f(x) = ʃ Sqrt[9+X2 DX]

Answer:

(4x+7)(4x-7)

Step-by-step explanation:

Use DoS (x+y)(x-y)=x^2-y^2

27 cubic inches make up the volume of a cube.

Part A: The side length is 3 inches

Part B: The total surface area of the cube is 54 square inches

Part A:

The formula for the volume of a cube is V = s^3, where V is the volume and s is the side length.

We are given that the volume of the cube is 27 cubic inches, so we can plug this into the formula and solve for s:

27 = [tex]s^3[/tex]

By taking the cube root of both sides, we arrive at:

s = 3

Therefore, the side length of the cube is 3 inches.

Part B:

The formula for the surface area of a cube is A = 6[tex]s^2[/tex], where A is the surface area and s is the side length.

Plugging in the value we found for s in Part A, we get:

A = 6([tex]3^2[/tex])

A = 6(9)

A = 54

Therefore, the total surface area of the cube is 54 square inches.

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The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:

a = (279/10) cm x (178/10) cm

Simplifying this expression, we get:

a = 4953/100 cm^2

So, the correct equations are:

B) 178/10 x 279/10 = a

and

D) a ÷ 178/10 = 279/10

The profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex] .

To determine which graph corresponds to the given situation, we need to understand the relationship between cost, profit, and revenue.

The revenue (R) of a small business is given by the product of the price per unit (p) and the number of units sold (x):

[tex]R = px[/tex]

The profit (P) of a small business is the difference between its revenue and cost (C):

[tex]P = R - C = px - (3000 + 12x) = (p - 12)x - 3000[/tex]

The profit will be positive when P > 0, which means that the revenue is greater than the cost:

[tex](p - 12)x > 3000[/tex]

[tex]x > 3000/(p - 12)[/tex]

This inequality tells us that the business will be profitable for all values of x greater than [tex]3000/(p - 12).[/tex]

Graph A: This graph shows a linear revenue function (R = 20x) and a linear cost function [tex](C = 3000 + 10x).[/tex] The profit function [tex](P = R - C)[/tex] is also linear.

To find the profit region, we need to shade the area above the profit function  [tex](P > 0)[/tex]. However, we cannot determine if this corresponds to the given situation without knowing the price per unit.

Graph B: This graph shows a linear revenue function  [tex](R = 25x)[/tex] and a quadratic cost function  [tex](C = 3000 + 15x + 0.5x^2).[/tex] The profit function [tex](P = R - C)[/tex]  is also quadratic. To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex] .

We can solve for the roots of the quadratic equation [tex]P = 25x - (3000 + 15x + 0.5x^2) = -0.5x^2 + 10x - 3000[/tex] and find the interval of x-values for which [tex]P > 0.[/tex]

This corresponds to the range of x-values for which the graph of P is above the x-axis. We can see that this region is shaded in blue, so Graph B corresponds to the given situation.

Graph C: This graph shows a linear revenue function [tex](R = 15x)[/tex] and a linear cost function  [tex](C = 3000 + 20x).[/tex]The profit function  [tex](P = R - C)[/tex]  is also linear.

To find the profit region, we need to shade the area above the profit function  [tex](P > 0)[/tex]. However, we can see that the profit function intersects the x-axis at [tex]x = 150.[/tex]

Therefore, the profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex].

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x^2-16÷ (x-16 )(x+4)

= (x^2)-(4^2)÷ (x-16)(x+4)

= (x+4)(x-4)÷ (x-16) (x+4)

=(x-4)÷(x-16)

a. The periodic deposit should be $643.28 (rounded to the nearest cent).

b. $15,438.72 of the $27,000 comes from deposits, and $11,561.28 comes from interest.

a. To determine the periodic deposit, we can use the formula for the future value of an annuity:

FV = Pmt x [(1 + r)^n - 1] / r

where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, FV = $27,000, r = 8% / 4 = 2%, n = 6 x 4 = 24 (since there are 4 quarters in a year and the time period is 6 years).

Substituting these values into the formula, we get:

$27,000 = Pmt x [(1 + 0.02)^24 - 1] / 0.02

Solving for Pmt, we get:

Pmt = $643.28

b. The total amount contributed by deposits is:

$643.28 x 24 = $15,438.72

To find the amount of interest earned, we subtract the total deposits from the financial goal:

$27,000 - $15,438.72 = $11,561.28

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The differentiation of the trigonometric function gives:

dy/dx = sin(x) - cos(x)

Here we want to find dy/dx for:

y = sec⁻¹(x) + csc⁻¹(x)

Remember that these two are the inverses of the sine and cosine function, then we can write that just as:

y = cos(x) + sin(x)

Now the differentiation is part by part, we know that:

d(cos(x))/dx = -sin(x)

d(sin(x))/dx = cos(x)

Then:

dy/dx = sin(x) - cos(x)

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The answer of the given question based on the triangle is the value of angle G or x  is approximately 52.6° degrees (rounded to the nearest tenth of a degree).

