Choose the equation of the vertical line passing through the point (−4, 2).y = −4

x = −4

y = 2

x = 2

Answers

Answer 1
Answer:

Answer:

Equation would be  x = - 4 .

Step-by-step explanation:

Given :  vertical line passing through the point (−4, 2).

To find : Choose the equation of the vertical line .

Solution : We have given that  point (−4, 2).

We know that vertical line always passes through the x axis .

Here, line passes through at x = -4  which has no slope .

Therefore , equation would be  x = - 4 .

Answer 2
Answer: Vertical line has no slope. so only look at the x value. x=-4.

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If A and B are independent events, P(A and B) =

Answers

Answer:

If A and B are independent events, then the events A and B' are also independent. Proof: The events A and B are independent, so, P(A ∩ B) = P(A) P(B). From the Venn diagram, we see that the events A ∩ B and A ∩ B' are mutually exclusive and together they form the event A.

Answer:

Step-by-step explanation:

Given A and B are independent events, P(A and B) = P(A)*P(B)

A battery manufacturer makes batteries that have a failure rate of .015. That is, 15 out of each 1,000 batteries are defective. What is the probabilitythat a batch of 10,000 batteries will contain at least 175 defective batteries?

Answers

p(success) = 0.015
p(failure) = 1 - 0.015 = 0.985
let x be the random variable that a battery is defective, then
p(x >= 175) = 1 - P(x <= 175)
= 1 - P[z <= (175 - np)/(sqrt(npq))]
= 1 - P[z <= (175 - 10000 * 0.015)/(sqrt(10000 * 0.015 * 0.985))]
= 1 - P[z <= (175 - 150)/(sqrt(147.75))]
= 1 - P[z <= (25/12.16)]
= 1 - P(z <= 2.057)
= 1 - 0.9801
= 0.0199

Simplify 5t + (t - 3) - [(7t + 5) - (8 - 3t)].

Answers

This process is: 

Distribute of the Negative Sign:
5t+t−3+−1(7t+5(8−3t))
5t+t+−3+−1(7t)+(−1)(5)+(−1)(−8)+−1(3t)
5t+t+−3+7t+−5+8+3t
Now simple, Just Combine Like Terms:
5t+t+−3+7t+−5+8+3t
(5t+t+7t+3t)+(−3+−5+8)
4t

-4t would be the answer.

~Evie 

I presume that this is talking about simplification with the rule of PEMDAS. First, look at the parenthesis and brackets. Let's do the [(7t + 5) - (8 - 3t)] part first. The parenthesis can go away on the inside if you distribute the negative in (8 - 3t), which flips the signs of those. You should then have [7t + 5 - 8 + 3t], then work it out to form just (10t - 3). The negative will also carry for the brackets that were there before, so - (10t - 3) turns into -10t + 3. Now, you just have 5t + t - 3 - 10t + 3. Work that out to get your final answer of -4t.

-4t is the answer.

One day at St. Philip's High School, 1/2 of the pupils walked to school, 1/5 of the pupils came to school by bus, and the remaining 57 pupils came by car.What fraction came to school by car?

Answers

The first thing to do is the make the denominators of the fractions the same. 

5/10 of the pupils walked to school and 2/10 of the pupils came to school by bus. 
5/10 + 2/10 = 7/10. 
10/10 - 7/10 = 3/10. 

3/10 of the pupils came to school by car. 

Determine the constant of variation for the direct variation given.R varies directly with S. When S is 16, R is 80.
1/5
5
16

Answers

Answer:

The constant of variation is k=5

Step-by-step explanation:

Proportions

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

y=k\cdot x

Where k is the constant of proportionality.

We know R varies directly with S. Their relationship is:

R=k\cdot S

We also have when S=16, R=80. Thus:

80=k\cdot 16

Solving for k:

k=80/16=5

The constant of variation is k=5

8(3x – 2) ≤ 2(7x + 12)?

Answers

Answer:

The answer is x ≤ 4