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2 years ago

What does it mean to factor an expression?

1 answer:

vladimir1956 [14]2 years ago

8 0

Factoring an expression means to break the expression down into small bits where we can multiply them together to find its original expression.

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What is the equation of the trend line? Enter your answers in the boxes. K = _J +_

MrRissso [65]

The y-intercept of the trend line is (0,28). The slope of this line is
28-0
m = --------- = 2
14-0

Thus, the equation of the trend line, in variables K and J, is

K = 2J + 28

8 0

2 years ago

The diameter of a circle is 36 yards. What is the circle's circumference? Use 3.14 for .

Firlakuza [10]

Answer:
113.04

Explanation:
So, the formula is C=pi x d

Once you substitute in the number given the equation is now .. C= pi x 36

36 x 3.14=113.04

Therefore, the circles circumference is 113.04

6 0

2 years ago

Read 2 more answers

Write the log equation as an exponential equation. you do not need to solve for x.

vovikov84 [41]

Answer:

2x^5log=1/6

Step-by-step explanation:

using the natural log (e), we were able to give the power of 5 to 2x and then take it out from the parantheses

5 0

2 years ago

What is an equation of the line that passes through the points (-4, -2) and (8, 1)? Put your answer in fully reduced form.

Alexxx [7]

Answer:

y=1/4x-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(1-(-2))/(8-(-4))

m=(1+2)/(8+4)

m=3/12

m=1/4

y-y1=m(x-x1)

y-(-2)=1/4(x-(-4))

y+2=1/4(x+4)

y=1/4x+4/4-2

y=1/4x+1-2

y=1/4x-1

8 0

3 years ago

A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. In a random sam

soldi70 [24.7K]

Answer:

a) $52.8-2.02\frac{3.9}{\sqrt{40}}=51.554$

b) $52.8+2.02\frac{3.9}{\sqrt{40}}=54.046$

c) $52.8-2.71\frac{3.9}{\sqrt{40}}=51.129$

d) $52.8+2.71\frac{3.9}{\sqrt{40}}=54.471$

e) Yes, depends of the confidence level.

At 95 % of confidence the value 54.1985 pounds is not included on the interval. At 5% of significance the statement is FALSE.

At 99 % of confidence the value 54.1985 pounds is included on the interval. So at 1% of significance the statement is TRUE.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X =52.8$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=3.9 represent the sample standard deviation

n=40 represent the sample size

a) What is the lower limit of the 95% interval? Give your answer to three decimal places

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=40-1=39$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,39)".And we see that $t_{\alpha/2}=2.02$

Now we have everything in order to replace into formula (1):

$52.8-2.02\frac{3.9}{\sqrt{40}}=51.554$

b) What is the upper limit of the 95% interval? Give your answer to three decimal places

$52.8+2.02\frac{3.9}{\sqrt{40}}=54.046$

So on this case the 95% confidence interval would be given by (51.554;54.046)

c) What is the lower limit of the 99% interval? Give your answer to three decimal places

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,39)".And we see that $t_{\alpha/2}=2.71$

Now we have everything in order to replace into formula (1):

$52.8-2.71\frac{3.9}{\sqrt{40}}=51.129$

d) What is the upper limit of the 99% interval? Give your answer to three decimal places

$52.8+2.71\frac{3.9}{\sqrt{40}}=54.471$

So on this case the 99% confidence interval would be given by (51.129;54.471)

e) Consider the claim that the mean amount of garbage per bin is 54.1985 pounds. Is the following statement true or false? The decision about the claim would depend on whether we use a 95% or 99% confidence interval: True/False

Yes, depends of the confidence level.

At 95 % of confidence the value 54.1985 pounds is not included on the interval. At 5% of significance the statement is FALSE.

At 99 % of confidence the value 54.1985 pounds is included on the interval. So at 1% of significance the statement is TRUE.

3 0

3 years ago