The number of people left to play if 10 of 15 have played

Simplify 3a^2b^2x2ab+6a^3b^2

ira [324]

$3 {a}^{2} \times {b}^{2} \times 2ab + 6 {a}^{3} \times {b}^{2} =$

$6 {a}^{3} {b}^{3} + 6 {a}^{3} {b}^{2} =$

Factoring 6a^3 b^2

$6 {a}^{3} {b}^{2}(b + 1)$

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3 0

3 years ago

Use technology or a z-score table to answer the question.

Alik [6]

Answer:

The second choice: Approximately $65.2\%$ of the pretzel bags here will contain between 225 and 245 pretzels.

Step-by-step explanation:

This explanation uses a z-score table where each $z$ entry has two decimal places.

Let $\mu$ represent the mean of a normal distribution of variable $X$ . Let $\sigma$ be the standard deviation of the distribution. The z-score for the observation $x$ would be:

$\displaystyle z = \frac{x - \mu}{\sigma}$ .

In this question,

$\mu = 240$ .
$\sigma = 9.3$ .

Calculate the z-score for $x_1 = 225$ and $x_2 = 245$ . Keep in mind that each entry in the z-score table here has two decimal places. Hence, round the results below so that each contains at least two decimal places.

$\begin{aligned} z_1 &= \frac{x_1 - \mu}{\sigma} \\ &= \frac{225 - 240}{9.3} \approx -1.61\end{aligned}$ .

$\begin{aligned} z_2 &= \frac{x_2 - \mu}{\sigma} \\ &= \frac{245 - 240}{9.3} \approx 0.54\end{aligned}$ .

The question is asking for the probability $P(225 \le X \le 245)$ (where $X$ is between two values.) In this case, that's the same as $P(-1.61 \le Z \le 0.54)$ .

Keep in mind that the probabilities on many z-table correspond to probability of $P(Z \le z)$ (where $Z$ is no greater than one value.) Therefore, apply the identity $P(z_1 \le Z \le z_2) = P(Z \le z_2) - P(Z \le z_1)$ to rewrite $P(-1.61 \le Z \le 0.54)$ as the difference between two probabilities:

$P(-1.61 \le Z \le 0.54) = P(Z \le 0.54) - P(Z \le -1.61)$ .

Look up the z-table for $P(Z \le 0.54)$ and $P(Z \le -1.61)$ :

$P(Z \le 0.54)\approx 0.70540$ .
$P(Z \le -1.61) \approx 0.05370$ .

$\begin{aligned}& P(225 \le X \le 245) \\ &= P\left(\frac{225 - 240}{9.3} \le Z \le \frac{245 - 240}{9.3}\right)\\&\approx P(-1.61 \le Z \le 0.54) \\ &= P(Z \le 0.54) - P(Z \le -1.61)\\ &\approx 0.70540 - 0.05370 \\& \approx 0.65.2 \\ &= 65.2\% \end{aligned}$ .

3 0

4 years ago

Beverley has quarters and dimes in her pocket. She has 21 coins with a total value of $3.00. How many of each type of coin does

forsale [732]

Answer:

6 quarters and 15 dimes

Step-by-step explanation:

6 quarters = $1.50

15 dimes = $1.50

6 quarters + 15 dimes = $3.00

8 0

3 years ago

Type the inequality from the graph below

WARRIOR [948]

Answer:

x > 0

Step-by-step explanation:

It shows on the number line.

7 0

2 years ago

Find two numbers if their ratio is 4:7 and their difference is 123.<br> help

Karo-lina-s [1.5K]

Answer:

164 and 287

Step-by-step explanation:

Their difference is 7-4 = 3 ratio units, so each ratio unit must stand for 123/3 = 41.

Then the numbers are 4·41 and 7·41, or 164 and 287.

5 0

3 years ago

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