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3 years ago

PROBLEM #1

Mathematics

1 answer:

lesantik [10]3 years ago

8 0

Answer:

500 - 25w ≥ 200

Explanation:

Translate every verbal statement into an algebraic statement,

1. Keith has $500 in a savings account at the beginning of the summer.

Initial amount: 500

2. He wants to have at least $200 in the account by the end of summer.

Final amount ≥ 200

3. He withdraws $25 a week for his cell phone bill.

Call w the number of weeks

Withdrawls = 25w

4. Write an inequality that represents Keith's situation.

Create your model: Final amount = Initial amount - withdrawals ≥ 500

500 - 25w ≥ 200

With that inequality you can calculate how many week will pass before his account has less than the amount he wants to have in the account by the end of summer:

500 - 200 ≥ 25w

300 ≥ 25w

300/25 ≥ w

12 ≥ w

w ≤ 12

That represents that he can afford spending $ 25 a week during 12 weeks to have at least $ 200 in the account.

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Use the number line below, where RS = 7y +5. ST = 3y +5, and RT = 70. a. What is the value of y?

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Answer:

Step-by-step explanation:

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3 years ago

A drawer contains 4 white socks, 5 black socks, and 3 brown socks. Find the probability that...

IRINA_888 [86]

Answer:

5/12

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3 years ago

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Answer:

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Assuming:

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Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

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$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

We need to check the conditions in order to use the normal approximation.

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So we see that we satisfy the conditions and then we can apply the approximation.

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$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

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The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$