Answer:
Neither
Step-by-step explanation:
In direct variation, as one number increases, the other number also increases and as one number decreases, the other number also decreases. In inverse variation, as one number increases, the other number decreases and as as one number decreases, the other number increases.
For direct variation, [tex]y=kx[/tex] and for indirect variation, [tex]y=\frac{k}{x}[/tex] where k is a constant.
x 2 5 20 40
y 40 20 5 2
Here,
[tex]\frac{2}{40}=\frac{1}{20}\\ \frac{5}{20}=\frac{1}{4}\\ \frac{20}{5}=4 \\\frac{40}{2} =20[/tex]
So, this is neither a direct variation nor an indirect variation.
what is the equation of the line that passes through the point (8,-8) and has a slope of -1 ?
The equation of the line that passes through the point (8,-8) and has a slope of -1 is y = -x.
Explanation:The equation of the line that passes through the point (8,-8) and has a slope of -1 can be found using the point-slope form: y - y1 = m(x - x1).
Using the given point (8,-8) and slope -1, the equation becomes y - (-8) = -1(x - 8).
Simplifying the equation, we have y + 8 = -x + 8. Rearranging the terms gives us the final equation: y = -x.
Kate baked some cookies. She put 12 cookies on each cookie sheet. If she baked 24 cookie sheets of cookies, how many cookies did she bake in all?
Answer:
She baked 288 cookies
Step-by-step explanation:
24 X 12 equals 288
Answer:
288 cookies
Step-by-step explanation:
can someone plz answer this quick
It takes Andre 4 minutes to swim 5 laps. How many laps per minute is that?
A. 1 1/4
B. 4/5
C. .75
D. 5/4
E. 1.25
The number of laps per minute is equal to 1.25 laps.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, time is 4 minutes and the number of laps is 5.
We can calculate as Number of laps per minute = Total number of laps/Number of minutes
= 5/4
= 1.25 laps
Hence, the number of laps per minute is 1.25 laps.
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Last week, Ida bought 8 cartons of raspberries for $7. How many cartons of raspberries can Ida
buy this week if she has $21?
Answer:
24 cartons
Step-by-step explanation:
8c=7
7/8=0.875
21/0.875=24
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2 : Suppose a sample of 517 suspected criminals is drawn. Of these people, 211 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.
Answer:
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.3583 , 0.4579)
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 517
Given data Suppose a sample of 517 suspected criminals is drawn. Of these people, 211 were captured.
'x' =211
The sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{211}{517} =0.4081[/tex]
[tex]q^{-} = 1-p^{-} = 1- 0.4081 = 0.5919[/tex]
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
[tex](p^{-} - Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} + Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} }{n} } )[/tex]
[tex](0.4081 - 2.326 \sqrt{\frac{0.4081 (0.5919 )}{517} } , 0.4081+ 2.326\sqrt{\frac{0.4081(0.5919 }{517} } )[/tex]
(0.4081-0.0498 , 0.4081 +0.0498)
(0.3583 , 0.4579)
Conclusion:-
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.3583 , 0.4579)
The perimeter of a square is represented by 4x − 16. What is the length of a side of this square?
Answer:
(x-4)
Step-by-step explanation:
Since a square has 4 equal sides, the perimeter of a square is 4 times one of the sides (which is equal to adding all the sides together). So:
Perimeter = 4(a side) = 4x-16
a side = (4x-16)/4 = (x-4)
The length of a side of a square with perimeter 4x - 16 is x - 4.
perimeter of a square is represented as follows:
perimeter = 4lwhere
l = length
Therefore,
4l = 4x - 16
divide both sides by 4
l = x - 4
The length = x - 4
Note a square have all its side equal to each other.
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what’s the circumference of a circle with radius of 18 in.
Answer:
C = 36 pi or approximately 113.04
Step-by-step explanation:
The circumference of a circle is given by
C = 2*pi*r
C = 2*pi*18
C = 36 pi
We can approximate pi by 3.14
C = 36*3.14
C =113.04
The diameters of computer parts made in a factory followed a normal distribution with a mean diameter of 6.5 inches and a standard deviation of 0.24 inches. The company considers all parts that are below the 16th percentile and all parts that are above the 84th percentile defective. What are the diameters of those defective parts? Show all of your work for full credit.
