Select the number that would make this statement true: 496 ÷ _______

A homeowner plans to enclose a 200 square foot rectangular playground in his garden, with one side along the boundary of his pro

tigry1 [53]

Answer:

The dimensions are 50 and 100 square foot

Step-by-step explanation:

Let x = length of fenced side parallel to the side that borders the playground

y = length of each of the other two fenced sides

Then, x + 2y = 200

<=> x = 200-2y

The Area = xy = y(200-2y)

The dimensions of the playground that will minimize the homeowner's total cost for materials when the area of the playground is maximum. He can cover more area but with the same cost.

The graph of the area function is a parabola opening downward.

The maximum area occurs when y = -200/[2(-2)] = 50

=> x = 100

So the dimensions are 50 and 100 square foot

6 0

4 years ago

A salesman for a new manufacturer of cellular phones claims not only that they cost the retailer less but also that the percenta

professor190 [17]

Answer:

$z=\frac{0.094-0.04}{\sqrt{0.0642(1-0.0642)(\frac{1}{180}+\frac{1}{225})}}=2.203$

$p_v =P(Z>2.203)= 0.0138$

Comparing the p value with the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then the claim from the retailer makes sense at 1% of significance.

Step-by-step explanation:

Use a significance level of α=0.01 for the test.

Data given and notation

$X_{1}=17$ represent the number of defectives from the retailer

$X_{2}=9$ represent the number of defectives from the competitor

$n_{1}=180$ sample 1 selected

$n_{2}=225$ sample 2 selected

$p_{1}=\frac{17}{180}=0.094$ represent the proportion estimated for defectives from the retailer

$p_{2}=\frac{9}{225}=0.04$ represent the proportion estimated for defectives from the competitor

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.01$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the percentage of defective cellular phones found among his products, ( p1), will be no higher than the percentage of defectives found in a competitor's line, ( p2), the system of hypothesis would be:

Null hypothesis: $p_{1} \leq p_{2}$

Alternative hypothesis: $p_{1} > p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{17+9}{180+225}=0.0642$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.094-0.04}{\sqrt{0.0642(1-0.0642)(\frac{1}{180}+\frac{1}{225})}}=2.203$

Statistical decision

Since is a right sided test the p value would be:

$p_v =P(Z>2.203)= 0.0138$

Comparing the p value with the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then the claim from the retailer makes sense at 1% of significance.

5 0

3 years ago

Please answer i need help

White raven [17]

Answer:

5-3í

Step-by-step explanation:

Because the root of nine is three, equaling 5-3í

3 0

3 years ago

Read 2 more answers

Find the length of a rectangle with a diagonal of 10 and a height of 8.

Dmitry_Shevchenko [17]

Answer:

The length of the rectangle is 6.

Step-by-step explanation:

Given: The diagonal of a rectangle is 10 and the height is 8.

Please understand, that a diagonal, divides the rectangle into two tringles.

To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!

EXTRA:

If you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.

Instead of 5, a diagonal of 10 is given (factor of 2 bigger).

Instead of 4, the height of 8 is given (factor of 2 bigger). By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?

Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).

a² + b² = c²

a = length (and is unknown)

b = height = 8

c = hypothenusa/diagonal = 10

Substitute the numbers given:

a² + 8² = 10²

Subtract 8² left and right of the = sign.

a² +8² -8² = 10² - 8²

a² + 0 = 100 - 64

a² = 36

a = + - √36

a = + - 6

EXTRA:

You can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.

a = 6

So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.

8 0

3 years ago

What is the expanded form of 70.26?

valentinak56 [21]

Can someone please help me with this problem

6 0

3 years ago

Select the number that would make this statement true: 496 ÷ ________ = 49.6 (3 points)