Which set of steps could be used to solve this story problem? Helen read 4 books per week for the first 3 weeks of her summer vacation. She read 2 books per week for the last 4 weeks. She also read 2 magazines each week. How many books did Helen read over summer vacation? A. Multiply 4 by 3. Then multiply 2 by 4. Add the two products. B. Add 3 and 4. Then add 2 and 4. Add the two sums. C. Multiply 3 × 4. Then add 4 to that product. Then subtract 2. D. Add 4 and 4. Then divide that sum by 2 and add 3 to the quotient.

The volume of a cube with a side length of 1 foot is 1 cubic foot, or 1728 cubic inches. So, 1 cubic foot is equal to 1728 cubic inches. The ratios of 1 cubic inch to 1/1728 cubic foot and 1 cubic foot to 1728 cubic inches can be used to convert between cubic inches and cubic feet.

When dealing with volumes, it's crucial to understand the relationship between cubic feet and cubic inches. Since 1 foot is equivalent to 12 inches, 1 cubic foot contains 12 × 12 × 12 = 1728 cubic inches. This conversion factor arises because volume is a measure of three-dimensional space, so each dimension is multiplied by itself three times.

To convert between cubic feet and cubic inches, you can use the conversion factor: 1 cubic foot = 1728 cubic inches. This means that to convert cubic feet to cubic inches, you multiply the volume in cubic feet by 1728, and to convert cubic inches to cubic feet, you divide the volume in cubic inches by 1728.

Understanding this relationship allows for easy conversion between the two units, whether you're dealing with measurements in feet or inches.

The probable question may be:

The volume of a cube with a side length of 1 foot is __ cubic foot, or __ cubic inches. So, 1 cubic foot is equal to __ cubic inches. The ratios of __ cubic inches to __ cublc foot and __ cubic foot to __ cubic inches can be used to convert between cubic inches and cubic feet.

2x=x+30

-x    -x

x=30

The value of x is 30

Answer:

144 (Answer B)

Step-by-step explanation:

We must do exponentiation first.  Next comes multiplication and division.  Last comes addition and subtraction.

the proper evaluation (not solution)  of  100 ÷ 5 × 4 + 4³ is as follows:

Evaluate 4³ first; it is 64.

Next, do the division:  20 · 4 + 64 = 80 + 64 = 144 (Answer B)

Answer:

C) 40% of 84

Step-by-step explanation

i don't know how to explain it T~T

The expression to estimate 36% of 84 is option D, 35% of 84, as it is the closest value to 36% that is also straightforward to calculate. Hence correct option D.

To estimate 36% of 84, you would want to choose the option that is closest to 36% without being too complicated to calculate quickly in your head. Among option A (30% of 84), option B (25% of 84), option C (40% of 84), and option D (35% of 84), the best estimate would be option D (35% of 84). This is because 35% is the closest value to 36% listed in the options and it would provide a reasonably accurate estimate that is easy to compute.

Answer:

1. observational study

2.survay

3.experiment

Step-by-step explanation:

The answer would be 31 inches long and 12 inches wide because you would subtract 36 - 5 and 24 - 12

Answer: [tex]128cm^2[/tex]

Step-by-step explanation:

You need to find the ratio of the area.

Knowing that the larger base of smaller trapezoid is 15 centimeters and the larger base of the larger trapezoid is 20 centimeters, you can find the ratio of the area:

[tex]r_{A}=(\frac{20cm}{15cm})^2\\\\r_{A}=\frac{16}{9}[/tex]

Then, to calculate the area of the larger trapezoid, you need to multiply the area of the smaller trapezoid by the ratio of the area.

Therefore you get that the area of the larger trapezoid is:

[tex]A_l=(r_{A})(A_s)\\\\A_l=(\frac{16}{9})(72cm^2)\\A_l=128cm^2[/tex]

Answer:

Step-by-step explanation:

pentagonal

Pentagonal pyramid is the type of pyramid.

A pentagonal pyramid in geometry is a pyramid with a pentagonal base and five triangular sides that intersect at a point. It has two sides, much like every pyramid. The lateral faces of the regular pentagonal pyramid are equilateral triangles, while the base is a regular pentagon.

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ANSWER

[tex]\frac{9x - 2}{3x + 5} [/tex]

EXPLANATION

We want to find the difference;

[tex] \frac{9x}{3x + 5} - \frac{2}{3x { + 5}} [/tex]

This are like fractions or equivalent fractions.

We keep one of the denominators and subtract the numerators.

The difference is:

[tex]\frac{9x - 2}{3x + 5} [/tex]

Note that, we cannot simplify this further.

So we live the difference as it is.

Answer:

The correct answer is,

(9x - 2)/(3x + 5)

Step-by-step explanation:

It is given two expression with variable x

9x/(3x + 5) and 2/(3x + 5)

To find the difference

Here the denominators of two expression are same, so we can write,

9x/(3x + 5) - 2/(3x + 5) = (9x - 2)/(3x + 5)

Therefore the correct answer is

(9x - 2)/(3x + 5)

The probability of the gambler winning the jackpot is calculated using the hypergeometric distribution, dividing the number of favorable outcomes by the total outcomes.

The scenario describes a hypergeometric distribution because the gambler's selections are made without replacement. The total number of outcomes, i.e., possible ways to draw nine numbers from twelve, is given by combination C(12,9).

The gambler wins if all four selected numbers are among the drawn numbers, which is represented by the combination C(4, 4) and the remaining five numbers are from the eight not selected by the gambler, represented by C(8, 5). Therefore, the favorable number of outcomes is C(4,4)*C(8,5).

To calculate the probability that the gambler wins the jackpot, we divide the favorable outcomes by the total outcomes: P(win) =  [C(4,4)*C(8,5)] / C(12,9).

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The probability that the gambler wins the jackpot is: 0.0000092

To calculate the probability that the gambler wins the jackpot, we need to determine the total number of ways the casino can draw nine numbers from the first twelve positive integers and then divide this by the number of ways that the casino can draw nine numbers from the twelve positive integers without including any of the gambler's four selected numbers.

The total number of ways the casino can draw nine numbers from the first twelve positive integers is 12C9 = 220.

To calculate the number of ways that the casino can draw nine numbers from the twelve positive integers without including any of the gambler's four selected numbers, we first need to calculate the number of ways the casino can draw nine numbers from the eight positive integers that are not selected by the gambler. This is 8C9 = 8.

However, this does not take into account the order in which the numbers are drawn. Since the numbers are drawn without replacement, the order matters. Therefore, we need to multiply 8C9 by 9! to account for all the possible orderings of the nine numbers. This gives us 8C9 * 9! = 302,400.

Therefore, the probability that the gambler wins the jackpot is:

220 / (302,400 * 8) ≈ 0.0000092

Answer:

2x+6=24

Step-by-step explanation:

Simplify the expression using the definition of an imaginary number i = sqrt -1

i32 = 1

i25 = i

i86 = -1

i51 = -i

Answer:

Sample answer for Edmentum

Like and Rate!

Step-by-step explanation:

Answer:

2. distributive property

4. addition property of equality

5. addition property of equality

Hope this helps! :)

Answer: 10 inches per year.

If the snake is now 3 foot 9 inches, we can add up how many inches that is by converting feet to inches. 1 foot=12 inches, so 3 feet is 36 inches. We then add the 9 inches.

36+9= 45

Since the snake had already accomplished being 5 inches at birth, we can subtract 5 from 45.

This gives us 40.

Since the snake was born 4 years ago we divide 40 by 4.

40÷4= 10

Answer:

73.21% annual percentage rate.

Step-by-step explanation:

3 foot 9 inches = 45 inches

45 = 5(1 + r)4

9 = (1 + r)4

91/4 = 1 + r

r = 0.73205

therefore,

r = 73.21%

Answer:

Option D) multiply y by 4 in the first equation and subtract the second equation

Step-by-step explanation:

we have

2x+y=-10 ----> first equation

3x+4y=-20 ---> second equation

Verify each case

case A) multiply the first equation by 4 and subtract the second equation

so

(2x+y)*4=-10*4 ------> 8x+4y=-40

[8x+4y=-40]-[3x+4y=-20] -----> 5x=-20 -----> x=-4

This step is correct

case B) multiply the first equation by -4 and add the second equation

so

(2x+y)*-4=-10*-4 ------> -8x-4y=40

[-8x-4y=40]+[3x+4y=-20] ----->-5x=20 -----> x=-4

This step is correct

case C)  add 8 times the first equation and −2 times the second equation

so

(2x+y)*8=-10*8 ------> 16x+8y=-80

(3x+4y)*-2=-20*-2 ----> -6x-8y=40

[16x+8y=-80]+[-6x-8y=40] ----->10x=-40 -----> x=-4

This step is correct

case D) multiply y by 4 in the first equation and subtract the second equation

so

2x+4y=-10

[2x+4y=-10]-[3x+4y=-20] -----> -x=-10+20 -----> x=-10

This step is incorrect

NOT produce a system with the same solution

ANSWER

[tex]320.28 {cm}^{2} [/tex]

EXPLANATION

The surface area of a cylinder is given by

[tex]SA = 2\pi \: r(r + h)[/tex]

From the diagram, r=3cm and h =14cm.

We substitute the known values into the formula to get:

[tex]SA = 2\pi \: 3(3+ 14)[/tex]

[tex]SA = 2(3.14)\: 3(3+ 14) [/tex]

[tex]SA =320.28 {cm}^{2} [/tex]

The second choice is correct.

Answer:  B) 3 out of 20

Step-by-step explanation:

[tex]\text{3 out of 30: }\dfrac{3}{30}=10\%\\\\\text{3 out of 20: }\dfrac{3}{20}=15\%\\\\\text{3 out of 15: }\dfrac{3}{15}=20\%\\\\\text{3 out of 12: }\dfrac{3}{12}=25\%[/tex]

The only option that results in 15% rotten apples is (B) 3 out of 20

Answer:

1. Yes

2. No

3. No

4. No

By analyzing the sampling methods, we conclude that:

a) Yes.

b No

c) No

d) No

Here we need to analyze the given options.

a) The survey is given to random fans, the only thing connecting the fans is that all of them are fans of the team and all of them go to the arena, so there is some biasing, but the sample is random.

b) Here the fans decide if they want to answer or not, so this is more biased than the previous method.

c) This is also more biased than the first case, as these 80 persons also have in common the fact that they leave early.

d) Again, these 80 persons also have something in common, they could afford the best seats, so this is less random than the first option.

Then the answers are:

a) Yes.

b No

c) No

d) No

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Answer:

the price of a 250-milligram bottle is $8

he price of a 500-milligram bottle is $12

Step-by-step explanation:

Let,

x = price of a 250 mg dosage

y = price of a 500 mg dosage

Last month, the company sold 2,200 bottles of 250-milligram tablets and 1,800 bottles of 500-milligram tablets. The total sales revenue was $39,200

2200*x + 1800*y = 39200

The sales team has targeted sales of $44,000 for this month, to be achieved by selling of 2,200 bottles of each dosage.

2200*x + 2200*y = 44000

The system of equations result

2200*x + 1800*y = 39200

2200*x + 2200*y = 44000

We can easily solve it by graphing both equations, please see attached image

The answer is

x = $8

y = $12

(x-3)(x+3) this is the answer

Answer:

(x + 3)(x - 3)

Step-by-step explanation:

x² - 9 ← is a difference of squares and factors as

x² - 9 = (x + 3)(x - 3)

Answer:

The percent of error in the measurement is 2%

Step-by-step explanation:

The percent of error associated with a reported measurement is calculate using the formula;

[tex]percenterror=\frac{error}{measurement}*100[/tex]

The error associated with a measurement is defined as half of the smallest unit of measurement used. The measurement reported was 2.5. The smallest unit of measurement for this reading is 0.1. The error is thus;

error = 0.1/2 = 0.05

The percent of error is thus;

[tex]\frac{0.05}{2.5}*100=2[/tex]

Answer:

2

Step-by-step explanation:

Answer:

The sum of the first 53 terms of the sequence is 3286

Step-by-step explanation:

* Lets talk about the arithmetic sequence

- There is a constant difference between each two consecutive numbers

Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic Progression:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms and n is the position of

  the term in the sequence

* Sum of an Arithmetic Progression:

  is calculate from  Sn = n/2[2a + (n - 1)d]

* Lets solve the problem

- The sequence is 140 , 137 , 134 , 131 , .........

∵ 137 - 140 = -3 and 134 - 137 = -3

∴ The sequence is arithmetic

- The first term a = 140

- The common difference d = -3

- n = 53

∵ Sn = n/2[2a + (n - 1)d]

∴ S53 = 53/2[2 × 140 + (53 - 1)(-3)]

∴ S53 = 53/2[280 + 52(-3) = 53/2[280 + -156] = 53/2[124]

∴ S53 = 3286

* The sum of the first 53 terms of the sequence is 3286

Answer:

S =3,286

Step-by-step explanation:

We are given the following sequence and we are to find the sum of the first 53 terms of this sequence:

[tex]140, 137, 134, 131, ...[/tex]

Finding the common difference [tex]d[/tex] = [tex]137-140[/tex] = [tex]-3[/tex]

[tex]a_1=140[/tex]

[tex]a_n=?[/tex]

[tex]a_n=a_1+(n-1)d[/tex]

[tex] a_n = 140 + (53 - 1 ) -3 [/tex]

[tex] a _ n = -16 [/tex]

Finding the sum using the formula [tex]S_n = \frac{n}{2}(a_1+a_n)[/tex].

[tex]S_n = \frac{53}{2}(140+(-16))[/tex]

S = 3,286

Answer:

ABC, ACB, BCA, BAC, CAB, CBA

Answer:

We have 3 students and 3 positions.

Angie (A), Bradley (B) and Carnell (C)

The total number of combinations can be calculated as:

For the president option we have 3 options:

For the vice president, we have 2 options because we already took one of the students for the president's place.

For the treasurer, we only have one option, so the number of combinations is:

3*2*1 = 6 we have 6 possible combinations; those are:

[tex]\left[\begin{array}{ccc}pres&vice&treas\\A&B&C\\A&C&B\\B&A&C\\B&C&A\\C&A&B\\C&B&A\end{array}\right][/tex]

Answer:

B. [tex]f(x) = x^4-5x^2+4[/tex]

Step-by-step explanation:

The graph of the given function falls at the left side and rises on the right,

This means that the degree of the function represented by the graph must be even and the leading coefficient must be positive.

The y-intercept of the graph is also 4.

Using the end behavior and the y-intercept the function represented in the graph should be  [tex]f(x) = x^4-5x^2+4[/tex]

The correct choice is B.

Answer:

B

Step-by-step explanation:

Answer:

1. graph 4

2. graph 3

3. graph 1

4. graph2

Step-by-step explanation:

1. x- -2,-1,0,1,2

  y- 16,4,1,.25,.062

2. x- -2,-1,0,1,2

   y- .062,.25,1,4,16

3. x- -2,-1,0,1,2

   y- .25,.5,1,2,4

4- x- -2,-1.0,1,2

   y- 4,2,1,.5,.25

Answer:

1. graph 4

2. graph 3

3. graph 1

4. graph 2

Step-by-step explanation:

Problem

If you deposit $500 into an account paying 12% annual interest compounded yearly , how much money will be in the account after 10 years?

Result

The amount is $1552.92 and the interest is $1052.92.

Problem

If you deposit $500 into an account paying 12% annual interest compounded yearly , how much money will be in the account after 20 years?

Result

The amount is $4823.15 and the interest is $4323.15.

Problem

If you deposit $500 into an account paying 12% annual interest compounded yearly , how much money will be in the account after 30 years?

Result

The amount is $14979.96 and the interest is $14479.96.

Final answer:

The investment grows to $1,555.88 in 10 years, $4,822.49 in 20 years, and $14,974.46 in 30 years.

Explanation:

To calculate the future value of an investment with compound interest, you can use the formula A = P(1 + r/n)[tex]^{(nt)}[/tex], where:

P is the principal amount (the initial amount of money)

r is the annual interest rate (decimal)

n is the number of times that interest is compounded per year

t is the time the money is invested for, in years

For your case, where you invest $500 at 12% compounded annually, this becomes:

A = 500(1 + 0.12/1)[tex]^{(1t)}[/tex]

Calculating for 10, 20, and 30 years:

A = 500(1 + 0.12)¹⁰ = $1,555.88 after 10 years

A = 500(1 + 0.12)²⁰ = $4,822.49 after 20 years

A = 500(1 + 0.12)³⁰ = $14,974.46 after 30 years

[tex]\bf \stackrel{5}{\boxed{1}\boxed{2}\boxed{3}\boxed{4}\boxed{5}}\stackrel{to}{\qquad }\stackrel{3}{\boxed{6}\boxed{7}\boxed{8}}\qquad \textit{ratio}[/tex]

Answer:

3.  x = 4, NOT extraneous

4. x=12, extraneous

Step-by-step explanation:

3. Solve for x, √(2x +1) = 3 and identify if it's an extraneous solution or not.

Since the square root is already isolated on its side, the first step is to put both sides to their square value to get rid of the square root.  We then get:

2x + 1 = 9  =>   2x = 8   =>   x = 4

To see if x = 4 is an extraneous solution, we enter it in the original equation and see if it works:

√(2x +1) = √(2 * 4 +1)  = √9 = 3

3  equals 3... so it's NOT an extraneous solution

4. Solve for x, -4√(x-3) = 12 and identify if it's an extraneous solution or not.

This time the square root isn't alone on its side yet... so we have to isolate it, by dividing each side by -4:

-4√(x-3) = 12 becomes √(x-3) = -3

Then we raise each side to their square value to get rid of the square root:

x - 3 = 9  which becomes x = 12

To see if x = 12 is an extraneous solution, we enter it in the original equation and see if it works:

-4√(x-3) = -4√(12-3) = -4√(9) = -4 (3) = -12

-12 does not equal 12... so it's an extraneous solution

Answer:

21

Step-by-step explanation:

21

The number that is impossible to divide by is 0, and your original number (X) cannot be 0 either. The possible values for your number are 11 and 22, and the corresponding numbers you divided it by are 1 and 2.

Let's assume the number you thought of is X, and the number you divided it by is Y. Based on the given information, we have the following equation:

X / Y = 11

To find the possible values for X and Y, we need to consider the factors of 11, which are 1 and 11. These factors provide us with potential pairs of X and Y:

X = 11 and Y = 1: When dividing 11 by 1, the result is indeed 11.

X = 22 and Y = 2: Dividing 22 by 2 gives us 11 as well.

So, the possible values for your number (X) are 11 and 22, and the corresponding numbers you divided it by (Y) are 1 and 2.

Now, let's discuss the numbers that are impossible to divide by or cannot be your original number. Any number divided by zero is undefined in mathematics. Hence, dividing by zero is not possible in this scenario. Therefore, the number 0 is impossible to divide by.

Additionally, your original number (X) cannot be 0. If X were 0, the equation would be:

0 / Y = 11

But any number divided by 11 is not equal to 0, which means X cannot be 0.

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We know that there are 60 seconds in one minute

We know that it took Bob 55 minutes to clean the garage