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3 years ago

Write a function rule for the table. x f(x) (–3, 1) (–2, 2) (–1, 3) (0, 4)

Mathematics

2 answers:

inn [45]3 years ago

7 0

The answer is (1,1) a liner function

Mila [183]3 years ago

3 0

Hope this helps but the function rule for this table is f(x)=x+4

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The ages of john and carl add up to 28 years total. John is 20 years older than carl. How many years old is carl?

natima [27]

The correct answer would be that Carl is 4 years old. If John is 20 years older than Carl, that would make him 24. 24 + 4 = 28 years. Therefore, Carl must be 4 years old.

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3 years ago

What's the equivalent algebraic expression?

densk [106]

-10c+70, just distribute the the -10 to everything in the expression

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3 years ago

The original price is $60.The sales price is $45. What is the percent of discount?

MariettaO [177]

Hey there!

To start, first subtract 45 from 60 to find the amount of money taken off from the discount:
60-45
=15

Because 15 dollars have been taken off the original price, you can find the percent of discount by setting up this proportion where x represents the percent of discount:
15/60=x/100

Now, cross multiply and solve for x:
1500=60x
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Therefore, your discount would be 25%.

Hope this helps and have a marvelous day! :)

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3 years ago

Which sequence is modeled by the graph below?

shepuryov [24]

Answer:6

Step-by-step explanation:Which sequence is modeled by the graph below?

9Hold on, our servers are swamped. Wait for your answer to fully load.

• (5,8)

7 7.

4 +

. (4,4)

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(2, 1)

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3 years ago

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm197.5 cm and a standard deviation

fiasKO [112]

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

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 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.

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.

In this question, we have that:

$\mu = 197.5, \sigma = 8.3$

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

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

$Z = \frac{210.9 - 197.5}{8.3}$

$Z = 1.61$

$Z = 1.61$ has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now $n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14$

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

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

By the Central Limit Theorem

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

$Z = \frac{196 - 197.5}{2.14}$

$Z = -0.7$

$Z = -0.7$ has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

5 0

4 years ago