After production, an electrical circuit is given a quality score of A, B. C, or D. Over a certain period of time, 77% of the circuits were given a quality score A. 11% were given a quality score B, 7% were given a quality score C, and 5% were given a quality score D. Furthermore, it was found that 2% of the circuits given a quality score A eventually failed, and the failure rate was 10% for circuits given a quality score B. 14% for circuits given a quality given a quality score C, and 25% for circuits given a quality score D. Show all your work and circle your final answers. Use four decimal places for your calculations. a) Find the probability of a circuit failing. b) If a circuit failed, what is the probability that it had received a quality score either C or D?

Answer: String variables

Step-by-step explanation:

SPSS means Statistical Package for Social Sciences.

The SPSS has only two variables namely:

1. String variables which includes numbers,letters and other characters.

The string variables cannot perform calculations. It is basically used to type names of people, age,occupation,home addresses,email addresses e.t.c Which is what is what the researcher was trying to do.

2. Numeric variables which include only numbers. It can perform calculations too using mathematical operations like addition,multiplication,division and subtraction.

Answer:

Hurricanes

Step-by-step explanation:

We are given the following in the question:

Scientists are studying hurricanes to determine the number of hurricanes in the past 50 years that have caused greater than $1 million in damages.

Population:

Thus, for the given scenario

Population of interest:

Hurricanes

From this population a sample of hurricanes that have caused greater than $1 million in damages is taken.

Answer:

A)Hurricanes

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

In the first instance, he wanted buying euros in exchange for his dollars. He had $540 and wanted to buy euros. The conversion factor here is that for every 1 euro, he pays $1.80

Now at the second instance, he wanted buying dollars with his left over euros. This means for every 1 euro, he gets $1.4

Since, he is having 40 euros, the total amount in dollars he would get will be 40 * $1.4 = $56

Answer:

(1, -2)

(-8, -2)

Step-by-step explanation:

(1 , -6) and (-8 , -6)

1 - (-8) = 9

we know that the length of the side that we know the vertices is 9

from there we make an equation with the sum of the sides equal to the perimeter

we will have 2 times 9 and 2 times x beacause it is a rectangle

x + x + 9 +9 = 26

2x + 18 = 26

2x = 26 - 18

2x = 8

x = 8/2

x = 4

Now that we know the missing side we just have to add or subtract this value to the coordinate in and of the vertices we have and we will obtain the missing vertices

(1, -6 + 4)

(1, -2)

( -8, -6+4 )

(-8, -2)

The coordinates of the other two vertices of the rectangle are (1, -2) and (-8, -2), found by calculating the length of one side using the given vertices and then applying the rectangle's perimeter to find the length of the adjacent sides.

The subject of the question is to find the other two vertices of a rectangle given two of its vertices and the perimeter. We know that the opposite sides of a rectangle are equal in length. So, to solve this, we can use the distance formula to find the length of one side with the two given points (1, -6) and (-8, -6). The length of this side is the absolute value of the difference in the x-coordinates, which is 9 units. Since the perimeter is 26, and this length is 9, the sum of the lengths of the other two sides is 26 - 2*9 = 8 units. Therefore, each of these sides is 4 units long. Because the given points have the same y-coordinate, they lie on a horizontal side of the rectangle, so the other two vertices will have the same x-coordinates as the given ones and will be 4 units vertically away. If we add and subtract 4 units from the y-coordinate of the given points, we get the other two vertices: (1, -6 +4) and (-8, -6 +4). So the coordinates of the other two vertices are: (1, -2) and (-8, -2).

Answer:

There are 18 Sedans in the dealership shop.

Step-by-step explanation:

Let x represent the number of Sedans in the dealership shop.

Let y represent the number of SUV's in the dealership shop.

If there are a combined 24 sedans and SUVs, it means that

x + y = 24 - - - - - - - - - - - -1

At a car dealership, there are three times as many sedans as SUVs. This means that

x = 3y

Substituting x = 3y into equation 1, it becomes

3y + y = 24

4y = 24

y = 24/4 = 6

x = 3y = 6 × 3

x = 18

The coordinates of A'  after rotation  of 270 counterclockwise and then shifted down 3 units are (2, 4).

To find the coordinates of point A' after a 270-degree counterclockwise rotation around the origin and then shifting down 3 units, we first perform the rotation.

A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. So, when we rotate point A(-7, -2) 90 degrees clockwise, we swap the coordinates and change the sign of the former x-coordinate, which gives us the new point A''(2, 7). Next, we shift A'' down 3 units, which means we subtract 3 from the y-coordinate, resulting in A'(2, 4).

Answer:

$261

Step-by-step explanation:

The team hopes to earn three times more than it did last year

Last year the team earned $ 87

We are required to determine the team's goal this year.

Therefore;

Since they hope to raise three times than last year;

Then;

Goal this year = 3 × last year's earnings

                        = 3 × $ 87

                        = $261

Therefore, the team's goal this year is $261

Answer:

P (Cheese) = 0.199, P (Sausage) = 0.259, P (Pepperoni) = 0.181,

P (Supreme) = 0.130, P (Another Kind) = 0.144

and P (Does not like any kind) = 0.088

Step-by-step explanation:

Given:

Number of students who prefer cheese = 43

Number of students who prefer sausage = 56

Number of students who prefer pepperoni = 39

Number of students who prefer supreme = 28

Number of students who prefer another kind = 31

Number of students who did not like any kind = 19

∴ The total number of students surveyed = [tex]43+56+39+28+31+19=216[/tex]       The number of students who prefer pizza = [tex]43+56+39+28+31=197[/tex]

The probability that a students likes pizza is,

[tex]P(Student\ likes\ pizza)=\frac{No.\ of\ students\ who\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]

                                     [tex]=\frac{197}{216} \\=0.912[/tex]

The probability that a students does not likes pizza is,

[tex]P(Student\ does\ not\ likes\ pizza)=\frac{No.\ of\ students\ who\ does\ not\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                   [tex]=\frac{19}{216} \\=0.088[/tex]

The probability distribution of students who prefer different kinds of pizza is:

       [tex]P(A\ Student\ prefers\ cheese)=\frac{No.\ of\ students\ who\ prefer\ cheese}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                       [tex]=\frac{43}{216}\\=0.199[/tex]

        [tex]P(A\ Student\ prefers\ sausage)=\frac{No.\ of\ students\ who\ prefer\ sausage}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                           [tex]=\frac{56}{216}\\=0.259[/tex]

       [tex]P(A\ Student\ prefers\ pepperoni)=\frac{No.\ of\ students\ who\ prefer\ pepperoni}{Total\ no.\ of\ students\ surveyed}[/tex]  

                                                             [tex]=\frac{39}{216}\\=0.181[/tex]

       [tex]P(A\ Student\ prefers\ supreme)=\frac{No.\ of\ students\ who\ prefer\ supreme}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                           [tex]=\frac{28}{216}\\=0.130[/tex]

        [tex]P(A\ Student\ prefers\ another\ kind)=\frac{No.\ of\ students\ who\ prefer\ another\ kind}{Total\ no.\ of\ students\ surveyed}[/tex]

                                                                   [tex]=\frac{31}{216}\\=0.144[/tex]

Thus, the probability distribution table is displayed below:

See the explanation

I have corrected your diagram so ∅ is the angle at the top of the diagram. In order to solve this problem we have to use Pythagorean theorem and the law of sines. Moreover, I have named two sides as w and z so those variables will help us to solve this problem. So:

The triangle at the bottom is right, so by Pythagorean theorem is true that:

[tex]w^2=4^2+(2\sqrt{2})^2 \\ \\ w^2=24 \\ \\ w=\sqrt{24} \\ \\ w=2\sqrt{6}[/tex]

By law of sines:

[tex]\frac{z}{sin\theta}=\frac{w}{sin60^{\circ}} \\ \\ z=\frac{wsin\theta}{sin60^{\circ}} \\ \\ z=\frac{2\sqrt{6}sin\theta}{\sqrt{3}/2} \\ \\ z=4\sqrt{2}sin\theta[/tex]

By law of sines again:

[tex]\frac{y}{sin45^{\circ}}=\frac{z}{sin\phi} \\ \\ y=\frac{zsin45^{\circ}}{sin\phi} \\ \\ y=\frac{4\sqrt{2}sin\theta \sqrt{2}/2}{sin\phi} \\ \\ \\ Finally: \\ \\ \boxed{y=\frac{4sin\theta}{sin\phi}}[/tex]

Classification of triangles: https://brainly.com/question/10379190

#LearnWithBrainly

Answer:

There are 3120 chocolate eggs.                                

Step-by-step explanation:

We are given the following in the question:

Total number of eggs = 4680

Number f chocolate eggs =

[tex]\dfrac{2}{3}[/tex]  the number of real eggs

We have to find the number of chocolate eggs.

Number of chocolate eggs =

[tex]\dfrac{2}{3}\times \text{Total number of eggs}[/tex]

[tex]=\dfrac{2}{3}\times 4680\\\\=3120[/tex]

Thus, there are 3120 chocolate eggs.

Answer:

Like terms are numbers with or without variables that have the same variables.

Step-by-step explanation:

5x and 3x are like terms because they have the same variable.

5x and 3y are not like terms because the variables are different.

To combine them, just add or subtract them. You cannot combine non-like terms!

Answer:

Definition: Like terms - Term in math that have the same variables or powers.

Ex. 2x, -5x, and 7x.

Combine Them: 2x + 7x = 9x - 5x = 4x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Why shouldn't classes overlap when one summarizes continuous data? If classes overlap, then some observations will be counted in more than one class. This means that certain observations will end up in more than one bar of a histogram, which will misrepresent the data!

Answer:

There were 180 voters for blue color.

Step-by-step explanation:

Let the total number of voters be 'x'.

Given:

Number of Voters for blue color = [tex]\frac{5}{8}x[/tex]

Number of Voters for green color = [tex]\frac{5}{9}(x-\frac58x)=\frac59x(1-\frac58)[/tex]

Now we will use LCM to make the denominator common we get;

Number of Voters for green color = [tex]\frac59x(\frac88-\frac58)=\frac59x(\frac{8-5}{9})=\frac59x(\frac38)=\frac{15x}{72}[/tex]

Number of Voters for red color = 48

We need to find the number of voters for blue color.

Solution:

Now we can say that;

total number of voters is equal to sum of Number of Voters for blue color, Number of Voters for green color and Number of Voters for red color.

framing in equation form we get;

[tex]x=\frac58x+\frac{15x}{72}+48[/tex]

Combining like terms we get;

[tex]x-\frac58x-\frac{15x}{72} = 48[/tex]

Now we will make denominators common using LCM we get;

[tex]\frac{72x}{72}-\frac{5x\times9}{8\times9}-\frac{15x\times1}{72\times 1} = 48\\\\\frac{72x}{72}-\frac{45x}{72}-\frac{15x}{72} = 48[/tex]

Now denominators are common so we will solve the numerators we get;

[tex]\frac{72x-45x-15x}{72}=48\\\\\frac{12x}{72}=48\\\\\frac{x}{6}=48[/tex]

Now multiplying both side by 6 we get;

[tex]\frac{1}{6}x\times6=48\times6\\\\x = 288[/tex]

Number of voters for blue color = [tex]\frac{5}{8}x=\frac{5}{8}\times 288= 180[/tex]

Hence There were 180 voters for blue color.

Yo sup??

Since there is an x^2 term therefore this equation is of a parabola

By taking LCM and then cross multiplying it.

6y=x^2-9x+26

6y=x^2-9x+(9/2)^2+23/4

6y-23/4=(x-9/2)^2

we see that this is of the form

X^2=4AY

(x-9/2)^2=4(3y/2-23/16)

Hope this helps.

Answer:

[tex]f(x) =- \sqrt{x-1}+3[/tex]

Step-by-step explanation:

This looks like a square root function [tex]f(x) = \sqrt{x}[/tex]  but symmetric with respect to the x axis and shifted to the right for 1 and up for 3:

Lets take  [tex]f(x) = \sqrt{x}[/tex] . The function symmetric with respect to the x axis would be [tex]-f(x)[/tex], so now we have:

                                                [tex]f(x) = -\sqrt{x}[/tex]

Lets take [tex]f(x) = -\sqrt{x}[/tex] and shift it up for y = 3. Now we have:

                                               [tex]f(x) =- \sqrt{x}+3[/tex]

Lets take [tex]f(x) = -\sqrt{x}+3[/tex] and shift it right for x = 1. That means that instead of x we will have x-1:

                                            [tex]f(x) =- \sqrt{x-1}+3[/tex]

Answer:

7y²

Step-by-step explanation:

First u group them like 4+3+y+y=7y²

Answer:

x is a binomial random variable because a trial is independent and number of trials, n = 10.                                            

Step-by-step explanation:

We are given the following information:

We treat adult  reading at least one book in the past 12 months as a success.

P(Adult reading atleast one book) = 74% = 0.74

Then the number of adults follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

If x is a random variable representing the number of people who have read at least on book, then x follows a binomial distribution because:

Thus,

x is a binomial random variable because a trial is independent and number of trials, n = 10.

Answer:

X = 93

Step-by-step explanation:

Angles of a polygon = (n - 1)180

The above polygon is heptagon (with 6 sides)

(6-1) × 180

5×180 = 900

Add the given Angles and equate it to 900 (as gotten above)

4x + 3x + 47 + 93 + 46 + 62 = 900

7x + 248 = 900

Collect like term of the number

7x = 900-248

7x = 652

Divide both side by the coefficient of x

7x/7 =652/7

X = 93.1429

Answer:

In order the sequences defined by the expressions on the left are ...

Step-by-step explanation:

One of the first steps in working multiple choice questions (in any subject) is to look at the answers to see what you need to know to be able to tell a correct answer from an incorrect one.

Here, all of the first terms are different, except for the two sequences that both starts with 1. Those differ in the ratio between terms (1/2 vs 2).

This means you only have to evaluate the expression for the first domain value (x=1) and you can tell right away what the answer is. It is not complicated, and your calculator can help if you can't do it in your head.

___

Starting at the top of the list on the left, ...

  2^1 = 2 . . . . matches 2, 4, 8, ...

  2(2^1) = 4 . . . . matches 4, 8, 16, ...

  (1/2)^1 = 1/2 . . . . matches 1/2, 1/4, 1/8, ...

  2(1/2)^1 = 1 . . . .  double the previous sequence, so 1, 1/2, 1/4, ...

  1/2(2^1) = 1 . . . . half the first sequence, so 1, 2, 4, ...

  1/2(1/2)^1 = 1/4 . . . . matches 1/4, 1/8, 1/16, ...

Question:

A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units.

Which equation can be used to solve for x, the side length of the original square?

x2 − 2x − 120 = 0

x2 + 2x − 120 = 0

x2 − 2x + 120 = 0

x2 + 2x + 120 = 0

Answer:

Option a: [tex]x^{2} -2x-120=0[/tex] is the equation

Explanation:

It is given that the area of the square paper is [tex]x^{2}[/tex] square units.

The area of the remaining piece of paper is 120 square units.

It is also given that the area of the remaining piece of paper is [tex]x^{2}-2 x[/tex]

Thus, equating the area of the remaining piece of paper, we have,

[tex]x^{2} -2x=120[/tex]

Subtracting 120 from both sides of the equation, we have,

[tex]x^{2} -2x-120=0[/tex]

Thus, the equation [tex]x^{2} -2x-120=0[/tex] can be used to solve for x.

Hence, Option a is the correct answer.

Answer: $13,114

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 9000

r = 3.8% = 3.8/100 = 0.038

n = 2 because it was compounded 2 times in a year.

t = 10 years

Therefore,.

A = 9000(1+0.038/2)^2 × 10

A = 9000(1+0.019)^20

A = 9000(1.019)^20

A = $13114

The final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B:  $13114 approx.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

For this case, we are given that:

Thus, the final amount at the end of 10 years is given by:

[tex]A = P(1 +\dfrac{1.9}{100})^T\\\\A = 9000(1 + \dfrac{1.9}{100})^{20} = 9000(1.019)^{20} \approx 13114 \text{\: \: (in dollars)}[/tex]

Thus, the final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B:  $13114 approx.

Learn more about compound interest here:

https://brainly.com/question/11897800

Answer: the shipping and handling fee is 8 percent of the cost of the order.

Step-by-step explanation:

Shipping and handling fee of $35 is charged to all furniture orders over $250.

If the order is $437.50, it means that there would be a handing and shipping fee of $35 because the price of the order is above $250.

The percentage of the original price of the order that is the shipping and handling fee would be

35/437.5 × 100 = 0.08 × 100

= 8%

Final answer:

To find the percent that the shipping and handling fee is of the total order, divide the fee by the order amount and multiply by 100. For an order of $437.50 with a fee of $35, the shipping fee is 8% of the total order.

Explanation:

The question asks us to determine what percent the shipping and handling fee is of the total furniture order.

To calculate this percentage, we can use the formula:

Percentage = (Part / Whole)  imes 100

In this case:

Now, we insert the values into the formula:

Percentage = ($35 / $437.50)  imes 100

Percentage = 0.08  imes 100

Percentage = 8%

Therefore, the shipping and handling fee is 8% of the total order.

Answer: he open the account 9 years ago.

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount deposited.

P represents the principal or amount deposited.

R represents interest rate

T represents the time for which the amount deposited was left in the account.

From the information given,

P = 400

R = 7.5%

I = 670 - 400 = $270

Therefore,

270 = (400 × 7.5 × T)/100 = 30T

T = 270/30

T = 9 years

Step-by-step explanation:

9 years thank you yw bubye

Answer:

26/3 or 8.67

Step-by-step explanation:

Arc lengths are congruent and the radii are the same implies angle at the centre is also equal,

Hence length of the chords are equal too

4x+2 = x+7

3x = 5

x = 5/3 or 1.67

Length of QR = 4x+2

= 4(5/3) +2

= 20/3 + 2

= 26/3 = 8.67

Answer:

8.67

Step-by-step explanation:

Answer:

19 wrong answers.

Step-by-step explanation:

Given:

Sahil got 28 questions right.

Angelina got 7 more wrong answers than Sahil.

There where 40 questions on the test.

Question asked:

How many answers did Angelina get wrong on the math test ?

Solution:

Total questions on the test = 40

Number of right answers, Sahil got = 28

Number of wrong answers, Sahil got = 40 - 28 = 12

As Angelina got 7 more wrong answers than Sahil,

Number of wrong answers, Sahil got = 12

Then, number of wrong answers, Angelina got = 12 + 7 = 19

Therefore, 19 answers did Angelina get wrong on the math test out of 40.

Angelina got 35 wrong answers on the math test.

To find the number of wrong answers Angelina got on the math test, we need to know how many questions she got right. Since Sahil got 28 questions right and there were 40 questions on the test, we can subtract Sahil's score from the total number of questions to find Angelina's score. Sahil got 28 questions right, so Angelina would have gotten 40 - 28 = 12 questions right. And since Angelina got 7 more wrong answers than Sahil, we can subtract Sahil's wrong answers from Angelina's total wrong answers to find the specific number. If Sahil got 12 questions right, then he must have gotten 40 - 12 = 28 questions wrong. And since Angelina got 7 more wrong answers than Sahil, we can add 7 to Sahil's wrong answers to find Angelina's total wrong answers. Therefore, Angelina got 28 + 7 = 35 wrong answers on the math test.

Answer:

12 (5x - 2)

Step-by-step explanation:

First to know if we can get a common factor we have to find a number by which it is divisible on 24 and 60

first we will try with 2

60/2 = 30            both are divisible by 2

24 /2 = 12

then we will take common factor 2

60x - 24

we multiply and divide by 2

2 (60x - 24)/2

we distribute the 2

2(60x/2 - 24/2)

and solve

2(30x - 12)

Now we continue with the same procedure until there is no more number in common to divide

we will try with 2

30/2 = 15            both are divisible by 2

12 /2 = 6

then we will take common factor 2

2(30x - 12)

we multiply and divide by 2

2*2 (30x - 12)/2

we distribute the 2

4(30x/2 - 12/2)

and solve

4(15x - 6)

continue with the same procedure

we will try with 2

15/2 = X            only one is divisible by 2

6 /2 = 3

we will try with 3

15/3 = 5          both are divisible by 3

6 /3 = 2

then we will take common factor 3

4(15x - 6)

we multiply and divide by 3

4*3 (15x - 6)/3

we distribute the 3

12(30x/3 - 6/3)

and solve

12(5x - 2)

there is no number other than 1 by which we can divide 5 and 2

12(5x - 2)

Step-by-step explanation:

[tex]m \angle \: C = \frac{1}{2} (m \: arc \: AB)\\(By\:inscribed \:\angle\:theorem) \\ \\ \therefore \: (x + 5) \degree =\frac{1}{2} (4x)\degree \\ \\ \therefore \: x + 5=\frac{1}{2} \times 4x \\ \\ \therefore \: x + 5=2x \\ \\ \therefore \: x - 2x = - 5 \\ \\ \therefore \: - x = - 5 \\ \\ \: \: \: \: \: \huge \purple{ \boxed{\therefore \: x = 5}}[/tex]

Answer:

[tex]d = 670,616,629h \ mi[/tex]

Step-by-step explanation:

Given:

Speed of the light = 670,616,629 mi\hr

We need to find the direct variation equation represents given situation.

Solution:

Speed is defined as the ratio of distance and time. So, the equation of the speed is as follows:

[tex]Speed = \frac{Distance}{Time}[/tex]

And also written as.

[tex]S = \frac{d}{h}[/tex]

Now, we write the above equation for distance.

[tex]d = S\times h[/tex] ------------(1)

Where:

d = distance travel by object.

S = speed of the object.

h = Total time taken

Substitute S = 670,616,629 mi\hr in equation 1.

[tex]d = 670,616,629h \ mi[/tex]

Therefore, direct variation equation to represents the given situation

[tex]d = 670,616,629h \ mi[/tex]

Part 1:

Replace "v0" in the given equation with the given velocity of 15 ft/sec:

y = -16t^2 + 15t +6.5

Part 2:

Now set the equation to 0 which would be when the basketball hits the ground:

-16t^2 +15t +6.5 = 0

A quadratic equation is solved using the formula:

t = -b +/- sqrt(b^2-4ac)/2a

Using the given equation: a = -16, b = 15 and c = 6.5

Replace the values and solve:

t = -(15)+/- sqrt(15^2 -4(-16)(6.5))/2(-16)

This solves to get both -0.32 and 1.26 seconds.

The time has to be a positive value so t = 1.26 seconds.

Part3:

Using the quadratic form at^2 + bt + c

The maximum is found using t = -b/2a = -15/2(-16) = = 0.47 seconds

The maximum height would be at 0.47 seconds

Part 4:

Replace t with 0.47 and solve for maximum height:

y = -16(0.47)^2 + 15(0.47) +6.5

Maximum height would be 3.52 feet

Answer:

  d.  about 9 years​

Step-by-step explanation:

There is a "rule of thumb" for doubling time* that says the product of the percentage rate of change per year and the doubling time in years is about 72. Here, that means the doubling time is about ...

  72/8 = 9 . . . . years

_____

You can write the exponential equation ...

  multiplier = (1 +.08)^n

and solve for multiplier = 2:

  2 = 1.08^n

  log(2) = n·log(1.08) . . . . . take logs

  log(2)/log(1.08) = n . . . . . divide by the coefficient of n

  9.00647 ≈ n

It will take about 9 years for the participation to double.

_____

* The farther away from 8% the rate of change is, or the more times per year it is compounded, the less accurate is the "rule of 72." When compounding is continuous, the "rule of 72" becomes the "rule of 69.4". For this problem, answer choices are sufficiently far apart that the rule of thumb is adequate for making a correct choice.

Answer:

4x + 3x = 42

Step-by-step explanation: