Identify the remainder when 4x3 - 4x + 12<br> is divided by x + 2.

Determine the intercepts of the line.

aleksley [76]

Answer:

x-intercept : (-250, 0)

y-intercept : (0,100)

Step-by-step explanation:

Looking at the line plotted, you can see when and where the blue line intersects with the x-axis and y-axis.

6 0

3 years ago

It is known that 50% of adult workers have a high school diploma. If a random sample of 8 adult workers is selected, what is the

son4ous [18]

Answer:

85.56% probability that less than 6 of them have a high school diploma

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have a high school diploma, or they do not. The probability of an adult having a high school diploma is independent of other adults. So we use the binomial probability distribution 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.

50% of adult workers have a high school diploma.

This means that $p = 0.5$

If a random sample of 8 adult workers is selected, what is the probability that less than 6 of them have a high school diploma

This is P(X < 6) when n = 8.

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

In which

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

$P(X = 0) = C_{8,0}.(0.5)^{0}.(0.5)^{8} = 0.0039$

$P(X = 1) = C_{8,1}.(0.5)^{1}.(0.5)^{7} = 0.0313$

$P(X = 2) = C_{8,2}.(0.5)^{2}.(0.5)^{6} = 0.1094$

$P(X = 3) = C_{8,3}.(0.5)^{3}.(0.5)^{5} = 0.2188$

$P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734$

$P(X = 5) = C_{8,5}.(0.5)^{5}.(0.5)^{3} = 0.2188$

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0039 + 0.0313 + 0.1094 + 0.2188 + 0.2734 + 0.2188 = 0.8556$

85.56% probability that less than 6 of them have a high school diploma

7 0

3 years ago

Julie has 4/3 cups of flour.She needs 2/5 cups of flour.How will she get the amount.

valentina_108 [34]

Answer:

Step-by-step explanation:

You need to set up a ratio for the original recipe and then use that ratio for the new one.

If we need 3 cups of flour for every 4 cups of sugar, we have a 3 c flour/4 c sugar ratio, or 3/4

The new ratio is 9 c of flour for ? c of sugar. Those ratios have to be the same, so we set up an equation like this:

3/4 = 9/?

In order to keep the same ratio, you have to multiply by the same number. Since 3*3 = 9, multiply 4*3 to get your answer.

8 0

3 years ago

Determine the vertical asymptote for the rational function f(x) = x-4 over 3x +2

Ghella [55]

Answer: (b) x = -2/3

<u>Step-by-step explanation:</u>

The vertical asymptote is the restriction on x.

The denominator cannot be equal to zero so that it the restriction.

Set the denominator equal to zero and solve for x to find the asymptote.

3x + 2 = 0

3x = -2

x = -2/3

8 0

3 years ago

--Marking Brainliest whoever answers this first, please hurry

Studentka2010 [4]

The slope of the line is 0.35

x = number of items sold

y = total price in dollars

Therefore,

using slope formula,

The slope is rise over run. The slope of a line is the measure of its steepness.

<h3>Slope equation:</h3>

m = y₂ - y₁ / x₂ - x₁

where

y₂ = 3.85

y₁ = 2.45

x₂ = 11

x₁₁ = 7

Therefore,

m = 3.85 - 2.45 / 11 - 7

m = 1.4 / 4

m = 0.35

learn more on slope here; brainly.com/question/24911901

5 0

2 years ago

Identify the remainder when 4x3 - 4x + 12 is divided by x + 2.