A survey revealed that 36% of people are entertained by reading books, 32% are entertained by watching TV, and 13% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV

A perpendicular line to PQ must have a slope equal to 1/3, then the correct options are B and C.

Two lines are perpendicular if the slope of one is equal to the opposite of the inverse of the other line's slope.

We know that PQ passes through (-8, 7) and (-4, 5), then the slope of PQ is:

[tex]s = \frac{-5 - 7}{-4 - (-8)} = -3[/tex]

A perpendicular line to PQ must have a slope equal to:

[tex]s' = -(\frac{1}{-3} ) = (\frac{1}{3})[/tex]

So we have two correct options (two lines with that slope) which are options B and C.

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The range of sales Dr. Spencer Lewis must exceed to profit the most from the second deal is 15,000 sales.

To find the range that will benefit Dr. Spencer Lewis the most with the second deal, we must perform the following operation:

We must replace the X with several numbers and buy the result, when the result of operation B exceeds the result of operation A, it means that it will be more profitable.

According to the above, if we replace the X with 15,000, the values will be the same, however, each number that we increase will mean a greater profit in agreement B.

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Answer:

Step-by-step explanation:

You did not post any question and I just retrieved all possible information from whatever is given.

Step-by-step explanation:

L = 10W

L + W = 132/2 = 66

---

10W + W = 66

W = 6

L = 60

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[tex] \sf{\purple{Step \: \: By \: \: Step \: \: Explanation}} [/tex]

Perimeter = 2(L + W)

132 = 2(L + L/10)

132 = 2(10L/10 + L/10)

132 = 2(11L/10)

132 : 2 = 11L : 10

66 = 11L : 10

66 : 11 = L : 10

6 = L : 10

Answer:

1. b=(d-c)/a

Step-by-step explanation:

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The measure of angle ABD (m∠ABD) is 104°

From the question, we are to determine the measure of angle ABD

In the diagram,

∠ABC = ∠ABD + ∠DBC

Thus,

m∠ABC = m∠ABD + m∠DBC

From the given information,

m∠ABC = 140°

m∠DBC = 36°

∴ 140° =  m∠ABD + 36°

m∠ABD = 140° - 36°

m∠ABD = 104°

Hence, the measure of angle ABD (m∠ABD) is 104°

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The value of x which is the missing angle of the triangles is; x = 30°

We know that Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

Thus, if we label the vertex with the unknown angle in the smaller triangle as A, then by the alternate angle theorem, we can say that;

∠A = 2x

Thus, from sum of angles in a triangle equals to 180°, we can say that;

x + 2x + 90 = 180

3x + 90 = 180

3x = 180 - 90

3x = 90

x = 90/3

x = 30°

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The simplified expression for the following expression are:

7a + 3a - 2a + 5a

= 15a - 2a

= 13a

0.7 - 0.3g - 0.02g + 5

= 5.7 - 0.32g

5g² + 3g - 4g + 5g²

= 10g² - g

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Answer:

When the volume of a gas in a container varies inversely with the pressure on the gas and a container of nitrogen has a volume of 29.5 litres with 2000 psi. So, if the tank has a 14.7 psi pressure, then the volume of the tank would be 4013.6 litres.

Step-by-step explanation:

Step 1 of 2

Write the inversely proportionality relation between the volume and pressure of a gas in container.

[tex]$v \propto \frac{1}{p}$[/tex]

Where volume is represented by v and pressure is represented by p.

Remove the proportionality and place a constant say k.

[tex]$v=\frac{k}{p}$[/tex]

Substitute the given values of nitrogen that v=29.5 and

p=2000 and calculate the value of k from above equation.

[tex]$$\begin{aligned}&29.5=\frac{k}{2000} \\&\Rightarrow k=29.5 \times 2000 \\&\Rightarrow k=59000\end{aligned}$$[/tex]

Step 2 of 2

Substitute the value p=14.7 and above calculated k value in the equation

[tex]$$\begin{aligned}&v=\frac{k}{p} . \\&v=\frac{59000}{14.7} \\&\Rightarrow v=4013.6\end{aligned}$$[/tex]

Answer: 130

Step-by-step explanation:

Let the measure of arc DB be x.

