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3 years ago

The product of (a − b)(a − b) is a perfect square trinomial

Mathematics

1 answer:

SOVA2 [1]3 years ago

6 0

Answer:

always

Step-by-step explanation:

this product can also be written as a^2 - ab - ab + b^2

which is a^2 - 2(ab) + b^2

a perfect square trinomials equation is

a^2 + 2(ab) + b^2

and this qualifies

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Information about the proportion of a sample that agrees with a certain statement is given below. Use StatKey or other technolog

lara31 [8.8K]

Answer:

$SE=\sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.35 (1-0.35)}{100}}=0.048$

If we replace the values obtained we got:

$0.35 - 1.96\sqrt{\frac{0.35(1-0.35)}{100}}=0.257$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.443$

The 95% confidence interval would be given by (0.257;0.443)

Step-by-step explanation:

Notation and definitions

$X=35$ number of people that agree.

$n=100$ random sample taken

$\hat p=\frac{35}{100}=0.35$ estimated proportion of people that agree

$p$ true population proportion of peopl that agree

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The standard error is given by:

$SE=\sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.35 (1-0.35)}{100}}=0.048$

If we replace the values obtained we got:

$0.35 - 1.96\sqrt{\frac{0.35(1-0.35)}{100}}=0.257$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.443$

The 95% confidence interval would be given by (0.257;0.443)

6 0

4 years ago

Read 2 more answers

What should the following rate be divided by to convert it to a unit rate? 6 inches 12 hours

iragen [17]

Answer:

0.5 Inches per hour

Step-by-step explanation:

Most normal people won't know exactly what unit rate is, or how to calculate it. So I'm here to help!

This is a fraction equal to

6 inches ÷ 12 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 12

6 inches ÷ 12

12 hours ÷ 12

0.5 inches

1 hour

0.5 inches

hour

= 0.5 inches per hour

Glad I was able to help!

7 0

3 years ago

From a point on the ground, Geoff measures the angle of elevation of a 130m tower to be 36°. How far from the base of the tower

Gala2k [10]

Answer:

Geoff is 16.77 m far from base of tower.

Step-by-step explanation:

steps are in the picture below.

<h3>Note:if you need to ask any question please let me know.</h3>

6 0

3 years ago

What is the congruence correspondence, if any, that will prove the given triangles congruent?

alina1380 [7]

Answer:

SAS

Step-by-step explanation:

the two triangles have two congruent sides and one congruent angle

5 0

3 years ago

The equation y=0.002x-0.20 can be used to determine the approximate profit,y in dollars,of producing x items.solve for x. How ma

lakkis [162]

Answer:

1966600 items must be produced in other to profit $3933

Step-by-step explanation:

from the equation y = 0.002x -0.20

where y is the profit in dollars

and x is the number of items

then to get the number of item to be produced in other to profit $3933 ?

will be by substituting $3933 for y in the equation and solving for x,

3933 = 0.002x - 0.20

Firstly you will add 0.20 to both sides, which will be

3933 + 0.20 = 0.002x - 0.20 + 0.20

3933.20 = 0.002x

then we will divide both sides by 0.002

3933.20 / 0.002 = 0.002x / 0.002

therefore, x = 1966600

5 0

4 years ago