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3 years ago

Please help, I'm stuck on this answer.

2 answers:

8 0

I agree with what that person told you. The expression -2(x+10) is equivalent to -2x-20

Multiply the outer -2 with the inner x to get -2 times x = -2x

Multiply the outer -2 with the inner term 10 to get -2 times 10 = -20

So overall, -2(x+10) = -2x-20

--------------------------------------------

So that's how we're able to go from this $-2(x+10) \ge 75$ to this $-2x-20 \ge 75$

The only thing that changes is the left side. The inequality sign will not flip. It only flips if we multiply both sides by a negative number.

erik [133]3 years ago

6 0

Answer:True

Step-by-step explanation:

Yes, you don't have to reverse the inequality symbol since the variables are not from the other side (right).

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What is the answer and reminder of this equation: 2,617,449 ÷ 18?

AleksandrR [38]

Answer:145,413.833

Step-by-step explanation:

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3 years ago

Driving at a constant speed, Reggie travels 300 kilometers in 1 hour.

vredina [299]

Wouldn't it just be 300 kilometers per hour as the answer?

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3 years ago

If a = {6 6 4 7 -4 4 -6 9 -3} and B= {1 5 -8 9 -5 -8 9 -5 2}, find 3a +9B Matrix operations

V125BC [204]

Answer:

$3A+9B=\begin{bmatrix} 27 & 63 & -60 \\\\ 102 & -57 & -60\\\\ 63 & -18 & 9 \end{bmatrix}$

Step-by-step explanation

$A=\begin{bmatrix} 6 & 6 & 4\\\\7 & -4 & 4\\\\ -6 & 9 & -3\end{bmatrix}\: and \: B=\begin{bmatrix}1 & 5 & -8\\\\ 9 & -5 & -8\\\\ 9 & -5 & 2\end{bmatrix}$

$\rightarrow 3A=3\begin{bmatrix} 6 & 6 & 4\\\\7 & -4 & 4\\\\ -6 & 9 & -3\end{bmatrix},\: \: 9B =9\begin{bmatrix}1 & 5 & -8\\\\ 9 & -5 & -8\\\\ 9 & -5 & 2\end{bmatrix}$

$\rightarrow 3A=\begin{bmatrix} 3*6 & 3*6 & 3*4\\\\3*7 & 3(-4) & 3*4\\\\ 3(-6) & 3*9 & 3(-3)\end{bmatrix},\:\: 9B =\begin{bmatrix}9*1 &9* 5 &9( -8)\\\\ 9*9 & 9(-5) & 9(-8)\\\\ 9*9 & 9(-5) & 9*2\end{bmatrix}$

$\rightarrow 3A=\begin{bmatrix} 18 & 18 & 12 \\\\ 21 & -12 & 12\\\\ -18 & 27 & -9\end{bmatrix},\:\: 9B =\begin{bmatrix} 9 & 45 & -72 \\\\ 81 & -45 & -72\\\\ 81 & -45 & 18\end{bmatrix}$

$\rightarrow 3A+9B=\begin{bmatrix}18+9 & 18+45 & 12+(-72) \\\\ 21+81 & -12 +(-45) & 12+(-72)\\\\ -18+81 & 27+(-45) & -9+18 \end{bmatrix}$

$\rightarrow 3A+9B=\begin{bmatrix} 18+9 & 18+45 & 12-72 \\\\ 21+81 & -12 -45 & 12-72\\\\ -18+81 & 27-45 & -9+18 \end{bmatrix}$

$\rightarrow \purple{\bold{3A+9B=\begin{bmatrix} 27 & 63 & -60 \\\\ 102 & -57 & -60\\\\ 63 & -18 & 9 \end{bmatrix}}}$

6 0

2 years ago

Suppose that you take a sample of 250 adults. If the population proportion of adults who watch news videos is 0.58, what is the

aliina [53]

Answer:

0.36% probability that fewer than half in your sample will watch news videos

Step-by-step explanation:

To solve this question, i am going to use the binomial approximation to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 250, p = 0.58$

$\mu = E(X) = 250*0.58 = 145$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.58*0.42} = 7.80$

If the population proportion of adults who watch news videos is 0.58, what is the probability that fewer than half in your sample will watch news videos

Half: 0.5*250 = 125

Less than half is 124 or less

So this is the pvalue of Z when X = 124

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{124 - 145}{7.8}$