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Answer:

The truck is worth $5,135 when 9 years have passed

Step-by-step explanation:

Initial value of Alex's new truck: $42,935

Loss of value per year: $4,200

If n years passed, the truck would have lost

[tex]4,200n\ dollars[/tex]

The current value of the truck will be

[tex]V(n)=42,935-4,200n[/tex]

We want to know the value of n at which V is 5,135

[tex]5,135=42,935-4,200n[/tex]

Solving for n

[tex]n=\frac{42,935-5,135}{4,200}[/tex]

n=9 years

The truck will depreciate to a value of $5,135 in approximately 9 years, given a yearly depreciation rate of $4,200.

This problem involves finding the duration it will take for the truck to depreciate from $42,935 to $5,135, given it depreciates at a rate of $4,200 per year. The difference in value is $42,935 - $5,135 which equals $37,800. This depreciation amount has to be distributed over the years so we divide it by the yearly depreciation rate. This is represented by the equation 37,800 = 4,200x, with x being the number of years. Thus, solving for x gives x = 37,800 / 4,200 which is approximately 9 years. Therefore, it will take about 9 years for the truck to depreciate to a value of $5,135.

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The equation 2cos²x + sinx - 1 = 0 can be solved by converting terms involving cosine to sine, simplifying the equation, and then solving the resulting quadratic equation for sinx and consequently solving for x.

To solve the trigonometric equation 2cos²x + sinx - 1 = 0, we can first convert the terms in the equation involving cosine to terms involving sine.

We know that cos²x= 1 - sin²x. Substituting this into the equation, we will have 2(1 - sin^2x) + sinx - 1 = 0.

This simplifies to 2 - 2sin²x + sinx - 1 = 0. Reordering terms, we get 2sin²x - sinx + 1 = 0. If we solve this quadratic equation for sinx, we can then solve for x. Assuming the domain 0<=x<=2pi, this will give us the possible values of x that satisfy the original equation.

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Answer:

20 seconds

Step-by-step explanation:

The distance to cover between the lead skater and trailing skater is 40 meters

The lead skater's rate is 12 m/s

The trailing one's rate is 14 m/s

So, we can say:

second skater is accelerating, or covering up the distance, in 14 - 12 = 2 m/s

So, at a rate of 2 meters per second, how long would it take to cover 40 meters??

We use the distance formula, substitute the known and solve for unknown.

Distance Formula = D = RT

Where

D is distance

R is speed/rate

T is time

We know

r = 2 m/s

d = 40 m

t = ?

Now,

D = RT

40 = 2t

t = 40/2

t = 20 (seconds)

Hence,

it will take 20 seconds for the second skater to catch up (pass)

We can use the points (2, -2) and (4, -1) to solve.

Slope formula: y2-y1/x2-x1

= -1-2/4-(-2)

= -3/6

= -1/2

Point slope form: y - y1 = m(x - x1)

y - 2 = -1/2(x + 2)

Solve for y-intercept.

-2 = -1/2(2)  + b

-2 = -1 + b

-2 + 1 = -1 + 1 + b

-1 = b

Slope Intercept Form: y = mx + b

y = -1/2x - 1

______

Best Regards,

Wolfyy :)

[tex]\bf \textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d = 6 \end{cases}\implies C=6\pi \implies C\approx 18.85[/tex]

The volume of the solid is 420 cm³

Step-by-step explanation:

The volume a rectangular prism is calculated as the product of its length, width and height.

Mathematically, V=l*w*h where l is length of the prism, w is width and h is the height

Given that the dimensions of the rectangular prism as;

Length=20 cm

Width= 5 cm

Height = 5 cm

V=20*5*5= 500 cm³

The rectangular prism shaped hole dimensions are;

Length= 20 cm

width= 2 cm

Height= 2 cm

Volume= 20*2*2=80 cm³

The volume of the solid will be: volume of rectangular prism-volume of the hole

Volume= 500-80=420 cm³

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The volume of the solid rectangular prism with a hole is 420 cm³.

To find the volume of the solid rectangular prism with a hole, we follow these steps:

Volume of the Outer Rectangular Prism:

Using the formula V = l * w * h, where l is the length, w is the width, and h is the height of the outer rectangular prism:

Volume of the outer prism (V_outer) = 20 cm * 5 cm * 5 cm = 500 cm³.

Volume of the Rectangular Prism-shaped Hole:

Using the same formula for the inner rectangular prism:

Volume of the hole (V_hole) = 20 cm * 2 cm * 2 cm = 80 cm³.

Volume of the Solid:

Subtracting the volume of the hole from the volume of the outer prism:

Volume of the solid (V_solid) = V_outer - V_hole = 500 cm³ - 80 cm³ = 420 cm³.

Therefore, the volume of the solid rectangular prism with a hole is 420 cm³.

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Answer:

The simple interest on the given principal after 1 year = Rs. 1,000

The amount Rishav has to pay after an year  = Rs 11,000

Step-by-step explanation:

Here, the Principal amount taken = Rs 10,000

Rate of Interest = 10%

Time Period  = 1 year

Now, the SIMPLE INTEREST  = [tex]\frac{P \times R \times T}{100}[/tex]

or, [tex]SI = \frac{10,000 \times 10 \times 1}{100}  = 1,000[/tex]

So, the simple interest on the given principal after 1 year = Rs. 1,000

Now, Amount = Principal + Simple Interest

or , A = 10,000 + 1,000 =  11, 000

Hence, the amount Rishav has to pay after an year  = Rs 11,000

Answer:

C

Step-by-step explanation:

Inverse of function(x,y) is equal to (y,x)

The total number of game booths is 36, with the students setting up 30 booths denoting 5/6 of the total, and teachers setting up the remaining 6 booths which corresponds to 1/6 of the total.

The student question asks about finding the total number of game booths if 5/6 of them were set up by students, and it is known that students set up 30 booths. First, we assume the fraction 5/6 represents the portion of booths that the students were responsible for setting up. Since 5/6 equates to the 30 booths the students set up, each fraction of 1/6 represents 6 booths (30 divided by 5). As there are 6 fractions of 1/6 in a whole, to find the total (which is 6/6), you simply multiply 6 (the value of 1/6) by 6.

The calculation is as follows: 6 booths per 1/6 x 6 = 36 game booths in total. Therefore, the teachers set up the remaining sixth, which corresponds to 6 game booths, making the combined total 36. This result indicates that there is a total of 36 game booths when we include the contributions from both students and teachers.

In this case, There are 36 game booths in total.

Let's denote the total number of game booths as T.

According to the information given, 5/6 of the game booths were set up by the students.

Since the students set up 30 game booths, we can write the following equation:

[tex]\[\frac{5}{6}T = 30\][/tex]

To find the total number of game booths, T, we need to solve for T.

We can do this by multiplying both sides of the equation by the reciprocal of 5/6, which is 6/5:

[tex]\[T = 30 \times \frac{6}{5}\][/tex]

Now, we calculate the value of T:

[tex]\[T = 30 \times \frac{6}{5}\][/tex]

T = 36

 Therefore, there are 36 game booths in total.

Answer:

All Of these Answer are INCORRECT!

Step-by-step explanation:

You Can tell by the first three fives in the first answer..

5*5=25*5=125=NOT GONNA WORK!

7+7+7+7+7=35= NOT GONNA WORK!

7x7 wont make it= NOT GONNA WORK!

There Never Gonna Work!

The factors of a number is are those which produce the same number when two numbers are multiplied together. It can be written as 3 × 5² or also as 15 × 5 and also as 1 × 75. The given options are not correct.

The factors of 75 are defined as the numbers which are multiplied in pairs resulting in the original number 75. In other words, the factors of 75 are also the numbers which divide the number 75 exactly without leaving the remainder.

