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Rom4ik [11]
1 year ago
12

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

Mathematics
1 answer:
Nataliya [291]1 year 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}

<u>Probability Formula</u>

\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 <u>student is male</u>:

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

And the probability that the <u>student is a freshman </u><u>and </u><u>male:</u>

\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:

<u>Conditional Probability Formula</u>

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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Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = ta
Irina-Kira [14]

Answer:

The inner function is u = \pi x.

The outer function is f(u) = \tan{u}.

\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}

Step-by-step explanation:

The inner function is the one we apply the outer function to.

So

y = \tan{\pi x}

We apply the outer function tangent to \pi x.

So, the inner function is u = \pi x.

The outer function is f(u) = \tan{u}.

The derivative of a compositve function

y = f(u) in which u = g(x) is given by the following function.

y^{\prime} = f^{\prime}(u)*g^{\prime}(x)

So

f(u) = \tan{u}

f^{\prime}(u) = \sec^{2}{u}

u = g(x) = \pi x

g^{\prime}(x) = \pi

So

y^{\prime} = f^{\prime}(u)*g^{\prime}(x)

\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}

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2 years ago
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masha68 [24]
They are vertical angles. They are congruent. 

(2x+2)= (3x-52)

Add 52 to the other side. 

2x+54=3x

Subtract 2x on both sides.

54=x

I hope this helps!
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3 years ago
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Answer:

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Step-by-step explanation:

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Solve the system of linear equations by elimination.<br><br> 4x−3y=8<br> 5x−2y=−11
AleksandrR [38]

Answer:

(-7, -12)

Step-by-step explanation:

4x-3y=8

5x-2y=-11

Is there any of the like terms can be added and the result will be 0? No, so we have to multiple one OR both of the equations to make that one number do that.

(I will try to remove the y like terms so i will multiple both of them by the opposite so both of the ys will be 6)

2(4x-3y=8)

-3(5x-2y=-11)

8x-6y=16

-15x+6y=33

(now the easy part… cancel the 6s and add the equations)

8x+(-15x)=-7x

16+33=49

-7x=49

(divide 49 by -7)

x=-7

Replace x in any of the equations and you’ll get the y value.

4x-3y=8

4(-7)-3y=8

-28-3y=8

-3y=36

y=12

Threfore, there is one solution which is….. (-7,-12)

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2 years ago
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