If f(x) is a one-to-one function f(8)=-2 then which of the following points must lie on the graph of its inverse, I.e y=f^-1(x)

They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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Answer:

The correct answer is: 3, 4, 5, 6.

Step-by-step explanation:

The correct answer is: 3, 4, 5, 6.

To check, we can substitute each number into the inequality:

When x = 3: 9 - 2(3) ≥ 3, which simplifies to 3 ≥ 3 (true)

When x = 4: 9 - 2(4) ≥ 3, which simplifies to 1 ≥ 3 (false)

When x = 5: 9 - 2(5) ≥ 3, which simplifies to -1 ≥ 3 (false)

When x = 6: 9 - 2(6) ≥ 3, which simplifies to -3 ≥ 3 (false)

Therefore, only the numbers in the set {3, 4, 5, 6} satisfy the inequality.

Answer:

a 20

Step-by-step explanation:

Answer:

1372 ft^3

Step-by-step explanation:

Volume of sphere =\(\frac{4}{3}\)πr^3

here π is 3 and radius = 7

4/3 * 3 * 7^3

1372ft^3

Answer:

14ft

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods

1/PV (FV) = (PV(1 + r^n)1/PV divide by PV

ln(FV/PV) = ln(1 + r^n) convert to natural log function

ln(FV/PV) = n[ln(1 + r)] by simplifying

n = ln(FV/PV) / ln(1 + r) solve for n

n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually

n = 9

n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly

n = 104 months or 8.69 years

n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily

n = 3163 days or 8.67 years

Alternatively

A = P e ^(rt)

Given that r = 8%

= 8/100

= 0.08

2 = e^(0.08t)

ln(2)/0.08 = t

0.6931/0.08 = t

t= 8.664yrs

t = 8.67yrs

Which ever approach you choose to use,you will still arrive at the same answer.

Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.

It can be calculated as:

\(f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )\)

where:

c is the speed of light (c = 332m/s)

all the subscripted s is related to the Source (frequency, velocity);

all the subscripted o is related to the Observer (frequency, velocity);

As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.

So, the frequency perceived by the observer:

\(f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)\)

\(f_o=460\huge \text(\dfrac{364}{292}\huge \text)\)

\(f_o=460(1.247)\)

\(f_o= 573.6 \ \text{Hz}\)

At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz

Answer:

The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time

The perceived frequency you hear is

370.9 Hertz

The function is given as:

\(f_{o}=\frac{c+V_{o} }{c-V_{o} }\) x  \(f_{s}\)

From the question

\(c=332\) --- speed of the sound

\(V_{o} =32\) ---current speed of the train

\(V_{s} = 40\) --- speed of the opposite train

\(f_{s} =460\) --- frequency of the sound wave

This gives:

\(f_{o}= \frac{332-32}{332+40}\)  ×\(460\)

\(f_{o}= \frac{300}{372} x460\)

Rewrite as:

\(f_{o}= \frac{300x460}{372}\)

\(f_{o}= 370.9\)

Answer:

Step-by-step explanation:

3x / (x + 2).

Answer:

So we can use geometric progression each time multiplying by 0.0475

so thats (275*0.0475)*10

So that means that we would get

130.625 so we subtract that from 275

275-130.625=144.375

That would be

Step-by-step explanation:

Answer:

1073.45 in²

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The equation to solve for the area of a circle is:

But wait, we don't have a radius to fix in the equation! Well to solve for the radius when given diameter, we can use the expression:

Now that we know this, we can insert 37 in for the diameter:

So, the radius of the circle is 18.5 inches.

Inserting 18.5 into the expression for the radius:

Using 3.14 for pi:

Therefore, the area of a circle with a diameter of 37 inches is 1073.45 in².

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

9.6

Step-by-step explanation:

I think!

-2 1/2 - (-1 3/4)

When subtracting a negative vile the equation becomes addition:

-2 1/2 + 1 3/4 = -3/4

Answer: -3/4

Answer:

40$,160$ & 60

Step-by-step explanation:

First,find the equation using y-y1/ y1-y2=x-x1=x1-x2

y-0/0-20=x-0/0-3

y=20x/3

Now put the values of x& y in the equation, for the 1st one,

y=20×6/3

=40

2nd one.y=20×24/3

=160

3rd one,

400=20x/3

X=400×3/20

=60

The values at different number of tickets and the tickets that can be bought at $400 has been determined.

When a variable varies directly with the other variable, i.e. on increasing one variable the other variable also increases, this relation is called Direct Variation.

Let x represent the number of tickets sold

Let y represent the amount of money earned from ticket sales.

y ∝ x

y = kx

k is the proportionality constant.

The value in the table will be used to determine the value of k,

For 3 tickets, the ticket amount is $20

20 = k * 3

k = 20/3

The relation is given by

y = (20/3) x

For 6 tickets, the value will be,

y = (20/3 ) *6 = $40

For 24 tickets the value will be,

y = (20/3) * 24 = $160

For $400, how many tickets can be bought,

400 = (20/3) * x

400*3 /20 = x

60 tickets can be bought for $400

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Answer:

The correct answer is the first one

Step-by-step explanation:

Given:

h = 22 yd

a (base) = 152 yd^2

Find: v - ?

First, let's write down the formula of the rectangular prism's volume:

\(v = a(base) \times h\)

Since we know both the area of the base and the height, we can easily find the volume:

\(v = 152 \times 22 = 3344 \: {yd}^{3} \)

This problem is about find the patter on the number line to complete them all.

To know the unit rate, we just need to divide 10 by 3, since there are only three spots from 0 to 10.

Rounded to the nearest hundredth.

This means the first number is 3.33, the second number is 6.66, and then we have 10. You can also express the first number as 10/3, and the second number as 20/3, expressing them as fractions you will be more accurate. The image below shows the complete number line

Answer:

Step-by-step explanation:

Answer:

there is no picture

Step-by-step explanation:

Answer:

it depends on what triangle it is. if it an equilateral then the answer is 6.7 (20 divided by 3)

Step-by-step explanation:

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The height of the television transmission tower is approximately 1298 feet.

The height of the television transmission tower, we can use trigonometry and the concept of tangent.

Let's denote the height of the tower as h.

We know the length of the shadow is 1130 feet and the angle formed by the ground and the line from the top of the tower to the tip of the shadow is 48.3 degrees.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

The height of the tower is the opposite side and the length of the shadow is the adjacent side.

Using the tangent function, we can set up the following equation:

tan(48.3°) = h / 1130

To solve for h, we can multiply both sides of the equation by 1130:

1130 × tan(48.3°) = h

Using a calculator, we find:

h ≈ 1130 × 1.1477

≈ 1297.601 feet

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Answer:

3m=number of marbles tim has

3m-m=how much more tim has than tom

3m+m=how much marbles they have together

Step-by-step explanation:

Answer:Domar range x

Step-by-step explanation:

Answer:

95-9 (3+7)

95-9 (10)

86 (10)

= 8600

Step-by-step explanation:

I hope this was helpful!

God bless you!

Answer:

9/9

Step-by-step explanation:

Answer:

9/9

Step-by-step explanation:

nine divided by nine equals 1

The value of the expression is 142.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

To solve this expression, we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Let's start with the parentheses first:

14 x 0.5 x (4 + 2) + exponent 10*2

= 14 x 0.5 x 6 + exponent 10*2

Next, we can simplify the multiplication and division from left to right:

= 7 x 6 + exponent 10*2

= 42 + exponent 10*2

Now we can evaluate the exponent:

= 42 + 100

= 142

Therefore, the value of the expression is 142.

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Answer:

The answer is 170

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Step-by-step explanation:

If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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