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DanielleElmas [232]
2 years ago
7

4 Consider the triangle below.

Mathematics
1 answer:
Maurinko [17]2 years ago
6 0
<h2>=>> <u>Solution (part A</u>) :</h2>

Given :

▪︎Triangle AMG is an isosceles triangle.

▪︎Measure of segment AM = (x+1.4) inches

▪︎Measure of segment MG = (2x+0.1) inches

▪︎Measure of segment AG = (3x-0.4) inches

▪︎segment AG is the base of triangle AMG.

Since AG is the base of the isosceles triangle AMG, segment AM and segment MG will be equal.

Which means :

= \tt x + 1.4 = 2x + 0.1

= \tt x + 1.4 - 0.1 = 2x

=  \tt \: x + 1.3 = 2x

= \tt 1.3 = 2x - x

\color{plum} \hookrightarrow  \tt x = 1.3

Thus, the value of x = 1.3

Therefore :

▪︎The value of x = 1.3

<h2>=>> <u>Solution (Part B)</u> :</h2>

We know that :

▪︎The value of x = 1.3

Which means :

The length of the leg AM :

= \tt x + 1.4

= \tt 1.3 + 1.4

\color{plum} \tt leg \: AM= 2.7 \: inches

Thus, the length of the leg AM = 2.7 inches

The length of leg MG :

= \tt 2x + 0.1

=  \tt2 \times 1.3 + 0.1

= \tt 2.6 + 0.1

\color{plum} \tt\: leg \:MG = 2.7 \: inches

Thus, the length of the leg MG = 2.7 inches

Since the measure of the two legs are equal (2.7=2.7), we can conclude that we have found out the correct length of each leg.

Therefore :

▪︎Measure of leg AM = 2.7 inches

▪︎Measure of leg MG = 2.7 inches

<h2>=>> <u>Solution </u><u>(</u><u>part C</u><u>)</u> :</h2>

We know that :

Value of x = 1.3

Then, measure of the base AG :

=  \tt 3x - 0.4

= \tt 3 \times 1.3 - 0.4

= \tt 3.9 - 0.4

\color{plum}\tt \: Base  \: AG = 3.5 \:  inches

Thus, the measure of the base = 3.5 inches

Therefore :

▪︎ the length of base AG = 3.5 inches.

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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

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2 years ago
Jonathan saved money to have a party if he spends to eight of his money on food 1/5 of his money on prices and two tenths of his
erik [133]

Answer:

7/20 is left

Step-by-step explanation:

2/8 (reduced is 1/4) for food

1/5 for prizes

2/10 (reduced is 1/5) for decorations

? for what's left

Add all the fractions up by finding a common denominator.

1/4 + 1/5 + 1/5

5/20 + 4/20 +4/20 = 13/20

He spent 13/20 of his money on this stuff. What part of that is left?

1 - 13/20 (AKA 20/20 - 13/20)

= 7/20

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goldenfox [79]

Answer:

Step-by-step explanation: WELL i cant help lm really sorry

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A bowl contained 250 skittles. The result of 25 fruit-flavored candies pulled at random is given below. Based on this informatio
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OK so you have 250 skittles. But you only pull out 25. You pull out 5 red skittles, 7 yellow skittles,8 orange skittles,2 green skittles and 3 purple skittles. So how many red skittles are in the whole box. The way i would look at it is theres 5 red skittles in every 25 skittles. So whats 250 divided by 25 that would be 10. So you can imagine you have 10 groups of skittles. In each group theres 5 skittles. So all together there would be 50 red skittles. Sooo based on the infromation there would be 50 red skittles expected in the box. I hope this helped pls mark me as brainliest!!

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chocolate chip cookie can be separated by physical means and it is not the same throughout. How would you classify it
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