inverse function of f(x)= \frac{5}{x} +4

Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to find the amount you'll have in the account at the end of Year 6. An annuity is a series of equal payments made at equal intervals of time, and the future value of an annuity is the amount you'll have in the future if you invest those payments and earn a given rate of interest.

The formula for the future value of an annuity is:

FV = PMT * (((1 + r)^n - 1) / r)

where:

FV = future value of the annuity

PMT = annual payment amount

r = annual interest rate as a decimal

n = number of payments

In this case:

PMT = $1,500

r = 0.05

n = 6

Plugging in the values:

FV = $1,500 * (((1 + 0.05)^6 - 1) / 0.05)

FV = $1,500 * (1.328867 - 1) / 0.05

FV = $1,500 * 0.328867 / 0.05

FV = $1,500 * 6.577340

FV = $9,865.61

So, the amount in the account at the end of Year 6 will be $9,865.61. To find the last payment, we subtract this amount from the desired future value of $10,000:

$10,000 - $9,865.61 = $134.39

Therefore, your last payment will be $134.39.

Answer:

Alex spends more time 2/5 of 100 is 40%

The expression for its distance d (measured in feet) from the intersection t seconds later is d = x + 79200 t (feet)

Since the balloon is moving due east, we only need to consider its horizontal motion, ignoring its vertical motion at a constant altitude of 95 feet.

Let's call the initial distance of the balloon from the intersection x. The distance of the balloon from the intersection t seconds later can be found using the formula for distance traveled at a constant speed:

d = x + vt

where v is the speed of the balloon (15 miles per hour) and t is the time elapsed (in hours). To convert the speed from miles per hour to feet per second, we can multiply by the conversion factor of 5280 feet per mile:

d = x + (15 miles/hour) * (5280 feet/mile) * (t hours)

d = x + (15 * 5280) t feet

d = x + 79200 t feet

So the expression for the distance of the balloon from the intersection t seconds later is:

d = x + 79200 t (feet)

Note: In this expression, x represents the initial distance of the balloon from the intersection, which is unknown.

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Answer:

To approximate the area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2], we can use the right rectangle method, where the heights of the rectangles are given by the value of the function at the right endpoint of each subinterval. If we divide the interval [0, 2] into 4 equal subintervals of width 0.5, the right endpoint of each subinterval would be 0.5, 1, 1.5, 2.

The height of the first rectangle would be f(0.5) = 0.5^2 + 4 = 4.25, the height of the second rectangle would be f(1) = 1^2 + 4 = 5, the height of the third rectangle would be f(1.5) = 1.5^2 + 4 = 6.25, and the height of the fourth rectangle would be f(2) = 2^2 + 4 = 8.

The sum of the areas of the rectangles is equal to (0.5) × (4.25 + 5 + 6.25 + 8) = (0.5) × 24 = 12.

So, the approximate area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2] is 12.

Answer:

So, the answer is (b) 320 feet.

Step-by-step explanation:

Let's call the length and width of the first playground "x".

The perimeter of the first playground is 160 feet, so 2 times the length plus 2 times the width is equal to 160:

2x + 2x = 160

Simplifying:

4x = 160

Dividing both sides by 4:

x = 40

So the length and width of the first playground are both 40 feet.

The second playground is twice as long and twice as wide as the first playground, so the length and width of the second playground would be 2 * 40 = 80 feet.

The perimeter of the second playground would then be 2 * 80 + 2 * 80 = 320 feet.

So, the answer is (b) 320 feet.

It is important to understand the concept of interest beacause it is a part of our life and it hels us to understand the economic situation of ourselves.

It is the interest calculated on the principal at a given rate for a time period.

We have.

There are two types of interest commonly studied.

1)

Simple interest

2)

Compound interest

Now,

Simple interest is the interest calculated only on the principal year after year.

Whereas compound interest is the interest calculated on the principal as well as the interest after the first year.

Example:

Principal = $100

Rate = 10%

Time = 2 years

Simple interest after two years.

= 2 x (10% of 100)

= 2 x (1/10 x 100)

= 2 x 10

= $20

Compound interest after two years.

Ist year:

=  (10% of 100)

= (1/10 x 100)

= $10

2nd year:

= 10% of (100 + 10)

= 1/10 x 110

= $11

So,

= 10 + 11

= $21

Thus,

The concept of interest is given above.

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Answer:

To find the time it takes a car traveling at 40 mph to stop after covering a distance of 30 feet, we need to use the formula for distance, speed, and time, which is:

distance = speed * time

Rearranging the formula, we get:

time = distance / speed

Since the speed is in miles per hour (mph), we need to convert it to feet per second (fps). One mph is equivalent to 1.47 fps, so 40 mph is equivalent to 40 * 1.47 = 58.8 fps.

Now we can plug in the values for distance and speed into the formula:

time = 30 feet / 58.8 fps

time = 0.5104 seconds

Rounding to the nearest second, we get:

time = 0.51 seconds

So, it would take the car approximately 0.51 seconds to stop after traveling 40 mph.

Step-by-step explanation:

Answer:

x = 80

Step-by-step explanation:

supplementary angles sum to 180°

sum the 2 angles and equate to 180

x + 40 + x - 20 = 180

2x + 20 = 180 ( subtract 20 from both sides )

2x = 160 ( divide both sides by 2 )

x = 80

Answer: 266

Step-by-step explanation:

I = prt

p= 1900

r=.07

t=2

1900x.07x2=266

The solution of the radical expression ∛(4+3) will be 1.91.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

The radical sign, which may be read as either the nth root of x or x radical n, expresses the root of a number. The vinculum, or horizontal line that encircles the number, and the radicand, or number beneath it, are both technical terms.

Given that the expression is ∛(4+3). The solution of the medical expression will be,

E = ∛ ( 4 + 3)

E = ∛(7)

The value of the cube root of the number 7 will be,

E = 1.91

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The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.

What is area of square ?

Area of square can be defined as the square of given side.

Given ,

Let's assume that the side length of the original square is 's'. The perimeter of the original square is then 4s and its area is s².

The perimeter of the dilated square will be 4 times longer than the original square, so it will be 4 * 4s = 16s.

The area of the dilated square will be 4 times greater than the original square, so it will be 4^2 * s² = 16s².

Here s is 12

so ,

16s = 16 * 12 = 192

16s*s = 16 * 12 * 12 = 2304

Therefore, The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.

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Answer:

1. The monthly premium for workers' compensation insurance for the Winston Tree Farm and Nursery can be calculated as follows:

Monthly payroll: $3,560 Base rate: $5.93 per $100 Rate per $1,000: $5.93 * 10 = $59.30 Premium: $3,560 / 1,000 * $59.30 = $209.51

So, the monthly premium for workers' compensation insurance is $209.51.

2. The amount that Takis Machine Shop will pay each year for workers' compensation insurance can be calculated as follows:

Old base rate: $9.40 per $100 New base rate: $10.40 per $100 Monthly payroll: $53,896.84 Old rate per $1,000: $9.40 * 10 = $94.00 New rate per $1,000: $10.40 * 10 = $104.00 Old premium: $53,896.84 / 1,000 * $94.00 = $5,045.65 New premium: $53,896.84 / 1,000 * $104.00 = $5,610.71 Increase in premium: $5,610.71 - $5,045.65 = $565.06

So, Takis Machine Shop will pay an additional $565.06 each year for workers' compensation insurance.

3.The real estate tax for the home in Madison County can be calculated as follows:

Market value: $590,000 Rate of assessment: 40% of market value = $590,000 * 0.4 = $236,000 Tax rate: 42.73 mills = 0.04273 Tax: $236,000 * 0.04273 = $10,130.68

So, the real estate tax for the home in Madison County is $10,130.68.

4. The fair market value of Vanesa Vasquez's Roth IRA at age 65 can be calculated as follows:

Contribution: $2,500 Years of contribution: 65 - 35 = 30 Annual interest rate: 7.4% Future value: $2,500 * (1 + 0.074)^30 = $29,706.74

So, the fair market value of her Roth IRA at age 65 is $29,706.74.

The amount of interest earned can be calculated as follows:

Future value: $29,706.74 Present value: $2,500 Interest earned: $29,706.74 - $2,500 = $27,206.74

So, Vanesa Vasquez will have earned $27,206.74 in interest.

5. The interest rate as a percent for the GNMA Mortgage issue bond can be calculated as follows:

Face value: $10,000 Selling price: $10,000 * 103.7% = $10,370.00 Yield: 8.75% Price: $10,370.00 Interest: $10,370.00 - $10,000 = $370.00 Interest rate: ($370 / $10,000) * (12 / 1) = 0.09375 = 9.375%

So, the interest rate for the GNMA Mortgage issue bond is 9.375%, rounded to the nearest hundredth of a percent.

