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3 years ago

Can a triangle be formed with side lengths: 10, 12, 22

1 answer:

8 0

No. A squared plus b squared must equal c squared (Pythagorean theorem). 10 squared is 100, 12 squared is 144, they add up to 244 but 22 squared is 484…..much too large

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A. f(x) = l-2xl - 3 Domain: {1, 2, 3} Find the range

gizmo_the_mogwai [7]

Hello there!

We are given the function:

$\displaystyle \large{ f(x) = | - 2x| - 3} \\$

To find the range, we know that domain is the set of all x-values and also called 'input' while range is the set of all y-values and also called 'output'.

Basic Function - you add the input, you get the output. You add x-value in a function, you get y-value. You add domain, you get range.

So, we substitute x = 1,2 and 3 in the function.

x = 1

$\displaystyle \large{ f(1) = | - 2(1)| - 3} \\ \displaystyle \large{ f(1) = | - 2| - 3} \\$

Recall that any numbers in absolute value are always positive.

$\displaystyle \large{ f(1) = 2 - 3} \\ \displaystyle \large{ f(1) = - 1} \\$

x = 2

$\displaystyle \large{ f(2) = | - 2(2)| - 3} \\ \displaystyle \large{ f(2) = | - 4 | - 3} \\ \displaystyle \large{ f(2) = 4 - 3} \\ \displaystyle \large{ f(2) = 1}$

x = 3

$\displaystyle \large{ f(3) = | - 2(3)| - 3} \\ \displaystyle \large{ f(3) = | - 6| - 3} \\ \displaystyle \large{ f(3) = 6 - 3} \\ \displaystyle \large{ f(3) = 3}$

Therefore, Range: {-1,1,3}

Let me know if you have any questions!

Topic: Absolute Value Function / Modulus Function

6 0

3 years ago

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a st

madam [21]

Answer:

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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 $Z \leq 2$ or $Z \geq 2$ , the outcome X is considered to be unusual.

In this question:

$\mu = 8.21, \sigma = 1.9$

Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

This is the pvalue of Z when X = 5. So

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

$Z = \frac{5 - 8.21}{1.9}$

$Z = -1.69$

$Z = -1.69$ has a pvalue of 0.0455.

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

8 0

3 years ago

Nate and his friends are building a skateboard ramp for an upcoming contest. The length of the ramp on the blueprint is 7.6 inch

ICE Princess25 [194]

Answer:

30.4 feet.

Step-by-step explanation:

We have been given the length of the ramp on the blueprint is 7.6 inches. The scale on the blueprint is 1 inch to 4 feet. We are asked to find the actual length of the ramp.

We will use proportions to solve our given problem as:

$\frac{\text{Actual length}}{\text{Scale length}}=\frac{4\text{ ft}}{1\text{ inch}}$