The sum of a brother's and sister's ages is 57 years.If the brother is 5 years older than his sister,find their ages.

​

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.

Answer:14In

Step-by-step explanation:

volume(v)=768π

height(h)=3

Radius=√(v ➗ πxh)

Radius=√(768π ➗ 3π)

Radius=√(256)

Radius=14 In

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.

Answer:

6

Step-by-step explanation:

I did it

Answer:7.71

Step-by-step explanation:

Fusion 360

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.

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:

So, the length of side a (or b) is approximately 12.75 meters.

https://brainly.com/question/18124581

#SPJ2

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.

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:

where

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.

read more: https://brainly.com/question/5602071?referrer=searchResults

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.

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.

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.

https://brainly.com/question/34171008

#SPJ3

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:

Factors used:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

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.

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.

https://brainly.com/question/29805701

#SPJ12

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.

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.

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.

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.

Answer:

Rotation

Step-by-step explanation:

Given:  

Triangle DEF is congruent to Triangle GHJ by the SSS theorem

To find: transformation required to map Triangle DEF onto Triangle GHJ

Solution:

Two figures are said to be congruent if they overlap each other.

Two polygons are said to be congruent if they have same size and shape.

A rotation is a transformation that turns a figure about  the center of rotation.

Rotation transformation is required to map Triangle DEF onto Triangle GHJ

Answer:

translation

Step-by-step explanation:

Answer:

24 cartons

Step-by-step explanation:

8c=7

7/8=0.875

21/0.875=24

Answer:

4.7

Step-by-step explanation:

The number of laps per minute is equal to 1.25 laps.

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.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ3

Answer:

2

Step-by-step explanation:

edge

The positive slope of the asymptote of a hyperbola is a straight line with positive slope.

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.

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:

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%

Answer:

Perimeter =

[tex]2(length + width) \\ 2(5x + 1 + 4x - 1) \\ 2(5x + 4x + 1 - 1) \\ 2(9x ) \\ 9 \times 2 \\ = 18[/tex]

Without sufficient context or additional information, it is not possible to accurately determine the measure of the missing angle in the question.

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.

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!

Answer:

-7<x<6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variables

Mark me brainliest please!

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.

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.

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.

https://brainly.com/question/35114770

#SPJ3

The equation of the line that passes through the point (8,-8) and has a slope of -1 is y = -x.

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.

Answer:

11> x

Step-by-step explanation:

-5 > x-16

Add 16 to each side

-5+16 > x-16+16

11> x