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notka56 [123]
3 years ago
5

Using the graph below, identify 2 solutions to the inequality y<-3/2x+2

Mathematics
1 answer:
lora16 [44]3 years ago
3 0
Any point in that shaded area  is a solution
(0,0) is a solution
(-1,-1) is a solution
(-3,3) is a solution
etc
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Jason has 4 gallons of hand sanitizer that contains 25% alcohol. He wants to make a hand sanitizer that contains 50% alcohol. Ho
alexandr402 [8]

Answer:

2 gallons of pure alcohol

Step-by-step explanation:

Let x represent the number of gallons of pure alcohol needed, and create an equation:

4(0.25) + x(1) = (x + 4)0.5

1 + x = 0.5x + 2

x = 0.5x + 1

0.5x = 1

x = 2

So, 2 gallons of pure alcohol should be added.

8 0
3 years ago
Which equation best matches the scenario below?
siniylev [52]

Answer:

Definetly t = 4n

4 0
3 years ago
Each contestant in the Hunger Games must be trained to compete. Suppose that the time it takes to train a contestant has mean 5
LiRa [457]

Answer:

11.51% probability that it will take less than 450 days to train all the contestants.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n variables, the mean is \mu*n and the standard deviation is s = \sigma\sqrt{n}

In this question:

n = 100, \mu = 100*5 = 500, s = 4\sqrt{100} = 40

Approximate the probability that it will take less than 450 days to train all the contestants.

This is the pvalue of Z when X = 450.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{450 - 500}{40}

Z = -1.2

Z = -1.2 has a pvalue of 0.1151

11.51% probability that it will take less than 450 days to train all the contestants.

8 0
3 years ago
you and 3 friends go to lunch and ordered nachosthat cost 10.30. each person also orders a soda at 1.50. write an equation to sh
kicyunya [14]

Answer:

y = 4(10.30+1.50)

Step-by-step explanation:

Since there are 4 people, you and 3 others, you would multiply everything by 4. Inside the parenthesis, would be the nachos and a drink that everyone got. Since all four people got the same thing, it would be 4x10.30 + 4x1.50, which together would be y = 4(10.30+1.50)

5 0
3 years ago
Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)^4.
omeli [17]

Answer:

Step-by-step explanation:

x=-2,0,4

it is of 6 th degree (even)

coefficient of leading term is 1 (positive)

so it starts from top on the left and ends also positive direction of y-axis.

7 0
3 years ago
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