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4 years ago

Find the dimensions and maximum area of a rectangle if the perimeter is 52

Mathematics

1 answer:

Ray Of Light [21]4 years ago

5 0

Answer: l

Explanation:

Step-by-step explanation:

Perimeter of rectangle is

(

)

is length and

is breadth.

Area of rectangle is

⋅

160

∴

160

;

∴

(

160

)

(

160

)

160

−

160

−

160

(

−

)

−

(

−

)

(

−

)

(

−

)

∴

;

160

and if

;

160

The dimension of rectangle is

[Ans]

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A jar contains two blue and five green marbles. A marble is drawn at random and then replaced. A second marble drawn at random.

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corrected question:A jar contains two blue and five green marbles. A marble is drawn at random and then replaced. A second marble drawn at random. For each of the following, find the probability that: a) both marbles are blue b) both marbles are the same color c)the marbles are different in color

Answer:

Step-by-step explanation:

<u><em>The probability was done with replacement.</em></u>

Probaility of an event happening $=\frac{number of required outcomes}{number of possible outcomes}$

number of blue marbles= 2

number of green marbles=5

total number of marbles=7

(a) probability that both marbles are blue = pr(first is blue)*pr(second is blue)

$=\frac{2}{7}*\frac{2}{7}$

$=\frac{4}{49}$

(b)probability that both marbles are the same color =pr(first is blue)*pr(second is blue) + Pr(first is green)*Pr(second is green)

$=\frac{4}{49} + \frac{5}{7}*\frac{5}{7}$

$=\frac{4}{49} + \frac{25}{49}$

$=\frac{29}{49}$

(c)Probability that the marbles are different in colors=pr(first is blue)*pr(second is green) + Pr(first is green)*Pr(second is blue)

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Answer:

$(b)\ P(Green) = \frac{3}{8} ; P(Yellow) = \frac{1}{8}$

$(c)\ P(Green) = \frac{1}{4} ; P(Yellow) = \frac{1}{4}$

Step-by-step explanation:

Given

$P(Red) = \frac{2}{7}$

$P(Blue) = \frac{3}{14}$

Required

Which completes the model

Let the remaining probability be x.

Such that:

$P(Red) + P(Blue) + x = 1$

Make x the subject

$x = 1 - P(Red) - P(Blue)$

So, we have:

$x = 1 - \frac{2}{7} - \frac{3}{14}$

Solve

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This mean that the remaining model must add up to 1/2

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$P(Green) + P(Yellow)= \frac{2}{7} + \frac{2}{7}$

Take LCM

$P(Green) + P(Yellow)= \frac{2+2}{7}$

$P(Green) + P(Yellow)= \frac{4}{7}$

This is false because: $\frac{4}{7} \ne \frac{1}{2}$

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$P(Green) + P(Yellow)= \frac{3}{8} + \frac{1}{8}$

Take LCM

$P(Green) + P(Yellow)= \frac{3+1}{8}$

$P(Green) + P(Yellow)= \frac{4}{8}$

$P(Green) + P(Yellow)= \frac{1}{2}$

This is true

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$P(Green) + P(Yellow)= \frac{1}{4} + \frac{1}{4}$

Take LCM

$P(Green) + P(Yellow)= \frac{1+1}{4}$

$P(Green) + P(Yellow)= \frac{2}{4}$

$P(Green) + P(Yellow)= \frac{1}{2}$

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