A circular swimming pool has a radius of 20 feet. A fence is going to be built so that there is a 4-foot space around the entire pool. What is the length of the fence? Sunitha solved the problem as shown.Kevin needs to run 320 meters a day for his training program. He plans on running around the high school track shown. If he runs around the track once, will he meet his daily goal?

Answer:

y = x^2 + 8x + 19

Step-by-step explanation:

y=(x+4)²+3

First expand the parentheses:

y = x^2 + 4x + 4x + 16 + 3

y = x^2 + 8x + 19

The equation of the circle with center (5,5) containing the point (0,-2) is [tex](x - 5)^2 + (y - 5)^2 = 74[/tex]

The standard equation of a circle is given by: (x-h)2 + (y-k)2 = r2 Where (h,k) is the coordinates of center of the circle and r is the radius.

To determine the equation of the circle, we need to find the radius first. Since the center of the circle is (5,5), we can use the distance formula to find the distance between the center and the given point (0,-2):

[tex]distance = \sqrt{[(x2 - x1)^2 + (y2 - y1)^2]}\\distance = \sqrt{[(0 - 5)^2 + (-2 - 5)^2]}\\distance = \sqrt{[(-5)^2 + (-7)^2]}\\distance = \sqrt{[25 + 49]}\\distance = \sqrt{[74]}[/tex]

Therefore, the radius of the circle is sqrt[74].

Now, we can use the standard form of the equation of a circle to find the equation of the circle:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h,k) is the center of the circle, and r is the radius.

Plugging in the values we have:

[tex](x - 5)^2 + (y - 5)^2 = (\sqrt{[74]})^2[/tex]

Simplifying the equation:

[tex](x - 5)^2 + (y - 5)^2 = 74[/tex]

Therefore, the equation of the circle with center (5,5) containing the point (0,-2) is [tex](x - 5)^2 + (y - 5)^2 = 74.[/tex]

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As, the scale factor is less than 1 . So, the dilation is the reduction for the image of triangle ABC.

How very much larger (as well as smaller) any item becomes following the transformation is indicated by the dilation factor.

Given data:

A'B'C' is the dilation of triangle ABC.

Scale factor = 1/2  = 0.5

As, the scale factor is less than 1 . So, the dilation is the reduction for the image of triangle ABC

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y=f(x) has vertex (-4,6)

g(x)=-f(x-2) shifts the graph 2 units to the right, not to the left, and the graph is reflected over the x-axis

therefore the vertex is (-2,6) and the reflection over the x-axis has no affect on the vertex

The difference between the median high temperature and median low temperature is 22.5°F

The data set has an odd number of values, the median is the middle value when the data is arranged in numerical order.

Hence Median of the data is given by

Median = value at position (n + 1) / 2,

where n is the number of data points.

Here we have

The weather forecast is shown.

High 84°F 90°F 82°F  79°F  83°F  92°F  82°F

Low  56°F 63°F 60°F  52°F  60°F  61°F  53°F  

To find the difference between the median high temperature and the median low temperature, Calculate the median temperatures for both high and low temperatures.

To find the median, we need to first arrange the temperatures in ascending order  

For the high temperatures, we have:

79°F, 82°F, 82°F, 83°F, 84°F, 90°F, 92°F

Here median = 4th term [ Since the number of terms 7 is an odd number ]

The median of high temparature = 83°F

For the low temperatures, we have:

52°F, 53°F, 56°F, 60°F, 60°F, 61°F, 63°F

Here median = 4th term [ Since the number of terms 7 is an odd number ]

The median of low temparature = 60°F

The difference between the median high temperature and median low temperature is:

83°F - 60.5°F = 22.5°F

Therefore,

The difference between the median high temperature and median low temperature is 22.5°F

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To  draw the image of triangle △ABC under a dilation with center C and scale factor 2, we need to draw the original triangle, draw lines from C to each vertex,

To draw the image of triangle △ABC under a dilation with center C and a scale factor of 2, we need to follow a few steps. Firstly, we need to draw the original triangle △ABC. Then, we need to draw a straight line from the center of dilation C to each vertex of the triangle. These lines will act as our guides for where the new vertices will be located.

Next, we need to use the scale factor of 2 to determine the distance between the original vertices and the new vertices. This means that we need to multiply the distance between each vertex and the center of dilation by 2. We can then plot the new vertices along the lines we drew in the previous step.

Finally, we can connect the new vertices to form the image of the triangle under the dilation. This image will be twice as large as the original triangle and will be located in the same direction as the lines we drew from the center of dilation to each vertex.

use the scale factor to determine the new vertex locations, and finally connect the new vertices to form the image.

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Answer:

the only correct statement is B: the upper quartile value is 96.

Step-by-step explanation:

First, let's put the temperatures in order: 76, 80, 82, 89, 89, 91, 96, 98, 98, 100.

A. To find the median, we need to find the middle value in the ordered set of data. Since there are an even number of values, we take the average of the two middle values. The two middle values are 89 and 91, so the median is (89+91)/2 = 90. Therefore, statement A is false.

B. To find the upper quartile, we need to find the value that separates the highest 25% of the data from the rest. Since there are 10 values, the upper quartile is the 7th value when the data is ordered. The 7th value is 96, so statement B is true.

C. To find the lower quartile, we need to find the value that separates the lowest 25% of the data from the rest. Since there are 10 values, the lower quartile is the 3rd value when the data is ordered. The 3rd value is 82, so statement C is false.

D. The interquartile range is the difference between the upper quartile and the lower quartile. From our previous calculations, we know that the upper quartile is 96 and the lower quartile is 82. Therefore, the interquartile range is 96-82 = 14. Statement D is false.

Therefore, the only correct statement is B: the upper quartile value is 96.

Answer:

-46

Step-by-step explanation:

-7×-7= 49

3-49= -46

-46 is the answer

Answer:

20

Step-by-step explanation:

You can find this answer multiple ways.

One way is that each y value increases by 5 so following the pattern of 5, 10, 15 the next one would be 20.

Another way is that the the x value is 3 times the y value so we would just have to divide 60 by 3 to get 20.

Answer: 20

Step-by-step explanation:

y is a result of dividing x by 3

15/3 = 5

30/3 = 10

...

60/3 = 20

Answer:

0.0399148483 is the answer

Answer:

Your answer is 0.0399

Step-by-step explanation:

In the frequency table, we can see that the most common reason for taking a gap year is travel, with a frequency of 5.

To draw up a frequency table for the given question, we can use the following : List down the reasons:

List down the five different reasons for taking a gap year.

Count the frequency of each reason:

Tally the number of times each reason appears in the data.

Let's say we have the following data:

Reasons for taking a gap year:

Travel Work Experience Family Medical Total Tally

the number of times each reason appears in the data:

Reasons for taking a gap year Tally Frequency Travel Work Experience Family Medical Total

Draw the frequency table:

Draw the frequency table by filling in the tally and frequency columns.

The final frequency table should look like this:

Frequency Table Reasons for taking a gap year Tally Frequency Travel [tex]||||5Work|||3Experience||||4Family||2Medical|1|2| Total5 3 4 2 2 16[/tex]

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The family will have approximately $13,444.03 in the account at the end of 15 years.

To find the value of the account at the end of 15 years, we'll use the formula for compound interest, which is:
A = P * (1 + r)^n
Where A is the final amount,

P is the principal amount (the initial deposit),

r is the annual interest rate (as a decimal), and n is the number of years.
In this case, P = $500,

r = 7% (0.07),

and n = 15.
Step 1: Convert the interest rate to a decimal:

7% = 0.07
Step 2: Add 1 to the interest rate: 1 + 0.07 = 1.07
Step 3: Raise the result from Step 2 to the power of the number of years:

[tex](1.07)^15[/tex]≈ 2.7591
Step 4: Multiply the principal amount by the result from Step 3:

$500 * 2.7591 ≈ $1377.55.

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Answer:

x=-2

Step-by-step explanation:

Answer:

2.083 yards

Step-by-step explanation:

1 inch ≈ 0.0278 yard

75 inches ≈ 2.083 yards

So, 75 inches is about 2.083 yards.

Answer:

75/36 or 2.083

Step-by-step explanation:

We know that there are 36 inches in a yard so just take 75 inches and divide by 36 and you get 2.083

It would take the faster computer 525/20 minutes to do the job on its own.

