The box plots represent the length of 100 randomly sampled commercial breaks for two different television stations Length of Commercial Breaks Channel 1 Channel 2 20 40 60 140 160 80 100 120 Time (seconds) Which statement about the difference in the medians of the two data sets is true?

ANSWER

14.75

EXPLANATION

To write a fraction as a decimal we have to do the division. In this case we have a mixed number, so we have the whole part of the decimal and we just have to find the decimal part - which is 3/4.

3/4 is 0.75:

So 14 3/4 is:

Explanation:

Given the equation:

Comparing it with the slope-intercept form: y=mx+b

Definition: Two lines are perpendicular if the product of the slopes is -1.

Let the slope of the new line = n

Substitute the slope, -2 and point (4,-5) in the slope-point form:

We then express it in the slope-intercept form:

The equation of the perpendicular line is y=-2x+3.

Answer:

The grpah is plotted with the number of strides along the x axis and the distance travelled along the y axis.

So, the slope of the graph gives the distance travelled by Robin per stride or the stride length. The approximate value of slope of the graph is,

So, the stride length or the unit rate of Robin is approximately 2.67 feet.

Use the identity

Then the expression becomes

Now, sec x is the reciprocal of cos x.

Answer:

(a)Range: {-5, -2 ,1 ,4}

Explanation:

The function f is defined below:

The domain of f(x) = {-1, 0, 1, 2}.

(a)To find the range of f(x), we evaluate f(x) for each value in the domain.

Therefore, the range of f is:

(b)Next, we graph f.

After 3 hours, Selma is approximately 130 miles from home and Didi is approximately 52 miles from home

1) Let's find the results of each inequality/equality so that we write out the right choices.

2) Let's begin with the equation. We're going to resort to Algebra:

Based on that, we can tell that and filling in the gap with other whole numbers the following:

Note that we picked whole numbers and it is clear that the greater the denominator the lesser the value.

The given images are 1, 2, 3, 4, 5

The total number of participants = 24

The frequency of each image is the number of times it appears in the distribution

Frequency of 1 = 6

Frequency of 2 = 5

Frequency of 3 = 4

Frequency of 4 = 3

Frequency of 5 = 6

The frequency distribution table is therefore shown below:

Given:-

A right angled triangle with side length 1.

To find the required angle value.

So now we use different trigonometric ratios such as,

So we get,

So the required angle is 45 degree.

The required number would be 2 which represents "the sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2."

The sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2.

Let's assume the number would be x

As per the given condition, the algebraic form would be as

⇒ 4(x - 2) = 5(x - 2)

Apply the distributive property of multiplication,

⇒ 4x - 8 = 5x - 10

Rearrange the terms of variable x,

⇒ 5x - 4x = 10 - 8

Apply the subtraction operation,

⇒ x = 2

Therefore, the required number would be 2.

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If two triangles are similar, it means that the ratio of their corresponding sides is the same. By applying this to the given triangles, it means that

20/n = 16/24

By crossmultiplying, we have

n x 16 = 20 x 24

16n = 480

n = 480/16

n = 30

The second option is correct

we have that y=k*x, therefore we can say that k=y/x

so, if we have y= 10.5 we get that

x=24.5

1. The rotation of a point in 180 degrees is given by reflecting both of its coordinates. In this case the original point is (-4, 3), so the rotated point will be (4, -3).

2. When we reflect a point around the x-axis we need to invert the signal of the y-coordinate. When we make a translation to the right we need to add the number of units to the x-coordinate of the point, therefore.

Translation:

A' = (-4 + 2, 3) = (-2, 3)

Reflection x-axis:

C = (-2, -3)

3. When we reflect a point around the y-axis we invert the signal of x-coordinate. To perform a translation to the right we add the number of units to the x-coordinates, therefore:

Reflection y-axis:

A'' = (4, 3)

Translation:

D = (4 + 2, 3) = (6,3)

Start by distributing the negative sign

Then group terms that have the same literal parts

Since we have to solve it graphically, we need to plot the function:

Here, we can see that the point where the graph touches the y axis is when x = 2

The solution to the equation is x = 2

Given data:

The given right angle triangle.

The expression for tan(D) is,

Substitute the given values in the above expression.

