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3 years ago

One solution of x^2-64=0 is 8. what is the other solution?

2 answers:

8 0

Step 1: Add 64 to both sides.
x2−64+64=0+64
x2=64
Step 2: Take square root.
x=±√64
x=8 or x=−8
Answer:x=8 or x=−8

Hope this helps :D

ivann1987 [24]3 years ago

4 0

X² - 64 = 0
(x - 8)(x + 8) = 0

x = - 8, 8

Your other solution is - 8

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Answer:

The 85% onfidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is (0.151, 0.205).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

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For this problem, we have that:

Sample of 421 new car buyers, 75 preferred foreign cars. So $n = 421, \pi = \frac{75}{421} = 0.178$

85% confidence level

So $\alpha = 0.15$ , z is the value of Z that has a pvalue of $1 - \frac{0.15}{2} = 0.925$ , so $Z = 1.44$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 - 1.44\sqrt{\frac{0.178*0.822}{421}} = 0.151$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 + 1.44\sqrt{\frac{0.178*0.822}{421}} = 0.205$

The 85% onfidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is (0.151, 0.205).

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2 years ago

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3 years ago

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3 years ago

Teacl Smolts are young salmon at a stage when their skin becomes covered with silvery scales and they start to migrate from fres

erma4kov [3.2K]

Answer:

a) s = 8.81

b) Q1 = 43.4, Q2 = 49.4, Q3 = 57.35

c) See below

Step-by-step explanation:

(a) Find the standard deviation of the reflectance for these smolts. (Round your answer to two decimal places.)

In order to find the standard deviation, we need the mean first. The mean is defined as

$\bar x=\displaystyle\frac{\displaystyle\sum_{i=1}^{n}x_i}{n}$

where the $x_i$ are the values of the data collected and n=50 the size of the sample.

So, the mean is

$\bar x=50.882$

Now, the standard deviation of the sample is defined as

$s=\sqrt{\displaystyle\frac{\displaystyle\sum_{i=1}^n(x_i-\bar x)^2}{n-1}}$

and we have that our standard deviation is

s = 8.81

(b) Find the quartiles of the reflectance for these smolts

To find the quartiles, we must sort the data from lowest to largest:

33.6, 37.7, 38.3, 38.7, 42, 42, 42.2, 42.4, 42.7, 42.8, 42.9, 43.1, 43.7, 43.8, 44.2, 44.6, 45.5, 45.7, 46.3, 46.6, 47.4, 47.6, 47.7, 47.9, 49.2, 49.6, 50.5, 50.9, 51.3, 53, 53.9, 54.8, 54.9, 55.5, 56, 56, 56.2, 57.1, 57.6, 58.3, 59, 59.5, 60.4, 63.2, 63.4, 63.5, 64.6, 68, 69.1, 69.2

The first quartile is the number between the 12th and the 13th data (so 25% of the data are below it and 75% above it)

So the 1st quartile is

$Q_1=\displaystyle\frac{43.1+43.7}{2}=43.4$

The 2nd quartile is the median, the point between the 25th and 26th data, it splits the data in two halves.

$Q_2=\displaystyle\frac{49.2+49.6}{2}=49.4$

The 3rd quartile is the point between the 38th and 39th data (so 75% of the data are below it and 25% above it)

$Q_3=\displaystyle\frac{57.1+57.6}{2}=57.35$

(c) Do you prefer the standard deviation or the quartiles as a measure of spread for these data? Give reasons for your preference.

In this case, we prefer the quartiles as a measure of spread since the data are very scattered around the mean and there is no a central tendency.

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