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.

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:

2x=x+30

-x    -x

x=30

The value of x is 30

Janeka forgot to divide by 2 to get the radius and then square and multiply by pi.

since the diameter is 20 the radius would be 10. so i the equation you would replace the 20 with 10 bc she but the diameter in instead of the radius which r=radius

In quadrant II, if sinΘ = 1/2, the value of cosΘ is -√(3/4).

In quadrant II, sine is positive and cosine is negative. Since sinΘ = 1/2, we can use the Pythagorean identity to find the value of cosΘ:

sin²Θ + cos²Θ = 1

Plugging in the value of sinΘ and solving for cosΘ, we get:

(1/2)² + cos²Θ = 1

1/4 + cos²Θ = 1

cos²Θ = 3/4

Taking the square root, we get:

cosΘ = ±√(3/4)

Since Θ lies in quadrant II where cosine is negative, the value of cosΘ is:

cosΘ = -√(3/4)

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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

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

Answer:

[tex]\$1,920[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5*12=60\ months\\ P=\$1,200\\r=0.01[/tex]

substitute in the formula above

[tex]A=\$1,200(1+0.01*60)[/tex]

[tex]A=\$1,200(1.6)=\$1,920[/tex]

Answer:

A

Step-by-step explanation:

Multiply them according to the problem.

[tex]6x+2y=6 \\ \\ -3(6x+2y)=(6)*-3 \\ \\ -18x-6y=-18 \\ \\ \\ 7x+3y=9 \\ \\ 2(7x+3y)=(9)*2 \\ \\ 14x+6y=18[/tex]

As you can see, the only terms in the two equations that can cancel out are [tex]-6y[/tex] and [tex]6y[/tex].

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%

Please ignore the x above,,

Answer: 30%

Step-by-step explanation:

Given: the number of employees in the office = 80

The number of employees are managers = 24

Then, the percent of employees are manger is given by :-

[tex]\dfrac{\text{Number of mangers}}{\text{Total employees}}\times100\\\\=\dfrac{24}{80}\times100\\\\=30\%[/tex]

Hence, the percent of the employees are managers = 30%

Answer:

1. observational study

2.survay

3.experiment

Step-by-step explanation:

(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:

2x+6=24

Step-by-step explanation:

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 answer is $50 for the full price of the sweater

Step-by-step explanation:

if you know $20 is 40% what is 20% it is $10 and then multiple it by 5 because  20 times 5 is 100 and you get 50

Answer:

$50

Step-by-step explanation:

Sale on sweater = 40% .

Money saved = $20 .

Let original price be x then ,

=> 40% of x = $20

=> 40x/100 = $20

=> x = $20 *100/40

=> x = $ 50

Answer:

B

Step-by-step explanation:

In one complete rotation the wheel rotates 360°

Assuming the seats are equally spaced around the wheel then the

angle between each seat = [tex]\frac{360}{15}[/tex] = 24°

The angle measurement between each bucket is 24 degrees if the Ferris wheel has 15 seat buckets option (B) 24° is correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

A Ferris wheel has 15 seat buckets.

The total angle of the wheel is 360 degrees, which is a complete revolution of the wheel.

The angle measurement between each bucket is:

= 360/15

= 24 degree

Thus, the angle measurement between each bucket is 24 degrees if the Ferris wheel has 15 seat buckets option (B) 24° is correct.

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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:

17.54 ft

Step-by-step explanation:

Moving along the line from (–4.2, –6.4, 4.5) to (7.1, 2.2, 5.8), x increases by 11.3, y by 8.6 and z by 10.3.

Applying the Pythagorean Theorem twice, we get

(length of clothesline) = √( 11.3² + 8.6² + 10.3²), or 17.54 ft.

We know that there are 60 seconds in one minute

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

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

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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he can either send one half or the other half.

Answer:

70

Step-by-step explanation:

Given : There are 8 people on the debate team.

To Find: In how many ways can the coach choose 4 members to send to competition?

Solution:

We will use combination over here

Formula : [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Now There are 8 people on the debate team and the coach have to choose 4

So, n = 8

r = 4

So, number of ways of choosing 4 people out of 8 = [tex]^8C_4[/tex]

                                                                                    = [tex]\frac{8!}{4!(8-4)!}[/tex]  

                                                                                    = [tex]\frac{8!}{4!4!}[/tex]  

                                                                                    = [tex]70[/tex]  

Hence there are 70 ways of choosing 4 members out of 8 to send to competition

Answer:

  35.9 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Tan = Opposite/Adjacent

  tan(U) = VW/WU

  tan(65°) = (77 ft)/WU

  WU = 77 ft/tan(65°) ≈ 35.9 ft

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:

The answer is perfect square.

Step-by-step explanation:

A number whose square roots are integers or quotients of integers - perfect square.

The square of a number is a number multiplied by itself. Like 2 x 2 , 5 x 5 etc.

The perfect squares are the squares of the whole numbers like : 1, 4, 9, 16, 25, 36,  and so on.

Arc GHE is 40 + 80 or 120 so arc GFE is 360 (total measurement in a circle) - 120 which is 240. The circumference of a circle is 2*pi*r so in this case it will be 2*pi*5 or 10pi (you can also write it as approximately 31.4). The area of a circle is pi*r² so it'll be pi*5² or 25pi (you can write it as approximately 78.5 also). The equation of a circle is (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius. Input your values. The equation of this circle is (x+1)² + (y-2)² = 6² (The radis is 6 because the diameter is 12)

I hope this helps!

A full circle is 360 degrees.

You are given the angles for GH, HE and FE, subtract those from 360 to find the angle for FG:

360 - 110 - 80 - 40 = 130 degrees.

Now for the arc GFE add FG and FE:

Arc GFE = 130 + 110 = 240 degrees.

Circumference = 2 x PI x r

Using 3.14 for PI:

Circumference  = 2 x 3.14 x 5 = 31.4 mm or 10PI

Area = PI x r^2 = 3.14 x 25 = 78.5 mm^2 or 25PI mm^2

Equation of a circle with center at (-1,2) and diameter of 12:

The equation is written as (x-x1)^2 + (y-y1)^2 = r^2

x1 and y1 are the values of the center (-1,2) and r is the radius, which would be half the diameter.

The equation is: (x+1)^2 + (y-2)^2 = 36

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]

The answer is:

[tex]f'(2)=-1[/tex]

To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.

The given function is:

[tex]f(x)=\frac{4}{x}[/tex]

It's a quotient, so, we need to use the following formula to derivate it:

[tex]f'(x)=\frac{d}{dx}(\frac{u}{v}) =\frac{v*u'-u*v'}{v^{2} }[/tex]

Then, of the given function we have that:

[tex]u=4\\v=x[/tex]

So, derivating we have:

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*(4)'-4*(x)'}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*0-4*1}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{0-4}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }[/tex]

Hence,

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }[/tex]

Now, evaluating with x equal to 2, we have:

[tex]f'(2)=\frac{-4}{(2)^{2} }[/tex]

[tex]f'(2)=\frac{-4}{4}[/tex]

[tex]f'(2)=-1[/tex]

Therefore, the answer is:

[tex]f'(2)=-1[/tex]

Have a nice day!

ANSWER

[tex]f'(2) = -1[/tex]

EXPLANATION

The given function is

[tex]f(x) = \frac{4}{x} [/tex]

Recall that:

[tex] \frac{c}{ {a}^{ m} } = c {a}^{ - m} [/tex]

We rewrite the given function using this rule to obtain,

[tex]f(x) = 4 {x}^{ - 1} [/tex]

Recall again that,

If

[tex]f(x)= a {x}^{n} [/tex]

then

[tex]f'(x)=n a {x}^{n - 1} [/tex]

We differentiate using the power rule to obtain,

[tex]f'(x) = - 1 \times 4 {x}^{ - 1 - 1} [/tex]

[tex]f'(x) = - 4 {x}^{ - 2} [/tex]

We rewrite as positive index to obtain,

[tex]f'(x) = - \frac{4}{ {x}^{2} } [/tex]

We plug in x=2 to obtain,

[tex]f'(2) = - \frac{4}{ { (2)}^{2} } = - \frac{4}{4} = - 1[/tex]

Answer:

1,048,576

Step-by-step explanation:

We can tell that this is a geometric sequence because each new term is a multiple of the previous term.  The common ratio is -2.

The pertinent formula is a(n) = -2 · (-2)^(n-1).

Thus, the 20th term of this sequence is a(20) = -2 · (-2)^(20-1), or

a(20) = -2 · (-2)^19, or 2^20, which comes out to 1,048,576 (same as the fourth possible answer).

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)