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3 years ago

What are the steps to 3(5b+6)=30+3b

Mathematics

2 answers:

solong [7]3 years ago

6 0

15b+18=30+3b
15b=30+3b-18
15b=3b+12
15b-3b=12
12b=12
B=1

kykrilka [37]3 years ago

4 0

3(5b+6) = 30 + 3b

1. Use the distributive property and multiply what's outside the parenthesis by whats on the inside.

15b + 18 = 30 + 3b

2. Next get rid of the 18 by subtracting it from itself and 30.

15b = 12 + 3b

3. After that you need to get rid of the 3b, so you would subtract 3b from itself and 15b.

12b = 12.

4.Next divide both sides by 12.

b= 1

Go back and insert your answer.

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3 years ago

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Solve for ax-b=c for x

Artyom0805 [142]

Answer:

x = $\frac{c+b}{a}$

Step-by-step explanation:

Given

ax - b = c ( add b to both sides )

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4 years ago

Given values: 54, 65, 76, 43, 45, 76, 87 12, 23, 34, 67,65, 78, 45, 34. Given 95% confidence and sigma (population standard devi

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Answer:

Option (D) None of the above.

Step-by-step explanation:

We are given the following data:

54, 65, 76, 43, 45, 76, 87, 12, 23, 34, 67,65, 78, 45, 34

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{804}{15} = 53.6$

Sum of squares of differences = 0.16 + 129.96 + 501.76 + 112.36 + 73.96 + 501.76 + 1115.56 + 1730.56 + 936.36 + 384.16 + 179.56 + 129.96 + 595.36 + 73.96 + 384.16 = 6849.6

$S.D = \sqrt{\frac{6849.6}{15}} = 21.4$

Confidence interval:

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

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3 years ago

What is the solution of the system?

Serjik [45]

Answer:

(-13,-4)

Step-by-step explanation:

4x-8y=-20

9x+113=y

Substitute in y for 9x+113

4x-8y=-20

Substitute

4x-8(9x+113)=-20

Simplify

4x-72x-904=-20

Simplify

-68x-904=-20

Additive Prop. of Equality

-68x-904+904=-20+904

Simplify

-68x=884

Isolate the variable(x)

-68x -68x

Simplify

x=-13

Solve for y

9x+113=y

9(-13)+113=y

-117+113=y

-4=y

Check

4x-8y=-20

4(-13)-8(-4)=-20

-52+32=-20

-20=-20

9x+113=y

9(-13)+113=-4

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-4=-4

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3 years ago

You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 1536cm3. Deter

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Answer:

The dimensions of the box are:

Length = 11.53cm

Breadth = 11.53cm

Height = 11.53cm

Step-by-step explanation:

The volume of the box can be calculated with this formula:

The volume of the box = area of square base X height of the box.

We are given that the length of one side of the square base is = x cm, and its height is h cm.

Area of square base = $x^{2}cm^{2}$

The surface area of the box will be minimized if the height of the box, is the same as its length. hence, we can take the height of the box to be x cm also.

In this case, the volume of the box will be $x^{3}=1536cm^{3}$

from this, $x =3\sqrt{1536}= 11.53cm$

There fore, the box has its length, height, and width all having the same values.

The dimensions of the box are:

Length = 11.53cm

Breadth = 11.53cm

Height = 11.53cm

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4 years ago