A pet store owner has huge aquarium tanks of the same size, A and B.


Tank A has 2 feet of water and is filled at a rate of 2. 2 inches per minute.


Tank B has 8 feet of water and is filled at a rate of 5 inches per minute.

The volume of the cone in cubic feet is approximately 0.0 cubic feet

We need to convert the given dimensions from inches to feet before calculating the volume in cubic feet.

The height of the cone is 6 inches, which is equivalent to 6/12 = 0.5 feet (since there are 12 inches in 1 foot).

The radius of the cone is 4.5 inches, which is equivalent to 4.5/12 = 0.375 feet.

Using the formula for the volume of a cone, which is:

V = (1/3) * π * r^2 * h

Substituting the given values, we get:

V = (1/3) * 3.14 * (0.375 feet)^2 * 0.5 feet

V ≈ 0.0221 cubic feet

Rounding this to the nearest tenth gives:

V ≈ 0.0 cubic feet

Therefore, the volume of the cone in cubic feet is approximately 0.0 cubic feet. None of the given options match this result.

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The transformation of f(x) = √(4x) from the parent function g(x) = √(x) includes a horizontal stretch by a factor of 1/4, with no horizontal or vertical shifts.

The function f(x) = √(4x) is a transformation of the parent function, g(x) = √(x). The transformations include a horizontal stretch, a horizontal shift, and a vertical shift. Let's break down each transformation step-by-step:
1. Horizontal Stretch: The factor 4 inside the square root function multiplies the input (x) by 4. This results in a horizontal stretch by a factor of 1/4, meaning the graph is compressed horizontally towards the y-axis.

2. Horizontal Shift: There is no additional value added or subtracted from the input (x), so there is no horizontal shift in this function. The graph remains in its position along the x-axis.
3. Vertical Shift: Similarly, there is no additional value added or subtracted from the output (the entire function), so there is no vertical shift in this function. The graph remains in its position along the y-axis.
This results in the graph of f(x) being compressed towards the y-axis compared to the graph of g(x).

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Answer:

gf(x) = g(f(x)) = (x+4)(2x/x-2) = 2x^2 + 8x - 8

The answer is 37.5.

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Neave should mark 12 sections as "win" on the prize wheel to achieve the expected number of winners of 60 out of 200 students.

To determine how many sections should be marked "win" on Neave's prize wheel, we need to consider the expected number of winners and the total number of sections on the wheel.

Neave wants the expected number of winners to be 60 out of 200 students. This means that the probability of winning should be 60/200 = 0.3 or 30%.

If the wheel is split into 40 equally sized sections, we can assume that each section has an equal probability of being selected by a student. Therefore, to have a 30% chance of winning, we need to mark a proportionate number of sections as "win".

To calculate the number of sections to mark as "win", we multiply the total number of sections by the desired probability of winning:

40 sections * 0.3 = 12 sections.

It's important to note that the concept of expected value assumes an idealized scenario with perfect randomness. In reality, the actual number of winners may vary due to random chance and individual spin outcomes.

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Answer:

Part (a):  Because the survey was held at basketball championship.

Part (b): The survey among students should held at school or in any common place.

Step-by-step explanation:

You lose 515 dollars every time you lose 10 dollars.

Now that we know it takes 50 hours to lose 10 dollars, we can calculate how much money you lose every 10 dollars by

the hourly rate of 10.50 dollars by 50 hours and subtracting that amount from 10 dollars:

Money lost = (10.50 dollars/hour) x 50 hours - 10 dollars

Money lost = 525 dollars - 10 dollars

Money lost = 515 dollars

Therefore, you lose 515 dollars every time you lose 10 dollars.

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The median for the number of pencils can be found by locating the middle value on the dot plot, which appears to be 3 pencils.

The dot plot displays the number of pencils each boy has at his desk in class. By locating the middle value of the data on the dot plot, the median number of pencils can be determined to be 3.

This indicates that half of the boys have 3 pencils or fewer, while the other half have 4 pencils or more.

The dot plot provides a visual representation of the distribution of the data and allows for easy identification of the median value.

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It should be noted that to calculate the mean and standard deviation of the sampling distribution, you need to know the population mean (μ) and standard deviation (σ) and the sample size (n) of the distribution.