Then,

[tex]80=\frac{x+30}{2}\\\\160=x+30\\\\x=130[/tex]

The length of one leg of the right triangle is h = 12√2 inches

The length of a right triangle can be found as follows;

sin 45 = opposite / hypotenuse

Therefore,

hypotenuse = 24 inches

Hence,

sin 45 = h / 24

h = 24 sin 45

h = 24 × 1 / √2

Therefore,

h = 24 / √2 × √2 / √2

h = 24√2 / 2

h = 12√2 inches

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Answer: B. 12√2 inches

Step-by-step explanation: TRUST ME!!! Answer correct on Edge!!! :)

The set of points which includes all of the solutions for y in the given equation is the set of all real numbers.

The equation given in the task content whose solution set is go be determined is;

y = (5/2)x + 3/2.

It therefore follows that the solution set for.tge equation includes all real numbers as the equation is linear.

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An interval to estimate the true average tip is  (14.62,13.78).

According to statement is

we know that the

confidence interval = sample mean ± standard deviation /(n)^1/2

substitute the values in it then

confidence interval = 14.2  ± 2.5/(35)^1/2

confidence interval = 14.2 ± 2.5/5.91

confidence interval = 14.2 ± 0.42

confidence interval = 14.2 + 0.42 , confidence interval = 14.2 - 0.42

confidence interval = (14.62,13.78)

So, an interval to estimate the true average tip is  (14.62,13.78).

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Answer:

[tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex]

Step-by-step explanation:

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We can solve the quadratic by using the Quadratic Formula.

Standard form of a Quadratic: [tex]ax^2 + bx +c = 0[/tex]

Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Given our equation: [tex]2x^2 + x - 4 = 0[/tex]

Plug in the values into the quadratic formula to solve.

The solution to the quadratic is [tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex].

The conditional probability formula is P(X|Y) = P(X and Y)/P(Y)

The conditional formula is represented as:

P(A|B) = P(A and B)/P(B)

In this case:

A = X

B = Y

So, we have:

P(X|Y) = P(X and Y)/P(Y)

Hence, the conditional probability formula is P(X|Y) = P(X and Y)/P(Y)

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Answer:

A, B and D

Step-by-step explanation:

Answer:

Answer B , D , E

Step-by-step explanation:

Answer:

(0,-2)

Step-by-step explanation:

the answer is (0,-2) because -2 is where the line crosses over the y-axis. If we looked at a graph you would see that the line goes over 0 on the X-axis, which causes the line to touch the y-axis and intercept it at the -2 mark.

An easy way to find the answer for these sorts of questions is to draw out a graph and mark the coordinates on it and draw the line conecting them. Once you've done that you can easily see where the line intercepts on both the y and x axis.

Answer:

(0,-2)

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Using the Fundamental Counting Theorem, it is found that there are 648 ways to paint the spinner.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem, we have that the first sector can be painted in any of the 4 colors, the others until the 5th can be painted in 3 colors(not the adjacent), and the sixth in only 2, as it is adjacent to both the 5th and the 1st sectors, hence:

[tex]n_1 = 4, n_2 = n_3 = n_4 = n_5 = 3, n_6 = 2[/tex]

Hence the number of ways is given by:

N = 4 x 3 x 3 x 3 x 3 x 2 = 648.

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Answer:

Find total surface area. Multiply material unit cost by the total surface area.

Step-by-step explanation:

To find the cost of a container, you must first find the total surface area of the container. Then since you are given the unit cost for the material, you multiply the total surface are by the unit cost ($0.0015/in.²).

The height of the smallest tank if the larger is 300cm tall will be 240cm.

Similar figures are those figures which are identical in shape, but not necessarily in size.

Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.

We can utilize scale factors because the tanks have comparable shapes.

The scale factor for volume will be given as,

The volume of small tank/volume of big tank = 512000/1000000 = 0.512

Since volume, if the cube so,

Scale factor = [tex](0.512)^{1/3}[/tex] = 0.8

With this scale factor the height of the smaller tank = 300 x 0.8 = 240cm

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Step-by-step explanation:

So you can check for extraneous solutions by plugging in the 5 and -2 as x.

Plug 5 in as x

[tex]5=\sqrt{3(5)+10}\\5=\sqrt{15+10}\\5=\sqrt{25}\\5=5[/tex]

I'm not sure if this is exactly considered an extraneous solution, but I'm assuming it is, since technically the radical doesn't have a plus/minus in front of it, so it's the principle square root which means it only outputs the positive values. This would mean that the -2 wouldn't be a solution, since the principle square root doesn't output negative values, so it's a function, since if it outputted 2 values, then it wouldn't be a function by definition.

