Need help with practice problem please

Answer:

[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]

The inverse function is to calculate the number of rides; given the amount paid

Step-by-step explanation:

Given

[tex]Admission = 15[/tex]

[tex]Ride = 3[/tex] per ride

Required

Explain the inverse function

First, we calculate the function

Let x represents the number of rides

So:

[tex]f(x) = Admission + Ride * x[/tex]

[tex]f(x) = 15 + 3 * x[/tex]

[tex]f(x) = 15 + 3x[/tex]

For the inverse function, we have:

[tex]y = 15 + 3x[/tex]

Swap x and y

[tex]x = 15 + 3y[/tex]

Make 3y the subject

[tex]3y = x - 15[/tex]

Make y the subject

[tex]y =\frac{x}{3} - 5[/tex]

Replace y with the inverse function

[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]

The above is to calculate the number of rides; given the amount paid

Answer:

step 4 I believe

Step-by-step explanation:

Answer:

Increasing the number of people allows more variety and diversity, which makes the sample more accurate.

Answer:

[tex]2x + 8[/tex]

Step-by-step explanation:

Area of triangle equal

[tex] \frac{b \times h}{2} = a[/tex]

where b is the base and h is the height.

Plug in what we know.

[tex] \frac{b \times 6x}{2} = 6 {x}^{2} + 24x[/tex]

Multiply 2 by both sides.

[tex]b \times 6x = 2(6 {x}^{2} + 24x)[/tex]

Divide 6x by both sides.

[tex]b = \frac{12 {x}^{2} + 48x }{6x} = 2x + 8[/tex]

Answer:

silly question...I used technology to "cheat"

it is 11/23

34155 32775 33649 34485

72105 72105 72105 72105

Step-by-step explanation:

30,816 books would go into 1,284 containers which would weigh 15,408kg with all the books in them or 2,568kg with the books not in them.

Answer :

Let in Triangle abc,

a=90,

b = (we have to find)

c = (we have to find)

c + 144=180 (linear pair)

c = 180 - 144

c = 36

a + b + c = 180 (Angle sum property)

90 + b + 36 = 180

126 + b = 180

b = 180-126

b = 54

Answer:

4444

Step-by-step explanation:

Answer:

819

Step-by-step explanation:

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Answer:

[tex]60x+75[/tex]

Step-by-step explanation:

We want to find the total amount of money (in cents) of the expression:

[tex]\text{$x$ nickels, $(x+3)$ quarters, and $3x$ dimes}[/tex]

Since each nickel is worth five cents, each quarter 25 cents, and each dime ten cents, we can write that:

[tex]\displaystyle \text{Total}=5(x)+25(x+3)+10(3x)[/tex]

Simplify. Distribute:

[tex]T=5x+25x+75+30x[/tex]

Combine like terms. Therefore, the total amount of money (in cents) is represented by:

[tex]T=60x+75[/tex]

Answer:

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{101}{\sqrt{90}} = 27.4[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 436 - 27.4 = 408.6.

The upper end of the interval is the sample mean added to M. So it is 436 + 27.4 = 463.4.

460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460

Answer:

the quotient of x and 3

Step-by-step explanation:

x divided by 3

division answers are called quotients

Answer:

Step-by-step explanation:

x/3

• the difference of x and 3

• the quotient of 3 and x

• the product of 3 and x

• the quotient of x and 3  is correct.  We are dividing x into 3, not 3 into x.

Answer: 50yd

Step-by-step explanation:

We know that the area of any rectangle is length times width.  The perimeter is the sum of twice the length and twice the width.

Let width = x

Let length = 4x

Area = 100m2

Next, we can write an equation using these variables and formula for area.

4x2 = 100

x2 = 25

x = -5      and        x = 5

Since the dimensions cannot be negative, we accept the positive value:

x = 5

Next, we can substitute this value of x into the variables.

width = 5 m

length = 20 m

Finally, we can find the perimeter by plugging in these dimensions into the perimeter formula,

Perimeter = 2(5 m) + 2(20 m)

              = 10 m + 40 m

              = 50 m  

Answer:

Santino rented the canoe for 8 hours.

Step-by-step explanation:

The total bill is represented by the formula r(h) = $10 + ($7.50/hour)h,

where h is the number of hours over which the canoe is rented.

If the total bill is $70, then $70 = $10 +  ($7.50/hour)h.

Solve this for h.  Start by subtracting $10 from both sides, obtaining:

$60 =  ($7.50/hour)h.

Dividing both sides by ($7.50/hour), we get:

           $60

h = --------------------- = 8 hours

      ($7.50/hour)

Santino rented the canoe for 8 hours.

Answer:10.2 inches

Step-by-step explanation:

we know that

In this problem we have two cases

First case

The given lengths are two legs of the right triangle

so

Applying the Pythagoras Theorem

Find the length of the hypotenuse

substitute

Second case

The given lengths are one leg and the hypotenuse

so

Applying the Pythagoras Theorem

Find the length of the other leg

substitute

Find the difference between the two possible lengths of the third side of the triangle

so

Answer:

The difference between the two possible lengths for the third side of the triangle is about 10.21 inches.

