(a) If you invest Po dollars at 7% annual interest and the future value is computed by continuous com- pounding, how long will it take for your money to double?
(b) Suppose you invest Po dollars at r% annual interest and the future value is computed by continuous compounding. If you want the value of the account to double in 2 years, what is the required interest rate?
(c)A rule of thumb used by many people to determine the length of time to double an investment is the rule of 70. The rule says it takes about t = 70/r years to double the investment. Graphically compare this rule to the one isolated in part b. of this problem.

Answer:

f(3) = 14

Step-by-step explanation:

f(x) = 3x +5

Let x = 3

f(3) = 3*3 +5

      = 9 + 5

      = 14

Answer:

Step-by-step explanation:

fș

The volume of the solid is 32/3.

The volume of the solid whose base is bounded by the circle x2 + y2 = 4 and the cross sections perpendicular to the x-axis are squares can be calculated using the formula for the volume of a solid of revolution. This formula states that the volume is equal to the integral of the area of the cross sections from the lower limit to the upper limit.

Since the cross sections are squares, the area of each cross section is given by the equation A = x2. The lower limit is given by the equation x2 + y2 = 4, which is x=-2, and the upper limit is x=2. Thus, the volume is given by the integral ∫(-2)2x2dx = 8∫x2dx = 8(x3/3)|(-2)2 = 8(2^3/3 - (-2)^3/3) = 8(8/3 - -8/3) = 32/3. Therefore, the volume of the solid is 32/3.

Learn more about volume of the solid here:

https://brainly.com/question/12649605

#SPJ4

The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable  sum range of .05 fluid ounces or less.

The simulation did not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces, indicating that the variability of the juice dispensed was within the acceptable sum of range

The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable range of .05 fluid ounces or less.

Learn more about sum here

https://brainly.com/question/641910

#SPJ4

To solve the radical equation √4z²-13z+9+3=3z, we need to get rid of the radical sign in order to isolate the variable.

First, we can add 9 to both sides to get:

√4z²-13z+12=3z+9

Then we can square both sides of the equation:

4z²-13z+12 = 9z²+27z+81

Now, we can rearrange the equation to get:

9z²-40z+69 = 0

Now we can use the quadratic formula to find the solutions for z:

z = (40 ± √(40²-4969)) / 2*9

z = (40 ± √(1600-2772)) / 18

z = (40 ± √(-1172)) / 18

Since the square root of a negative number is an imaginary number, this equation has no real solutions, which means that there are no values of z that will make the equation true.

So the radical equation √4z²-13z+9+3=3z doesn't have any solution.

The inverse demand function is P = 2400 + 5Q

Given that

Q = 480 - 0.2P

We simply make P the subject of the formula

So, we have

0.2P = 480 - Q

Divide by 0.2

P = 2400 + 5Q

To find the marginal revenue function, we can use the inverse demand function P = 2400 + 5Q, and take the derivative of this function with respect to Q.

The derivative of P with respect to Q is dP/dQ = 5. This represents the change in price for a one unit change in the quantity of operations performed.

So the Marginal Revenue function is MR = dP/dQ * Q = 5Q

To maximize profit, the doctor should equate marginal revenue to marginal cost, which is

MC = dAVC/dQ

So, we have

MC = d(2Q² - 15Q + 400)/dQ

Evaluate

MC = 4Q - 15.

So, we have

5Q = 4Q - 15

Q = -15

Take the absolute value

Q = 15

So, the number of operations is 15

We have

P = 2400 + 5Q

This gives

P = 2400 + 5 * 15

Evaluate

P = 2475

To find the profit, we need to subtract the total cost from the total revenue.

The total revenue is found by multiplying the price by the quantity of operations performed: TR = P * Q = 2475 * 15 = 37125

The total variable cost is found by multiplying the average variable cost by the quantity of operations performed: TVC = AVC * Q = (2Q^2 - 15Q + 400) * Q = 2Q^3 - 15Q^2 + 400Q

The total fixed cost is the fixed cost that doesn't change regardless of the level of output : TFC = $8000

The total cost is the sum of the total variable cost and total fixed cost: TC = TVC + TFC = 2Q^3 - 15Q^2 + 400Q + $8000

The profit is the difference between total revenue and total cost:

π = TR - TC = 37125 - (2Q^3 - 15Q^2 + 400Q + $8000)

When Q = 15,

profit is π = 37125 - (2(15)^3 - 15(15)^2 + 400(15) + $8000)

= 19750

Read more about marginal revenue at

https://brainly.com/question/13444663

#SPJ1

It is a sample size proportion. 0.16 is the proportion of the 1,000 college students that reported using Ecstasy, which is a measure of the sample.

The number 0.16 is a sample proportion. This means that it is the proportion of the sample of 1,000 college students that reported using the drug Ecstasy. A sample proportion is a measure of the sample, not of the population. It is not a randomly chosen number and it is not a margin of error. A margin of error is a measure of how accurate a sample statistic is likely to be, usually expressed as a percentage or a number of standard deviations. A population proportion is the proportion of the total population that holds a certain characteristic or has had a certain experience. Thus, 0.16 is a sample proportion and not a population proportion, margin of error, or randomly chosen number

Learn more about sample size here

https://brainly.com/question/25894237

#SPJ4

The correct expression is a) [tex]x^2-6x+9[/tex].

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is ,

=> [tex](x-3)^2[/tex]

Now using formula [tex](a-b)^2=a^2-2ab+b^2[/tex] then

=> [tex]x^2-2.x.3+3^2[/tex]

=> [tex]x^2-6x+9[/tex]

Hence the correct answer is a) [tex]x^2-6x+9[/tex].

To learn more about expression refer the below link

https://brainly.com/question/112703

#SPJ1

The value of the company after 5 years is given as follows:

$75,631.5.

The value will decline below $140,000 when:

3.27 years.

The exponential function for this problem is defined as follows:

V(x) = 450000(0.7)^x.

The value after 5 years is found replacing the lone instance of x by 5, hence:

V(5) = 450000(0.7)^5

V(5) = $75,631.5.

The value will decline below $140,000 when at x for which V(x) = 140000, hence:

140000 = 450000(0.7)^x.

(0.7)^x = 140000/450000

(0.7)^x = 0.311111

xlog(0.7) = log(0.311111)

x = log(0.311111)/log(0.7)

x = 3.27 years.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The two solutions that satisfy the equation 4lx+8l=4 are -9 and -7.

Given the equation,

4lx+8l=4

|x+8| = 4/4

|x+8| = 1

x + 8 = ± 1

When x = + 1

Then,

x = 1 - 8

x = -7

When x = - 1

x = -1 - 8

x = -9

Therefore the two solution of equation is -9 and -7.

To learn more about solution refer to :

https://brainly.com/question/22688504

#SPJ1

We got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

Therefore, x³+2x² +x-7=0 is correct answer.

An a non real solution uses non real numbers to solve the equation, which cannot be solved with real numbers. Back to the school answer: A non-real solution to a math equation is a solution that has “imaginary numbers” (also called “complex numbers”) in it because it cannot be solved with real numbers.

Step1

We need to find equation that has exactly two real and two non real solutions

2 real  and 2 non real solution means 4 solutions

x³ equation has maximum of 3 solutions

So we ignore equation that has largest exponent x³

We ignore options B  and D

Let check option A

x⁴ 36x² =0

factor the left hand side

Factor out x^2

x² (x² -36)=0

WE set each factor =0  and solve for x

x² =0  so x=0

x²  - 36 =0 so x= +-6

So solutions are x=0, x=6 , x= -6. Only 3 real solutions we got

LETS check with option C

x⁴  - 5x² -36=0

Factor left hand side

(x² -9)(x² +4)=0

set each factor =0  and solve for x

x² -9 =0  so x= -3, + 3

x² + 4 =0 , x² = -4, so x= +2i, -2i

So we got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

To learn more about non real solution refers to;

https://brainly.com/question/11802225

#SPJ1

Answer:11160              

i calculated

According to the information, the concentration of sugar in this solution is 62.5%.

To calculate the concentration of sugar we have to divide the mass of the solute by the mass of the solution and then multiply it for 100.

Equation:

The sugar concentration = 50g/80g x 100 = 62.5%

Therefore, the sugar concentration is 62.5%.

Learn more about concentration in: https://brainly.com/question/10725862

#SPJ1

There is not enough evidence to conclude that the percent at her school is less than 40%.

The conclusion of the hypothesis test is reached depending on the confidence interval as follows:

The upper bound of the interval is given as follows:

0.4240 = 42.40%.

Hence not enough evidence to conclude that the percent at her school is less than 40%.

More can be learned about the test of an hypothesis at https://brainly.com/question/13873630

#SPJ1

a) There is a 60% probability that the boy picks up a blue pen and recognizes it as blue.

b) There is a 62.5% probability that the boy chooses a pen and thinks it is blue.

c) Given that the boy thinks he chose a blue pen, there is a 96% probability that he actually chose a blue pen.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The following probabilities are given -

A 75% probability that a pen is blue.

A 25% probability that a pen is green.

If a pen is blue, an 80% probability that the boy thinks it is a blue pen.

If a pen is blue, a 20% probability that the boy thinks it is a green pen.

If a pen is green, a 90% probability that the boy thinks it is a green pen.

If a pen is green, a 10% probability that that the boy thinks it is a blue pen.

a) The probability that the boy picks up a blue pen and recognizes it as blue.

There is a 75% probability that he picks up a blue pen.

There is a 80% probability that he recognizes a blue pen as blue.

So, the equation will be -

P = 0.75 × 0.8

P = 0.6

Therefore, there is a 60% probability.

b) The probability that the boy chooses a pen and thinks it is blue.

There is a 75% probability that he picks up a blue pen.

There is a 80% probability that he recognizes a blue pen as blue.

There is a 25% probability that he picks up a green pen

There is a 10% probability that he thinks a green pen is blue.

So, the equation will be -

P = (0.75 × 0.80) + (0.25 × 0.10)

P = 0.6 + 0.025

P = 0.625

Therefore, there is a 62.5% probability.

c) Given that he thinks he chose a blue pen, the probability that he actually chose a blue pen.

There is a 62.5% probability that he thinks that he choose a blue pen.

There is a 60% probability that he chooses a blue pen and think that it is blue.

So, the equation will be -

P = 0.6/0.625

P = 0.96

Therefore, there is a 96% probability.

To learn more about probability from the given link

https://brainly.com/question/25688842

#SPJ4

A boy has color blindness and has trouble distinguishing blue and green. There are 75 blue pens and 25 green pens mixed together in a box. Given that he picks up a blue pen, there is a 80% chance that he thinks it is a blue pen and a 20% chance that he thinks it is a green pen. Given that he picks a green pen, there is an 90% chance that he thinks it is a green pen and a 10% chance that he thinks it is a blue pen. Assume that the boy randomly selects one of the pens from the box.

a) What is the probability that he picks up a blue pen and recognizes it as blue?

b) What is the probability that he chooses a pen and thinks it is blue?

c) (Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?

The triangle is obtuse because 11^2 + 21^2 does not equal 29^2.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.

We can use this theorem to determine the type of triangle by calculating the square of the longest side (29^2), and then comparing it to the sum of the squares of the other two sides (11^2 + 21^2). Since 11^2 + 21^2 does not equal 29^2, the triangle is obtuse.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

The unit value should Royal Decking use for each of its products,

Product A: $8 (loss),

Product B:  $16 (loss),

Product C: $10 (profit),

Product D: $9 (profit),

Product E: $8 (profit).

The sum of the quantities divided by the total value of purchases and sales yields the unit value of a group of similar goods. As a result, it represents a quantity-weighted average of the various prices at which the good is bought and sold.

Given inventory,

                      Product Cost               Selling Price

A                            $130                          $150

B                             $170                         $190

C                             $130                         $170

D                              $90                         $120

E                               $50                         $70

a sales commission equal to 10% of the selling price and shipping costs equal to 10%,

Product A :

the unit value is given by,

Value = selling price - (product cost + sales commission + shipping cost)

= $150 - ($130 + 10% x selling price + 10% x product cost)

= $150 - ($130 + 10% x $150 + 10% x $130)

= $150 - ($130 + $15 + $13)

= -$8 = $8 (loss)

Product B :

Value = selling price - (product cost + sales commission + shipping cost)

= $190 - ($170 + 10% x selling price + 10% x product cost)

= $190 - ($170 + 10% x $190 + 10% x $170)

= $190 - ($170 + $19 + $17)

= -$16 = $16 (loss)

Product C :

Value = selling price - (product cost + sales commission + shipping cost)

= $170 - ($130 + 10% x selling price + 10% x product cost)

= $170 - ($130 + 10% x $170 + 10% x $130)

= $170 - ($130 + $17 + $13)

