Adriana and Sophie have summer jobs selling newspaper subscriptions door-to-door, but their
compensation plans are different. Adriana earns a base wage of $6 per hour, as well as $2 for
every subscription that she sells. Sophie gets $3 per subscription sold, in addition to a base
wage of $4 per hour. If they each sell a certain number of subscriptions in an hour, they will
end up earning the same amount. How much would each one earn?
Write a system of equations, graph them, and type the solution.

The magnitude of the electrical force acting between both the given charges which are separated by 0.008 m is 6.07 N.

Given Charges 2.4*[tex]10^{-8} C[/tex] and 1.8 *[tex]10^{-6} C[/tex] that are separated by 0.008 m.

We have to find the magnitude of the electrical force acting between the charges. Magnitude is the property which determines the size of an object or process. Force is an influence that can change the direction of an object.

To find the magnitude we have to use Coulomb's law which says that

[tex]F_{E}=K*(q_{1}*q_{2}/d^{2}[/tex]

where K is Coulomb's constant whose value is [tex]8.9910^{9}Nm^{2} C^{2}[/tex].

[tex]q_{1}[/tex]=[tex]2.6*10^{-8} C[/tex] and

[tex]q_{2}=1.8*10^{-6} C[/tex] are the electric charges.

d=0.008m is the separation distance between the charges.

Putting  the values in the given formula we get:

[tex]F_{E} =8.99(10)^{9}Nm^{2}/C^{2} *(2.4(10)^{-8}C(1.8(10)^{-6}C)/(0.008m)^{2}[/tex]

=6.07 N

Hence the magnitude of force acting between [tex]2.4*10^{-8} C[/tex] and [tex]1.8*10^{-6}C[/tex] is 6.07 N.

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Answer:

Step-by-step explanation:

The correct answer is Option A , D , E.

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.

Ratio in it's simplest form means when the ratio can't be simplified anymore  by cancelling out the common factors.

The ratio in Option(A) can't be simplified anymore because 29 is a prime number.

The ratio in Option(B) can be simplified to 1 / 7.

The ratio in Option(C) can be simplified to 5 / 2.

The ratio in Option(D) can't be simplified.

The ratio in Option(E) can't be simplified because 19 is prime number.

Hence, the correct answer is Option A , D , E.

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The total volume of air that coach Tim will need to fill is [tex]1,340^{3} inches[/tex].

To find  the total volume of air that coach Tim will need:

The formula of volume = [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex] × [tex]r^{3}[/tex]

Given - Diameter of volleyball = 8 inches

So, the radius of volleyball = [tex]\frac{8}{2}[/tex] = 4 inches

Now, put the values in the formula of volume as follows:

[tex]\frac{4}{3} * \pi * 4^{3}[/tex]

[tex]\frac{4}{3} * \pi * 64[/tex]

[tex]\frac{4}{3} * 3.14 * 64\\\frac{4}{3} * 201.06\\4 * 67.02\\268.08[/tex]

To find total volume = [tex]268.08 * 5[/tex]

[tex]= 1340.4[/tex]

Rounding off to the nearest whole number = [tex]1,340^{3} inches[/tex]

Therefore,  the total volume of air that coach Tim will need to fill is [tex]1,340^{3} inches[/tex].

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Answer:

D

Step-by-step explanation:

the volume (V) of a cube is calculated as

V = s³ ( s is the side length ) , then

V = 14³ = 2744 cm³

Answer:

D. 2744 cm³

Step-by-step explanation:

volume can be found by multiplying length × width × height

because we know that this is a cube, all side lengths are the same (meaning length, width, and height will all be the same)

so, we know our side length is 14cm, meaning that all of our measurements {length/width/height} are 14cm

length × width × height = volume

14 × 14 × 14 = 2744

when we write volume, we write it as cubed (x³)

{similarly, when we write area,  we write it as squared (x²)}

so, we would write the volume of this cube to be 2744 cm³

(option D)

hope this helps! have a lovely day :)

The pooled estimate of the variance is 187.650 and the test statistic is -2.32

The dataset is given as:

Regular price 138 124 89 112 116 123 98

Reduced price 124 134 154 135 118 126 133 132

Let the regular price be dataset 1 and the reduced price be dataset 2.

So, we have:

#1: 138 124 89 112 116 123 98

#2: 124 134 154 135 118 126 133 132

Calculate the sample means and the sample standard deviations using a graphing calculator.

#1

[tex]\sigma_1 = 16.56[/tex]

[tex]\bar x_1 = 114.29[/tex]

[tex]\sigma_1^2 = 274.24[/tex]

#2

[tex]\sigma_2 = 10.65[/tex]

[tex]\bar x_2 = 132[/tex]

[tex]\sigma_2^2 = 113.43[/tex]

The pooled estimate of the variance is:

[tex]\sigma_p^2 = \frac{\sigma_1^2(n_1 - 1) + \sigma_2^2(n_2 - 1)}{(n_1 - 1) + (n_2 - 1)}[/tex]

This gives

[tex]\sigma_p^2 = \frac{274.24 * (7 - 1) + 113.43 * (8 - 1)}{(7- 1) + (8- 1)}[/tex]

Evaluate the factors

[tex]\sigma_p^2 = \frac{2439.45}{13}[/tex]

Divide

[tex]\sigma_p^2 = 187.65[/tex]

Hence, the pooled estimate of the variance is 187.650

This is calculated using:

[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\sigma_p^2} * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}[/tex]

This gives

[tex]t = \frac{114.29 - 132}{\sqrt{187.650} * \sqrt{\frac{1}{7} + \frac{1}{6}}}[/tex]

This gives

[tex]t = \frac{-17.71}{\sqrt{187.650} * \sqrt{\frac{13}{42}}}[/tex]

Evaluate the product

[tex]t = \frac{-17.71}{\sqrt{58.08214}}[/tex]

Evaluate the exponent

[tex]t = \frac{-17.71}{7.62}[/tex]

Divide

t = -2.32

Hence, the test statistic is -2.32

The critical value at 0.025 significance level is -1.96

-2.32 is less than -1.96

This means that we accept the null hypothesis

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We have [tex]x^{-n} = \frac1{x^n}[/tex] if [tex]n[/tex] is a positive integer and [tex]x\neq0[/tex], as well as [tex]x^0 = 1[/tex] if [tex]x\neq0[/tex]. So right away we can simplify to

[tex]\left(x^{-1} y^2\right) \left(-3 x^2 y^0\right) = \left(\dfrac{y^2}x\right) \left(-3x^2\right) = -\dfrac{3x^2y^2}x[/tex]

If [tex]x=0[/tex], then the starting expression is undefined. So we accept that [tex]x=0[/tex], in which case [tex]\frac xx = 1[/tex], and the overall expression simplifies to

[tex]\left(x^{-1} y^2\right) \left(-3 x^2 y^0\right) = \boxed{-3xy^2}[/tex]

The amount of money that Glenn lost on last tool set is $30.60.

Given sale value of 15 tool set 1 year before is $54.60 and the sale value of last tool at year end is $24.00 by Glenn.

Sale value is the price which we get by selling the good including the profit and cost of the product.

In this question it is given that 15 tools sets, it does not mean that 15 sets are sold.

Using the formula

Amount lose=Original amount paid- selling price.

Now put the values in the formula:

Amount lose=$54.60-$24.00

Amount lose=$30.60.

Hence the amount of money he lost on the last tool set is $30.60.

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Answer:

a.) y = 5x - 7

Explanation:

Equation:

[tex]\sf y - y_1 = m(x - x_1)[/tex]

insert values

[tex]\sf y - (-7) = 5(x - 0)[/tex]

simplify

[tex]\sf y + 7 = 5x[/tex]

rewrite

[tex]\sf y = 5x - 7[/tex]

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Which linear equation would produce a y-int. of (0,-7) and a slope of 5?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Take the second co-ordinate of the point (0,-7), this is your y-intercept.

Next, just put it into y=mx+b in the place of b.

[tex]\bf{y=mx-7}[/tex] | now put in the slope, 5

[tex]\bf{y=5x-7}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{=y=5x-7}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]

∞

The ratio of the number of marbles in the first bag to the number of marbles in the second bag is 2:7.

First of all, we would assign the variables x and y to the marbles in the first and second bag respectively. Also, let F and S represents the first and second bag respectively.

For the first bag, we have:

Ratio = 3:5 = 3x:5x = 3x + 5x = 8x

For the first bag, we have:

Ratio = 3:2 = 3y:2y = 3y + 2y = 5y

Tabulating these values, we have:

                         Red        Blue

First bag              3x          5x

Second bag         3y          2y

The two red marbles = 3x + 3y.

The two blue marbles = 5x + 2y.

Next, we would write the ratio of the total red marbles to the total blue marbles:

Total red/Total blue = 11/9

(3x + 3y)/(5x + 2y) = 11/9

Cross-multiplying, we have:

27x + 27y = 55x + 22y

27y - 22y = 55x - 27x

5y = 28x

y = 28x/5

y = (28/5)x

y = 5.6x

Remember from the second bag, S = 5y:

S = 5(5.6x)

S = 28x.

Thus, the ratio of the number of marbles in the first bag to the number of marbles in the second bag is given by:

F/S = 8x/28x

F/S = 8/28

F/S = 2/7

F:S = 2:7.

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The probability that either the score on the green die is 1 or the score on the red die is 6, but not both, is 11/36.

To find the probability that either the score on the green die is 1 or the score on the red die is 6 (but not both), we can break it down into two mutually exclusive events and then calculate their probabilities separately.

Event A: The score on the green die is 1.

Event B: The score on the red die is 6.

We need to find the probability of either event A or event B occurring but not both.

The probability of event A occurring is the probability of rolling a 1 on the green die.

Since each die is six-sided, the probability of rolling a 1 on the green die is 1/6.

The probability of event B occurring is the probability of rolling a 6 on the red die. Similarly, the probability of rolling a 6 on the red die is 1/6.

To calculate the probability of either event A or event B occurring but not both, we need to subtract the probability of both events occurring simultaneously from the sum of their individual probabilities.

The probability of both event A and event B occurring simultaneously is the product of their individual probabilities, which is (1/6) x (1/6) = 1/36.

So, the probability of either event A or event B occurring but not both is:

Probability = (Probability of event A) + (Probability of event B) - (Probability of both events occurring)

= (1/6) + (1/6) - (1/36)

= 6/36 + 6/36 - 1/36

= 11/36

Therefore, the probability is 11/36.

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If five regular six sided dice are rolled then there are 540 ways through which sum of numbers coming after rolling will be 14.

Given Five regular six sided dices are rolled.

From stars and bars the number of n tuples of natural numbers summing up to k is given by

[tex](k-1\\n-1)[/tex]

For k=14 and n=5

[tex](14-1 \\5-1)[/tex]

=[tex](13\\4)[/tex]

=715

Some of these will contains a number greater than 6.To get the number of 5 tuples that correspond to 5 rolls of a six sided dice we need to subtract from 715.

Total 5 tuples summing up to 14 for which no element is greater the 6 is given as under:

N=[tex](13/4)-5(6/3)-5(5/3)-5(4/3)-5(3/3)[/tex]

where last term comes from the 5 tuples containing one 10 and fours'

=715-100-50-20-5

=540

Hence there  are 540 such ways which sum to 14 when five six sided dices are rolled.

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[tex]24x =( 96 \div 2) + (55 - 50 - 4 + 5 - 6) \\ \\ 24 x = 48 + 0 \\ \\ 24x = 48 \\ \\ x = \frac{48}{24} \\ \\ x = 2.[/tex]

Answer:

I did this quickly, so please check carefully.

d/a = -(11/12)

Step-by-step explanation:

a/(b+c+d)=4/3

3a = 4(b+c+d)    [Cross multiply]

3a = 4((b+c)+d)   [Note that b and c can be grouped as (b+c)]

---------------------

We can see the second equation also has a (b+c) group.  Isolate it to one side:

a/(b+c)=3/5

5a = 3(b+c)

(b+c) = (5a/3)

------------------

Now use this definition of (b+c) in the first equation:

3a = 4((b+c)+d)

3a = 4((5a/3)+d)   [Use the new value of (b+c), which is (5a/3)]

3a = 4(5a/3+3d/3)

3a = 4((5a + 3d)/3)

3a = (4/3)(5a + 3d)

3a = (20/3)a + 4d

9/3a = (20/3)a + 4d

-(11/3)a = 4d

4d = -(11/3)a

d = -(11/12)a

d/a = -(11/12)

Answer:

[tex]A) \sf \ \sf \dfrac{x^8}{16y^4}[/tex]

Explanation:

 [tex]\sf \left(\dfrac{2y}{x^2}\right)^{-4}[/tex]

inverse of the expression

 [tex]\sf \left(\dfrac{x^2}{2y}\right)^{4}[/tex]

distribute power inside parenthesis

 [tex]\sf \left(\dfrac{(x^2)^4}{(2y)^4}\right)[/tex]

apply exponent rules: [tex]\s(a^b )^c = a^{bc}[/tex]

   [tex]\sf \dfrac{x^8}{16y^4}[/tex]

Answer and Explanation:

Area is the measure of how large a 2-dimensional space is.

For example, a 6 × 2 grid of eggs contains 12 egg spaces.

In math, the unit for area is always a linear measurement squared (for example [tex]m^2[/tex], [tex]cm^2[/tex], and [tex]ft^2[/tex]).

Perimeter is the measurement of the border of a space.

For example, the fence around a 5 × 10 ft garden can be solved for by adding up each individual side of fencing (see the attached image).

The unit for perimeter is always a linear measurement, like m, cm, or ft.

Using this knowledge, for question a, simply multiply the side lengths to get the area. Remember to use [tex]ft^2[/tex] as the unit.

For question b, the answer is perimeter, since it is measuring the border length of the model court.

For question c, the answer is area, since it is measuring the size of the model court's wooden floor.

Option C. The truth statement about the figure is that it has  no reflectional symmetry.

This is the term that is also used to refer to mirror symmetry. It is known to be used in respect to reflections.

The shape that we have here can be seen that it does not have this type of symmetry.

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Answer:

on the percentage of the buses on time ,30 is not included

Answer:

the numbering on the y axis

Answer:

(0.4)⁴

Step-by-step explanation:

• The probability that each individual light bulbs work is :

1 - 0. 6 = 0.4

Then

•• the probability that none of the 4 light bulbs work is :

(0.4)×(0.4)×(0.4)×(0.4)

= (0.4)⁴

= 0.0256

Answer:

what would happen is that the dotted line that is at 2 and down right now would go up to 5

Hope This Helps!!!

25 square feet would mr. potato head be able to walk inside the box.

Given,

          length and breadth of sandbox is 5 ft.

         Now, We apply formula of area of square.

                            5 × 5 = 25 ft²

  Therefore, 25 ft² would mr. potato head be able to walk inside the box.

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Answer:

None of them.

Step-by-step explanation:

Each and every straight line is of one kind in terms of its pattern: it can be presented in the view of [tex]y = kx + b[/tex]: [tex]k[/tex] is the slope or gradient of the line, [tex]b[/tex] is the y-intercept of the line. I will not let the cat out of the bag if I say that any parallel lines do not intersect one another, hence they should have the same value of coefficient [tex]k[/tex].

[tex]2x + 4y = 16 \Leftrightarrow x + 2y = 8 \Leftrightarrow 2y = -x + 8 \Leftrightarrow y = - \frac{1}{2}x + 4[/tex]

Therefore, our line has [tex]k = - \frac{1}{2}[/tex] and [tex]b = 4[/tex] coefficients.

(A) [tex]k = 2, b = 5;[/tex]

(B) [tex]k = -1, b = 4;[/tex]

(С) [tex]k = -1, b = 8;[/tex]

(D) [tex]k = 2, b = 5;[/tex]

Recapitulating this: none of them have the same coefficient [tex]k[/tex], thus none of them suit us.

The number of guests on Saturday is 210 and it is greater than the party of Friday (15 guests)

Last Friday had 15 guests

The sum total of guests on Saturday= 210 guests (using Arithmetic progression)

Using the arithmetic progression sum formula:

1 * 20  + (20 * 19/2) * 1= 210

Therefore, 210 > 15, so we can conclude that the Saturday night party was bigger than Friday's own.

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[tex]|\Omega|=12+5+6+4=27\\|A|=12\\\\P(A)=\dfrac{12}{27}=\dfrac{4}{9}=44.4\%[/tex]

Answer:  44.44% approximately

Work Shown:

P(red) = (number of red)/(number total)

P(red) = (12 red)/(12 red + 5 green + 6 yellow + 4 blue)

P(red) = (12 red)/(27 total)

P(red) = 12/27

P(red) = 4/9

P(red) = 0.4444 approximately

P(red) = 44.44% approximately

Answer:

-3 < x < 7

Step-by-step explanation:

The domain of a graph is all of the x-values that are included in the function. Since the graph is continuous (one connected line), you can determine the domain by identifying the x-values associated with the line's endpoints. These values are x = -3 and x = 7. Remember, the x-value located on a closed dot is not included in the domain. Therefore, the domain of the graph is -3 < x < 7.

Answer:

  x = 192

Step-by-step explanation:

The three right triangles in the figure are all similar, so their sides are proportional.

The length marked x is the long side of the smallest triangle, and the short side of the middle-size triangle. The long side of the middle-size triangle is ...

  400 -144 = 256

We now have enough information to write the proportion ...

  long side/short side = x/144 = 256/x

Multiplying by 144x gives ...

  x² = (144)(256)

  x = √(144×256) = 12×16 = 192

The length x is 192 units.

The addition property of equality is applied to find the value of r which equals 50.

The addition property of equality states that, if a - b = c, then a = c + b.

Given the expression, r - 20 = 30, to find the value of r, apply the addition property of equality as shown below:

Add 20 to both sides

r - 20 + 20 = 30 + 20

r = 50

The value of r using the addition property of equality is: 50.

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The given equation, when solved for d gives d = c/p

From the question, we are to solve for d in the given equation

The given equation is

c = pd

To solve for d, we will divide both sides by p

c/p = (pd)/p

c/p = d

∴ d = c/p

Hence, the given equation, when solved for d gives d = c/p

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Answer:

-9/12 < -5/12

Step-by-step explanation:

-5/12 = -5/12

-3/4 = -9/12

-9/12 < -5/12

Answer: 1.66666666667