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Sauron [17]
3 years ago
15

Find the distance between points C(-1, -1) and D(6, 2) to the nearest tenth.

Mathematics
1 answer:
givi [52]3 years ago
8 0

Answer:

≈ 7.6

Step-by-step explanation:

Calculate the distance using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (6, 2)

d = \sqrt{(6+1)^2+(2+1)^2}

  = \sqrt{7^2+3^2}

  = \sqrt{49+9}

  = \sqrt{58} ≈ 7.6 ( to the nearest tenth )

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Christine deposits $700 into an account that pays simple interest at a rate of 2 per year. How much interest will she be paid in
xxMikexx [17]

Answer:

$56

Step-by-step explanation:

A=P(1+i.n)

A is final amount

P is amount deposited

i is interest rate

n is number os years

A = $700(1+2%×4)

=$756

$756-$700=$56

7 0
3 years ago
Baseball's division series is a best of five game series. That is, the first team to win 3 games is the winner. Team A and team
iris [78.8K]

Answer:

1. 27.46% probability that A wins the series in 3 games.

2. There is a 28.84% probability A wins the series in 4 games.

3. There is a 20.18% probability A wins the series in 5 games.

4. There is a 76.48% probability A wins the series.

5. There is a 71.825% probability A wins the series if a "best-of-three" game series is played.

Step-by-step explanation:

For each game, there are these following probabilities:

A 65% probability team A wins.

A 35% probability team B wins.

The combination formula is important to solve this problem:

This is because for example, team A winning games 1,2 and 4 and team B winning game 3 is the same as team A winning games 1,3,4 and team B winning game 2. That is, the order is not important.

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

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

1. What the probability that A wins the series in 3 games?

This is team A winning all 3 games. For each game, there is a 65% probability that team A wins. So

P = (0.65)^{3} = 0.2746

There is a 27.46% probability that A wins the series in 3 games.

2. What is the probability A wins the series in 4 games?

This is the team A winning three games and the team B 1. The team B win cannot happen in the fourth game, so the number of possibilities is a combination of 3 by 2. So

C_{3,2} = \frac{3!}{2!1!} = 3

The probability that team A wins the series in 4 games is:

P = 3*(0.65)^{3}*(0.35) = 0.2884

There is a 28.84% probability A wins the series in 4 games.

3.What is the probability A wins the series in 5 games?

This is the team A winning three games and the team B 2. The team B second win cannot happen in the fifth game, so the number of possibilities is a combination of 4 by 2. So

C_{4,2} = \frac{3!}{2!1!} = 6

The probability that team A wins the series in 5 games is:

P = 6*(0.65)^{3}*(0.35)^{2} = 0.2018

There is a 20.18% probability A wins the series in 5 games.

4. What is the probability A wins the series (period)?

They can win the series in 3,4 or 5 games. So this is the sum of the answers for 1,2,3.

So

P = 0.2746 + 0.2884 + 0.2018 = 0.7648

There is a 76.48% probability A wins the series.

5. What is the probability A wins the series if a "best-of-three" game series is played?

These three following outcomes are accepted:

A - A

A - B - A

B - A - A

So

P = (0.65)^{2} + 2*(0.65)^{2}*(0.35) = 0.71825

There is a 71.825% probability A wins the series if a "best-of-three" game series is played.

3 0
3 years ago
Juan sells 2 sizes of dried wreaths it takes him 3 hours to make each large and 2 hours to make each small one. he has material
Karo-lina-s [1.5K]

Answer:  The answer is (2,9) and (6,3).


Step-by-step explanation: Given that Juan sells 2 sizes of dried wreaths. He takes 3 hours to make each large one and tales 2 hours to make each small one. Also, he has material for maximum 6 large wreaths or maximum 9 small wreaths.

Let, 'x' and 'y' be the number of number of large wreaths and number of small wreaths respectively made by Juan.

So, according to the given information, we have the following relations -

3x+2y\leq 24,~~x\leq 6,~~y\leq 9.

We tried plotting these inequalities in the graph paper (please see the attached figure), and found that the following two solutions will fit the situation perfectly.

Point A (x = 2, y = 9)   and   point B (x = 6, y = 3).

Thus, the two possible combinations are

(i) 2 large wreaths and 9 small wreaths, and

(ii) 6 large wreaths and 3 small wreaths.


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4 years ago
Function g can be thought of as a translated (shifted) version of f(x) = x2.
yawa3891 [41]

Answer: 3

Step-by-step explanation:

5 0
1 year ago
(6 x 9 = f) f x 16 = b <br><br> what dose b equal
Tcecarenko [31]

Step-by-step explanation:

f=6×9

aubstituting f=6×9

6×9×16=b

864=b

4 0
3 years ago
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