SLOPE AND PARALLELISM

At a certain coffee shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the n

wolverine [178]

Answer:

(1) The probability that the shop owner sells over 2000 cups of coffee in a week is 0.2514.

(2) The shop owner has no reasonable chance to expect earning a profit more than $300.

(3) The probability that the shop owner will sell a doughnut to more than half of his coffee customers is 0.2611.

Step-by-step explanation:

Let X = number of cups of coffee sold and Y = number of donuts sold.

The random variable X follows a Normal distribution with parameters μ = 320 and σ = 20.

The random variable Y follows a Normal distribution with parameters μ = 150 and σ = 12.

The shop owner opens the shop 6 days a week.

(1)

Compute the probability that the shop owner sells over 2000 cups of coffee in a week as follows:

$P(X>2000)=P(\frac{X-\mu}{\sigma}>\frac{2000-(6\times320)}{6\times20})\\=P(Z>0.67)\\=1-P(Z$

Thus, the probability that the shop owner sells over 2000 cups of coffee in a week is 0.2514.

(2)

The equation representing the profit earned on selling 1 cup of coffee and 1 doughnut in a day is:

P = 0.5X + 0.4Y

Compute the probability that the shop owner earns more than $300 as profit as follows:

$P(Profit>300)=P(\frac{Profit-\mu}{\sigma}>\frac{300-((0.5\times320)+(0.4\times150))}{\sqrt{0.5^{2}(20)^{2}+0.4^{2}(12)^{2}}})\\=P(Z>7.21)\\\approx0$

The probability of earning a profit more then $300 is approximately 0.

Thus, the shop owner has no reasonable chance to expect earning a profit more than $300.

(3)

The expression representing the statement "he'll sell a doughnut to more than half of his coffee customers" is:

Y > 0.5X

Y - 0.5X > 0

Compute the probability of the event (Y - 0.5X > 0) as follows:

$P(Y - 0.5X > 0)=P(\frac{(Y - 0.5X) -\mu}{\sigma}>\frac{0-(150-(0.5\times320}{\sqrt{12^{2}+0.5^{2}20^{2}}})\\=P(Z>0.64)\\=1-P(Z$

Thus, the probability that the shop owner will sell a doughnut to more than half of his coffee customers is 0.2611.

8 0

3 years ago

What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5

jeyben [28]

Answer:

$\displaystyle c = \frac{20}{3}$

Step-by-step explanation:

According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one c within (a, b) such that f'(c) = 0.

We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a c in (5, 8) such that g'(c) = 0.

So, differentiate the function. We can take the derivative of both sides with respect to x:

$\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right]$

Differentiate:

$g'(x) = -21x^2+182x-280$

Let g'(x) = 0:

$0 = -21x^2+182x-280$

Solve for x. First, divide everything by negative seven:

$0=3x^2-26x+40$

Factor:

Zero Product Property:

$x-2=0 \text{ or } 3x-20=0$

Solve for each case. Hence:

$\displaystyle x=2 \text{ or } x = \frac{20}{3}$

Since the first solution is not within our interval, we can ignore it.

Therefore:

$\displaystyle c = \frac{20}{3}$

3 0

3 years ago

On a line segment, M is between L and N. If MN = 10.4 and LN = 19.4, what is LM?

algol [13]

Answer:

GOOGLE

Step-by-step explanation:

GOOGLE MY HUMAN

8 0

3 years ago

Malik is making 36 small pack of chili spices and 15 large packs of chili spices. A small pack contains 2.35 ounces of spices.A

Elena L [17]

The answer is
To find how many ounces you need to make, you multiply the number of packs by how many ounces.
So, it would look like:
36*2.35=84.6
15*10.8=162

Then you add the ounces together and you have your answer:
162+84.6=246.6 ounces

5 0

3 years ago

Read 2 more answers

Solve for t. -5 − 2t = 3t

allsm [11]

T is equal to -1.

Add 2t to both sides of the equation. -5 = 5t
Divide both sides of the equation by -5. 1 = -t
Multiply both sides of the equation by -1. -1 = t

4 0

3 years ago

Read 2 more answers