1. The number of letters received in the mail over the past week is recorded.

Factor completely: x³ - 9x

scoray [572]

Answer:

x(x+3)(x-3)

Step-by-step explanation:

Factor out common term x

=x(x^2-9)

Factor x^2-9;

(x+3)(x-3)

=x(x+3)(x-3)

3 0

2 years ago

Read 2 more answers

Owens birthday cake weights 6 T. (LOL). How many pounds does it weigh?

Inga [223]

Answer:

12000 pounds is your answer

8 0

2 years ago

R+6<10 what’s the answer?

Vera_Pavlovna [14]

Answer:

r < 4

Step-by-step explanation:

r+6<10

r < 4

3 0

2 years ago

Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. assume that σ is known to be 36.8

Delvig [45]

We are given the following data:

Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22

We are to find the confidence intervals for 90%, 95% and 98% confidence level.

Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.

Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.645* \frac{36.8}{ \sqrt{22}}=110.69$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.645* \frac{36.8}{ \sqrt{22}}=136.51$

Thus the 90% confidence interval will be (110.69, 136.51)

Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.96* \frac{36.8}{ \sqrt{22}}=108.22$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.96* \frac{36.8}{ \sqrt{22}}=138.98$

Thus the 95% confidence interval will be (108.22, 138.98)

Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-2.327* \frac{36.8}{ \sqrt{22}}=105.34$
Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+2.327* \frac{36.8}{ \sqrt{22}}=141.86$

Thus the 98% confidence interval will be (105.34, 141.86)

Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)

As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.

3 0

3 years ago

5 Quick algebra 1 questions for 50 points! Only answer if you know all 5, Tysm! :)

PIT_PIT [208]

The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

<h3>How to determine the equations?</h3>

When a linear equation is represented as:

Ax + By = C

The slope (m) is:

m = -A/B

When the linear equation is represented as:

y = mx + c

The slope is m

A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m

Using the above highlights, the equations of the lines are:

6. y = -2x + 5; (2, 7)

The slope is:

m = -2

The perpendicular slope is:

n = 1/2

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/2(x - 2) + 7

Evaluate

y = 1/2x - 1 + 7

This gives

y = 1/2x + 6

7. y = -5; (11, 15)

The slope is:

m = 0

The perpendicular slope is:

n = 1/0 = undefined

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 15

8. Graph ; (-12, 10)

The slope is:

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

Using the points on the graph, we have:

m = (2 - 3)/(3 - 4)

m = 1

The perpendicular slope is:

n = -1

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = -1(x + 12) + 10

y = -x - 12 + 10

Evaluate

y = -x - 2

9. y = -1/6x + 1; (-2, -9)

The slope is:

m = -1/6

The perpendicular slope is:

n = 6

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 6(x + 2) - 9

Evaluate

y = 6x + 12 - 9

This gives

y = 6x + 3

10. 6x + 2y = 14; (12, 0)

The slope is:

m = -6/2

m = -3

The perpendicular slope is:

n = 1/3

The equation of the perpendicular line is:

y = n(x - x1) + y1

This gives

y = 1/3(x - 12) + 0

Evaluate

y = 1/3x - 4

Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4

Read more about linear equations at:

brainly.com/question/13763238

#SPJ1

5 0

1 year ago