Let the rate of the faster computer be F and the rate of the slower computer be S. Since they can complete the job together in 15 minutes, we have:

F + S = 1/15

We also know that the slower computer takes 35 minutes to do the job on its own, so:

S = 1/35

Now, we can substitute the value of S into the first equation to solve for F:

F + 1/35 = 1/15

F = 1/15 - 1/35

F = (35 - 15) / (15 * 35)

F = 20 / 525

Therefore, the rate of the faster computer is 20/525. To find how long it takes the faster computer to do the job on its own, we take the reciprocal of this rate:

Time = 1/F = 525/20

So, it would take the faster computer 525/20 minutes to do the job on its own.

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The area of a rectangle is 140.00 square meters.

What is a rectangle?

A rectangle is a 2-dimensional geometric shape with four sides, where each interior angle is a right angle (90 degrees). It is a special case of a parallelogram, where opposite sides are equal in length and parallel to each other.

I assume you are looking for the area of a rectangle with sides 10 m and 14 m, rounded to the nearest hundredth using the approximation π ≈ 3.14.

The area of a rectangle is given by the formula A = lw, where l and w are the length and width of the rectangle, respectively. In this case, l = 14 m and w = 10 m, so:

A = lw = (14 m)(10 m) = 140 m²

Rounding 140 to the nearest hundredth gives 140.00, so the final answer is:

140.00 square meters.

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Full question:

What is the area of a rectangle with sides of length 10 meters and 14 meters, rounded to the nearest hundredth using the approximation π ≈ 3.14?

3,523 gallons

A horizontal compression is identified by a factor inside the function, affecting the input variable, while a vertical compression is identified by a factor outside the function, affecting the output variable.

When examining the formula of a function that is the result of multiple transformations, a horizontal compression can be identified by a factor that appears inside the function, affecting the input variable (typically x). For example, if the original function is f(x) and the horizontal compression is by a factor of 2, the function would be written as f(x/2), indicating that the input values are being compressed horizontally.

On the other hand, vertical compression can be identified by a factor that appears outside the function, affecting the output variable (typically y). For example, if the original function is f(x) and the vertical compression is by a factor of 1/2, the function would be written as (1/2)f(x), indicating that the output values are being compressed vertically.

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Answer:

covered distance = 97.75 kilometers

Step-by-step explanation:

It's known that:

[tex]speed = \frac{distance}{time}[/tex]

Hence,

[tex]distance = speed\times time[/tex] (*)

Given That:

time = 4.25 hours
speed = 23 km/h

then, by substituting in (*):

[tex]distance = 23 \times 4.25 = 97.75 kilometers[/tex]


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The prove that a WXYZ is a parallelogram and WXYZ is a rectangle is given based on the image attached.

To be able to prove that the parallelogram WXYZ is a rectangle, one need to show that it has all the properties of a rectangle. An example of the properties of a rectangle is that it is one that has four right angles.

Hence

From the question, WXYZ is a parallelogram, and ZX = WY.

So to Prove: WXYZ is a rectangle

Therefore, based on the properties listed above, one can prove that the parallelogram is a rectangle.

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Answer: The full price was 275

The recursive and explicit formulae of the given arithmetic expression are:

Recursive formular = [tex]a_{n+1} = a_{n-5}[/tex]

Explicit formular is Tn = 68 - 53n

You can determine the value of any term in a series using an explicit formula. A subset of integers are the natural numbers, which are 1, 2, 3, 4, etc. If you know the value of the (n-1)th term in a series and have access to its recursive formula, you can use it to determine the value of the nth term. The primary distinction between recursive and explicit formulas is that the former provides the value of a particular phrase based on the preceding term, while the latter provides the value of a particular term based on the position.

