The environmental science club is printing T-shirts for its 15 members. The printing company charges a certain amount for each shirt plus a setup fee of $20. If the T-shirt order costs a total of $162.50, how much does the company charge for each shirt?

Answers

Answer 1

Answer:

Final answer:

After subtracting the setup fee from the total cost, the remaining amount ($142.50) is divided by the number of t-shirts (15) to find the cost of each shirt, which is $9.5.

Explanation:

The total cost for the T-shirt order is $162.50 and this includes a $20 setup fee. If you subtract this setup fee from the total cost, you will be left with the total cost of the actual T-shirts.

This gives us: $162.50 - $20 = $142.50.

The total cost of the T-shirts is $142.50, and this is for the 15 members of the club. To find out a cost of each shirt, you would divide this amount by the number of shirts, which is 15:

$142.50 / 15 = $9.5.

So, the company charges $9.5 for each shirt.

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Answer 2

Answer:

Answer:

x=9.5

Step-by-step explanation:

Let be the cost of each shirt. From the information provided in the problem, we can setup the following equation:

Solving for will give us the answer:

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According to a recent survey of households, the poll found that 41 % of the adults watching a special event on TV enjoyed the commercials more than the event itself. Consider a random sample of nine adults who watched the special event. Complete parts a through d below.a. For this experiment, define the event that represents a "success".
i. A success is an adult who did not enjoy the commercials more than the event on TV itself.
ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b. What is the probability that less than four people enjoyed the commercials more than the event?
c. What is the probability that exactly six or seven people enjoyed the commercials more than the event?
d. What is the mean for this binomial distribution?

Answers

Answer:

a) ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b) P(X < 4) = 0.4576

c) P(X=6) + P(X=7) = 0.1064

d) Mean = 3.69

Step-by-step explanation:

a) The population parameter stated in the survey is the event that represents a success. Hence, A success is an adult who enjoyed the commercials more than the event on TV itself.

b) The probability that less than four people enjoyed the commercials more than the event

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of adults sampled = 9

x = Number of successes required = number of people that enjoyed the commercial more than the event on TV = less than 4

p = probability of success = probability of enjoying the commercial more than the event = 0.41

q = probability of failure = probability of NOT enjoying the commercial more than the event = 1 - 0.41 = 0.59

P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.00866299582 + 0.05418043148 + 0.15060323326 + 0.24419846296

P(X < 4) = 0.45764512351 = 0.4576

c) The probability that exactly six or seven people enjoyed the commercials more than the event = P(X=6) + P(X=7)

Using the Binomial distribution formula

P(X=6) + P(X=7) = 0.08194801935 + 0.02440582659 = 0.106353846 = 0.1064

d) Mean = expected value of people that would enjoy the commercial more than the main event = np = 9×0.41 = 3.69

Hope this Helps!!!

Answer:

a) ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b) $P(X=0)=(9C0)(0.41)^0 (1-0.41)^(9-0)=0.0087$

$P(X=1)=(9C1)(0.41)^1 (1-0.41)^(9-1)=0.0.54$

$P(X=2)=(9C2)(0.41)^2 (1-0.41)^(9-2)=0.151$

$P(X=3)=(9C3)(0.41)^3 (1-0.41)^(9-3)=0.244$

And adding we got:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)=0.0087+0.054+0.151+0.244=0.458$

c) $P(6 \leq X \leq 7)$

$P(X=6)=(9C6)(0.41)^6 (1-0.41)^(9-6)=0.082$

$P(X=7)=(9C7)(0.41)^7 (1-0.41)^(9-7)=0.0244$

And adding we got:

$P(6 \leq X \leq 7)=0.082+0.0244=0.106$

d) $\mu = np =9*0.41=3.69$

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:

$X \sim Binom(n=9, p=0.41)$

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:

$nCx=(n!)/((n-x)! x!)$

Part a

The success on this case is:

ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

Part b

For this case we want this probability:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)$

And we can find the individual probabilities and we got:

$P(X=0)=(9C0)(0.41)^0 (1-0.41)^(9-0)=0.0087$

$P(X=1)=(9C1)(0.41)^1 (1-0.41)^(9-1)=0.0.54$

$P(X=2)=(9C2)(0.41)^2 (1-0.41)^(9-2)=0.151$

$P(X=3)=(9C3)(0.41)^3 (1-0.41)^(9-3)=0.244$

And adding we got:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)=0.0087+0.054+0.151+0.244=0.458$

Part c

For this case we want this probability:

$P(6 \leq X \leq 7)$

$P(X=6)=(9C6)(0.41)^6 (1-0.41)^(9-6)=0.082$

$P(X=7)=(9C7)(0.41)^7 (1-0.41)^(9-7)=0.0244$

And adding we got:

$P(6 \leq X \leq 7)=0.082+0.0244=0.106$

Part d

For this case the mean is given by:

$\mu = np =9*0.41=3.69$

A die is rolled twice.What is the probability that the first roll was a 6 and the second roll was an odd number?

Answers

Answer:

1/12

Step-by-step explanation:

1/6 * 3/6 (First roll has a one in 6 chance, second 3 in 6)

1*3 / 36 =

3 / 36 =

1/12

How much of a 3/4 of cup serving is in a 2/3 cup of yogurt?

Answers

Answer:

8/9

Step-by-step explanation:

could i have brailiest plz it isnt a must tho thx

Find the surface area of the cone in terms of pie 18 height 12 radius

Answers

144π cm²

Answer:

Solution given:

diameter (d)= 12cm

radius (r)=12/2=6 cm

slant height(l)=18cm

Now

Total surface area of cone=πr(r+l)π*6(6+18)=144π cm²

Please help! Will Mark brainliest!

Answers

Answer:

Step-by-step explanation:

i not fully sure if this is right

Miguel has 22 cans of regular soda and 99 cans of diet soda. If he decides to sell it by package with the same number of regular soda and diet soda in one pack without leaving one, how many equal packages can he make? How many of regular soda and diet soda in one package?

Answers

3 regular sodas and 1 diet

Final answer:

The greatest common divisor (GCD) of 22 and 99 is 11. Therefore, Miguel can make 11 equal packages where each package has 2 cans of regular soda and 9 cans of diet soda.

Explanation:

This problem is about finding the greatest common divisor (GCD) of two numbers, also known as the greatest common factor. The number of packages Miguel can make, and the amount of regular and diet soda in each, depend on the GCD of 22 (number of regular soda) and 99 (number of diet soda).

To find the GCD, you can use the Euclidean Algorithm. However, it is easily observed in this case that 22 and 99 can both be divided exactly by 11, hence, 11 is the greatest common divisor. This means Miguel can prepare 11 packages where each package contains 2 cans of regular soda and 9 cans of diet soda.

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