5. Caroline is 12 years younger than
twice Anna's age.
Caroline is 32 years old. How old is
Anna?

To find the production level that maximizes profit, we need to determine the point where the revenue and cost functions intersect.

The revenue function is given by R(x) = x * p(x), where p(x) represents the demand function. The profit function is defined as P(x) = R(x) - C(x).

First, let's find the revenue function. Since p(x) = 2900 - 7x, we can express the revenue function as R(x) = x * (2900 - 7x) = 2900x - 7x^2.

Now, we can substitute the cost and revenue functions into the profit equation and simplify it as follows:

P(x) = R(x) - C(x)

    = (2900x - 7x^2) - (18000 + 500x - 2.2x^2 + 0.004x^3)

    = -0.004x^3 + 2.2x^2 + 2400x - 18000

To find the production level that maximizes profit, we need to find the critical points of the profit function by taking its derivative and setting it equal to zero:

P'(x) = -0.012x^2 + 4.4x + 2400

Solving P'(x) = 0, we can find the production level that maximizes profit.

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When a cone is sliced in a direction parallel to the base, the resulting cross section is a circle.

A plane parallel to the base will intersect the curved surface of the cone at the same distance from the vertex all the way around, creating a circular shape.

This type of cross section is called a parallel cross section, and it is one of three types of cross sections that can be made when slicing a cone (the others being perpendicular and oblique).

In practical terms, this means that if you were to slice a cone-shaped cake or piece of fruit parallel to the base, you would end up with circular slices. This type of slicing can also be useful in engineering and construction, as it can create cylindrical shapes that can be used as columns or supports.

In summary, when a cone is sliced parallel to the base, the resulting cross section is a circle, and this type of slicing can be useful in a variety of applications.

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Answer:

The least common multiple 150 is a product of common & odd prime factors between the integers which is divisible by each one an integer of this same group.

Answer:

150

Step-by-step explanation:

25*6=150

10*15=150

30*5=150

Answer:

11 now brain list

Step-by-step explanation:

Answer: I hope this is helpful

Step-by-step explanation:

The square root of 121 is 11, as 121 is a perfect square number. √121 can be either positive or negative.The square root of 121 equals 11. Since 11 is a whole number, 121 is a perfect square.There are three factors of 121. They are 1, 11 and 121

Answer:

No Solution

Explanation:

Given the trigonometric equation:

Add 2 to both sides:

Divide both sides by √3.

Take the arccos of both sides:

Answer: 25.5 miles per gallon. 16.8 gallons x 25.5 miles = 428.4 miles

Answer:

Exact Form:

17/30

Decimal Form:

0.56

Step-by-step explanation:

Answer:

0.56 i think

Step-by-step explanation:

Answer:

15 gallons red paint and 9 gallons blue paint

Step-by-step explanation:

1 gallon unique purple shade = red 5:3 blue

Let's see how many parts are there in total, 5+3=8

24 gallons divided by 8 parts = 3

5x3 =15

3x3=9

Step-by-step explanation:

Y= 3x + b

As, to know the total, which is y, we need to solve for the cost

So first for money per square foot = $3

For square foot = x

So, price for x square foot = $3x (here this is the value of m)

Now, for value b,

$100 is added to the cost as its the charge, as the flat fee

So the value of b = $100

So, y=3x+100

Answer:

[see answer below]

Step-by-step explanation:

\(9*10^{-5}\)

We would move the decimal 5 places to the left.

\(9*10^{-5}\\\\\rightarrow\boxed{0.00009}\)

Hope this helps!

Answer:

\(\sqrt[4]{x}\)

Step-by-step explanation:

The radical form of the given expression ( x¹ / ⁴ ) is  \(\sqrt[4]{x}\).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

In mathematics, a number r is said to be the nth root of a number x if it is raised to the power n.

Radical expression = ( x¹ / ⁴ ) = \(\sqrt[4]{x}\).

Therefore, the radical form of the given expression ( x¹ / ⁴ ) is  \(\sqrt[4]{x}\).

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The work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

To calculate the work required to pump all the water over the edge of the tank, we need to consider the weight of the water in the tank and the height it is lifted.

First, let's find the volume of the water in the tank. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Plugging in the values, we have:

V = (1/3)π(3²)(12)

= (1/3)π(9)(12)

= 36π

Next, we need to find the weight of the water. The weight of an object is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity. The mass of the water can be found by multiplying its volume by the density of water, which is approximately 62.4 pounds per cubic foot:

m = (36π)(62.4)

≈ 22619.47 pounds

Now, we can calculate the work done by multiplying the weight of the water by the height it is lifted. In this case, the height is 12 feet:

W = (22619.47)(12)

≈ 271433.64 foot-pounds

Therefore, the work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

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The work required to pump water out of an inverted conical tank involves calculating the pressure-volume work at infinitesimally small volumes within the tank and integrating this over the entire volume of the tank. This provides an interesting application of integral calculus in Physics.

