MATHEMATICS COLLEGE

If a 20-foot tree casts a 40-foot shadow, how tall is a tree that casts a 48-foot shadow?

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Answer 1
Answer: the tree that casts a 48 foot shadow is 24 feet

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Kyle has 64 baseball cards and must give away 1/4 of his figures away. How many cards will Kyle give away? What fractions of his cards does he have left?

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kyle regalara 16 figuras y le quedara 3/4 de ellas

1 is 25% of what number?​

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Answer:

25% of 4 is 1.

Step-by-step explanation:

100% of 4 is 4, therefore 25 percent of 4 equals 1.

Suppose we express the amount of land under cultivation as the product of four factors:Land = (land/food) x (food/kcal) x (kcal/person) x (population)

The annual growth rates for each factor are:
1. the land required to grow a unit of food, -1% (due to greater productivity per unit of land)
2. the amount of food grown per calorie of food eaten by a human, +0.5%
3. per capita calorie consumption, +0.1%
4. the size of the population, +1.5%.

Required:
At these rates, how long would it take to double the amount of cultivated land needed? At that time, how much less land would be required to grow a unit of food?

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following annual growth rates:

land/food = - 1%

food/kcal = 0.5%

kcal/person = 0.1%

population = 1.5%

Σ annual growth rates = (-1 + 0.5 + 0.1 + 1.5)% = 1.1% = 0.011

Exponential growth in Land :

L = Lo * e^(rt)

Where Lo = Initial ; L = increase after t years ; r = growth rate

Time for amount of cultivated land to double

L = 2 * initial

L = 2Lo

2Lo = Lo * e^(rt)

2 = e^(0.011t)

Take the In of both sides

In(2) = 0.011t

0.6931471 = 0.011t

t = 0.6931471 / 0.011

t = 63.01 years

Land per unit of food at t = 63.01 years

L = Fo * e^(rt)

r = growth rate of land required to grow a unit of food = 1% = 0.01

L/Fo = e^(-0.01* 63.01)

L/Fo = e^(−0.6301)

= 0.5325385 = 0.53253 * 100% = 53.25%

Land per unit now takes (100% - 53.25%) = 46.75%

What is the result of 72 divided by 12? 6 8 9 12

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Answer:

the answer is 6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Hope this helps!!!!!!

In how many ways can a committee of two men and two women be formed from a group of twelve men and ten women?

Answers

Answer:

Step-by-step explanation:

number of ways=12c2×10c2

=(12 * 11)/(2 *1) * (10 *9)/(2 * 1) \n=2970~ways

NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X ~ Bin(15, 0.05). (Round your probabilities to three decimal places.) (a) Determine both P(X ≤ 3) and P(X < 3). P(X ≤ 3) = P(X < 3) = (b) Determine P(X ≥ 4). P(X ≥ 4) = (c) Determine P(1 ≤ X ≤ 3). P(1 ≤ X ≤ 3) = (d) What are E(X) and σX? (Round your answers to two decimal places.) E(X) = σX = (e) In a sample of 90 children, what is the probability that none has a food allergy?

Answers

Answer:

a) P(X ≤ 3) = 0.9946

P(X < 3) = 0.9639

b) P(X ≥ 4) = 0.0054

c) P(1 ≤ X ≤ 3) = 0.5313

d) E(X) = 0.75

σX = 0.84

e) P(X=0) = 0.0099

Step-by-step explanation:

We have x: number in the sample who have a food allergy. As the sample is of n=15 and p=0.05, we have:

X \sim Bin(15, 0.05)

a) We have to determine P(X ≤ 3) and P(X < 3)

We can calculate P(X ≤ 3) as the sum of P(0), P(1), P(2) and P(3).

P(x\leq 3)=\sum_(k=0)^3P(k)\n\n\nP(x=0) = \binom{15}{0} p^(0)q^(15)=1*1*0.4633=0.4633\n\nP(x=1) = \binom{15}{1} p^(1)q^(14)=15*0.05*0.4877=0.3658\n\nP(x=2) = \binom{15}{2} p^(2)q^(13)=105*0.0025*0.5133=0.1348\n\nP(x=3) = \binom{15}{3} p^(3)q^(12)=455*0.0001*0.5404=0.0307\n\n\nP(x\leq 3)=0.4633+0.3658+0.1348+0.0307=0.9946

P(x<3) can be calculated from the previos result as:

P(x<3)=P(X\leq3)-P(3)=0.9946-0.0307=0.9639

b) We can calculate P(X ≥ 4) as:

P(X\geq4)=1-P(X<4)=1-P(X\leq3)=1-0.9946=0.0054

c) We can calculate P(1 ≤ X ≤ 3) as:

P(1 \leq X \leq 3)=P(1)+P(2)+P(3)=0.3658+0.1348+0.0307=0.5313

d) The expected value of a binomial variable is the product of the sample size n and the probability of success p:

E(X)=np=15*0.05=0.75

The standard deviation is calculates as:

\sigma_x=√(np(1-p))=√(15*0.05*0.95)=√(0.7125) =0.84

e) In this case, the sample size is n=90.

We can calculate the probability that none has a food allergy as:

P(x=0) = \binom{90}{0} p^(0)q^(90)=0.95^(90)=0.0099
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