A new car is purchased for 17600 dollars. The value of the car depreciates at 11. 75% per year. What will the value of the car be, to the nearest cent, after 11 years?.

The cosine functions are used to find the angle if the length of the hypotenuse and the length of the adjacent side is known.

The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and is given the symbol cos.

The cosine function in a triangle is the ratio of the adjacent side to that of the hypotenuse.

The general formula for cosine is:

cos α = Adjacent Side/Hypotenuse

Cosine has a few properties, which are periodic and even.

It is the ratio of the length of the side that is ADJACENT the angle to the length of the longest side, or HYPOTENUSE, of the triangle.

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The expected number of airplanes circling the airport, waiting in queue for clearance to land, if this new radar system were to be used is zero.

The new radar system is being considered as a means of reducing congestion, which implies that there is currently an issue with congestion at the airport. One way to reduce congestion is to process planes at a faster rate, which is exactly what the new radar system aims to do.

The statement "planes can be processed at a constant rate of 15 per hour (i.e., the variance is zero)" indicates that the system is able to process planes at a consistent rate of 15 per hour, with no variation in this rate. This means that there should be no planes waiting in queue for clearance to land, as they can all be processed at the constant rate of 15 per hour. Therefore, the expected number of airplanes circling the airport and waiting in queue for clearance to land is zero.

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Answer:

$140

Step-by-step explanation:

First you would order the numbers from smallest to largest like the answer has done.

$125, $130, $135, $135, $140, $140, $165, $190, $195

then you can cross off numbers from either side to get the middle number.

$130, $135, $135, $140, $140, $165, $190

$135, $135, $140, $140, $165

$135, $140, $140

$140

Since the middle number is $140, that would be the median.

Hope this helps!

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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Answer:

1.   y = 7x + 2

2.   y = 1/3x - 1  or 3y = x - 3

Step-by-step explanation:

Use this formula y = mx + b   where the slope is represent by "m" and the y-intercept is represent by "b"

1.    y = mx + b

     y = 7x + 2

2.   y = mx + b

     y = 1/3 x + (-1)      Let clean this up by multiplying each term by 3

     3y =  1x - 3  or 3y = x - 3

We will get the solution of the equation g(x) = f(x) by finding the rule for the linear equation g(x) and solving the linear equation, the solution is x = 2.

Here we have two functions, one graphed, which is g(x), and the other defined by a rule:

f(x) = -x + 1

For g(x) we can use the graph to find the rule, notice that this is a linear equation so we can write:

g(x) = m*x + b

Where m is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = -3, then:

g(x) = m*x - 3

To find the value of m we can use another point on the graph, for example, (3, 0)

Replacing that we get:

g(3) = 0 = m*3 - 3

3 = m*3

3/3 = m

1 = m

Then g(x) = x - 3

Now we can solve:

g(x) = f(x)

Replacing the functions we get:

x - 3 = -x + 1

Now we can solve this linear equation for x:

x - 3 = -x + 1

x + x = 3 + 1

2x = 4

x = 4/2

x = 2

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Answer:

I really wish I could answer this

Step-by-step explanation:

The question seems fairly easy, only we don't have a number to go off of. If Edward walks x miles per hour, then he'll walk x miles in that hour.

The length of the shortest straight  is approximately 28.01 ft.

What is the right triangle?

A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".

To find the length of the shortest straight beam,we can use the Pythagorean theorem.

Let's denote the length of the beam as L and  a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.

Using the Pythagorean theorem,

\(L^2 = (28 ft)^2 + (1 ft)^2\)

Simplifying the equation:

\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)

\(L = \sqrt{785}ft\)

Calculating the value of L:

L ≈ 28.01 ft

Therefore, the length of the shortest straight beam  is approximately 28.01 ft.

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Randy can buy six gallons of gas for $18. He would pay $24 for 8 gallons of gas.

We can see that he pays three dollars per gallon by dividing the per gallon. 18 dollars/6 gallons equals 3 dollars, and 21 dollars/7 gallons equals 3 dollars. So, if he pays the same $3 per gallon rate, he will pay $24.

Fuel costs can be estimated using this calculator based on trip distance, vehicle fuel efficiency, and gas prices in various units. Gas prices fluctuate, but for most drivers, it is always a significant expense.

If you use mpg (miles per gallon), the total gas consumption formula is as follows: as an example The total amount of fuel required is 500 / 20 = 25 gallons if the distance is 500 miles and the consumption rate is 20 miles per gallon


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Provided that the value of k is 120%, the scale factor is 1.2

The scale factor is a number used to enlarge or compress a shape or a function. The number can be integers and it can be fractions

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

k = 120%

In transformation and geometry, the variable k is used to denote the scale factor of dilation

This means that

Scale factor of dilation, k = 120%

Rewrite the scale factor of dilation as

k = 120%

Express the percentage as fraction

So, we have the following representation

k = 120/100

Evaluate the quotient

So, we have the following representation

k = 1.2

Hence, the value of the scale factor is 1.2

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Answer:

y = - 2x - 300

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 3 ← is in slope- intercept form

with slope m = - 2

Parallel lines have equal slopes, then

y = - 2x + c ← is the partial equation

To find c substitute (- 100, - 100 ) into the partial equation

- 100 = 200 + c ⇒ c = - 100 - 200 = - 300

y = - 2x - 300 ← equation of parallel line

The breakeven point in the CVP (Cost-Volume-Profit) graph indicates the point where a company's total revenue equals its total costs, resulting in zero profit or loss. In this case, the correct answer is option A) Step 5.

Step 5 on the CVP graph represents the point where the total revenue line intersects the total cost line. At this point, the company has sold enough units to cover all its fixed and variable costs, resulting in neither profit nor loss. It is the point of equilibrium for the company's operations.

To better understand this concept, let's consider an example. Suppose a company manufactures and sells a product. The fixed costs include expenses like rent and salaries, while variable costs include the cost of raw materials and direct labor. The total revenue is determined by multiplying the selling price per unit by the number of units sold.

As the company increases its sales volume, it moves from step 1 to step 2, step 3, and so on, until it reaches step 5, which represents the breakeven point. Beyond the breakeven point, the company starts generating profit.

In summary, the breakeven point in the CVP graph is indicated by step 5, where total revenue equals total costs. It is the point at which a company neither makes a profit nor incurs a loss.

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Answer:35.4

Step-by-step explanation:

for this one you would subtract 172.5-137.1 for the answer 35.4 which is where the shark will end up.

Missing part of the question is;

Find a formula for the number of seats sold if the ticket price is P dollars.

Answer:

(680 - P)/3

Step-by-step explanation:

A) Let x be equal to the number of seats and hence we can conclude that (160 - x) is equal to the number of seats after the increase in price.

Similarly, the increase in ticket price would be equal to (P - 200)

Due to the fact that for every $3 increase, the number of seats decrease by 1, the equation that links the change in the number of seats to the change in ticket price is;

P - 200 = 3(160 - x)

P = 3(160 - x) + 200

Making x the subject;

P = 480 - 3x + 200

P = 680 - 3x

3x = 680 - P

x = (680 - P)/3

The mean, standard deviation, of the average number of moths in 30 traps is approximately 0.5 ± 0.018 and is approximately 0.5 respectively. The probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

The mean of the average number of moths in 30 traps can be calculated as the mean of a sample of 30 trap counts, where the mean of each sample follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30) (using the standard error of the mean formula). Therefore, the mean of the average number of moths in 30 traps is:

mean = 0.5 ± 0.1/sqrt(30) = 0.5 ± 0.018

So the mean of the average number of moths in 30 traps is approximately 0.5 ± 0.018.

The standard deviation of the average number of moths in 30 traps can also be calculated using the standard error of the mean formula:

standard deviation = standard error of the mean * sqrt(sample size)

standard deviation = 0.5/sqrt(30) * sqrt(30) = 0.5

So the standard deviation of the average number of moths in 30 traps is approximately 0.5.

Using the central limit theorem, we can assume that the sample mean of the 30 traps follows a normal distribution with mean 0.5 and standard deviation 0.5/sqrt(30). We want to find the probability that the average number of moths in 30 traps is greater than 0.4.

To do this, we can standardize the sample mean using the formula:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

z = (0.4 - 0.5) / (0.5/sqrt(30)) = -1.8257

Using a standard normal distribution table or calculator, we can find the probability that Z is greater than -1.8257, which is approximately 0.965. Therefore, the probability that the average number of moths in 30 traps is greater than 0.4 is approximately 0.965 ± 0.01.

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Answer:

Step 1: Substitute the value of x into the equation

x= 3-3/2y

-3x+5y=10

Step 2: Solve the equation

-3(3-3/2y)+5y=10

Step 3: Substitute the value of y into the equation

Y=2

Step 4: Solve the equation

X=3-3/2×2 = X=0

Answer: (0,2)

1) Considering that x is for pounds of apples and y is a total cost of an apple let's find the cost per pound of the apples, given that the y=2.57x +4.5

Let's turn that function into an equation

0=2.57x +4.5 Subtract 2.57x from both sides

-2.57x=4.5 Divide both sides by -2.57

x=-1.75

2) So if no one pie crust is sold, there is going to be a loss of $-1.75, according to that equation.

Therefore, we can infer that the cost per pound of the apples is $1.75

The required competition mark is given as 60, as of the given condition.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
A competition mark is calculated by doubling the sum of the top and bottom four scores and then averaging them.
According to the question,
Competition mark = 2 [7 + 6 + 8 + 5] + [7 + 9] / 2
Competition mark = 52 + 8 = 60

Thus, the competition mark is  60.

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The logarithmic equation for 1/4 = 8⁻²/₃ is :

\(log_8(\frac{1}{4}) = \frac{-2}{3}\)

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   \(log_ax=N\)

where, a is the base of function or equation

           x define expression

Mathematically, if  is an exponential function is  \(a^N=x\) then, this can be converted to logarithmic function as  \(log_ax=N\)

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

According to statement,

1/4 = 8⁻²/₃

as , exponential function is  \(a^N=x\)  can be converted to logarithmic function as  \(log_ax=N\)

here, a = 8, N= -²/₃ , x = 1/4

therefore, logarithmic equation is :

\(log_8(\frac{1}{4}) = \frac{-2}{3}\)

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The rent expense allocated to each department is as follows: Jewelry department: $30,800, Cosmetics department: $46,200, Housewares department: $21,000, Tools department: $9,000, Shoes department: $18,000.

The retailer allocates 70% of the total rent expense to the first floor and 30% to the second floor. Then, the rent expense for each floor is allocated to the departments based on the square footage they occupy. By applying these allocation percentages and calculations, we determined the rent expense for each department.

Rent expense allocation:

- Jewelry department (1,760 sq ft on the first floor): ($130,000 * 70% * 1,760 sq ft) / (1,760 sq ft + 2,640 sq ft) = $30,800

- Cosmetics department (2,640 sq ft on the first floor): ($130,000 * 70% * 2,640 sq ft) / (1,760 sq ft + 2,640 sq ft) = $46,200

- Housewares department (1,848 sq ft on the second floor): ($130,000 * 30% * 1,848 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $21,000

- Tools department (792 sq ft on the second floor): ($130,000 * 30% * 792 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $9,000

- Shoes department (1,760 sq ft on the second floor): ($130,000 * 30% * 1,760 sq ft) / (1,848 sq ft + 792 sq ft + 1,760 sq ft) = $18,000

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Given:

Total number of students = 147

Number of students taking math = 95

Number of students taking science = 73

Number of students taking both = 52

To find:

The theoretical probability of randomly choosing a student who is taking math.

Solution:

We have,

Total number of students = 147

Number of students taking math = 95

Now, the theoretical probability of randomly choosing a student who is taking math is

\(P(M)=\dfrac{\text{Number of students taking math}}{\text{Total number of students}}\times 100\)

\(P(M)=\dfrac{95}{147}\times 100\%\)

\(P(M)=64.62585\%\)

\(P(M)\approx 64.6\%\)

The theoretical probability of randomly choosing a student who is taking math is 64.6%.

Therefore, the correct option is C.

David takes a car to get to the airport in time for his trip. 210 miles distance is the airport from his house in miles.

Given that,

David takes a car to get to the airport in time for his trip. He travels 35 miles in the first hour but understands that if he keeps going at this rate, he will be one hour late. For the final 15 miles to the airport, he speeds up by 15 mph and gets there 30 minutes early.

We have to find how far is the airport from his house in miles.

Distance traveled after 1 hour

Let us take the distance traveled after first 1 hour as y

Distance/speed = time

After 1 hour his speed = (35 + 15) = 50 mph

Total time count of 1 hour and 30 mins is 1.5 hr

y/50 + 1.5 = y/35

Multiply through by350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Therefore, the distance between David's home and the airport is 210 miles.

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Answer:

Pythagorean theorem

Step-by-step explanation:

You can use the Pythagorean theorem to find the third side of a triangle.

A^2 + B^2 = C^2.

The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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Answer: Its a whole number. It is a composite number.

Step-by-step explanation:

Answer:

-4x^2+5x-28

Step-by-step explanation:

3x^2 +5x - 7(x^2 +4)

Distribute the -7

3x^2+5x-7x^2-28

Combine like terms

-4x^2+5x-28