Test the null hypothesis that there is no difference between the estimates of the two garages. Be sure to specify the null and alternative hypotheses, the test statistic with degrees of freedom, and the P-value. What do you conclude using the 0.05 significance level

Answer:

The sum of their ages is 29, which we can express as the equation:

P + (P - 11) = 29

Simplifying the equation:

2P - 11 = 29

Adding 11 to both sides:

2P = 40

Dividing both sides by 2:

P = 20

Therefore, Pete's age, represented by "P," is 20 years old.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

\(f'(x) = e^{x}(x^{3} + 3x^{2} + 1)\)

and \(f''(x) = e^{x}(x^{3}+6x^{2} + 6x + 1)\)

Step-by-step explanation:

From the question,

f(x) = (x3 + 1)ex

That is,

\(f(x) = (x^{3} +1)e^{x}\)

Then , we can write that

\(f(x) = x^{3}e^{x} +e^{x}\)

To find f'(x), we will differentiate \(x^{3}e^{x}\) and then add it to the differential of \(e^{x}\)

First, we will differentiate \(x^{3}e^{x}\),

Let \(y(x) = x^{3}e^{x}\) (This is a product)

Then,

\(f(x) = y(x) + e^{x}\)

Hence,

\(f'(x) = y'(x) + (e^{x})'\)

Given \(y(x) = u(x) v(x)\), Using the product rule

\(y'(x) = u(x).v'(x) + u'(x).v(x)\)

Hence,

\(y'(x) = x^{3}(e^{x})' + (x^{3})'e^{x}\)

\(y'(x) = x^{3}e^{x} + 3x^{2}e^{x}\)

and

\((e^{x})' = e^{x}\)

\(f'(x) = y'(x) + (e^{x})'\)

∴ \(f'(x) = x^{3}e^{x} + 3x^{2}e^{x} + e^{x}\)

\(f'(x) = e^{x}(x^{3} + 3x^{2} + 1)\)

For f ''(x)

To find f ''(x), will differentiate f '(x)

\(f'(x) = e^{x}(x^{3} + 3x^{2} + 1)\)

This is also a product, then we will apply the product rule

From the product rule,

Given \(y(x) = u(x) v(x)\), Using the product rule

\(y'(x) = u(x).v'(x) + u'(x).v(x)\)

Here, Let\(u(x) = e^{x}\) and \(v(x) = x^{3} + 3x^{2} + 1\)

Then,

\(f''(x) = e^{x}(x^{3} + 3x^{2} + 1)' + (e^{x})'(x^{3} + 3x^{2} + 1)\)

\(f''(x) = e^{x}(3x^{2} + 6x ) + (e^{x})(x^{3} + 3x^{2} + 1)\)

∴\(f''(x) = e^{x}(x^{3}+6x^{2} + 6x + 1)\)

Hence,

\(f'(x) = e^{x}(x^{3} + 3x^{2} + 1)\)

and \(f''(x) = e^{x}(x^{3}+6x^{2} + 6x + 1)\)

Answer: C

Step-by-step explanation: 0.571 is greater than 0.4. Therefore, 4/7 is greater than 2/5 and the answer to the question "Is 4/7 greater than 2/5?" is yes. Note: When comparing fractions such as 4/7 and 2/5, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.

Answer:

x=3

Step-by-step explanation:

Assuming X3 means 3x, then you would have:

5x+3 = 18, 5x = 15, x=3

The missing value in the table include the following: B. 4 1/2 in.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

50 5/8 = 5 × W × 2 1/4

Width, W = 4 1/2 inches.

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Complete Question:

The volume of a rectangular prism is 50 5/8 cubic inches.

The dimensions are given below.

What is the missing value in the table?

Length Width Height

5 in. 214 in.

A. 79in.

B. 412in.

C. 134in.

D. 1018in.

The table that represents the function for a lawn being mowed more quickly than by Killian's rate is given as follows:

Second table.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

Killian can cut grass at a rate of 1000 square feet each 10 minutes, hence his average rate of change is given as follows:

1000/10 = 100 square feet per minute.

For the second table, in 7 minutes, 1100 square feet of lawn is mowed, hence the rate is given as follows:

1100/7 = 157 square feet per minute.

It is more quickly than Killian's as the rate of change is greater.

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Answer:

Step-by-step explanation:

365 x 24 = 8,760

365 x 6 = 2,190

8,760 - 2,190 = 6,570

6,570 / 24 = 273 3/4

The person sleeps 91 (1/4) days per year.

Multiplication is the process of adding a number up to a given number.

Given that, the person sleeps 6 hours a day.

The total hours of sleeping over a year are:

365 × 6

= 2190 hours per year

Since there are 24 hours in a day, divide 2190 by 24 to get the answer in days per hour:

2190/24

= 91 (1/4)

Hence, the person sleeps 91 (1/4) days per year.

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Answer:

8 hours

Step-by-step explanation:

−0.75x + 18 = -x+20

0.25x = 2

x = 8

Answer:

Oldest to newest:

10^-35, 10 ^-10, 0

Step-by-step explanation:

Scientific notation

To figure out the power of 10 think "how many places do I move the decimal point?"

