A group of friends wants to go to the amusement park. They have $284.25 to spend on parking and admission. Parking is $9.25, and tickets cost $27.50 per person, including tax. How many people can go to the amusement park?

The inverse of the function f(x) = (4x - 1)/(-2x +2) is equal to f⁻¹(x) = (2x + 1)/(4 + 2x).

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of this function f(x) = (4x - 1)/(-2x +2), we would interchange both the input value (x) and output value (y) as follows:

y = (4x - 1)/(-2x +2)

x = (4y - 1)/(-2y +2)

Cross-multiplying, we have:

x(-2y +2) = 4y - 1

2x - 2xy = 4y - 1

Next, we would rearrange the function by collecting like terms as follows:

4y + 2xy = 2x + 1

y(4 + 2x) = 2x + 1

Dividing both sides of the function by (4 + 2x), we have:

y = (2x + 1)/(4 + 2x)

y = f⁻¹(x) = (2x + 1)/(4 + 2x)

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Answer: 50, 99

Step-by-step explanation:

we just have to substitute the values of x and y in the given expressions.

7(2)+4(9)=50

4(9)+7(9)=99

Answer:

Step-by-step explanation:

7x + 4y= 50 and 4y + 7y= 99

Since, x=2 and y=9

7x + 4y= 7*2 + 7*9= 14 + 36= 50

and similarly

4y + 7y= 4*9 + 7*9= 36 + 63= 99

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The area of the rectangular land is 208,607 square meters,

A rectangle is defined as a quadrilateral whose opposite sides are equal and parallel

How to find the area of a rectangle?

The lengths of a rectangle are denoted by L and W

where: L=length

            w=width

Area of the land (A)= Area of the larger land  minus Area of the smaller land carved out

A= (LW) - (lw)

A=(513x466.5)-(267x113)

A=239,312-30705

A=208.607 meters square

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Using the conversion factor, the height of Valerie in centimeters is (C) 160 cm.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

For instance, 12 inches equals one foot when converting between inches and feet.

So, 64 inches in cm is:

We know that:

1 inch = 2.5 cm

Then, 64 inches is:
64 inches = 2.5 × 64

64 inches = 160

Therefore, using the conversion factor, the height of Valerie in centimeters is (C) 160 cm.

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Correct question:
Valerie is 64 inches tall. About how many centimeters tall is Valerie?

(1 inch -2.5 centimeters)

A. 25.5

B. 30.6

C. 160

D. 180

The number of times that the cube will land on 5 if the number cube was rolled 500 times is 83 times.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

It should be noted that in a number cube, we hage numbers from 1 to 6. The probability of getting a 5 is 1/6.

Therefore, when it's rolled 500 times, the possible number will be:

= 1/6 × 500

= 83 times.

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The rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.

We know that the rate of change of a function is nothing but the slope of the line.

The slope of the line is given by;

Slope = Change in y-coordinate / change in x-coordinate

We are given;

[tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex]

We need to find the rate of change of function for x = 4 and x = 9.

Let us find the value of y or f(x) for the given value of x.

For x = 4, [tex]f(x) = \sqrt{4} - \frac{1}{\sqrt{4}}[/tex]   = 2 - 1/2 = 4 - 1 / 2 = 3 / 2

For x = 9, [tex]f(x) = \sqrt{9} - \frac{1}{\sqrt{9}}[/tex]   = 3 - 1/3 = 9 - 1 / 3 = 8 / 3

Put the values of x and y in the slope formula, we will get;

Slope = (8 / 3 - 3 / 2) / (9 - 4) = 7 / 6*5 = 7 / 30

So, the rate of change of function is 7 / 30.

Thus, the rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.

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The point slope form of equation is y- 3 = -4/3( x- (-3)).

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Points= (-3, 3) and (9, -13)

Now,

slope= (-13 - 3)/ (9 - (-3))

slope= -16 / 12

slope= -4/3

Now, the point slope form

y- [tex]y_1[/tex] = m (x- [tex]x_1[/tex])

y- 3 = -4/3( x- (-3))

y- 3= -4/3x - 4

y= -4/3x - 1

Hence, the point slope for of equation is y- 3 = -4/3( x- (-3)).

