Which of the following statements is true

1 answer:

6 0

Hello There!

The first statement is incorrect as congruent angles have the same measure but it doesn't have to 45°. It can be any value.
The second one is also incorrect. Congruent angles have the same measure but don't always total to 180° (which is what supplementary means). It would only be true if they are congruent right angles.
The third one is also incorrect as they don't always total to 90° either (Which is what complementary means).
The fourth one is correct, this is because congruent angles are simply angles with the same measure.

In short, you're answer is 4. Congruent angles always have the same measure.

Hope This Helps You!
Good Luck :)

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The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation

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Answer:

a. X~N(2,885, 651)

b. 0.086291

c. 0.00058

d. 3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

$P(X$

#substitute the given values in the formula to solve for P:

$P(X$

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

$P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058$

Hence, the proportion of customers consuming over 5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

$0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09$