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Sloan [31]
3 years ago
5

A neighborhood child is selling lemonade and cookies in front of his house. He has up to 20 cookies available and enough lemonad

e for 50 glasses. The child makes a $1 profit off of each cookie and $0.50 profit off of each glass of lemonade and hopes to make at least $30.
Write a system of inequalities to represent the combination of the number of glasses of lemonade and cookies the child can sell.
Mathematics
1 answer:
prohojiy [21]3 years ago
7 0

Answer:

The child can sell 15 cookies and 30 lemonade glasses, or 10 cookies and 40 glasses of lemonade, etc

Step-by-step explanation:

If the child wants to make $30 and gets $1 per cookie and $0.50 per lemonade glass, he could sell 15 cookies and 30 glasses, 10 cookies and 40 glasses, etc. He has to sell at least 5 cookies, though, as the lemonade is only worth $25.

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Estimate the limit<br><br> A <br> B <br> C<br> D
Lera25 [3.4K]

Answer:

C. \lim_{x\rightarrow f(x)=2

Step-by-step explanation:

Given problem is \lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}.

Now we need to evaluate the given limit.

If we plug \x=\frac{\pi}{4}, into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule

take derivative of numerator and denominator

\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}

=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}

=\frac{sec^2(\frac{\pi}{4})-0}{1-0}

=\frac{(\sqrt{2})^2}{1}

=\frac{2}{1}

=2

Hence choice C is correct.

5 0
3 years ago
The record low for Florida is 2 degrees below zero Fahrenheit and was set on February 13, 1899. The record high is 109 degrees F
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Step-by-step explanation:

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3 years ago
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3,100 mg is how many grams
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3 years ago
A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters
natita [175]

Answer:

0.0479 = 4.79% probability that fewer than 11 of them will vote

Step-by-step explanation:

For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this question.

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}.p^{x}.(1-p)^{n-x}

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

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

And p is the probability of X happening.

70% of all eligible voters will vote in the next presidential election.

This means that p = 0.7

20 eligible voters were randomly selected from the population of all eligible voters.

This means that n = 20

What is the probability that fewer than 11 of them will vote?

This is:

P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308

P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120

P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039

P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010

P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002

P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0

The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then

P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479

0.0479 = 4.79% probability that fewer than 11 of them will vote

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3 years ago
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