Given:

a1 = 63

a2 = 67 = 63 - 5 = a1 - 5

Recursive formular = [tex]a_{n+1} = a_{n-5}[/tex]

a = 63, d = -5

F(11) = a + (n - 1)d = 63 + (n - 1)-5 = 63 - 5n + 5 = 68 - 53n

Explicit formular is Tn = 68 - 53n

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Solving for q will give us the optimal quantity that maximizes the profit,  a function that gives the total profit earned can be written as:

Profit(q) = (Revenue per item - Cost per item) * q

Assuming that the revenue and cost are functions of the quantity sold (q), the total profit can be calculated as follows:

Profit(q) = Revenue(q) - Cost(q)

To find the quantity which maximizes the profit, we can take the derivative of the profit function with respect to q and set it equal to zero, and then solve for q:

Profit'(q) = Revenue'(q) - Cost'(q) = 0

Solving for q will give us the quantity that maximizes the profit. However, without knowing the specific forms of the revenue and cost functions, we cannot write a specific profit function or find the quantity that maximizes the profit.

In general, the profit function can be written as:

Profit(q) = (Revenue per item - Cost per item) * q

where the revenue per item and cost per item are functions of q. To find the quantity that maximizes the profit, we need to differentiate the profit function with respect to q and set it equal to zero:

Profit'(q) = Revenue'(q) - Cost'(q) = 0

Solving for q will give us the optimal quantity that maximizes the profit.

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Answer:

155.5 square feet

Step-by-step explanation:

A = (1/2)(10)(8.6 + 6.3 + 8.6 + 7.6)

= 5(31.1)

= 155.5 square feet

Answer:

put 23  

and be my freind pleas i only have 2

The 100th permutation in the list is 75931, which starts with the digit 7 and is the 4th permutation starting with 7.

To find the 100th permutation, we can use the formula for the total number of permutations of n distinct objects, which is n! (n factorial).

In this case, there are 5 digits, so there are 5! = 120 permutations in total. Since the permutations are listed in numerical order, we can divide the total number of permutations by 5 to find the number of permutations starting with each digit.

120 ÷ 5 = 24

This tells us that there are 24 permutations starting with each digit. To find the 100th permutation, we need to determine which digit it starts with. We can do this by dividing 100 by 24 and taking the quotient and remainder:

100 ÷ 24 = 4 with a remainder of 4

This tells us that the 100th permutation starts with the fourth digit in the sequence: 7. We now need to find the 4th permutation starting with 7. To do this, we can list all the permutations starting with 7 in numerical order:

7 _ _ _ _ (4! = 24 permutations)

7 1 _ _ _

7 3 _ _ _

7 5 _ _ _

7 9 _ _ _

The 4th permutation starting with 7 is 75_9_, which is the 100th permutation in the list.

Therefore, the 100th permutation in the list is 75931.

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The experimental probability that the number rolled was even is 53 over 100.

In a die 2, 4 and 6 are even numbers so sum of there frequency are possible outcome.

Frequency of 2 4 and 6 are 20,18 and 15 respectively.

Possible outcome = 20+18+15 = 53

Total outcome is sum of all frequency, total outcome = 17+20+14+18+16+15 = 100

P(even) = 53/100

Therefore the experimental probability that the number rolled was even is 53 over 100.

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.

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Lakeside Olds can expect around 2.6 automobiles to be lined up at the opening time for service.

To find the expected number of automobiles lined up at the opening time, we can use the following  formula is used

Expected value = Σ (number of automobiles * probability)

Using the probability distribution provided in the question, we have:

Expected value = (10.20) + (20.20) + (30.40) + (40.20)

Expected value = 0.20 + 0.40 + 1.20 + 0.80

Expected value = 2.6

Therefore, on a typical day, Lakeside Olds can expect around 2.6 automobiles to be lined up at the opening time for service.

Note that since the expected value is not a whole number, it is an estimate and may not represent the actual number of automobiles on any given day.

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The p-value for this hypothesis test is 0.263.

In this case, the null and alternative hypotheses for a hypothesis test of the difference in two population proportions are:

null hypothesis: p1 = p2

alternative hypothesis: p1 > p2

Notice that the alternative hypothesis is a one-tailed test.

Suppose proportions z test method from stats models is used to perform the test and the output is (1.13, 0.263).

To find the p-value for this hypothesis test, we need to use the output from the statsmodels function.

The second number in the output is the p-value.

Therefore, the p-value for this hypothesis test is 0.263.

The first number in the output is the z-value, which is not relevant to finding the p-value. Therefore, we can ignore it. Answer: 0.263

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