Find the volume of each solid

Using trigonometric identity,  the exact value of sin(A + B) in simplest radical form is 17√5 / 25√13.

We can use the trigonometric identity for the sine of the sum of two angles:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

We know that Tan A = 8 and that angle A is in quadrant 1. We can use the fact that Tan A = sin(A)/cos(A) to find sin(A) and cos(A)

[tex]Tan A = sin(A)/cos(A)\\sin(A) = Tan A * cos(A) = 8 * (1 / \sqrt(1 + Tan^2 A)) = 8 / \sqrt(65)\\cos(A) = 1 / \sqrt(1 + Tan^2 A) = 1 / \sqrt(65)[/tex]

We also know that sin B = 1/sqrt(5). Since angle B is in quadrant 1, we can use the Pythagorean identity cos^2(B) + sin^2(B) = 1 to find cos(B):

[tex]cos(B) = \sqrt(1 - sin^2(B)) = \sqrt(1 - 1/5) = 2\sqrt(5) / 5[/tex]

Now we can substitute these values into the formula for sin(A + B):

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

[tex](8 / \sqrt(65)) * (2\sqrt(5) / 5) + (1 / \sqrt(65)) * (1 / \sqrt(5)) = (16\sqrt(5) + 1) / (5\sqrt(325))[/tex]

We can simplify this fraction by multiplying the numerator and denominator by √5:

[tex]sin(A + B) = ((16\sqrt(5) + 1) / (5\sqrt(325))) * (\sqrt(5) / sqrt(5))\\ = (16\sqrt(5) + \sqrt(5)) / (25\sqrt(13))\\ = (17\sqrt(5)) / (25\sqrt(13))[/tex]

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The expression in terms of cosine is (1 - cos^2(x))^2

From the question, we have the following parameters that can be used in our computation:

sin^4(x)

This can be expressed as

sin^4(x) = (sin^2(x))^2

As a general rule:

sin^2(x) = 1 - cos^2(x)

Using the above as a guide, we have the following equation

sin^4(x) = (1 - cos^2(x))^2

Hence, the solution is (1 - cos^2(x))^2

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Answer:

Step-by-step explanation:

B will not be a random sample because it is your friend, not a random person.

C a customer may be ordering another pizza that is not their favorite.

D Five is not enough and you may be bias (Ex: You need to ask 1 more person and there are 2 people: one with a dog, and one without. Let's say you like dogs, than you may go to the dog person more likely)

Answer:

Step-by-step explanation:

According to the given plan   for area codes, the first digit can be any number from 3 through 7, the second digit can be 6, 7, or 8, and the third digit can be any number except 6 or 7.

There are 5 possible choices for the first digit (3, 4, 5, 6, or 7), 3 possible choices for the second digit (6, 7, or 8), and 8 possible choices for the third digit (0, 1, 2, 4, 5, 8, 9). This is because there are 10 possible digits in total, but we cannot use 6 or 7 for the third digit.

Using the multiplication principle of counting, we can multiply these choices together to find the total number of possible area codes:

5 x 3 x 8 = 120

Therefore, there are 120 different area codes possible with this plan.

Answer:

f(x) /x-3

Step-by-step explanation:

Jolie's working time increased by 20 %

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, Jolie’s time at work increases from 25 hours per week to 30 hours per week, we need to find that by  what percentage did the time at work per week increase,

Using the concept of percentage,

Initial working hours = 25 hours per week

Final working hours = 30 hours per week

Increased hour = 30 - 25 = 5 hours

Percentage increased = 5 / 25 x 100 = 20%

Hence, Jolie's working time increased by 20 %

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Answer:

y= -2

X= 7

[tex]using \: elimination \: method \\ x + 3y = 1 \\ - 3x - 3y = - 15 \\ add \: the \: two \: equations \\ - 2x = - 14 \\ divide \: both \: sides \: by \: 2 \\ x = 7 \\ replace \: x \: with \: 7 \: to \: find \: value \: of \: y \\ (7) + 3y = 1 \\ y = - 2[/tex]

Answer:

The formula to calculate the minimum sample size required to estimate the population mean is given as:

n = (z^2 * σ^2) / E^2

Where,

z = the z-value for the given confidence level, which is 1.96 for c = 0.95

σ = the population standard deviation

E = the maximum error of estimate, also known as the margin of error

Plugging in the values, we get:

n = (1.96^2 * 9.1^2) / 1^2

n = 301.63

Rounding up to the nearest whole number, the minimum sample size required is 302.

