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2 years ago

Simplify. 3/(square root)-125n^12 -5 n9 -5 n4 5 n4

Mathematics

1 answer:

Alex17521 [72]2 years ago

7 0

Answer:

B) $-5n^4$

Step-by-step explanation:

We want to simplify $\sqrt[3]{-125n^{12}}$

$\sqrt[3]{-125n^{12}} = \sqrt[3]{-1 * - 1 * -1 * 5 * 5 * 5 * n^4 * n^4 * n^4} \\\\= \sqrt[3]{(-1)^3 * 5^3 * (n^4)^3}\\\\= -1 * 5 * n^4\\\\= -5n^4$

The answer is $-5n^4$

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Recent studies indicate that the typical 50-year-old woman spends $350 per year for personal-care products. The distribution of

jek_recluse [69]

Answer:

P ( x_bar > 335 ) = 0.9826

Step-by-step explanation:

Given:

- Mean amount u = 350

- standard deviation s.d = 45/year

- Sample size n = 40

Find:

- The probability of sample mean P( x_bar > 335 )

Solution:

- P ( x_bar > 335 ) = P ( Z > sqrt(n)*(x_bar - u)/s.d)

= P ( Z > sqrt(40)*(335-350)/45)

= P ( Z > -2.111) = P ( Z < 2.111)

= 0.5 + P( 0 < Z < 2.111)

= 0.5 + 0.4826

= 0.9826

4 0

1 year ago

Savannah is working two summer jobs, making $12 per hour babysitting and $7 per hour washing cars. Savannah must earn a minimum

postnew [5]

Answer:

The inequality that represents the given situation is 12b + 7w ≥ 55

Step-by-step explanation:

Let us solve the question

∵ Savannah is working two summer jobs

∵ She is making $12 per hour babysitting

∵ The number of hours babysitting is b

→ Multiply 12 by b to find the amount earning from babysitting

∴ She is making 12b dollars from working as a babysitting

∵ She is making $7 per hour washing cars

∵ The number of hours washing cars is w

→ Multiply 7 by w to find the amount earning from washing cars

∴ She is making 7w dollars from working in washing cars

∵ Savannah must earn a minimum of $55 this week

→ minimum means ≥,

∴ The total earning ≥ 55

∵ The total earning is 12b + 7w

→ Use the two expressions of the total earning to write the inequality

∴ 12b + 7w ≥ 55

∴ The inequality that represents the given situation is 12b + 7w ≥ 55

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2 years ago

Jason’s savings account has a balance of $2179. After 5 years , what will the amount of interest be at 6% compounded quarterly?

satela [25.4K]

Answer:

$755.80

Step-by-step explanation:

Determine the compound amount first and then subtract the principal from it, to find the amount of interest.

The compound amount formula is A = P (1 + r/n)^(nt), where

P is the initial principal, r is the interest rate as a decimal fraction, n is the number of compounding periods per year, and t is the number of years. Here, P = $2179; t = 5 yrs; r = 0.06; and n = 4 (quarterly compounding).

We get:

A = $2179(1 + 0.06/4)^(4*5), or $2179(1.015)^20, or $2179(1.347) = $2937.80.

The compound amount is $2934.80. Subtracting the $2179 principal results in the interest earned: $755.80.

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2 years ago

An engineer is trying to produce as much hydrogen gas as the company can using the equipment they have.

Oduvanchick [21]

Answer:

Step-by-step explanation:

7 0

1 year ago

The angle \theta_1θ

enyata [817]

Answer:

$sin\theta_1 = \dfrac{\sqrt{217}}{19}$

Step-by-step explanation:

It is given that:

$cos\theta_1 = -\dfrac{12}{19}$

And we have to find the value of $sin\theta_1 = ?$

As per trigonometric identities, the relation between $sin\theta\ and \ cos\theta$ can represented as:

$sin^2\theta + cos^2\theta = 1$

Putting $\theta_1$ in place of $\theta$ Because we are given

$sin^2\theta_1 + cos^2\theta_1 = 1$

Putting value of cosine:

$cos\theta_1 = -\dfrac{12}{19}$

$sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}$

It is given that $\theta_1$ is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

$\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}$

8 0

1 year ago