The point A(-3,5) and the point B(1,-15) lie on the line L. Find the equation of the line L.

Answer : The fraction of the animals at the zoo are male monkeys, [tex]\frac{1}{7}[/tex]

Step-by-step explanation :

As we are given that:

Fraction of animals at a zoo are monkeys = [tex]\frac{1}{5}[/tex]

Fraction of monkeys are male = [tex]\frac{5}{7}[/tex]

So,

Fraction of the animals at the zoo are male monkeys = Fraction of animals at a zoo are monkeys × Fraction of monkeys are male

Fraction of the animals at the zoo are male monkeys = [tex]\frac{1}{5}\times \frac{5}{7}[/tex]

Fraction of the animals at the zoo are male monkeys = [tex]\frac{1}{7}[/tex]

Thus, the fraction of the animals at the zoo are male monkeys, [tex]\frac{1}{7}[/tex]

The variance for the number of voters who favor the ballot measure in groups of 21 is calculated using the formula for a binomial distribution, which yields an answer of 3.78. The closest option to this value is 3.6, answer option d.

In the question about a town where 22% of voters favor a given ballot measure, we are asked to find the variance for the number of voters who favor the measure in groups of 21 voters. To calculate the variance, we use the formula for the variance of a binomial distribution, which is np(1-p), where 'n' is the number of trials (voters in this case), 'p' is the probability of a voter favoring the measure, and '1-p' is the probability of a voter not favoring the measure.

Using the information provided:

Thus, the variance (Var) is:

Var = np(1-p) = 21 × 0.22 × (1 - 0.22) = 21 × 0.22 × 0.78 = 3.78

The closest answer to 3.78 is 3.6, which is option d.

Variance formula: [tex]\(npq\)[/tex]. Substitute [tex]\(n = 21\), \(p = 0.22\), \(q = 0.78\)[/tex]. Calculate to get variance. Answer: d. 3.6

To find the variance for the number who favor the measure in groups of 21 voters, we can use the binomial distribution formula.

The variance of a binomial distribution is given by [tex]\(npq\)[/tex], where:

- [tex]\(n\)[/tex] is the number of trials (number of voters in each group),

- [tex]\(p\)[/tex] is the probability of success (proportion of voters favoring the measure), and

- [tex]\(q\)[/tex] is the probability of failure (proportion of voters not favoring the measure).

Given:

- [tex]\(n = 21\)[/tex],

- [tex]\(p = 0.22\)[/tex] (22% favor the measure), and

- [tex]\(q = 1 - p = 1 - 0.22 = 0.78\)[/tex],

Let's calculate the variance:

[tex]\[ \text{Variance} = npq = 21 \times 0.22 \times 0.78 \][/tex]

[tex]\[ \text{Variance} = 21 \times 0.1716 \][/tex]

[tex]\[ \text{Variance} = 3.5976 \][/tex]

Rounded to one decimal place, the variance is approximately [tex]\(3.6\)[/tex].

So, the correct answer is d. 3.6.

Answer:  Length of tent would be 2.3 meters.

Step-by-step explanation:

Since we have given that

Perimeter of tent = 7.2 meters

Width of tent = 1.3 meters

Since we have given that

Perimeter = 2( length + width)

[tex]7.2=2(Length+1.3)\\\\\dfrac{7.2}{2}=Length+1.3\\\\3.6=Length+1.3\\\\3.6-1.3=Length\\\\2.3\ m=Length[/tex]

Hence, Length of tent would be 2.3 meters.

The distance traveled by the taxi on trip is 4 miles.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Flat fee of a taxicab = $2.05

Fees per mile = $0.90

The total cost = $5.65

Distance traveled by the taxi on trip is

⇒ [tex]\frac{5.65-2.05}{0.90}[/tex]

⇒ [tex]\frac{3.60}{0.90}[/tex]

⇒ [tex]4[/tex]

Hence we can conclude that the distance traveled by the taxi on trip is   4 miles.

Learn more about word problems here

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Final answer:

To find the candy consumption per person per month, divide the total consumption of candy by the population and then divide by 12 months. The calculation shows that each person consumes approximately 1.815 pounds of candy per month.

Explanation:

To calculate the amount of candy consumed per person per month, we first need to divide the total annual consumption by the population of the country. The total annual consumption is 6.6 billion pounds of candy, and the population is 303 million people. So, the annual consumption per person is:

(6.6 billion pounds) / (303 million people) = 21.78 pounds/person/year.

Now, to find the monthly consumption per person, we divide the annual consumption per person by 12 (months in a year):

(21.78 pounds/person/year) / (12 months/year) = 1.815 pounds/person/month.

Therefore, each person in the country consumes approximately 1.815 pounds of candy per month.

Answer:

he read the scripture and saw that all human beings sin and are doomed

Step-by-step explanation:

We are given that:

m∠AOB = m∠AOC + m∠COB

We are also given that:

m∠AOC = m∠COB + 15

m∠AOB = 155

Therefore:

155 = m∠COB + 15 + m∠COB

2 m∠COB = 140

m∠COB = 70°

and,

m∠AOC = m∠COB + 15 = 85°

Answers:

m∠COB = 70°

m∠AOC = 85°

The derivative of f(x) = arctan(e^(5x)) at x=0 is 2.5, using chain rule and the derivative of the arctan function.

The function given is f(x) = arctan(e^(5x)). To find its derivative at the point where x=0, we have to use the chain rule and the derivative of the arctan function.

Firstly, the derivative of arctan(u) is 1 / (1 + u^2). Therefore, if u = e^(5x), then the derivative of arctan(e^(5x)) is: 1 / (1 + (e^(5x))^2).

Secondly, because u = e^(5x), the derivative of u is 5e^(5x). We incorporate this using the chain rule to get the derivative: 5e^(5x) / (1 + (e^(5x))^2).

Finally, substitute x=0 into the derivative equation. We find that the derivative of the function at x=0 is: 5 / (1 + 1) = 2.5.

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This answer pertains to the computation of expected and variance values for a discrete random variable y using its given probability distribution function. Relevant principles include multiplying each value of y with its corresponding probability and then summing the products for the expected value, and further operations for other expected values and variance.

The subject pertains to finding the expected and variance values of a discrete random variable y, based on its probability distribution function (PDF). In this case, we have four values for y (i.e., 1, 2, 3, and 4) with corresponding probabilities given as .4, .3, .2, and .1 respectively.

E(y) or the expected value of y is obtained by multiplying each value of y with its corresponding probability and then summing the products, according to the formula E(y) = Σ y*P(y).

e(1/y) is the expected value of the reciprocal of y, obtained similarly by multiplying each 1/y with its corresponding P(y) and summing up the products.

e(y 2 − 1) represents the expected value of y-squared minus one, obtained by squaring each y, subtracting one, multiplying with the corresponding P(y), and then adding the results.

Finally, for v(y) or the variance of y, one would first need to find the expected value of y-squared [E(y^2)], and then use the identity v(y) = E(y^2) - {E(y)}^2 to compute the variance.

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n=277

Hope this will help!