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gayaneshka [121]
2 years ago
6

Solve each equation. Be sure to check for extraneous solution -7= |a-3|/-2

Mathematics
1 answer:
stepan [7]2 years ago
4 0

Answer:

a = -11, 17.

Step-by-step explanation:

-7 =  |a-3| / -2

Multiply both sides by -2:

|a - 3| = 14

So a - 3 = 14

Giving a = 17

or

a - 3 =- -14

giving a = -11.

Checking these values:

-7 = |17-3| / -2 = 14/-2 = -7  

- so a = 17 is a solution.

-7 = |-11-3| / -2 = 14/-2 = -7

so a = -11 is also a solution.

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Find the probability of rolling an odd sum or a sum less than 7 when a pair of dice is rolled
Nutka1998 [239]

Answer:

For the pairs that satisfy that the sum is less than 7 we have:

(1,1) (2,1) (1,2) (3,1) (2,2) (1,3) (4,1) (3,2) (2,3) (1,4) (5,1) (4.2) (3,3) (2,4) (1,5)

So we have a total of 15 pairs where the sum is less than 7

And for an odd sum we have the following pairs

(2,1) (1,2) (4,1) (3,2) (2,3) (1,4) (6,2) (5,2) (4,3) (3,4) (2,5) (1,6) (6,3) (5,4) (4,5) (3,6) (6,5) (5,6)

A total of 18 pairs and we have 6 pairs who are in both cases for the sum less than 7 and the sum an odd number that represent the intersection and using the total probability rule we got:

P = \frac{15+18-6}{36}= \frac{27}{33}= 0.818

Step-by-step explanation:

For this case when a pair of dice is rolled we have the following sample pace for the outcomes:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

We see 36 possible outcomes and we want to find how many of these pairs we got rolling an odd sum or a sum less than 7

For the pairs that satisfy that the sum is less than 7 we have:

(1,1) (2,1) (1,2) (3,1) (2,2) (1,3) (4,1) (3,2) (2,3) (1,4) (5,1) (4.2) (3,3) (2,4) (1,5)

So we have a total of 15 pairs where the sum is less than 7

And for an odd sum we have the following pairs

(2,1) (1,2) (4,1) (3,2) (2,3) (1,4) (6,2) (5,2) (4,3) (3,4) (2,5) (1,6) (6,3) (5,4) (4,5) (3,6) (6,5) (5,6)

A total of 18 pairs and we have 6 pairs who are in both cases for the sum less than 7 and the sum an odd number that represent the intersection and using the total probability rule we got:

P = \frac{15+18-6}{36}= \frac{27}{33}= 0.818

7 0
3 years ago
You have $900 in a checking account. You pay a $60 cell phone bill each month using this account.
S_A_V [24]

Answer:

$660

Step-by-step explanation:

You multiply 60 by 4 and get 240

Subtract 240 from 900

7 0
3 years ago
Mrs. Olga’s $250 investment earns 19% interest compounded annually. What will her balance be after 3 years?
Maurinko [17]

Answer:

The answer is A. $421.29

Step-by-step explanation:

Just keep finding 19% of the numbers next, and you add that all up and you get the answer.

250 x 19%=47.5. (250+47.5)=> 297.5x19%= 56.525. (297.5+56.525) =>354.025x19%=67.26475

354.025+67.26475=> 421.28975, which can round up to 421.29.

6 0
3 years ago
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MrRa [10]

Answer:

-1,-3,-9,-27,-81,-243...

Step-by-step explanation:

8 0
3 years ago
Help its due tmmr and i dont under stand
const2013 [10]

If we want rice per person, that's

\dfrac{25}{3}

1a. Answer: 25/3

That's between 24/3 and 27/3 i.e. between

1b. Answer: 8 and 9


6 0
3 years ago
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