Money is invested into an account earning 4.25% interest compounded annually. If the accumulated value after 18 years will be $25,000, approximately how much money is presently in the account?
a.
$5,875
b.
$11,820
c.
$19,125
d.
$23,960

Answer: So, the possible number of additional senators who must vote in favor of the treaty in order to radify it is given by

[tex]19\leq x\leq 52[/tex]

Step-by-step explanation:

Since we have given that

Number of states = 50

Number of senators from each of the 50 states = 2

Total number of senators would be

[tex]50\times 2\\\\=100[/tex]

Since [tex]\dfrac{2}{3}[/tex] of the senators present must approve the treaty.

[tex]\dfrac{2}{3}\times 100\\\\=66.67[/tex]

Number of senators have voted in favor of a treaty = 48

So, remaining senators would be

[tex]67-48\\\\=19[/tex]

Let x be the number of senators needed.

So, Inequality would be

[tex]x\geq 19[/tex]

Now, [tex]100-48=52[/tex]

[tex]x\leq 52[/tex]

So, the possible number of additional senators who must vote in favor of the treaty in order to radify it is given by

[tex]19\leq x\leq 52[/tex]

The revenue function is R = -1/20x^2 + 1060x and the profit function is P = -1/20x^2 + 940x - 5000. The value of x that maximizes profit is 9400, and the maximum profit is calculated by substituting this value into the profit function. The price to charge to maximize profit is $590.

a) To express revenue (R) as a function of x, we multiply the price (p) by the quantity (x):

R = p * x

Substituting the demand equation (p = -1/20x + 1060):

R = (-1/20x + 1060) * x

Simplifying:

R = -1/20x^2 + 1060x

b) Profit (P) is given by subtracting the cost (c(x)) from the revenue (R):

P = R - c(x)

Substituting the expressions for R and c(x):

P = (-1/20x^2 + 1060x) - (120x + 5000)

Simplifying:

P = -1/20x^2 + 940x - 5000

c) To find the value of x that maximizes profit, we take the derivative of the profit function with respect to x and set it equal to zero:

dP/dx = -1/10x + 940

Solving for x:

-1/10x + 940 = 0

x = 9400

d) To find the price that maximizes profit, we substitute the value of x (9400) into the demand equation:

p = -1/20(9400) + 1060

simplifying:

p = 1060 - 470

p = $590

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a) First, we must express the revenue, denoted as 'R'. Revenue is simply the price per item multiplied by the quantity of items sold. Given the demand equation 'p', we can express the revenue as follows:

R = p * x = ( -1/20 * x + 1060 ) * x

This simplifies to:

R = x * (1060 - 0.05*x)

b) Profit is revenue minus cost. We use the revenue equation from part a) and the given cost equation 'c = 120x + 5000'. Plug these into the profit equation:

P = R - c = ( x * (1060 - 0.05*x) ) - ( 120x + 5000 )

This simplifies to

P = x * (1060 - 0.05*x) - 120*x - 5000

c) To maximize profit, we need to find the derivative of the profit function and then solve for x when this derivative is equal to zero (this will find the quantity that maximizes profit). After doing this, we find that the quantity that maximizes profit is x = 9400.

If we substitute x = 9400 into the profit function, we get the maximum profit which turns out to be 4413000.

d) The price that should be charged to maximize profit is found by substituting the value of x that gave us the maximum profit into the price function. In this case, substituting x = 9400 gives us the price = 590.

Therefore, in order to maximize profit, 9400 lawnmowers should be produced and sold at a price of 590 per lawnmower, which will yield a profit of 4413000.

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The equivalent equation is: -100k + 3 + 101k = -245 - 181k

Finding the Equivalent Equation

We need to find the equation equivalent to:

-k + 0.03 + 1.01k = -2.45 - 1.81k

To eliminate decimals, we can multiply the entire equation by 100:

100*(-k + 0.03 + 1.01k) = 100*(-2.45 - 1.81k)

This simplifies to: -100k + 3 + 101k = -245 - 181k

Therefore, the equivalent equation is: -100k + 3 + 101k = -245 - 181k

Complete question:

Which equation is equivalent to –k + 0.03 + 1.01k = –2.45 – 1.81k?

–100k + 3 + 101k = –245 – 181k

–100k + 300 + 101k = –245 – 181k

–k + 3 + 101k = –245 – 181k

–k + 300 + 101k = –245 – 181k

Answer:

[tex]h(x)=\frac{x}{2}-\frac{1}{2}[/tex]

Step-by-step explanation:

Hello

Step1

Let f(x)=y

f(x) = 2x + 1

(1)y= 2x + 1  

to find the inverse of f(x)

Replace every x with a y and replace every y with an x

y= 2x + 1

replacing  

x=2y+1

Step 2

Now solve the equation for y

x=2y+1

subtract 1 on both sides

x-1=2y+1-1

x-1=2y

divide boths dies by 2

(x-1)/2=2y/y

[tex]\frac{x-1}{2} =\frac{2y}{2} \\y=\frac{x-1}{2}[/tex]

let this last equation h(x)= inverse of f(x)

[tex]h(x)=\frac{x-1}{2}\\h(x)=\frac{x}{2}-\frac{1}{2}[/tex]

Have a great day

Length of the rectangle= 42 feet

Width of the rectangle =14 feet

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Given,

Ratio of length to width of rectangle = 3:1

Let width be x then length will be 3x

Perimeter of the rectangle = 112 feet

2(Length + Width) = 112

2(3x + x) = 112

2(4x) = 112

8x = 112

x = 112/8

Width x = 14 feet

length = 3x = 3×14 = 42feet

Hence, 42 feet is length and 14 feet is width of the rectangle.

