What is the value of f(3) on the following graph?

The general formula for determining the nth term of a geometric sequence is expressed as

an = ar^(n - 1)

where

a1 represents the first term

n represents the number of terms

r represents the common ratio

From the information given,

a1 = 5, r = - 1

Since we are looking for the 12th term, a12, n = 12

Thus, we have

a12 = 5(-2)^(12 - 1)

a12 = 5(-2)^11

a12 = - 10240

The amount of the profit will be $50,738.

A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.

The profit is given as,

Profit = Selling price - Cost price

The Wind Up Corp computed their monthly expense equation is given below.

E = 3.2q + 56,000

Its products will be sold to retailers at a wholesale price of $9 each. If 18,403 units are sold. Then  the expense will be

E = 3.2 x 18403 + 56000

E = $114,889

Then the selling price will be

S = 9 x 18403

S = 165,627  

Then the amount of the profit will be

P = 165,627 - 114,889

P = $50,738

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Answer:

8 units

Step-by-step explanation:

Area of square:

length * width

2 * 3

= 6  units

Area of triangle:

1/2 * base * height

1/2 * 2 * 2

= 2 units

Area of entire shape:

6 + 2

= 8 units

So, the area of the shape is 8 units.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

4221 birhs

Step-by-step explanation:

. Find the mean number of births per day, then use that result to find the probability that in a day, there are 15 births.

Answer:

the main amount pules the additional amount

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The expression that can be used to find the total amount earned for m sessions where n students attend the session.

10m + 5n

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount earned per session = $10

Amount earned per student = $5

The amount earned for n students in one session.

= 10 + 5n

The amount earned for x students in m session.

= 10m + 5n

Thus,

The expression that can be used to find the total amount earned for m sessions where n students attend the session.

10m + 5n

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We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

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Let's solve your equation step-by-step.

Step 1: Simplify both sides of the equation.

Step 2: Subtract 3x from both sides.

Step 3: Subtract 1 from both sides.

Let's solve your equation step-by-step.

1/3 (9x+3)=3x+1

Step 1: Simplify both sides of the equation.

1/3(9x+3)=3x+1

(1/3)(9x)+(1/3)(3)=3x+1(Distribute)

3x+1=3x+1

Step 2: Subtract 3x from both sides.

3x+1−3x=3x+1−3x

1=1

Step 3: Subtract 1 from both sides.

1−1=1−1

0=0

Answer:

All real numbers are solutions.

Answer:

\(\boxed{\sf \ \ \ k = 1 \ \ \ }\)

Step-by-step explanation:

hello,

saying that p-1 is a factor of \(p^4+p^2-p-k\)

means that 1 is a root of this expression, so it comes

1+1-1-k=0

<=> 1-k=0

<=> k = 1

Answer:

Step-by-step explanation:

A transformation that changes the orientation of a figure but not the orientation of the vertices is called a "reflection."

A reflection is a transformation that flips a figure over a line, called the "line of reflection." The line of reflection can be a line on a coordinate plane, or it can be a line in the space of the figure. The transformed figure, or the image, is a mirror image of the original figure, with respect to the line of reflection. The line of reflection is the perpendicular bisector of the line connecting any two non-adjacent vertices of the figure, then the figure's orientation remains unchanged but it's flipped over that line.

For example, if you reflect a square over its diagonal line, the square will be flipped but its vertices will still be in the same order, so the orientation won't change.

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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The nth term of the sequence 4/5, 1/5, 1/20. 1/80..... is an = 4/5(1/4)^(n - 1)

The definition of the function is given as

4/5, 1/5, 1/20. 1/80.....

The above definitions imply that we simply multiply 1/4 to the previous term to get the current term

Using the above as a guide, we have

First term, a = 4/5

Ratio, r = 1/4

So, we have the following equation

an = 4/5(1/4)^(n - 1)

Hence, the value of the nth term is an = 4/5(1/4)^(n - 1)

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

The triangle is equilateral, so all sides are equal.

4x = 3x + 2

x = 2

4x = 8

All sides measure 8 units.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

The equation of the line is y = (3/2)x - 1/2.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Let's say you need to know the answer about the equation of a line that passes through points (3, 4) and (5, 7).

Now,

The equation of a line.

y = mx + c

The line passes through points (3, 4) and (5, 7).

m = (7 - 4) / (5 - 3)

m = 3/2

Slope = 3/2 _____(1)

Now,

(3, 4) = (x, y)

4 = 3/2 x 3 + c

4 = 9/2 + c

c = 4 - 9/2

c = (8 - 9) / 2

c = -1/2

y-intercept = -1/2 ____(2)

Now,

y = mx + c

From (1) and (2),

y = (3/2)x - 1/2

Thus,

The equation of the line is y = (3/2)x - 1/2.

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The complete question.

Find the equation of a line that [passes through the point (2, 4), and (5, 7).

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}\)

\(\Delta = b^{2} - 4ac\)

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

\(\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}\)

\(\frac{1}{4} = \frac{15 + x + x}{x(15+x)}\)

\(\frac{1}{4} = \frac{15 + 2x}{x(15+x)}\)

Applying cross multiplication.

\(x^2 + 15x = 4(15 + 2x)\)

\(x^2 + 15x = 60 + 8x\)

\(x^2 + 7x - 60 = 0\)

Quadratic equation with \(a = 1, b = 7, c = -60\). So

\(\Delta = 7^{2} - 4*1*60 = 289\)

\(x_{1} = \frac{-7 + \sqrt{289}}{2} = 5\)

\(x_{2} = \frac{-7 - \sqrt{289}}{2} = -12\)

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

Answer:  \(y=\frac{-15}{7}x-\frac{4}{7}\)

Slope: -15/7

y-int:-4/7

Step-by-step explanation:

slope: rise/run

\(\frac{x^2-x^1}{y^2-y^1}\)

\(\frac{-7-8}{-4-3}=\frac{-15}{-7} =\frac{-15}{7}\)

thats the answer :)

~rere

Answer:

step 1 :

2.5+ 13.5 =16

step 2 :

16× 10 =160

Step-by-step explanation:

10(2.5+13.5)

10*16

160

Answer: 4 hours

Step-by-step explanation:

okay so you have to know your times tables 2*4=8 so 20*40=80 then if he paid a tip of 10$ that would equal $90 witch is what he paid.

Answer: c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer: It will be A that is the best answers

The normalized input admittances are the inverse of the normalized input impedances and can be found on the Smith Chart.

The Smith Chart is a graphical tool used to quickly calculate the reflection coefficient, impedance, admittance, and other characteristics of a transmission line. To find the normalized input admittances corresponding to the normalized input impedances, we first need to find the normalized reflection coefficient for the given normalized input impedances. This can be done by locating the given normalized impedance on the Smith Chart and then determining the normalized reflection coefficient from the radial and angular coordinates. Once the normalized reflection coefficient has been determined, the normalized input admittance can be found by using the formula Y = 1/Z. The normalized input admittance is then located on the Smith Chart in the same manner as the normalized input impedance, using the radial and angular coordinates.

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SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

If one of the pedestrian deaths is randomly selected.

Find the probability that the driver was not intoxicated but the pedestrians were.

We are expected to enter 4 decimal places.

Now, from the table, we can see clearly that:

CONCLUSION:

The final answer is 0. 2528 ( 4 decimal places).

Answer:

Let A bc the first number

Let B be the second number

Let C be the third number

A= b+6

C= 3a

Step-by-step explanation:

Hope this helps :) Have a great day!!!!

Answer:

9.8 cm

Step-by-step explanation:

Volume of a sphere, V = 4/3 πr³

V = 500cm³

π = 3.14

500 = 4/3 * 3.14 * r³

500 * 3 = 4 * 3.14 * r³

1500 = 12.56r³

r³ = 1500 / 12.56

r³ = 119.42675

r = (119.42675)^1/3

r = 4.9245574

Diameter = 2r

Diameter = 2 * 4.9245574

Diameter = 9.849

= 9.8cm