When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.

When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.

Answer:

1.5 lbs

Step-by-step explanation:

We know that there are 16 ounces in 1 pound.

To find how many pounds are in 24 ounces, simply divide 24 by 16.

Doing this, you get 1.5 pounds.

Answer:

2y-6

Step-by-step explanation:

(y-3)2=2y-6

The mathematical expression for twice the difference of y and 3 is 2(y - 3); the answer is 2(y - 3).

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete:

The complete question is:

Write the mathematical expression for "Twice the difference of y and 3"

It is given that:

Twice the difference of y and 3

The number is y:

The difference between y and 3:

= (y - 3)

Twice the above number:

= 2(y - 3)

The above expression representing a linear expression; If in the linear expression, one variable is present, then the expression is known as the linear expression in one variable.

Thus, the mathematical expression for twice the difference of y and 3 is 2(y - 3); the answer is 2(y - 3).

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40 percent of 30 is equal to 25 percent of 48.

We have to find first 40% of the number 30.

40% of 30 = 40% × 30

                 = (40 / 100) 30

                 = 0.4 × 30

                 = 12

Now we have to find what percent of 48 is 12.

Let the required percentage be x.

x% of 48 = 12

(x/100) 48 = 12

x/100 = 12/48

x/100 = 0.25

x = 0.25 × 100

x = 25%

Thus, 40% of 30 equals 25% of 48.

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Answer:

20

Step-by-step explanation:

10 x 1 = 10. 10 x 2 = 20.

Answer:

20

Step-by-step explanation:

10 x 1 = 10

Then, 10 x 2 = 20

The solution to the given equation is answer A.

x = (-5 ± √5) / 2 or x = (-5 - √5) / 2.

What is the solution?

We can use the quadratic formula to solve the equation x² + 5x + 5 = 0:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 5, and c = 5.

Substituting these values into the formula, we get:

x = (-5 ±√(5² - 4(1)(5))) / 2(1)

x = (-5 ±√5) / 2

Therefore, the solutions to the equation are:

x = (-5 + √5) / 2 or x = (-5 - √5) / 2

These solutions cannot be simplified further, so the answer is A.

x = (-5 ± √5) / 2 or x = (-5 -√5) / 2.

What is quadratic formula?

The quadratic formula is a formula used to find the solutions (or roots) of a quadratic equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the unknown variable. The formula is:

x = (-b ± √(b² - 4ac)) / 2a

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Since the initial displacement is made by s0 and body moves with initial velocity and acceleration after that, the final displacement after time t is

\(s= \frac {1}{2} at ^{2} + v_{0}t+s_{0}\)

The displacement is only the difference between the locations of the two marks and is unrelated to the route used to get there.

The formula is:

\(a= \frac {Velocity}{Time}\) (Acceleration)

\(v= \frac {Displacement}{Time}\)(Velocity)

Initial Displacement = s0

Displacement from position s0 after time t  = \(\frac {1}{2} at ^{2} + v_{0}t\)

Total Final Displacement (s) = \(\frac {1}{2} at ^{2} + v_{0}t+s_{0}\)

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Answer:

This is what I put:

"Putting extra effort into your work would include actions like using synonyms, avoiding too many contractions (words like "can't" or "don't" in grammar), and refraining from including your opinion in order to stay professional (unless the topic requires it). The "6 Trait Philosophy/Writing" strategy is what I plan to use in future papers. This strategy contains the 6 "steps" or "tips" for better writing, which are organization, conventions, ideas, fluency, voice, and word choice. And, of course, the standard formatting guidelines."

Step-by-step explanation:

I got 100% on Edge.

Answer:

"Putting extra effort into your work would include actions like using synonyms, avoiding too many contractions (words like "can't" or "don't" in grammar), and refraining from including your opinion in order to stay professional (unlin ess the topic requires it). The "6 Trait Philosophy/Writing" strategy is what I plan to use in future papers. This strategy contains the 6 "steps" or "tips" for better writing, which are organization, conventions, ideas, fluency, voice, and word choice. And, of course, the standard formatting guidelines."

Step-by-step explanation:

When the domain is substituted, the Range of the function will be

7 ≤ y < ∞

The range of a function is the the spread of minimum value of the function to maximum value. We can find the range by substituting different domains into the function.

Given a function  f(x) = |x| + 7

This |x| show that it is a modulus. That is, the domain will always be positive numerals.

The minimum domain = 0, so the minimum f(x) = 0 + 7 = 7

The maximum domain = ∞, so the maximum f(x) = ∞ + 7 = ∞

y = f(x)

Therefore, the range of of the function f(x) = |x| + 7 will be 7 ≤ y < ∞

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Answer:

58.8 feet per second

CONVERTING MPH TO FPS

If you are moving at the rate of 40MPH, how many feet do you travel in a second? At 40 miles per hour, you are traveling 58.8 feet per second. To convert miles per hour to feet per second, multiply the miles per hour figure by 1.47. There are 5280 Feet in a mile and 3600 Seconds in an hour.