Answer:
The diameters below 0.41 inches and above 0.89 inches are considered as defective.
Step-by-step explanation:
Let X = diameters of computer parts.
The random variable X is normally distributed with mean, μ = 6.5 inches and standard deviation, σ = 0.24 inches.
The pth percentile is a data value such that at least p% of the data set is less than or equal to this data value and at least (100 - p)% of the data set are more than or equal to this data value.
Compute the 16th percentile of X as follows:
P (X < x) = 0.16
⇒ P (Z < z) = 0.16
The value of z for this probability is:
z = -0.99
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-0.99=\frac{x-6.5}{0.24}\\\\x=0.65-(0.99\times 0.24)\\\\x=0.4124\\\\x\approx 0.41[/tex]
The value at the 16th percentile is 0.44 inches.
Compute the 84th percentile of X as follows:
P (X < x) = 0.84
⇒ P (Z < z) = 0.84
The value of z for this probability is:
z = 0.99
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\0.99=\frac{x-6.5}{0.24}\\\\x=0.65+(0.99\times 0.24)\\\\x=0.8876\\\\x\approx 0.89[/tex]
The value at the 84th percentile is 0.89 inches.
Thus, the diameters below 0.41 inches and above 0.89 inches are considered as defective.
Many everyday decisions, like who will drive to lunch or who will pay for the coffee, are made by the toss of a (presumably fair) coin and using the criterion "heads, you will; tails, I will." This criterion is not quite fair, however, if the coin is biased (perhaps due to slightly irregular construction or wear). John von Neumann suggested a way to make perfectly fair decisions, even with a possibly biased coin. If a coin, biased so that P(x)equals 0.4700 and P(t)equals 0.5300, is tossed twice, find the probability
Answer:
P(hh) = 0.2209
P(ht) = 0.2491
P(th) = 0.2491
P(tt) = 0.2809
John von Neumann suggested that if both tosses results in same outcome then discard the result and start again. If each result is different then accept the first one
Step-by-step explanation:
We are given that a coin is unfair and the probabilities of getting a head and tail are
P(h) = 0.47
P(t) = 0.53
John von Neumann suggested a way to make perfectly fair decisions, even with a possibly biased coin.
He suggested to toss the coin twice, so the possible outcomes are
Sample space = {hh, ht, th, tt}
The probabilities of these outcomes are
P(hh) = P(h)*P(h)
P(hh) = 0.47*0.47
P(hh) = 0.2209
P(ht) = P(h)*P(t)
P(ht) = 0.47*0.53
P(ht) = 0.2491
P(th) = P(t)*P(h)
P(th) = 0.53*0.47
P(th) = 0.2491
P(tt) = P(t)*P(t)
P(tt) = 0.53*0.53
P(tt) = 0.2809
He suggested that if both tosses results in same outcome then discard the result and start again.
If each result is different then accept the first one, for example,
if you get heads on the first toss and tails on the second toss then result is heads.
if you get tails on the first toss and heads on the second toss then result is tails.
If you notice the probability of P(ht) and P(th) are same therefore, this strategy allows to make fair decision even when the coin is biased.
Match the type of valuation with the factors used in its calculation.
cash flows
profit
NOPAT
earnings
total cost of financing
weighted average
cost of capital
EVA
Here's the matching of the valuation types with the factors used in their calculation:
1. Cash flows: The actual cash generated or received by a business.
2. Profit: The amount of money a company makes after subtracting its expenses from its revenue.
3. NOPAT (Net Operating Profit After Tax): It is a company's operating profit after deducting taxes.
4. Earnings: The amount of money a company makes after subtracting its expenses from its revenue. It's often used interchangeably with profit.
5. Total cost of financing: The total cost associated with raising capital, including interest payments and other financing costs.
