Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length

To address this issue, we will utilize the formula for determining the distance from a point to a line.

The formula is:

distance = | a x + b y + c | / sqrt (a^2 + b^2)

We have the line equation:

y = 2 x + 4

Rearranging it results in:

<span>y – 2 x – 4 = 0 --> a = -2, b = 1, c = -4</span>

The coordinates given are:

(-4, 11) = (x, y)

Substituting into the distance formula:

distance = | -2 * -4 + 1 * 11 + -4 | / sqrt [(- 2)^2 + (1)^2]

distance = 15 / sqrt (5)

distance ≈ 6.7

<span>Thus, the tree is approximately 6.7 ft from the zip line.</span>

Answer:

75 dollars in coupons.

250 dollars in dividends.

She achieved a profit of 600 - 425 = 175 from her stock investment.

Her complete income sums up to 250 + 75 + 175 = 500.

If all this is taxed at 10%, her tax will be 500 *.1 = 50.

Answer:

a) The likelihood that none of the sampled employees are from the Hawaii plant is 1.74%.

b) The chance that exactly 1 employee from the sample is found working in the Hawaii plant is 8.70%.

c) There is an 89.56% chance that 2 or more employees in the sample are from the Hawaii plant.

d) The probability that 9 employees from the sample are working at the Texas plant is 8.70%.

Step-by-step explanation:

Each employee has two potential employment locations: either Texas or Hawaii. Thus, the binomial probability distribution can be utilized to solve this scenario.

Binomial probability distribution

This distribution defines the probability of achieving exactly x successes in n trials where there are only two outcomes.

Here, denotes the number of ways to choose x objects from a set of n, represented by the subsequent formula.

And p is the probability of success occurring.

In this context, we know:

The sample comprises 10 employees, therefore .

a. Calculate the probability that none of the sampled employees are from the Hawaii plant (to 4 decimals)?

Given that 20 out of 60 employees are based in Hawaii:

We aim to find P(X = 0).

Thus, the likelihood that none in the sample are from Hawaii stands at 1.74%.

b. Calculate the probability that 1 employee from the sample is from the Hawaii plant?

This is represented as P(X = 1).

Therefore, there is an 8.70% possibility that 1 employee in the sample comes from Hawaii.

c. Calculate the probability that 2 or more employees in the sample are from the Hawaii plant?

We can observe two scenarios: either fewer than 2 employees are from Hawaii or 2 and beyond. The combined probabilities equal decimal 1. So:

We seek to find .

From problems a and b, we possess values for both probabilities.

Accordingly, the chance that 2 or more employees in this sample operate at the Hawaii plant is 89.56%.

d. Calculate the likelihood that 9 employees in the sample are working at the Texas plant?

This corresponds to the probability found in part b for 1 employee working in Hawaii.

Consequently, there is an 8.70% chance that 9 employees belong to the Texas plant.

Answer:

According to my cupcake recipe, it yields $12$ cupcakes and calls for $1\frac{1}{2}$ sticks of butter. I can only purchase whole sticks of butter.

Consequently, a single whole stick of butter will suffice to prepare $100$ cupcakes.

Answer: Ana should produce more fudge, and Leo should produce more toffee.

Step-by-step explanation:

Comparative advantage defined: A person or country has a comparative advantage producing a good if their opportunity cost for it is lower than someone else's.

In this case, Ana and Leo will both benefit if they focus on the product for which they have the lower opportunity cost.

(a) Ana’s production possibilities:

If she spends all her time making fudge: 3 pounds; or toffee: 2 pounds.

Opportunity cost of 1 pound fudge = 2/3 = 0.66 pounds toffee

Opportunity cost of 1 pound toffee = 3/2 = 1.5 pounds fudge

(b) Leo’s production opportunities:

All time making fudge: 4 pounds; or toffee: 5 pounds.

Opportunity cost of 1 pound fudge = 5/4 = 1.25 pounds toffee

Opportunity cost of 1 pound toffee = 4/5 = 0.8 pounds fudge

Since Ana’s opportunity cost for fudge is lower than Leo’s, she should specialize in fudge production.

Conversely, Leo has a lower opportunity cost for toffee, so he should focus on producing toffee.