Some values of functions f, g, h, and k are provided in the table below. Find a
possible equation of each function. Verify your results with a graphing calculator
table.

If a 4-pound bag of oranges costs $5.00, and a "x" pound bag of oranges costs $8.00, then the value of "x" for which, the cost per pound of both the above cases will be proportional is $6.40.

As per the question statement, a 4-pound bag of oranges costs $5.00, and since no information is provided in the statement about the number of pounds for the second case, we are assuming that "x" pound bag of oranges costs $8.00,

And we are required to calculate the  value of "x" for which, the cost per pound of both the above cases is proportional.

To solve this question, we simply have to calculate the per pound cost of oranges in both the cases, and then equate them; this is will give us an equation in single variable "x", on solving which, we will obtain our desired answer.

Since a 4-pound bag of oranges costs $5.00,

Then, a 1-pound bag of oranges should cost $(5/4)

And, another "x" pound bag of oranges costs $8.00,

Then, a 1-pound bag of oranges should cost $(8/x)

Now, for the per pound costs of oranges in both the above cases to be proportional,

[(5/4) = (8/x)]

Or, [x = {(8 * 4)/5}]

Or, [x = (32/5)]

Or, (x = $6.4)

That is, the value of "x" for which, the cost per pound of oranges in both the above cases will be proportional should be $6.40.

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Answer:

75ft

Step-by-step explanation:

Hello There! With the information given in the problem we can set up a ratio in order to help us solve for the actual length that the model is scaled upon.

This ratio can be written as:

\(\frac{1ft}{15ft}\)

From this we just set up another ratio in relation to the original. In this one we will be solving for x.

\(\frac{1ft}{15ft}\)  x  \(\frac{5ft}{x}\)

After solving for x we find that the actual model should be roughly 75ft.

Hope this helps!

-HM

(i) Use the formula for the determinant of a 2×2 matrix.

\(\begin{vmatrix}a&b\\c&d\end{vmatrix} = ad-bc\)

\(\implies \det(A) = \begin{vmatrix}4 & -3 \\ 2 & 5\end{vmatrix} = 4\times5 - (-3)\times2 = \boxed{26}\)

(ii) The adjugate matrix is the transpose of the cofactor matrix of A. (These days, the "adjoint" of a matrix X is more commonly used to refer to the conjugate transpose of X, which is not the same.)

The cofactor of the (i, j)-th entry of A is the determinant of the matrix you get after deleting the i-th row and j-th column of A, multiplied by \((-1)^{i+j}\). If C is the cofactor matrix of A, then

\(C = \begin{pmatrix}5&-2\\3&4\end{pmatrix}\)

Then the adjugate of A is the transpose of C,

\(\mathrm{adj}(A) = C^\top = \boxed{\begin{pmatrix}5&3\\-2&4\end{pmatrix}}\)

(iii) The inverse of A is equal to 1/det(A) times the adjugate:

\(A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A) = \boxed{\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix}}\)

(iv) The system of equations translates to the matrix equation

\(A\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}6\\16\end{pmatrix}\)

Multiplying both sides on the left by the inverse of A gives

\(A^{-1}\left(A\begin{pmatrix}x\\y\end{pmatrix}\right)=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}\)

\(\left(A^{-1}A\right)\begin{pmatrix}x\\y\end{pmatrix}=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}\)

\(\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix} \begin{pmatrix}6\\16\end{pmatrix}\)

\(\begin{pmatrix}x\\y\end{pmatrix}=\boxed{\begin{pmatrix}3\\2\end{pmatrix}}\)

Answer:

The correct solutions to the equation 2x^2 = -10x + 12 are x = -2 and x = 3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We will use the idea here that the first 2 pipes can get 1/4 of the job done in an hour, and that the third pipe can get 1/3 of the job done in an hour. We need to know then the number of hours it will take to fill the tank if all 3 work together. The equation looks like this:

\(\frac{1}{4}+ \frac{1}{4}+ \frac{1}{3}= \frac{1}{x}\) Now we find a common denominator and solve for x. The common denominator is 12x. Multiplying everything by 12 x gives us

3x + 3x + 4x = 12 and

10x = 12 so

x = 1.2 hours

Answer:

1.2 hours

Step-by-step explanation:

we need to see how much each pipes does in the same amount of time

The least common multiple of 3 hours and 4 hours is 12 hours

In 12 hours:

Pipe 1 at 4 hours to fill a tank fills 3 tanks

Pipe 2 at 4 hours to fill a tank fills 3 tanks

Pipe 3 at 3 hours to fill a tank fills 4 tanks

All three pipes can fill 10 tanks in 12 hours

12 hours/10 tanks = 1.2 hours to fill one tank

-------------------------

Doing just the math

1/4 + 1/4 + 1/3 = x

3/12 + 3/12 + 4/12 = 10tanks/12 hours

12hours/10tanks = 1.2 hours

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

First step:-

Right triangular prism=1⁵/₆ inches= 11/6 inches

Height of the base=8²/₃ inches = 26/3 inches

Second step:-

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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Answer: From R:(c, d), draw line segment RA perpendicular to the x-axis. Let O denote the origin (0,0).

area ΔPQR = area trapezoid OPRA- area ΔQAR - area ΔOPQ

=

2

1

c(a+d) -

2

1

d(c−b)-

2

1

ab=

2

1

(ac+bd−ab).

If c area ΔPQR = area trapezoid OPRA + area Δ QAR - areaΔOPQ=

2

1

c(a+d)

2

1

d(b−c)−

2

1

ab=

2

1

(ac+bd−ab).

Step-by-step explanation: done

Answer:

The weight that does not round to 2.46 pounds is C 2.454 pounds.

Step-by-step explanation:

Based on the given information, the weights of the four similar packs of tomatoes are as follows:

Malcolm rounds the weights to the nearest hundredth pound. To round to the nearest hundredth pound, we look at the digit in the hundredths place. If it is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is. Therefore, we can obtain the rounded weights as follows:

From the above rounded weights, we see that Pack C rounds to 2.45 pounds and does not round to 2.46 pounds. Therefore, the weight that does not round to 2.46 pounds is C 2.454 pounds.

Answer:

Incomplete question, but I gave a primer on the hypergeometric distribution, which is used to solve this question, so just the formula has to be applied to find the desired probabilities.

Step-by-step explanation:

The resistors are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

12 resistors, which means that \(N = 12\)

3 defective, which means that \(k = 3\)

4 are selected, which means that \(n = 4\)

To find an specific probability, that is, of x defectives:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = x) = h(x,12,4,3) = \frac{C_{3,x}*C_{9,4-x}}{C_{12,4}}\)

Money borrowed from x, y, z banks on loan are $5000, $5000, $9000 respectively.

What is loan?

A loan is the lending of money by one or more people, businesses, or other entities to other people, businesses, or other entities. The recipient incurs a debt and is often responsible for both the principal amount borrowed as well as interest payments until the debt is repaid.

Main Body:

The equations formed from the information given in question are:

x+y+z = 19000

16x+18y+15z = 305000 and,

2x-y = 5000

by solving these equation we get

x= $5000

y= $5000

z= $9000

Hence the answer to this question are $5000 for x, y bank and $9000 from z bank.

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Answer:

Mutually exclusive is a statistical term describing two or more events that cannot happen simultaneously. It is commonly used to describe a situation where the occurrence of one outcome supersedes the other.

Since in this question, we have selected one card from a deck, and is obtaining a 2 and a queen.

I think the answer for this would be No/False but if i'm wrong, tell me!

As the point moves along the helix, it traces out a three-dimensional surface in space.The space curve would look like a helix in graph.

1. First, we need to find the vector-valued function r(t) using the given parameter.

2. We can use the parameter x+z=2 to solve for the y-coordinate in terms of t:

y = √(4 − (1+sin t)2 − (1 − sin t)2).

3. We can now substitute this expression into the vector-valued function to obtain:

r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k

4. The space curve represented by the intersection of the surfaces is a helix in a graph.

The space curve represented by the intersection of the surfaces is a helix. It is a three-dimensional curve that can be described by a vector-valued function r(t) with parameter t. The vector-valued function r(t) is given by:

r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k.

The helix can be visualized as a spiral that wraps around a cylinder and is generated by a point travelling around the circumference of the cylinder at a constant speed. This can be observed by noting that the x- and z-coordinates of the vector-valued function are constant and only the y-coordinate changes over time. As the point moves along the helix, it traces out a three-dimensional surface in space.

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Answer:

Step-by-step explanation:

First get the (m) which is the gradient by using the formula y2-y1/x2-x1

Pick any random 2 values from the table. I will pick. (1,4) (2,8)

Y2=8  Y1=4   X2=2  X1=1

8-4/2-1    4/1  = 4

Y=4x+c

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Okay, here are the steps to solve this problem:

* The purchase price of the motorcycle is $9,100

* The down payment on the lease is $600

* The monthly lease payment is $250

So to find the function that describes the total cost (p) in terms of time (t) in months:

p(t) = 600 + 250t

* The initial down payment is $600

* Each month, you pay $250

* So the total paid after t months is $600 + $250t

To find how long it will take to pay more than the purchase price:

600 + 250t > 9,100

250t > 8,500

t > 34

So in this case, it will take 35 months or slightly over 2 years of lease payments to exceed the purchase price of the motorcycle.

Does this make sense? Let me know if you have any other questions!

Answer:

p = 600 + 250t

t = 34

Step-by-step explanation:

To find a function that describes how the cost of the lease depends on time, we need to consider the initial cost and the monthly cost of the lease. The initial cost is the down payment of $600, which is paid once at the beginning of the lease. The monthly cost is $250, which is paid every month for the duration of the lease. Therefore, the total cost of the lease after t months is:

p = 600 + 250t

This is the function that models the situation. It is a linear function with a slope of 250 and a y-intercept of 600.

To find how long can the motorcycle be leased before more than the purchase price has been paid, we need to compare the cost of the lease with the purchase price of $9100. We need to find the value of t that makes p equal to 9100. We can do this by solving the equation:

p = 600 + 250t

9100 = 600 + 250t

Subtracting 600 from both sides, we get:

8500 = 250t

Dividing both sides by 250, we get:

t = 34

This means that after 34 months, the cost of the lease will be equal to the purchase price. Therefore, to pay more than the purchase price, the motorcycle must be leased for more than 34 months.

Here's a funny way to remember this:

Why did the motorcycle renter cross the road? To get to his monthly payment!

What do you call a motorcycle that costs more than its worth? A cycle-path!

How do you make seven an even number? Just remove the "s"!

A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

The function f(x) = -|x| − 3 can be graphed by following these steps:

Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

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Multiplication of the given matrix is not possible by definition of matrix multiplication.

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Expression for multiply,

⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]

Since, We can see that;

First matrix have order 1 x 6

And, Second matrix have order 1 x 4

We know that;

Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.

Hence, By given matrices we get;

Number of column in first matrix (6) ≠ number of rows in second matrix (1)

So, Multiplication of the given matrix is not possible by definition of matrix multiplication.

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Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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Answer:

independent variable is pens and dependent variable is $5 each Im pretty sure

The value of angle a is approximately 36.87°.

We are given that;

Height = 6 and hypotenuse = 10

Now,

To find the angle a in a right triangle, we can use the trigonometric ratios12:

sin(a) = opposite/hypotenuse cos(a) = adjacent/hypotenuse tan(a) = opposite/adjacent

where opposite is the side opposite to the angle a, adjacent is the side next to the angle a, and hypotenuse is the longest side of the right triangle.

we can use the sine ratio to find the angle a:

sin(a) = 6/10 a = sin^-1(6/10) a ≈ 36.87°

Therefore, by Pythagoras theorem the answer will be 36.87°.

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Answer:

$47.48

Step-by-step explanation:

Let x = the amount owed Sept.

x + x - 2.23 = 292.43  Combine like terms

2x -2.23 = 292.43  Add 2.23 to both sides

2x - 2.23 + 2.23 = 292.43 + 2.23

2x = 294.66  Divide both sides by 2

\(\frac{2x}{2}\) = \(\frac{294.66}{2}\)

x = 147.33 this is the bill for September

Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.

Total:

147.33 + 145.10 = 292.43

292.43 ÷ 3 = 97.48  This is what each will owe rounded to the nearest penny.

Answer:

C

Step-by-step explanation:

0.2(7x + 18) ← multiply each term in the parenthesis by 0.2

= 1.4x + 3.6 → C

In a directly proportional relationship, increasing one variable will increase another. The weight of the roof whose depth is 1.75 inches is 6,300 pounds.

In a directly proportional relationship, increasing one variable will increase another. This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.

Let there are two variables p and q. Then, p and q are said to be directly proportional to each other if p = kq, where k is some constant number called the constant of proportionality.

Given the hail's weight varies directly with its depth. Therefore, the relation can be written as,

Weight ∝ Depth

W∝D

Introducing the constant to remove the proportionality we will get the equation as,

W = kD

1800pounds = k × 0.5 inches

3600ponds/inches = k

Now, the weight of the roof whose depth is 1.75 inches can be written as,

W = kD

W = 3600 × 1.75

W = 6,300 pounds

Hence, the weight of the roof whose depth is 1.75 inches is 6,300 pounds.

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