Sammy bought a new car. The depreciation equation is given by f(x) = 30,000(.85)x, where x represents the number of years since the purchase of the car, and f(x) represents the value of the car. By what percent does Sammy's car depreciate each year?

Multiply the amount of money he had by the percent of the game:

200 x 0.22 = 44

The game cost $44

The solution is Option B.

The recursive formula to calculate Marta's salary is given by the equation

f ( n ) = f ( n - 1 ) + 2700

The salary of Marta after 4 years will be $ 33,000

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the initial salary of Marta be f ( 0 ) = $ 24,900

The increment in Marta's salary every year = $ 2700

So , the equation will be

f ( n ) = f ( n - 1 ) + 2700

when n = 1

Substitute the value of n = 1 in the equation , we get

f ( 1 ) = f ( 1 - 1 ) + 2700

f ( 1 ) = f ( 0 ) + 2700

f ( 1 ) =  24,900 + 2700

f ( 1 ) = $ 27,600

when n = 2

Substitute the value of n = 2 in the equation , we get

f ( 2 ) = f ( 2 - 1 ) + 2700

f ( 2 ) = f ( 1 ) + 2700

f ( 2 ) =  27,600 + 2700

f ( 2 ) = $ 30,300

when n = 3

Substitute the value of n = 3 in the equation , we get

f ( 3 ) = f ( 3 - 1 ) + 2700

f ( 3 ) = f ( 2 ) + 2700

f ( 3 ) =  30,300 + 2700

f ( 3 ) = $ 33,000

Hence , after 4 years the salary of Marta will be $ 33,000

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Marta's annual salary increases by $2700 each year. Applying the recursive formula: f(n) = f(n-1) + 2700; f(4)=f(3)+2700=f(2)+2700+2700=f(1)+2700+2700+2700=f(0)+2700+2700+2700+2700=24900+4*2700=35500, we determine that Marta's salary in 4 years would be $35,500.

The subject of the question involves recursion, or constructing a sequence of numbers in a specific way. In Marta's case, her salary can be calculated using a recursive formula that builds upon her previous salary. This formula relies on the concept of numerical patterns and can be represented as follows: f(n) = f(n-1) + 2700; where f(n) is Marta's salary after n years and f(n-1) is her salary the previous year.

At the start, Marta's salary is 24,900, which serves as the base case for our recursive function. Therefore, her income increases by $2700 each year. To get Marta's salary in 4 years, we would use the recursive formula: f(4) = f(3) + 2700 = f(2) + 2700 + 2700 = f(1) + 2700 + 2700 + 2700 = f(0) + 2700 + 2700 + 2700 + 2700 = 24,900 + 4*2700 = 35,500. So, Marta's salary is $35,500 after 4 years.

Therefore, the correct option among choices provided is none from the given options.

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Answer: 2500 meters²

Step-by-step explanation:

Perimeter: 200 = 4w  

             ⇒    50 = w

Area = w²

        = (50)²

        = 2500

The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The perimeter of the rectangle = 2( length + Width)

                                             200 = 2( length + Width)

                                         100 - w = L

The area of the rectangle = length × Width

                                            = w(100 - w)

                                            = (-w)²+ 100w

So,  (-w)²+ 100w where, a = -1 and b = 100

w = -100/2(-1)

w = 50

The area of the rectangle = (-w)²+ 100w

                                            = (-50)²+ 100(50)

                                           = 2500

Thus, The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.

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The solution to the inequality is [tex]\(x > -17\).[/tex]

To solve the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\)[/tex], let's first find a common denominator and then combine the fractions:

[tex]\(\frac{5-2x}{-3} - 4 < -x\)[/tex]

Multiply each term by -3 to clear the fraction:

[tex]\(5 - 2x + 12 < -3x\)[/tex]

Combine like terms:

[tex]\(-2x + 17 < -3x\)[/tex]

Add [tex]\(2x\)[/tex] to each side:

[tex]\(17 < -x\)[/tex]

Multiply each side by -1 (remember to reverse the inequality when multiplying by a negative number):

[tex]\(-17 > x\)[/tex]

So, [tex]\(x > -17\).[/tex]

The value of x in the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\) is \(x \in \left(-\infty, -\frac{7}{5}\right)\).[/tex]

Step 1: Start with the given inequality:

[tex]\[\frac{5-2x}{-3} - 4 < -x\][/tex]

Step 2: Multiply both sides of the inequality by -3 to clear the fraction:

[tex]\[5-2x + (-3) \cdot 4 > -3 \cdot (-x)\][/tex]

[tex]\[5-2x -12 > 3x\][/tex]

Step 3: Combine like terms:

[tex]\[-7-2x > 3x\][/tex]

Step 4: Add 2x to both sides:

[tex]\[-7 > 5x\][/tex]

Step 5: Divide both sides by 5 (remembering to reverse the inequality when dividing by a negative number):

[tex]\[\frac{-7}{5} < x\][/tex]

So, the solution to the inequality is:

[tex]\[x \in \left(-\infty, -\frac{7}{5}\right)\][/tex]

The value of x in the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\) is \(x \in \left(-\infty, -\frac{7}{5}\right)\).[/tex]

The equation of the line that passes through the point (-1,5) and has a slope of -7 is y = -7x - 2. This can be determined by substituting the given values into the equation y = mx + b and solving for 'b'.

In mathematics, the equation of a line is commonly represented as y = mx + b, where 'm' represents the slope and 'b' is the y-intercept. In this equation, the slope '-7' is the rate at which 'y' changes for a unit change in 'x'. The y-intercept is the 'y' value when 'x' is zero.

It's given that the line passes through the point (-1,5). We can substitute these values into the equation to find 'b':

5 = -7(-1) + b, which simplifies to 5 = 7 + b. Therefore, 'b' equals to -2 after rearranging.

So, the equation of the line that passes through the point (-1,5) and has a slope of -7 is y = -7x - 2.

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Answer:

y=-4x-3

Step-by-step explanation:

Answer:

Price $0.75 per ounce of confetti

Step-by-step explanation:

Given the statement: Yuki bought a pound of confetti for $12.

⇒[tex]1 pound = \$ 12[/tex]                 ......[1]

Also, it is given that there are 16 ounces in 1 pound.

⇒ 16 ounces = 1 pound                       .....[2]

To calculate the price, in dollars per ounce of confetti.

From [1] and [2] we have;

[tex]16 ounces = \$12[/tex]

then;

1 ounces =  [tex]\frac{12}{16} = \frac{3}{4} = \$0.75[/tex]

Therefore, the price, in dollars per ounce of confetti is, $0.75  per ounce.

Answer:

Hey There so i saw your question. Solving it is very easy so i'm gonna help you step by step.

Step-by-step explanation:

(-3,4) (5,6) the slope formula y2-y1 over x2-x1  

so its 6-4/5-(-3)  which you gonna get 2/8 which is 1/4 so thats your slope.

*just know that your slope will flip since it's perpendicular and not parallel

so now you gonna find "b" on the equation Y=mx=b so out of your 2 points, choose one. I choose (5,6) all you gotta do is plug it into y=mx+b

so it's gonna be 6= 4 (the flipped slope)*5+b    {1.4*5 = 1.25}

so you gonna take 6 - 20 = -14 whcih is your b

so your new equation + the answer is Y= 4x-14

Answer:

16m

Step-by-step explanation:

Since the length of the park is 7m, then the other side is also 7m so 46-14 is 32. So 32/2 is 16.

Answer:

The probability is 17.36%

Step-by-step explanation:

In order to find this, we first need to find the probability of pulling one green marble. You can do this by dividing the number of marbles by the amount of marbles in the bag.

10/24 = 41.67%

Now in order to find the likelihood of doing this twice, you multiply that number by itself.

