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3 years ago

Solve the following equations 5^2x-2(5^x)-15=0

Mathematics

1 answer:

castortr0y [4]3 years ago

5 0

Answer:

x = 1

Step-by-step explanation:

${5}^{2x} - 2( {5}^{x} ) - 15 = 0$

$( {5}^{x} {)}^{2} - 2 \times {5}^{x} - 15 = 0$

${t}^{2} - 2t - 15 = 0$

${5}^{x} t = - 3 \: \: .5$

${5}^{x} = 5$

$x = 1$

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$Var(X) = E(X^2) -[E(X)]^2 = 4.97 -(1.61)^2 =2.3779$

And the deviation would be:

$Sd(X) =\sqrt{2.3779}= 1.542 \approx 1.54$

Step-by-step explanation:

For this case we have the following distribution given:

X 0 1 2 3 4 5 6

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$E(X)= 0*0.3 +1*0.25 +2*0.2 +3*0.12 +4*0.07+ 5*0.04 +6*0.02=1.61$

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3 years ago

Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find

natka813 [3]

Answer:

The width of the football field is 160 feet.

The length of the football field is 360 feet.

Step-by-step explanation:

Let w represent width of the football field.

We have been given that the length is 200 ft more than the width, so the length of the field would be $w+200$ .

We are also told that the perimeter is 1,040 ft. We know that football field is in form of rectangle, so perimeter of field would be 1 times the sum of length and width. We can represent this information in an equation as:

$2(w+w+200)=1040$

Let us solve for w.

$2(2w+200)=1040$

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$4w=640$

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$w=160$

Therefore, the width of the football field is 160 feet.

Upon substituting $w=160$ in expression $w+200$ , we will get length of field as:

$w+200\Rightarrow 160+200=360$

Therefore, the length of the football field is 360 feet.

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