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Answer:

x = 15 , y = 4

Step-by-step explanation:

If 3 or more parallel lines are intersected by two or more transversals, the parallel lines divide the transversals proportionally. then

[tex]\frac{x}{5}[/tex] = [tex]\frac{18}{6}[/tex] = 3 ( multiply both sides by 5 )

x = 15

and

[tex]\frac{12}{y}[/tex] = 3 ( multiply both sides by y )

12 = 3y ( divide both sides by 3 )

4 = y

Answer: 88

Step-by-step explanation:

For every 7 grey goats there are 4 white goats. 160/7=22  4*22=88

well, from the end of year 5 to the end of year 6 is only 1 year later, so

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3315.30\\ P=\textit{original amount deposited}\dotfill & \$3203.19\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 3315.30=3203.19[1+(\frac{r}{100})(1)] \implies \cfrac{3315.30}{3203.19}=1+\cfrac{r}{100} \\\\\\ \cfrac{3315.30}{3203.19}-1=\cfrac{r}{100}\implies 100\left( \cfrac{3315.30}{3203.19}-1 \right)=r\implies \stackrel{\%}{3.5}\approx r[/tex]

It is very easy, we just have to take the square root as it tells us in the problem:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{ \sqrt{441 }} = \orange{21}[/tex]

You may ask ¿why 21?

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{21 \times 21} = \orange{441} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf So , \: the \: result \: is \\ \sf \longmapsto \orange{21} [/tex]

The equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0 and the slope of the line is 1/8

Slope of the line that passes through the points (9,9) and (1, 8)

The equation of the line is

y -y₁ = ((y₂ - y₁)/ (x₂ - x₁)) (x - x₁)

y - 9 = ((8 - 9)/(1 - 9)) (x - 9)

y - 9 = (1/8) (x - 9)

8y - 72 = x - 9

8y - x - 63 = 0

8y = 1/8 (x + 63)

Therefpre, the equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0

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The best course grade your friend can earn is 88%.

The minimum score your friend needs to have on the final to earn a 75% for the course is 35%.

If the final counts for 20% of the course grade, it means that the average of 85% counts for 80% (100 - 20%) of the total score.

The linear expression that can be used to determine the best course grade your friend can earn is:

(average that has already been accumulated x 80%) + (score on the finals x 20%)

(85% x 80%) + (20% x 100%)

(85% x 0.80) + (0.2 x 100%)

68 + 20 = 88%

The linear equation that can be used to determine the minimum score that can be earned on the final to have75% in the course is

Final grade = (total average before the final x 80%) + (score on the final x 20%)

75% = (85% x 80%) + (f x 20%)

75% = (85% x 0.80) + (0.20 x f)

75% = 68% + 0.20f

75% - 68% = 0.20f

7 =  0.20f

f = 7% / 0.20

f = 35%

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Since fractions are the same as division, divide 617 by 50. The remainder will remain in fraction form.

617/50
600/50 = 12
617/50 = 12 17/50

Based on this information we can conclude that in one hour, Oliver and his sister would get all of the windows washed. This means that it would take 5/6 hours which is equal to 50 minutes) for them to get all of the windows washed.

Information is defined as the content of a message which is passed from a source to its receiver.

The number of hours it takes for Oliver to wash the house windows = 2 hours, so in an hour = 1/2

The number of hours it takes his sister to wash the same house windows = 3 hours, so in an hour = 1/3.

To calculate for one hour for both would be addition of the derived fractions;

= 1/2 + 1/3

= 3+2/6

= 5/6

When converter to minutes, multiple by 60;

= 5/6 × 60

= 300/6

= 50 minutes.

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The number of ways he can form the teams would be = 336 ways.

Badminton is a type of racket game that makes use of single or double players where by they make use of a racket to hit a shuttlecock over the net to their opponents side.

The number of players available for the badminton game = 8

The number of teams to the formed = 4

To find the number of ways to form 4 double teams from these 8 players would be to find the factorials of 8 divided by factorial 4.

That is ;

8!/4! = 8×7×6×4×3×2×1/4×3×2×1

= 8064/ 24

= 336 ways.