Here 75 is a composite number and it has many factors other than the number itself. The factors of 75 are 1, 3, 5, 15, 25 and 75. In order to obtain a pair factor, multiply the two numbers in a pair to get the original number.

The pair factors of 75 are:

3 × 25 = 75

5 × 15 = 75

25 × 3 = 75

15 × 5 = 75

So the given options are not correct.

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To find the annual simple interest rate for the certificate of deposit, divide the total interest earned by the principal amount. In this case, the annual interest rate is 16%.

The amount of simple interest Luis earns each month is $20, and he earns this for the next 36 months. We can find the total interest earned by multiplying the monthly interest by the number of months: $20 x 36 = $720.

To find the annual simple interest rate for the certificate of deposit, we need to divide the total interest earned by the principal amount. In this case, the principal amount is $4500. So, the annual interest rate is calculated as: $720 / $4500 = 0.16 or 16%.

Therefore, the annual simple interest rate for the certificate of deposit is 16%.

Answer:

Simplify the expression.

16y^2a - 36x^2b

Step-by-step explanation: hope this helps!

Answer:

16 square meters per square inch

Step-by-step explanation:

we know that

The scale drawing is

[tex]\frac{(1/2)}{2}=\frac{1}{4}\ \frac{in}{m}[/tex]

That means ---> 1 in in the drawing represent 4 meters in the actual

Find the dimensions of the blackboard in the drawing

Divide by 4

[tex]\frac{9}{10}\ m=\frac{9}{10}/4=\frac{9}{40}\ in[/tex]

[tex]\frac{7}{10}\ m=\frac{7}{10}/4=\frac{7}{40}\ in[/tex]

Find the area of the blackboard

[tex](\frac{9}{10})(\frac{7}{10})=\frac{63}{100}\ m^2[/tex]

Find the area in the drawing

[tex](\frac{9}{40})(\frac{7}{40})=\frac{63}{1,600}\ in^2[/tex]

Find out the unit rate of area in square meters of the blackboard per square inch of area in the drawing

[tex](\frac{63}{100})/(\frac{63}{1,600})=\frac{1,600}{100}=16\ \frac{m^2}{in^2} [/tex]

Answer:

4

Step-by-step explanation:

The square of 4 is 16, or 4 times 4.

When you subtract 4 from it, it becomes 3 times 4.

Therefore, 4 is the answer.

Answer:

The positive solution is 4.

Step-by-step explanation:

x^2-4=3x

x^2-3x-4=0

factor out the trinomial

(x-4)(x+1)=0

zero property,

x-4=0, x+1=0

x=0+4=4

x=0-1=-1

-------------

x=4, -1

Answer:

There would be an 83.3% chance (0.83 chance) that the die would not land on 5.

Step-by-step explanation:

Use the probability formula: [tex]\frac{desired}{total}[/tex] (desired events over total events)

[tex]\frac{desired}{total} =\frac{5}{6}= 0.8333333[/tex]

Rounded to two decimal places, there would be a 0.83 chance that the die would not land on 5.

Answer: 3/100

Step-by-step explanation: Using the place value chart, we can see that 0.03 means 3 hundredths so 0.03 can be written as the fraction 3/100.

3/100 is a proper fraction so it can't be changed to a mixed number.

Answer:

k=9

Step-by-step explanation:

1/4k=3(-1/4k+3)

1/4k=-3/4k+9

1/4k-(-3/4k)=9

1/4k+3/4k=9

k=9

Answer:

[tex]y = \frac{1}{2} x + 2[/tex].

Step-by-step explanation:

From the given table it is clear that x and y are linearly related.

Now, any two points that satisfy the relation between x and y are sufficient to express the equation.

The first two given points are (2,3), and (4,4).

Therefore, the equation is [tex]\frac{y - 4}{4 - 3} = \frac{x - 4}{4 - 2}[/tex]

⇒ [tex]y - 4 = \frac{1}{2} (x - 4)[/tex]

⇒ [tex]y - 4 = \frac{1}{2} x - 2[/tex]

⇒ [tex]y = \frac{1}{2} x + 2[/tex]. (Answer)

Answer:

A

Step-by-step explanation:

bc i said so

Answer:

Step-by-step explanation:

       A line passes through the points [tex](2,-6)[/tex] and [tex](4,-3)[/tex].

To find the point-slope form of the line, we need a point on the line and the slope of the line.

As we have two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], the slope can be calculated as [tex]\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].

       Slope of the line = [tex]\dfrac{-3-(-6)}{4-2}=\dfrac{3}{2}[/tex]

Given a line with slope [tex]m[/tex] and a point [tex](x_{1},y_{1})[/tex], slope-point form is [tex]y-y_{1}=m(x-x_{1})[/tex]

       Line is given by [tex]y+6=\frac{3}{2}(x-2)[/tex]

∴ The line is given by [tex]y+6=\frac{3}{2}(x-2)[/tex]

Final answer:

The correct point-slope form equation with the points (2, -6) and (4, -3) is y + 6 = 3/2(x - 2), after finding the slope of 3/2 and applying it to the point-slope formula using either of the points.

Explanation:

Firstly, let's find the slope of the line passing through the points (2, -6) and (4, -3). The slope formula is
(y₂ - y₁) / (x₂ - x₁), so plug in the values to get (-3 - (-6)) / (4 - 2) = 3 / 2.

Now we know the slope is 3/2, we can write a point-slope form equation, which is y - y₁ = m(x - x₁). We can use either of the given points; let's use (2, -6). Substituting these values into the point-slope formula gives us: y - (-6) = 3/2(x - 2).

Thus, the correct point-slope form equation produced with the points (2, -6) and (4, -3) is: y + 6 = 3/2(x - 2).

The width of the rectangle is [tex]\frac{2}{9}[/tex] unit

Step-by-step explanation:

The given is:

We need to find the width of the rectangle

Assume that the width of the rectangle is x units

∵ The area of the rectangle = length × width

∵ The width of the rectangle = x units

∵ The length of the rectangle = 19 units

∴ The area of the square = 19 × x = 19 x units²

∵ The width of the rectangle is 4 less than its area

- That means subtract 4 from the area to find the width

∴ x = 19 x - 4

- Subtract 19 x from both sides

∴ -18 x = -4

- Divide both sides by -18

∴ x = [tex]\frac{-4}{-18}[/tex]

- Reduce the fraction by dividing up and down by -2

∴ x = [tex]\frac{2}{9}[/tex]

The width of the rectangle is [tex]\frac{2}{9}[/tex] unit

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Answer:

the creature 268 inches tall

Step-by-step explanation:

set it up and cross multiply!

10 = 40

67    X

67*40=10*X

2680=10X

then divide 10 from both sides:

so X=268

Answer:

249 gallons of 7% butterfat milk and 83 gallons of 3% butterfat milk

Step-by-step explanation:

If x is the gallons of 7% butterfat milk, and y is the gallons of 3% butterfat milk, then:

x + y = 332

0.07x + 0.03y = 0.06(332)

Solve the system of equations using substitution:

0.07x + 0.03(332 − x) = 0.06(332)

0.07x + 9.96 − 0.03x = 19.92

0.04x = 9.96

x = 249

y = 332 − x

y = 83

You need 249 gallons of 7% butterfat milk and 83 gallons of 3% butterfat milk.

Answer:

The given function is an odd function.

Step-by-step explanation:

We define a function f(x) as even function when f(-x) = f(x) and odd function when f(-x) = - f(x) and otherwise it is neither even nor odd function.

Now, we are given a function of x as [tex]f(x) = x + \frac{4}{x}[/tex] and we have to deternime whether the function f(x) is even, odd, or neither even nor odd.

Now, [tex]f(-x) = - x + \frac{4}{- x} = - x - \frac{4}{x} = - [x + \frac{4}{x}] = - f(x)[/tex]

Therefore, the given function is an odd function. (Answer)

Answer:

$1677

$40677

Step-by-step explanation:

Compared to the price of the current model sports can the next model price will be 4.3% higher.

The cost of the current model sports car is $39000.

Therefore, the price will increase in the next model by [tex]\frac{39000 \times 4.3}{100} = 1677[/tex] dollars. (Answer)

Now, the price of the next model will be $(39000 + 1677) = $40677 (Answer)

The price increase in dollars for the next sports car model, priced at 4.3% more than the current value, is $1,677. So, the next model of the sports car will cost $40,677.

The subject of this question is about the calculation of a price increase in mathematical terms. If the next model of a sports car is going to cost 4.3% more than the current model, which costs $39,000, then first we need to find out how much exactly 4.3% of $39,000 is. The calculation involves multiplying 39,000 by 4.3%, which comes out to $1,677.

Therefore, the price of the next model of a sports car will be the current price which is $39,000 plus the price increase in dollars i.e., $1,677. Hence, adding the two amounts gives us a total cost of $40,677 which is the price of the upcoming model.

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The Answer:

D

Step-by-step explanation:

d=53

Answer:

A² - B² = 0 (Proved).

Step-by-step explanation:

Given that  

[tex]A = \frac{\cot \theta + \csc \theta - 1}{\cot \theta - \csc \theta + 1}[/tex]

⇒[tex]A = \frac{\csc \theta + \cot \theta - (\csc^{2} \theta - \cot^{2} \theta)}{\cot \theta - \csc \theta + 1}[/tex]

{Since, we know the identity as [tex]1 = \csc^{2} \theta - \cot^{2} \theta[/tex]}

⇒ [tex]A = \frac{\csc \theta + \cot \theta - (\csc \theta + \cot \theta)\times (\csc \theta - \cot \theta)}{\cot \theta - \csc \theta + 1}[/tex]

⇒ [tex]A = \frac{(\csc \theta + \cot \theta) (\cot \theta - \csc \theta + 1)}{\cot \theta - \csc \theta + 1}[/tex]

⇒ [tex]A = \csc \theta + \cot \theta[/tex]

Again, given that [tex]B = \csc \theta + \cot \theta[/tex]

So, A = B . ⇒ (A - B) = 0.

Hence, A² - B² = (A + B)(A - B) = 0 (Proved)

Answer:

y=3.72

Step-by-step explanation:

y/2+3.2=5.06

y/2=5.06-3.2

y/2=1.86

y=1.86*2

y=3.72

Answer:

y= 3.72

Step-by-step explanation:

reverse the operations

5.06-3.2= 1.86

1.86*2= 3.72

y=3.72

Answer:

slope of a line perpendicular to the line -3x + 6y = -15 is -2

Step-by-step explanation:

-3x + 6y = 15

solve for y,

y = 1/2 x + 15/6

slope of a line perpendicular is the "negative reciprocal" of the slope of the original line, thus

y = -2 x + b

The total number of chairs there are in the theater and balcony is; 3027 chairs.

According to the question;

In essence, The number of chairs in the theater is;

Additionally, there are 102 chairs in the balcony;

In essence, the total number of chairs is;

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Final answer:

To find the total number of chairs in the theater, multiply the number of rows by chairs per row and add the chairs in the balcony, resulting in approximately 3027 chairs.

Explanation:

To calculate how many chairs there are in total, we need to add the number of chairs in the rows to the number of chairs in the balcony.

First, multiply the number of rows by the number of chairs per row to find the total number of chairs in the rows: 325 rows × 9 chairs per row = 2925 chairs.

Then, add the number of chairs in the balcony to this total: 2925 chairs + 102 chairs in the balcony = 3027 chairs. So, there are approximately 3027 chairs in the theater.