Answer:
9.65×10¹⁴
Step-by-step explanation:
The 9 of 9.65 has been moved 14 places to the left to get to its position in 965,000,000,000,000. That is, its value has been multiplied by 10¹⁴.
_____
If you were to write 965,000,000,000,000 in expanded form, you would write it as ...
... 9×10¹⁴ +6×10¹³ +5×10¹² +0×10¹¹ +... +0×10⁰ = 9.65×10¹⁴
The first term of this sum is a clue as to how the number is written in scientific notation,
the answer is 9.65×10¹⁴
14+3n=8n-3(n-4) this is really hard please help me
how do i find the range and domain? please leave detailed steps because i'm struggling with this :(
Solve the system by substitution . 2x+y=-11 3x-4y=11
(3,5)
(-5,-3)
(-3,-5)
(5,3)
A country's people consume 6.6 billion pounds of candy (excluding chewing gum) per year. Express this quantity in terms of pounds per person per month. Note that the population of the country is 303 million.
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.
Find dy/dx
√(x+y) = x - 2y
(b) we often read that iq scores for large populations are centered at 100. what percent of these 78 students have scores above 100? (round your answer to one decimal place.)
1/5 of the animals at a zoo are monkeys. 5/7 of the monkeys are male. What fraction of the animals at the zoo are male monkeys?
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]
A small piece of metal weighs 0.77 gram. What is the value of the digit in the tenths place
Determine the unit rate of a marathon runner who travels 5/2 miles in 1/4 hour.
what is the y intercept of c=0.05m+4.95
What is .0091 rounded to thousands?
Another tent has the perimeter of 7.2 metres. If the width is 1.3 metres, what is the length?
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.
Is the difference of two rational numbers always rational? Explain
7x2+3[81-(4x6)]
Simplify
The crime rate in New York City has been steadily dropping over the past decades. In 1970, the murder rate was 15.8 per 100,000 people. In 2012, it had dropped to 3.5 per 100,000 people. What was the rate of decline?
Ray
OC
divides ∠AOB into two angles. Find the measurement of ∠AOC, if m∠AOB = 155°, and m∠AOC is by 15° greater than m∠COB.
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°
Round to the nearest hundred thousand
89, 659
Answer:
The nearest hundred thousand of the provided number is 100,000.
Step-by-step explanation:
Consider the provided number 89, 659
According to place value.
Hundred Th. Ten Th. Thousands hundreds Tens Ones
100,000 10,000 1000 100 10 1
We need to round it to the nearest hundred thousand.
The provided number can be written as 089,659
The digit at the hundred thousand place is 0.
The rule of rounding a number is:
If 0, 1, 2, 3, or 4 follow the number, then no need to change the rounding digit.
If 5, 6, 7, 8, or 9 follow the number, then rounding digit rounds up by one number.
Here, the number at the ten thousands place is 8, so to round up the number increase the digit of hundred thousand place by 1.
The digit at the hundred thousand place is 0 so increase it by 1.
Thus, the number can be rounded to the nearest hundred thousand is shown as:
100,000
The nearest hundred thousand of the provided number is 100,000.
Let y be a random variable with p(y) given in the accompanying table. find e(y ), e(1/y ), e(y 2 − 1), and v(y ). y 1 2 3 4 p(y) .4 .3 .2 .1
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.
Explanation: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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In a certain town, 22% of voters favor a given ballot measure. for groups of 21 voters, find the variance for the number who favor the measure.
a. 1.9
b. 13
c. 4.6
d. 3.6
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.
Explanation: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:
n = 21 (the number of voters in a group)p = 0.22 (the probability of a voter favoring the measure)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.
lynne took a taxicab from her office to the airport. she had to pay a flat fee of $2.05 plus $0.90 per mile. the total cost was $5.65. how many miles was the taxi trip?
The distance traveled by the taxi on trip is 4 miles.
What is a word problem?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.
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Give the derivative of f(x) = arctan(e^(5x)) at the point where x=0
The derivative of f(x) = arctan(e^(5x)) at x=0 is 2.5, using chain rule and the derivative of the arctan function.
Explanation: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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a triangle with a base of 12 millimeters and height of 11 millimeters
Is 0.5 equal to 9/18
The sales tax for an item was $24.50 and it cost $350 before tax. Find the sales tax rate.
To determine the sales tax rate, divide the sales tax amount by the item's pre-tax cost and convert to a percentage, yielding a 7% sales tax rate for this scenario.
To find the sales tax rate, you need to divide the amount of sales tax by the cost before tax and then convert it to a percentage. For an item that cost $350 before tax and had a sales tax of $24.50:
Divide the sales tax ($24.50) by the cost before tax ($350): $24.50 \/ $350 = 0.07.
Convert the decimal to a percentage: 0.07 x 100 = 7%.
Therefore, the sales tax rate for the item is 7%.
In Christopher Marlowe's The Tragical History of Doctor Faustus, why did Faustus begin to believe that human salvation was impossible? Faustus first began to believe that human salvation was impossible because In addition, he had
Answer:
he read the scripture and saw that all human beings sin and are doomed
Step-by-step explanation:
can someone please help me
Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression.
(tan 45° + tan 60°)2
A population has a mean of 40 and a standard deviation of 15. a sample of size 100 is taken at random from this population. the standard deviation of the sampling distribution of sample mean equals:
Suppose a box contains 10 red balls, 10 green balls, and 10 orange balls. you will be choosing 3 balls from the box without replacement. 13. what is the probability of drawing an orange on the first draw and a red on the second draw?
A woman who is 64 inches tall has a shoulder width of 16 inches. Write an equation relating height to the width. Find the height of a woman who has a shoulder width of 18.5 inches.
The height of woman who has a shoulder width of 18.5 inches is 74 inches
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the height of a woman who has a shoulder width of 18.5 inches be = A
Now , the equation will be
The height of the woman be = 64 inches
The shoulder width of the woman be = 16 inches
So , the equation will be
Let the height of a woman who has a shoulder width of 18.5 inches be = 18.5 x ( height of the woman be / shoulder width of the woman )
Substituting the values in the equation , we get
The height of a woman who has a shoulder width of 18.5 inches be A =
18.5 x ( 64 / 4 )
The height of a woman who has a shoulder width of 18.5 inches be A =
18.5 x 4
The height of a woman who has a shoulder width of 18.5 inches be A =
74 inches
Therefore , the value of A is 74 inches
Hence ,
The height of woman who has a shoulder width of 18.5 inches is 74 inches
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