Use a double integral to find the volume of the tetrahedron bounded coordinate planes and the plane 3x + 6y + 4x-12 = 0.

Answer: x = -y+28

Step-by-step explanation:

Answer:

Joseph recieved a discountwof $85.

The translation 1 unit left of f ( x ) =–7x+10  then g(x) is -7x + 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in its range(involving values of y) or in its domain(involving values of x).

The up and down movements are in the vertical direction by the y coordinate.

The left and right movements are in the horizontal direction by the x coordinate.

When translating a graph, adding units moves the graph to the left, and eliminating units moves the graph to the right.

hence we say that;

f(x) = –7x+10

g(x) = f(x + 1)

= –7(x + 1)+10

= -7x - 7 + 10

= -7x + 3

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The point estimate that can be used to estimate the true mean population is 11.97 inches.

To find the point estimate that can be used to estimate the true population mean, we need to take the sample mean of the given observations. The formula for the sample mean is:

Mod(X)= (Σx) / n

where Mod(X)  is the sample mean, Σx is the sum of all the observations, and n is the size.

Using the given observations, we can calculate the sample mean as follows:

Mod(X) = (11.3 + 10.7 + 12.4 + 15.2 + 10.1 + 12.1 + 16.2 + 10.5 + 11.4 + 11.0 + 10.7 + 12.0) / 12

Mod(X) = 11.97

Therefore, the point estimate that can be used to estimate the true mean population is 11.97 inches.

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We need to convert kilograms to pounds.

1 kilogram is equal to 2.20462 pounds.

Therefore, we can use the rule of three to find the value of 74 kilograms in pounds:

1 kilogram ------------- 2.20462 pounds

74 kilogram ----------- x

Where x = (74 kilogram * 2.20462 pounds)/ 1 kilogram = 163.14188

Rounded to the nearest hundred x = 163.14

Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

The solution is, sin∅ =3/√34.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

from the given figure we get,

by using Pythagorean theorem,

hypotenuse is = √9+25

                       =√34

so, sin∅ = height/hypotenuse

             = 3/√34

Hence, The solution is, sin∅ =3/√34.

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the value of angle α will be 31° approx.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given a right-angle triangle that has a base of 5 and a height of 3.

From the general formula of sin for right angle triangle

Sin α = height/ hypotenuse

In our case height = 3

And for the hypotenuse,

From the Pythagorean theorem,

 hypotenuse² = base² +height²

 hypotenuse² = 5*5 + 3*3

 hypotenuse²  = 34

 hypotenuse = √34

thus,

Sin α = 3/√34

α = 30.963757°

α ≈ 31°

Therefore, the value of angle α will be 31° approx.

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There are 30 different combinations of two members who can be selected to serve on the spring formal committee.

Permutation is the arrangement of elements in a specific order. In this scenario, the elements are the six members of the student council, and the order in which they are arranged is important.

To find the number of permutations, we use the formula nPk, where n is the number of elements and k is the number of elements we want to arrange.

In this case, n = 6 and k = 2,

so we have

=> 6P2 = 6!/(6-2)!

=> 6!/(4!) = 6 x 5/1 = 30.

So, there are 30 possible spring formal committees that can be formed from the six members of the student council.

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To find the profit function, maximum profit quantity, and maximum profit for a firm with revenue\(R(q) = 15q - 0.5q^2\) and cost \(C(q) = q^3 - 13.5q^2\\\) + 50q + 40, we first subtract the cost from the revenue to obtain the profit function \(\prod(q) = R(q) - C(q)\). Then, we can determine the quantity where the profit is maximized by using the second derivative test. Finally, we can calculate the maximum profit by substituting the quantity found in part (b) into the profit function \(\prod(q)\).

a. The profit function \(\prod(q)\) is obtained by subtracting the cost function C(q) from the revenue function R(q). Therefore, \(\prod(q) = R(q) - C(q)\) =\((15q - 0.5q^2) - (q^3 - 13.5q^2 + 50q + 40\)). Simplifying this expression gives \(\prod(q)\) = \(-q^3 + 14q^2 - 35q - 40\).

b. To determine the quantity where the profit is maximized, we can use the second derivative test. The second derivative of the profit function \(\prod(q)\) is obtained by differentiating \(\prod(q)\) with respect to q twice. Taking the second derivative of \(\prod(q)\), we get \(\prod''(q) = -6q + 28\). To find the quantity where the profit is maximized, we set \(\prod''(q)\) equal to zero and solve for q: -6q + 28 = 0. Solving this equation gives q = 28/6 = 14/3.

c. Once we have found the quantity q = 14/3, we can substitute this value into the profit function Π(q) to find the maximum profit. Plugging q = 14/3 into \(\prod(q)\), we have \(\prod(14/3) = -(14/3)^3 + 14(14/3)^2 - 35(14/3) - 40\). Evaluating this expression gives the maximum profit value.

