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Roman55 [17]
3 years ago
15

a farmer wants to fence in three sides of a rectangular field shown below with 960 feet of fencing. The other side of the rectan

gle will be a river. If the enclosed area is to be a maximum, find the dimensions of the field. ​

Mathematics
1 answer:
Alika [10]3 years ago
3 0

9514 1404 393

Answer:

  240 ft by 480 ft

Step-by-step explanation:

Area is maximized when the long side is half the total length of the fence. That makes the short side (out from the river) be half the length of the long side.

The fenced field dimensions are 240 feet by 480 feet.

__

You can let x represent the length of the long side. Then the length of the short side is half the remaining fence: (960 -x)/2.

The total area is the product of these dimensions:

  A = x(960 -x)/2

We note that this is the equation of a parabola with zeros at x=0 and x=960. The maximum will be found on the line of symmetry, halfway between the zeros. That is at x = (0 +960)/2 = 480.

The area is maximized for a long-side dimension of 480 feet. The short sides are 240 feet.

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According to government data, 20% of employed women have never been married. If 10 employed women are selected at random, what i
Ierofanga [76]

Answer:

a) P(X=2) = (10C2) (0.2)^2 (1-0.2)^{10-2}= 0.302

b) P(X\leq 2) = P(X=0) + P(X=1) +P(X=2)

P(X=0) = (10C0) (0.2)^0 (1-0.2)^{10-0}= 0.107

P(X=1) = (10C1) (0.2)^1 (1-0.2)^{10-1}= 0.268

P(X=2) = (10C2) (0.2)^2 (1-0.2)^{10-2}= 0.302

And replacing we got:

P(X\leq 2) = 0.107+0.268+0.302=0.678

c) For this case we want this probability:

P(X\geq 8) = P(X=8) + P(X=9) +P(X=10)

But for this case the probability of success is p =1-0.2= 0.8

We can find the individual probabilities and we got:

P(X=8) = (10C8) (0.8)^8 (1-0.8)^{10-8} =0.302

P(X=9) = (10C9) (0.8)^9 (1-0.8)^{10-9} =0.268

P(X=10) = (10C10) (0.8)^{10} (1-0.8)^{10-10} =0.107

And replacing we got:

P(X \geq 8) = 0.677

And replacing we got:

P(X\geq 8)=0.0000779

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Let X the random variable of interest, on this case we now that:  

X \sim Bin (n=10 ,p=0.2)

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}  

Solution to the problem

Let X the random variable "number of women that have never been married" , on this case we now that the distribution of the random variable is:  

X \sim Binom(n=10, p=0.2)  

Part a

We want to find this probability:

P(X=2)

And using the probability mass function we got:

P(X=2) = (10C2) (0.2)^2 (1-0.2)^{10-2}= 0.302

Part b

For this case we want this probability:

P(X\leq 2) = P(X=0) + P(X=1) +P(X=2)

We can find the individual probabilities and we got:

P(X=0) = (10C0) (0.2)^0 (1-0.2)^{10-0}= 0.107

P(X=1) = (10C1) (0.2)^1 (1-0.2)^{10-1}= 0.268

P(X=2) = (10C2) (0.2)^2 (1-0.2)^{10-2}= 0.302

And replacing we got:

P(X\leq 2) = 0.107+0.268+0.302=0.678

Part c

For this case we want this probability:

P(X\geq 8) = P(X=8) + P(X=9) +P(X=10)

But for this case the probability of success is p =1-0.2= 0.8

We can find the individual probabilities and we got:

P(X=8) = (10C8) (0.8)^8 (1-0.8)^{10-8} =0.302

P(X=9) = (10C9) (0.8)^9 (1-0.8)^{10-9} =0.268

P(X=10) = (10C10) (0.8)^{10} (1-0.8)^{10-10} =0.107

And replacing we got:

P(X \geq 8) = 0.677

3 0
3 years ago
What is the following simplified product? Assume x greater-than-or-equal-to 0 2 StartRoot 8 x cubed EndRoot (3 StartRoot 10 x Su
dalvyx [7]

The simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x  - 4x³√10x

<h3>How to determine the simplified product?</h3>

The complete question is added as an attachment

From the attached figure, the product expression is:

2√8x³(3√10x⁴ - x√5x²)

Evaluate the exponents

2√8x³(3√10x⁴ - x√5x²) =  2 *2x√2x(3x²√10 - x²√5)

Evaluate the products

2√8x³(3√10x⁴ - x√5x²) =  4x√2x(3x²√10 - x²√5)

Open the bracket

2√8x³(3√10x⁴ - x√5x²) =  12x³√20x  - 4x³√10x

Evaluate the exponents

2√8x³(3√10x⁴ - x√5x²) = 24x³√5x  - 4x³√10x

Hence, the simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x  - 4x³√10x

Read more about expressions at:

brainly.com/question/12990602

#SPJ1

5 0
1 year ago
Jeanine is twice as old as her brother Marc. If the sum of their ages is 24. How old is Jeanine?
Tanya [424]
Let Marc's age be x. If Jeanine is twice as old as Marc, then her age will be 2x. If their ages added together are 24, then you can create the following equation:

2x + x = 24
3x = 24
x = 8

Remember that x is Marc's age. So if Marc is 8, and Jeanine is twice as old, she will be 16. 
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3 years ago
Aaaaaaaaahahahahahqq What’s the answer?
Svetllana [295]

Answer:

2.5

Step-by-step explanation:

-2+5 equals 3-8= -5 divided by 2 equals -2.5

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8 0
3 years ago
Given that 'n' is any natural numbers greater than or equal 2. Prove the following Inequality with Mathematical Induction
Oliga [24]

The base case is the claim that

\dfrac11 + \dfrac12 > \dfrac{2\cdot2}{2+1}

which reduces to

\dfrac32 > \dfrac43 \implies \dfrac46 > \dfrac86

which is true.

Assume that the inequality holds for <em>n</em> = <em>k </em>; that

\dfrac11 + \dfrac12 + \dfrac13 + \cdots + \dfrac1k > \dfrac{2k}{k+1}

We want to show if this is true, then the equality also holds for <em>n</em> = <em>k</em> + 1 ; that

\dfrac11 + \dfrac12 + \dfrac13 + \cdots + \dfrac1k + \dfrac1{k+1} > \dfrac{2(k+1)}{k+2}

By the induction hypothesis,

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Now compare this to the upper bound we seek:

\dfrac{2k+1}{k+1}  > \dfrac{2k+2}{k+2}

because

(2k+1)(k+2) > (2k+2)(k+1)

in turn because

2k^2 + 5k + 2 > 2k^2 + 4k + 2 \iff k > 0

6 0
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