The mean (μx) of the sampling distribution of the sample mean (x) is equal to the population mean (μ):

μx = μ

The standard deviation (σx) of the sampling distribution of the sample mean (x is equal to the population standard deviation (σ) divided by the square root of the sample size (n):

σx = σ / √n

Therefore, in order to calculate the mean and standard deviation of the sampling distribution, you just need to plug in the values of μ, σ, and n into these formulas.

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How does one calculate mean and standard deviation of the sampling distribution.

How to interpret the standard deviation from part (1).

The mean of all possible differences in sample proportions (Brand R minus Brand S) is given by:

mean = pR - pS,

where pR is the population proportion of kernels that will pop for Brand R, and pS is the population proportion of kernels that will pop for Brand S.

Substituting the given values, we get:

mean = 0.90 - 0.85 = 0.05

However, the consumer group claims that the mean of all possible differences in sample proportions is 0.3. This claim is not supported by the calculations above.

Therefore, the correct answer is:

C) No. The mean is 0.90+0.85/2=0.875. No. The mean is the fraction 0.90 plus 0.85 over 2 equals 0.875.

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The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans.

The marginal cost function of  C(x) = 2300 + 5x + 0.01x2 + 0.0002x is $3100

Process of finding marginal cost:

(a) To find the marginal cost function, we need to take the derivative of the cost function C(x) with respect to x. This gives us:

C'(x) = 5 + 0.02x + 0.0006x^2

So the marginal cost function is:

MC(x) = 5 + 0.02x + 0.0006x^2

(b) To find C'(100), we simply plug in x = 100 into the marginal cost function we just found:

C'(100) = 5 + 0.02(100) + 0.0006(100)^2 = 11

This predicts the exact cost of manufacturing the 101st pair of jeans.

The approximate cost of the 101st pair of jeans can be found by plugging in x = 101 into the original cost function C(x):

C(101) = 2300 + 5(101) + 0.01(101)^2 + 0.0002(101) ≈ $3120.02

The approximate cost of the 101st pair of jeans.

The exact cost of the 100th pair of jeans can be found by plugging in x = 100 into the original cost function C(x):

C(100) = 2300 + 5(100) + 0.01(100)^2 + 0.0002(100) = $3100

Hence the marginal cost is $3100

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Therefore , the solution of the given problem of function comes out to be Line B  to the function y = x+5.

On the midterm exam, there will be a variety of inquiries in each subject, including inquiries concerning both hypothetical and actual places as well as inquiries relating the creation of numerical variables. a diagram showing the relationships between different elements that cooperate to generate the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

The function is represented as

=> y = x + 5, which has a y-intercept of 5, a slope of 1, and a slope of 1.

By comparing the slope and y-intercept of each line to those of the function, we may determine which line best fits it.

Line A does not fit the function because it has a slope of 1 and a y-intercept of 0.

The function y = x + 5 is satisfied by line B, which has a slope of 1 and a y-intercept of 5.

Line C does not fit the function because it has a slope of 2 and a y-intercept of 0.

Line D does not fit the function because it has a slope of 3 and a y-intercept of 2.

Line B therefore corresponds to the function y = x+5.

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Reactions at points A, C, and F are as follows: RA = -RC, RAy = RCy, and RF = 10 kN.

To determine reactions at points A, C, and F for the assembly consisting of two 10mm diameter rods (A-B and C-D), a 20mm diameter rod (E-F), and a rigid bar (H), with point G located midway between points E and F, and a force of 10 kN applied:

First, calculate the cross-sectional areas of the rods:
A1 = π(10mm)² / 4 = 78.54 mm² (for rods A-B and C-D)
A2 = π(20mm)² / 4 = 314.16 mm² (for rod E-F)

Next, calculate the effective modulus of elasticity for each rod:
E1 = E2 = 101 GPa

Now, use equilibrium equations to determine reactions at points A, C, and F:
ΣFx = 0: RAx + RCx = 0
ΣFy = 0: RAy + RCy + RF = -10 kN
ΣMG = 0: (RAy)(L/2) - (RCy)(L/2) = 0

Solving the equilibrium equations, we get:
RAx = -RCx
RAy = RCy
RF = 10 kN

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The number of years apart between Eratosthenes was born in 276 BC (Before Christ) Abraham Lincoln died in 1865 is 2140 years.

Eratosthenes was born in 276 BC

Abraham Lincoln died in 1865 AD

BC = Before Christ

AD = anno dominie

The difference between the born date of Eratosthenes and the death date of Abraham Lincoln is to be calculated by

Year difference = BC year + AD year - 1

Year difference = 276 + 1865 - 1

Year difference = 2140

hence the  difference between the born date of Eratosthenes and the death date of Abraham Lincoln is 2140

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True, The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely to be.

We have,

The factors which are be used to member a request are the segmentation variables. Common variables include demographic, geographic, psychographics and behavioral considerations.

Quantifiable population characteristics, similar as age, gender, income, education, family situation.

The primary ideal of segmentation is to identify guests with analogous attributes, and to find which parts of guests that are seductive from a profit perspective.

Understanding the request segmentation allows marketers to produce a more effective and effective marketing blend.

Hence, True, The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely to be.

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complete question:

The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely ot be.[See p.104]Group of answer choicesTrueFalse

The equation that has given solutions x = -5 and x = 2 is [tex]x^2 + 3x - 10 = 0.[/tex]

If the given solutions of an equation are x = -5 and x = 2, then the equation can be written as a product of two linear factors, (x + 5) and (x - 2), because when either of these factors is equal to zero, the corresponding solution is obtained.

So, the equation is:

(x + 5)(x - 2) = 0

Expanding the product, we get:

[tex]x^2 + 3x - 10 = 0[/tex]

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The absolute maximum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8 is 2√2, which occurs at the point (2,2).

The absolute minimum of the function is -8, which occurs at the point (0,2).

To find the absolute maximum and minimum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8, we need to evaluate the function at the critical points and at the boundary of the domain.

The critical points of the function are the points where the partial derivatives with respect to x and y are both zero. Solving these equations, we get:∂f/∂x = -1 + y/(√(x-y^2)) = 0∂f/∂y = √(x-y^2) - 1 + 3 = 0Solving these equations, we get two critical points: (0,2) and (2,2). Evaluating the function at these points, we get:f(0,2) = -8f(2,2) = 2√2Next, we need to evaluate the function at the boundary of the domain. This includes the points (0,y), (9,y), (x,0), and (x,8).

Evaluating the function at these points, we get:f(0,y) = -x+3yf(9,y) = y√(9-y^2)-6f(x,0) = -xf(x,8) = 8√(x-64/9)-x+24Taking the maximum and minimum values of the function at the critical points and on the boundary of the domain, we see that the absolute maximum of the function is 2√2, which occurs at the point (2,2), and the absolute minimum of the function is -8, which occurs at the point (0,2).

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There are 252 different combinations of shirts, the correct option is B.

Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:

[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]

There are 252 different combinations, so the correct option is B.

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1) Note that t is either 4 or -0.25 by virtue of the quadratic function.

2) the vertex and line of summer try are t = 1.875. See the attached graph.

First, identify the values of a, b, and c in the equation...

a = -16

b = 60

c = 16

substitute these values into the quadratic formula

t = (-b ± √(b² - 4ac)) / 2a

t = (-60 ± √(60² - 4(-16)(16))) / 2(-16)

t = (-60 ± √(3600 + 1024)) / (-32)

t = (-60 ± √(4624)) / (-32)

t = (-60 ± 68) / (-32)

So, t can be:

t = (-60 + 68) / (-32) = -1/4

or

t = (-60 - 68) / (-32) = 4

2) To find the line of symmetry, we used t = -b/2a

-60/2(-16)

t = 1.875

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The perimeter of the bedroom is 116ft

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel.

The perimeter of a rectangle is expressed as;

P = 2(l+w)

where l is the length and w is the width of the rectangle.

length = √ 21-21)²+ 18-(-7)²

= √25²

l = 25 ft

width = √ 21-(-12)²+18-18)²

= √ 33²

= 33

Perimeter = 2(33+25)

= 2 × 58

= 116ft

therefore the perimeter of the bedroom is 116ft.

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Answer:

IT depends on how many kids there are per group.

Step-by-step explanation:

The nth term of the sequence 4 5 6 7 5 6 7 8 is given by a_n = 3 + (n-1)/2 for odd n and a_n = 4 + (n-2)/2 for even n.

To find the nth term of the given sequence, we need to observe the pattern in the sequence. We can see that the sequence consists of two parts:

the first part is a consecutive sequence of integers starting from 4, and the second part is a consecutive sequence of integers starting from 5, where the second part starts right after the first part ends.

