Brayden's horse gained 9 pounds over a 3 week

I struggle on this one to

Ksenya-84 [330]

Answer:

13. acute

14. right

15. 36

16. x = 14

Step-by-step explanation:

8 0

3 years ago

Prove that √2 is an irrational number and hence show that 3+5√3 is also irrational

cupoosta [38]

Answer:

square rooted numbers like the square root of 2 are irrational because when calculated they don't equal a whole number.

Step-by-step explanation:

3+5√3 = 11.66 // not whole - irrational

√2 = 1.4 // not whole - irrational

√25 = 5 // whole - rational

4 0

2 years ago

Suppose that A and B each randomly, and independently, choose 3 of 10 objects. Find the expected number of objects (a) chosen by

makkiz [27]

Answer:

a) N(A∩B) = 0.9

b) N(A∩B) = 4.9

c) N(A or B) = 4.2

Step-by-step explanation:

Given that A and B each randomly, and independently, choose 3 of 10 objects;

P(A) = P(B) = 3/10 = 0.3

P(A') = P(B') = 1 - 0.3 = 0.7

a) chosen by both;

Probability of being chosen by both;

P(A∩B) = 0.3 × 0.3 = 0.09

Expected Number of objects being chosen by both;

N(A∩B) = P(A∩B) × N(total) = 0.09×10

N(A∩B) = 0.9

b) not chosen by either A or B;

Probability of not being chosen by either A or B;

P(A'∩B') = 0.7 × 0.7 = 0.49

Expected Number of objects being chosen by both;

N(A'∩B') = P(A'∩B') × N(total) = 0.49×10

N(A∩B) = 4.9

c) chosen by exactly one of A and B.

Probability of being chosen by exactly one of A and B

P(A∩B') + P(A'∩B) = 0.3×0.7 + 0.7 × 0.3 = 0.42

Expected Number of objects being chosen by both;

N(A or B) = 0.42 × 10

N(A or B) = 4.2

6 0

3 years ago

Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa

Debora [2.8K]

Answer:

a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

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 8.7% and standard deviation 20.2%.

This means that $\mu = 8.7, \sigma = 20.2$

40 years:

This means that $n = 40, s = \frac{20.2}{\sqrt{40}}$

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

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

By the Central Limit Theorem

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

$Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}$

$Z = 1.35$

$Z = 1.35$ has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

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

$Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}$

$Z = -0.22$

$Z = -0.22$ has a pvalue of 0.4129

0.4129 = 41.29% probability that the mean return will be less than 8%

8 0

3 years ago

Which term describes the right of a lender to sell collateral to get back the principal if the borrower cannot repay the loan?

Ivanshal [37]

Answer:

Lien.

Step-by-step explanation:

A loan can be defined as an amount of money that is being borrowed from a lender and it is expected to be paid back at an agreed date with interest.

Generally, the financial institution such as a bank lending out the sum of money usually requires that borrower provides a collateral which would be taken over in the event that the borrower defaults (fails) in the repayment of the loan.

Lien is a term which describes the right of a lender to sell collateral to get back the principal if the borrower cannot repay the loan. In order to be able to determine whether a borrower would default on the repayment of a loan, lenders usually check the credit score of the borrower.

A credit score can be defined as a numerical expression between 300 - 850 that represents an individual's financial history and credit worthiness. Therefore, a credit score determines the ability of a borrower to obtain a loan from a lender.

This ultimately implies that, the higher your credit score, the higher and better it is to obtain a loan from a potential lender. A credit score ranging from 670 to 739 is considered to be a good credit score while a credit score of 740 to 799 is better and a credit score of 800 to 850 is considered to be excellent.

8 0

3 years ago