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3 years ago

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Leo is working part time as a server in a restaurant. He makes $8.14 for each hour he works, and on average earns an additional

$300 per week in tips. Which function, f(x), can Leo use to model his average weekly salary in terms of the number of hours, x, he works?

1 answer:

Mazyrski [523]3 years ago

8 0

Answer:

f(x) = 8.14x + 300

Step-by-step explanation:

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Solve the equation 6w2 – 7w – 20 = 0.

azamat

For this case we have the following quadratic equation:

$6w ^ 2-7w-20 = 0$

Where:

$a = 6\\b = -7\\c = -20$

Its roots will be given by:

$w = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\w = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (6) (- 20)}} {2 (6)}\\w = \frac {7 \pm \sqrt {49 + 480}} {12}\\w = \frac {7 \pm \sqrt {529}} {12}\\w = \frac {7 \pm23} {12}$

The roots are:

$w_ {1} = \frac {7 + 23} {12} = \frac {30} {12} = \frac {15} {6} = \frac {5} {2}\\w_ {2} = \frac {7-23} {12} = \frac {-16} {12} = - \frac {8} {6} = - \frac {4} {3}$

Answer:

$w_ {1} = \frac {5} {2}\\w_ {2} = - \frac {4} {3}$

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3 years ago

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Five individuals from an animal population thought to be near extinction in a certain region have been caught, tagged, and relea

Talja [164]

Answer:

a) For this case the random variable X follows a hypergometric distribution.

b) $E(X)= n\frac{M}{N}=10 \frac{5}{25}=2$

$Var(X)=n \frac{M}{N}\frac{N-M}{N}\frac{N-n}{N-1}=10\frac{5}{25}\frac{25-5}{25}\frac{25-10}{25-1}=1$

c) $P(X=0)= \frac{(5C0)(25-5 C 10-0)}{25C10}=\frac{1*184756}{3268760}=0.0565$

d) $P(X=5)= \frac{(5C5)(25-5 C 10-5)}{25C10}=\frac{1*15504}{3268760}=0.00474$

Step-by-step explanation:

The hypergometric distribution is a discrete probability distribution that its useful when we have more than two distinguishable groups in a sample and the probability mass function is given by:

$P(X=k)= \frac{(MCk)(N-M C n-k)}{NCn}$

Where N is the population size, M is the number of success states in the population, n is the number of draws, k is the number of observed successes

The expected value and variance for this distribution are given by:

$E(X)= n\frac{M}{N}$

$Var(X)=n \frac{M}{N}\frac{N-M}{N}\frac{N-n}{N-1}$

a. What is the distribution of X?

For this case the random variable X follows a hypergometric distribution.

b. Compute the values for E(X) and Var(X)

For this case n=10, M=5, N=25, so then we can replace into the formulas like this:

$E(X)= n\frac{M}{N}=10 \frac{5}{25}=2$

$Var(X)=n \frac{M}{N}\frac{N-M}{N}\frac{N-n}{N-1}=10\frac{5}{25}\frac{25-5}{25}\frac{25-10}{25-1}=1$

c. What is the probability that none of the animals in the second sample are tagged?

So for this case we want this probability:

$P(X=0)= \frac{(5C0)(25-5 C 10-0)}{25C10}=\frac{1*184756}{3268760}=0.0565$

d. What is the probability that all of the animals in the second sample are tagged?

So for this case we want this probability:

$P(X=5)= \frac{(5C5)(25-5 C 10-5)}{25C10}=\frac{1*15504}{3268760}=0.00474$

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I need your help please❤️ you place $6543 in a savings account which earns.7% interest compounded semi annually, after 3 years h

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$8043 is what you have now
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Gnoma [55]

The answer is 5+5+5=15

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What is the gfc of 24 and 36

Alexandra [31]

Answer:

6 is the gfc

Step-by-step explanation:

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