Solve the system: (MAFS.912-A-REI.3.6)

If w = -2 and v = -8, which of the following expressions shows the values correctly substituted in for the variables in the expr

Ahat [919]

Answer:

Step-by-step explanation:

When you substitute values into an algebraic equation, you need to input the values exactly how they are given. "w" must go where there are "w"s, and "v" must go where the "v"s are, otherwise you will get an incorrect answer. All values must also carry over their signs--they are one unit--and must be inserted as such, which is why - (-8) is correct, but not - (8) or - 8. (This is because those two negatives will cancel each other out and become +8 when solving). The parenthesis around the values are important because they protect the original values of the variables, which is why (-2)2 is correct. In the case of (-2)2, it also signifies that they are "attached" by multiplication, and when solving would become -4. Without signifying that the variables are separate from the rest of the equation via the parenthesis, it becomes very easy to solve it incorrectly.

5 0

3 years ago

Read 2 more answers

An office supply Store A is offering copy paper for $3.00 per pack. Store B is running a special of buy two for $4.20 each and g

iVinArrow [24]

A. would be the answer

7 0

3 years ago

Read 2 more answers

First one please thanksssa

serious [3.7K]

In order to find this, we need to count exactly how many times each of them blinks within 60 seconds. Then, we find which numbers are the same.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Now, I will bold the numbers that are the same.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Now, we have our answer.

Answer: The two neon lights will blink on the 12, 24, 36, 48, and 60 second marks.

Hope I helped!

5 0

3 years ago

Robert collected 330 aluminum cans. If 100 aluminum cans weigh 4 pounds, and the recycling center is paying 25 cents a pound, ho

Phantasy [73]

Step-by-step explanation:

Cost per pound, c = 25cents

number of cans per pound, n = 100/4 = 25cans

total cans collected, t = 330cans

payment for total cans collected,p

where p = (t/n)×c = (330/25)×25 = 330cents

7 0

3 years ago

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

crimeas [40]

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

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

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

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago