A local running group collected data on the number of miles its group members run each week, x, and their average mile time, y. The results are shown in the table below. Weekly Mileage, x 10 25 12 10 15 20 22 25 20 24 Avg. Mile Time, y 9.3 8.75 8.2 5.5 6.3 8.5 6.7 6.35 5.45 6.25 Calculate the correlation coefficient using technology and interpret what it represents. The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, the average mile time decreases. The correlation coefficient of the data is 0.87, which means as the weekly mileage increases, the average mile time increases. The correlation coefficient of the data is 0.87, which means as the weekly mileage increases, it has no affect on the average mile time. The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.

Answer:

45

Step-by-step explanation:

15 x 3 = 45 - 3 = 42

"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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Answer:

y=39

Step-by-step explanation:

according to question;

13=1/3×y

or;13/y=1/3

or;13×3/y=1

or;39/y=1

or;39=y

Answer:

9/3

Step-by-step explanation:

could also be simplified to 3, but just the reciprocal is 9/3

Answer:  9/3

Step-by-step explanation:

Answer:

eight less than a number

Answer:

9 laps takes 5 minutes 25 seconds.

Step-by-step explanation:

Here is given:

4 laps takes 6 minutes 12 seconds.

We have to find how long 1 lap takes.

4/4 6/4 12/4 --> 1 lap takes 2 minutes 33 seconds.

Now, multiply each by 9 because you want to find 9 laps, so:

1x9 2x9 33x9 --> 9 laps takes 5 minutes 25 seconds.

Hope this helps :)

Answer:

faster then the other one

Equation of the given line will be :

now, let's plug the value of x as the x - coordinate of the above point (-2 , 9) to check whether it lies on the line or not.

now, since value of isn't equal to the y - coordinate of the given point, so the point doesn't lies on the line.

Answer:

Equation of the given line will be :

y = 4x - 3

now, let's plug the value of x as the x - coordinate of the above point (-2 , 9) to check whether it lies on the line or not.

y = 4( - 2) - 3y=4(−2)−3

y = - 8 - 3y=−8−3

y = - 11y=−11

now, since value of isn't equal to the y - coordinate of the given point, so the point doesn't lies on the line.

The quadratic function for the path of the basketball as it is thrown indicates;

The path of the basketball will not make the shot

The height reached is about 5.24 meters

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.

The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2

The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;

n(x) = The vertical height of the basketball

Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;

b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2

(-1/7)·x² + 1.36·x + 2 - 3 = 0

(-1/7)·x² + 1.36·x - 1 = 0

(1/7)·x² - 1.36·x + 1 = 0

Solving the above equation, we get;

x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717

Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.

Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)

Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76

The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters

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The exponential function showing the relationship is y = 2300(1 + 0.12)^t

The exponential function showing the relationship between y and t can be written as:

y = 2300(1 + 0.12)^t

where 2300 is the initial number of bacteria cells, 0.12 is the growth rate (12% expressed as a decimal), and t is the time in hours since the start of the study.

This function is obtained by using the formula for exponential growth, which is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is the time.

In this case, a = 2300, r = 0.12, and y represents the amount of bacteria cells after t hours.

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Answer:

x = 7    y = -3

Step-by-step explanation:

x - y = 10   ⇒   x = 10 + y

Substitute  x = 10 + y  into 2x - y = 17:

2(10 + y) - y = 17

20 + 2y - y = 17

y = -3

Substitute the found value of y into x = 10 + y to find x:

x = 10 - 3 = 7

The set using Roster method is, D = {76, 90, 92, 94, 96}

The roster technique is defined as a method for displaying the elements of a set by listing the elements within brackets.

A roster method example is to write the set of numbers from 1 to 10 as

{1, 2, 3, 4, 5, 6, 7, 8, 9, and 10}.

Given:

Set D is the set of positive two-digit even numbers greater than 74

that do not contain the digit 8

First, Even numbers greater than 74 are

76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98.

Now, Even Number doe not contain 8 are 76, 90, 92, 94, 96.

Using Roster method the set is

D= {76, 90, 92, 94, 96}

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By using graph of function y = x² - 5x - 2, the solution of the equation

- 4 = x² - 5x - 2 are,

⇒ (2, - 4) and (3, - 4)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ y = x² - 5x - 2

⇒ - 4 = x² - 5x - 2

Now, We can draw the graph of function y = x² - 5x - 2 as shown in figure.

Then, For equation - 4 = x² - 5x - 2;

Value of y = - 4

Hence, By the graph of y = x² - 5x - 2 we can see that at y = - 4 there are two value of x;

⇒ x = 2, 3

Thus, By using graph of function y = x² - 5x - 2, the solution of the equation - 4 = x² - 5x - 2 are,

⇒ (2, - 4) and (3, - 4)

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Answer:

0.42

Step-by-step explanation:

To solve the problem, we need to add the probability of picking a club to the probability of picking a face card, and then subtract the probability of picking a club that is also a face card (because we would have counted it twice).

There are 13 clubs in a standard deck, so the probability of picking a club is 13/52 or 0.25.

There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck, so the probability of picking a face card is 12/52 or 0.23.

However, there are 3 cards that are both clubs and face cards (the jack of clubs, queen of clubs, and king of clubs), so we need to subtract the probability of picking one of those cards. There are 3 of them out of 52 total cards, so the probability of picking a club that is also a face card is 3/52 or 0.06.

