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dezoksy [38]
2 years ago
9

What are the integer solutions to the inequality below? 3 ≤ 3 x − 4 ≤ 2 x + 1

Mathematics
1 answer:
Nimfa-mama [501]2 years ago
4 0

Answer:

x can be 3, 4, or 5

Step-by-step explanation:

Let's split the inequality and solve it piece by piece.

Case: 3

We add 4 to both sides to get 7.

We divide both sides by 3 to get 7/3.

So, x>=7/3.

Case: 3x-4

We subtract 2x from both sides to get x-4.

We add 4 to both sides to get x.

So, we want to find the integer solutions to 7/3.

7/3= 2 1/3, so x can be 3, 4, or 5.

So, x can be 3, 4, or 5 and we're done!

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All but -1 <x <1
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Step-by-step explanation:

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3 years ago
You roll two six-sided dice. Match each event with its probability.
Nina [5.8K]

Answer:

A) probability the sum is 8 or 11= 4/21

B) probability that sum is 12 or less than 10 = 6/7

C) Probability that the sum is 3 or less than 3 = 2/21

D) Probability that the sum is 2 or 10 = 1/7

Step-by-step explanation:

Since we have the same probability of each event in each dice, the answer would be just to check the different outcomes, two dices, each with 1 to 6;

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

Thus, there are 21 possible outcomes.

Now,

A) probability that the sum is 8 or 11;

From the outcomes above, the number of outcomes that have a sum as 8 or 11 are;

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

So,probability = 4/21

B) From the outcomes above, the number of outcomes that are 12 or less than 10 are;

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

There are 18 possible outcomes.

So, probability that sum is 12 or less than 10 = 18/21 = 6/7

C)From the initial 21 outcomes, the number of outcomes that the sum is 3 or less than 3 are;(1,1);(1,2)

Thus,

Probability that the sum is 3 or less than 3 = 2/21

D) From the initial 21 outcomes, the number of outcomes that the sum is 2 or 10 are;

(1,1); (4,6) ; (5,5)

Thus,

Probability that the sum is 2 or 10 = 3/21 = 1/7

6 0
3 years ago
If the measure of angle 1 is (3 x minus 4) degrees and the measure of angle 2 is (4 x + 10) degrees, what is the measure of angl
arlik [135]

Answer:

58 degrees

Step-by-step explanation:

If angle 1 + angle 2 = 90 degrees, then:

(3x - 4) + (4x+10) = 90

Combine like terms:

(3x+4x) + (10-4) = 90

7x + 6 = 90

Subtract 6 from both sides:

7x = 84

Divide both sides by 7:

x = 12

**Plug x back into angle 2 (This step is easy to forget!):

angle 2 = 4(12) + 10

angle 2 = 48 + 10

angle 2 = 58 degrees

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2 years ago
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