At an amusement park, 25 riders ride the race cars every 30 minutes and 20 riders ride the spinning swings every 20 minutes. Which ride will have more Riders each hour and how much more?​

Answer:

The correct answer is B.

Explanation:

Putting it into your calculator as you see it gives you the correct answer.

Have a good day! :)

Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Answer:

P=2(L+W)

42=2(12+W)

42=24+2w

2w=42-24

2w/2=18/2

w=9

Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

Answer:

the perimeter is given in__in__, the height in_in___, and area of the base in_in²__.

so

none of the above.

Answer:

d

Step-by-step explanation:

none of the above

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

m<2 = 70degrees

m<3 = 70degrees

m<4 = 110degrees

m<5 = 110degrees

m<6 = 70degrees

m<7 = 70degrees

m<8 = 110degrees

Step-by-step explanation:

A line has the angles of 180 degrees so if m<1 is 110 then m<2 must be 70degrees. Then m<4 is opposite side of m<1 so it has to be the same number of degrees and the same for m<3 is the opposite side of m<2.

You repeat the process with 5678

Answer:

3

Step-by-step explanation:

Answer:

distance is 5

mark me Brainliest please if satisfied with my answer

Step-by-step explanation:

A(-2, -3)

B (3, -1)

C(3, -3)

Steps:

Distance: 5

Steps:

Distance (d) = √(3 - -2)2 + (-3 - -3)2

= √(5)2 + (0)2

= √25

= 5

Slope and Angle:

ΔX = 3 – -2 = 5

ΔY = -3 – -3 = 0

Slope (m) =

ΔY

ΔX

= 0

θ =

arctan( ΔY )

ΔX

= 0°

Equation of the line:

y = 0x – 3

When x=0, y = -3

The distance between points A and C is 5 units.

Here, we have to find the distance between two points A(-2, -3) and C(3, -3), we can use the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²).

Where (x₁, y₁) are the coordinates of point A and (x₂, y₂) are the coordinates of point C.

Given:

Point A: (-2, -3)

Point C: (3, -3)

Plugging these values into the distance formula:

Distance = √((3 - (-2))² + (-3 - (-3))²)

Distance = √(5² + 0²)

Distance = √25

Distance = 5.

So, the distance between points A and C is 5 units.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The random number simulator of Molly's throws is an illustration of probability.

The probability of making both free throws is 30%

From the complete question, we understand that:

The simulator is based on numbers 0 to 9

Given that she makes 70% of her free throws, then it means that 7 of the 10 numbers would represent a successful throw, while the other three would represent a missed throw

So, we have:

From the random numbers, she has two successful free throws in:

21 50 64 66 42 03 --- 6 numbers of 20

The probability of making two free throws is then calculated as:

P = 6/20

Evaluate

P = 30%

Hence, the probability of making both free throws is 30%

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Answer:

b and d i think hope this helps

Step-by-step explanation:

Answer:

46.8 cm^3

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

Answer:

About 384 miles (correct me if I'm wrong but I think that's the answer)

The answer to the given question is 169.

13 * (((6 square) / (( 5 squared ) - (4 square))) + 9)

= 169

Therefore,  the correct value of the given question is 169

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Answer: x = 41

For x in the equation

5/25=9/(x+4)

5(x+4) =9(25)

5x + 20 = 225

5x = 205

x = 41

Therefore, the value of x for the equation 5/25=9/(x+4) is x = 41

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Answer:

b & c

Step-by-step explanation:

If the length of HJ is 7 unit then the length of EI is 14 unit.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

We are given a circle with center H.

Therefore, the radius of the circle is found as; HJ

Then the Diameter is the line from one point in the circle to the other point through the center of the circle.

Diameter of the circle = EI

Since we know that One of the theorems of a circle states that the angles in the same segments or on the same chord are equal.

Then the name of the chord is FG.

If the length of HJ is 7 unit then the length of EI is;

EI = 2 HJ

EI = 14 unit.

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The graph of the linear inequality is given by the image presented at the end of the answer.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The function for this problem is given as follows:

y = -3x/4 + 2.

Hence the graph crosses the y-axis at y = 2, and when x increases by 4, y decays by 3.

The inequality is given as follows:

y < -3x/4 + 2.

Meaning that points below the dashed line are the solution to the inequality.

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The number 1234567 cannot be written as a sum of two squares.

Let q = x^2+y^2,

Let a and b be two even numbers, such that

a= 2x and b = 2y

then

n = (2x)^2 + (2y)^2 = 4 (x^2+y^2)

implies n = 4q

Let a and b be two odd numbers, such that

a = 2x+1 and b = 2y+1

then

n = (2x+1)^2 + (2y+1)^2 = 4x^2+4y^2+1 = 4q+2

Let a be an even number and b be an odd number, such that

a= 2x and b = 2y+1

then

n = (2x)^2 + (2y+1)^2 = 4q+1

But, the given number 1234567 = (4×308641)+3 which is of the form 4q+3, hence it cannot be written as the sum of two squares.

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Answer:

First, remember that:

\(tan(x) = \frac{sin(x)}{cos(x)}\)

and:

\(sec(x) = \frac{1}{cos(x)}\)

Then we can rewrite the expression:

\(tan(x)*sin(x) + sec(x)*cos^2(x) = A\)

Where A is an equivalent expression.

as:

\(\frac{sin(x)}{cos(x)} *sin(x) + \frac{1}{cos(x)}*cos^2(x) = A\)

Then this is:

\(\frac{sin^2(x)}{cos(x)} + cos(x) = A\)

Now we can multiply both sides by cos(x), then:

\((\frac{sin^2(x)}{cos(x)} + cos(x))*cos(x) = A*cos(x)\)

\(sin^2(x) + cos^2(x) = A*cos(x)\)

And we know that the left term of the above equation is equal to 1, then:

\(1 = A*cos(x)\)

\(\frac{1}{cos(x)} = sec(x) = A\)

And A is equivalent to the original expression, then we get:

\(tan(x)*sin(x) + sec(x)*cos^2(x) = sec(x)\)

The simplification of the expression is sec(x)

Answer: D: 4.5

Step-by-step explanation:

So the Equation I used for this would be

6(2x+3) = 3(6x-3)

In Which the left is the Hexagon (The 6 is for the 6 Sides) and the right of the equation is the triangle (given the 3 for the 3 sides. In order to solve, we need to solve for x. Distribute the equation and your left with

12x+18=18x-9

-12x            +9

27=6x

Divide to get X by itself

and your left with

4.5 = x

Hope it helped.

Answer:

57

Step-by-step explanation:

this is the boybfiend

Answer:

The answer is option C : 6 tenths

Answer:

B. x = 62 because 147 – 85 = 62 and 85 + 62 = 147

Step-by-step explanation:

We are given that

\(\angle ABC=85^{\circ}\)

Exterior angle=\(147^{\circ}\)

We have to find the value of x.

We know that

Exterior angle=Sum of opposite interior angles of triangle

Using the property

\(x+85=147\)

Subtract 85 from both sides we get

\(x=147-85\)

\(x=62\)

Option B is true.

B. x = 62 because 147 – 85 = 62 and 85 + 62 = 147

Answer:

10/11

Step-by-step explanation: