000 - 4x

2000 - 4x = 0

x = 500

So the width of the rectangle should be 500 yards, and the length should be (2000 - 2(500)) = 1000 yards.

Therefore, the dimensions of the largest area that can be enclosed with 2000 yards of fencing along a straight portion of the river are 500 yards by 1000 yards.

Takes into account the dimensions of the rectangle, the perimeter of the fencing, and the process for finding the maximum area.

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Answer:

Short answer, we need a value for d, longer answer is \(b = \frac{d}{2} + 4.5\) (I think)

Step-by-step explanation:

[1] Find b:

2b-9=d

[2] First we need to get b alone:

- \(\frac{b-9}{2}\)=\(\frac{d}{2}\)

- \(b - 4.5 = \frac{d}{2}\)

[3] Then continue

- Add 4.5 to both sides

- \(b = \frac{d}{2} + 4.5\)

Lori will make more than Darryl, then the after 10 years Lori will have make $27.00 more in their account.

Darryl deposits into a savings = $1,500

Account that has a simple interest rate = 2.7%.

Lori deposits into a savings = $1,400

Account that has a simple interest rate = 3.8%.

Let us assume,

\(P_{1}\) = $1,500

\(r_{1}\) = 2.7%.

\(r_{1}\) =  2.7/100

\(r_{1}\) = 0.027

After 10 years = t = 10years

The formula to calculate simple interest is,

\(A_{1}\) = \(P_{1} (1+r_{1} t)\)           (Equation-1)

\(P_{1}\) = Principal amount

\(r_{1}\) = rate of interest ( in decimal )

t = time

First we calculate Darryl's deposit,

So we can substitute values in the equation-1,

\(A_{1}\) = 1,500(1 + 0.027×10)

\(A_{1}\) = 1,500 ( 1+0.27 )

\(A_{1}\) = 1,500 × 1.27

\(A_{1}\) = $1905

Now we will calculate Lori's deposit,

\(A_{2}\) = \(P_{2} (1+r_{2} t)\)                (Equation-2)

\(P_{2}\) = $1,400

\(r_{2}\) = 3.8%.

\(r_{2}\) =  3.8/100

\(r_{2}\) = 0.038

So we can substitute values in the equation-2,

\(A_{2}\) = 1,400 ( 1 + 0.038 × 10 )

\(A_{2}\) = 1,400 ( 1 + 0.38 )

\(A_{2}\) = 1,400 × 1.38

\(A_{2}\) = $1,932

Darryl will make money after 10 years = $1905

Lori will make money after 10 years = $1,932

Hence,

Lori will make more than Darryl,

Then the difference will be = 1,932 - 1,905 = $27

Therefore,

After 10 years Lori will have make $27.00 more in their account.

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The ratio of f to g to h is:

1:3:5

First, we know that g is the 60% of h, then we can write:

g = 0.6*h

Now we can write the 0.6 as a fraction, then 0.6 = 3/5.

g = (3/5)*h

So we can write:

5*g = 3*h

So the ratio of g to h is 3:5

Now, we know that f is a third of g:

f = (1/3)*g

3f = g

So the ratio of f to g is:

1:3

notice that the value that represents the proportion of g is 3 in both ratios, so we can just write:

The ratio of f to g to h is:

1:3:5

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If the expression be 23 x² + 3x + 8 then the constant exists 8.

The addition, subtraction, multiplication, and division arithmetic operators are used to write a group of numbers together to form a numerical statement in mathematics. The expression of a number can take on various forms, including verbal form and numerical form.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

During the course of a program's execution, a constant's value cannot change. As a result, the value is constant, as implied by its name. During the course of a program's execution, a variable's value can change. As a result, the value might change, as implied by its name.

Let the expression be 23 x² + 3x + 8

then the constant exists 8.

Therefore, the correct answer is option C. 8.

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Answer:

x = 36

Step-by-step explanation:

16 / (4/9) = 36

That's all there is to it. Hope I helped

Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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Answer:

i did the work its the third one

Step-by-step explanation: