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3 years ago

X+2/4 = 3/8 solve for x

Mathematics

1 answer:

Anna007 [38]3 years ago

4 0

Answer:

Step-by-step explanation:

Isolate x on one side of the equation.

x+2/4=3/8

2/4=1/2 (First, use the common factor of 2.)

x+1/2=3/8

x+1/2-1/2=3/8-1/2 (Then, subtract 1/2 from both sides.)

3/8-1/2 (Solve.)

3/8-1/2=-1/8

-1/8=-0.125

x=-1/8=-0.125

In conclusion, the final answer is x=-1/8=-0.125.

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(a) Point estimate = 7.10

(b) The critical value is 1.960

(d) Confidence Interval = (6.3, 7.9)

(e) We are 90% confident that the average number of hours worked by the students is between 6.3 and 7.9

Step-by-step explanation:

Given

$\bar x = 7.10$ -- sample mean

$\sigma=5$ --- sample standard deviation

$n = 150$ --- samples

Solving (a): The point estimate

The sample mean can be used as the point estimate.

Hence, the point estimate is 7.10

Solving (b): The critical value

We have:

$CI = 90\%$ --- the confidence interval

Calculate the $\alpha$ level

$\alpha = 1 - CI$

$\alpha = 1 - 90\%$

$\alpha = 1 - 0.90$

$\alpha = 0.10$

Divide by 2

$\frac{\alpha}{2} = 0.10/2$

$\frac{\alpha}{2} = 0.05$

Subtract from 1

$1 - \frac{\alpha}{2} = 1 - 0.05$

$1 - \frac{\alpha}{2} = 0.95$

From the z table. the critical value for $1 - \frac{\alpha}{2} = 0.95$ is:

$z = 1.960$

Solving (c): Margin of error

This is calculated as:

$E = z * \frac{\sigma}{\sqrt n}$

$E = 1.960 * \frac{5}{\sqrt {150}}$

$E = 1.960 * \frac{5}{12.25}$

$E = \frac{1.960 *5}{12.25}$

$E = \frac{9.80}{12.25}$

$E = 0.800$

Solving (d): The confidence interval

This is calculated as:

$CI = (\bar x - E, \bar x + E)$

$CI = (7.10 - 0.800, 7.10 + 0.800)$

$CI = (6.3, 7.9)$

Solving (d): The conclusion

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6 0

3 years ago

Drag steps into order to correctly solve the equation 4x = 112 for x.

alekssr [168]

4x=112
x=112/4 ( '/' means divide)
x=28

5 0

3 years ago

Read 2 more answers

Find the accumulated value of an investment $10,000 for 3 years at an interest of 7% if the money is compounded semiannually; co

asambeis [7]

Answer:

Correct answer: 1) AV = 12,290 $, 2) AV = 12,310 $, 3) AV = 12,330 $,

4) AV = 12,337 $

Step-by-step explanation:

Given:

I = 10,000$

n = 3 years

p = 7% = 0.07

Accumulated value of an investment is calculated with next formula:

AV = I · (1 + (p/a))ᵃⁿ where is:

AV - accumulated value

I - investment

p - interest

a - number of calculation parts during one year as the accounting period

n - number of years as the accounting period

1) money is compounded semiannually

a = 2 and a · n = 2 · 3 = 6

AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/2))⁶ = 10,000 · 1.229 = 12,290 $

AV = 12,290 $

2) money is compounded quarterly

a = 4 and a · n = 4 · 3 = 12

AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/4))¹² = 10,000 · 1.231 = 12,310 $

AV = 12,310 $

3) money is compounded monthly

a = 12 and a · n = 12 · 3 = 36

AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/12))³⁶ = 10,000 · 1.233 = 12,330 $

AV = 12,330 $

4) money is compounded continuously

Accumulated value of an investment continuously compounded is calculated with next formula:

AV = I · eⁿᵇ where is:

n - number of years as the accounting period

b = p = 7% = 0.07

n · b = 3 · 0.07 = 0.21

AV = 10,000 e⁰²¹ = 10,000 2.7183⁰²¹ = 10,000 1.2337 = 12,337 $

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