Evaluate (f+2)(g+8) , when f=4 and g=2.

Using sampling concepts, it is found that the population of interest is given by:

All American teens who are between the ages of 13 and 17.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

In this problem, a sample of American teenagers aged 13 to 17 was taken, hence all American teenagers aged 13 to 17 is the population of interest.

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The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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a) The annual demand is 420.

b) The weekly demand forecast is 8.08

c) The EOQ would be approximately 41

d) The reorder point is 45.12

e) The total annual cost is 102439.02

f) The pipeline inventory is 32.32

g) The new reorder point is 48.82

a) To calculate the annual demand, you need to use your student number. For example, if your student number is BBAW190102, the last digit is 2. So, the annual demand would be 400 + 10 x 2 = 420.

b) To calculate the weekly demand forecast for 2021, you need to divide the annual demand by the number of weeks in a year. Assuming there are 52 weeks in a year, the weekly demand forecast would be 420 / 52 = 8.08 (rounded to two decimal places).

c) The economic order quantity (EOQ) can be calculated using the formula EOQ = sqrt((2DS) / H), where D is the annual demand, S is the ordering cost per order, and H is the annual holding cost. In this case, D is the annual demand calculated in part a, S is $1000, and H is $500. Plugging in these values, the EOQ would be sqrt((2 x 420 x 1000) / 500) = sqrt(840000 / 500) = sqrt(1680) ≈ 41 (rounded to the nearest whole number).

d) The reorder point is the level of inventory at which a new order should be placed. It can be calculated using the formula reorder point = demand during lead time + safety stock. The demand during lead time is the average demand per week multiplied by the lead time, which is 8.08 x 4 = 32.32 (rounded to two decimal places). The safety stock is the z-score multiplied by the standard deviation of weekly demand. The z-score for a 90% cycle service level is 1.28 (given in the question) and the standard deviation of weekly demand is 10 (given in the question). So, the safety stock would be 1.28 x 10 = 12.8 (rounded to one decimal place). Therefore, the reorder point would be 32.32 + 12.8 = 45.12 (rounded to two decimal places).

e) The total annual cost of managing the inventory can be calculated using the formula TC = (S x D/Q) + (H x (Q/2 + s)), where S is the ordering cost per order, D is the annual demand, Q is the economic order quantity, H is the annual holding cost, and s is the safety stock. Plugging in the values, the total annual cost would be (1000 x 420/41) + (500 x (41/2 + 12.8)) = 102439.02 (rounded to two decimal places).

f) The pipeline inventory refers to the inventory that is in transit or being processed. In this case, since the lead time is 4 weeks, the pipeline inventory would be the average demand per week multiplied by the lead time. So, the pipeline inventory would be 8.08 x 4 = 32.32 (rounded to two decimal places).

g) To achieve a 95% cycle service level, we need to calculate the new safety stock and reorder point. The z-score for a 95% cycle service level is 1.65 (given in the question). Using the same formula as in part d, the new safety stock would be 1.65 x 10 = 16.5 (rounded to one decimal place). Therefore, the new reorder point would be 32.32 + 16.5 = 48.82 (rounded to two decimal places).

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Answer:

n × 2

Step-by-step explanation:

Because the numbers are the multiples of 2, if also the number times 2.

The sample size increases, the probability of obtaining a sample mean less than 3500 decreases. The mean of the sample mean distribution is equal to the population mean, which is 7500.

a) The probability that, on a single test, x is less than 3500 can be calculated using the standard normal distribution. We need to standardize the value using the z-score formula: z = (x - μ) / σ. Substituting the given values, we get z = (3500 - 7500) / 1750 ≈ -2.286.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -2.286. The probability is approximately 0.0116, or 1.16%. Therefore, there is a 1.16% chance that a single test result will be less than 3500, indicating leukopenia.

(b) When the doctor uses the average x (sample mean) for two tests taken about a week apart, the probability distribution of x (sample mean) follows a normal distribution. The mean of the sample mean distribution is equal to the population mean, which is 7500. The standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 2.

The probability distribution of x (sample mean) < 3500 can be calculated by standardizing the value using the z-score formula and then finding the corresponding probability from the standard normal distribution table or a calculator. With two tests, the probability distribution will be narrower compared to a single test. The exact probability depends on the specific value of the sample mean and the standard deviation of the sample mean distribution.

(c) When considering three tests taken a week apart, the process is similar to part (b). The mean of the sample mean distribution remains the same at 7500, but the standard deviation of the sample mean distribution is now divided by the square root of 3, since the sample size is 3. As the sample size increases, the standard deviation of the sample mean distribution decreases, resulting in a narrower distribution.

