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3 years ago

The legs of a right triangle measure 5√2 cm and 4√2 cm. Find the area.

Mathematics

2 answers:

lianna [129]3 years ago

4 0

The area of right triangle=1/2*leg1*leg2=20 cm2

Eduardwww [97]3 years ago

3 0

Area of a triangle = 1/2 × 1st leg × 2nd leg
A = 1/2 × 5√2 × 4√2
A = 1/2 × 20×2
A = 20 cm²

In short, Your Answer would be 20 cm²

Hope this helps!

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The random variable x has the following probability distribution: x f(x) 0 .25 1 .20 2 .15 3 .30 4 .10 a. Is this probability di

Reptile [31]

Answer and Explanation:

Given : The random variable x has the following probability distribution.

To find :

a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

b. Calculate the expected value of x.

c. Calculate the variance of x.

d. Calculate the standard deviation of x.

Solution :

First we create the table as per requirements,

x P(x) xP(x) x² x²P(x)

0 0.25 0 0 0

1 0.20 0.20 1 0.20

2 0.15 0.3 4 0.6

3 0.30 0.9 9 2.7

4 0.10 0.4 16 1.6

∑P(x)=1 ∑xP(x)=1.8 ∑x²P(x)=5.1

a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.

$\sum P(X)=0.25+0.20+0.15+0.30+0.10$

$\sum P(X)=1$

Yes it is a probability distribution.

b) The expected value of x is defined as

$E(x)=\sum xP(x)=1.8$

c) The variance of x is defined as

$V=\sum x^2P(x)-(\sum xP(x))^2\\V=5.1-(1.8)^2\\V=5.1-3.24\\V=1.86$

d) The standard deviation of x is defined as

$\sigma=\sqrt{V}$

$\sigma=\sqrt{1.86}$

$\sigma=1.136$

5 0

2 years ago

Add me on Playstation NathanTheSnail for 200 points! Please.

mars1129 [50]

Answer:

You aren't even giving 200 points.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The Slow Ball Challenge or The Fast Ball Challenge.

cupoosta [38]

Answer:

Fast ball challenge

Step-by-step explanation:

Given

Slow Ball Challenge

$Pitches = 7$

$P(Hit) = 80\%$

$Win = \$60$

$Lost = \$10$

Fast Ball Challenge

$Pitches = 3$

$P(Hit) = 70\%$

$Win = \$60$

$Lost = \$10$

Required

Which should he choose?

To do this, we simply calculate the expected earnings of both.

Considering the slow ball challenge

First, we calculate the binomial probability that he hits all 7 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 7$ --- pitches

$x = 7$ --- all hits

$p = 80\% = 0.80$ --- probability of hit

So, we have:

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

$P(7) =^7C_7 * 0.80^7 * (1 - 0.80)^{7 - 7}$

$P(7) =1 * 0.80^7 * (1 - 0.80)^0$

$P(7) =1 * 0.80^7 * 0.20^0$

Using a calculator:

$P(7) =0.2097152$ --- This is the probability that he wins

i.e.

$P(Win) =0.2097152$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 -0.2097152$

$P(Lose) = 0.7902848$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.2097152 * \$60 + 0.7902848 * \$10$

Using a calculator, we have:

$Expected = \$20.48576$

Considering the fast ball challenge

First, we calculate the binomial probability that he hits all 3 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 3$ --- pitches

$x = 3$ --- all hits

$p = 70\% = 0.70$ --- probability of hit

So, we have:

$P(3) =^3C_3 * 0.70^3 * (1 - 0.70)^{3 - 3}$

$P(3) =1 * 0.70^3 * (1 - 0.70)^0$

$P(3) =1 * 0.70^3 * 0.30^0$

Using a calculator:

$P(3) =0.343$ --- This is the probability that he wins

i.e.

$P(Win) =0.343$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 - 0.343$

$P(Lose) = 0.657$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.343 * \$60 + 0.657 * \$10$

Using a calculator, we have:

$Expected = \$27.15$

So, we have:

$Expected = \$20.48576$ -- Slow ball

$Expected = \$27.15$ --- Fast ball

<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>

5 0

2 years ago

302.406 + 7,710.826 What is the sum?

Alexus [3.1K]

Hi! I believe your answer is <u>8,013.232</u>. The work is shown below. I hope this helps you! Good luck and have a great day. ❤️✨

4 0

3 years ago

Read 2 more answers

Please answer -24x + 16y

Alex787 [66]

Answer:

-8(3x-2y)

Step-by-step explanation:

Factor out each number because 8 times 3 equals 24

And -2 times -8 is 16

3 0

3 years ago