What is the equation of the linear function represented by the table?

Fred and Sue want to fence in a rectangular area in their yard for a vegetable garden. Suppose that they have 30 feet of fencing

larisa [96]

Answer:

a=35x−x^2

Step-by-step explanation:

Having

70 ft of fencing with a

width of x

feet and knowing the perimeter of a rectangle is

p=2w+2l

we can state the length of the garden as:

70=2x+2l

and solving for l

we know the length with be:

2l=70−2x or l=35−x

And then knowing the formula for the area of a rectangle is

a=w⋅l

we can write the equation as:

a=x⋅(35−x)a=35x−x^2

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2 years ago

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A random sample of 150 men found that 88 of the men excercise regularly, while a random sample 200 women found that 130 of the w

melamori03 [73]

Answer:

The hypothesis is:

H₀: $p_{X}-p_{Y}=0$ .

Hₐ: $p_{X}-p_{Y}$ .

Step-by-step explanation:

Let X = number of men who exercise regularly and Y = number of women who exercise regularly.

The information provided is:

$n_{X}=150\\X=88\\n_{Y}=200\\Y=130$

Compute the sample proportion of men and women who exercise regularly as follows:

$\hat p_{X}=\frac{X}{n_{X}}=\frac{88}{150}=0.587$

$\hat p_{Y}=\frac{Y}{n_{Y}}=\frac{130}{200}=0.65$

The random variable X follows a Binomial distribution with parameters n = 150 and $\hat p_{X}=0.587$ .

The random variable Y also follows a Binomial distribution with parameters n = 200 and $\hat p_{Y}=0.65$ .

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\hat p=p$