The probability distribution of x (sample mean) < 3500 can be calculated using the z-score formula and finding the corresponding probability from the standard normal distribution table or a calculator. With three tests, the probability distribution will be even narrower compared to two tests.

In summary, as the sample size increases, the probability of obtaining a sample mean less than 3500 decreases. With more tests, we can have greater confidence in the accuracy of the sample mean and draw stronger conclusions about the individual's condition. If a person had a sample mean less than 3500 based on three tests, it would indicate a higher level of certainty about the presence of leukopenia, potentially leading to further investigation or treatment options.

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Answer:  

∠A= 60

Step-by-step explanation:  

SinA = 13/15  

SinA = 0.866  

A = inverse sin (0.866)  

A = 59.997

A = 60

The object weighs 24 pounds on Earth. The weight of an object on a certain planet is 2/5 of the weight on Earth. We know that an object weighs 9 3/5 pounds on the planet. So, we can use this information to find the weight of the object on Earth.

The equation to solve for w to find the object's weight on Earth in pounds is given by; w = 9 3/5 / 2/5 = 9.6 / 0.4 = 24

The object weighs 24 pounds on Earth. How to solve the equation?

The weight of an object on a certain planet is 2/5 of the weight on Earth. We know that an object weighs 9 3/5 pounds on the planet. So, we can use this information to find the weight of the object on Earth. To do this, we use the equation:

w = (2/5) * x

where w is the weight of the object on the planet and x is the weight of the object on Earth. We can substitute the values given into this equation to get:

w = (2/5) * x9 3/5 = (2/5) * x

Multiplying both sides by 5/2, we get:

x = 9 3/5 * 5/2x = 48/5

On simplification, we get: x = 9 3/5 pounds

So, the object weighs 24 pounds on Earth. This is our final answer.

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Answer:

x = 2 ; y = 152

Step-by-step explanation:

15x - 2 = 9x + 10

15x - 9x = 10 + 2

6x = 12

6/6 x = 12/6

x = 2 degrees

9 * 2 + 10 + y + 180

18 + 10 + y = 180

28 + y = 180

y = 180 - 28

y = 152 degrees

Answer:

10

Step-by-step explanation:

divide 20 by 2. so the answer is 10.

Answer:

Circumference ~ 233.7

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is about 37.2. Plug 37.2 into the formula 2(pi)r to find the Circumference. The answer is 233.7 rounded to the nearest tenth.

Answer:

Total net earnings = 80+15(x-8)

If Daisy works 13 hours, she will be paid $155.

Step-by-step explanation:

Let Daisy works for x hours a day

She is paid $10 per hour for the first 8 hours she works in a day.

So, pay for the first 8 hours =10\times8=80 dollars

For every extra hour she works, she is paid 1.5 times her hourly wage.

The number of hours worked over 8 hours is given by = x-8

So, pay for the hours worked over 8 hours = 15(x-8) dollars

Total net earnings = 80+15(x-8)

And when x = 13

The pay is : 80+15(13-8)

= 80+15(5)

= 80+75 = 155 dollars

Answer:

1) y = 15(x-8) + 80

2) $155

Step-by-step explanation:

First blank:

use the linear expression form: y = mx + b

If Daisy is working more than 8 hours, (since the problem says x > 8), then she is getting $10 per hour guaranteed, which is $80 overall. So 80 will be our constant term, b

for every hour after 8, she is being paid 1.5 x 10, which is $15. This is our slope term, m.

So our expression is: y = 15(x-8) + 80

The reason we use x-8 instead of just x, is because x is the number of hours she works, but she will only be paid 15 bucks/hour when she works after 8 hours. So we need to subtract 8 from x to get the number of hours she works after the minimum 8.

Second Blank:

If Daisy works 13 hours, just replace x with 13 in our formula:

y = 15(x-8) + 80

y = 15(13-8) + 80

y = 15(5) + 80

y = 75 + 80

y = $155

If she works for 13 hours, she gets paid $85

Hare Krishna! :)

The series Σa_n, where a_n = 1/n!, converges is determined using the ratio test.

The given series Σa_n with a_n = 1/n! and asked to determine its convergence using the ratio test. The ratio test states that if the limit of |a_(n+1)/a_n| as n approaches infinity is less than 1, the series converges, and if the limit is greater than 1, the series diverges. If the limit equals 1, the test is inconclusive.

Let's apply the ratio test to our given series:

|a_(n+1)/a_n| = |(1/(n+1)!)/(1/n!)| = |n!/((n+1)!)| = |1/(n+1)|

Now, let's find the limit as n approaches infinity:

lim(n→∞) |1/(n+1)| = 0

Since the limit is less than 1, the series converges according to the ratio test.

Using the ratio test, we have determined that the series Σa_n, where a_n = 1/n!, converges.

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The no of student tickets sold, x = 30

The no of adult tickets sold, y = 37

Algebra is a branch of mathematics in which problems are represented by mathematical expressions. To form a meaningful mathematical expression, variables such as x, y, and z are used, as well as mathematical operations such as addition, subtraction, multiplication, and division.

The drama club is selling tickets to their play in order to cover the costs of the production.

Let x represent a student ticket and y represent an adult ticket.

Cost of student ticket, x = $7

Cost of an adult ticket, y = $9

The total number of tickets, x + y = 67 ... (1)

There was a total of $543 in revenue from the sale of 67 total tickets.

7x + 9y = 543 ...(2)

Multiplying eq(1) by 7, we get

7x + 7y = 469 ...(3)

Subtract eq (3) from (2), and we get

2y = 74

y = 37,

Now substitute the y value in eq (1)

x + 37 = 67

x = 67-37

x = 30

Therefore The no of student tickets sold, x = 30

The no of adult tickets sold, y = 37

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Answer:

10√2

Step-by-step explanation:

√200=√2*100=10√2

Ans.is 10√2

the topic is Surds in math

The total number of squares that can be formed with 4 of the 200 points as vertices is 39,600.

The equation for calculating the total number of squares that can be formed with 4 of the 200 points as vertices are:

Number of squares = (200 Choose 4) x (4!/2) = (200!/196! x 4!) x (4!/2)

Using the factorial notation, this simplifies to:

Number of squares = (200 x 199 x 198 x 197) x (2) / (4 x 3 x 2 x 1)

The number of squares = 39,600.

Solving the equation, the total number of squares that can be formed is 39,600.

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Answer:

17

Step-by-step explanation:

11 - 2(-3) = 11 + 6 = 17

should put -3 where x is

Answer:

1. 1114/117        2. 212/123       3. -256/29       4. -27/79

Step-by-step explanation:

1. 1114/117

2. 212/123

3. -256/29

4. -27/79

The test's pooled t statistic has a value of 1.2. This indicates that the f statistic's value will be 1.44.

As contrast to a one-sided hypothesis, that is always bounded either by above or below, a two-sided hypothesis is just an alternate hypothesis that is not bounded either by above or below.

As the question stated-

The same two-sided hypothesis was tested by a researcher comparing the sample means from two distinct populations using two different exams: a one-way anova f test and a two-sample t test using t statistic using pooled variance.

Thus,

f statistic's value = 1.2² = 1.44

Thus, the test's pooled t statistic has a value of 1.2. This indicates that the f statistic's value will be 1.44.

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Answer:

7,880.85, not 100% sure - might want to check other answers

Answer:

$43.70 dollars

Step-by-step explanation:

Given the following question:

9.25% of 40

In order to find the answer, we will use the formula to calculate percentages, and then add that answer to the initial cost of the item we are buying.

\(\frac{p\times c}{100}\)
\(\frac{9.25\times40}{100} =9.25\times40=370\div100=3.70\)
\(=3.70\)

Now add:
\(40+3.70=43.70\)
\(=43.70\)

Which means after a tax rate of 9.25% the item would cost "$43.70 dollars."

Hope this helps.

The original budget for the shopping is equal to $450.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that while shopping for a big event you look at your budget and discover that you’ve already used 85% of the available funds, and you only have $67.50 left.

The left budget of $67.50 is equal to 15%. The original budget is calculated as,

15% of budget ⇒ $67.50

1% of budget ⇒ $67.50 / 15

100% of budget ⇒ ($67.50 x 100)/15

100% of budget ⇒ $450

Therefore, the original budget for the shopping is equal to $450.

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The required equation of the line is 2x + 5y + 5 = 0

What is an equation?

Equations are used to describe geometric shapes in Cartesian geometry. Because the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions, the goal has shifted: instead of directly stating the solutions or counting them, which is impossible, one utilizes equations to investigate the features of figures. This is the fundamental concept of algebraic geometry, a significant branch of mathematics. Algebra is concerned with two types of equations: polynomial equations and the particular case of linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial, while linear equations have the form ax + b = 0, where a and b are parameters, when there is only one variable. Algorithms are used to solve equations from either family.

Given equation of the line is 2x + 5y = 10

or, 5y = -2x + 10

or, y = -2x/5 + 2

slope of the equation, m = -2/5

Since the lines are parallel, so the required equation of the line is

y-1 = (-2/5)(x+5)

or, 5(y-1) = -2(x+5)

or, 5y-5 = -2x-10

or, 2x + 5y + 5 = 0

Hence, the required equation of the line is 2x + 5y + 5 = 0

i.e. 2x + 5y = -5

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Answer:

4

Step-by-step explanation:

L x W = A

A ÷ L = W

Answer:

  about 1.3885 miles ≈ 7331 ft

Step-by-step explanation:

The height of the helicopter can be found using the tangent relation, which we know relates the sides and angles of a right triangle by ...

  Tan = Opposite/Adjacent

__

With reference to the attached diagram, the above relation can be used to find the lengths of AC and BC, which we know total 4 miles.

  tan(28°) = h/AC   ⇒   AC = h/tan(28°) = h·tan(90° -28°) = h·tan(62°)

  tan(45°) = h/BC   ⇒   BC = h/tan(45°) = h·tan(90° -45°) = h·tan(45°)

The total distance between A and B is then ...

  AB = AC +BC

  4 = h·tan(62°) +h·tan(45°) = h(tan(62°) +tan(45°))

Dividing by the coefficient of h, we have the value of h:

  h = 4/(tan(62°) +tan(45°)) = 4/(1.88073 +1) ≈ 1.38854 . . . . miles

In feet, that is ...

  (1.38854 mi)(5280 ft/mi) = 7331 ft

The height of the helicopter is 1.38854 miles, or 7331 feet.

sample B is harder than sample A.To compare the hardness values of samples A and B, we need to convert them to the same scale.

Rockwell hardness scales are designated by a letter, such as B or F, and each scale has a different range and units of measurement.

To convert sample A's hardness value from the B scale to the F scale, we can use the conversion chart. According to the chart, the conversion formula from B to F scale is HRF = (HRB x 1.000) + 18. Therefore, the converted hardness value for sample A is:

HRF = (59 x 1.000) + 18 = 77 HRF

Now we can compare the hardness values of both samples, and we see that sample B has a higher hardness value of 90.5 HRF, compared to sample A's value of 77 HRF. Therefore, we can conclude that sample B is harder than sample A.

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The child wants to build towers using identically shaped cubes of different colors. They have 22 red cubes, 33 blue cubes, and 44 green cubes. The goal is to build a tower with a height of 88 cubes, using all the cubes except for one.

To find out how many different towers can be built, we can approach this problem using combinations.

First, let's consider the number of ways to select the cubes for the tower. We have three different colors of cubes: red, blue, and green. To build a tower with a height of 88 cubes, we need to select 88 cubes out of the total available cubes. However, we have to exclude one cube, so we have a total of 22 + 33 + 44 - 1 = 98 cubes to choose from.

Using the concept of combinations, we can calculate the number of ways to select 88 cubes out of 98 cubes. This can be represented as "98 choose 88" or written as C(98, 88). The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of items and r is the number of items to be selected. The exclamation mark (!) denotes the factorial of a number.

So, we can calculate C(98, 88) as:

98! / (88! * (98 - 88)!)

Simplifying this expression will give us the number of ways to select the cubes for the tower.

Once we have selected the cubes, we need to consider the number of ways to arrange them to build towers. Since all the cubes are identical in shape, the only difference is in color. Therefore, the number of different towers that can be built will be the same as the number of ways to arrange the colors of the selected cubes.

To calculate the number of ways to arrange the colors, we can use the formula for permutations of identical items, which is given by:

n! / (n1! * n2! * ... * nk!)

where n is the total number of items and n1, n2, ..., nk are the counts of identical items. In this case, we have three colors: red, blue, and green, so we can calculate the number of ways to arrange the colors as:

3! / (22! * 33! * 44!)

Finally, we can multiply the number of ways to select the cubes by the number of ways to arrange the colors to get the total number of different towers that can be built with a height of 88 cubes using 22 red cubes, 33 blue cubes, and 44 green cubes.

Please note that calculating the actual values may result in very large numbers, so it may be more practical to use a calculator or a computer program to perform the calculations.

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Answer:

Solution in photo

Step-by-step explanation:

The coordinate of the point that is 2/5 of the way from A to B for the given points is (3/2, -3/5).

The coordinate of the point can be obtained thus :

√((-6 - 4)² + (-7 - 9)²) = 18.867962264113206

2/5 * 18.867962264113206 = 7.547174916044816

Add this value to the x-coordinate of A.

-6 + 7.54 = 1.54 = 1.5 = 3/2

Add this value to the y-coordinate of A.

-7 + 7.54 = -0.5 = -3/5

Therefore, the required coordinates are (3/2, -3/5)

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If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two

When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.

Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .

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The values of a and b will be -2 and 22 while the other factor in the function is x - 3/2.

The function is given as:

f(x) = ax³ - x² + bx - 24.

Since (x - 2) and (x - 4) are the factors, they will give functions of 8a + 2b = 28 and -16a - b = 10.

This will be solved by elimination method and the values of a and b will be -2 and 22.

Therefore, f(x) = -2x³ - x² + 22x - 24

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