= $10 = $10 (profit)

Product D :

Value = selling price - (product cost + sales commission + shipping cost)

= $120 - ($90 + 10% x selling price + 10% x product cost)

= $120 - ($90 + 10% x $120 + 10% x $90)

= $120 - ($90 + $12 + $9)

= $9 = $9 (profit)

Product E :

Value = selling price - (product cost + sales commission + shipping cost)

= $70 - ($50 + 10% x selling price + 10% x product cost)

= $70 - ($50 + 10% x $70 + 10% x $50)

= $70 - ($50 + $7 + $5)

= $8 = $8 (profit)

Hence unit value for each product is -$8, -$16, $10, $9, and $8.

Learn more about unit value;

https://brainly.com/question/20857111

#SPJ1

Two numbers have the sum of 19. If one of the numbers is c, express the other number in terms of c. The other number is 19 - c.

Given: two numbers have the sum of 19

Let: c be one of those numbers

We want to express the other number in terms of c

The other number = 19 - c

Given two numbers, we want to express one of them in terms of the other. We can let one of the numbers be represented by the variable c. Since the sum of the two numbers is 19, the other number can be expressed as 19 minus c. Therefore, the other number can be written as 19 - c.

We are given two numbers and we want to express one of them in terms of the other. We can represent one of the numbers with the variable c. Since the sum of the two numbers is 19, the other number can be expressed as 19 minus c. In other words, the other number can be written as 19 - c. This means that if the value of c is known, the value of the other number can be calculated by subtracting c from 19. For example, if c is 10, then the other number is 19 - 10 = 9. Similarly, if c is 5, then the other number is 19 - 5 = 14. Therefore, the other number can be expressed as 19 - c.

Learn more about sum here

https://brainly.com/question/641910

#SPJ4

Box1: x = -9 Box2: x = 7

For this equation, we need to factor the left side of the equation to solve it. To do this, we need to find two numbers that multiply to give us 63 and add to give us 16.

The two numbers are -9 and +7.

So, the factored equation is (x - 9)(x + 7) = 0.

For this equation, we need to factor the left side of the equation to solve it. To do this, we need to find two numbers that multiply to give us 63 and add to give us 16.

To solve the equation, we set each factor equal to zero and solve for x.

x - 9 = 0  -> x = 9

x + 7 = 0  -> x = -7

Therefore, the larger solution is x = -9, and the smaller solution is x = 7.

Therefore, the answer is Box1: x = -9 and Box2: x = 7.

Learn more about linear equation here

https://brainly.com/question/11897796

#SPJ4

Number of 7 students have both a dog and a cat, out of the 39 eighth grade students at Lincoln Middle School.

Total number of 8th grade students: 39

Number of students with a dog: 20

Number of students with a cat: 26

Number of students with both a dog and a cat: 20 + 26 - 39 = 7. Therefore, 7 have both a dog and a cat.

There are 39 students in the 8th grade at Lincoln Middle School. Of those students, 20 have a dog, 26 have a cat, and 7 have both a dog and a cat. To calculate this number, we added the number of students with a dog (20) and the number of students with a cat (26) and then subtracted the total number of students (39). The result of this calculation, 7, is the number of students who have both a dog and a cat. This means that 7 out of 39 8th grade students at Lincoln Middle School have a dog and a cat.

Learn more about number here

https://brainly.com/question/17429689

#SPJ4

Answer:

The answer is 85/1. To calculate 5 × 17, first multiply 5 × 10 = 50, then add 5 to the result to get 50 + 5 = 55. Finally, divide the result by 1 to get 55/1 = 85/1.

Answer:

The fraction is 5/7

Step-by-step explanation:

5 * 1/7

Multiplying a whole number times a fraction

Multiply the whole number times the numerator.

5 * 1 = 5

Divide by the denominator

5/7

The fraction is 5/7

If Ellie purchased a laptop for $1,400, but she still owes $600 which she borrowed to purchase the laptop. Her equity in the case of the laptop is; A. $1400+ $600 = $2000.

Using this formula to determine her equity

Equity = Cost of laptop + Amount owes

Where:

Cost of laptop = $1,400

Amount owes = $600

Let plug in the formula

Equity = $1,400 + $600

Equity = $2,000

Therefore we can conclude that the correct option is A.

Learn more about equity here:https://brainly.com/question/11556132

#SPJ1

This matches the given volume of 108 cubic inches.

Volume is a measure of the amount of space an object or substance occupies. It is measured in units such as liters, gallons, cubic meters, and milliliters. It is often used to measure the size of a container, the amount of a material, or the size of a space. Volume is an important property for understanding physical objects, as it helps to determine mass and density.

The volume of a triangular prism can be calculated by taking the area of the base, which is the area of an equilateral triangle (all sides equal) multiplied by the height of the prism. In this case, the area of the triangle is ((√3/4)*(12^2)) = 108 square inches and the height is 9 inches, so the volume is 108*9 = 108 cubic inches. This matches the given volume of 108 cubic inches.

To know more about volume click-
https://brainly.com/question/463363
#SPJ1

Answer:

An algebraic expression for the total amount of money in both accounts is m+2000

Step-by-step explanation:

If there are 2000 dollars in one account and m dollars in the other, the sum of both accounts can be expressed as 2000+m (or m+2000).

Answer:

9(5 + 8)

Step-by-step explanation:

Using division operation, the number of weeks a bag of cat food lasts is 4 weeks.

Division operation is one of the four basic mathematical operations.

The division operation produces a result known as the quotient.

The quotient results when the dividend is divided by the divisor.

The quantity in a bag of cat food = 3lbs

The quantity that the cat eats per week = 3/4 = 0.75

The number of weeks that the bag of 3lbs will last = 4 (3/0.75)

Thus, we can conclude that the shopper's one bag of cat food will last her cat for 4 weeks.

Learn more about mathematical operations at https://brainly.com/question/20628271

#SPJ1

Consider the problem: A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4lb each week. How many weeks does one bag last?

The determinant of an n-by-n tridiagonal matrix containing only 1s can be calculated by iterating over the diagonal elements and summing the products of each element and its corresponding power of 1

The determinant of an n-by-n tridiagonal matrix containing only 1s as nonzero elements is given by the formula:

det(A) = 1^n-2 + 1^n-3 + ... + 1^2 + 1

For example, consider the 3x3 matrix:

A = [1 1 0; 1 1 1; 0 1 1]

Using the formula above, the determinant of A can be calculated as:

det(A) = 1^2 + 1 = 2

More generally, the determinant of an n-by-n tridiagonal matrix containing only 1s can be calculated by iterating over the diagonal elements and summing the products of each element and its corresponding power of 1. This sum can then be taken to the power of 1 to obtain the determinant of the matrix.

Learn more about determinants here:

https://brainly.com/question/4470545

#SPJ4

Reason:

c = Craig's score

c+12 = twelve more than Craig's score

c+12 = 70 because the key term "is" translates to "equals". As an example, saying "x is 5" means "x = 5".

The result of the quotient expression as required to be determined in the task content is; 2^(8x + 3).

It follows from the laws of indices that 8 = 2³.

On this note, the given expression; 8^(3x + 1) ÷ 2^x can be solved as follows;

2^( 3 (3x + 1) ) ÷ 2^x

= 2^( 9x + 3 ) ÷ 2^x

= 2^(9x + 3 - x)

= 2^(8x + 3)

Ultimately, the result of the quotient is; 2^(8x + 3).

Read more on indices;

https://brainly.com/question/170984

#SPJ1

The value of the missing number will be 3.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The equation for the missing number is given as x + (-4) = -1. the missing number will be calculated as:-

x + (-4) = -1

x -4 = -1

x = 4 - 1

x = 3

To know more about number lines follow

https://brainly.com/question/24644930

#SPJ1

The degree measure of angle BCD is 130.

What is the measure of angle?

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Given:  the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4: 5.

We can let  ∠AEB be 4x and  ∠ABE be 5x because they are in the ratio 4: 5.

When an inscribed angle contains the diameter, the inscribed angle is a right angle. Therefore by the triangle sum theorem,

= 4x+5x+90 = 180

x = 10 and

∠ABE = 50.

∠ABE =∠BED because they are alternate interior angles and AB||ED.

Opposite angles in a cyclic quadrilateral are supplementary,

so ∠BED + ∠BCD = 180

Use substitution to get ∠ABE + ∠BCD = 180

50 + ∠BCD = 180

∠BCD = 130

Hence, the degree measure of angle BCD is 130.

To learn more about the measure of angle from the given link

https://brainly.com/question/25770607

#SPJ4