1. Which of the following segments in the triangle below is the hypotenuse? <br>A<br>B<br>C<br>D

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

3 years ago

Which property is shown in the following statement? (46 + 17) + 3 = 46 + (17 + 3) identity property of addition associative prop

maksim [4K]

Answer: the associative property of addition

Step-by-step explanation: when adding three or more terms, you can combine the middle terms with either the first term or the last term and as you add the results, the sum will be the same either way.

3 0

3 years ago

Read 2 more answers

Question 5. How do I find the answer? I am lost

Svetach [21]

Easy, its b because that is the average deviation

6 0

3 years ago

Walter pays $4 for each gallon, g, of gas for his lawn mower. He uses a gift card worth $5 to reduce the amount he owes for his

dem82 [27]

Hope this helps check a website calles math-way without the dash

4 0

3 years ago

]solomon needs to justify the formula for the arc length of a sector. which expression best completes this argument? the circumf

Anna35 [415]

Answer:

$\frac{2 \pi r}{\frac{360^{\circ}}{n^{\circ}}}$ best completes this argument

Step-by-step explanation:

Circumference of circle = $\pi \cdot d$

Where d is the diameter of circle

We are given that if equally sized central angles, each with a measure of n°, are drawn, the number of sectors that are formed will be equal to $\frac{360^{\circ}}{n^{\circ}}$

So, Number of sectors = $\frac{360^{\circ}}{n^{\circ}}$

The arc length of each sector is the circumference divided by the number of sectors

$\Rightarrow \frac{\pi \cdot d}{\frac{360^{\circ}}{n^{\circ}}}$

Diameter d = 2r (r = radius)

$\Rightarrow \frac{2 \pi r}{\frac{360^{\circ}}{n^{\circ}}}$

Option b is true

Hence $\frac{2 \pi r}{\frac{360^{\circ}}{n^{\circ}}}$ best completes this argument

7 0

4 years ago

1. Which of the following segments in the triangle below is the hypotenuse? ABCD​

1. Which of the following segments in the triangle below is the hypotenuse? ABCD