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2 years ago

What is the cube root of 216?

2 answers:

8 0

Hey there :)

Cube root of 216
$\sqrt[3]{216}$

Break it into 6 × 6 × 6 = 6³

$\sqrt[3]{6^3}$

The cube power of on 6 inside the cube root cancels with the cube root

Therefore, the final answer is 6

svetlana [45]2 years ago

6 0

$\sqrt[3]{216}= \sqrt[3]{6^3}=6$

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If m∠ATB = 20°, m∠BTD = 72°, and m∠CTD = 38°, what is m∠ATC?

Ber [7]

Answer: m∠ATC = 54°

Step-by-step explanation:

Ok, we know that:

m∠ATB = 20° and m∠BTD = 72°

then we must have that the angle between A and D, is equal to the sum of the angles between A and B, and B and D, or:

m∠ATD = m∠ATB + m∠BTD = 20° + 72° = 92°

Now, we also know that m∠CTD = 38°

And the angle:

m∠ATC will be equal to the angle between A and D, minus the angle between C and D, or:

m∠ATC = m∠ATD - m∠CTD = 92° - 38° = 54°

7 0

2 years ago

What is the first step in solving for z in the equation 5z - 4 = 26

Andrei [34K]

You would 4 to both sides of the equation

3 0

2 years ago

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$

5 0

2 years ago

A bag contains 30 lottery balls numbered 1-30. A ball is selected, replaced, then another is drawn. Find each probability.

swat32

Answer:

17÷3 ok so it was just a compliment sometime soon

3 0

2 years ago

Write the equation of the line that is parallel to the line y = -3x + 12 and passes through the point (-1, 6). select one:

lapo4ka [179]

Y-6=-3(x+1)
y=-3x+3 answer is b

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3 years ago