6. Weighted average: A calculated average where each value is weighted according to its significance.
7. Cost of capital: The cost of obtaining funds, which is typically the weighted average cost of debt and equity.
8. EVA (Economic Value Added): A measure of a company's financial performance based on the residual wealth calculated by deducting its cost of capital from its operating profit.
These factors are used in various combinations to perform different types of valuations, such as discounted cash flow analysis, earning-based valuation models, and economic value-added analysis.
The question is:
Match the type of valuation with the factors used in its calculation.
Types of valuation:
Cash flowsProfitNOPATEarningsTotal cost of financingWeighted averageCost of capital EVAFactors used:
Actual cashExpenses - RevenueProfit after deducting taxesProfitInterest paymentsCalculated averageAverage cost of debt and equityMeasure of a company's financial performancewhat does an individual's effective tax rate indicate?
The effective tax rate signifies the actual percentage of an individual's total income that is paid in taxes. It reflects the overall tax burden an individual faces, considering all forms of income and tax provisions. It gives a comprehensive view of the tax situation of an individual.
Explanation:An individual's effective tax rate refers to the percentage of their total income that they pay in taxes. It is calculated by dividing their total tax paid by their total income counts from all sources such as wages, profits, interest, rental income, and government transfers. The effective tax rate provides an accurate picture of an individual's tax burden and gives a holistic view of one's tax situation, considering all factors and tax code complexities.
For example, in the federal income tax, a progressive tax system, people with higher incomes tend to have a higher effective tax rate. To illustrate, in 2009, top 1% of households with an average income of $1,219,700 per year in pre-tax income had an average federal tax rate of 28.9%, but their effective tax rate was 20.4%. This is because the effective tax rate considers all sources of income and provisions like the earned income tax credit, not just tax from wages.
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Final answer:
An individual's effective tax rate represents the percentage of their total income that is paid in taxes, which may be different from the marginal tax rate applied to their last dollar of income.
Explanation:
An individual's effective tax rate indicates the proportion of their total income that is paid in taxes. This rate is calculated by dividing the tax liability by the total income. It contrasts with the marginal tax rate, which is the tax rate applied to an additional dollar of taxable income.
For example, with an income of $20,000 and a tax payment of $2,581.25, the effective tax rate would be $2,581.25 divided by $20,000, equaling 12.9 percent. This rate reflects the average percentage of income paid in taxes, as opposed to the marginal tax rate, which in this case could be higher, such as 15 percent. The marginal tax rate is particularly important for understanding economic decisions, as it affects the tax paid on any additional income earned.
Given:
f(x) = x2 - 6x + 13
What is f (4)?
Answer:
5
Step-by-step explanation:
f(x) = x^2 -6x+13
Let x=4
f (4) = 4^2 -6(4) +13
= 16 -24 +13
= 5
The value of f(4) for the function f(x) = x^2 - 6x + 13 is 5.
Explanation:In order to find f(4) for the function f(x) = x2 - 6x + 13, we replace each x in the equation with 4. So, f(4) = (4)2 - 6(4) + 13. Squaring 4 gives us 16, and 6 times 4 gives us 24.
Therefore, our equation is now f(4) = 16 - 24 + 13. Solving for f(4), we subtract 24 from 16 to get -8, and then add 13 to get 5.
Thus, f(4) = 5.
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Roger Brown works for the sanitation department. He earns a salary of $721.00 biweekly. His boss gave him
a raise that will go into effect at the first of the year. His new annual salary will be $20.995.00. How much
more money will Roger make next year than this year?
Answer:
2249 dollars more
Step-by-step explanation:
52 weeks in one year so divide by 2 and then multiply by 721 and then take that amount and dubtract the new salary 20.995 and subtract the previous annual amount and then boom 2295 more
Final answer:
Roger will make $2,249.00 more money next year than he did this year.
Explanation:
To determine how much more money Roger will make next year compared to this year, we need to find the difference between his new annual salary and his current biweekly salary.
To calculate the annual salary, we can multiply the biweekly salary by the number of biweekly periods in a year. There are 26 biweekly periods in a year (52 weeks / 2). So, Roger's current annual salary is $721.00 x 26 = $18,746.00.
The difference between his new annual salary and his current annual salary is $20,995.00 - $18,746.00 = $2,249.00. Therefore, Roger will make $2,249.00 more money next year than he did this year.
The volume of a cylinder is 768 Π in3. Find the radius of the cylinder (in inches) if the height is 3 in.
Answer:14In
Step-by-step explanation:
volume(v)=768π
height(h)=3
Radius=√(v ➗ πxh)
Radius=√(768π ➗ 3π)
Radius=√(256)
Radius=14 In
Jay wants his money to double in eight years. What interest rate does he need to earn? *
Answer:
The rate of interest is 12.5%
Step-by-step explanation:
Let the principal be P
We are given that Jay wants his money to double in eight years.
So, Amount = 2P
Simple interest = Amount - Principal = 2P-P = P
Time taken to double the money is 8 years
So,[tex]SI = \frac{P \times T \times R}{100}\\P=\frac{P \times 8 \times R}{100}\\100=8 \times R\\\frac{100}{8}=R\\12.5 =R[/tex]
Hence The rate of interest is 12.5%
Select all the correct answers. What were the three main social reform movements of the nineteenth century in United States? abolitionist movement labor reform movement mental health reform movement women’s rights movement
Answer:
What were the three main social reform movements of the nineteenth century in United States?
abolitionist movement
mental health reform movement
women’s rights movement
Step-by-step explanation:
Mark bought a brand new car for $35,000 in 2008. If the car depreciates in value approximately 8% each year, write an exponential function to model the situation. Then, find the value of the car in 2015. Is this considered growth or decay?
Answer:
[tex]V(t) = 35000(0.92)^{t}[/tex]
Decay function
The value of the car in 2015 is $19,525.
Step-by-step explanation:
A exponential value function has the following format:
[tex]V(t) = V(0)(1+r)^{t}[/tex]
In which V(t) is the value after t years, V(0) is the initial value and 1+r is the yearly variation rate.
If 1+r>1, the function is a growth function.
If 1-r<1, the function is a decay function.
Mark bought a brand new car for $35,000 in 2008.
This means that [tex]V(0) = 35,000[/tex]
If the car depreciates in value approximately 8% each year
Depreciates, then r is negative. So [tex]r = -0.08[/tex]
Then
[tex]V(t) = V(0)(1+r)^{t}[/tex]
[tex]V(t) = 35000(1-0.08)^{t}[/tex]
[tex]V(t) = 35000(0.92)^{t}[/tex]
0.92 < 1, so decay function.
Then, find the value of the car in 2015.
2015 is 2015-2008 = 7 years after 2008. So this is V(7).
[tex]V(t) = 35000(0.92)^{t}[/tex]
[tex]V(7) = 35000(0.92)^{7}[/tex]
[tex]V(7) = 19525[/tex]
The value of the car in 2015 is $19,525.
The surface area for a rectangular prism is given by the formula SA = 2ab + 2bc + 2ac, where a, b, and c are the lengths of the
prism
If the surface area of a rectangular prism with side c measuring 9 meters is 350 square meters and length of side a measuring the
same length as side b, then what is the length of side a of the rectangular prism?
We are given
[tex]2ab + 2bc + 2ac = 350 \iff ab + bc + ac = 175[/tex]
We are also given [tex]a=b[/tex] and [tex]c=9[/tex], which allows us to rewrite the equation as
[tex]a^2 + 9a + 9a = 175 \iff a^2+18a-175=0[/tex]
(I substituted every "b" with "a" and every "c" with "9").
The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.
The length of sides a and b of a rectangular prism, given a surface area of 350 square meters and side c measuring 9 meters, is approximately 12.75 meters each.
Explanation:In this question, we have a rectangular prism whose surface area is 350 square meters, with side c measuring 9 meters and sides a and b of equal lengths. The formula for the surface area of a rectangular prism is SA = 2ab + 2bc + 2ac. Since a = b, we can rewrite the equation as SA = 2a^2 + 2ac. Therefore, inserting the given measurements into the formula and solving for a we get:
350 = 2a^2 + 2a*9 350 = 2a^2 + 18a325 = 2a^2 a^2 = 325/2 = 162.5 a = sqrt(162.5) = 12.75.So, the length of side a (or b) is approximately 12.75 meters.
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If a woman making $35 an hour gets a 10% raise (35 x 0.10 = 3.50 so $35 + $3.50 = $38.50/hour), how much will she now make in a 6 hour work day? (multiply by 6!) *
What is the positive slope of the asymptote of the hyperbola? The positive slope of the asymptote is .
Answer:
2
Step-by-step explanation:
edge
The positive slope of the asymptote of a hyperbola is a straight line with positive slope.
Explanation:The positive slope of the asymptote of a hyperbola is a straight line with positive slope (option b). A positive slope indicates that the line moves up the y-axis as the x-value increases, while a negative slope means that the line moves down the y-axis. The appearance of positive slope differs from negative slope and zero slope in that it moves up the y-axis as the x-value increases, while negative slope moves down the y-axis and zero slope means a horizontal line.
When working properly, a machine that is used to makes chips for calculators does not produce more than 4% defective chips. Whenever the machine produces more than 4% defective chips, it needs an adjustment. To check if the machine is working properly, the quality control department at the company often takes samples of chips and inspects them to determine if they are good or defective. One such random sample of 200 chips taken recently from the production line contained 12 defective chips. Find the p-value to test the hypothesis whether or not the machine needs an adjustment. What would your conclusion be if the significance level is 2.5%
Answer:
The proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.
Step-by-step explanation:
In this case we need to test whether the proportion of defective chips produced by the machine is more than 4%.
The hypothesis can be defined as follows:
H₀: The proportion of defective chips produced by the machine is not more than 4%, i.e. p ≤ 0.04.
Hₐ: The proportion of defective chips produced by the machine is more than 4%, i.e. p > 0.04.
The information provided is:
X = 12
n = 200
α = 0.025
The sample proportion of defective chips is:
[tex]\hat p=\frac{X}{n}\\\\=\frac{12}{200}\\\\=0.06[/tex]
Compute the test statistic as follows:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\=\frac{0.06-0.04}{\sqrt{\frac{0.04(1-0.04)}{200}}}\\\\=1.44[/tex]
The test statistic value is 1.44.
Decision rule:
We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.
Compute the p-value of the test:
[tex]p-value=P(Z>1.44)\\=1-P(Z<1.44)\\=1-0.92507\\=0.07493\\\approx 0.075[/tex]
The p-value of the test is 0.075.
p-value = 0.075 > α = 0.025
The null hypothesis was failed to be rejected at 2.5% level of significance.
Thus, it can be concluded that the proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.
To test the hypothesis whether or not the machine needs an adjustment, we can use a one-sample proportion test. Calculate the sample proportion, the standard error of the proportion, and the test statistic. Find the p-value and compare it to the significance level to make a conclusion.
Explanation:To test the hypothesis whether or not the machine needs an adjustment, we can use a hypothesis test. The null hypothesis (H0) is that the machine is working properly and the alternative hypothesis (Ha) is that the machine needs an adjustment. We can use a one-sample proportion test since we are testing the proportion of defective chips.
Calculate the sample proportion, which is the number of defective chips divided by the sample size: p-hat = 12/200 = 0.06.Calculate the standard error of the proportion: SE = sqrt((p-hat * (1 - p-hat)) / n) = sqrt((0.06 * 0.94) / 200) = 0.0212.Calculate the test statistic, which is the difference between the sample proportion and the hypothesized proportion divided by the standard error: z = (p-hat - p) / SE = (0.06 - 0.04) / 0.0212 = 0.9434.Find the p-value associated with the test statistic using a standard normal distribution table or a calculator. In this case, the p-value is the probability of observing a test statistic as extreme as 0.9434 or more extreme if the null hypothesis is true.If the p-value is less than the significance level (2.5%), we reject the null hypothesis and conclude that the machine needs an adjustment. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the machine needs an adjustment.
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Blake has only nickels and dimes. He has twice as many nickels as
dimes. The total value of his coins is 40 cents.
Answer:
Blake has 2 dimes and 4 nickels
Step-by-step explanation:
2 dimes = 20 cents
4 nickels = 20 cents
20 + 20 = 40 cents
2 × 2 = 4 dimes
Final answer:
Explanation of the relationship between the number of nickels and dimes in a coin collection yielding a total value of 40 cents.
Explanation:
Problem Statement:
Blake has only nickels and dimes. He has twice as many nickels as dimes. The total value of his coins is 40 cents.
Solution:
Let the number of dimes be 'x', so the number of nickels is '2x'.
Value of dimes = 10x cents, value of nickels = 5(2x) = 10x cents.
Given total value is 40 cents, so 10x + 10x = 40.
Solving the equation, x = 2. Therefore, Blake has 2 dimes and 4 nickels.
Four entrees are on next Friday’s menu: BBQ ribs, seafood platter, roast beef, and filet mignon. The number of each item sold the last time this menu was offered was 76, 118, 96, and 154, respectively, for a total of 444 entrees sold. For the past five Fridays, the following noon meal counts were recorded: 447, 423, 437, 444, and 429. For next Friday, how many portions of roast beef will be forecasted?
Answer:
95.
Step-by-step explanation:
Step one: the first step here is to find the mean or average of the data for the six(6) weeks of total entrees. That is, we will have;
Average = (444 + 447 + 423 + 437 + 444 + 429)/ 6 = 2,624 / 6 = 437.3.
Average = 437.3.
Step two: the next step here is to determine the popularity index for the roast beef roast beef will be forecasted and that will be;
popularity index = 96 / 444.
popularity index = 21.6%.
Step three: the quantity of roast beef that should be forecasted for next Friday will be;
Popularity index × Average.
0.216 × 437.3 = 95.
Hence, the quantity of roast beef that should be forecasted for next Friday will be 95.
To forecast the number of roast beef portions, we first determine the proportion of roast beef sold the last time this menu was offered, then average the total meal counts from the past five Fridays, and apply the proportion to this average to get the forecasted demand.
To forecast the number of portions of roast beef for next Friday, we can apply a demand ratio approach, which uses historical sales data to predict future demand.
Since we have the last time sales data for the entrées, and the counts of total meals sold for the past five Fridays, the first step is to calculate the proportion of each entrée sold relative to the total sales from the last time this menu was offered.
The number sold for each entrée the last time was: BBQ ribs - 76, seafood platter - 118, roast beef - 96, and filet mignon - 154, summing up to a total of 444 entrées.
The proportion for roast beef is calculated by dividing the number of roast beef meals sold by the total number of entrées sold: 96/444. This gives us the portion of meals that were roast beef.
To forecast the demand for roast beef for next Friday, we need to apply this proportion to an estimate of the total number of meals to be served. We can get this estimate by averaging the total meal counts from the past five Fridays: (447 + 423 + 437 + 444 + 429)/5 which equals 436 meals on average (rounded to the nearest whole number).
Multiplying this average by the roast beef proportion (96/444), we get the forecast for roast beef portions: 436 * (96/444) ≈ 93 portions.
Find the perimeter of the window to the nearest hundredth.
3 ft
Answer:7.71
Step-by-step explanation:
Fusion 360
Question 9 of 20
Find the measure of the missing angle.
14
?
29
Without sufficient context or additional information, it is not possible to accurately determine the measure of the missing angle in the question.
Explanation:The question asks to find the measure of a missing angle but does not provide sufficient context or information such as a diagram or type of geometric figure involved, making it impossible to determine the correct answer without additional information. The provided references include various angle measures and different contexts (e.g., clocks, projectile motion, trigonometry), none of which pertain directly to the question at hand. Due to the lack of relevant details, the measure of the missing angle cannot be calculated or estimated. Mathematics often requires precise information, and without it, we cannot solve for unknown angles or other values.
The mean annual precipitation for a large city in the Midwest is 30.85 inches with a standard deviation of 3.6 inches. Assume that the variable is normally distributed. a) What is the probability that a randomly selected month will have at least 30 inches of precipitation? b) What is the probability that of a random sample of 32 months taken will have a mean amount of precipitation between 30 and 31.5 inches?
Given Information:
Mean annual precipitation = 30.85 inches
Standard deviation of annual precipitation = 3.6 inches
Required Information:
a) P(X ≥ 30) = ?
b) P(30 < X < 31.5) = ?
Answer:
a) P(X ≥ 30) = 59.48%
b) P(30 < X < 31.5) = 16.62%
Explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
a) We want to find out the probability that a randomly selected month will have at least 30 inches of precipitation.
At least 30 inches of precipitation means equal to or greater than 30.
[tex]P(X \geq 30) = 1 - P(X \leq 30)\\\\P(X \geq 30) = 1 - P(Z \leq \frac{x - \mu}{\sigma} )\\\\P(X \geq 30) = 1 - P(Z \leq \frac{30 - 30.85}{3.6} )\\\\P(X \geq 30) = 1 - P(Z \leq \frac{-0.85}{3.6} )\\\\P(X \geq 30) = 1 - P(Z \leq -0.24)\\[/tex]
The z-score corresponding to -0.24 is 0.4052
[tex]P(X \geq 30) = 1 - 0.4052\\\\P(X \geq 30) = 0.5948\\\\P(X \geq 30) = 59.48 \%\\[/tex]
Therefore, the probability that a randomly selected month will have at least 30 inches of precipitation is 59.48%
b) We want to find out the probability that of a random sample of 32 months taken will have a mean amount of precipitation between 30 and 31.5 inches.
[tex]P(30 < X < 31.5) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(30 < X < 31.5) = P( \frac{30- 30.85}{3.6} < Z < \frac{31.5 - 30.85}{3.6} )\\\\P(30 < X < 31.5) = P( \frac{-0.85}{3.6} < Z < \frac{0.65}{3.6} )\\\\P(30 < X < 31.5) = P( -0.24 < Z < 0.18 )\\[/tex]
The z-score corresponding to -0.24 is 0.4052 and 0.18 is 0.5714
[tex]P(30 < X < 31.5) = P( Z < 0.18 ) - P( Z < -0.24 ) \\\\P(30 < X < 31.5) = 0.5714 - 0.4052 \\\\P(30 < X < 31.5) = 0.1662\\\\P(30 < X < 31.5) = 16.62 \%[/tex]
Therefore, the probability that of a random sample of 32 months taken will have a mean amount of precipitation between 30 and 31.5 inches is 16.62%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.2, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.24 then go for 0.04 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Please help me .which number is less than 4.703
Answer:
4.7
Step-by-step explanation:
Giving brainliest for CORRECT awnser.
Answer:
11> x
Step-by-step explanation:
-5 > x-16
Add 16 to each side
-5+16 > x-16+16
11> x
What is the range of this set of data?
111.97, 63, 84, 100, 119,72
Answer:
56
Step-by-step explanation:
The range of a data set is the difference between the largest and the smallest values in that data set. In this case, the largest value in the data set is 119, and the smallest is 63. 119-63=56, which is the range. Hope this helps!
he following probabilities are based on data collected from U.S. adults during the National Health Interview Survey 2005-2007. Individuals are placed into a weight category based on weight, height, gender and age. Probability Underweight 0.019 Healthy weight 0.377 Overweight (not obese) 0.35 Obese 0.254 Based on this data, what is the probability that a randomly selected U.S. adult weighs more than the healthy weight range?
Answer:
60.4% probability that a randomly selected U.S. adult weighs more than the healthy weight range
Step-by-step explanation:
We have these following probabilities:
1.9% probability that a randomly selected U.S. adult is underweight.
37.7% probability that a randomly selected U.S. adult has healthy weight.
35% probability that a randomly selected U.S. adult is overweight.
25.4% probability that a randomly selected U.S. adult is obese.
Based on this data, what is the probability that a randomly selected U.S. adult weighs more than the healthy weight range?
More than the healthy weight range: overweight or obese
35% + 25.4% = 60.4%
60.4% probability that a randomly selected U.S. adult weighs more than the healthy weight range