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Sergeeva-Olga [200]

3 years ago

12

Sabrina and Christie are running in a relay. Sabrina runs 100 meters in 13.6 seconds.Christie runs the same distance in 12.2 sec

onds.what is their total time

1 answer:

klasskru [66]3 years ago

3 0

Answer: 35.8 seconds

Step By Step:
13.6
+12.2
———
35.8

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Special right triangles

fiasKO [112]

Answer:

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Step-by-step explanation:

8 0

3 years ago

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A rectangle's perimeter and area have the same value. The width of the rectangle is 6 units. What is the length of the rectangle

Sliva [168]

Answer:

The length ot rectangle is 3 units.

Step-by-step explanation:

The formula for perimeter is P = 2l + 2w and the area is A = l×w. Assuming that the perimeter and area have the same values so you have to compare it :

$perimeter = 2l + 2w$

$area= l \times w$

$perimeter = area$

$2l + 2w = lw$

$let \: w = 6$

$2l + 2(6) = 6l$

$2l + 12 = 6l$

$12 = 6l - 2l$

$4l = 12$

$l = 3 \: units$

8 0

3 years ago

Prove the equation (2x+5)2 = 4x (x + 5) +25

shtirl [24]

Answer: x = -5/2 and x = -3/2

Step-by-step explanation:

(2x + 5)2 = 4x (x + 5) +25

4x + 10 = 4x² + 20x + 25

[minus 4x on both sides.]

10 = 4x² + 16x + 25

[minus 10 on both sides.]

0 = 4x² + 16x + 15

ac = 4(15) = 60,then find the factors that add up to 16, which is 6 and 10.

0 = 4x² + 6x + 10x + 15

0 = 2x(2x + 3) + 5(2x + 3)

0 = (2x + 5)(2x + 3)

2x + 5 = 0 2x + 3 = 0

2x = -5 2x = -3

x = -5/2 x = -3/2

3 0

2 years ago

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I don’t know how to do this

Rina8888 [55]

Slope is .5/5
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5 0

3 years ago

Two teams A and B play a series of games until one team wins three games. We assume that the games are played independently and

Olenka [21]

Answer:

The probability that the series lasts exactly four games is $3p(1-p)(p^{2} + (1 - p)^{2})$

Step-by-step explanation:

For each game, there are only two possible outcomes. Either team A wins, or team A loses. Games are played independently. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

We also need to know a small concept of independent events.

Independent events:

If two events, A and B, are independent, we have that:

$P(A \cap B) = P(A)*P(B)$

What is the probability that the series lasts exactly four games?

This happens if A wins in 4 games of B wins in 4 games.

Probability of A winning in exactly four games:

In the first two games, A must win 2 of them. Also, A must win the fourth game. So, two independent events:

Event A: A wins two of the first three games.

Event B: A wins the fourth game.

P(A):

A wins any game with probability p. 3 games, so n = 3. We have to find P(A) = P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(A) = P(X = 2) = C_{3,2}.p^{2}.(1-p)^{1} = 3p^{2}(1-p)$

P(B):

The probability that A wins any game is p, so P(B) = p.

Probability that A wins in 4:

A and B are independent, so:

$P(A4) = P(A)*P(B) = 3p^{2}(1-p)*p = 3p^{3}(1-p)$

Probability of B winning in exactly four games:

In the first three games, A must win one and B must win 2. The fourth game must be won by 2. So

Event A: A wins one of the first three.

Event B: B wins the fourth game.

P(A)

P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(A) = P(X = 1) = C_{3,1}.p^{1}.(1-p)^{2} = 3p(1-p)^{2}$

P(B)

B wins each game with probability 1 - p, do P(B) = 1 - p.

Probability that B wins in 4:

A and B are independent, so:

$P(B4) = P(A)*P(B) = 3p(1-p)^{2}*(1-p) = 3p(1-p)^{3}$

Probability that the series lasts exactly four games:

$p = P(A4) + P(B4) = 3p^{3}(1-p) + 3p(1-p)^{3} = 3p(1-p)(p^{2} + (1 - p)^{2})$

The probability that the series lasts exactly four games is $3p(1-p)(p^{2} + (1 - p)^{2})$

8 0

4 years ago