Can someone explain how you would figure this out step by step.

Romashka [77]

9.9
With right triangles you can use the equation a^2 + b^2 = c^2. Since both a and b are 7, that makes it 7^2 + 7^2 = c^2 and from there 49 + 49 = c^2 and then 98 = c^2. Then go find C, you find the square root of 98 which is 9.899494937 or rounded as 9.9

Keep in mind a^2 + b^2 = c^2 only works for right triangles, it won’t work for any other ones.

3 0

3 years ago

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In a statistics class of students, have volunteered for community service in the past. If two students are selected at random fr

Lynna [10]

Answer:

We do not have the total number of students or volunteers.

I will put variables (and then random numbers) and solve it, then you can put the numbers that you need in the equations.

Suppose that the class has Y students, and X of these students have volunteered.

The probability of picking at random a student that has volunteered is equal to the number of students that had volunteered divided by the total amount of students:

p1 = X/Y

now, we must choose another student, but now the volunteers are X - 1, and the total number of students is also Y - 1 (because we already took one student)

now, the probability of selecting other will be:

p2 = (X- 1)/(Y - 1)

Then, the joint probability of both events is equal to the product of both probabilities:

P = p1*p2 = (X/Y)*((X-1)/(Y -1))

Suppose that there are 20 students, and 10 students that have volunteered, then the equations are:

P = (10/20)*(9/19) = 0.237

3 0

3 years ago

Direct stock plans are only offered by brokerage firms? <br> True or False

Hoochie [10]

Answer – False
Direct stock purchase plans (DSPPs) are not offered by brokerage firms; they are offered by companies. The company may however allow investors to purchase stock either purchase stock directly from the company or through a third party agent. Actually, the greatest advantage of using a DSPP is that it gives investors the ability to avoid paying commissions by not necessarily having to go through brokers <span>
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7 0

3 years ago

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A common way for two people to settle a frivolous dispute is to play a game of rock-paper-scissors. In this game, each person si

Leokris [45]

Answer:

(a) P(A) = 0.34

(b) P(B) = 0.33

(c) P(C) = 0.33

(d) The Complement of event A = 1 - P(A) = 0.66

Step-by-step explanation:

We are given that in the long run, roommate A chooses rock 36% of the time, and roommate B chooses rock 22% of the time; roommate A selects paper 32% of the time, and roommate B selects paper 25% of the time; roommate A chooses scissors 32% of the time, and roommate B chooses scissors 53% of the time.

Let the probability that roommate A chooses rock = P( $R_A$ ) = 0.36

The probability that roommate A chooses paper = P( $P_A$ ) = 0.32

The probability that roommate A chooses scissors = P( $S_A$ ) = 0.32

The probability that roommate B chooses rock = P( $R_B$ ) = 0.22

The probability that roommate B chooses paper = P( $P_B$ ) = 0.25

The probability that roommate B chooses scissors = P( $S_B$ ) = 0.53

(a) Let A = event that roommate A wins the game and thus does not have to wash the dishes.

This will happen only when roommate A chooses rock and roommate B chooses scissors or roommate A chooses paper and roommate B chooses rock or roommate A chooses scissors and roommate B chooses paper.

So, P(A) = $P(R_A) \times P(S_B) + P(P_A) \times P(R_B) + P(S_A) \times P(P_B)$

= (0.36 $\times$ 0.53) + (0.32 $\times$ 0.22) + (0.32 $\times$ 0.25)

= 0.1908 + 0.0704 + 0.08

P(A) = 0.34

(b) Let B = event that roommate B wins the game and thus does not have to wash the dishes.

This will happen only when roommate B chooses rock and roommate A chooses scissors or roommate B chooses paper and roommate A chooses rock or roommate B chooses scissors and roommate A chooses paper.

So, P(B) = $P(R_B) \times P(S_A) + P(P_B) \times P(R_A) + P(S_B) \times P(P_A)$

= (0.22 $\times$ 0.32) + (0.25 $\times$ 0.36) + (0.53 $\times$ 0.32)

= 0.0704 + 0.09 + 0.1696

P(B) = 0.33

(c) Let C = event that the game ends in a tie.

This will happen only when roommate A chooses rock and roommate B also chooses rock or roommate A chooses paper and roommate B also chooses paper or roommate A chooses scissors and roommate B also chooses scissors.

So, P(C) = $P(R_A) \times P(R_B) + P(P_A) \times P(P_B) + P(S_A) \times P(S_B)$

= (0.36 $\times$ 0.22) + (0.32 $\times$ 0.25) + (0.32 $\times$ 0.53)

= 0.0792 + 0.08 + 0.1696

P(C) = 0.3288 ≈ 0.33

(d) The complement of event A = P(A') = 1 - P(A)

= 1 - 0.34 = 0.66.

4 0

3 years ago

The physical plant at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The

Nikolay [14]

Answer:

$P(62< X< 72)= P(X$

Step-by-step explanation:

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

Let X the random variable who represent the courtship time (minutes).

From the problem we have the mean and the standard deviation for the random variable X. $E(X)=62, Sd(X)=5$