\(\prod(14/3) = -((14/3)^3) + 14((14/3)^2) - 35(14/3) - 40.\)

Simplifying this expression gives:

\(\prod(14/3) = -2744/27 + 2744/9 - 490/3 - 40.\)

Combining the terms and finding a common denominator:

\(\prod(14/3) = (-2744 + 8192 - 4410 - 1080)/27.\)

Further simplification:

\(\prod(14/3) = 958/27.\)

Therefore, the maximum profit at the quantity q = 14/3 is 958/27.

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The number of polynomials that can be formed with -2 and 5 as zeroes are more than 1.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.x² -3x - 7 is an illustration of a polynomial with a single indeterminate x.

Given that the zeros of a polynomial are -2 and 5.

The polynomial that has a and b as zeors is p(x) = k[x² + (a+b)x + ab].

where k is a real number.

The polynomial that has -2 and 5 zeros is

p(x) = k[x² + (-2 + 5)x + (-2)×5]

p(x) = k[x² + 3x - 10]

Where k is a real number.

The number of real numbers is infinity.

The number of polynomials is infinity.

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Answer:

y=114 degrees

z=21

Step-by-step explanation:

66+y=180

180-66=144

144-30=84

84/4=21

Answer:

$70

Step-by-step explanation:

Daria's total income = fixed income + variable income

Let

Daria's Fixed income = x

additional $30 if the buyer gets an extended warranty

Daria's variable income = 30s

Where,

s = number of televisions with extended warranties she sells

If Daria sells 15 televisions with extended warranties, she earns \$1,500. Find her fixed income

Daria's total income = fixed income + variable income

1500 = x + 30(15)

1500 = x + 450

1500 - 450 = x

1,050 = x

x = $1,050

Daria's total fixed income = $1,050

How much is the fixed amount Daria for each television?

Fixed income per television = Total fixed income / number of television sold

= 1050 / 15

= 70

Fixed income per television = $70

Answer:

1.

Proportional:Yes

Equation:y=27*x

Number of tickets:x

Total cost:y

2.

Proportional:yes

Equation:y=4.35x

Weight:x

Total cost:y

Step-by-step explanation:

Sorry for answering late!

Answer:

3+10=13+17=30+24=54+0=54

Answer: 4 o clock

Step-by-step explanation:

Answer:

5 o' clock

Step-by-step explanation:

The angle between the hands of a clock on an hourly basis is 30°

thus for the hands to be 90° apart would be 3 hours

then 2 o' clock + 3 hours = 5 o' clock

The most common error when entering a formula is to reference the wrong cell in the formula.

This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.

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The area of the paperboard that remains is 613.92 square inches.

To find the area of the paperboard that remains after a semicircle is cut out, we need to calculate the area of the rectangular paperboard and subtract the area of the semicircle.

The rectangular paperboard has dimensions of 35 inches long and 24 inches wide. Therefore, the area of the rectangular paperboard is:

Area_rectangular = length * width = 35 in * 24 in = 840 in²

Now, let's calculate the area of the semicircle. The semicircle is cut out of the rectangular paperboard, and the diameter of the semicircle is equal to the width of the rectangular paperboard (24 inches).

The formula to calculate the area of a semicircle is:

Area semicircle = (π * r²) / 2

where r is the radius of the semicircle.

Since the diameter of the semicircle is 24 inches, the radius is half of that, which is 12 inches.

Plugging in the values into the formula, we get:

Area_semicircle = (3.14 * 12²) / 2 = (3.14 * 144) / 2 = 226.08 in²

Finally, to find the area of the paperboard that remains, we subtract the area of the semicircle from the area of the rectangular paperboard:

Area remaining = Area rectangular - Area semicircle = 840 in² - 226.08 in² = 613.92 in²

Therefore, the area of the paperboard that remains is 613.92 square inches.

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Answer:

There are more permutations when repetitions are allowed.

Explanation:

There are more permutations if repetition is allowed because in this case, we can include numbers like 1122, 4444, and 1321, which won't be included when repetitions are not allowed.

The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.

Given that a card is randomly chosen from 8 cards shown in figure.

We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.

Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Number of cards=8

Number of repeated cards=0

Number of cards showing Q and R =1 each.

Probability of getting Q or R is P(X=Q)+P(X=R)

= 1/8+1/8

=2/8

=1/4

=0.25

Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Descriptive statistics is a branch of statistics that deals with the collection, analysis, interpretation, and presentation of data. It focuses on summarizing and describing the characteristics of a sample or population. The purpose of descriptive statistics is to provide a clear and concise summary of the data, including measures of central tendency, variability, and distribution.

True,This information can be used to make inferences about the population as a whole. Therefore, descriptive statistics helps statisticians to better understand and interpret the population data.

False, Descriptive statistics is a branch of statistics that focuses on summarizing and organizing data from a sample or population. It provides insights into the basic features of the data, such as the mean, median, and standard deviation, but does not make inferences about the population.

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The quotient is 1111. The process continues until the result is less than the divisor.

To perform the division using the restoring-division algorithm with the given divisor and dividend, follow these steps:

Step 1: Initialize the dividend and divisor

Divisor: 00011

Dividend: 1011

Step 2: Append zeros to the dividend

Divisor: 00011

Dividend: 101100

Step 3: Determine the initial guess for the quotient

Since the first two bits of the dividend (10) are greater than the divisor (00), we can guess that the quotient bit is 1.

Step 4: Subtract the divisor from the dividend

101100 - 00011 = 101001

Step 5: Determine the next quotient bit

Since the first two bits of the result (1010) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

Step 6: Subtract the divisor from the result

101001 - 00011 = 100110

Step 7: Repeat steps 5 and 6 until the result is less than the divisor

Since the first two bits of the new result (1001) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100110 - 00011 = 100011

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100011 - 00011 = 100001

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100001 - 00011 = 011111

Since the first two bits of the new result (0111) are less than the divisor (00011), we guess that the next quotient bit is 0.

011111 - 00000 = 011111

Step 8: Remove the extra zeros from the result

Result: 1111

Therefore, the quotient is 1111.

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I can help you with that problem i just did that on my own.

Function 1

Let us calculate the equation of the line of function 1 picking any two points

The two points picked are (1 , 0) and (0 , -4)

The formula for the equation given two points is

Given:

Hence,

Therefore, the equation for the function is

Where, the coefficient of x is the slope and the constant variable is the y-intercept.

Hence,

Function 2

Let us calculate the equation of the line of function 2 picking any two points from the data in the table.

The two points picked are (-2 , 8) and (2 , -12)

Therefore,

Hence,

Where,

Function 3

The given equation is

Function 4

Given:

Hence,

a) The functions that have graphs with slopes less than 3 are Function 2, Function 3 and Function 4.

b) The function that has the graph with a y-intercept closest 0 is Function 3.

c) The function that has the graph with greatest y-intercept is Function 4.

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Limits function lim p(x) can be calculated if p is a polynomial function by:

To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:

Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.

Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:

Lim p(2) =  a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀

Then, we just need to simplify our finding:

Lim p(2) =  8a₃ + 4a₂ + 2a₁ + a₀

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The simplified form of the expression \(\(7 x^{2} y+9+6 x y-7 x y-21-7 x^{3} y\) is \(-7 x^{3} y+7 x^{2} y- x y-12\)\). In this expression, like terms have been combined by adding their coefficients.

In the given expression, we have terms involving \(\(x^{2} y\), \(x y\)\), and constants. To simplify the expression, we combine the like terms by adding or subtracting their coefficients.

The terms \(\(7 x^{2} y\) and \(-7 x^{3} y\)\) involve the variable \(\(y\)\) raised to the power of 1, and the variable \(\(x\)\) raised to the power of 2 and 3, respectively. Since the exponents are different, these terms cannot be combined. Similarly, the terms \(\(6 x y\) and \(-7 x y\)\) involve the variable \(\(y\)\) raised to the power of 1 and the variable \(\(x\)\) raised to the power of 1. Combining these terms gives us \(\(- x y\)\).

Lastly, we combine the constant terms \(\(9\), \(-21\), and \(-12\) to get \(-12\)\).

Putting it all together, we obtain the simplified expression \(\(-7 x^{3} y+7 x^{2} y- x y-12\)\).

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The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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This simplified form still represents the original statement of "nine less than the quotient of a number and four, increased by three." So, the correct expression, after simplification, is (n/4) - 6.

The expression that correctly represents "nine less than the quotient of a number and four, increased by three" is:

(n/4) - 9 + 3

Let's break it down step by step:

"The quotient of a number and four" can be represented as n/4, where n is the number.

"Nine less than the quotient of a number and four" can be expressed as (n/4) - 9. This means subtracting 9 from the quotient.

"Increased by three" implies adding three to the previous expression. So, we add 3 to (n/4) - 9.

Therefore, the correct expression is (n/4) - 9 + 3. This expression captures the required operations: dividing a number by 4 to get the quotient, subtracting 9 from the quotient, and finally, adding 3 to the result.

To simplify the expression further, we can combine like terms:

(n/4) - 6

This simplified form still represents the original statement of "nine less than the quotient of a number and four, increased by three." It is equivalent to the previous expression but in a more compact form.

So, the correct expression, after simplification, is (n/4) - 6.

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Answer:i think its 115 degres

Step-by-step explanation: