A certain statistics instructor participates in triathlons. The accompanying table lists times​ (in minutes and​ seconds) he recorded while riding a bicycle for five laps through each mile of a​ 3-mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a​ hill? Find F distribution and p-value? anova
Mile 1 ​3:14 ​3:23 ​3:24 ​3:22 ​3:21
Mile 2 ​3:19 ​3:23 ​3:20 ​3:17 ​3:20
Mile 3 ​3:33 ​3:31 ​3:29 ​3:31 ​3:28

Therefore, the two values of c in (0,5) such that uf(p) = 21 are p = 2.5 ± 5/3 and p = 2.5 ± 10/3.

To find two values of c in (0, 5) such that uf(p) = 21, we first need to determine what uf(p) represents. uf(p) is the average value of the function f(x) over the interval [0, 5] with weight function u(x) = 1 - |x - p|/5.
Using the formula for average value with weight function, we have:
uf(p) = 1/(5-0) * ∫0^5 f(x)u(x) dx
Substituting f(x) = x and u(x) = 1 - |x-p|/5, we get:
uf(p) = 1/5 * ∫0^5 x(1 - |x-p|/5) dx
Simplifying this integral and solving for uf(p) = 21, we get:
|p-2.5| = 5/3 or |p-2.5| = 10/3

Therefore, the two values of c in (0,5) such that uf(p) = 21 are p = 2.5 ± 5/3 and p = 2.5 ± 10/3.

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Answer:

The answer is x ≤ 4                        

Given:

The two functions are:

\(f(x)=\sqrt{32x}\)

\(g(x)=\sqrt{2x}\)

To find:

The \((f\cdot g)(x)\). Assume \(x\geq 0\).

Solution:

We have,

\(f(x)=\sqrt{32x}\)

\(g(x)=\sqrt{2x}\)

Now,

\((f\cdot g)(x)=f(x)\cdot g(x)\)

\((f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}\)

\((f\cdot g)(x)=\sqrt{32x\times 2x}\)

\((f\cdot g)(x)=\sqrt{64x^2}\)

\((f\cdot g)(x)=8x\)

Therefore, the correct option is A.

The answer is that approximately 68% of the data is between 73 and 83.

To answer this question, we can use the empirical rule, also known as the 68-95-99.7 rule. This rule states that for a normal distribution, approximately:
- 68% of the data falls within one standard deviation of the mean
- 95% of the data falls within two standard deviations of the mean
- 99.7% of the data falls within three standard deviations of the mean
Since the mean is 78 and the standard deviation is 5, one standard deviation below the mean is 73 and one standard deviation above the mean is 83. Using the empirical rule, we can say that approximately 68% of the data falls between 73 and 83.

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Answer: B

Step-by-step explanation:

The range of a function is every valid y value, in this case represented by B

Answer:

9 dollars per pound of salmon

The directional derivative of the function f(x, y) in the direction of the vector v = (0, -2) can be calculated using the formula Duf = ∇f · v, where ∇f is the gradient of f.

First, let's find the gradient of f(x, y):

∇f = (∂f/∂x, ∂f/∂y)

= (-3y sin(3xy) + 2y², -3x sin(3xy) + 1)

Next, we calculate the dot product of the gradient ∇f and the vector v = (0, -2):

Duf = ∇f · v

= (-3y sin(3xy) + 2y²)(0) + (-3x sin(3xy) + 1)(-2)

= 6x sin(3xy) - 2

Therefore, the directional derivative of f in the direction of v = (0, -2) is Duf = 6x sin(3xy) - 2.

In summary, the directional derivative of the function f(x, y) in the direction of the vector v = (0, -2) is given by Duf = 6x sin(3xy) - 2. This means that the rate of change of the function f in the direction of the vector v is determined by the expression 6x sin(3xy) - 2

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The area of Rachel's bedroom is 72 square feet. The bedroom area that is eight times of Rachel's closet. The length of the closet if it is 3 feet wide is 3.

Given that,

The area of Rachel's bedroom is 72 square feet. The bedroom has an area that is eight times that of Rachel's closet.

We have to find what is the length of the closet if it is 3 feet wide.

First we divide the area of Rachel's bedroom is 72 square feet and eight times that of Rachel's closet.

72/8=9

Now, we multiply 3 and the length as l is equal to 9 feet wide

3×l=9

l=9/3

l=3

Therefore, The length of the closet if it is 3 feet wide is 3.

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The numerical or verbal descriptions that usually result from measurements are called data or observations.

When measurements are conducted, whether in scientific experiments, surveys, or other data collection processes, the outcome is typically a set of data or observations.

These measurements can be represented numerically, such as numerical values or quantities, or verbally, using descriptive terms or categories.

Numerical descriptions provide precise quantitative information, such as measurements of length, weight, temperature, time, or any other measurable attribute. These measurements are often expressed using numbers or units of measurement.

Verbal descriptions, on the other hand, use words or qualitative descriptions to convey information about the observations.

For example, when conducting a survey, respondents might provide verbal responses that describe their opinions, preferences, or experiences.

Both numerical and verbal descriptions play important roles in data analysis and interpretation.

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============================================================

Work Shown:

Corresponding angles are congruent when we have parallel lines.

5x-10 = 2x+20

5x-2x = 20+10

3x = 30

x = 30/3

x = 10

-------------------------

5x-10 = 5*10-10 = 50-10 = 40

2x+20 = 2*10+20 = 20+20 = 40

Each angle is 40 degrees, which helps confirm our answer.

Answer:

we have

tan ø=perpendicular/base

tan30=3/y

y=3/tan30

y=3√3 is your answer

a.) 990 is the TOP volume.

b.) 825 is the BOTTOM volume.

c.) 1815 is the total volume.

Hope it helps!

- JK Mitsu

#SpreadTheLove

_________________________________________

Some help so you can be independent next time!

1.) Finding the top volume mean multiplying the height of the top (6 m) , width, and length.

2.) Finding the bottom is the height of the bottom (5 m) , width, and length.

3.) Finding the total is adding both bottom and top!

Answer:

3.407

Step-by-step explanation:

Step 1: Plug in variables

[2(-3/5)-1/3]÷-6.75/15

Step 2: Solve inside parenthesis

(-6/5-1/3)÷-6.75/15

Step 3: Find common denominator in the parenthesis

(-18/15-5/15)÷-6.75/15

-23/15÷-6.75/15

Step 4: Divide

Step 5: Make sure answer is positive number when multiplying two negatives

Answer: 3.407

Sorry if this isn't right in your books I'll try to improve, Thanks.

Answer:

Hi

Step-by-step explanation:

The volume of the candle is approximately 94 cubic inches.

A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.

The volume of a right circular cylinder is given by the formula:

V = πr²h

Where

Substituting the given values into the formula, we get:

V = 3.14 x 2² x 7.5

V = 3.14 x 4 x 7.5

V = 94.2

Rounding to the nearest cubic inch, we get:

V ≈ 94 cubic inches

Therefore, the volume of the candle is approximately 94 cubic inches.

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0.734

Probability is a branch of mathematics that deals with the occurrence or non-occurrence of an event. The probability is a number between 0 and 1 that represents the possibility of an event occurring.What is the probability that a new worker will meet the production quota?Given that an electronics plant has the probability 0.83 that a new worker who has attended the company's training program will meet the production quota and that the corresponding probability is 0.35 for a new worker who has not attended the company's training program, then the probability that a new worker will meet that production quota is 0.8(0.83) + 0.2(0.35) = 0.734Therefore, the probability that a new worker will meet that production quota is 0.734.

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Answer:

square rhombus

same-both have 4 sides

diff- im not thats sure

Step-by-step explanation:

Answer: a ticket to an amusement park is $100 per person. you have a coupon for $20 off of the admission price. the amusement park is also having a promotion where if you bring an empty pepsi can you can take an additional $4 off of the total admission cost. how much do you have to pay to be admitted to the amusement park after the coupons? (it would be $76)

Step-by-step explanation: my brain thought this up

Answer:

Step-by-step explanation:

Mikes mom gave him 100 dollars to spend and his favorite toy shop. Mike bought a Lego set which cost him 20 dollars. When he bought a lollipop which cost him 4 dollars.