Therefore, a sample size of at least 302 is needed to estimate the population mean with a 95% confidence level, assuming a population standard deviation of 9.1 and a maximum error of estimate of 1.

Step-by-step explanation:

There are 10⁹(1 billion) possible Social Security numbers that can be formed. The probability of correctly guessing the Social Security number of the president of the United States is practically zero. This is because there are so many possible combinations, and it is highly unlikely that anyone would guess the correct number.

Number is a mathematical object used to count, measure, and label. It is used to express amounts, or magnitude of a quantity. Numbers are used in almost every field of life, such as science, engineering, economics, finance, and many other areas. Numbers are used in a wide range of contexts and are essential to modern life. They are used to communicate information, to measure time, and to represent values. Furthermore, numbers are used to represent abstract ideas, such as the probability of an event occurring. Numbers are also used to create patterns, which are essential to understanding complex systems. Without numbers, it would be impossible to measure anything, make estimates, or draw conclusions.

(a) There are a total of 10^9 (1 billion) possible Social Security numbers. This is calculated by multiplying the 10 possible digits (0-9) for each of the nine positions in the number, which gives 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10⁹.

(b) The probability of correctly guessing the Social Security number of the president of the United States is 1 in 10⁹. This is because there are a total of 10^9 possible Social Security numbers, and the president's number is only one of those.

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la surface de l'écharpe est de 1 1 56 cm² car la formule pour calculer l'air d'un carré est A= coté * coté soit coté²

donc :  Aécharpe=34²=1156

Answer:

$732.00

Step-by-step explanation:

Down payment 20% of 915.00

20% = 0.2

915 x 0.2 = $183.00

Down payment = $183.00

Financed the remainder:

915.00 - 183.00 = $732.00

So, she finance $732.00

The table of values for the equation of line y = ( -3/4 )x + 3 is given by

x = { -4 , 0 , 4 , 8 }

y = { 6 , 3 , 0 , -3 }

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = ( -3/4 )x + 3

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m = -3/4

when x = -4

y = ( -3/4 ) ( -4 ) + 3

y = 3 + 3

y = 6

when x = 0

y = ( -3/4 ) ( 0 ) + 3

y = 0 + 3

y = 3

when x = 4

y = ( -3/4 ) ( 4 ) + 3

y = -3 + 3

y = 0

when x = 8

y = ( -3/4 ) ( 8 ) + 3

y = -6 + 3

y = -3

Hence , the table of values are x = { -4 , 0 , 4 , 8 } and y = { 6 , 3 , 0 , -3 }

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Answer:

3(x + 12)(x + 2)

Step-by-step explanation:

Given

3x² + 42x + 72 ← factor out 3 from each term

= 3(x² + 14x + 24) ← factor the quadratic

Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term.

The factors are + 12 and + 2, since

12 × 2 = 24 and 12 + 2 = 14, thus

x² + 14x + 24 = (x + 12)(x + 2) and

3x² + 42x + 72

= 3(x + 12)(x + 2) ← in factored form

a) The finance charge for the financing of the company airplane priced at $250,000 with 15% down payment is $66,308.

b) The monthly payments Vista's aircraft loan are $4,646.80.

The finance charge and the monthly payments can be determined using an online finance calculator as follows:

The finance charge represents the total interest and other fees that the financier charges for the loan.

The monthly payments are the periodic payments that must be made to settle the loan and compounded interest with the installment period of 60 months.

Company Airplane Price = $250,000

Down Payment = 15%

Loan Term = 60 months (5 years x 12)

Interest Rate = 11.25%

Results:  

Monthly Payment (PMT):  $4,646.80

House Price = $250,000

Down Payment = $37,500 ($250,000 X 15%)

Loan Amount = $212,500 ($250,000 - $37,500)

Total of 60 Mortgage Payments = $278,808

Total Interest (Finance Charge) = $66,308 ($278,808 - $212,500)

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The correct students are Nico, Aditi, and Erick.

What is equation?

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

The correct approaches to solving the equation are those that lead to the correct solution. We can check which students are correct by solving the equation and seeing if their approach leads to the correct answer.