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). Trigonometric functions can be used to solve problems involving angles and sides of right triangles, as well as to model periodic phenomena such as waves and oscillations.

To find angle G, we need to use the trigonometric function tangent since we know the opposite and adjacent sides of angle G in the right triangle EFG.

Recall that the tangent of an angle is defined as the ratio of the opposite side to the adjacent side, i.e.,

tan(G) = opposite/adjacent = FG/EF

Substituting the given values, we get:

tan(G) = 3.4/2.6 = 1.3076

Using a calculator, we can find the inverse tangent of 1.3076, which gives us:

G ≈ [tex]tan^{-1}[/tex](1.3077) ≈ 52.6° degrees

Therefore, the value of angle G is approximately 52.6° degrees (rounded to the nearest tenth of a degree).

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Answer:

Step-by-step explanation:

Let A represent "The children are sick."

Let B represent "The doctors are not here."

Argument: A and ¬B

Rule(s) used to prove or disprove: Conjunction (AND)

Answer: (n - 2) + 20

Step-by-step explanation:

     We will create a mathematical expression using the statement given. 'Less' implies subtraction, let n be a number.

     'than a number' ➜ n

     'Two less' ➜ - 2

     'plus twenty.' ➜ + 20

'Two less than a number plus twenty.' ➜ (n - 2) + 20

Answer:

54 =)

Step-by-step explanation:

m^2+7m-6
5^2+7(5)-6
25+35-6
Answer is 54

0.1728 proportion of suburban park users bike on the park trail .the answer is option O 0.1728.

what you mean by proportion?

Proportion refers to the relationship between a part and the whole. In statistics, a proportion is a measure that describes the size of a subset relative to the size of the entire set. It is usually expressed as a fraction or a percentage.

In the given question,

To find the proportion of suburban park users who bike on the park trail, we need to divide the number of suburban park users who bike by the total number of suburban park users.

From the table, we can see that the number of suburban park users who bike is 42 and the total number of suburban park users is 243.

So, the proportion of suburban park users who bike on the park trail is:

42/243 = 0.1728

Therefore, the answer is option O 0.1728.

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Answer:

B. $365

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The false statement is 3)sin30=cos40.

This is because the sine of 30 degrees is 0.5, whereas the cosine of 40 degrees is approximately 0.766. These two values are not equal to each other.

The following claims, however, are accurate:

Therefore, the false statement is 3)sin30=cos40.

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The number "0.0505505550..." is an irrational number. The reason for it is that the number can't be expressed as the quotient of two integers. SInce it has the ellipsis (...) at the end, it indicates that the number isn't showing all its significant figures, therefore, can't be represented as the ratio of two integers. Thus, it is irrational.

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Answer:

No, it's not

Step-by-step explanation:

A rational number can be written in the form [tex]\sf{\dfrac{p}{q}}[/tex], where q ≠ 0.

While an irrational number cannot  be written in such a form.

Well, not only can't we express 0.0505505550... as [tex]\sf{\dfrac{p}{q}}[/tex], we also see three dots in the end that indicate that the number goes on forever.

It's impossible to express a number that goes on for ever, as a fraction.

Therefore the number is irrational.

Answer:

Rounding down to a whole number, we get:

6,666 people

Step-by-step explanation:

First, we need to calculate the total area of the beach:

1000 ft x 200 ft = 200,000 sq ft

Next, we divide the total area by the desired area per person:

200,000 sq ft ÷ 30 sq ft per person = 6,666.67 people

Answer:
B) 46 degrees

Answer:

Step-by-step explanation:

10x+y=10y+x-18 multiply the tens digit by 10 and leave the one's digit alone

9x=9y-18 divide by 9

x=y-2

x-y=-2

x+y=10

add above two equations

2x=8 divide by 2

x=4

y=10-4=6

numbers are 46 and 64

64=46+18 4+6=10

Answer:

1. To estimate the number of products sold after 48 months, we can assume that the sales follow a linear pattern over time. We can use the data given to find the rate of change (slope) of the line and then use that to predict the sales after 48 months.