If a linear system has more unknown equations then it must have infinitely many solutions, which is true.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If there is only one equation with more than one parameter, then the number of the solution will be infinite.

If a linear system has more unknown equations then it must have infinitely many solutions, which is true.

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Answer:

1. m³ + m

= m( m² + 1) [ a² + b²]

= (a-b)² + 2ab

= m { (m –1)² + 2× m × 1 }

= m { ( m–1)² + 2m}

2. 25 – y² [ a² – b²]

= 5² – y²

= (5+y) (5–y)

3. x² + 3x –28 [ middle term factorisation]

= x² + 7x –4x –28

= x( x +7) –4 ( x + 7 )

= ( x–4) (x+7)

➊ Factorise :- \(\sf{m^{3} + m}\)

Solution :-

\(→ \ \ \sf\purple{m^{3} + m}\)

\(→\:\:\bf\red{ m \times (m^{2} + 1)}\)

➋ Factorise :- \(\sf{25-y^{2}}\)

Solution :-

\(→\:\:\sf\purple{25-y^{2}}\)

\(→\:\:\sf\green{5^{2} - y^{2}}\)

\(→\:\:\bf\red{(5-y)\times (5+y)}\)

➌ Factorise :- \(\sf{x^{2}+3x - 28}\)

Solution :-

\(→\:\:\sf\purple{x^{2}+3x - 28}\)

\(→\:\:\sf\green{x^{2}+7x-4x-28}\)

\(→\:\:\sf\orange{x \times (x +7) -4 (x+7)}\)

\(→\:\:\bf\red{(x + 7)\times (x - 4)}\)

The stopping distance for a car traveling at 55 mph is 60,500 feet.

The equation to solve this problem would look like the following

s = v²/k

The stopping distance s will increase (varies directly) as the velocity increases.

Putting in the values we know

45 = 30²/k

⇒ k = 45/900

⇒ k = 0.05

Now,

at 55 mph we would have

    s = 55²/0.05

⇒ s = 3025/0.05

⇒ s = 60,500

s = 60,500 feet to stop

Complete Question:

The stopping distance s of a car varies directly as the square of its speed v. If a car traveling at 30 mph requires 45ft to stop, find the stopping distance for a car traveling at 55 mph.

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The equation that requires the multiplication property of equality to be solved is:

\(\boxed{\sf \dfrac{a}{6}=420}\)

Multiplication property of equality states that if both the sides of an equation are multiplied by the same number, the expressions on the both sides of the equation remain equal to each other.

The multiplication property states that:

Out of the given options, \({\sf \dfrac{a}{6}=420}\) requires the multiplication property of equality to be solved.

That is:

\(\text{If} \ {\sf \dfrac{a}{6}=420}\)

\({\sf \dfrac{a}{6}\times6=420\times6\)

\(\sf a=2520\)

Hence, the equation that requires the multiplication property of equality to be solved is:

\({\sf \dfrac{a}{6}=420}\)

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Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.

To determine which point is a solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2, we can test each point to see if it satisfies both inequalities.

a) Point E at (4, -2):

Substituting the coordinates into the inequalities:

-2 > -2(4) + 10 -> -2 > -8 + 10 -> -2 > 2 (False)

-2 > (1/2)(4) - 2 -> -2 > 2 - 2 -> -2 > 0 (False)

b) Point K at (2, 3):

Substituting the coordinates into the inequalities:

3 > -2(2) + 10 -> 3 > -4 + 10 -> 3 > 6 (False)

3 > (1/2)(2) - 2 -> 3 > 1 - 2 -> 3 > -1 (True)

c) Point B at (4, 7):

Substituting the coordinates into the inequalities:

7 > -2(4) + 10 -> 7 > -8 + 10 -> 7 > 2 (True)

7 > (1/2)(4) - 2 -> 7 > 2 - 2 -> 7 > 0 (True)

d) Point D at (-7, 1):

Substituting the coordinates into the inequalities:

1 > -2(-7) + 10 -> 1 > 14 + 10 -> 1 > 24 (False)

1 > (1/2)(-7) - 2 -> 1 > -3.5 - 2 -> 1 > -5.5 (True)

Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.

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A plan with sufficient specifics to carry out a task or goal is called an action plan.

An action plan is a document used in project management that outlines the activities to take in order to accomplish the project's goals and objectives. Therefore, an action plan specifies the resources you'll need to achieve those goals, creates a timeframe for the tasks or action items, and establishes the team members you'll need to complete it all.

An action plan is a detailed checklist of the steps and materials required to finish a project or reach a goal. It can be viewed as a visual countdown to project completion or a list of tasks necessary to produce desired results.

A plan with sufficient specifics to accomplish a task or goal is called an action plan.

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Answer:

Step-by-step explanation:

solve for x

2x+14=-21-5

2x+14=-26

subtract 14 from both sides

2x+(14-14)=-14-26

2x=-14-26

2x=-40

divide both sides of 2x = -40 by 2

\(\frac{2x}{2} =\frac{-40}{2}\)

2/2=1

x=\(\frac{-40}{2}\)

x= -20

Answer:

3/70

Step-by-step explanation:

3 orange,6 pink , 1 yellow , and 5 red = 15

P(pink) = number of pink/ total = 6/15 = 3/5

Then without putting it back

3 orange,5 pink , 1 yellow , and 5 red = 14

P(yellow) = number of yellow/ total = 1/14

P(pink, no replacement, yellow) = 3/5*1/14 = 3/70

Louis total distance of 8/5 km. Louis rose his bicycle a total distance of 8/5 km.

Louis rose his bicycle a total distance of 1/2 km + 3/4 km + 7/10 km.

To find the total distance, we need to find a common denominator for the fractions: 2, 4, and 10.

The least common denominator is 20.

So, 1/2 km can be written as 10/20 km, 3/4 km can be written as 15/20 km, and 7/10 km remains the same.

Adding these fractions together, we have:

10/20 km + 15/20 km + 7/10 km = 32/20 km

Simplifying this fraction, we get:

32/20 km = 8/5 km

Therefore, Louis rose a total distance of 8/5 km.

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Louis rode a total distance of 8/5 km or 1 and 3/5 km

Louis rode his bicycle a total of 1/2 km to school, 3/4 km to a ball field, and 7/10 km back home. To find the total distance Louis traveled, we need to add up these three distances.

First, let's add 1/2 km and 3/4 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 2 and 4 is 4.

Converting 1/2 to have a denominator of 4, we get 2/4. Now we can add 2/4 + 3/4, which equals 5/4.

Next, we need to add 5/4 km and 7/10 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 4 and 10 is 20.

Converting 5/4 to have a denominator of 20, we get 25/20. Now we can add 25/20 + 7/10, which equals 32/20.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 32/4 and 20/4, we get 8/5.

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Answer:

after 4 months dan and sydney will have paid the same amount

Step-by-step explanation:

Answer:

Step-by-step explanation:

dan and sydney are getting high speed internet access at the same time.dans provider charges $60 for installation and $42.95 each month. sydney's provider has free installation and charges 57.95 per month. after how many months will dan and sydney have paid the same amount?

let 'm' represent the number of months they have subscribed

dan's total:

42.95m + 60

sydney's total:

57.95m

we want to calculate 'm' when the two totals are equal:

42.95m + 60 = 57.95m

60 =15m

m = 60/15 = 4

after 4 months dan and sydney will have paid the same amount

Answer:

Step-by-step explanation:

hope this helps. pls mrk me branliest :)

Answer:

1)24.25

2)21

Step-by-step explanation:

1) (a/4)^2=(20/4)^2=25

b/2/8=6/8=3/4

25-3/4

=100/4-3/4

=97/4

=24.25

2)2(x-y)^2=2(3)^2=18

x-y=3

=18+3

=21

Hope this helps!

Answer: A

Step-by-step explanation:

If you plug in the numbers from the x column into the equation in the place of x, you can figure out the answer.

Example:    -10x - 15

                   -10(1) - 15 = -25

                   -10(2) - 15 = -35 and so on...

You're Welcome! :)