A shop is selling notebooks for £1.50 each.

Members of the student concil are conducting a fundraiser by selling school calendars. After selling 80 calendars, they had a lo

Oksana_A [137]

Answer:

a) $y=8x-1000$

b) $profit=\$8$

c) They'd have lost $1000 if they had sold no calendars.

Step-by-step explanation:

a) The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

In this case we know that "y" represents the profit of loss and "x" the number of calendars sold.

Then, according to the exercise, the line passes through these two points:

$(80,-360)$ and $(200,600)$

Then, we can find the slope of the line with the formula $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-360-600}{80-200}=8$

Now, we can substitute the slope and one of those points into $y=mx+b$ and solve for "b":

$600=8(200)+b\\\\b=-1000$

Then, subtituting values, we get that the equation that describes the relation between the profit of loss and the number of calendars sold, is:

$y=8x-1000$

b) The slope of the line is the profit they made from selling each calendar

$profit=8$

c) The y-intercept is the amount they would have lost if they had sold no calendars:

$b=-1000$

They'd have lost $1000 if they had sold no calendars.

6 0

3 years ago

Lori bought a shirt and a hat at half-off sale. If she spent a total of $21 on the two items, what was the original price of the

Rzqust [24]

Answer:

41

Step-by-step explanation:

first you do 21×2 and that's literally it

3 0

3 years ago

One year, the population of a city was 64,000. Several years later it was 53,120. Find the percent decrease.

ohaa [14]

Answer:

17% i think

Step-by-step explanation:

4 0

2 years ago

(8x² + 3x) - 4x² + x-4

serg [7]

Answer:

4x^2+4x-4

Step-by-step explanation:

8x^2 + 3x - 4x^2 + x - 4

= 8x^2 - 4x^2 + 3x + x - 4

= 4x^2 + 4x - 4

4 0

1 year ago

(10 points)Assume IQs of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice

vesna_86 [32]

Answer:

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Step-by-step explanation:

To solve this question, we need to use the binomial and the normal probability distributions.

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.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Probability the president will have an IQ of at least 107.5

IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that $\mu = 100, \sigma = 15$

This probability is 1 subtracted by the p-value of Z when X = 107.5. So

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

$Z = \frac{107.5 - 100}{15}$

$Z = 0.5$

$Z = 0.5$ has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 probability that the president will have an IQ of at least 107.5.

Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So

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

$Z = \frac{130 - 100}{15}$

$Z = 2$

$Z = 2$ has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549$

$P(X \geq 1) = 1 - P(X = 0) = 0.0451$

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?

0.3085 probability that the president will have an IQ of at least 107.5.

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Independent events, so we multiply the probabilities.

0.3082*0.0451 = 0.0139

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

8 0

3 years ago