So, we can express the nth term of the sequence as follows:

If n is odd, then the nth term is given by:

a_n = 3 + (n-1)/2

If n is even, then the nth term is given by:

a_n = 4 + (n-2)/2

Using this formula, we can find any term of the given sequence by plugging in the corresponding value of n. For example:

When n=1, the first term is 4: a_1 = 4.

When n=6, the sixth term is 6: a_6 = 6.

When n=7, the seventh term is 7: a_7 = 7.

When n=8, the eighth term is 8: a_8 = 8.

Note that this formula works only for n = 1, 2, 3, 4, 5, 6, 7, 8, ... , since the sequence has only 8 terms.

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The values of the variables are:

c = 86 degrees

d = 168 degrees

a = 57 degrees

b = 94 degrees

Since the polygon is inscribed in a circle, the opposite angles of the polygon are supplementary. Thus, we have:

The top and bottom angles of the polygon are supplementary to angle "d":

c + 92 + 123 = 180 + d

The left and right angles of the polygon are supplementary to angle "c":

c + 94 = 180, so c = 86

The angle "a" is supplementary to angle "d":

a + 123 = 180 + d

The angle "b" is supplementary to angle "c":

b + 86 = 180

Substituting the values of "c" and solving the system of equations, we get:

d = 168

a = 57

b = 94

Therefore, the values of the variables are:

c = 86 degrees

d = 168 degrees

a = 57 degrees

b = 94 degrees

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The particular solution Yp(t) is found by following these steps and combining it with the complementary solution Yc(t) to get the general solution Y(t) = Yc(t) + Yp(t).

To find the particular solution to [tex]y'' + y' - 12y = -340sin(t)[/tex] using variation of parameters, follow these steps:
1. Find the complementary solution Yc(t) for the homogeneous equation [tex]y'' + y' - 12y = 0[/tex]. The characteristic equation is[tex]r^2 + r - 12 = 0[/tex], which has roots r1 = -4 and r2 = 3. Thus, [tex]Yc(t) = C1e^(-4t) + C2e^(3t)[/tex].

2. Assume the particular solution Yp(t) is in the form [tex]Yp(t) = u1(t)e^(-4t) + u2(t)e^(3t)[/tex]. Calculate the Wronskian [tex]W(Y1, Y2) using Y1 = e^(-4t) and Y2 = e^(3t).[/tex]  3. Find u1'(t) and u2'(t) using the given nonhomogeneous equation: -340sin(t) = -Y1(t)u1'(t) + Y2(t)u2'(t).

4. Integrate u1'(t) and u2'(t) to find u1(t) and u2(t).
5. Plug u1(t) and u2(t) back into the particular solution [tex]Yp(t) = u1(t)e^(-4t) + u2(t)e^(3t[/tex]).

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If the point starts at the π/2 position, the equation for the blade of the wind turbine will be sin(θ + π/2) = sin(θ - π/2)cos(β) + cos(θ - π/2)sin(β).

The equation for the blade of the wind turbine is given by the expression sin(θ) = sin(θ - β)cos(α) + cos(θ - β)sin(α), where θ represents the angle of the blade, β represents the angle between the wind direction and the blade, and α represents the pitch angle of the blade.

If the point starts at the π/2 position, we need to substitute θ + π/2 for θ in the equation. This gives us sin(θ + π/2) = sin(θ - β + π/2)cos(α) + cos(θ - β + π/2)sin(α).

Using trigonometric identities, we can simplify this expression to sin(θ + π/2) = cos(θ - β)cos(α) - sin(θ - β)sin(α).

Finally, substituting β for (π/2 - β) in the above equation, we get sin(θ + π/2) = sin(θ - π/2)cos(β) + cos(θ - π/2)sin(β). This is the required equation for the blade of the wind turbine if the point starts at the π/2 position.

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The depth of trail mix box that is shaped like a rectangular prism must be 2.4 inches.

We are going to use the formula for determining volume to work out the depth of the rectangular prism.

The volume of a rectangular prism is given by the formula:

V = l × w × h

where:

V = the volume

l = the length

w = the width

h = the height.

Given:

w = 7.5 inches

h = 9 inches

V = 162 cubic inches

Now, we are to find the value of d, the depth of the box, which corresponds to the length of the rectangular prism.

Substituting the values into the formula for volume:

162 = d × 7.5 × 9

Simplifying the right-hand side:

162 = 67.5d

Dividing both sides by 67.5, we get:

d = 162 ÷ 67.5

d = 2.4 inches

Therefore, the depth of the box shaped as rectangular prism = 2.4 inches.

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A. Melissa's monthly payment is approximately $146.89.

B. The total amount of the monthly payments over the four-year period is approximately $7,052.72.

C. The finance charge on the loan is approximately $1,052.72.

The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

To calculate the monthly payment, we can use the formula:

Monthly payment = [P x r x (1 + r)ⁿ] / [(1 + r)ⁿ⁻¹]

where P is the principal (the amount of the loan), r is the monthly interest rate, and n is the number of monthly payments.

A. To find the monthly payment, we first need to calculate the values of r and n.

Since the APR is 10%, the monthly interest rate is 10% / 12 = 0.00833 (rounded to 5 decimal places).

The number of monthly payments over four years is 4 x 12 = 48.

Using these values, we can calculate the monthly payment:

Monthly payment = [6000 x 0.00833 x (1 + 0.00833)⁴⁸] / [(1 + 0.00833)⁴⁸⁻¹]

Monthly payment ≈ $146.89

So Melissa's monthly payment is approximately $146.89.

B. To find the total amount of the monthly payments, we can multiply the monthly payment by the number of payments:

Total amount of monthly payments = Monthly payment x Number of payments

Total amount of monthly payments = $146.89 x 48

Total amount of monthly payments ≈ $7,052.72

So the total amount of the monthly payments over the four-year period is approximately $7,052.72.

C. To find the finance charge, we can subtract the original principal from the total amount of the monthly payments:

Finance charge = Total amount of monthly payments - Principal

Finance charge = $7,052.72 - $6,000

Finance charge ≈ $1,052.72

So the finance charge on the loan is approximately $1,052.72.

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Answer:

Here we try the method of trial and error to find out if the equations have a common answer as zero

Step-by-step explanation:

Now,

(a) x²-4=0

(b) x²=-4

(c) 3x²+12=0

(d) 4x²=16

(e) 2(x-2)2=0

Here if we check the first equation i.e x²-4=0

Equating - 2²-4=4-4

=0

2²-4= 4-4

=0

So option (a) is true

Now x²=-4

Substituting, - 2²=4 & 2²=4

So here we get 4≠-4

Therefore, (b) is not true

Now 3x²+12=0

3(-2)²+12= 3(4)+12

=12+12= 24

3(2)²+12= 12+12

= 24

4x²=16

Substituting, 4(-2)²= 4(4)= 16

4(2)²= 4(4)= 16

So option (d) is also true

Now, 2(x-2)2=0

Substituting, 2(-2-2)2= 2(-4)2

4(-4)= - 16

2(2-2)2= 2(0)2

=4(0)=0

Here when we put x=-2, we get - 16

when we put x=2, we get 0

So the following equation is true only for x=2 and not x=-2

I hope this helps ;)

The values of the variables are x = 4 and y = 1

We have the equations as;

3(x-2) + y = 7

4x - 3(y-1) = 16

Using the substitution method

Make 'y' the subject of formula from equation (1), we have;

y = 7 - 3(x-2)

Now, substitute the expression as y in equation (2), we get;

4x - 3(7 -  3(x-2) - 1) = 16

expand the bracket, we have;

4x - 3(7 - 3x + 6 - 1) = 16

collect the like terms

4x - 3(12 - 3x) = 16

4x - 36 + 9x = 16

collect the like terms

13x = 52

x = 4

Substitute the value

y = 7 - 3(4 -2 )

y = 7 -3(2)

y = 1

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The estimated contribution for Rosemary's first-year college fee is $6,500 including all her savings and available funds.

Savings of Rosemary = $2,500

Savings from bond = $1000

To calculate the contribution needed for Rosemary from other sources, to pay her college fee, we need to add all the available funds and subtract the money for her college fee.

Let us imagine that the total cost of Rosemary's college = $10,000

Total available funds = $2,500  + $1,000

Total available funds = $3500

The remaining amount needed = $10,000 - $3,500 = $6,500

Therefore, we can conclude that Rosemary would need an estimated contribution of $6,500.

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