Ask question

Ask question

All categories

3 years ago

14

Tyina is buying 12 shirts for the drama club. She will choose a style for the blank shirts and then pay an additional charge of

$2.75 for each shirt to have the club logo. If Tyina cannot spend more than $99, how much can she spend on each blank shirt? Write and solve an inequality to find the possible cost of each blank shirt.

1 answer:

tensa zangetsu [6.8K]3 years ago

6 0

Answer:

Cost of each blank shirt is less than or equal to $ 5.5

Step-by-step explanation:

Let x denotes cost of each blank shirt.

Total number fo shirts bought by Tyina = 12

Amount charged for each shirt to have the club logo = $2.75

So,

Amount charged for 12 shirts to have the club logo = $12(2.75)=\$33$

As Tyina cannot spend more than $99,

$12x+33\leq 99$

Now solve the inequality.

$12x+33\leq 99\\12x\leq 99-33\\12x\leq 66\\x\leq \frac{66}{12}\\ x\leq 5.5$

So,

Cost of each blank shirt is less than or equal to $ 5.5

You might be interested in

Ou have found a house that you would like to purchase. The amount of the home is $225,000. You would like to finance the home th

Tpy6a [65]

Answer:

A. $22,500

Step-by-step explanation:

10% = 10/100 = 1/10

To divide a decimal number by 10, move the decimal point one place to the left (remove a zero):

$225000./10 = $22500.0 = $22500

5 0

3 years ago

A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40

bezimeni [28]

Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

a. How large was the sample used in this survey?

We have that $s = 25, \sigma = 400$ . We want to find n, so:

$s = \frac{\sigma}{\sqrt{n}}$

$25 = \frac{400}{\sqrt{n}}$

$25\sqrt{n} = 400$

$\sqrt{n} = \frac{400}{25}$

$\sqrt{n} = 16$

$(\sqrt{n})^2 = 16^2[tex][tex]n = 256$

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

45.14% probability that the point estimate was within ±15 of the population mean

3 0

2 years ago

An apartment complex rents an average of 2.3 new units per week. If the number of apartment rented each week Poisson distributed

masya89 [10]

Answer:

$P(X\leq 1) = 0.331$

Step-by-step explanation:

Given

Poisson Distribution;

Average rent in a week = 2.3

Required

Determine the probability of renting no more than 1 apartment

A Poisson distribution is given as;

$P(X = x) = \frac{y^xe^{-y}}{x!}$

Where y represents λ (average)

y = 2.3

<em>Probability of renting no more than 1 apartment = Probability of renting no apartment + Probability of renting 1 apartment</em>

<em />

Using probability notations;

$P(X\leq 1) = P(X=0) + P(X =1)$

Solving for P(X = 0) [substitute 0 for x and 2.3 for y]

$P(X = 0) = \frac{2.3^0 * e^{-2.3}}{0!}$

$P(X = 0) = \frac{1 * e^{-2.3}}{1}$

$P(X = 0) = e^{-2.3}$

$P(X = 0) = 0.10025884372$

Solving for P(X = 1) [substitute 1 for x and 2.3 for y]

$P(X = 1) = \frac{2.3^1 * e^{-2.3}}{1!}$

$P(X = 1) = \frac{2.3 * e^{-2.3}}{1}$

$P(X = 1) =2.3 * e^{-2.3}$

$P(X = 1) = 2.3 * 0.10025884372$

$P(X = 1) = 0.23059534055$

$P(X\leq 1) = P(X=0) + P(X =1)$

$P(X\leq 1) = 0.10025884372 + 0.23059534055$

$P(X\leq 1) = 0.33085418427$

$P(X\leq 1) = 0.331$

Hence, the required probability is 0.331

6 0

2 years ago

HELP!!! Please I need work shown I have no clue how to do this and I need a good answer please and thank you

zheka24 [161]

Factorize x²+7x+12 ===> (x+3)(x+4)

Factorize x²-3x-28 ===> (x-7)(x+4)

4x + 12 can be written====> 4(x+3)

Then the question could be written as follows:

[(x+3)(x+4) / (x-7)(x+4) ] / 4(x+3) = [(x+3)(x+4) / (x-7)(x+4) ].[4(x+30]
After simplification you get 1 / 4(x-7)

7 0

3 years ago

The ratio of men to women working for a company is 5 to 7 if there are 133 women working for the company what is the total numbe

Mrrafil [7]

228 employees in total

6 0

2 years ago