Expand the binomial (2x^2+y^2)^4

A student scored 75 and 97 on her first two quizzes. Write and solve a compound inequality to find the possible values for a thi

Rainbow [258]

Answer:

$85 \le \frac{75 + 97 + n}{3} \le 90$ ; $83 \le n \le 98$

Step-by-step explanation:

Score of the first two quizzes: 75 and 97

Let n represent the third score

Average score would be: $\frac{75 + 97 + n}{3}$ .

Given that the average score fall between 85 and 90, this can be represented by the compound inequality as shown below:

$85 \le \frac{75 + 97 + n}{3} \le 90$

Solve for n in each statement that makes up the compound inequality:

$85 \le \frac{75 + 97 + n}{3}$

$85 \le \frac{172 + n}{3}$

Multiply both sides by 3

$85*3 \le 172 + n$

$255 \le 172 + n$

Subtract 172 from each side of the inequality

$255 - 172 \le n$

$83 \le n$

Also,

$\frac{75 + 97 + n}{3} \le 90$

$\frac{172 + n}{3} \le 90$

Multiply both sides by 3

$172 + n \le 90*3$

$172 + n \le 270$

Subtract 172 from both sides of the inequality

$n \le 270 - 172$

$n \le 98$

Combining both together, the possible values of her third quiz score would be:

$83 \le n \le 98$

3 0

2 years ago

One less than three times a number is eight

fiasKO [112]

3 * 3 = 9 - 1 = 8

Hope this helped! Please mark brainliest if this helped at all! Thank you, I hope you have a great rest of your day!

8 0

3 years ago

Read 2 more answers

A formula is given that states 6x-k=wk. Solve this formula for k in terms of the other variables in the equation.

nadya68 [22]

Answer:

k = 6x/(w + 1)

Step-by-step explanation:

6x - k = wk

6x = wk + k

k(w+1) = 6x

k = 6x/(w + 1)

3 0

3 years ago

Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?

Drupady [299]

Answer:

B

Step-by-step explanation:

$y \times {4 \div 14 \frac{10}{4 |25 \\ | } }^{2}$

8 0

2 years ago

For which of the following counts would a binomial probability model be reasonable? a. The number of traffic tickets written by

timama [110]

Answer:

c. The number of 7's in a randomly selected set of five random digits from a table of random digits.

True, for this case we have a value fixed for n =5 and the probability is defined for each number 1/10 assuming numbers (0,1,2,3,4,5,6,7,8,9) so then the random variable "The number of 7's in a randomly selected set of five random digits" can be modelled with the binomial probability function.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n, p)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The conditions to apply this distribution is that we have the parameters fixed n and p.

Let's analyze one by one the possible solutions:

a. The number of traffic tickets written by each police officer in a large city during one month.

False, the number of traffic tickets written by each police is not a fixed amount always, so then the value of n change and we can't apply a binomial model for this case.

b. The number of hearts in a hand of five cards dealt from a standard deck of 52 cards that has been thoroughly shuffled.

False, not all the hands of size 5 are equal and since we can't ensure this condition then the binomial model not apply for this case

c. The number of 7's in a randomly selected set of five random digits from a table of random digits.

True, for this case we have a value fixed for n =5 and the probability is defined for each number 1/10 so then the random variable "The number of 7's in a randomly selected set of five random digits" can be modelled with the binomial probability function.

d. The number of phone calls received in a one-hour period.

False, the number of phone calls change by the hour and is not always fixed so then we don't have a valu for n, and the binomial model not applies for this case.

e. All of the above.

False option C is correct.

5 0

3 years ago