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3 years ago

Is the length of the hypotenuse of a right triangle with legs that mea-

Mathematics

1 answer:

icang [17]3 years ago

4 0

Answer:
Irrational Number

Step-by-step explanation:
So, since it's a right triangle, you can use Pythagorean Theorem to calculate the measure of the hypotenuse.

Pythagorean Theorem says the hypotenuse squared = the sum of the sides squared.

5² + 6² = 25 + 36 = 61

And the square root of 61 is 7.8102496.... and the decimal continues in no distinguishable pattern. Therefore, the length of the hypotenuse is an irrational number.

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Money Spent on Road Repair A politician wishes to compare the variances of the amount of money spent for road repair in two diff

Mkey [24]

Answer:

(A) Null Hypothesis, $H_0$ : $\sigma_1^{2} =\sigma_2^{2}$ {means that there is no significant difference in the variances of the amounts spent in the two counties}

Alternate Hypothesis, $H_A$ : $\sigma_1^{2} \neq \sigma_2^{2}$ {means that there is a significant difference in the variances of the amounts spent in the two counties}

(B) The F-table gives critical values of 0.359 and 2.781 for (14,17) degrees of freedom for the two-tailed test.

(C) The value of the F-test statistic is 0.611.

(D) We conclude that there is no significant difference in the variances of the amounts spent in the two counties.

Step-by-step explanation:

We are given that a politician wishes to compare the variances of the amount of money spent on road repair in two different counties.

The data are given here below;

County A County B

s1 = $11,596 s2 = $14,837

n1 = 15 n2 = 18

Let $\sigma_1^{2}$ = variances of the amounts spent in County A.

$\sigma_2^{2}$ = variances of the amounts spent in County B.

(A) So, Null Hypothesis, $H_0$ : $\sigma_1^{2} =\sigma_2^{2}$ {means that there is no significant difference in the variances of the amounts spent in the two counties}

Alternate Hypothesis, $H_A$ : $\sigma_1^{2} \neq \sigma_2^{2}$ {means that there is a significant difference in the variances of the amounts spent in the two counties}

The test statistics that would be used here Two-sample F-test statistics distribution;

T.S. = $\frac{s_1^{2} }{s_2^{2} } \times \frac{\sigma_2^{2} }{\sigma_1^{2} }$ ~ $F__n_1_-_1,_ n_2_-_1$

where, $s_1$ = sample standard deviation for County A = $11,596

$s_2$ = sample standard deviation for County B = $14,837

$n_1$ = sample size for County A = 15

$n_2$ = sample size for County B = 18

(B) Now at 0.05 level of significance, the F-table gives critical values of 0.359 and 2.781 for (14,17) degrees of freedom for the two-tailed test.

(C) So, the test statistics = $\frac{11,596^{2} }{14,837^{2} } \times 1$ ~ $F__1_4,_ 1_7$

= 0.611

The value of the F-test statistic is 0.611.

Now, as we can see that our test statistics lie within the range of critical values of F, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

(D) Therefore, we conclude that there is no significant difference in the variances of the amounts spent in the two counties.

7 0

3 years ago

Pleaseee help me!!!

Rus_ich [418]

Answer:

3 hours

Step-by-step explanation:

Since it will take the sprinkler 12 times longer to mow the entire lawn than 1/12 of it, it will take 1/4*12=3 hours, or the last answer choice. Hope this helps!

7 0

3 years ago

Lisa purchased almonds for $3.00 per pound and she spent $24.90. How many pounds of almonds did she purchase? The price went up

aleksandr82 [10.1K]

Answer:

1. Lisa purchased almonds for $3.00 and spent $24.90.

The quantity of almonds bought is therefore:

= Total amount spent / Cost per pound

= 24.90 / 3

= 8.3 pounds

2. If the price goes up to $3.50 per pound and the maximum Lisa can spend is $25, the number of pounds she can get is:

= Maximum amount for almonds / Price per almonds

= 25 / 3.5

= 7.14 pounds

5 0

3 years ago

Walter buys a bus pass for $30. Every time he rides the bus, money is deducted from the value of the pass. He rode 12 times and

Elenna [48]

50cent, 6 divided by 12 is 0.5

4 0

4 years ago

A church window consisting of a rectangle topped by a semicircle is to have perimeter p . find the radius of the semicircle if t

Y_Kistochka [10]

Answer:

$r=\dfrac{p}{4+\pi}$

Step-by-step explanation:

Let r be the radius of the semicircle, then 2r is the width of the rectangle. Let y be the length of the rectangle. The perimeter of the window consists of two lengths, one width and length of semicircle, then

$p=2y+2r+\pi r.$

Express y:

$y=\dfrac{p-2r-\pi r}{2}.$

The area of the window is

$A=y\cdot 2r+\dfrac{1}{2}\pi r^2.$

Substitute y into the area expression:

$A=\dfrac{p-2r-\pi r}{2}\cdot 2r+\dfrac{1}{2}\pi r^2=pr-2r^2-\pi r^2+\dfrac{1}{2}\pi r^2=pr-2r^2-\dfrac{1}{2}\pi r^2.$

Find the derivative A':

$A'=p-4r-\pi r.$

Equate A' to 0:

$p-4r-\pi r=0\Rightarrow r=\dfrac{p}{4+\pi}.$

When $r$ then $A'>0$ and the function A is increasing, when $r>\dfrac{p}{4+\pi},$ then $A'$ and the function A is decreasing. This means that at point $r=\dfrac{p}{4+\pi}$ the function A takes it maximal value (the area is maximal).

7 0

3 years ago