Step-by-step explanation:

We are given that the lengths of two sides of a right triangle is 12 inches and 15 inches.

And we want to find the difference between the two possible lengths of the third side.

In the first case, assume that neither 12 nor 15 is the hypotenuse of the triangle. Then our third side c must follow the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute in known values:

[tex](12)^2+(15)^2=c^2[/tex]

Solve for c:

[tex]c=\sqrt{12^2+15^2}=\sqrt{369}=\sqrt{9\cdot 41}=3\sqrt{41}[/tex]

In the second case, we will assume that one of the given lengths is the hypotenuse. Since the hypotenuse is always the longest side, the hypotenuse will be 15. Again, by the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute in known values:

[tex](12)^2+b^2=(15)^2[/tex]

Solve for b:

[tex]b=\sqrt{15^2-12^2}=\sqrt{81}=9[/tex]

Therefore, the difference between the two possible lengths for the third side is:

[tex]\displaystyle \text{Difference}=(3\sqrt{41})-(9)\approx 10.21\text{ inches}[/tex]

Answer:

121.857

Step-by-step explanation:

6×7r = 5118

42r = 5118

r = 121.857

Answer:

121.8571428571429

Step-by-step explanation:

r=  5118/42

Answer:

37

Step-by-step explanation:

In the given figure the angles are vertically opposite angles so ;

4x + 2 = 150

or, 4x = 148

or, x = 37 ans .

Answer:

75 hombres y 125 mujeres

Step-by-step explanation:

lo siento, yo no hablo español bien

Answer:

... ..... C is the answer

Answer:

Paige is incorrect.  g(x) has a steeper slope

Step-by-step explanation:

The slope for f(x)  is

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

   = (17/2 - 5/2) / ( -1 - -6)

    = (17/2 - 5/2) / ( -1 +6)

    = (12/2)/5

    = 6/5

The slope for g(x)  is

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

   = (-1 - 13/3) / ( 6 - 2)

    =(-3/3 -13/3) / (6-2)

    (-16/3)/4

     -16/3 * 1/4

   - 4/3

Comparing the magnitudes

|6/5|   |-4/3|

|6/5*3/3|     |-4/3*5/5|

|18/15|           |20/15|

|20/15| is greater so it has a steeper slope

g(x) has a steeper slope

Answer:

y = 5x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 5, then

y = 5x + c ← is the partial equation

To find c substitute (2, 3) into the partial equation

3 = 10 + c ⇒ c = 3 - 10 = - 7

y = 5x - 7 ← equation of line

Answer: 1547 bricks are required to build the staircase.

Step-by-step explanation:

We are given:

Number of bricks in the first step, [tex]a_1[/tex] = 131

Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126

Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121

Sequence become:

131, 126, 121, .....

These are in arithmetic progression where a = 131 and d (common difference) = -5

To calculate the sum of an AP, we use the formula:

[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]

where,

n = number of terms = 17

Putting values in above equation, we get:

[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]

Hence, 1547 bricks are required to build the staircase.

Answer:

[tex]x(x+y)^2[/tex]

Step-by-step explanation:

We are given that

[tex]x^3y+2x^2y^2+xy^3[/tex] and [tex]2x^3+4x^2y+2xy^2[/tex]

We have to find HCF.

[tex]x^3y+2x^2y^2+xy^3=xy(x^2+2xy+y^2)[/tex]

=[tex]xy(x+y)^2[/tex]

By using the formula

[tex](x+y)^2=x^2+2xy+y^2[/tex]

[tex]xy(x+y)^2=x\times y\times (x+y)^2[/tex]

[tex]2x^3+4x^2y+2xy^2=2x(x^2+2xy+y^2)[/tex]

[tex]=2x(x+y)^2[/tex]

[tex]2x(x+y)^2=2\times x\times (x+y)^2[/tex]

HCF of ([tex]x^3y+2x^2y^2+xy^3,2x^3+4x^2y+2xy^2[/tex])

[tex]=x(x+y)^2[/tex]

The last equation says z = 3, so that in the second equation we get

y + 2z = y + 6 = 5   ==>   y = -1

and in turn, the first equation tells us

x - 2y + 2z = x + 2 + 6 = x + 8 = 9   ==>   x = 1

So the solution to the system is (x, y, z) = (1, -1, 3).

Answer:

It's letter c

Step-by-step explanation:

you have to × the 0.5 and 1

Answer:

-3

Step-by-step explanation:

Answer:

10145

Step-by-step explanation:

5 times 950 equals 4750

and 6.5 times 830 equals 5395

add first and second value

4750 + 5395 equals 10145

there is no arguing

Answer:

10145 km

Step-by-step explanation:

Time x speed = Distance

5 x 950 = 4750

6.5 x 830 = 5395

add together = 10145

The Answer is -0.985

I just took the test.