Learn more about rectangle here:

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The inverse Laplace transform of (2s+5)/(s^2+6s+34) is found by completing the square in the denominator and then matching the result to a known form in the Laplace transform table.

The question asks for the inverse Laplace transform of the function (2s+5)/(s^2+6s+34). To find the inverse Laplace transform, we usually decompose the given function into a form that matches entries in the Laplace transform table. A common technique involves completing the square for the quadratic denominator, which enables us to match the form with the inverse transform for exponential or trigonometric functions as per standard Laplace tables.

In this case, the denominator can be rewritten as (s+3)^2 + (5^2 - 3^2) to make it resemble the denominator of the Laplace transform of a damped sine or cosine function. Next, we would separate the original function into partial fractions if necessary or directly find a corresponding entry in the Laplace transform table. Unfortunately, without further simplification, we cannot provide the exact inverse Laplace transform but you should use the approaches mentioned along with your extended Laplace table or use the convolution theorem if the function can be expressed as a product of functions.

Answer:

t = 11

Step-by-step explanation:

From the equation that gives, the number of games you can get the number t of players who participated in the ronund-robin tormeo, is:

[tex]N = \frac{t ^ 2-t}{2}[/tex]

[tex]55 = \frac{t ^ 2-t}{2}[/tex]

[tex]110 = t ^ 2-t[/tex]

[tex]t ^ 2-t -110 = 0[/tex]

[tex](t-11) (t + 10) = 0[/tex].  Then

[tex]t - 11 = 0\\t = 11\\t + 10 = 0\\t = -10[/tex]

Since t cannot take negative values, then t = 11.

Answer:  D. [tex]\pi=\dfrac{C}{2r}[/tex]

Step-by-step explanation:

Given : The formula to find the circumference is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle.

To find the formula for [tex]\pi[/tex] , we need to divide 2r on both of the sides in the above equation, we get

[tex]\pi=\dfrac{C}{2r}[/tex] , where  r is the radius of the circle.

Hence, the correct formula for [tex]\pi[/tex] : Option D [tex]\pi=\dfrac{C}{2r}[/tex]

Answer:

LM= 4

Step-by-step explanation:

In the triangle KLM, ON is the mid segment of KLM

WE use triangle Mid segment theorem

MN= twice of ON

MN= 2 times of ON

4x= 2(x+1)

distribute 2 inside the parenthesis

4x= 2x+2

Subtract 2x on both sides

4x-2x= 2x+2-2x

2x= 2

divide by 2 on both sides

x= 1

To find length of MN, we plug in 1 for x

MN= 4x= 4(1)= 4

Answer:

The arc's length is 1.8 ft

Step-by-step explanation:

For calcaulate the arc length S we used the formula below:

[tex] S=\frac{\pi.\alpha(\º)}{180}*R[/tex]

Here alpha is the arc angle in degrees and R is the circle radius. Thus, if alpha is equal to 26 and R equals to 4 ft:

[tex] S=\frac{\pi.26}{180}\ *\ 4ft[/tex]

[tex] S=0.45\ *\ 4ft[/tex]

[tex] S=1.8\ ft[/tex]

Domain:{−2,7,2}

Range:{7,2}

Final answer:

To calculate the number of different responses in the survey, we multiply the number of potential responses for each issue. With 5 options for each of the 3 issues, there are 5 x 5 x 5 = 125 different possible combinations.

Explanation:

To determine the number of different responses to the survey conducted by a union, we need to calculate the total possible combinations that can occur when members are asked to rate the importance of three issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Since there are five different responses allowed for each issue, we would use a combination formula.

Each member can choose from 5 different responses for each of the 3 issues. This is a situation where we use the 'fundamental counting principle' where you multiply the number of options for each independent choice to get the total number of possibilities:

The total number of different responses to the survey is 5 x 5 x 5, which equals 125.

So, members have 125 different ways to respond to the survey based on how they rate the importance of each issue.

To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. If we want to convert [tex]\frac{3}{20}[/tex] to a percent, we need to find a fraction equivalent to [tex]\frac{3}{20}[/tex] that has a 100 in the denominator. We can do this by setting up a proportion.

[tex]\frac{3}{20}[/tex] = [tex]\frac{n}{100}[/tex]

Now, we can use cross products to find the missing value.

3 × 100 = 300

20 × n = 20n

300 = 20n ← Divide both sides by 20.

15 = n

Therefore, [tex]\frac{3}{20}[/tex] as a percent would be 15%.

Answer:

Option d is correct

[tex]Csc \ \theta =\frac{1}{y}[/tex]

Step-by-step explanation:

Here P(x,y) is the point on unit circle  ( unit circle has radius 1 and center (0,0))

Now in a diagram we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

[tex]Csc\ \theta =\frac{hypotenuse }{opposite \ side} \\Csc\ \theta =\frac{OP}{AP}[/tex]

[tex]Csc \ \theta =\frac{1}{y}[/tex] ( since OP =1 and AP =y)

Answer:

1/y

Step-by-step explanation:

apex