If h(x) = x - 7 and g(x) = x2, which expression is equivalent to (g0h)(5)?
O (5 – 7)^2
O (5)² – 7
0 (5²(5 – 7)
O (5 – 7)x^2

The 48 units of X and 16 units of Y. The correct answer is option C.

To determine the optimal consumption of goods X and Y for the consumer with the utility function \($U(X,Y) = X^{1/2}Y^{1/4}$\), we need to maximize utility subject to the given prices and income.

Let's denote the quantities of X and Y consumed as $x$ and $y$, respectively. The consumer's problem can be formulated as the following constrained optimization:

\(Maximize} \quad & U(X,Y) = X^{1/2}Y^{1/4} \\Subject to} \quad & Px \cdot x + Py \cdot y = I\)

where Px and Py are the prices of goods X and Y, and I is the consumer's income.

Given Px = 2, Py = 3, and I = 144, we can substitute these values into the constraint equation:

\($$2x + 3y = 144$$\)

To solve this problem, we can use the Lagrange multiplier method. We construct the Lagrangian function:

\($$\mathcal{L}(x, y, \lambda) = X^{1/2}Y^{1/4} - \lambda(2x + 3y - 144)$$\)

Taking partial derivatives and setting them equal to zero:

\(\frac{\partial \mathcal{L}}{\partial x} &= \frac{1}{2}X^{-1/2}Y^{1/4} - 2\lambda = 0 \\\\\frac{\partial \mathcal{L}}{\partial y} &= \frac{1}{4}X^{1/2}Y^{-3/4} - 3\lambda = 0 \\\\\\\frac{\partial \mathcal{L}}{\partial \lambda} &= -(2x + 3y - 144) = 0\)

Simplifying these equations, we obtain:

\(\frac{Y^{1/4}}{2X^{1/2}} &= 2\lambda \\\\\frac{X^{1/2}}{4Y^{3/4}} &= 3\lambda \\\\2x + 3y &= 144\)

By equating the two expressions for $\lambda$, we can eliminate it:

\(\frac{Y^{1/4}}{2X^{1/2}} &= \frac{X^{1/2}}{4Y^{3/4}} \\\\4Y^{7/4} &= 2X \\\\2Y^{7/4} &= X^{1/2} \\\\16Y^{7/2} &= X\)

Substituting this expression for X in the budget constraint:

\($$2(16Y^{7/2}) + 3Y = 144$$\)

Simplifying:

\($$32Y^{7/2} + 3Y = 144$$\)

This equation can be solved numerically, and the solution is \($Y \approx 16.81$\). Substituting this value back into the expression for X:

\($$X \approx 47.35$$\)

Rounding these values to the nearest whole number, the optimal consumption of goods X and Y at the equilibrium is approximately 47 units of X and 17 units of Y.

Therefore, the correct answer is option (c): 48 units of X and 16 units of Y.

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The trip lasted 38 hours 37 minutes.

Through addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

Given, If a bus left the station at 7:17 am and arrived at its destination at 9:54 pm on the next day.

That means,

7:17 AM to 7:17 AM next day

= 24 hours

And 7:17 AM to 7:17 PM on the same day

= 12 hours

And 9:54 - 7:17

= 2 hours 37 minutes.

The total time of the trip:

Adding all the time duration,

= 24 + 12 + 2:37

= 38 hours 37 minutes.

Therefore, the trip's duration is 38 hours 37 minutes.

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Answer: The Answer is 3rd

Answer:

I think it does not have zeros if it doesn't cross the x-axis .

Step-by-step explanation:

Good luck ^_^

Answer:

The answer is d. Hope this helps :D

Please mark brainliest!

Answer:

D

Step-by-step explanation:

Becuase You add 600+80+4 and you'll get 684

If firm issues​ commercial paper with $1000000 face-value and pays EAR of​ 7.4%, then amount the firm will receive is $981500.

To calculate the amount the firm receives from issuing the three-month commercial paper, we need to determine the total interest earned over the three-month period.

The Effective Annual Rate (EAR) of 7.4% indicates the annualized interest rate. Since the commercial paper has 3-month term, we adjust the EAR to account for the shorter period.

To find the quarterly interest rate, we divide the EAR by the number of compounding periods in a year. In this case, since it is a 3-month period, there are 4-compounding periods in a year (quarterly compounding).

Quarterly interest rate = (EAR)/(number of compounding periods)

= 7.4%/4

= 1.85%,

Now, we calculate interest earned on "face-value" of $1,000,000 over 3-months,

Interest earned = (face value) × (quarterly interest rate)

= $1,000,000 × 1.85% = $18,500,

So, amount firm receives from issuing 3-month commercial paper is the face value minus the interest earned:

Amount received = (face value) - (interest earned)

= $1,000,000 - $18,500

= $981,500.

Therefore, the amount that firms receives is $981500.

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The domain of this function p is (9,000 - x)/30, the marginal cost is 30 dollars per TV and revenue function is x(9,000 - x)/30. The marginal revenue is  (9,000 - 2x)/30 and  profit function in terms of x is R(x) -.

(A) To express the price p as a function of the demand x, we can solve the price-demand equation for p:

x = 9,000 - 30p

30p = 9,000 - x

p = (9,000 - x)/30

The domain of this function is the set of values of x for which the price is non-negative, since negative prices do not make sense in this context. Therefore, the domain is 0 ≤ x ≤ 9,000.

(B) The marginal cost is the derivative of the cost function with respect to x: C'(x) = 30

So the marginal cost is a constant value of 30 dollars per TV.

(C) The revenue function R(x) is the product of the demand x and the price p: R(x) = xp = x(9,000 - x)/30

The domain of this function is the same as the domain of the price function, which is 0 ≤ x ≤ 9,000.

(D) The marginal revenue is the derivative of the revenue function with respect to x: R'(x) = (9,000 - 2x)/30

(E) To find R'(3,000) and R'(6,000), we substitute x = 3,000 and x = 6,000 into the expression for R'(x):

R'(3,000) = (9,000 - 2(3,000))/30 = 100

R'(6,000) = (9,000 - 2(6,000))/30 = -100

Interpretation: R'(3,000) represents the extra money made from selling one more TV at a constant price when the demand is 3. When the demand is 6,000 TVs and the price remains the same, R'(6,000) represents the decrease in revenue from selling one fewer TV.

(F) To graph the cost function and the revenue function, we can plot the two functions on the same coordinate system, using the given domain of 0 ≤ x ≤ 9,000. The break-even points are the values of x for which the cost and revenue are equal, or C(x) = R(x).

C(x) = 150,000 + 30x

R(x) = x(9,000 - x)/30

Setting C(x) = R(x), we get:

150,000 + 30x = x(9,000 - x)/30

900,000 - 30x^2 = 30(150,000 + 30x)

900,000 - 30x^2 = 4,500,000 + 900x

30x^2 - 900x + 3,600,000 = 0

x^2 - 30x + 120,000 = 0

(x - 6,000)(x - 20) = 0

The break-even points are x = 6,000 and x = 20. These correspond to the intersections of the cost and revenue curves. The region to the left of x = 6,000 is a region of loss, since the revenue is less than the cost for x < 6,000. The region between x = 6,000 and x = 20 is a region of profit, since the revenue exceeds the cost for 6,000 < x < 20. The region to the right of x = 20 is again a region of loss, since the revenue is less than the cost for x > 20.

(G) The profit function is given by subtracting the cost function from the revenue function:

P(x) = R(x) -

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Answer:

x = 1

Step-by-step explanation:

A rectangle has two diagonals that are equal in length and bisect each other. That means they divide each other into two equal parts. So, if E is the intersection of the diagonals of rectangle ABCD, then AE = EC and BE = ED.

Also, since a diagonal divides a rectangle into two right triangles, we can use the fact that the sum of angles in a triangle is 180 degrees to find x.

Let’s look at triangle AEB first. The measure of angle AEB is 13x, so we can write:

13x + angle ABE + angle EBA = 180

We don’t know angle ABE or angle EBA yet, but we can use the fact that opposite angles of a parallelogram are equal to find them. Since ABCD is a parallelogram (a rectangle is a special case of a parallelogram), we have:

angle ABE = angle CDE angle EBA = angle DCA

Now we can substitute these values into our equation:

13x + angle CDE + angle DCA = 180

Next, let’s look at triangle CED. The measure of angle ECD is 3x-5, so we can write:

3x - 5 + angle CDE + angle DEC = 180

We don’t know angle DEC yet, but we can use the fact that adjacent angles of a parallelogram are supplementary to find it. Since ABCD is a parallelogram, we have:

angle DEC + angle DAB = 180 angle DEC = 180 - angle DAB

Now we can substitute this value into our equation:

3x - 5 + angle CDE + (180 - angle DAB) = 180

Simplifying both equations by subtracting 180 from both sides, we get:

13x + angle CDE + angle DCA = 0 3x - 5 + angle CDE - angle DAB = 0

Now we have two equations with three unknowns: x, angle CDE and angle DAB. To solve for x, we need to eliminate one of the unknown angles. We can do this by adding or subtracting the two equations.

Let’s try adding them first:

(13x + angle CDE + angle DCA) + (3x - 5 + angle CDE -angle DAB) = 0 16x -5 +2(angle CDE) =0

This gives us an equation with only x and one unknown:

16x -5+2(angleCDE)=0

To solve for x, we need to find out what (angleCDE)is.

We can do this by using another fact about rectangles: The diagonals of a rectangle are perpendicular to each other. That means they form four right angles at their intersection point E.

So,

angle AEB+angleBEC=90 13x+angleBEC=90 angleBEC=90-13x

Similarly,

angleCED+angleDEC=90 3x-5+angleDEC=90 angleDEC=95-3x

Since opposite angles of a parallelogram are equal,

angleBEC=angleDEC 90-13x=95-3x 10=10x X=1

Therefore,

the constantofproportionalityis 1.

The correct answer is X=1.

Step-by-step explanation:

do you that is responsible for that another is probability

The rule that accounts for this scenario is Probability. It is the ratio of the times an event is likely to occur divided by the total possible events.

The Given problem says that If rolling 10 times give 8 desired result. Than the probability becomes 8:10.

And if I roll it 100 times, and only get 8 desired result out of 100, than the probability for it is 8:100.

Now the total probability = Total number of events ÷ total possible events

⇒ 16 ÷ 110

⇒8:55 is the answer.

Therefore going by the result, we can say that it is a scenario of probability.

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\(\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}\)

Let the number of girls = \( x \)

Then, According to the question,

number of the boys = \( 9 + 3x \)

Total students in class = 60, so

\(9 + 3x + x = 60 \\ = > 9 + 4x = 60 \\ = > 4x = 60 - 9 \\ = > 4x = 51 \\ = > x = 51 \div 4 \\ = > x = 12.75\)

On rounding off

Then, number of girls = 13

Let the number of girls = x

Then, According to the question,

number of the boys = 9 + 3x9+3x

Total students in class = 60, so

\begin{gathered}9 + 3x + x = 60 \\ = > 9 + 4x = 60 \\ = > 4x = 60 - 9 \\ = > 4x = 51 \\ = > x = 51 \div 4 \\ = > x = 12.75\end{gathered}9+3x+x=60=>9+4x=60=>4x=60−9=>4x=51=>x=51÷4=>x=12.75

On rounding off

Then, number of girls = 13

Answer:

The test  has 10 3-point questions and 14 5-point questions.

Step-by-step explanation:

x + y = 24

3x + 5y = 100

From the first equation:

3x + 3y = 72

Subtracting:

3x - 3x + 5y - 3y = 100 -72

2y = 28

so y = 14

x + 14 = 24 so x = 10.

10*3 + 5*14

= 30 + 70 = 100 points.

Answer:

4 people can go

Step-by-step explanation:

Answer:

Equation:  18.75x+5=80

Answer : x= 4

Answer:

Hey there!

The domain is the range of all the x values.

So for this graph, the domain would be \(-10<x\leq 8\).

Note that the open circle means < or > and the closed circle means ≤ or ≥.

Let me know if this helps :)

The unit price of the disk is $0.549

The unit price of goods are the price of one portion of the goods in question.

From the given question,  a package of blank compact discs on sale at 10 for $5.49, this can be expressed as;

10 disc = $5.49

The unit price of the disc is the price of just one of the disc. The unit price is expressed as;

1 disc = x

Find the ratio

10/1 = 5.49/x

Cross multiply

10x = 5.49

Divide both sides by 10

10x/10 = 5.49/10

x = $0.549

Hence the unit price of the disk is $0.549

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Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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Answer:

A

Step-by-step explanation:

Answer:

630

Step-by-step explanation:

1st = 3

2nd = 6

3rd = 9 ...

20th = 60

Súmalos todos juntos para encontrar la suma.

3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 + 33 + 36 + 39 + 42 + 45 + 48 + 51 + 54 + 57 + 60 = 630

La suma de los primeros 20 múltiplos de 3 es 630

¡Espero que esto ayude!

The variation in the independent variable is 0.81%. Thus option C is correct option.

According to the statement

We have given that the coefficient of determination is .90, and we ahve to find the variation in the independent variable.

So, For this purpose, we know that the

An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects.

And

We know that the

The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.

Due to this reason the variation in the independent variable is 0.81%.

So, The variation in the independent variable is 0.81%. Thus option C is correct option.

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Answer:

m= 70

s= 40

a= 110

d= 40

Step-by-step explanation:

Angle M is equal to 70 because it is an isoleases triangle.

The 3 sides of a triangle is equal yo 180. So if angle m is 70, then 70+70 is 140. 180-140 is 40. This makes angle s= 40.

Now we have to find angle a. Angle a and 70 make a straight line. So the line is 180. 180-70 is 110. Angle a is equal to 110.

Now we have to find angle d. As I said before All the angles of a triangle equal to 180. 30+110= 140 now 180 - 140= 40. This makes angle d= 40.

The sequence is defined as \(a_{1} = 10\), and \(a_{n} = a_{n-1} - 8\)for n >= 2. The first four terms of the sequence are 10, 2, -6, and -14.

The sequence is defined recursively, where each term is obtained by subtracting 8 from the previous term. The first term is given as 10, so the second term is obtained by subtracting 8 from 10, giving 2. The third term is obtained by subtracting 8 from the second term, giving -6, and the fourth term is obtained by subtracting 8 from the third term, giving -14. Therefore, the first four terms of the sequence are 10, 2, -6, and -14.

To find the next term of the sequence, we can use the recursive definition  \(a_{n} = a_{n-1} - 8\). For example, the fifth term is obtained by subtracting 8 from the fourth term, giving -22. In general, we can find any term of the sequence by subtracting 8 from the previous term. The sequence appears to be decreasing rapidly, with each term being 8 less than the previous term. The sequence is an example of an arithmetic sequence, where each term is obtained by adding or subtracting a constant value (in this case, -8) to the previous term.

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Answer:

negative

Step-by-step explanation:

negative because you are losing something

The correct answer is (a) event. An event is a subset of outcomes from the sample space. It represents a specific outcome or set of outcomes that we are interested in. Events can be simple, consisting of a single outcome, or they can be compound, consisting of multiple outcomes.

For example, consider rolling a fair six-sided die. The sample space is {1, 2, 3, 4, 5, 6}. Let's say we are interested in the event of rolling an even number. The event in this case would be {2, 4, 6}, which is a subset of the sample space.