We can Add 7 black beads to make ratio 3 : 1.

Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.

There are three white beads in the picture.

Total beads we will have (b meaning black)b : 3

Ratio black : white beads 3 : 1

Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.

Find common ratio by dividing total by ratio white beads: 3/1 = 3

Multiply ratio black beads by common ratio. 3 X 3 = 9

We need 9 black beads in total.

Check answer

9 : 3    

Both sides divisible by 3; reduce ratio

= 3 : 1        

Which is Correct ratio

Hence, There will be a total of 9 black beads, but we already have 2 black beads:

(9 total) - (2 original) = (7 to add)

Therefore , we need to add 7 black beads.

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Answer:

15 °C

Step-by-step explanation:

°C = (°F - 32) * (5/9)

Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.

Initial temperature: 77 °F

Converting to Celsius:

°C = (77 - 32) * (5/9)

°C ≈ 25

The temperature dropped by 10 °C, so the final temperature is:

Final temperature = Initial temperature - Temperature drop

Final temperature ≈ 25 - 10 = 15 °C

Therefore, the temperature after the storm was approximately 15 °C.

Answer:

7.21+4.2

for 4.2 we can write it as 4.20 because 0 has no value after decimal point

then 7.21+4.20

by adding both we get 11.41

hope it helps you mate

please mark me as brainliast

Answer:

11.41

Step-by-step explanation:

7.21

+4.2

= 11.41

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

2. The transformations are given as follows:

3. The transformations are given as follows:

For item 2, the transformations in this problem are given as follows:

For item 3, the transformations are given as follows:

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Answer:

S. A. =ph where p represents the perimeter of the base and h represents the height of the prism

Answer:

The answer to the questions is

a)1

b)60°

Step-by-step explanation:

tan 45°=1

sin‐¹(√3/2)=60°

The values of the given trigonometric expression are:

(a) tan 45° = 1

(b) \(\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ\)

Use the concept of trigonometric identity defined as:

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

(a) The given trigonometric ratio is,

tan 45°

Since we know that,

In the trigonometric ratio table for the measure 45°,

The value of tangent is 1.

Hence,

tan 45° = 1

For the given trigonometric exprssion,

\(\text{sin}^{-1}(\frac{\sqrt{3}}{2})\)

Since we know that,

Sin 60° = √3/2

Therefore,

\(\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = \text{sin}^{-1}(\text{sin }60^\circ)\\\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ\)

Hence,

The value of the given expression is 60°.

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Step 1

Find the constant rate of the soda

Hence the constant rate of soda = $2.5. Option B

a) The probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,850 and 10,150 is equal to 0.8903.

b) No, because n should be greater than 30 in order to apply the central limit theorem. So, right choice for answer is option (b).

The normal distribution forms a bell shaped curve. The parameter of normal distribution is \(\mu\) and \(\sigma ^2 \). It is a continuous distribution. Now, Mean value of breaking strength of a rivet = 9,950

Standard deviations = 502

Let's X be variable denotes breaking strength of a rivet.

a) Now, a random sample is choosen from X such that, Sample size, n = 40. By using central limit theorem, sample mean follows approximately normal distribution with mean 9950 and standard deviations = 502/√40 = 79.3732 that is \(\bar X \: \tilde \: \: N( 9950, ( 79.3732)²)\)

\(P( 9,850 < \bar X < 10,150 ) = P( \bar X < 10,150) -

P( \bar X < 9,850) \\ \)

= \( P(\frac{\bar X - \mu }{\sigma} < \frac{10,150 - 9950}{79.3732} )- P(\frac{\bar X - \mu }{\sigma} < \frac{10,150 - 9850}{79.3732}) \\ \)

= P( Z < 2.52 ) - P( Z < -1.26)

= 0.9941 - 0.1038

= 0.8903

b) If sample size,n is 15 instead of 40, then the probability requested in part (a) will not be calculated from the provide information. Because, for applying central limit theorem we have sample size must be grater than 30. So, option(b) is correct.

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For x ≤ -1, the function is given by f(x) = 4x + 1. This is a linear function with a slope of 4 and y-intercept of 1. The graph of this part of the function is a straight line passing through (0, 1) with a steep slope, extending towards negative x-values.

In mathematics, a function is a rule that associates each element in one set (called the domain) to a unique element in another set (called the range). Functions are one of the most important concepts in mathematics and have a wide range of applications in various fields.

A function is usually denoted by a letter, such as f(x), where x is an element in the domain and f(x) is the corresponding element in the range. The domain of a function is the set of all possible values of x for which the function is defined, and the range is the set of all possible values of f(x).

To graph the piecewise function f(x), we will graph each part of the function separately.

For -1 < x < 2, the function is given by f(x) = -2x - 3. This is also a linear function with a slope of -2 and y-intercept of -3. The graph of this part of the function is a straight line passing through (-1, 1) with a gentle slope, extending towards positive x-values until it reaches x=2.

For x ≥ 2, the function is given by f(x) = 5. This is a horizontal line at y=5, which is a constant function. The graph of this part of the function is a horizontal line at y=5 starting from x=2.

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