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2 years ago

An ice cream store has two new flavors: Fantasy and Ecstasy. Each barrel of Fantasy requires 4

Mathematics

1 answer:

Y_Kistochka [10]2 years ago

8 0

Answer:

Fantasy: 3 barrels
Ecstasy: 1 barrel

Step-by-step explanation:

Given

Fantasy uses 4 lb of nuts, 3 lb of chocolate, for a profit of $50

Ecstasy uses 4 lb of nuts, 1 lb of chocolate, for a profit of $40

In stock are 16 lb of nuts, 10 lb of chocolate

Find

amount of each to maximize profit

Solution

Let x and y represent barrels of Fantasy and Ecstasy, respectively. Then the limitations on production are ...

4x +4y ≤ 16 . . . lb of nuts

3x +y ≤ 10 . . . . lb of chocolate

We want to maximize

50x +40y

The graph shows the feasible region. Its vertices are ...

(0, 4), (3, 1), (3.33, 0)

Profit is maximized at $190 when production is 3 barrels of Fantasy and 1 barrel of Ecstasy.

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One of the sides of a parallelogram is 4.2 cm and the altitude to that side is 3.6 cm. Find the perimeter of the parallelogram i

dexar [7]

Area of parallelogram = base * height
base 1 = 4.2 cm
height 1 = 3.6 cm
∴ Area = 4.2 * 3.6 = 15.12

let the other base 2 = x
∴ the altitude of this base = height 2 = 2.4
∴Area = 2.4 x = 15.12
Solve for x
∴ x = 6.3 cm

∴ The perimeter of parallelogram = 2( base 1 + base 2)
= 2 ( 4.2 + 6.3 ) = 21 cm

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2 years ago

Kim solved the equation below by graphing a system of equations. log2(3x-1)= log4(x+8) What is the approximate solution to the e

kifflom [539]

Answer:

(1.35, 1.6)

Step-by-step explanation:

A screenshot of the graph is attached.

Once we graph the equations $y=\log_2(3x-1)$ and $y=\log_4(x+8)$ , the solution to this system will be their intersection point.

Tracing the graph on the calculator, we see that the point of intersection is at about (1.35, 1.6).

6 0

2 years ago

Read 2 more answers

When Ryan is serving at a restaurant, there is a 0.75 probability that each party will order drinks with their meal. During one

Triss [41]

Answer:

0.82 = 82% probability that at least one party will not order drinks

Step-by-step explanation:

For each party, there are only two possible outcomes. Either they will order drinks with their meal, or they will not. The probability of a party ordering drinks with their meal is independent of other parties. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

When Ryan is serving at a restaurant, there is a 0.75 probability that each party will order drinks with their meal.

This means that $p = 0.75$

During one hour, Ryan served 6 parties. Assuming that each party is equally likely to order drinks, what is the probability that at least one party will not order drinks?

6 parties, so n = 6.

Either all parties will order drinks, or at least one will not. The sum of the probabilities of these events is decimal 1. So

$P(X = 6) + P(X < 6) = 1$