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vladimir2022 [97]
2 years ago
14

The slope of GA is -5. Find the slope of the line perpendicular to the given line

Mathematics
1 answer:
Temka [501]2 years ago
5 0

Perpendicular slopes are opposite reciprocals.

This means the slope of the line perpendicular to GA will be the opposite reciprocal of -5.

Reciprocal of -5: -1/5

Opposite of -1/5: 1/5

The slope of the line perpendicular to GA is 1/5.

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20 subtracted from three times a number is 6 more than the number
kompoz [17]
<h3>20 subtracted from three times a number is 6 more than the number. Then the number is 13</h3>

<em><u>Solution:</u></em>

<em><u>Given statement is:</u></em>

20 subtracted from three times a number is 6 more than the number

We can translate the sentence into algebraic expression

Let "a" be the unknown number

Then,

20 subtracted from three times "a" is 6 more than "a"

Which means,

3a - 20 = 6 + a

3a - a = 6 + 20

2a = 26

Divide both sides by 2

a = 13

Thus the number is 13

3 0
3 years ago
What is five percent of 150
3241004551 [841]
7.5 .. multiply .05 times 150
6 0
3 years ago
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Simplify the expression 10-4x(6+5-1) divided by 8+7
Eddi Din [679]
Simple,

writing out the problem...

\frac{10-4x(6+5-1)}{15}

Simplify it...

-4x(6+5-1)

-4x(11-1)

-4x(10)

-40x

Making it look like...

\frac{10-40x}{15}

Cancel out the common factors...

Thus making the answer:

- \frac{2(4x-1)}{3}.

8 0
3 years ago
Evaluate Functions<br> Given f(x) = 2x + 6 and g(x) = 5x - 1<br> Evaluate f(-2)
ZanzabumX [31]

Answer:

f(-2) = -4x + 6

Step-by-step explanation:

f(x) = 2x + 6

f(-2) = -2(2x) + 6

f(-2) = -4x + 6

4 0
2 years ago
Read 2 more answers
A sample size 25 is picked up at random from a population which is normally
Margarita [4]

Answer:

a) P(X < 99) = 0.2033.

b) P(98 < X < 100) = 0.4525

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 100 and variance of 36.

This means that \mu = 100, \sigma = \sqrt{36} = 6

Sample of 25:

This means that n = 25, s = \frac{6}{\sqrt{25}} = 1.2

(a) P(X<99)

This is the pvalue of Z when X = 99. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{99 - 100}{1.2}

Z = -0.83

Z = -0.83 has a pvalue of 0.2033. So

P(X < 99) = 0.2033.

b) P(98 < X < 100)

This is the pvalue of Z when X = 100 subtracted by the pvalue of Z when X = 98. So

X = 100

Z = \frac{X - \mu}{s}

Z = \frac{100 - 100}{1.2}

Z = 0

Z = 0 has a pvalue of 0.5

X = 98

Z = \frac{X - \mu}{s}

Z = \frac{98 - 100}{1.2}

Z = -1.67

Z = -1.67 has a pvalue of 0.0475

0.5 - 0.0475 = 0.4525

So

P(98 < X < 100) = 0.4525

6 0
2 years ago
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