In the year 2001, a company made $7. 2 million in profit. For each consecutive year after that, their profit increased by 11%. How much would the company's profit be in the year 2005, to the nearest tenth of a million dollars?​

The measure of an angle that goes through 2/8 of a circle is 90°

A circle is a 2-dimensional shape that is round in shape it is equidistant from the center.

A circle has a total angle of 360°

That is the whole complete angle of the circle = 360°

The 2/8 th of the complete angle of the circle = 360 * 2/8

= 360 * 1/4

= 360/4

=90°

Thus, the 90° of the circle is given as 2/8th of an angle of the circle or we can say that the quarter angle of a circle comes out to 90°.

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Answer:

a = 16

b = 8z

Step-by-step explanation:

Expanding the given expression, we get:

(4y + z)^2 = (4y + z) × (4y + z)

= 16y^2 + 8yz + z^2

Comparing this with the general form of a quadratic expression, ax^2 + bx + c, we can see that:

a = 16

b = 8z

Therefore, the value of a is 16 and the value of b is 8z.

Since the derivative of a constant is always 0, we can drop the last term:
f’(x) = -21/x^4 + 4/x^3 + 1/x^2

Using the rules of differentiation, we can find the derivative of f(x) by taking the derivative of each term separately. The power rule and the constant multiple rule will come in handy here.

f(x) = 7/x^3 – 2/x^2 – 1/x + 140

f’(x) = d/dx(7/x^3) – d/dx(2/x^2) – d/dx(1/x) + d/dx(140)

To find the derivative of 7/x^3, we can use the power rule, which states that the derivative of x^n is nx^(n-1).

f’(x) = -21/x^4 – (-4/x^3) – (-1/x^2) + 0

To find the derivative of -2/x^2, we can again use the power rule:

f’(x) = -21/x^4 + 4/x^3 – (-1/x^2) + 0

To find the derivative of -1/x, we use the power rule once more:

f’(x) = -21/x^4 + 4/x^3 + 1/x^2 + 0

And since the derivative of a constant is always 0, we can drop the last term:

f’(x) = -21/x^4 + 4/x^3 + 1/x^2

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The truck would have lost 36% of its initial value.

The value in dollars, v(x), of a certain truck after x years can be represented by a mathematical function or equation. In the absence of a specific equation, it is difficult to provide an answer.

However, I can provide an example of a possible equation that represents the depreciation of a truck's value over time.

Let's assume that the truck loses 20% of its value every year. If the initial value of the truck is V0 dollars, then the value of the truck after x years, Vx, can be represented by the following equation:

Vx = [tex]V0(0.8)^x[/tex]

In this equation, the term [tex](0.8)^x[/tex] represents the percentage of the truck's value that remains after x years of depreciation. For example, after one year, the truck's value would be V1 = [tex]V0(0.8)^1[/tex] = 0.8V0,

which means that the truck would have lost 20% of its initial value. After two years, the truck's value would be V2 = V0[tex](0.8)^2[/tex]= 0.64V0,

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The number of bacteria contained in the human body is 40 times as great as the number of genes contained in the human body.

To find out how many times greater the number of bacteria in the human body is than the number of genes, we need to divide the number of bacteria by the number of genes:

4 × 10^13 (number of bacteria) ÷ 1 × 10^12 (number of genes)

= 40

Therefore, the number of bacteria contained in the human body is 40 times as great as the number of genes contained in the human body.

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Solving the equation, Boris needs to read 34 novels in 17 months.

Given that Boris needs to read 2 novels each month.

To relate the number of novels Boris needs to read (n) to the number of months he has to read them (m), we can use the equation:
n = 2m

This equation states that the number of novels (n) is equal to two times the number of months (m) since Boris needs to read 2 novels each month.

Now, to find the number of novels Boris needs to read in 17 months, we can substitute m = 17 into the equation:
n = 2m
n = 2(17)
n = 34

Therefore, Boris needs to read 34 novels in 17 months to meet his goal of reading 2 novels each month.

