Expand the following expression by using the distributive method. 6(3b

The graph shows the cost of a lunch in a school’s cafeteria since school started.

max2010maxim [7]

Answer: It's slope is zero

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Two bakeries sell muffins that can be customized with different kinds of berries. Berry Bakery sells muffins for $14.50 a dozen,

vfiekz [6]

Yes. The original price of the dozen added to the price of berries (.5) multiplied by the amount(b) is the same equational representation to the right of the equal sign.

5 0

2 years ago

Read 2 more answers

Use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle. Show all work for full credit.

liq [111]

Using Pythagorean identities:

If the sum of the height and base squared is greater than the hypotenuse squared, it would be an acute triangle.

If the sum of the height and base squared is less than the hypotenuse squared, it would be an obtuse triangle.

If the sum of the height and base squared is equal to the hypotenuse squared, it would be a right triangle.

The height = 10
The base = 24

10^2 + 24^2 = 100 + 576 = 676

The hypotenuse = 27 = 27^2 = 729

Because the sum of the height and base squared (676) is smaller than the hypotenuse squared (729) the triangle is an obtuse triangle.

5 0

2 years ago

Read 2 more answers

Justin weighs 15 pounds less than Greg weighs. Half of Greg’s weight is 75 pounds less than Justin’s weight. How much does each

sp2606 [1]

Lets take Gregs weight as “x”. This means that Justins weight is x-15, and x/2 = (x-15)-75.

If we take that last equation, lets combine like terms:

x/2 = x - 15 - 75
x/2 = x - 90
Now multiply both sides by 2 to get rid of the fraction
x = 2x - 180
Subtract 2x from both sides
x - 2x = -180
-x = -180
x = 180 — this is Gregs weight

Justins weight is x-15, so 180-15, which is 165 pounds. Hope this helped.

5 0

2 years ago

According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg

Sati [7]

Answer:

a) Mean blood pressure for people in China.

b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg

f) 157.44mmHg

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 X is two standard deviations from the mean or more, it is considered unusual.

In this question:

$\mu = 128, \sigma = 23$

a.) State the random variable.

Mean blood pressure for people in China.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the pvalue of Z when X = 135.

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

$Z = \frac{135 - 128}{23}$

$Z = 0.3$

$Z = 0.3$ has a pvalue of 0.6179

1 - 0.6179 = 0.3821

38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.

This is the pvalue of Z when X = 141.

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

$Z = \frac{141 - 128}{23}$

$Z = 0.565$

$Z = 0.565$ has a pvalue of 0.7140

71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.

This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So

X = 125

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

$Z = \frac{125 - 128}{23}$

$Z = -0.13$

$Z = -0.13$ has a pvalue of 0.4483

X = 120

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

$Z = \frac{120 - 128}{23}$

$Z = -0.35$

$Z = -0.35$ has a pvalue of 0.3632

0.4483 - 0.3632 = 0.0851

8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?

From b), when X = 135, Z = 0.3

Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.

f.) What blood pressure do 90% of all people in China have less than?

This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then

X = 120

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

$1.28 = \frac{X - 128}{23}$