"Reflex angles measure more than 180 degrees" has a counterexample. True or False?

The water level in a swimming pool decreases from 60 inches to 58.25 inches in one week.

Keith_Richards [23]

I think it’s gonna be A.

8 0

3 years ago

The resting heart rate for an adult horse should average about µ = 47 beats per minute with a (95% of data) range from 19 to 75

KatRina [158]

Answer:

a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean:

$\mu = 47$

(95% of data) range from 19 to 75 beats per minute.

This means that between 19 and 75, by the Empirical Rule, there are 4 standard deviations. So

$4\sigma = 75 - 19$

$4\sigma = 56$

$\sigma = \frac{56}{4} = 14$

a. What is the probability that the heart rate is less than 25 beats per minute?

This is the p-value of Z when X = 25. So

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

$Z = \frac{25 - 47}{14}$

$Z = -1.57$

$Z = -1.57$ has a p-value of 0.0582.

0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. What is the probability that the heart rate is greater than 60 beats per minute?

This is 1 subtracted by the p-value of Z when X = 60. So

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

$Z = \frac{60 - 47}{14}$

$Z = 0.93$

$Z = 0.93$ has a p-value of 0.8238.

1 - 0.8238 = 0.1762

0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. What is the probability that the heart rate is between 25 and 60 beats per minute?

This is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 25. From the previous two items, we have these two p-values. So

0.8238 - 0.0582 = 0.7656

0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

3 0

3 years ago

A student has received the following test scores: 71%, 89%, 72%,

lidiya [134]

Answer: 81%

Step-by-step explanation:

From the question, we are informed that a student received the following test scores: 71%, 89%, 72%,

84% and 83% in 5 tests and the student wants to maintain an average of 80%.

The lowest score/grade they can receive on the next test to maintain at least an 80% average first thus:

First, to make it easy we can remove the percent sign. Then we multiply 80 by 6 since we're calculating for 6 tests scores. This will be:

= 80 × 6

= 480

We then add all the 5 test scores. This will be:

= 71 + 89 + 72 + 84 + 83

= 399

We then subtract the values gotten. This will be:

= 480 - 399

= 81

This means the student must get at least 81%

5 0

4 years ago

How would I solve this?

Lelu [443]

If you help me with my last question I will help you with this one

3 0

3 years ago

A triangle has 2 sides that are 9 inches and the bottom is 6 inches what is the height?

Elanso [62]

The height of the isosceles triangle is 8.49 inches.

<h3>How to find the height of the triangle?</h3>

Here we have a triangle such that two of the sides measure 9 inches, and the base measures 6 inches.

So this is an isosceles triangle.

We can divide the isosceles triangle into two smaller right triangles, such that the side that measures 9 inches is the hypotenuse, the base is 3 inches, and the height of the isosceles triangle is the other cathetus.

By Pythagorean's theorem, we can write:

(9in)^2 = (3 in)^2 + h^2

Where h is the height that we are trying to find.

Solving that for h we get:

h = √( (9 in)^2 - (3in)^2) = 8.49 inches.

We conclude that the height of the isosceles triangle is 8.49 inches.

If you want to learn more about triangles:

brainly.com/question/2217700

#SPJ1

8 0

2 years ago