6. Let's call the number of days that Ricardo has to pay back the loan "d".

The interest on the loan can be calculated using the formula:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed, $2,500), r is the annual interest rate as a decimal (7.8% as a decimal is 0.078), and t is the time in years (d divided by 365).

So we have:

I = $2,500 * 0.078 * (d / 365)

We also know that the maturity value of the loan is the sum of the principal and the interest:

$2,548.75 = $2,500 + I

So we can substitute for I:

$2,548.75 = $2,500 + $2,500 * 0.078 * (d / 365)

Expanding the right-hand side:

$2,548.75 = $2,500 + $194.00 * (d / 365)

And solving for d:

d = 365 * ($2,548.75 - $2,500) / $194.00

d = 365 * ($48.75) / $194.00

d = 365 * 0.25191780821917808

d = 91.37 days

So Ricardo would have to pay back the loan in 91.37 days.

Step-by-step explanation:

Answer:  do you need me to answer all or anthor example.

Step-by-step explanation:

I will answer

Some way to solve binary operations are listed below

By definition, binary operations involve performing arithmetic operations on two operands in a specific way.

An example of a binary expression is a + b

Where a and b are the operands & + is the operator

Some common binary operations and how to solve them are highlited below

Other operations are

Multiplication (*), Division (/) and Modulus

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Answer:

C.Only Maryanne's equation has the same solution as the original equation.

The solution is : 39 is the solution to Mr. Smith's equation.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

the equation is:

(16-2w)^2 + (3y÷3z)

Let w=5 y=9 and z=3

(16-2*5)^2 + (3*9÷3*3)

PEMDAS says parentheses first

Multiply and divide in the parentheses

(16-10)^2 + (27÷9)

Then add and subtract in the parentheses

(6)^2 + (3)

Now the exponent

=36 +3

=39

Hence, The solution is : 39 is the solution to Mr. Smith's equation.

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complete question:

What is the solution to Mr. Smith's equation?

There will be about 95 counselors there with the help of expression 2375/50.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

Given that Total campers = 2375

and for each cabin there are 2 counselors and 50 campers

then no. of cabins = 2375/50

No. of counselors= 2*no. of cabins

=2*2375/50

=95

Hence,

            There will be about 95 counselors there with the help of expression 2375/50.

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Answer:

[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]

Step-by-step explanation:

Given polynomial:

[tex]f(x)=-3x^3-5x^2+x-7[/tex]

If P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

Possible p-values

Factors of the constant term:  ±1, ±7

Possible q-values

Factors of the leading coefficient:  ±1, ±3

Therefore, all the possible values of p/q:

[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]

Substitute each possible rational root into the function:

[tex]x=-1 \implies f(-1)=-3(-1)^3-5(-1)^2+(-1)-7=-10[/tex]

[tex]x=1 \implies f(1)=-3(1)^3-5(1)^2+(1)-7=-14[/tex]

[tex]x=-7 \implies f(-7)=-3(-7)^3-5(-7)^2+(-7)-7=770[/tex]

[tex]x=7 \implies f(7)=-3(7)^3-5(7)^2+(7)-7=-1274[/tex]

[tex]x=-\dfrac{1}{3} \implies f\left(-\dfrac{1}{3}\right)=-3\left(-\dfrac{1}{3}\right)^3-5\left(-\dfrac{1}{3}\right)^2+\left(-\dfrac{1}{3}\right)-7=-\dfrac{70}{9}[/tex]

[tex]x=\dfrac{1}{3} \implies f\left(\dfrac{1}{3}\right)=-3\left(\dfrac{1}{3}\right)^3-5\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)-7=-\dfrac{22}{3}[/tex]

[tex]x=-\dfrac{7}{3} \implies f\left(-\dfrac{7}{3}\right)=-3\left(-\dfrac{7}{3}\right)^3-5\left(-\dfrac{7}{3}\right)^2+\left(-\dfrac{7}{3}\right)-7=\dfrac{14}{9}[/tex]

[tex]x=\dfrac{7}{3} \implies f\left(\dfrac{7}{3}\right)=-3\left(\dfrac{7}{3}\right)^3-5\left(\dfrac{7}{3}\right)^2+\left(\dfrac{7}{3}\right)-7=-70[/tex]

As f(p/q) ≠ 0, none of the possible rational roots are actual roots of the given polynomial.

In right triangle ABC, the value of x is equal to 0.06.

