Find the sum of the first 50 terms of the sequence below.
An = 3n + 2

The total cost to produce 30 bicycles is $5599.89. The profit from first 30 bikes is $550.11. The marginal profit on the 31st bike is $126.57.

The marginal cost function given is 600/(0.3q+5). To find the total cost to produce 30 bicycles, we need to integrate the marginal cost from 0 to 30 and add the fixed cost of 2200.

The result of the integration is 2000*(ln|1+0.3q|). Calculating from 0 to 30 gives us 3599.89. Thus, the total cost to produce 30 bicycles considering the fixed cost is 5599.89.

The revenue of each bike sold is $205. So, the total revenue generated from selling 30 bikes is 30*$205 = $6150. The profit is then the difference between the revenue and the total cost, giving us $6150-$5599.89 = $550.11.

To find the marginal profit on the 31st bike, subtract the marginal cost at 31 bikes from the selling price. The marginal cost at 31 bikes is the marginal cost function evaluated at q=31, which is approximately $78.43, and hence, the marginal profit on the 31st bike is $205 - $78.43 = $126.57.

https://brainly.com/question/34407434

#SPJ12

To find the total cost, multiply the quantity by the marginal cost function and add the fixed cost. To find the profit or loss, subtract the total cost from the revenue. The marginal profit can be found by subtracting the marginal cost from the selling price.

To find the total cost to produce 30 bicycles, you need to calculate the variable cost and add it to the fixed cost. The variable cost can be found by multiplying the marginal cost function by the quantity of bikes. So, the variable cost is (600/0.3*30 + 5) = 6105. Adding the fixed cost of 2200 gives us a total cost of 8305.

To find the profit or loss on the first 30 bicycles, we need to subtract the total cost from the revenue, which is the selling price multiplied by the quantity. So, the revenue is 205 * 30 = 6150. The profit or loss is then 6150 - 8305 = -2155, indicating a loss of $2155.

The marginal profit on the 31st bicycle can be found by subtracting the marginal cost from the selling price. So, the marginal profit is 205 - (600/0.3*31 + 5) = -55, indicating a loss on the 31st bicycle.

https://brainly.com/question/33310893

#SPJ2

The equivalent factored form is A. 7x(2x + 5).

To factorize the expression 14x^2 + 35x completely, we look for the greatest common factor (GCF) of the terms and apply the distributive property.

In this case, the GCF of 14x^2 and 35x is 7x.

So, we can factor out 7x from the expression:

14x^2 + 35x = 7x(2x + 5)

Therefore, the equivalent factored form is A. 7x(2x + 5).

Learn more about expression at https://brainly.com/question/1859113

#SPJ2

Answer:

P(at least one phobic)

= 1 - P(none phobic)

= 1 - 0.89^2

= 1-0.7921

= 0.2079

Step-by-step explanation:

Answer:- A reflection of the line segment across the line y = –x .

Explanation:-

A reflection over the line y = -x, the x-coordinate and y-coordinate interchange their places and they are negated (the signs are changed).

Given :- A line segment has endpoints at (–1, 4) and (4, 1) such that it reflects produce an image with endpoints at (–4, 1) and (–1, –4).

(-1, 4)→(-4, 1) and

(4, 1)→(-1, -4)

Thus this shows a reflection of the line segment across the line y = –x.

Answer:

A reflection of the line segment across the line y = –x.

Step-by-step explanation:

Given : A line segment has endpoints at (–1, 4) and (4, 1).

To find : Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4).

Solution : We have given that endpoints at (–1, 4) and (4, 1).

After reflection endpoints become  (–4, 1) and (–1, –4).

Reflection:   (–1, 4)  →→ (–4, 1)

                    (4, 1)→→→ (–1, –4).

We can see x coordinate become -y coordinate and y coordinate become -x coordinate.

(x ,y) →→ (–y, -x)

This is the a reflection of the line segment across the line y = –x rule of reflection .

Therefore, a reflection of the line segment across the line y = –x.

Answer:

Step-by-step explanation:

7

It’s C on Ed It is C It is C

The corresponding equation is y = 1/5(x).

A graph of the equation is shown below.

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

y represents the y-variable​.

x represents the x-variable.

k is the constant of proportionality.

Next, we would determine the constant of proportionality (k) by using the various data points in table B as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 4/20

Constant of proportionality, k = 1/5.

In this context, the corresponding equation is given by;

y = 1/5(x)

The loser had 5.5 points in the chess match.

To find out how many points the loser had in the chess match, we can set up an equation. Let's say the loser had x points. The winner was 4 points ahead, so the winner had x + 4 points. Since there were 15 games in total, we can set up the equation:

x + (x + 4) = 15

Combining like terms, we get:

2x + 4 = 15

Subtracting 4 from both sides, we get:

2x = 11

Dividing both sides by 2, we get:

x = 5.5

Therefore, the loser had 5.5 points in the chess match.

https://brainly.com/question/12365627

#SPJ3

Answer: b)  the sum of six times a number and five

Step-by-step explanation:

The given expression is [tex]6b+5[/tex], where b represents any number.

The above expression has two terms combined by addition operation.

In the first term there is one variable b and 6 as coefficient of b and the second term is a constant term of 5.

Therefore, the correct description of the given expression [tex]6b+5[/tex] is " the sum of six times a number and five".

Option: b is the correct answer.

b) the sum of six times a number and five.

We are given an algebraic expression in term of a variable 'b' as:

                                  6b+5

As we could see that here there are two terms in an expression one is: 6b and the other is 5 which is separated by a summation sign.

  Hence, when 6 times of a number 'b' is added to 5 we get the given expression(i.e. 6b+5)

              Hence, the answer is:  Option: b

Answer:

The correct option is B) -3

Step-by-step explanation:

Consider the provided expression.

[tex]5x^3 + 2[/tex]

We need to solve the expression when x=-1.

Substitute the values of x in the provided expression.

[tex]5(-1)^3 + 2[/tex]

Simplify the expression.

[tex]5\times -1+ 2[/tex]

[tex]-5+ 2[/tex]

[tex]-3[/tex]

Hence, the value of the provided expression when x=-1 is -3.

Therefore, the correct option is B) -3

Answer:

distributive property (a)

Step-by-step explanation:

I got 100/100 so this should be correct for you too.

Answer:

Th answer is - protecting assets

Step-by-step explanation:

Planning for the possibility that your home might get struck by lightning and catch on fire is part of a plan for protecting assets.

The protection of assets is a module of financial planning where one is needed to protect his assets against anything like - natural disaster or creditor's claims etc.

Answer:

radius of the cylinder is, 8 inches

Step-by-step explanation:

Volume of cylinder(V) is given by:

[tex]V = \pi r^2h[/tex]            .....[1]

where,

r is the radius of the cylinder and

h is the height of the cylinder.

As per the statement:

A cylinder has a volume of 320 pi cu. in. and a height of 5"

⇒[tex]V = 320 \pi[/tex] cubic inches and h = 5 inches

Substitute these values in [1] we have

[tex]320 \pi = \pi r^2 \cdot 5[/tex]

Simplify:

[tex]320 = r^2 \cdot 5[/tex]

Divide both sides by 5 we have;

[tex]64=r^2[/tex]

or

[tex]r^2 = 64[/tex]

⇒[tex]r = \sqrt{64} = 8 in[/tex]

Therefore, the radius of the cylinder is, 8 inches

Final answer:

To find the radius of the cylinder, use the formula for the volume of a cylinder, V = πr²h. Rearrange the formula to solve for the radius, and solve the equation to find the value of r.So,radius of cylinder r=8inches.

Explanation:

To find the radius of the cylinder, we can use the formula for the volume of a cylinder, which is V = πr²h. In this case, we need to solve for the radius, so we rearrange the formula as follows:

320π = πr²(5)

We can cancel out the π's on both sides of the equation:

320 = r²(5)

Divide both sides of the equation by 5:

64 = r²

Take the square root of both sides to solve for r:

r = √64

r = 8

Therefore, the radius of the cylinder is 8 inches.

Answer:

x represents Annette speed in miles per minute. Hence, option b) is correct.

Step-by-step explanation:

Given that Annette rode her bike 6.8 miles at a constant rate for 90 minutes. Also to find how fast she traveled, she solved the equation [tex]6.8=x\times 90[/tex]. Now, we have to tell here what x represents.

As, [tex]Speed=\frac{Distance}{Time}[/tex]

Let speed of bike is x miles/min and given distance is 6.8 miles and at a constant rate for 90 minutes.

∴ [tex]x=\frac{6.8}{90}[/tex]

⇒  [tex]6.8=x\times 90[/tex]

which is the same equation as given.

Here x represents Annette speed in miles per minute. Hence, option b) is correct.