41.67% *41.67% = 17.36%

Answer

Tara puts 4 pennies if Sam puts 1 but Sam put 10 pennies in all so you multiply 10 by 4 and that gives you 40

Step-by-step explanation:

Answer:

6.25

Step-by-step explanation:

Because to know the answer we have to divide 75 by 12 which is 6.25

PPEERRPPEENNDDIICCUULLAARR

Answer:

hello : here is a solution

Answer: statue of liberty

Step-by-step explanation:

Answer:

when it says music its kinda a metaphor to peace when it says a flame that does burn it means the torch shes holding. She is over 40 years old shes 143 years old and she doesn't have any birth date she is the statue of liberty

Answer:

4 miles to the nearest mile.

Step-by-step explanation:

Circumference of the track = 2 pi r

= 2*pi*0.2 = 1.257  miles

Ellie ran 3 times around the track so

the distance she ran is 3* 1.257

=  4 miles

[tex]g(x)=x^3+5x^2-12x-36\\\\y-intercept\ for\ x=0:\\\\g(0)=0^3+5(0)^2-12(0)-36=-36\\\\\text{First or fourth graph.}\\\\\text{If the answer is 4th graph, then g(-2)=0}\\\\g(-2)=(-2)^3+5(-2)^2-12(-2)-36=-8+5(4)+24-36\\\\=-8+20+24-36=0[/tex]

The polynomial function utilizes only non-negative integers powers or positive integer exponent of the variable in a solution, like the quadratic equation, cubic equation, and so on, further calculation can be defined as follows:

Given:

[tex]\bold{g(x)=x^3+5x^2-12x-36}[/tex]

To find:

Graph the polynomial function=?

Solution:

[tex]\bold{g(x)=x^3+5x^2-12x-36}[/tex]

putting the value "1,2, -1, -2" into the above given function and calculate its value:

[tex]\to \bold{g(1)=1^3+5(1)^2-12(1)-36= 1+5-12-36= -42}\\\\\to \bold{g(-1)=(-1)^3+5(-1)^2-12(-1)-36= -1+5+12-36= 17-37=-20}\\\\\to \bold{g(2)=(2)^3+5(2)^2-12(2)-36= 8+5(4)-24-36= 8+20-24-36=-32}\\\\\to \bold{g(-2)=(-2)^3+5(-2)^2-12(-2)-36= -8+5(4)+24-36= -8+20+24-36=0}\\\\[/tex]Therefore, the answer is "4 choice".

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Answer:

The correct answer is 86.

Step-by-step explanation:

Because 82 is only one standard deviation below the mean, then to find the mean, only add 82 + 4 = 86

The mean score for the test is 86.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We are given that;

Score=82

Number of tests=4

Now,

We can substitute σ=4 and xi​=82 into the formula. We also know that there is only one data point that satisfies this condition, so we can use N=1.

[tex]\mu = \frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N\sigma^2} + \mu[/tex]

We get:

μ=(82−μ)^2/4^2 ​+μ

Simplifying and solving for μ, we get:

μ=86

Therefore, by standard deviation the answer will be 86.

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Answer:

5 hours

Step-by-step explanation:

given :

Distance between the cities = 540 miles

Speed of motorcycle =48 mph

TO CALCULATE THE TIME TAKEN BY MOTORCYCLE TO COVER THE TOTAL DISTANCE WE USE THE FORMULA :

[tex]\frac{DISTANCE}{SPEED}[/tex]

By putting given values in the formula we get :

[tex]\frac{540}{48}[/tex]

= 11.25 hours

Now, We are given that for a car to cover the same distance it takes 2.25 hours less than the time taken by motorcycle

⇒ 11.25 hours - 2.25 hours

⇒ 9 hours

Thus , Time taken by car to cover the same distance is 9 hours .

Now to calculate speed of car by using formula:

[tex]\frac{distance}{time}[/tex]

[tex]\frac{540}{9}[/tex]

= 60 mph

Let t be the time taken to meet if they start moving towards each other.