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The missing measure is  ∠P =∠X = 122°

Given △ACP ≅ △LNX

XL = 13 cm, m∠L = 29°

AC = 21 cm, m∠C = 29°

PC = 13 cm, m∠Y = ??  (there is no angle Y)

On the right shows the triangles are isosceles, with XL = XN. That means also PA = PC. Those side lengths are all the same: 13 cm.

PA = PC = XL = XN = 13 cm

In the same way, ...

LN = AC = 21 cm

Of course, the angles have a similar relationship:

∠A = ∠C = ∠L = ∠N = 29°

The two base angles in the triangle add to 58°, so the third angle is ...

180° -58° = 122°

∠P =∠X = 122°

As is often the case in over-specified problems, the numbers shown are not consistent. The length LN is actually incorrect for the angle and side specified for triangle ACP, or the angles are incorrect for the side lengths specified. What this means is that the answers you get will depend on how you work the problem. Above, we have taken the given numbers and relationships at face value, even though we know they are incorrect.

Hence the answer is The missing measure is  ∠P =∠X = 122°

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Answer:

42.2 ft

Step-by-step explanation:

The given scenario can be modelled as a right triangle (see attached diagram), where the angle of elevation is 32°, and the length of the kite string (75 ft) is the hypotenuse.

We want to find the distance the kite is above the ground, so we want to find the side of the right triangle that is opposite the given angle. To do this, we can use the sine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Substituting θ = 32° and H = 75 into the ratio, we get:

[tex]\sin 32^{\circ}=\dfrac{\sf O}{75}[/tex]

[tex]\textsf{O}=75\sin 32^{\circ}[/tex]

[tex]\textsf{O}=39.7439448...\; \sf ft[/tex]

The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object located at a higher position.

In this scenario, the angle of elevation is measured from Savannah's hand, which is a distance of 2.5 ft above the ground. Therefore, we need to add 2.5 ft to the value of O found using the sine ratio.

[tex]\implies 39.7439448...+2.5=42.2\; \sf ft\;(nearest\;tenth)[/tex]

Therefore, the kite is 42.2 ft above the ground (rounded to the nearest tenth).

5.1 The amount of money received by the man at the end of 4 years is

$10,217.39

5.2 The rate of interest per annum is 94.56%/year.

Given:

P=5000

r = 18%

t= 4 years.

5.1 First, convert R as a percent to r as a decimal

r = R/100

r = 18/100

r = 0.18 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.18/12)(12)(4)

A = 5,000.00(1 + 0.015)(48)

A = $10,217.39

5.2 Given:

P = 3700

A = 8360,34

t = 7 years.

r =?

Solving for rate r as a decimal

r = n[(A/P)1/nt - 1]

r = 2 × [(836,034.00/3,700.00)1/(2)(7) - 1]

r = 0.945604

Then convert r to R as a percentage

R = r * 100

R = 0.945604 * 100

R = 94.56%/year

Hence we get the required answer.

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Answer:

okay so step by step explanation,

first multiply  7[tex]x^{2}[/tex] with 5[tex]x^{2}[/tex] and -[tex]y^{2}[/tex]

35[tex]x^{4}[/tex]-7[tex]x^{2}[/tex][tex]y^{2}[/tex]

then do the second one

20[tex]x^{2}[/tex][tex]y^{2}[/tex]-4[tex]y^{4}[/tex]

take the sum of those,

35[tex]x^{4}[/tex]+13[tex]x^{2}[/tex][tex]y^{2}[/tex]-4[tex]y^{4}[/tex]

good luck<3!

If the square banquet has area = 3600m² then length of the room is 60 m .

The Area of the Square with side "s" can be calculated using the formula

Area = s × s

In the question ,

it is given that ,

the area of the Square banquet is = 3600m²  ,

let the length of the side of the room be "s" .

So , By the Area of the Square formula ,

we get ,

s × s = 3600

s² = 3600

taking quare root both the sides ,

we get

√s² = √3600

s = 60

the side = 60m

Therefore , If the square banquet has area = 3600m² then length of the room is 60 m .

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Answer:

Below

Step-by-step explanation:

Graphing the equation shows local max volume at x = 4  of 1024 cm^3

1024 cm^3  * RM . 30 / cm^3 = RM 307.2

The quadratic equation 6 · x² + 13 · x + 6 = 0 has a positive discriminant and its roots are two distinct real numbers.

In this problem we must infer the features of the two roots of a quadratic equation of the form a · x² + b · x + c = 0, this can be done by means of the discriminant from the quadratic formula:

D = b² - 4 · a · c

Where a, b, c are real coefficients of the quadratic equation.

There are three possibilities for the results of the discriminant:

First, write the quadratic equation:

6 · x² + 13 · x + 6 = 0

Second, collect the real coefficients of the polynomial:

(a, b, c) = (6, 13, 6)

Third, calculate the discriminant:

D = 13² - 4 · 6²

D = 169 - 144

D = 25

The quadratic equation has two roots that are real and different.

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Numbers between 2.6×10^-1 and 29.5% are

2.6 × 10^-1 in exponential form written in decimal as 0.26

29.5% in percentage written in decimal as 0.295

2/7 in fraction written in decimal as 0.2857

2.8%  in percentage written in decimal as 0.028

0.2875 already in decimal form

the problem asks of numbers from 0.26 to 0.295

comparing the numbers shows that the numbers in this range are

0.2875 and 2/7

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The formula for the area of a circle is given as follows:

A = πr².

The area of a circle of radius r is given by the multiplication of the number π and the square of the radius, according to the equation presented as follows:

A = πr².

Hence, for example, for a circle of radius of 5 units, the area is given as follows:

A = π x (5 units)² = 25π units².

The diameter of a circle is twice the radius, hence the radius is half the diameter, and as a function of the diameter, the area will be given as follows:

A = 0.25πd².

As the diameter in the context of this problem is:

r² = (0.5d)² = 0.25d².

The problem is incomplete, hence the area of the circle was explained in general terms.

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Answer: 56 miles

Step-by-step explanation:

Tristan ran 7 miles, multiply by 4 because Kimberly ran 4 times as many miles as Tristan. 7x4=28

Next, 28x2=56 because Dominic ran 2 times as many miles as Kimberly, which is 28 times 2.
So Dominic ran 56 miles in total.

Answer:

140

Step-by-step explanation:

It's 140 because 35 x 4 (4 TIMES) meaning you multiply. 35 x 4 is 140, meaning there are 140 alligators.

The amount of tax that the executive would pay on his income is; 20000 GBP

Tax is defined as a compulsory payment that is levied on the income or on the sales of specific goods and services. Tax is usually imposed by the government to get a variety of macroeconomic objectives.

Now, income tax is the tax that is levied on the income of an individual. There are different types of taxes, such as progressive tax which levies a higher tax percentage on those that earn higher incomes This means invariably that the tax rate increases as income increases.

We are given;

Gross Amount executive earns = 50,000 GBP.

We are told that any earnings between 33,500 GBP and 150,000 GBP are taxed at 40%.

Thus;

Tax that would be paid = tax rate * gross income

Tax that would be paid = 50000 * 0.4 = 20000 GBP

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Answer: 11,000

Step-by-step explanation:

The person earns 50,000 GBP, so they will stop at the tier 3 level of tax.

The first 11,500 GBP is tax free. They will be taxed 20% on (33,500−11,500)=22,000 GBP, and they will be taxed 40% on (50,000−33,500)=16,500 GBP. Hence the total tax (in GBP) they need to pay is

Total Income Tax=11,500×0%+22,000×20%+16,500×40%=0+22,000×20100+16,500×40100=0+4,400+6,600=11,000

Answer:

7. what are the fold down options for this question exactly?

1. C and E

3. B and D

Step-by-step explanation:

7.

1. function 1 has a slope of 2/3 and function 2 has a slope of 3 so they are both positive rates of change, and the y intercept (the value that y has when it passes through x = 0) for function 1 is -6 while the y intercept for function 2 is -3.

3. K has a y intercept of 8 compared to the 3 that J has, and J has a slope of 5 compared to the 3 that K has.