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3 years ago

Solve 2(a + 7) = 5a - 13

Mathematics

1 answer:

timurjin [86]3 years ago

4 0

Answer:

a = 9

Step-by-step explanation:

2(a + 7) = 5a - 13

We want to bring a to one side, I will choose to bring it to the right

First, expand the bracket by multiplying 2 with a + 7

2a + 14 = 5a - 13

Bring the -13 to the left by adding 13 to both sides

2a + 14 + 13 = 5a - 13 + 13

Simplify

2a + 27 = 5a

Bring the 2a to the right by subtracting 2a from both sides

2a - 2a + 27 = 5a - 2a

Simplify

27 = 5a - 2a

27 = 3a

Bring the 3 to the left by dividing both sides by 3

27÷3 = a

Simplify

a = 9

You might be interested in

The length of a rectangle is 5 inches less than twice its width. The perimeter of the rectangle is 26 inches. What is the width

Yakvenalex [24]

Answer:

w= 6

Step-by-step explanation:

I just started by making an educated guess using the values already given. Then I inserted that into the problem to see if it worked.

L= 2w - 5

I used 6 as a random, educated guess for the value of w.

L = 2(6) - 5

L = 12-5

L = 7

Then, multiply L by 2 to account for both side lengths of the rectangle.

7(2)= 14

Subtract that value from the total perimeter to find what the width must equal.

26 - 14 = 12

Divide that answer by 2 since there are two sides for width.

12/2 = 6

I know this was kind of long, but I hope it helps! :)

3 0

3 years ago

Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed

vlabodo [156]

Answer:

95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm)

Step-by-step explanation:

Our sample size is 11.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 11-1 = 10$ .

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 10 and 0.025 in the two-sided t-distribution table, we have $T = 1.812$

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{4}{\sqrt{11}} = 1.2060$

Now, we multiply T and s

$M = Ts = 1.812*1.2060 = 2.19/tex]For the lower end of the interval, we subtract the sample mean by M. So the lower end of the interval here is[tex]L = 97 - 2.19 = 94.81 = 94.8$ cm