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3 years ago

A line has a slope of -1/2 and a why intercept of -2

Mathematics

1 answer:

Mice21 [21]3 years ago

7 0

Answer:

y = -1/2x - 2

Step-by-step explanation:

The formula of the slope-intercept is y = mx + b. The m is the slope while y is the y-intercept.

y = -1/2x - 2

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Show that 2x +1 is a factor of 2x3 +5x2+4x+1 and factories completely

larisa [96]

$\text{According to the factor theorem, if f(b) = 0, then x-b is a factor of f(x).}\\\\\text{Given that,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\f\left(-\dfrac 12 \right) = 2\left( - \dfrac 12 \right)^3 +5 \left( - \dfrac 12 \right)^2 +4 \left( - \dfrac 12 \right) +1 \\\\\\~~~~~~~~~~~~=-2 \cdot \dfrac 18 + 5 \cdot \dfrac 14 -2 +1 \\\\\\~~~~~~~~~~~=\dfrac 54 -\dfrac14 -1\\\\\\~~~~~~~~~~~=\dfrac 44 -1 \\\\\\~~~~~~~~~~~=1-1\\\\\\~~~~~~~~~~~=0\\\\\text{So,}~ 2x +1 ~ \text{is a factor of f(x).}$

$\text{Now,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\~~~~~~=2x^3+x^2 +2x^2 +2x +2x+1\\\\~~~~~~=x^2(2x+1) +2x(2x+1) + (2x+1)\\\\~~~~~~=(2x+1)(x^2 +2x +1)\\\\~~~~~~=(2x+1)(x+1)^2$

3 0

2 years ago

ANSWER BOTH thanksss

NNADVOKAT [17]

Answer:

x=-400

x=-95

Step-by-step explanation:

They are negative because a negative times a negative is a positive.

3 0

3 years ago

Read 2 more answers

Can somebody please solve for x and y, if you get the answers correct I'll give you extra points

ohaa [14]

Answer:

1) x = 18 2) x = 7

Step-by-step explanation:

Edit: Decided to solve the second too! :)

12/16 = x/(x+6)

12x + 72 = 16x

72 = 4x

x = 18

(-4 + 4x)/64 = 27/72

-288 + 288x = 1,728

288x = 2,016

x = 7

6 0

2 years ago

Scores at a local high school on the American College Testing (ACT) college entrance exam follow the normal distribution with a

san4es73 [151]

Answer:

a) The mean is 18 and the standard deviation is 1.79.

b) The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

c) 0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 18 and a standard deviation of 8.

This means that $\mu = 18, \sigma = 8$

Sample of 20:

This means that $n = 20, s = \frac{8}{\sqrt{20}} = 1.79$

(a) Calculate the mean and standard deviation of the sampling distribution of x¯.

By the Central Limit Theorem, the mean is 18 and the standard deviation is 1.79.

(b) Interpret the standard deviation from part (a).

The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

(c) Find the probability that a sample of 20 students has a mean score of 19.5 or more.

This is 1 subtracted by the pvalue of Z when X = 19.5. So

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

By the Central Limit Theorem

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