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2 years ago

How do I factor an expression using the GCF?

Mathematics

1 answer:

Anni [7]2 years ago

4 0

Answer:

use the distributive property

Step-by-step explanation:

Use the distributive property to rewrite the expression with the GCF factored out.

<u>Example</u>:

ab +ac +ad . . . . has terms with a common factor of 'a'

When the common factor is factored out, the distributive property tells you the equivalent is ...

= a(b +c +d)

If 'a' is the greatest common factor, then b, c, d are mutually prime and no more factors can be removed to outside the parentheses.

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Name 3 non-collinear points

Evgen [1.6K]

Points A, B, C, D, E, F are called non - collinear points.

3 0

3 years ago

What is the width of a rectangle with length 14cm and area 161 cm^2

Inessa05 [86]

Answer:

Step-by-step explanation:

The area of a rectangle can be found with the formula $A = l*w$ , where $l$ is the length of the rectangle and $w$ is the width.

From the given problem statement, we know that $l = 14$ and $A = 161$ , so we can fill in those values in the formula anbd solve for $w$ to get the width:

$A = l*w$

$161 = 14w$

Divide both sides by $14$ to isolate $w$ by itself:

$\frac{161}{14} = \frac{14w}{14}$

$w = 11.5$

3 0

3 years ago

Read 2 more answers

A survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries,

Andru [333]

Answer:

A. Null and alternative hypothesis:

$H_0: \mu_d=0\\\\H_a:\mu_d\neq 0$

B. Yes. At a significance level of 0.05, there is enough evidence to support the claim that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

P-value = 0.00002

C. As the difference is calculated as (population 1 − population 2), being population 1: groceries and population 2: dinning out, and knowing there is evidence that the true mean difference is positive, we can say that the groceries annual credit card charge is higher than dinning out annual credit card charge.

The point estimate is the sample mean difference d=$840.

The 95% confidence interval for the mean difference between the population means is (490, 1190).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

Then, the null and alternative hypothesis are:

$H_0: \mu_d=0\\\\H_a:\mu_d\neq 0$

The significance level is 0.05.

The sample has a size n=42.

The sample mean is M=840.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1123.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1123}{\sqrt{42}}=173.2827$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{840-0}{173.2827}=\dfrac{840}{173.2827}=4.848$

The degrees of freedom for this sample size are:

$df=n-1=42-1=41$

This test is a two-tailed test, with 41 degrees of freedom and t=4.848, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=2\cdot P(t>4.848)=0.00002$

As the P-value (0.00002) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

We have to calculate a 95% confidence interval for the mean difference.

The t-value for a 95% confidence interval and 41 degrees of freedom is t=2.02.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.02 \cdot 173.283=350$