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2 years ago

Solve this inequality for x: -46 − 8x > 22. A. x < 8.5 B. x < -8.5 C. x > -8.5 D. x > 8.5

Mathematics

1 answer:

marissa [1.9K]2 years ago

7 0

Step one rewrite: -46-8x>22

Add 46 to both sides: -8x>68

Divide both sides by -8 to isolate x<-8.5

(remember to flip the inequality sign when multiplying or dividing by negative numbers in inequality problems)

So the correct answer is B. x < -8.5

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A track star runs two races on a certain day. The probability thathe wins the first race is 0.7, the probability that he wins th

NARA [144]

Answer:

a) 80% probability that he wins at least one race.

b) 30% probability that he wins exactly one race.

c) 20% probability that he wins neither race.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that he wins the first race.

B is the probability that he wins the second race.

C is the probability that he does not win any of these races.

We have that:

$A = a + (A \cap B)$

In which a is the probability that he wins the first race but not the second and $A \cap B$ is the probability that he wins both these races.

By the same logic, we have that:

$B = b + (A \cap B)$

The probability that he wins both races is 0.5.

This means that $A \cap B = 0.5$

The probability that he wins the second race is 0.6

This means that $B = 0.6$

$B = b + (A \cap B)$

$0.6 = b + 0.5$

$b = 0.1$

The probability that he wins the first race is 0.7.

This means that $A = 0.6$

$A = a + (A \cap B)$

$0.7 = a + 0.5$

$a = 0.2$

A) he wins at least one race.

This is

$P = a + b + (A \cap B) = 0.2 + 0.1 + 0.5 = 0.8$

There is an 80% probability that he wins at least one race.

B) he wins exactly one race.

This is

$P = a + b = 0.2 + 0.1 = 0.3$

There is a 30% probability that he wins exactly one race.

C) he wins neither race

Either he wins at least one race, or he wins neither. The sum of these probabilities is 100%.

From a), we have that there is an 80% probability that he wins at least one race.

So there is a 100-80 = 20% probability that he wins neither race.

6 0

2 years ago

What is the answer to 3/x-2 is ≥12

Tju [1.3M]

Answer:

The answer to your question is 0 < x ≤ 3/14

Step-by-step explanation:

Here are the steps to solve it.

First, you need to solve your inequality step-by-step:

3/x −2 ≥ 12

-2x + 3/x = ≥12

Next, find the critical points of the inequality:

2x + 3/x = 12

−2x + 3 = 12x (Multiply both sides by x)

−2x + 3 − 12x = 12x − 12x (Subtract 12x from both sides)

−14x + 3 = 0

−14x + 3 − 3 = 0 − 3 (Subtract 3 from both sides)

−14x = −3

-14x/ -14 = -3/ -14 (Divide both sides by -14)

So, that gives you your answer:

x = 3/14

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2 years ago

Akira recives a prize at a science fair for having the most information project her trophy is in the shape of a square pyramid a

liberstina [14]

Answer:

Step-by-step explanation:

Because I think it is

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2 years ago

What is the interest earned on $3000 at a rate of 0.04 for three years? The formula is interest equals (principal) (rate) (time)

bekas [8.4K]

<u>Answer:</u>

The interest after 3 years is $360

<u>Explanation:</u>

Given the principal amount (P) = $3000

Rate of interest (R) = 0.04

Time period (T) is given as 3 years

The Simple Interest is calculated by the formula;

$SI = Principal \times Rate of Interest \times Time$

Substituting the values in the above formula,

$SI = 3000 \times 0.04 \times 3$

SI = $360

Therefore, the interest after 3 years is $360

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2 years ago

A fair dice is rolled

iren2701 [21]

Answer:

1/6

Step-by-step explanation:

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3 years ago