Distributive property 6y+18

Use K to write an equation, y=kx, for the relationship.

frozen [14]

Y= 1x because the slope is 1 because rise over run 1

8 0

3 years ago

In Chicago, IL, the average wind speed is 10.4 miles per hour. In Great Falls, MT, the average wind speed is 13.1 miles per hour

Fed [463]

I think Great Falls' average wind speed is greater than Chicago's by 2.7 miles

8 0

3 years ago

Duck #1 lays eggs whose weights are normally distributed with a mean of 70gramsand a standard deviation of 6 grams.Duck #2 lays

Genrish500 [490]

Answer:

26.11% probability that Duck #2’s egg weighs more than Duck #1’s egg

Step-by-step explanation:

When the distribution is normal, we use 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.

If an egg is randomly chosen from each duck, what is the probability that Duck #2’s egg weighs more than Duck #1’s egg?

Duck #2 egg will weigh more if the subtraction of duck's 2 egg by duck's 1 egg is larger than 0.

When we subtract normal distributions, the mean is the subtraction of the means. So

$\mu = 65 - 70 = -5$

The standard deviation is the square root of the sum of the variances. So

$\sigma = \sqrt{6^2+5^2} = \sqrt{61} = 7.81$

Now, we have to find 1 subtracted by the pvalue of Z when X = 0. So

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

$Z = \frac{0 - (-5)}{7.81}$

$Z = 0.64$

$Z = 0.64$ has a pvalue of 0.7389

1 - 0.7389 = 0.2611

26.11% probability that Duck #2’s egg weighs more than Duck #1’s egg

4 0

3 years ago

HELP ASAP!! Find the total area of the figure below. Round your answer to the nearest tenth

nika2105 [10]

Answer:

area = 88 mi²

Step-by-step explanation:

all vertical dimensions = 8/2 = 4 mi

area = (4 x 11.9) +(4 x 6.1) + (4 x 4) = 88 mi²

6 0

3 years ago

You have a list of 1,000 random, normally distributed numbers with a mean of 20 and a standard deviation of 3. Which statement i

Ludmilka [50]

You're going to have to work out the z-scores of both values in each option and see if it makes sense.

n = m + sz

The mean is 20 and the standard deviation is 3.

So let's find try the z-scores of the outer range values and determine their probabilities:

from 14-20:

n = m + sz
20 = 20 + 3z and 14 = 20 + 3z
0 = 3z and -6 = 3z
z = 0 and z = -2

So now using a z-score table, such as the one below, find the probabilities.

z = 0 is easy, it's 0.5
z = -2 is 0.02275

Subtract the smaller from the larger to get the probability of getting in the range:

0.5 - 0.02275 = 0.47725 (so times 1000, you get 477.25, which is not about 340, so this option is wrong)
---
Now trying option 2, from 17-29:

n = m + sz
29 = 20 + 3z and 17 = 20 + 3z
9 = 3z and -3 = 3z
z = 3 and z = -1

0.99865 - 0.158655 = 0.839995 (not 680, so not the answer)
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Now trying option 3, from 20-23:

n = m + sz
23 = 20 + 3z and 20 = 20 + 3z
3 = 3z and 0 = 3z
z = 1 and z = 0

0.841345 - 0.5 = 0.341345 (close to 340, so is your answer)

8 0

3 years ago