3(y + 8) = 2y - 6, when y = 30

9. Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2(

fomenos

Length: 2(x + 6); Width: 3.5x

A rectangle has 4 sides. 2 sides are lengths and 2 sides are widths.

The perimeter is the sum of the measures of all 4 sides.

perimeter = length + length + width + width

perimeter = 2(x + 6) + 2(x + 6) + 3.5x + 3.5x

Use the distributive property on 2(x + 6).

perimeter = 2x + 12 + 2x + 12 + 3.5x + 3.5x

Now let's group all terms with x first, then all the numbers.

perimeter = 2x + 2x + 3.5x + 3.5x + 12 + 12

Now we add like terms. Like terms have exactly the same variables and the same exponents. All terms with x are like terms and can be added together. All terms with no variable are like terms and can be added together.

perimeter = 11x + 24

11x and 24 are not like terms since 11x contains the variable x and 24 has no variable. Since 11x and 24 are not like terms, they cannot be added together. No more simplification can be done, and 11x + 24 is the answer.

Answer: 11x + 24

8 0

3 years ago

2520=r(2r+18) This is a geometry problem

GREYUIT [131]

Distribute then divide

8 0

3 years ago

A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.1 in. Determine the minimum sample

leva [86]

Answer:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (2)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got $z_{\alpha/2}=1.96$ , replacing into formula (2) we got:

$n=(\frac{1.96(0.25)}{0.1})^2 =24.01$

So the answer for this case would be n=25 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

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".

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

$\mu$ population mean (variable of interest)

$\sigma=0.25$ represent the population standard deviation

n represent the sample size (variable of interest)

Solution to the problem

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

And on this case we have that ME =0.1 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (2)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got $z_{\alpha/2}=1.96$ , replacing into formula (2) we got:

$n=(\frac{1.96(0.25)}{0.1})^2 =24.01$

So the answer for this case would be n=25 rounded up to the nearest integer

8 0

4 years ago

At Chestatee Middle School, 120 students are in choir. The ratio of girls to boys in choir is 5:3.

Serhud [2]

Let the total number of students be x;
given that the ratio of girls to boys is 5:3, then:
The equation that represents the number of girls will be:
5/8x
The equation that represents the number of boys will be :
3/8x
The equation that represents the total number of boys and girls will be:
5/8x+3/8x

B] suppose there are g number of girls. The equation that represents the number of boys in terms of number of girls will be:
(ratio of boys to girls)×(number of girls)
3/5×(g)
=(3g)/5

8 0

3 years ago

Read 2 more answers

the hypotenuse of a right triangle is 16 and one of the angle is 45 . find the length of the side opposite to that angle ?

Hoochie [10]

In a 90 45 45 triangle, the 2 legs each have a
length = hypotenuse / square root of 2
length = 16 / square root of 2
length = 16 / 1.4142135624 
length = 11.313708499

6 0

4 years ago

3(y + 8) = 2y - 6, when y = 30​

3(y + 8) = 2y - 6, when y = 30