The line plot represents the afterschool activities at 15 middle schools.

A horizontal number line starting at 0 and increasing by units of two up to 30. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The title is Afterschool Activities, and the number line is labeled Number of Activities.

Which statement best describes the spread and distribution of the data?

The data is symmetric with an approximate range of 24. The most frequent number of activities was 16, which might mean about half of each class participated.
The data is skewed with an approximate range of 24. The most frequent number of activities was 10, which might mean there are 10 different sports and clubs for middle school students that are the most popular.
The data is bimodal with an approximate range of 24. The most frequent number of activities was either 16 or 28, which might show that the entire class needed to choose an activity.
The data is symmetric with an approximate range of 24. The most frequent number of activities was less than 10, which might mean that the schools do not have funding for the activities.

Answer:

-6x - 2y = 12

Step-by-step explanation:

The domain and range of the graph are domain = [-2, 5] and range is [-6, 2] and the graph is not a function

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the x values to be

x = -2 to 5

On the graph, we have the y values to be

y = -6 to 2

This means that domain = [-2, 5] and range is [-6, 2]

The graph is the graph of a circle

A circle does not represent a function

Hence, the graph is not a function

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The height will be  61.8 ft

Find the volume of prism

Volume = Base Area × Height

since height = 10 feet

5,119.5 ft³ / 10 ft

= 511.95 ft²

formula for the area of a regular polygon is:

Area = (Perimeter × Apothem) / 2

ide length of the pentagon as 's' and the apothem as 'a'

511.95 ft² = (5s × a) / 2

angle at the center of the pentagon is 360° / 5 = 72°

72 / 2 = 36  degrees

tan(36°) = (s/2) / 17.25

solve for the value of s

s = 2 × 17.25 × tan(36°)

= 12.36 ft

5 s =

5 x 12.36 ft

=  61.8 ft

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Answer:

[tex] {x}^{2} + 11x + 18 = [/tex]

[tex](x + 2)(x + 9)[/tex]

The two numbers are 2 and 9.

2 + 9 = 11, and 2 × 9 = 18.

Answer:

(3, 0)

Step-by-step explanation:

It might be first helpful to think about the function [tex]|x-3|[/tex], we will call this [tex]g(x)[/tex]. So, [tex]g(x)=|x-3|[/tex].

The modulus (absolute value) function reflects any points on a graph that go below the x-axis up into the positive x region.

We know that the graph of [tex]y=x-3[/tex], will cross the x-axis at (3,0). We can work this out by setting y to 0 and rearranging for x. At the x-axis, y = 0.

Therefore, when the modulus comes in, a vertex will be created at (3,0).

But that is the vertex of [tex]g(x)[/tex].

Using basic algebra we can derive from previous working that [tex]f(x)=2g(x)[/tex].

Graphically, the multiplier of 2 on the outside of [tex]g(x)[/tex] stretches the graph in y-axis, and does so by the scale factor of 2.

With our vertex (3,0), the y value is 0. And if you multiply 0 and 2 together, 0 is produced. The x value will remain unchanged as a result of this transformation.

Therefore, the vertex of [tex]f(x)[/tex] is (3,0).

The correct answer is option B:

⇒ Y decreases and X increases.

Given that;

the y value starts to decrease and the x value remains the same over time.

Now, We know that;

the slope remains constant, but the y value decreases as you move along the slope in the negative y direction, while the x value increases.

Hence,

If the y value starts to decrease while the x value remains the same over time on a consistent slope,

Thus, The correct answer is option B:

⇒ Y decreases and X increases.

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Answer:

The answer to your problem is, She spend more talking to her friend then her mother

Step-by-step explanation:

The question asking:

What fraction of the minutes did Emilia spend talking to either her mom or her best friend?

So we can see that she talks to her friend instead of her mother shown;

[tex]\frac{1}{12} < \frac{5}{12}[/tex]

The total equals to [tex]\frac{6}{12} or\frac{1}{2}[/tex]

So, She spend more talking to her friend then her mother

Thus the answer to your problem is, She spend more talking to her friend then her mother

Approximately, the amount of money, in cents, that Celine will save in 12 years is: B. 300

In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the money (in cents) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the years and the money (in cents), an equation for the line of best fit is given by

y = 26.9x - 18.5

when x = 12, the amount of money, in cents, that Celine will save in 12 years is given by;

y = 26.9(12) - 18.5

y ≈ 300 cents.

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The surface area of the polyhedron is calculated be equal to 224 square inches.

The polyhedron can be observed to have a large rectangle between two identical triangles by the sides

area of rectangle = length × width

The large rectangle have;

length = (12 + 10 + 10) in = 32 in

width = 4 in

area of large rectangle the = 32 in × 4 in = 128 in²

area of one identical triangles = 1/2 × 12 in × 8 in = 48 in²

area of 2 identical triangles = 2 × 48 in² = 96 in²

Surface area of the polyhedron = 128 in² + 96 in²

Surface area of the polyhedron = 224 in²

Therefore, the surface area of the polyhedron is calculated be equal to 224 square inches.

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The requried insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.

The insurance premium of a bus is GH¢93.30 plus 15% of the insured value.

Let's first calculate 15% of¢250.00:

15% of GH¢250.00 = 0.15 x 250.00 = GH¢37.50

Now, we can add this amount to the base premium of GH¢93.30 to find the total insurance premium for the bus:

GH¢93.30 + GH¢37.50 = GH¢130.80

Therefore, the insurance premium of a bus whose insured value is GH¢250.00 is GH¢130.80.

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Answer:

B) 0.08 and 0.1

The answer was 0.09, which is between 0.08 and 0.1

Answer:

43.96 = 2πr

r = 21.98/π

A = π(21.98/π)^2 = 483.1204/π = 153.78 square meters

A = 483.1204/3.14 = 153.86 square meters

The explicit rule for the sequence 4, 3 2/3, 3 1/3, 3.... is f(n) = 4 - 1/3(n - 1)

From the question, we have the following parameters that can be used in our computation:

4, 3 2/3, 3 1/3, 3....

In the above sequence, we can see that 1/2 is subtracted from the previous term to get the new term

Take for instance

2nd = 4 - 1/3 = 3 2/3

3rd = 3 2/3 - 1/3 = 3 1/3

4th = 3 1/3 - 1/3 = 3

And so on

This means that

So, the explicit rule is

f(n) = a + (n - 1)d

This gives

f(n) = 4 - 1/3(n - 1)

Hence, the explicit formula is f(n) = 4 - 1/3(n - 1)

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Complete question

Consider the sequence 4,3 2/3,3 1/3, 3....

What is the explicit rule for this sequence

The segment lengths on the right triangle are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The sum of the internal angle measures of a triangle is of 180º, hence the missing angle is given as follows:

m < L = 180 - (30 + 60)

m < L = 90º.

Hence the segment JL represents the hypotenuse of the figure.

JL is opposite to the angle K, hence it's length is obtained as follows:

sin(30º) = JL/26

1/2 = JL/26

2JL = 26

JL = 13.

Segment KL is adjacent to the angle of 30º, hence it's length is obtained as follows:

cos(30º) = KL/26

[tex]\frac{\sqrt{3}}{2} = \frac{KL}{26}[/tex]

[tex]2KL = 26\sqrt{3}[/tex]

[tex]KL = 13\sqrt{3}[/tex]

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Answer:

28 hours

Step-by-step explanation:

Let's use "B" to represent the number of hours Bianca practiced.

From the problem, we know that Filipe practiced 12 fewer hours than Bianca, which means:

Filipe's practice time = Bianca's practice time - 12

We are also told that Filipe practiced for 16 hours, so we can substitute that into the equation:

16 = B - 12

To solve for B, we can add 12 to both sides:

16 + 12 = B

So, Bianca practiced for a total of 28 hours.

The perimeter of the rectangle is P = 18 units

Given data ,

Let the rectangle be represented as ΔWXYZ

Now , the coordinates of the triangle are

W ( 3 , 3 ) , X ( 8 , 3 ) , Y ( 8 , 7 ) and Z ( 3 , 7 )

The perimeter of the rectangle = 2 ( length + width )

The width of the rectangle W = ( 7 - 3 ) = 4 units

The length of the rectangle L = ( ( 8 - 3 ) = 5 units

So , P = 2 ( 4 + 5 )

P = 2 x 9

P = 18 units

Hence , the perimeter is 18 units

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The statement that could be true for h is h(2) = 16.

Option A is the correct answer.

We have,

The function h has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25, and we know that h(8) = 19 and h(-2) = 2.

To determine which statement could be true for h, we can use the given domain and range, along with the two known function values, to narrow down the possible values of h(x) for different values of x.

h(2) = 16

We do not have enough information to determine whether this statement could be true or not.

It is possible that h(2) = 16, but it is also possible that h(2) could be a different value within the range of 1 ≤ h(x) ≤ 25.

h(8) = 21

This statement cannot be true, as we already know that h(8) = 19.

h(13) = 18

This statement cannot be true, as 13 is outside the given domain of -3 ≤ x ≤ 11.

h(-3) = -1

This statement cannot be true, as -1 is outside the given range of 1 ≤ h(x) ≤ 25.

Therefore,

The statement that could be true for h is h(2) = 16.

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Answer: The brother is 16 and she is 19.

Step-by-step explanation:

35 - 3 = 32

32 / 2 = 16

16 + 3 = 19

The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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Note that the probabilities are given below.

a) the probability of a randomly selected catch being a mouse caught by Cyd

p(Catching a mount) x p(Cyd made the catch)

= 0.5x .2

= 0.1

b) the   probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.

Thus

P(that a catch is a bird) x p(the Cyd didn't make the catch)

= 0.3 x 0.8

=0.24

c) The probability of a randomly selected catch being caught by Greg is 0.45

To calculate, we say

(0.5   x0.45) + (0.3 x 0.45) + (0.2 x .45)

= 0.45.

d)

P (mouse caught by Greg) = (0.45 x 0.5) / 1

= 0.225.

e) P(catch is a mouse caught by Ken and catch is a mouse)

= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)

= 0.05 x 0.1

= 0.005

f)

P (catch made by Cyd | catch is a mouse)

= 0.1    x 0.2 / 0.5

= 0.04

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Answer:The algebraic steps you have taken are incorrect, leading to an invalid conclusion. Let's go through each step and see where the mistake is made:

X = 1 (given)

X+X = 1+X (adding X to both sides)

2X = 1+X (combining like terms)

2X = X+1 (rearranging terms)

2X-2 = X+1-2 (subtracting 2 from both sides)

2X-2 = X-1 (simplifying)

2(x-1)/(x-1) = (x-1)/(x-1) (dividing both sides by x-1, note that x cannot be 1 as it would result in division by 0)

2 = 1 (canceling out the (x-1)/(x-1) on both sides)

The error lies in dividing both sides by (x-1) in step 7. Although (x-1) appears on both sides of the equation, it is not equal to zero as x cannot be 1 due to division by zero. Dividing by (x-1) effectively cancels it out, leading to the incorrect result of 2=1.

Step-by-step explanation:

The minimum number of people over age 30 they must include in their sample is: 829 people

The formula for calculating the standard error is:

SE = μ ± Z(σ/√N)

Where:

σ = the standard deviation,

N = the sample size,

Z = the Z value for the percent confidence level desired.

We must find the Z value, at the 85% confidence level from a Cumulative Standardized Normal table for the 99% confidence level. This gives us the value of Z = 1.44

σ = 1.4 liters

N = 0.07

Thus:

0.07 = 1.44(1.4/√N)

0.07/1.44 = 1.4/√N

1.4/√N = 0.04861

√N = 1.4/0.04861

N = (1.4/0.04861)²

N = 829 people

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The estimate of the population mean is 80 and the variability in the distribution is 120

Here, we have

The dot plots

From the dot plots, we can see that the data are normally distributed

This means that the mean, the median and the mode are equal

From the distribution of the random variable, we have the following readings

Hence, the estimate of the population mean is 80

Here, we use the range

So, we have

Variability = Highest - Least

This gives

Variability = 140 - 20

Variability = 120

So, the variability in the distribution is 120

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The function is :

[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex] the inverse function is:

Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]

Domain: (-[tex]\infty[/tex],9]

Range: [tex](-\infty,0][/tex]

If the inverse function of f is the function g, then x = f(x) gives x = g(y). We just need to reverse the function.

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.

If f and g are inverse functions, then f(x) = y if and only if g(y) = x

The function is :

[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]

We have to find the inverse of the function.

The inverse, interchange the variables solve for y,

Now,

[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]

[tex]f^-^x(x)=\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]

So, [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]

Hence,

Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]

Domain: (-[tex]\infty[/tex],9]

Range: [tex](-\infty,0][/tex]

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An equation for the height of the rocket after t seconds is h(t) = -16t² + 352t.

The time it takes for the rocket to reach a height of 0 is 22 seconds.

The time it takes to reach the top of its trajectory is 11 seconds.

The maximum height is 1,936 feet.

The time it takes to reach a height of 968 feet is 18.8 or 3.2 seconds.

Based on the information provided, we can logically deduce that the height (h) in feet, of this rocket above the​ ground is related to time by the following quadratic function:

h(t) = -16t² + Vit

When the initial velocity is 352 feet per seconds, the height function becomes;

h(t) = -16t² + 352t

Generally speaking, the height of this rocket would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:

0 = -16t² + 352t

352t = 16t²

Time, t = 352/16

Time, t = 22 seconds.

Next, we would determine the maximum height of this rocket by taking the first derivate in order to determine the time (t) it takes;

h(t) = -16t² + 352t

h'(t) = -32t + 352

352 = 32t

t = 352/32 = 11 seconds.

h(11) = -16(11)² + 352(11)

h(11) = 1,936 feet.

At a height of 968 feet, the time is given by;

968 = -16t² + 352t

16t² - 352t + 968 = 0

t² - 22t + 60.5 = 0

Time, t = 18.8 or 3.2 seconds.

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Step-by-step explanation:

Direct variation means    y = k x

when y = 2      x= 3

   2 =  k *3

   2/3 = k

so the variation becomes y = 2/3 x

            when x = 2

                     y = 2/3 (2)=   4/3