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3 years ago

7

Ariel has 20 bouncy balls. He later then sold them for a price of $2 per ball to his best friend, Mike Hawk. Later, Ariel has go

tten back 1/69 of his original amount of bouncy balls and got 20 more. How many bouncy balls does Ariel have?

1 answer:

ValentinkaMS [17]3 years ago

6 0

Ariel has 40 balls left

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A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast,

KengaRu [80]

Answer:

see below

Step-by-step explanation:

If we let X represent the number of bagels produced, and Y the number of croissants, then we want ...

(a) Max Profit = 20X +30Y

(b) Subject to ...

6X +3Y ≤ 6600 . . . . . . available flour

X + Y ≤ 1400 . . . . . . . . available yeast

2X +4Y ≤ 4800 . . . . . . available sugar

_____

Production of 400 bagels and 1000 croissants will produce a maximum profit of $380.

__

In the attached graph, we have shaded the areas that are NOT part of the solution set. (X and Y less than 0 are also not part of the solution set, but are left unshaded.) This approach can sometimes make the solution space easier to understand, since it is white.

The vertex of the solution space that moves the profit function farthest from the origin is the one we are seeking. The point that does that is (X, Y) = (400, 1000).

4 0

3 years ago

A study investigating the relationship between age and annual medical expenses randomly samples 400 individuals in a city. It is

ICE Princess25 [194]

Answer:

The probability is 0.789

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 normally distributed samples are solved using 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.

In this problem, we have that:

$\sigma = 16, n = 400, s = \frac{16}{\sqrt{400}} = 0.8$

Find the probability that the mean age of the individuals sampled is within one year of the mean age for all individuals in the city.

Using $\mu = 30$ , this is the pvalue of Z when X = 31 subtracted by the pvalue of Z when X = 29. So

X = 31

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

By the Central Limit Theorem

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

$Z = \frac{31 - 30}{0.8}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

X = 29

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

$Z = \frac{29 - 30}{0.8}$

$Z = -1.25$

$Z = -1.25$ has a pvalue of 0.1056

0.8944 - 0.1056 = 0.7888

Rounded to three decimal places, 0.789

The probability is 0.789

4 0

3 years ago

Read 2 more answers

(2x-3)(x+5)<br> SHOW WORK FOR POINTS

vagabundo [1.1K]

(2x-3)(x+5)
Use foil to simplify, First multiply together the first terms of the pairs, then the outer terms, the middle terms, and finally the last terms. Then combine like terms.
2x^2+10x-3x-15 equals 2x^2+7x-15

5 0

3 years ago

Alma ask money to buy a bicycle of $150. his mom give him $40 at the moment and gives kyle $10 each month to pay the total of th

Tanya [424]

Answer: $40+$10x

Step-by-step explanation:

1. We already know he has $40.

2. 10x represent the 10 dollars he is paid per month.

5 0

3 years ago

What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months?

Rom4ik [11]

Since only the principal value, interest rate and interest period are given, we can deduce that "finance charge" only includes the interest to be paid at the end of the term. This can be obtained by subtracting the principal value from the future value which we will solve for.

The future value can be solved by using the following compound interest formula:

Let:
F = Future value
P = Principal value
r<span> = annual interest rate </span>
n<span> = number of times that interest is compounded per year</span>
t<span> = number of years</span>

F = P(1 + r/n)^nt

Substituting the given values:
F = 4250(1 + 0.1325/12)^(12*2)
F = 5531.54

Subtracting P from F:
Finance charge = 5531.54 - 4250 = 1281.54

Therefore the finance charge is $1,281.54

6 0

3 years ago