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Vikki [24]
3 years ago
11

Explain how you find ordered-pair solutions of the equation 3x – 5y = 15, and then find two such solutions.'

Mathematics
1 answer:
Luda [366]3 years ago
5 0
The constant on the right is divisible by the coefficients on the left, so two solutions are
  (x, y) = (5, 0) or (0, -3)

The slope of the line is 3/5, so increaing y by 3 and x by 5 will result in another solution. One general parametric solution is then
  x = 5n
  y = 3n-3
_____
Integer values of n will result in integer solutions. Any value of n will yield numbers that satisfy the equation.

In general, the extended Euclidean algorithm can be used to find integer solutions. Then adding multiples of some number n to y and x in the ratio of the slope of the line will yield other solutions.
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A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the
hichkok12 [17]

Answer:

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

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 establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

A statistician calculates that 8% of Americans own a Rolls Royce.

This means that p = 0.08

Sample of 595:

This means that n = 595

Mean and standard deviation:

\mu = p = 0.08

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.08*0.92}{595}} = 0.0111

What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?

Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.

Probability the proportion is less than 5%:

P-value of Z when X = 0.05. So

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

By the Central Limit Theorem

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

Z = \frac{0.05 - 0.08}{0.0111}

Z = -2.7

Z = -2.7 has a p-value of 0.0035

2*0.0035 = 0.0070

0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%

8 0
3 years ago
Jennifer brought $ 24.75 to the baseball game. She spent $ 12.45 on drinks and snacks. How much money does she have left over?
Arturiano [62]
If you do 24.75-12.45 you get 12.30. So there you go!

5 0
3 years ago
Find the distance between (2,3) (4, -7)<br><br> Find the distance between (-9,-4) (-3,6)
stealth61 [152]

Answer:

Find the distance between (2,3) (4, -7)

= 6

Find the distance between (-9,-4) (-3,6)

= -10

5 0
3 years ago
Read 2 more answers
Hey there! posted picture of question help please
kakasveta [241]
For this case we have the following function:
 f (x) = (1/3) * (4 ^ x)
 We must evaluate the function for x = 2
 We have then:
 f (2) = (1/3) * (4 ^ 2)
 Rewriting:
 f (2) = (1/3) * (16)
 f (2) = 16/3
 Answer:
 
The function evaluated at x = 2 is:
 
f (2) = 16/3
 
option A
7 0
3 years ago
Enter the product.<br> 27<br> X 7
Kay [80]

Answer:

189

Step-by-step explanation:

7 x 27 = 189

3 0
3 years ago
Read 2 more answers
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