Thus, the value of angle D is 29.05 degrees.

(k,-3)

x-2y=-2

replace (x,y ) for (k,-3) and solve for k

k-2(-3)=-2

k+6 =-2

k= -2-6

k=-8

let's break down the expression to get the final result:

Since all rotations have a center of rotation at the origin, let us first give the coordinates of the vertices of the original figure

If an object M(x, y) is rotated about the origin, the image will have the coordinates M'(-x, -y)

F(-4, 2)

N(-1, -2)

K(3, 0)

P(2, 4)

The coordinates of the new vertices after rotation will be:

F'(4, -2)

N'(1, 2)

K'(-3, 0)

P'(-2, -4)

The graph is shown below:

The factored form is, x =3i and x = -3i

Given:

The objective is to write x^2+9 in factored form​.

The factored form can be written as,

Here, i stands for imaginary term due the square root of (-1).

Hence, the factored form is, x =3i and x = -3i.

Answer:

23.6%

Explanation:

A relative frequency table shows the number of times a specific event occurs compared to the total number of events.

First, we calculate the total number of vehicles.

Next, the number of red cars = 13.

Therefore, the relative frequency for red cars will be:

The percent that would go in the cell for red cars is 23.6%.

The formula for circumference is given by

C = pi *d where pi = 3.14 and d is the diameter

We can find the diameter from the radius

d = 2*r where r is the radius

C = pi * 2 *r

C = 3.14 * 2 * 15

C =94.2 ft

Answer : 0.16 is a rational number

Rational number is a number such that can be expressed as the quotient or fraction of two integers

An integer is a number that can be written without a fractional component

0. 16 can be written as

16 / 100

16 and 100 are both integers but 0.16 is not an integer but a rational number

16 / 100 = 0.16. This means that fraction of two integers that does does not gives an integer is a rational number

Hence, 0.16 is a ratioanal number

First, notice that 1/5 = 0.20. With this in mind, the examples that can be represented by the equation y = 1/5x are the following:

1.-Bananas are on sale for $0.20. Let x represent the number of bananas and y represent the total cost,in dollars

2.-For every 10 gallons of water, Jasmine adds 2 cups of Soap. Let x be the gallons of water and y the cups of soap.

The probability is 12/194580

The balls numbered 1 through 12 are:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

If 4 balls have the same number, then there are 12 types of this arrangement:

1, 1, 1, 1

2, 2, 2, 2

3, 3, 3, 3

and so on.

There is also 4 * 12 = 48 total number of balls.

We have a permutation:

Finally, we

This is the required probability.

When the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .

The given function is of the form f(x) = ·|x| .

Therefore we can say that this function will be vertically compressed.

From the properties of transformation of graphs we know that when a function is vertically compressed by a factor of a we get the transformed function as 1/a times the original function.

given function:

f(x) = |x|

vertically compressed by 5.

therefore new function = 1/5 |x|

Hence the transformed function is g(x) .

g(x) = 1/5 |x|

Let us take a few coordinates along the x-axis to get the values of the y and the graph of both modulus function pass through origin .

f(x) = |x|

at x = 10 , f(x) = 10

and g(x) = 2

Here we see that the function is compressed.

Therefore when the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .

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Answer:

B) π

Definition

A number is said to be Irrational if it cannot be expressed as a terminating or repeating decimal.

From the given options

• Option A when converted to a decimal number is a repeating decimal.

• Option C is also a repeating decimal

• Option D (1.5) is a Terminating decimal.

Therefore, the only number which is Irrational is π since it neither terminates nor repeats (or recur).

Solution:

Given;

What is 7/4 as a mixed number?

7/4 as a mixed number can be expressed as

Hence, the answer is 1 3/4

Answer

XY = 54 units

Explanation

We are told that W is in between X and Y. This means that

XY = XW + WY

WX = XW = 38

WY = 16

XY = ?

We just make the necessary substitutions

XY = XW + WY

XY = 38 + 16 = 54 units

Hope this Helps!!!

The statement is given as

The seventh decile is the ___ percentile in terms of the data set.

The seventh decile is the 70-th percentile in terms of the data set.

Hence the answer is 70th percentile in terms of data set.

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