In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

Since the angle formed by side A is a right triangle, we have the following complementary angles;

C + B = 90

sin(C) = cos(B)

x + 0.26 = 3x + 0.14

3x - x = 0.26 - 0.14

2x = 0.12

x = 0.12/2

x = 0.06

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The expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.

A polynomial expression is an algebraic expression made up of variables and coefficients, combined using only the operations of addition, subtraction, and multiplication. The variables are raised to a power, which is a non-negative integer, and the coefficients are real numbers. A polynomial can have any number of terms, but it always has a degree, which is the highest power of the variables in the expression.

For the polynomial expression, (1/2)x⁵ - 6 - x⁴ - 5x⁴

There are 4 terms which are: (1/2)x⁵, - 6, - x⁴, and - 5x⁴.

The constant term is -6

The leading term is (1/2)x⁵

The coefficient of the leading term is 1/2.

In conclusion, the expression represents a degree five polynomial with four terms. The constant term is -6, the leading term is (1/2)x⁵, and the leading coefficient is 1/2.

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Answer:

quadrinomial, 4, -6, 1/2x^5, 1/2

Step-by-step explanation:

quadrinomials are polynomials with 4 terms

constant is the number with no variable

leading term is the term at the beginning

leading coefficient is the number at the beginning

With percentage=76% of foreign coins of total 150 coins, Other coins collected were 36.

What is the percentage?

In mathematics, a percentage is a statistic or ratio that may be expressed as a fraction of 100. To find the percentage of a number, divide it by its total and multiply by 100. Hence, the percentage represents one part of a hundred. The phrase % stands for one hundred percent. It is represented by the symbol "%".

Here are some instances of percentages:

Now,

Given that total coins=150

Foreign coins=76% of total

then other coins are 24% of total

so other coins=150*24/100

=72/2

=36

Hence,

          Other coins collected were 36.

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The intervals of each behavior of the function are given as follows:

a) Increasing: (-∞, -1).

b) Decreasing: (-1, 1).

c) Constant: (1, 3).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable .

here, we have,

to classify the function as increasing, decreasing or constant:

The function is increasing when the graph moves right and up.

The function is decreasing when the graph moves right and down.

The function is constant when the graph of the function is an horizontal line.

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The area of the given parallelogram is 12 cm².

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

The formula to calculate the area of a parallelogram can thus be given as,

Area of parallelogram = b × h square units

where b is the length of the base and h is the height

According to the given parallelogram ABCD, we have

Length of the base b = 5 + 9 = 14 cm

The height h = 8 cm

Area of parallelogram = b × h

Area of parallelogram = 14 × 8

Area of parallelogram = 112 cm²

Thus, the area of the given parallelogram is 12 cm².

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The question seems incomplete, the missing figure has been attached below.

Step-by-step explanation:

We can start by using an equation to represent the given information. Let's call the number p, and the number k, then:

k = (1/5)p + 6

So, "six more than one-fifth of a number p is equal to a number k" can be represented mathematically as k = (1/5)p + 6. To find the value of p, we can solve for p:

p = 5k - 30

So, p is equal to 5 times the value of k minus 30.

The graph of the function is added as an attachment

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

h(x) = (1/3)ˣ - 4

The above function is an exponential function shifted down from the origin by 4 units

An exponential function of this form is represented as

h(x) = a(b)ˣ + c

Where

Initial value = a

Rate = b

Shift = c

Using the above as a guide, we have the following:

a = 1

b = 1/3

c = -4

Next, we plot the graph

See attachment for the graph of the function

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In the cyclic quadrilateral the value of R and S are

< S = 87 degrees

< R = 216 degrees

In a cyclic quadrilateral, the opposite angles are supplementary hence

< S + < Q = 180

in the problem we have that < Q = 93

< S + 93 = 180

< S = 180 - 93

< S = 87 degrees

Angle R is adjacent angle to angles 126 and 90 hence we have that

< R = 126 + 90

< R = 216 degrees

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Yes, it is possible to make an expression including all tiles simpler by grouping together the tiles with negative coefficients and the tiles with negative coefficients.

Simply put, negative coefficients are coefficients with negative values. A negative coefficient can be anything like -8 in the term -8z or -11 in the term -11xy. The result of multiplying the variables by the integer is negative.

A negative exponent signifies a very small number: The decimal in the coefficient is shifted eleven positions to the left as a result. A decimal number must also be moved in order to be expressed in scientific notation.

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