Therefore, the probability of picking a club OR a face card is:

0.25 + 0.23 - 0.06 = 0.42 (rounded to two decimal places).

So the answer is 0.42.

A circle having radius 5 and centre at (0,0) has equation x² + y² = 25.

What is the equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

Let (x,y) be any point on the circle.

Given that centre of the circle is origin (0,0).

Now, we know that the distance from any point on the circle to the centre is equal to the radius of the circle.

So, distance between point (x,y) and centre (0,0)  is equal to radius of the circle which is given 5 units.

Now, using the distance formula -

√[(x - 0)² + (y - 0)²] = 5

Squaring on both the sides of the equation -

(x - 0)² + (y - 0)² = 25

So, the equation of the circle with radius 5, centred at the origin is x² + y² = 25.

Therefore, the equation is x² + y² = 25.

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Answer:

nice

Step-by-step explanation:

whats the rest of the problem or is it just that she rolled a dice

To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

Answer:

hello my name Nidhi, please mark me as brainliest bcoz I need it

Answer:

The set of five numbers would be {2,4,4,4,6}

Answer:

The example set could be:

S

=

{

2

,

4

,

4

,

4

,

6

}

See explanation.

Explanation:

First you can notice that if the set was:

S

1

=

{

4

,

4

,

4

,

4

,

4

}

then it would fulfill 2 conditions: mean and median, but

the set does not have the mode because all numbers are the same,

the range is zero (again all numbers are the same)

To have the mode the set would have to have at least one element different from

4

, but if we changed only one element the mean would change, so at least two numbers need to be changed to keep mean equal to

4

..

Now to get the range the difference between the changed numbers should be

4

. That leads us to adding two to one number and subtracting two from the other.

Finally we can get the set from the answer.

Answer:

47.2

Step-by-step explanation:

The total surface area of the cylinder is 414.7 cm².

The curved surface area of the cylinder is calculated as follows;

C.S.A = 2πrh

where;

The curved surface area of the cylinder is calculated as;

C.S.A = 2π(6 cm) x (5 cm)

C.S.A = 188.5 cm²

The total surface area of the cylinder is calculated as follows;

T.S.A = 2πrh + 2πr²

circular area = 2πr² = 2π x (6cm)² = 226.2 cm²

The total surface area = 188.5 cm² + 226.2 cm² = 414.7 cm²

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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

The question is incomplete. The full question is below.

The path of a particular punt follows the quadratic function

\(h(x)=\frac{-1}{8}(x-25)^{2}+50\)

where h(x) is the height of the ball in yards and x corresponds to the horizontal distance in yards. Assume x=0 corresponds to midfield (the 50 yards line). For example, x=20 corresponds to the punter's own 30 yard line, whereas corresponds to the other team's 30 yard line.

a. Find the maximum height the ball achieves.

b. Find the horizontal distance the ball covers. Assume the height is zero when the ball is kicked and when the ball is caught.

Answer: a. Maximum height = 50

              b. Horizontal distance = 40

Step-by-step explanation: A quadratic function has its maximum or minimum point on its vertex.

When the function is negative, function has a maximum point.

The quadratic function h(x) is written in vertex form, meaning the coordinate of vertex is explicit in the function.

General vertex form: \(f(x)=A(x-h)^{2}+k\)

A is vertical scaling parameter

(h,k) are the coordinates of vertex

So, the quadratic function for the height for the ball:

\(h(x)=\frac{-1}{8}(x-25)^{2}+50\)

shows its vertex:

(h,k) = (25,50)

a. The maximum height the ball achieves the maximum value corresponds to the y-axis, which means, maximum height is 50 yards.

b. Horizontal distance is when h(x)=0, so:

\(\frac{-1}{8}(x-25)^{2}+50=0\)

\(\frac{-1}{8}(x-25)^{2}=-50\)

\((x-25)^{2}=400\)

\(x^{2}-50x+625=400\)

\(x^{2}-50x+225=0\)

Solving quadratic equation:

\(x_{1}=\frac{50+\sqrt{1600} }{2}\) = 45

\(x_{2}=\frac{50-\sqrt{1600} }{2}\) = 5

When ball is kicked, it is in position 5. When is caught, is position 45. So, distance the balls covers is 40 yards.

0.003x = 18

x = 18/0.003 = 6,000

Answer:

1 hundredth without 10 thousandths, so 18 hundredths is 18 x 10 = 180 thousandths

Step-by-step explanation:

Answer:

Sorry if its wrong

Step-by-step explanation: Here's my answer

YMCA

YMAC

YCAM

YACM

ACMY

CAMY

MACY

MCAY

Have a nice day ^-^

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

From the question, we have the following ordered pairs

x intercepts = (6,0) and (18, 0)

Vertex = (12, -36)

Points (21, 41.25)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is the calculated using

m = [f(21) - f(18)]/[21 - 18]

This becomes

m = [f(21) - f(18)]/3

Substitute the known values in the above equation

m = [41.25 - 0]/3

Evaluate the difference

m = 41.25/3

Evaluate the quotient

m = 13.75

Approximate

m=14

Hence, the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

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Complete question

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

See attachment for graph