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4 years ago

9

The hypotenuse of a right triangle is 50 millimeters long. One leg of the right triangle is 30 millimeters long. What is the len

gth of the other leg

1 answer:

alexandr1967 [171]4 years ago

6 0

First. we use the Pythagorean theorem:
$a {}^{2} + b {}^{2} = c {}^{2}$
Add the numbers in
${30}^{2} + {b}^{2} = {50}^{2}$
start simplifying
${b}^{2} = 1600$
$b = 40$

So, the leg has a length of 40 mm.

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The Delucci family traveled on the highway for two hours at 70 miles per hour, and then three hours at 35 miles per hour. How fa

Zinaida [17]

(2 * 70) + (3 * 35) = 140 + 105 = 245 miles

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4 years ago

The one whoever solved it until 11 :00 am will be markrd as the branliest plus 20 points it arrange in ascending order with meth

Monica [59]

Answer:

1) 1/6, 1/3, 1/2, 3/4

2) 3/10, 2/5, 7/10, 4/5

3) 1/4. 7/12. 2/3, 5/6

4) 4/15. 11/30, 2/5, 7/10

Step-by-step explanation: Either convert all in a set to a common denominator, or convert to decimal fractions.

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3 years ago

HELP PLSSSSS I GIVE BRAINLY

dedylja [7]

Answer: 40 unit²

Step-by-step explanation:

A square pyramid is composed of 1 square and 4 congruent triangles

STEP ONE. Find the area of the square.

A=b²

b=base

A=b²=4²=14

STEP TWO. Find the area of the triangle

A=(1/2)bh

b=base

h=height

A=(1/2)bh

A=(1/2)(4)(3)

A=(1/2)(12)

A=6

There are 4 congruent triangles, so 6×4=24

The surface area of whole=24+16=40 unit²

Hope this helps!! :)

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7 0

3 years ago

Consider the following hypothesis test. : : The following results are for two independent samples taken from two populations. Ex

I am Lyosha [343]

Answer:

$z = -1.53$ --- test statistic

$p = 0.1260$ --- p value

Conclusion: Fail to reject the null hypothesis.

Step-by-step explanation:

Given

$n_1 = 80$ $\bar x_1= 104$ $\sigma_1 = 8.4$

$n_2 = 70$ $\bar x_2 = 106$ $\sigma_2 = 7.6$

$H_o: \mu_1 - \mu_2 = 0$ --- Null hypothesis

$H_a: \mu_1 - \mu_2 \ne 0$ ---- Alternate hypothesis

$\alpha = 0.05$

Solving (a): The test statistic

This is calculated as:

$z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} }}$

So, we have:

$z = \frac{104 - 106}{\sqrt{\frac{8.4^2}{80} + \frac{7.6^2}{70} }}$

$z = \frac{104 - 106}{\sqrt{\frac{70.56}{80} + \frac{57.76}{70}}}$

$z = \frac{-2}{\sqrt{0.8820 + 0.8251}}$

$z = \frac{-2}{\sqrt{1.7071}}$

$z = \frac{-2}{1.3066}$

$z = -1.53$

Solving (b): The p value

This is calculated as:

$p = 2 * P(Z < z)$

So, we have:

$p = 2 * P(Z < -1.53)$

Look up the z probability in the z score table. So, the expression becomes

$p = 2 * 0.0630$

$p = 0.1260$

Solving (c): With $\alpha = 0.05$ , what is the conclusion based on the p value

We have:

$\alpha = 0.05$

In (b), we have:

$p = 0.1260$

By comparison:

$p > \alpha$

i.e.

$0.1260 > 0.05$

So, we fail to reject the null hypothesis.

4 0

3 years ago

Fred is running on the school track. He can run 10 3 4 laps in 4 5 of an hour. How many laps can Fred run in one hour?

Triss [41]

Answer:

$13\frac{7}{16}$ laps can Fred run in one hour.

Step-by-step explanation:

Given Statement: Fred is running on the school track. He can run $10\frac{3}{4}$ laps in $\frac{4}{5}$ of an hour.

Unit rate are expressed as a quantity of 1, such as 3 feet per second or 7 miles per hour, they are called unit rates

From the given condition we have;

In $\frac{4}{5}$ he can run $\frac{43}{4}$ laps

Unit rate per hour = $\frac{\frac{43}{4} }{\frac{4}{5} }$

= $\frac{43}{4} \times \frac{5}{4} = \frac{215}{16}$ laps

Therefore, Fred can run in one hour is, $13\frac{7}{16}$ laps.

3 0

3 years ago