11. Find the total surface area.
4 in.
6 in.
2 in.

For proof of 3 divisibility, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

The proof for divisibility of 3 implies that an integer is divisible by 3 if the sum of the digits is a multiple of 3.

111 = 1 + 1 + 1 = 3  (the sum is multiple of 3 = 3 x 1)  (111/3 = 37)

222 = 2 + 2 + 2 = 6 (the sum is multiple of 3 = 3 x 2)  (222/3 = 74)

213 = 2 + 1 + 3 = 6 ( (the sum is multiple of 3 = 3 x 2)  (213/3 = 71)

27 = 2 + 7 = 9  (the sum is multiple of 3 = 3 x 3)  (27/3 = 9)

Thus, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

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Answer:

  rule: f(n) = n³

  missing numbers: 125, 216, 343, 512, 729

Step-by-step explanation:

Your familiarity with the cubes of small integers helps you recognize each of these numbers is a cube. Their sequence is the sequence of cubes of increasing natural numbers.

  1 = 1·1·1 = 1³

  8 = 2·2·2 = 2³

  27 = 3·3·3 = 3³

  64 = 4·4·4 = 4³

__

The rule is ...

  f(n) = n³

The cubes of 5 through 9 will complete the set of numbers ...

  1, 8, 27, 64, 125, 216, 343, 512, 729

The number of hours it will take to burn 4 1/4 inches of candle is 8.5 hours in decimal.

Using ratio to solve, find the ratio of candle length to the time taken to burn down

let

4 1/2 : 9 = 4 1/4 : x

9/2 ÷ 9 = 17/4 ÷ x

9/2 × 1/9 = 17/4 × 1/x

1/2 = 17/4x

1 × 4x = 2 × 17

4x = 34

x = 34/4

x = 8.5 hours

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The correct value of (3cis(pi/6))³ is 27i.

Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra.

Given the complex number in polar coordinate expressed as

z = r(cos∅+isin∅)

zⁿ =  {r(cos∅+isin∅)}ⁿ

According to DeMoivre’s Theorem;

zⁿ =  rⁿ(cosn∅+isinn∅)

Given the complex number;

(3cis(pi/6))³

= {3(cosπ/6 + isinπ/6)}³

Using  DeMoivre’s Theorem;

= 3³(cos3π/6 + isin3π/6)

=  3³(cosπ/2 + isinπ/2)

= 3³(0 + i(1))

= 27i

Thus, the correct value of (3cis(pi/6))³ is 27i.

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Answer:

the second option is correct.

Step-by-step explanation:

that is the solution above.

The equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]

The expression is given as:

[tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex]

Start by dividing 18 by 6

[tex]3x^2\sqrt{14x^8} \div \sqrt{7x^4}[/tex]

Next, divide 14 by 7

[tex]3x^2\sqrt{2x^8} \div \sqrt{x^4}[/tex]

Take the square root of x^8 and x^4

[tex]3x^2 * x^4\sqrt{2} \div x^2[/tex]

Divide x^2 by x^2

[tex]3* x^4\sqrt{2}[/tex]

Evaluate

[tex]3x^4\sqrt{2}[/tex]

Hence, the equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]

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Answer: B or 3x^4 sqrt 2

explanation: only simplified answer above

The attached image represents the triangle after it has been enlarged

The given parameters are:

From the graph, the coordinates of the triangle are:

A = (-4,2)

B = (-4,-4)

C = (-1,-4)

The rule of dilation is calculated using:

[tex](x,y) \to (k(x - a) + a, k(y - b) + b)[/tex]

So, we have:

[tex]A' = (-\frac 13(-4 +1) - 1, -\frac 13(2 - 2) + 2)[/tex]

A' = (0, 2)

[tex]B' = (-\frac 13(-4 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]

B' = (0, 4)

[tex]C' = (-\frac 13(-1 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]

C' = (-1, 4)

See attachment for the image of the triangle, after it has been enlarged

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The cost of installing a bush is $7 and the cost of installing a tree is $28

Represent the trees with t and the bushes with b.

So, we have the following equations:

13b + 7t = 287

8b + 12t = 392

Make t the subject in 13b + 7t = 287

t = (287 - 13b)/7

Substitute t = (287 - 13b)/7 in 8b + 12t = 392

8b + 12 * (287 - 13b)/7 = 392

Multiply through by 7

56b + 12 * (287 - 13b) = 2744

Expand

56b + 3444 - 156b = 2744

Collect like terms

56b - 156b = 2744 - 3444

-100b = -700

Divide both sides by -100

b = 7

Substitute b = 7in t = (287 - 13b)/7

t = (287 - 13*7)/7

Evaluate

t = 28

Hence, the cost of installing a bush is $7 and the cost of installing a tree is $28

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Answer:

Yes Ben is correct

Step-by-step explanation:

For example:

If n² is the greater of the two consecutive square numbers, then the difference will be 2n-1. So for example, if you have two consecutive squares with the values of 25, and 36, their difference will be 11. Notice though that 11=2×6–1, so it conforms to 2n-1.

Answer:

358in²

Step-by-step explanation:

9 × 11 = Area of Face One = 99in²

99 × 2 = Face One + Face One on the opposite side = 198in²

4 × 11 = Area of Face Two = 44in²

44 × 2 = Face Two + Face Two on the opposite side = 88in²

9 × 4 = Area of Face Three = 36in²

36 × 2 = Area of Face Three + Face Three on the opposite side = 72in²

Total Surface Area = 198 + 88 + 72 = 358in²

The value of x in the triangle is 20

From the triangle, we have the following equivalent ratios:

5x+ 10 : 121 = 10 : 11

Express as fraction

5x  + 10/121 = 10/11

Multiply both sides by 121

5x + 10 = 110

Subtract 10 from both sides

5x  = 100

Divide both sides by 5

x = 20

Hence, the value of x in the triangle is 20

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Answer:

  B.  The function is nonlinear.

Step-by-step explanation:

A linear function graphs as a straight line. It is a polynomial function of degree 1. Any function that is not a linear function is a nonlinear function.

__

The function given is a polynomial function of degree 2. (Its highest-degree term is x^2, which has an exponent of 2.)

Since the degree is not 1, the function is nonlinear.

_____

Additional comment

A polynomial function will never be "linear at some points and nonlinear at other points." Such a description might apply to a piecewise-defined function.

The value of b that causes the system of equations to have infinite solutions is -6.

For that, we will try solving it first using the method of substitution in which we express one variable in another variable's form and then you can substitute this value in another equation to get a linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

In the given problem, our equations are:

y = 6x + b

-3x + (1/2)^y = -3

So the value of b needs to be such that these two equations must be equal.

In the second equation:

[tex](1/2)^y = -3 + 3x\\y = -3^2 + 3x^2 \\y = -6 + 6x[/tex]

Then we must have:

6x - 6 = 6x + b

-6 = b

Thus, the value of b that causes the system to have infinite solutions is -6.

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Answer:

-6

Step-by-step explanation:

trust

Answer:

0, 3 , 8

Step-by-step explanation:

substitute n = 1, 2, 3 into the pattern rule

T₁ = 1² - 1 = 1 - 1 = 0

T₂ = 2² - 1 = 4 - 1 = 3

T₃ = 3² - 1 = 9 - 1 = 8

Answer:

17.5%

Step-by-step explanation:

1879/10730=17.5%

Answer:

18%

Step-by-step explanation:

Locate the "receives aid" column and "graduate" row. The value 1879 is in this row and column combo.

There are 10730 students total as shown in the bottom right hand corner.

Roughly 1879/10730 = 0.1751 = 17.51% of the students are graduates who receive aid. This rounds to 18%

Answer:

- 8

Step-by-step explanation:

substitute q = - 14 and r = - 6 into the expression

q - r

= - 14 - (- 6)

= - 14 + 6

= - 8

Answer:

Pentagon

Step-by-step explanation:

Because as you can see, a regular pentagon is bigger than then the hexagon. If it's both in the circle below, the pentagon will most likely have an big advantage in this.

Answer:

See the attached graph.

Step-by-step explanation:

Answer:

i can't see the question i would love to help though

Step-by-step explanation:

Outlet A sold the greatest number of copies of album x in July and August

The tables of values are given as:

July

Album X Album Y Album Z

Outlet A 14 8 6

Outlet B 7 13 4

Outlet C 2 11 1

August

Album X Album Y Album Z

Outlet A 12 14 10

Outlet B 5 12 8

Outlet C 16 12 7

In July, the total sales of album x are:

Outlet A  = 14

Outlet B = 7

Outlet C = 2

In August, the total sales of album x are:

Outlet A  = 12

Outlet B = 5

Outlet C = 16

Add both sales

A = 14 + 12 = 26

B = 7 + 5 = 12

C = 2 + 16 = 18

26 (in outlet A) is greater than 12 and 18

Hence, outlet A sold the greatest number of copies of album x in July and August

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Answer:

Outlet D

Step-by-step explanation:

they sold 28 of album x

outlet a only sold 26

The equation c = 64 - d is a linear equation, and the value of c in the equation is 64 1/6

The equation is given as:

c = 64 - d

The value of d is given as:

d = -1/6

Substitute -1/6 for d in c = 64 - d

c = 64 - -1/6

Evaluate the difference

c = 64 1/6

Hence, the value of c in the equation is 64 1/6

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The length of the diagonal shown in the rectangular prism is; 9.5 ft

First of all, we have to find the length of the diagonal base to get;

x = √(4² + 7²)

x = √65

Thus;

Length of the diagonal shown = √(5² + (√65)²)

Length of the diagonal shown = √90

Length of diagonal shown = 9.4868

Length of diagonal shown ≈ 9.5 ft

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Answer:

got 100% on Plato

Step-by-step explanation:

Answer:

x = - 1

Step by step explanation:

The rational expression will be undefined if  the denominator is zero.

x+1 = 0

x =  -1

Hence, for x = -1, the given expression will be undefined.

Answer:

x=60

Step-by-step explanation:

First get x all alone on 1 side of the equation. Add 14.5 to both sides of the equation to cancel out the negative. You will then be left with

x/5= 12

Multiply both sides of the equation by 5 to cancel out the division and you'll get x=60

Answer: B

Explanation: Key word: Atleast. This shows that you can still get 16 but it's the lowest you can get. Meaning, if you were to say, atleast get a 16% done. It'll mean that getting 16% is good but also, you'll want to get a higher number of course.

Answer:

7ft; 8 minutes

Step-by-step explanation:

a. to find the height the person boarded at, plug in t=0 since this is right when the person got on the Ferris wheel. we then get:

h(0) = -45 * cos ((pi/4)*0) + 52 = 7 ft

b. to find the period, we have pi/4 * t = 2*pi, solve for t to get t=8

Answer:

8 cups = 2 quarts

Step-by-step explanation:

Answer:

Eight cups will give you 2 quarts of water

The probability that a student scored less than 55% on the exam is 0.134%.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of the sample = 70

Standard deviation = 5

= P(X<55%)

Z = (55-70)/5

Z = -3

P(X < -3)

From the Z table:

P(x<-3) = 0.0013499

or

P(x<-3) = 0.134%  

Thus, the probability that a student scored less than 55% on the exam is 0.134%.

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