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3 years ago

Work out the highest common factor of 42 and 63

Mathematics

1 answer:

emmainna [20.7K]3 years ago

6 0

3 | 42. 63
——————
14. 31

Nothing else’s can be divided into the others

The number on the side is the GCF which is 3

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Suppose that 35 people are divided in a random manner into two teams in such a way that one team contains 10 people and the othe

Effectus [21]

Answer:

0.5798 or 57.98%

Step-by-step explanation:

The total number of ways to form the two teams is the combination of choosing 10 people out of 35 (₃₅C₁₀). The number of possibilities that A and B are both on the 10-people team is given by the combination of choosing 8 people (since two are fixed) out of 33 (₃₃C₈).The number of possibilities that A and B are both on the 25-people team is given by the combination of choosing 10 people out of 33 (₃₃C₈).

Therefore, the probability that two particular people A and B will be on the same team is:

$P = \frac{_{33}C_8+_{33}C_{10}}{_{35}C_{10}} \\\\P=\frac{\frac{33!}{(33-8)!8!}+\frac{33!}{(33-10)!10!} }{\frac{35!}{(35-10)!10!}} \\\\P=\frac{69}{119} = 0.5798$

The probability is 0.5798 or 57.98%.

8 0

2 years ago

Which expression represents the phrase "three times the sum of a number and 4"?

Alexxandr [17]

The answer is D. 3(x+4)

3 0

3 years ago

In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,275 a

KATRIN_1 [288]

Answer:

100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

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 $2,275 and a standard deviation of $290.

This means that $\mu = 2275, \sigma = 290$

Sample of 65:

This means that $n = 65, s = \frac{290}{\sqrt{65}}$

Finding the mean to be at least $2,095 per month

This is 1 subtracted by the p-value of Z when X = 2095. So

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

By the Central Limit Theorem

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

$Z = \frac{2095 - 2275}{\frac{290}{\sqrt{65}}}$

$Z = -5$

$Z = -5$ has a p-value of 0.

1 - 0 = 1

100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

7 0

3 years ago

Any equation can be written in function notation O True False

Fynjy0 [20]

Answer: True

Step-by-step explanation:

7 0

2 years ago

Aiden buys two bags of chips at $1.09 each and a 20 ounce soda for $1.20 at the gas station.He knows that the state tax is 5.5.

Natalka [10]

Aiden will receive $1.43 from a $5 bill.

If the state tax is 5.5%, you can use the equation below to solve for the total cost, t.

t = 1.055 (2 × 1.09 + 1.20)
t = 1.055 (2.18 + 1.20)
t = 1.055 (3.38)
t = 3.5659

You can round 3.5659 to $3.57. Finally, you subtract 3.57 from 5 to find the amount of change Aiden will receive, c.

c = 5 - 3.57
c = 1.43

7 0

3 years ago