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The probability that each of the 4 is a criminal justice major is equal to 0.0003 (rounded to four decimal places).

The probability of selecting 4 criminal justice majors from a group of 125 students, without replacement,

Using the hypergeometric probability distribution.

Start by calculating the total number of ways to choose 4 students from the group of 125.

C(125,4) = 125! / (4! (125-4)!)

              = 125 x 124 x 123 x 122 / (4 x 3 x 2 x 1)

              = 9,691,375

Next, calculate the number of ways to choose 4 criminal justice majors from the group of 18.

C(18,4) = 18! / (4! (18-4)!)

           = 18 x 17 x 16 x 15 / (4 x 3 x 2 x 1)

           = 3060

Finally,

Probability of selecting 4 criminal justice majors

=  number of ways to choose 4 criminal justice majors / total number of ways to choose 4 students:

P(4 criminal justice majors selected) = C(18,4) / C(125,4)

⇒P(4 criminal justice majors selected) = 3060 / 9,691,375

                                                                = 0.0003157

Therefore, probability that each of the 4 students selected at random from the group of 125 students are criminal justice majors, without replacement is 0.0003 (rounded to four decimal places).

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To find the distance between the two banks of the river where the arch bridge is, we first need to determine the points where the bridge makes contact with the banks at a height of 4 meters.

We are given the parabola shape of the arch with the equation y = -0.1(x - 5)^2 + 12.

1. Set the height y equal to 4 meters:

4 = -0.1(x - 5)^2 + 12

2. Subtract 12 from both sides:

-8 = -0.1(x - 5)^2

3. Divide both sides by -0.1:

80 = (x - 5)^2

4. Take the square root of both sides:

sqrt(80) = x - 5

5. Now, we find the two x-values where the bridge contacts the banks:

x1 = sqrt(80) + 5

x2 = -sqrt(80) + 5

6. Calculate the distance between the two banks by subtracting x2 from x1:

Distance = x1 - x2 = (sqrt(80) + 5) - (-sqrt(80) + 5)

7. Simplify the expression:

Distance = 2 * sqrt(80)

8. Round your answer to the nearest whole number:

Distance ≈ 18 meters

The distance between the two banks of the river where the arch bridge is, is approximately 18 meters.

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Rectangles are relatable to factors because of their areas and perimeter equations

From the question, we have the following parameters that can be used in our computation:

Explaining why rectangles are relatable to factors

Rectangles are relatable to factors because of the following reasons

Perimeter = 2 * (Length + width)

Area = Length * width

This means that in calculating the areas and the perimeters of a rectangles, we make use of arithmetic expressions

These arithmetic expressions, when expanded form terms and factors of  expression

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The area of the shaded region is the expression 16(4 - π) square metres.

The shaded region is the remaining area in the square which is outside the circle, so it is derived by subtracting the area of the circle from the area of the square as follows:

area of the square = 8 m × 8 m

area of the square = 64 m²

area of the circle = π × 4 m × 4 m

area of the circle = 16π m²

area of the shaded region = 64 m² - 16π m²

area of the shaded region = 16(4 - π) m²

Therefore, the area of the shaded region is the expression 16(4 - π) square metres.

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12+13 = 25, therefor the answer is correct

If the events are exclusive, use the Rule of Sum. If the events are independent, use the Fundamental Counting Principle.

The Rule of Sum and the Fundamental Counting Principle are two common methods used in probability to calculate the total number of possible outcomes. Knowing which method to use depends on the nature of the problem and the type of events involved.

The Rule of Sum is used when we have two or more exclusive events. This means that only one of the events can happen at a time. For example, when rolling a die, the events of rolling a 2 or a 4 are exclusive because you cannot roll both at the same time.

The rule of sum states that the total number of possible outcomes is the sum of the number of outcomes for each event.

On the other hand, the Fundamental Counting Principle is used when we have a sequence of events that are independent of each other. This means that the outcome of one event does not affect the outcome of the next event.

For example, when flipping a coin, the outcome of the first flip does not affect the outcome of the second flip. The fundamental counting principle states that the total number of possible outcomes is the product of the number of outcomes for each event.