Events can also be mutually exclusive, meaning they cannot occur at the same time, or they can be independent, meaning the occurrence of one event does not affect the probability of the other event occurring.

In summary, an event is a subset of outcomes from the sample space and represents a specific outcome or set of outcomes that we are interested in. It is an important concept in probability theory.

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Craig will pay a total of $80,713.06 including interest over the 5-year period.

What is compound interest?

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

To calculate the total amount that Craig will pay back over the 5-year period, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(n*t)}\)

where:

A = the final amount

P = the principal (the amount Craig borrowed)

r = the annual interest rate (11%)

n = the number of times the interest is compounded per year (assume it's compounded monthly, so n = 12)

t = the number of years (5)

Substituting the given values into the formula, we get:

\(A = 45000(1 + 0.11/12)^{(12*5)}\\ \\A = 45000(1.00916666667)^60\)

A = 45000(1.79585694245)

A = 80713.0624

Therefore, Craig will pay a total of $80,713.06 including interest over the 5-year period.

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Answer:

Step-by-step explanation:

Let the initial number of books be x.

Set equation:

Answer:

50 books

Step-by-step explanation:

Forming the equation,

→ x + ((x/100) × 12) = x + 6

Now the value of x will be,

→ x + ((x/100) × 12) = x + 6

→ x - x + (12x/100) = 6

→ 0.12x = 6

→ x = 6/0.12

→ [ x = 50 books ]

Hence, answer is 50 books.

\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=65\pi \end{cases}\implies 65\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi}\cdot 65\pi =r^3 \\\\\\ \cfrac{195}{4}=r^3\implies \sqrt[3]{\cfrac{195}{4}}=r\implies 3.65\approx r\)

Hope this helps you

........

Answer:Vented Brake Rotors are common on most modern vehicles. They have a hollow channel between the inner and outer surfaces. This channel (or vent) allows the rotor to shed more heat. This helps to prevent Brake Fade

Step-by-step explanation:

The equation of the tangent line to the graph of y = arcsec(18x) at the point (2, 18) is y = (√3 / 6)x + (18 - √3 / 3).

To find the equation of the tangent line to the graph of the function y = arcsec(18x) at the point (2, 18), we need to determine the slope of the tangent line at that point.

The derivative of the arcsec(x) function is given by:

d/dx [arcsec(x)] = 1 / (|x| * sqrt(x^2 - 1))

Using this derivative, we can find the slope of the tangent line at x = 2:

m = 1 / (|2| * sqrt(2^2 - 1))

= 1 / (2 * sqrt(3))

= 1 / (2 * √3)

= √3 / 6

Now that we have the slope (m) and the point (2, 18), we can use the point-slope form of a linear equation to find the equation of the tangent line:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point (2, 18) and m is the slope (√3 / 6).

Plugging in the values:

y - 18 = (√3 / 6)(x - 2)

Simplifying further:

y - 18 = (√3 / 6)x - (√3 / 6)(2)

y - 18 = (√3 / 6)x - √3 / 3

Finally, rearranging the equation to the standard form:

y = (√3 / 6)x + (18 - √3 / 3)

So, the equation of the tangent line to the graph of y = arcsec(18x) at the point (2, 18) is y = (√3 / 6)x + (18 - √3 / 3).

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Answer:

-8

Step-by-step explanation:

Hello !

Answer:

\(\Large \boxed{\sf x=-11}\)

Step-by-step explanation:

We want to find the value of x that satisfies the following equation :

\(\sf 5x+2=4x-9\)

Let's isolate x !

First, substract 4x from both sides :

\(\sf 5x+2-4x=4x-9-4x\\x+2=-9\)

Now let's substract 2 from both sides :

\(\sf x+2-2=-9-2\\\boxed{\sf x=-11}\)

Have a nice day ;)

Hello!

5x + 2 = 4x - 9

5x - 4x = - 9 - 2

x = -11