Two-fifths (5 + x) = 8

Multiplying both sides by 5 gives:

5/5 * two-fifths (5 + x) = 5/5 * 8

One-fifth (5 + x) = 8/5

One-fifth (5) + One-fifth x = 8/5

1 + One-fifth x = 8/5

Subtracting 1 from both sides gives:

One-fifth x = 3/5

Multiplying both sides by 5 gives:

x = 3

So the solution is x = 3.

From the given approaches, Nico, Aditi, and Erick are correct. Their approaches are equivalent to the correct approach:

Two-fifths (5 + x) = 8

(5/2) * two-fifths (5 + x) = (5/2) * 8

(5/2) * (5/5 + x/5) = 20/5

5/2 + (5/2)x/5 = 4

5/2 + x/2 = 4

x/2 = 3/2

x = 3

Raj and Sandra's approaches are not correct, as they made errors in their calculations. Therefore, the correct students are Nico, Aditi, and Erick.

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By answering the supplied question, we may infer that the response is standard deviation As a result, 95% of requests for lightbulb replacements with a total number between 38 and 54 are in this range.

A statistic known as standard deviation may be used to indicate the variation or variability of a set of statistics. A low standard deviation means that the values tend to be closer to the established mean whereas a large standard deviation shows that the values are widely spread. The standard deviation serves as a gauge for how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is low, and are more scattered when the standard deviation is high. Standard deviation is a measurement of the data set's average variability. It displays the standard deviation of each score with respect to the mean.

The rule states approximately:

One standard deviation from the mean is shared by 68% of the requests.

The average request is within two standard deviations in 95% of cases.

The average request falls within three standard deviations in 99.7% of cases.

a mean three standard deviations away:

38 8 = 30 to 46 with one standard deviation

two standard deviations: 22 to 54 for 38 2(8)

38 3(8) = 14 to 62 for three standard deviations

We know that almost 95% of the requests fall within this range since we are interested in the proportion of requests between 38 and 54, which is within two standard deviations of the mean. As a result, 95% of requests for lightbulb replacements with a total number between 38 and 54 are in this range.

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Answer:

Jose can buy 0.086 shares at $15.88 with his dividend of $1.36 on each of his 398 shares.

Step-by-step explanation:

The relationship between hours worked and income earned is an example of data that shows a direct and positive correlation. As the number of hours worked increases, so does the amount of money earned. This is a direct correlation because the variables (hours worked and earnings) are positively related; as one variable rises, so does the other. The correlation is positive because the relationship between the variables is directional, i.e., as one variable increases, so does the other.

Answer:

Step-by-step explanation:

An example of data that would show direct and positive correlation is the relationship between the number of hours studied for an exam and the grade received on the exam. As the number of hours studied increases, the grade received on the exam also increases, indicating a direct and positive correlation between the two variables.

Answer:

Below

Step-by-step explanation:

sqrt(5x) * sqrt(x+3)  = sqrt ( 5x * x + 5x * 3) = sqrt ( 5x^2 + 15x)

Answer:

   1. Gross pay = hourly rate x hours worked

   Gross pay = $14 x 32 = $448

   2. Net pay = gross pay - deductions

   Federal taxes = 10% of gross pay = 0.1 x $448 = $44.80

   State taxes = 4.5% of gross pay = 0.045 x $448 = $20.16

   FICA = 6% of gross pay = 0.06 x $448 = $26.88

   Total deductions = $44.80 + $20.16 + $26.88 = $91.84

   Net pay = $448 - $91.84 = $356.16

   3. Gross pay = hourly rate x hours worked

   Gross pay = $17 x 40 = $680

   4. Regular pay = hourly rate x hours worked

   Regular pay = $20 x 40 = $800

   Overtime pay = (hourly rate x 1.5) x overtime hours

   Overtime pay = ($20 x 1.5) x 5 = $150

   Gross pay = regular pay + overtime pay

   Gross pay = $800 + $150 = $950

   5. Net pay = gross pay - deductions

   Federal taxes = 14% of gross pay = 0.14 x $950 = $133

   State taxes = 4.5% of gross pay = 0.045 x $950 = $42.75

   FICA = 6% of gross pay = 0.06 x $950 = $57

   Total deductions = $133 + $42.75 + $57 = $232.75

   Net pay = $950 - $232.75 = $717.25

Step-by-step explanation:

For the given information, the standard deviation are 30 and 103.25 respectively.

What is standard deviation?

The standard deviation measures the amount of variability or dispersion in the data set. It is the square root of the average of the squared deviations from the mean.

We can use the properties of a normal distribution to find the values given their distance from the mean. In particular, we can use the standard deviation to determine how far a given value is from the mean in terms of the number of standard deviations.

For the set of data with a mean of 45 and a standard deviation of 5:

A value that is 1 standard deviation above the mean is at 45 + 5 = 50

A value that is 2 standard deviations above the mean is at 45 + 2(5) = 55

A value that is 3 standard deviations below the mean is at 45 - 3(5) = 30

For the set of data with a mean of 90 and a standard deviation of 3.5:

A value that is 1 standard deviation above the mean is at 90 + 3.5 = 93.5

A value that is 2 standard deviations below the mean is at 90 - 2(3.5) = 83

A value that is 3.5 standard deviations above the mean is at 90 + 3.5(3.5) = 103.25

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C. During the observation period, period A's plant grew twice as quickly as period B's.

Graphs are a not unusual place technique to visually illustrate relationships withinside the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately withinside the textual content and in much less space.

Given, Mrs. Walker's Period A and Period B Biology classes each grew a plant and recorded the heights

from the graph. at the start of the observation period, Period A's plant was as tall as Period B's. So, A and B are wrong.

during the observation period, Period A's plant grew twice as quickly as Period B's.

C is right, and D is wrong

So, the answer is C.

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Complete question:

According to the range for each set of scores, Class A has a larger spread of scores. According to the interquartile range for each set of scores, Class B has a larger spread of scores.

In statistics, the interquartile range (IQR) is a measure of variability that represents the spread of the middle 50% of a dataset. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Quartiles divide a dataset into four equal parts, with the first quartile representing the 25th percentile and the third quartile representing the 75th percentile.

The interquartile range is useful because it is less sensitive to outliers than the range, which is calculated by subtracting the minimum value from the maximum value. Outliers are extreme values that are significantly different from the other values in the dataset and can skew the results of statistical analyses.

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Therefore, if Josh attends 1 group class per month, both membership plans will cost him a total of $37 per month.

In mathematics, the first 10 integers are referred to as the fundamental numbers. From 0 to 9, these foundational numbers are listed. The 0 to 9 range of basic integers includes 0 through 1, 2, 3, 4, 5, 6, 7 and 8.

Let's start by defining some variables. Let:

We can write the equations for the total cost of each plan as:

T1 = 35 + 2x

T2 = 34 + 3x

Since we know that the two plans end up costing the same total amount when Josh attends a certain number of classes in a month, we can set T1 equal to T2 and solve for x:

35 + 2x = 34 + 3x

35 = 34 + x

1 = x

So if Josh attends 1 group class per month, the two membership plans will cost the same total amount. Let's substitute x = 1 into our equations for T1 and T2 to find out what that total amount is:

T1 = 35 + 2(1) = 37

T2 = 34 + 3(1) = 37

Therefore, if Josh attends 1 group class per month, both membership plans will cost him a total of $37 per month.

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Answer: It would be 10.5

Step-by-step explanation:

You are inputting R or radius into question the radius is given to you which  is 10.5

The surface area of this cylinder will be 80π ft².

What is Total surface area ?

Total surface area is the total area, which includes the curved portion and any bases. It refers to the entire surface area of the thing. The total area will be equal to the sum of the two areas if the shape has a curved base and surface.

Given : height of cylinder = 3 ft

          radius of base of cylinder = 5 ft

We know that, Total surface area of cylinder = 2πrh + 2πr²

                                                                          = 2πr(h+r)

So, The surface area of given cylinder =  2π × 5 ( 3+5)

                                                                 = 10π (8)

                                                                 = 80π ft²

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The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is given as follows:

5/6.

The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is obtained applying the proportions in the context of the problem.

We have that both the x-coordinate and the y-coordinate of A and B have a difference of 6 units.

We also have that both the x-coordinate and the y-coordinate of point P(3,1) have a difference of five units from the coordinates of the starting point of the segment A.

Then the ratio is given as follows:

5/6.

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Answer:

8 3/4

Step-by-step explanation:

1 + 7 3/4 = 8 3/4 bbbbbbbbbbbbbb