The question requires the concept of work in Physics applied to a fluid, in this case, water lying within an inverted conical tank. Work is done when force is applied over a distance, as stated by work = force x distance. In the fluid analogy, the 'force' link is the pressure exerted on the water and the distance is the change in volume of the fluid. Therefore, work done (W) = Pressure x Change in Volume (ΔV).

In this scenario, you are required to pump out water from an inverted conical tank, hence, the work you do is against the gravitational force pulling the water downwards. To calculate the total work done, you have to consider the work done at each infinitesimally small (hence, constant pressure) strip of volume and integrate over the entire volume of the tank.

The detail of calculation would require the knowledge of integral calculus and the formula for volume of a cone. I recommend considering this as an interesting application of integrals in Physics. Also remember that the volume of a cone = 1/3πr²h, where 'r' is the radius of base and 'h' is the height of cone.

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The value of the powers is 40 × 10⁷ + 3 × 10⁷ = 43 × 10⁷.

Standard index form, commonly referred to as scientific notation, is a way to express integers as the product of a power of 10 and a decimal number between 1 and 10. The decimal point must be moved a certain number of places in order to return to the original value, which is represented by the power of 10. In mathematics, the standard index form is used to express extremely big or extremely small integers in a clear and understandable manner. In fields like astronomy, physics, and chemistry where extremely large or extremely tiny numbers frequently occur, it is frequently utilised in scientific and technical computations.

The given expression is (3 × 10⁶) + (4 × 10⁷).

To add the following we make the powers same by multiplying 10:

(3 × 10⁶) (10) = 3 × 10⁷

(4 × 10⁷) (10) = 40 × 10⁷

Thus, the value of the powers is 40 × 10⁷ + 3 × 10⁷ = 43 × 10⁷.

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The linear regression model for the weekly cost data is given by C(z) = ma + k, where z is the independent variable representing the weekly demand.



The values of m and k are determined through the regression analysis. Using this model, we can estimate the total weekly cost for a given weekly demand and calculate the per unit variable cost and weekly fixed cost.To find the linear regression model, we need to perform a regression analysis on the given weekly cost data. This analysis will determine the values of m and k in the equation C(z) = ma + k, where C(z) represents the weekly cost and z represents the weekly demand.

Once the values of m and k are obtained, we can use the model to estimate the total weekly cost when the weekly demand is 210. By plugging in z = 210 into the equation C(z) = ma + k, we can calculate the total weekly cost rounded to the nearest dollar.The per unit variable cost can be determined by the value of m in the model. It represents the change in cost per unit change in demand. By rounding m to one decimal place, we can obtain the per unit variable cost rounded to one decimal place.

The weekly fixed cost can be determined by the value of k in the model. It represents the cost that does not depend on the weekly demand. By rounding k to the nearest integer, we can obtain the weekly fixed cost rounded to the nearest dollar.Overall, by applying the linear regression model to the given data, we can estimate the total weekly cost, calculate the per unit variable cost, and determine the weekly fixed cost of producing sleeping bags.

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If you can earn 8 percent on your money, the prize worth to you is: $76,812.50. To calculate the present value of the prize, we need to determine the current worth of receiving $1000 per month for 9 years, given an 8 percent annual interest rate.

This situation can be evaluated using the concept of the present value of an annuity. The present value of an annuity formula is used to find the current value of a series of future cash flows. In this case, the future cash flows are the $1000 monthly payments for 9 years. By applying the formula, which involves discounting each cash flow back to its present value using the interest rate, we find that the present value of the prize is $76,812.50.

This means that if you were to receive $1000 per month for 9 years and could earn an 8 percent return on your money, the equivalent present value of that prize, received upfront, would be $76,812.50.

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Answer:

;)

Step-by-step explanation:

Q2) y=5x+7

Q3) option 4

Q4) y= -3

Q5) x= -2

Q6) y=1

Q7) y=2x-7

Q8) y=2x-3

Q9) x=1

Q10) false

Answer: x = -2

Step-by-step explanation:

To begin, consider the following equation:

-3 = -8x - 9 + 5x

To begin, add the x terms on the right side of the equation:

-3 = -8x + 5x - 9

Simplifying even more:

-3 = -3x - 9

We wish to get rid of the constant term on the right side (-9) in order to isolate the variable x. This can be accomplished by adding 9 to both sides of the equation:

-3 + 9 = -3x - 9 + 9

To simplify: 6 = -3x

We can now calculate x by dividing both sides of the equation by -3: 6 / -3 = -3x / -3

To simplify: -2 = x

As a result, the answer to the equation -3 = -8x - 9 + 5x is x = -2.

Option A) "Cannot be negative" is a correct statement about the F distribution. The F distribution is a probability distribution that is used in statistical hypothesis testing to compare the variances of two populations.

The assertion "cannot be positive" about the F distribution is erroneous. The F distribution can only accept positive values and cannot accept negative values; however, it can accept values greater than zero.

"Is the same as the t distribution" is an error. When the sample size is small or the population standard deviation is unknown, the t distribution is employed for testing hypotheses regarding the population mean.

"Is the same as the z distribution" is similarly erroneous. When the population standard deviation is known and the sample size is large, the z distribution is employed as a probability distribution.

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Answer:

The train appears to go the same distance each minute

9mins

The cost for each person appears to be the same

Step-by-step explanation:

So for the first qu you basically want to find  the distance the train travels each minute, so for

3mins : 9km

therefore

1min : 3km

basically divide 9 by 3

then the train travels 27km, how long does it take?

if 3km = 1min

then 27/3 = 9

so it takes the train 9 minutes

Then for the second qu you'll do the same thing

2ppl : $16

so one person : 16/2

so 1 person costs $8

so for 8 ppl you multiply 8 by 10

8ppl : $80

hope this helps:))))

Answer:

The answer is 4.

1. preteens and teenagers

2. 4

3. More information is possible.

Answer:

(-3.5,-2)

Step-by-step explanation:

Answer:

In the first ‘choose’ put -2

In the second ‘choose’ put -3.5

The approximate probability that the average price for 16 gas stations is over $4.69 is a. almost zero.

To calculate the probability, we need to assume a distribution for the average gas prices. Let's assume that the average gas prices follow a normal distribution with a mean of μ and a standard deviation of σ. Since the problem does not provide the values of μ and σ, we cannot calculate the exact probability.

However, we can make an approximate estimate using the properties of the normal distribution. The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution, regardless of the shape of the population distribution, as the sample size increases.

Considering this, if we assume that the population of gas prices is approximately normally distributed, and if we have a large enough sample size of 16 gas stations, we can use the properties of the normal distribution to estimate the probability.

In Excel, we can use the NORM.DIST function to calculate the cumulative probability. Assuming a mean of μ and a standard deviation of σ, we can calculate the probability that the average price is above $4.69 using the following formula:

=1 - NORM.DIST(4.69, μ, σ / SQRT(16), TRUE)

Note that μ and σ are unknown in this case, so we cannot provide an exact answer. However, if we assume that the distribution is centered around $4.69 and has a relatively small standard deviation, the approximate probability is expected to be almost zero.

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Answer:

x = 6

Step-by-step explanation:

Verticle angles are equal to each other...

m∠A = m∠B

Thus...

4x + 6 = 2x + 18

Now, we isolate x:

4x + 6 = 2x + 18

Subtract 6 from both sides

4x = 2x + 12

Subtract 2x from both sides

2x = 12

Divide both sides by 2

x = 6

The image of GHJ after translation is G' (-2.5, 4), H' (-3.5, 2) and J' (-5, 6).

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

As per the given data:

Coordinates of the vertices are:

G(0, 0), H(-1, -2), and J(-2.5, 2)

Translation: (x, y) → (x-2.5, y + 4).

For finding the image of GHJ:

Subtract 2.5 from x-coordinate of all points and 4 in y-coordinate of all points.

G(0, 0) → G' (-2.5, 4)

H(-1, -2) → H' (-3.5, 2)

J(-2.5, 2) → J' (-5, 6)

Hence, the image of GHJ after translation is G' (-2.5, 4), H' (-3.5, 2) and J' (-5, 6).

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Answer:

Step-by-step explanation:

30 tens is 30*10=300. 3 tens is 3*10=30 and 3 tenths is 3*0.1. So assuming you mean 30 tens minus 3 tens and 3 tenths, the answer would be 300-30.3 which would equal 269.7

Answer:

correlation

Step-by-step explanation:

I took the quiz

Answer: A. 5

Step-by-step explanation:

The length of the shorter leg is 2.53 feet and the length of the longer leg is 6.53 feet

From the question, we have the following dimensions

Hypotenuse = 7 feet

One leg = 4 feet longer than the other

This means that

x = 4 + y

h = 7

Where x and y are the dimensions

The hypotenuse of a right triangle is

h^2 = x^2 + y^2

Substitute the known values in the above equation

So, we have the following equation

(4+ y)^2 + y^2 = 7^2

Evaluate

16 + 8y + y^2 + y^2 = 49

So, we have

2y^2 + 8y - 33 = 0

Using a graphing tool, we have

y = 2.53

Substitute y = 2.53 in x = y + 4

x = 2.53 + 4

Evaluate

x = 6.53

Hence, the legs of the triangle are 2.53 and 6.53

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