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4 years ago

50 PTS ANSWER ASAP

Mathematics

2 answers:

Nat2105 [25]4 years ago

8 0

Answer:

y-2 = 4/3(x+3) (point slope form)

y = 4/3x+6 slope intercept form

Step-by-step explanation:

We need to find the slope of the line 4x -3y =12

Solve for y

Subtract 4x from each side

4x-4x -3y = -4x +12

-3y = -4x+12

Divide by -3

-3y/-3 =-4x/-3 +12/-3

y = 4/3 x -4

The slope is 4/3

We want a line that is parallel, so it will have the same slope

We have the slope and a point, so we can use point slope form

y-y1 = m(x-x1)

y-2 = 4/3(x--3)

y-2 = 4/3(x+3)

Distribute

y-2 = 4/3x +4

Add 2 to each side

y-2+2 = 4/3x +4

y = 4/3x +4+2

y = 4/3x+6

Alex17521 [72]4 years ago

3 0

Answer:

y = 4/3 x + 6

Step-by-step explanation:

The first step is to solve for y in the given equation.

4x - 3y = 12 Add 3y to both sides.

4x -3y+3y= 12 + 3y Combine

4x = 12 + 3y Subtract 12 from both sides.

4x-12 = 3y Switch

3y = 4x - 12 Divide by 3

3y/3=4x/3 - 12/3 Do the division

y = (4/3)x - 4

You went to all that trouble so that you could get the slope of the line. The slope is 4/3. It is the number in front of the x that is the slope when the number in front of the y = 1.

Now we need to use the point to get the value of the y intercept in the new line.

x = - 3

y = 2

y = (4/3)x + b where b is the intercept. Substitute

2 = 4/3 * - 3 + b Simplify

2 = - 4 + b Add 4 to both sides.

2 + 4 = b

b = 6

The lines equation is

y = 4/3 x + 6

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3 years ago

An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed fro

skad [1K]

Answer:

The probability is 70% that the sample mean amount of juice will be contained between 4.9168 ounces and 5.0832 ounces.

Step-by-step explanation:

To solve this question, the Normal probability distribution and the Central Limit Theorem are important.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 5, \sigma = 0.4, n = 25, s = \frac{0.4}{\sqrt{25}} = 0.08$

The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?

The lower end of this interval is the value of X when Z has a pvalue of 0.5 - 0.7/2 = 0.15

The upper end of this interval is the value of X when Z has a pvalue of 0.5 + 0.7/2 = 0.85

Lower end

X when Z has a pvalue of 0.15. So X when $Z = -1.04$ .