Using the points (12, 4), (18, 7), and (36, 15), we can find the slope of the line that represents the sales:

slope = (15 - 7) / (36 - 18) = 8 / 18 = 4/9

Now we can use the point-slope form of a line to find the equation of the line:

y - 4 = (4/9)(x - 12)

where x is the number of months and y is the number of products sold.

To find the estimated number of products sold after 48 months, we can substitute x = 48 into the equation and solve for y:

y - 4 = (4/9)(48 - 12)

y - 4 = 16

y = 20

Therefore, we can estimate that the company will sell 20 thousand products after 48 months.

2. Yes, the number of products sold is a function of the amount of months. It is a linear function because the sales appear to follow a straight line over time, as we assumed in our calculation above. This means that for every increase of 1 month, the number of products sold increases by a constant rate of 4/9 thousand.

Step-by-step explanation:

(a) The value of  [h/g] function is h/g = (3x² - 4) / (-4x + 6).

(b) The domain of [h/g] is all real numbers except x = 3/2.

In mathematics, the domain of a function is the set of all possible input values (usually denoted by x) for which the function is defined. It is the set of all values of the independent variable for which the function produces a valid output.

In the given question,

(a) To find h/g, we need to divide the function h(x) by the function g(x):

h/g = (3x² - 4) / (-4x + 6)

(b) To find the domain of [h/g], we need to determine which values of x would make the denominator equal to zero, since division by zero is undefined.

-4x + 6 = 0

-4x = -6

x = 6/4 = 3/2

So the only value that could make the denominator zero is x = 3/2. Therefore, the domain of [h/g] is all real numbers except x = 3/2.

[h/g] = (3x² - 4) / (-4x + 6), x ≠ 3/2.

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The coordinates of the rotation are

Problem 5:

(4, 0), (0, -2), and (0, 0)  

Problem 6:

(0, -4), (-2, 0), and (0, 0)  

Describing each rotation

1. 90 degrees counterclockwise rotation about the origin

2. 90 degrees clockwise rotation about the origin

Problem 5: The transformation rule for 90 degrees clockwise rotation about the origin is

(x, y) becomes (y, -x)

preimage coordinates           image coordinates

(0, 4)                becomes        (4, 0)

(2, 0)                becomes        (0, -2)

(0, 0)                becomes        (0, 0)

The image is plotted and attached

Problem 6: The transformation rule for 180 degrees counterclockwise rotation about the origin is

(x, y) becomes (-x, -y)

preimage coordinates           image coordinates

(0, 4)                becomes        (0, -4)

(2, 0)                becomes        (-2, 0)

(0, 0)                becomes        (0, 0)

The image is plotted and attached

Describing each rotation

1. 90 degrees counterclockwise rotation about the origin

This can be likened to the rotation as in problem 6, the polygon moves in the counterclockwise direction and this is according to the rule:

(x, y) becomes (-y, x)

2. 90 degrees clockwise rotation about the origin

This is similar to the rotation as in problem 5, the polygon moves in the clockwise direction and this is according to the rule:

(x, y) becomes (y, -x)

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An addition of the quantity negative 8 minus one fourth times p end quantity plus the quantity five eighths times p minus 7 end quantity is: C. 3 over 8 times p minus 15.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expressions:

Expression = -8 - 1/4(p)

Expression = 5/8(p) - 7

By adding the two expressions, we have:

Addition = -8 - 1/4(p) + 5/8(p) - 7

Addition = -8 - p/4 + 5p/8 - 7

Addition = -15 +(-p/4 + 5p/8)

Addition = -15 +(-2p + 5p)/8

Addition = -15 + (3p)/8

Addition = 3p/8 - 15

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The value of a given arithmetic expression is 1.

We have given that an arithmetic expression -

22-(1×5)-4 to the seccond

So we can write it -

22-(1×5)-4²

we shall solve it with the help of the BODMASS rule

BODMAS Rule: The BODMAS Rule is a crucial mathematical tool for resolving issues. It is a technique for using an arithmetic expression to resolve mathematical problems. The abbreviation BODMAS stands for brackets, order of powers or roots, division, and multiplication. S indicates for subtraction, whereas A stands for addition.

according to BODMASS

first, solve the brackets and square,

=22-(5)-16

now subtract all

=22-21

=1

The complete question is

Solve the given arithmetic expression -

22-(1×5)-4 to the seccond

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The probability that a freshman is selected is 0.39. the probability that an art major is chosen is 0.36. the probability that a freshman math major or a sophomore biology major is chosen is 0.23.

(a) To find the probability that a freshman is selected, we need to add up the probabilities of selecting any of the three types of majors among the freshman group. Thus:

Probability of selecting a freshman = Probability of selecting a freshman math major + Probability of selecting a freshman art major + Probability of selecting a freshman biology major

Probability of selecting a freshman = 0.12 + 0.09 + 0.18

Probability of selecting a freshman = 0.39

(b) To find the probability that an art major is chosen, we need to add up the probabilities of selecting an art major from both the freshman and sophomore groups. Thus:

Probability of selecting an art major = Probability of selecting a freshman art major + Probability of selecting a sophomore art major

Probability of selecting an art major = 0.09 + 0.27

Probability of selecting an art major = 0.36

(c) To find the probability that a freshman math major or a sophomore biology major is chosen, we need to add up the probabilities of selecting a freshman math major and a sophomore biology major. Thus:

Probability of selecting a freshman math major or a sophomore biology major = Probability of selecting a freshman math major + Probability of selecting a sophomore biology major

Probability of selecting a freshman math major or a sophomore biology major = 0.12 + 0.11

Probability of selecting a freshman math major or a sophomore biology major = 0.23

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Using square root property,

Square root of 4 is 2 and -2.

Both 2 and -2 are square roots of 4 as:

2 × 2 = 4

also,

-2 × -2 =4

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value.

It follows that a × a = b if "a" is the square root of "b." Every number has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number.

In the given question,

Square root of 4 is 2 and -2.

Both 2 and -2 are square roots of 4 as:

2 × 2 = 4

also,

-2 × -2 =4

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the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability theory is a branch of mathematics that deals with the study of random events and their probabilities

In the given question,

We are given that the population mean per capita daily water consumption is 83 liters and the standard deviation is 11.9 liters. We are also given that random samples of size 50 are drawn from this population and the mean of each sample is determined.

We can use the central limit theorem to approximate the distribution of the sample means. According to the central limit theorem, the distribution of the sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So, for a sample size of 50, the standard deviation of the sample mean is:

standard deviation of sample mean = 11.9 / √(50) = 1.68

To find the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person, we need to find the z-scores corresponding to these values and use the standard normal distribution table or calculator to find the probability.

The z-score for 80 liters per person is:

z = (80 - 83) / 1.68 = -1.79

The z-score for 82 liters per person is:

z = (82 - 83) / 1.68 = -0.60

Using the standard normal distribution table or calculator, we can find that the probability of getting a z-score between -1.79 and -0.60 is 0.1271.

Therefore, the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%

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The area of a rectangle is represented by an irrational number because the product of the two side lengths is an irrational number. This is because the product between an integer and an irrational number leads to another irrational number, which is the right answer.

A rectangle is a four-sided flat geometric form with right angles on all four sides. It is a quadrilateral, which implies that it has four sides. A rectangle's opposite sides are parallel and equal in length, whereas its adjacent sides are perpendicular to one other. A rectangle's area is computed by multiplying its length by its width, and its perimeter is computed by summing the lengths of all four sides.

According to this question, we know the lengths of the two sides of the rectangle, the length of a side is an positive integer and the length of the other one is an positive irrational number. The area of the rectangle is the product of the two sides lengths mentioned above.

By algebra, we know that the product between an integer and an irrational number leads to other irrational number. Therefore, the area of the rectangle is represented by an irrational number.

A = 3 x [tex]\sqrt{5}[/tex]

A = 3[tex]\sqrt{5}[/tex]

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The complete question is: A rectangle has side lengths of 3 inches and 5–√ inches. Which statement must be true about the area of the rectangle?

The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.

A whole number that can be either positive, negative, or zero is known as an integer. It is a number without a decimal or fractional component. Integer examples include: -3, -2, -1, 0, 1, 2, 3, etc

Lets check if 4 and 6 are divisible by both a and b and is a positive integer,

F. 124:

124/4 = 31, is a positive integer

124/6 = 20.6 is a not positive integer

Thus, 124 is not m.

G. 222:

222/4 = 55.5, is a not positive integer

Thus, 222 is not m.

H. 310:

310/4 = 77.5, is a not positive integer

Thus, 310 is not m.

J. 480:

480/4 = 120, is a positive integer

480/6 = 80 is a positive integer

Thus, 480 is m.

K. 544:

544/4 = 136, is a positive integer

544/6 = 90.6 is not  a positive integer

Thus, 544 is not  m.

Thus, The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.

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Complete question: