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10 months ago

Below, the two-way table is given for a class

Mathematics

1 answer:

Nataliya [291]10 months ago

8 0

Answer:

2/7 = 29% (nearest percent)

Step-by-step explanation:

Calculate the totals and add them to the table:

$\begin{array}{| c | c | c | c | c | c |}\cline{1-6} & \sf Freshman & \sf Sophmore & \sf Juniors & \sf Seniors & \sf Total \\\cline{1-6} \sf Male & 4 & 6 & 2 & 2 & 14\\\cline{1-6} \sf Female & 3 & 4 & 6 & 3 & 16\\\cline{1-6} \sf Total & 7 & 10 & 8 & 5 & 30\\\cline{1-6}\end{array}$

Probability Formula

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student is male

Use the given table to calculate the probability that the student is male:

$\sf \implies P(B)=\dfrac{14}{30}$

And the probability that the student is a freshman and male:

$\implies \sf P(A \cap B)=\dfrac{4}{30}$

To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of A given B is:

$\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}$

Substitute the found values into the formula:

$\implies \sf P(Freshman|Male)=\dfrac{\dfrac{4}{30}}{\dfrac{14}{30}}=\dfrac{4}{14}=\dfrac{2}{7}=0.28571...=29\%$

Therefore, the probability that the student is a freshman given they are male is 29% (nearest percent).

Learn more about conditional probability here:

brainly.com/question/28028208

brainly.com/question/23957743

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2 years ago

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Ira Lisetskai [31]

Answer: Choice D) $y = \pm \sqrt{x+5}$

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Extra info:

The inverse relation is not a function because of the plus minus. For instance, plugging x = 4 into $y = \pm \sqrt{x+5}$ leads to y = -3 and y = 3 simultaneously. You would have to apply a domain restriction on $y = x^2-5$ to make it a one-to-one function, to make the inverse a function. One possible domain restriction is $x > 0$ which would lead to the inverse function $y = \sqrt{x+5}$

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2 years ago

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2 years ago

Ron's recycle shop had an old paper-shredding machine. Business was good, so he bought a new paper-shredding machine. The old ma

levacccp [35]

Answer: 1 hour 20 minutes

Step-by-step explanation:

Given : The old machine could shred a truckload of paper in 4 hours.

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Rate of work done by new machine = $\dfrac{1}{2}$

Let 't' be the time taken by both of them working together , then we have the following equation:-

$\dfrac{1}{t}=\dfrac{1}{4}+\dfrac{1}{2}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{1+2}{4}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{3}{4}\\\\\Rightarrow t=\dfrac{4}{3}=1\dfrac{1}{3}\ \text{ hours}$

Since 1 hour = 60 minutes

Then, $\dfrac{1}{3}\ \text{ hours}=\dfrac{1}{3}\times60=20\text{ minutes}$

Hence, it will take 1 hour 20 minutes to shred the same truckload of paper if Ron runs both shredders at the same time.

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