So distance covered by motorcycle in t hours is

speed\times time

= 48t miles

Distance covered by car in t hours is

speed\times time

= 60t miles

⇒ 60t + 48t =540

⇒ 108t = 540

⇒ t= 5 hours

Therefore, time taken to meet if they start moving towards each other is 5 hours.

[tex]\mathsf{Given : \dfrac{(3x^2y^-^3)^3}{27(xy)^-^9}}[/tex]

[tex]\mathsf{\implies \dfrac{(3)^3(x^2)^3(y^-^3)^3}{27(x)^-^9(y)^-^9}}[/tex]

[tex]\mathsf{\implies \dfrac{27(x)^6(y)^-^9}{27(x)^-^9(y)^-^9}}[/tex]

[tex]\mathsf{\implies \dfrac{(x)^6}{(x)^-^9}}[/tex]

[tex]\mathsf{\implies x^6^+^9}[/tex]

[tex]\mathsf{\implies x^1^5}[/tex]

1. The slope of the line is 3.

2. The direct variation equation is y = 3x

3. The equation in slope-intercept form is:y = 4

4. The equation in slope-intercept form is y = 2/3x + 1.

5. The equation = −2/3 − 1

6. The equation of the parallel line is y = 5x - 11.

1. Slope of the line:

The slope (m) of the line passing through (-1, 2) and (0, 5) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

m = (5 - 2) / (0 - (-1))

m = 3 / 1

m = 3

Therefore, the slope of the line is 3.

2. Direct variation equation:

Since y varies directly with x, we can write their relationship as y = kx, where k is the constant of proportionality. We can find k using the given information:

y = 15 when x = 5

15 = k * 5

k = 3

Therefore, the direct variation equation is y = 3x

When x = 9, y = 3 * 9 = 27.

3. Equation in slope-intercept form: First, calculate the slope using the same formula as in question 1:

m = (4 - 4) / (1 - (-3))

m = 0 / 4

m = 0

Since the slope is 0, the line is horizontal. The equation in slope-intercept form is:

y = 4 (constant y-intercept because it passes through (1, 4))

4. Equation in slope-intercept form using point-slope form:

The point-slope form equation is:

y - y1 = m(x - x1)

Plug in the given values:

y - (-1) = 2/3(x - (-3))

y + 1 = 2/3(x + 3)

3y + 3 = 2x + 6

3y = 2x + 3 (subtract 3 from both sides)

y = 2/3x + 1 (divide both sides by 3)

Therefore, the equation in slope-intercept form is y = 2/3x + 1.

5. Writing the equation in standard form:

The equation = −2/3 − 1 is already in standard form (ax + by = c), where a = -2/3, b = 0, and c = -1.

6. Equation of the parallel line:

Since the parallel line has the same slope (5) as the given line, its equation will be of the form y = 5x + b. To find b, plug the point (2, -1) into this equation:

-1 = 5(2) + b

-1 = 10 + b

b = -11

Therefore, the equation of the parallel line is y = 5x - 11.

Answer:

16 correct.

Step-by-step explanation:

We need to change 80% to a decimal

80 % = .8

If there are 20 questions

20 * .80 = 16

He got 16 questions correct

Answer:

1. The correct answer is D) 1/36

Step-by-step explanation:

WE can tell this because the chance of rolling either is 1/6. To find the total probability we multiply those together.

1/6 * 1/6 = 1/36

Answer:

11x+8  cm = Perimeter

Step-by-step explanation:

A triangle has 3 sides.  We add up all three sides to get the perimeter.

s1+s2+s3 = Perimeter

(x+4) +( 3x+1) + (7x+3) = Perimeter

Combine like terms

11x+8 = Perimeter

94.46%  Is the amount of water in a tomato  

16/20 = 80/100

multiply both top and bottom by 5 to go from 16/20 to 80/100

80/100 = 80% by definition of what "percent" means, which is "per 100" or "for every 100"

So 16/20 = 80% meaning 80% of the tomato is water

Note on a calculator, 16/20 = 0.80 which converts to 80% if you move the decimal point 2 spots to the right.