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The height of the outside is given as 17.44 meters

The equation of hyperbola is :

[tex]y^2 - x^2 = 38[/tex]

=>[tex]y^2/38 - x^2/38 = 1[/tex]

(of the form [tex]y^2/a^2 - x^2/b^2 = 1[/tex] and transverse axis is y-axis.)

Here, [tex]a^2 = b^2 = 38[/tex]

[tex]c^2 = a^2 + b^2 = 38+38 = 76[/tex]

( a is the distance of vertices from the center and c is the distance of foci from the center.)

Distance between walls = 2 a = [tex]2*\sqrt(38) = 12.33[/tex] meters at the center

and = [tex]2c = 2*\sqrt(76) = 17.44[/tex] meters at the end when the line joining

end points of the wall on one side is through the foci point.

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The measure of angle M is 20°.

To solve the problem, we need to find the measure of angle M, given the information about Circle K with center O, diameter US, angle MRU = 50°, and angle MUT = 30°.

Step 1: Determine the relationship between angles MRU and MUT.
Since MRU and MUT are both inscribed angles in Circle K, they share the same intercepted arc, which is arc MU.

Step 2: Calculate the measure of arc MU.
The measure of an intercepted arc is twice the measure of the inscribed angle. Since angle MRU = 50°, the measure of arc MU will be 2 * 50° = 100°.

Step 3: Find the measure of angle M.
We know that angle MUT = 30°, and the measure of an intercepted arc is twice the measure of the inscribed angle. Therefore, the measure of arc MT = 2 * 30° = 60°. Now, since arc MU = 100°, we can determine the measure of arc MS (arc MS = arc MU - arc MT) which is 100° - 60° = 40°.

Step 4: Calculate the measure of angle M.
Finally, the measure of angle M can be found using the intercepted arc MS. Since the measure of an intercepted arc is twice the measure of the inscribed angle, angle M = 1/2 * arc MS = 1/2 * 40° = 20°.

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Answer:

11. x = 16

12. x = 26

Step-by-step explanation:

11. ∠1 + ∠2 = 90°

   ∠1 = 42°

   ∠2 = 90° - 42° = 48°

   3x = 48

   x = 16

12. ∠C + ∠D = 180°

∠C = 128°

∠D = 180° - 128° = 52°

2x = 52

x = 26

The venue breaks even when 1,250 people buy tickets, and the total value of tickets sold at that point is $100,000.

To find the break-even point for the venue, we need to set the musician's charges (C(x) = 64x + 20,000) equal to the venue's earnings from ticket sales ($80 per ticket).  Hence,

1. Set the musician's charges equal to the venue's earnings:

64x + 20,000 = 80x

2. Subtract 64x from both sides:

20,000 = 16x

3. Divide both sides by 16:

x = 1,250

At the break-even point, 1,250 people need to buy tickets. To find the value of the total tickets sold at this point:

1. Multiply the number of attendees (x) by the ticket price:

Total ticket sales = x * ticket price

2. Substitute the values:

Total ticket sales = 1,250 * $80

3. Calculate the total ticket sales:

Total ticket sales = $100,000

So, the breaks even point is 1,250 people buying tickets, and corresponding total value of tickets sold is $100,000.

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Hanif's training pulse rate at 70% intensity is approximately 142 beats per minute.

To find Hanif's training pulse rate at 70% intensity, we first need to calculate his maximum heart rate (MHR) using the formula:

MHR = 220 - age

Substituting Hanif's age, we get:

MHR = 220 - 14 = 206

Next, we need to calculate Hanif's target heart rate (THR) range at 70% intensity. This range is between 70% and 85% of his MHR. To calculate the lower end of the range, we multiply his MHR by 0.7:

THR lower = 0.7 × MHR = 0.7 × 206 = 144.2 (rounded to one decimal place)

To calculate the upper end of the range, we multiply his MHR by 0.85:

THR upper = 0.85 × MHR = 0.85 × 206 = 175.1 (rounded to one decimal place)

So Hanif's target heart rate range at 70% intensity is between 144.2 and 175.1 beats per minute.

To find his training pulse rate, we add his resting pulse rate (76 beats per minute) to the percentage of his target heart rate range which corresponds to 70% intensity. This is given by:

Training pulse rate = resting pulse rate + (0.7 × (THR upper - resting pulse rate))

Substituting the values we calculated, we get:

Training pulse rate = 76 + (0.7 × (175.1 - 76)) ≈ 142

Therefore, Hanif's training pulse rate at 70% intensity is approximately 142 beats per minute.

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The value of the algebraic expression from the given parameters is:

x³ + 1/x³ = 0

The given problem is simply based on the expansion.

In expansion, what we do is that we expand the mathematical terms by  first of all removing all the brackets that are in that mathematical expression.

In expanding a mathematical expression, what we have to do is that we have to make use some of the identities that can be gotten by multiplying one binomial with the another one and then this type of identities are called as Standard Identities.

For example:  

(x + a)(x + b) = x² + (a + b)x + ab

Thus:

(x + 1/x)² = 3

x + 1/x = √3

(x+1/x)³ = x³ + (1/x)³ + 3(x)(1/x) (x + 1/x)

√3³ = x³ + 1/x³ + 3(√3)

x³ + 1/x³ = 3√3 - 3√3

x³ + 1/x³ = 0

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Answer: less than

Step-by-step explanation:

If George's bicycle has a mass of 15 grams, then it is highly unlikely that he has stated the correct mass, as 15 grams is an extremely low mass for a bicycle.

A typical bicycle weighs anywhere from 7 to 15 kilograms. It is highly unlikely that a bicycle would weigh only 15 grams, as this is much lighter than the lightest bicycle ever made.

Therefore, it is reasonable to assume that George made a mistake and meant to say 15 kilograms instead of grams.

Assuming the mass of the bicycle is 15 kilograms, removing the front wheel will decrease the mass slightly, but not by a significant amount.

The front wheel typically accounts for around 1-2 kilograms of the total mass of the bicycle, so removing it would leave a mass of approximately 14 kilograms.

However, assuming he made a mistake and meant to say 15 kilograms, then the mass of the bicycle without the front wheel would be approximately 14 kilograms.

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The values of a, b, and c in the matrix equation are a = 3, b = 1 and c = 8

To determine the values of a, b, and c in the matrix equation:

4 a  +  3  0    = 7  3

3 4      5  b       c   5

By addition operation, we have

a + 0 = 3

3 + 5 = c

4 + b = 5

When the equations evaluated, we have

a = 3

c = 8

b = 1

The above are the values of a b and c

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Complete question

Determine the values of a, b, and c in the following matrix equation.

4 a  +  3  0    = 7  3

3 4      5  b       c   5

If the formula predicted Wendy's height to be 65 inches based on her hand length of 6.5 inches, the residual would be -2 inches

A residual is the difference between the predicted value of a variable (in this case, height) and the actual value of that variable. Residuals are often used in statistical analysis to assess the accuracy of a prediction or model.

In this case, if we were given the formula for predicting height from hand length, we could use it to predict Wendy's height and compare that to her actual height of 63 inches. The residual would be the difference between the predicted height and her actual height. If the prediction overestimated her height, the residual would be negative. If it underestimated her height, the residual would be positive.

For example, if the formula predicted Wendy's height to be 65 inches based on her hand length of 6.5 inches, the residual would be -2 inches (predicted height minus actual height). If the formula predicted her height to be 61 inches, the residual would be +2 inches.

Overall, residuals are a useful tool for assessing the accuracy of predictions or models, but the specific calculation of a residual depends on the formula being used to make the prediction.

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As per the probability, the expected demand for bananas per week is 182.5 pounds.

To model this problem, we can use decision analysis, which involves identifying the possible outcomes, assigning probabilities to each outcome, and calculating the expected value of each decision.

In this case, the possible outcomes are the demand for bananas, which can be 100, 150, 200, or 250 pounds per week. The probabilities of each demand level are given as 0.20, 0.25, 0.35, and 0.20, respectively.

Let X denote the demand for bananas in pounds. Then, the expected demand for bananas, denoted as E(X), can be calculated as follows:

E(X) = 100(0.20) + 150(0.25) + 200(0.35) + 250(0.20) = 182.5

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There are 6 cute numbers in total which are 14, 19, 49, 55, 79, 85.To find the cute numbers, we need to check all numbers greater than 9 and see if they satisfy the cute condition.

Let's start by analyzing the digits of a number. Suppose the number has two digits, x and y. The cute condition requires:

x + y + xy = 10x + y

Rearranging this equation, we get:

xy - 9x = y - x

xy - x - y = -9x

(x - 1)(y - 1) = 9x - 1

For a number to be cute, the right-hand side of the equation must be divisible by the left-hand side. Since 9x - 1 is odd, the left-hand side must also be odd, which means one of the factors (x - 1) or (y - 1) must be odd and the other even.

We can now check all possible pairs of (x,y) that satisfy this condition. We find that the cute numbers are:

14, 19, 49, 55, 79, 85. Therfore, there are total 6 cute numbers.

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Answer:

y = 5x + 5

Step-by-step explanation:

If x is the number of boxes sold and y is the cost

The first box costs $10

Each additional box costs $5.

If the total number of boxes sold is x, then after selling the first box for $10, there will be x - 1 boxes left to be sold

The cost of x -1 boxes at $5 per box = 5(x - 1) = 5x - 5

Therefore for a total of x boxes sold the total cost, y in dollars is
y = 10 (for the first box)  +  5x - 5 (for the remaining x - 1 boxes)

= 10 + 5x - 5

= 5 + 5x

which in standard form is written as
y = 5x + 5

We can verify our equation using specific numbers for x
For x = 1
y = 5 + 5(1) = 10   ; since only one box has been sold, the cost is fixed at $10

For x = 2 y = 5 + 5(2) = 5 + 10 = $15
This works out to since first box is sold at $10 and the second box at $5

Leave it to you to work out for other numbers

In the expression πr² + πrℓ, the part of the expression that is π is a constant.

A constant is a value that does not change in an expression, and in this case π represents a fixed value of approximately 3.14159. It is not a coefficient, which is a numerical factor that multiplies a variable, nor a variable or term, which represent varying quantities in an expression.

The height of the real boat is 3 inches and  length of the boat is 45 feet

What is Unit of Measurement?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

In a scale model of a boat 1 inch represents 5 feet

1 inch =  5 feet

The height of the real boat is 15 feet

We have to find in inches

1/5=x/15

x=3 inches

So height of the real boat is 3 inches

The length of the boat is 9 inches

We have to find in feet

1/5 = 9/x

x=45 feet

Hence, the height of the real boat is 3 inches and  length of the boat is 45 feet

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lim (1 - a^(1-a)) / (ln(a)) as x -> a This is the value of the given limit.

To find the value of the given limit, which can be represented as lim (a^x - x^a) / (x^x - a^a) as x approaches 'a', you can apply L'Hôpital's Rule, which states that if the limit of the ratio of the derivatives of two functions exists, then the limit of the original functions is equal to that limit.

First, differentiate the numerator and denominator with respect to x:

Numerator: d(a^x - x^a) / dx = a^x * ln(a) - a * x^(a-1)
Denominator: d(x^x - a^a) / dx = x^x * ln(x)

Now, we can find the limit of the ratio of the derivatives as x approaches 'a':

lim (a^x * ln(a) - a * x^(a-1)) / (x^x * ln(x)) as x -> a

After substituting 'a' for 'x' in the limit:

lim (a^a * ln(a) - a * a^(a-1)) / (a^a * ln(a)) as x -> a

Now, cancel out the common term a^a * ln(a):

lim (1 - a^(1-a)) / (ln(a)) as x -> a

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Answer:12.4

Step-by-step explanation:

18^2-13^2=155
Square root of 155 to the nearest tenth is 12.4