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scZoUnD [109]
3 years ago
5

He0pl me plsssssssss

Mathematics
1 answer:
Ganezh [65]3 years ago
8 0
<h2>Answer:</h2>

<h3>1)    \frac{1}{2}</h3><h3>3)   \frac{1}{6}</h3><h3>5)   \frac{2}{3}</h3><h3 /><h2>Step-by-Step Explanation:</h2><h3 />

1.<em> </em>Find the probability of rolling less than a four.

<u>Probability Outcomes</u> = 1, 2, 3, 4, 5, 6

<u>Outcomes lower than four</u> = 1, 2, 3

Then to answer it you need the probability in the form of a fraction.

\frac{3}{6} simplifies into \frac{1}{2}

2. Find the probability of rolling an even prime number.

<u>Probability Outcomes</u> = 1, 2, 3, 4, 5, 6

<u>Prime Numbers Through 1-6</u> = 2, 3, 5

<u>Even Prime numbers Through 1-6</u> = 2

So the probability in the form of a fraction.

<h3>\frac{1}{6}</h3><h3 />

3. Find the probability of rolling factors of 20.

<u>Probability Outcomes</u> = 1, 2, 3, 4, 5, 6

<u>Factors of 20 Through 1-6</u> = 1, 2, 4, 5

So probabilty in the form of a fraction.

\frac{4}{6} simplifies into \frac{2}{3}

<h3>That's all! I hope this helps! If you ever need my help, just friend me and message me!</h3>
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Answer:

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Answer:

Dimensions:  125 m x 250 m

Area:  31,250 m²

Step-by-step explanation:

Given information:

  • Total amount of fencing = 500m
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First, let us assume that the land is <u>rectangular</u> in shape.

Let y = length of the side opposite the river

Let x = length of the other 2 sides of the land

Therefore, we can create two equations from the given information:

  <u>Area of land</u>:   A= xy

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Rearrange the equation for the perimeter of the fence to make y the subject:

\begin{aligned} \implies 2x + y & = 500\\ y & = 500-2x \end{aligned}

Substitute this into the equation for Area:

\begin{aligned}\implies A & = xy\\& = x(500-2x)\\& = 500x-2x^2 \end{aligned}

To find the value of x that will make the area a <em>maximum</em>, <u>differentiate</u> A with respect to x:

\begin{aligned}A & =500x-2x^2\\\implies \dfrac{dA}{dx}& =500-4x\end{aligned}

Set it to zero and solve for x:

\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 500-4x & =0 \\ x & = 125 \end{aligned}

Substitute the found value of x into the original equation for the perimeter and solve for y:

\begin{aligned}2x + y & = 500\\\implies 2(125)+y & = 500\\250+y & = 500\\y & = 250\end{aligned}

Therefore, the dimensions that will give Christine the maximum area are:

125 m x 250 m (where 250 m is the side opposite the river)

The maximum area is:

\begin{aligned}\implies \sf Area_{max} & = xy\\& = 125 \cdot  250\\& = 31250\: \sf m^2 \end{aligned}

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