The solution to the division of the given polynomial expression is:

k = (x+3)(x-4)

The division of the given polynomial can be determined by using the rational root theorem which is a method that is popularly used in determining the solutions to a polynomial equation.

From the information given:

[tex]\mathbf{\dfrac{x^3 -3x^2 - 10x +24}{x-2}}[/tex]

Using the rational root theorem;

[tex]\mathbf{\dfrac{(x-2) \dfrac{x^3 -3x^2 - 10x +24}{x-2} }{x-2}}[/tex]

[tex]\mathbf{\dfrac{(x-2)(x^2 -x-12)}{x-2} }}[/tex]

Factor: x² - x - 12

[tex]\mathbf{\dfrac{(x-2)(x+3)(x-4)}{x-2} }}[/tex]

Cancel out the common factor (x-2)

[tex]\mathbf{=(x+3)(x-4) }}[/tex]

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Answer:

[tex]180\ in.^2[/tex]

Step-by-step explanation:

The area of a rectangle can is defined as [tex]A = wl[/tex] where w is the width and l is the length. The width in this case is 12 and the length is 15. Also it doesn't really matter what order you put it in. This gives you an area of [tex](15\ in.) (12\ in.) = 180\ in.^2[/tex]

Similarity transformations involve two types of transformations required to map a  given object onto a similar object without a change in its dimensions. Thus the answers required are:

a. Similarity transformations - translation and dilation.

b. The first transformation is translation.

c. The second transformation is dilation.

Transformation is a process required to change the size or orientation of a given shape to form an image. The types are reflection, translation, rotation, and dilation.

i. Reflection is a type of rigid transformation in which a given shape is flipped about a given point or line.

ii. Translation involves moving a given shape in a certain direction without a change in its initial orientation.

iii. Rotation is a type of rigid transformation where a shape is turned about a given point or line at a required angle.

iv. Dilation is a process that requires either increasing or decreasing the dimension of a given shape.

Also, similarity transformations involve two types of transformations required to map a  given object onto a similar object without a change in its dimensions.

The appropriate answers to the given question are:

a. similarity transformations - translation and dilation

b. The first transformation is translation.

c. The second transformation is dilation.

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Step-by-step explanation:

25 (divided by 5) 5

__ = __

40 (divided by 5) 8

[tex]|\Omega|=25+15=40\\|A|=25\\\\P(A)=\dfrac{25}{40}=\dfrac{5}{8}=62.5\%[/tex]

Answer:

OB. (2, 4), (3, 9), (4, 16), (5, 25)

Step-by-step explanation:

none of the points in this ordered pair have the same x-pos. In all the other options, at least 2 of the points have the same x-pos, preventing them from being functions. Therefore, OB is the only right answer.

The equation of the line is y = -7/5x + 56/5

The formula for expressing equation of a line is given as y = mx + b

where

m is the slope

b is the y-intercept

Given the coordinates A(8, 0) and (3, 7)

Determine the slope

Slope =7-0/3-8

Slope = -7/5

For the intercept

0 = -7/5(8) + b

b = 56/5

Hence the equation of the line is y = -7/5x + 56/5

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Answer:

Step-by-step explanation:

Solution

Start with the product

The product is 7*x where x is a number but not specified.

Now add 6

Answer: 7x + 6      

This cannot be simplified any more than what it is now.

Represent the following sentences as an algebraic expression:

Assuming:

6 is added to the product of 7 and a number.

Product : 7 × x = 7x

Now we will add 6.

Add : 7x + 6.

Final Answer:

7x + 6.

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Answer:

It would take 1.5 hours for all three to finish the work if they worked together.

Step-by-step explanation:

Elon and Jeff can complete the work in 3 hours.

Jeff and Bruce can complete the work in 6 hours.

Elon and Bruce can complete the work in 4 hours.

3 + 6 + 4 = 13

13 / 3 = 4.33

4.33 / 3 = 1.44

Answer:

x=5[tex]\sqrt{2\\[/tex]

Step-by-step explanation:

Answer:

5 sqrt 2

Step-by-step explanation:

Log 2x + log x = 2

log ( 2x * x ) = 2

log (2x^2) = 2

2x^2 = 100

x^2 = 50

x = sqrt (50) =  5 sqrt 2