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3 years ago

A wheel has 10 equally sized slices numbered from 1 to 10.

1 answer:

4 0

The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1

Total numbers on wheel = total possible outcomes = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Grey colored portion = {3}

White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}

X = Event that wheel stops on a white slice

P(X) = number of white slices ÷ total number of slices

P(X) = 9 / 10 = 0.9

P(not X) = 1 - P(X)

P(not X) = 1 - 0.9 = 0.1

Therefore, the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1

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Design a Roller Coaster Portfolio

scoray [572]

1) The domain is [0,300]. The range is [0,250]

2) The slope for the initial climb is 3.57. The equation of the line is $y=3.57 x$

3) The rate of change of the second hill is -1.4

4) The rate of change of the third hill is -2.1

5) The blue hill is steeper

6) It is not a function

Step-by-step explanation:

The domain of a function is the set of values of x (the input) for which the function itself is defined.

Instead, the range of a function is the set of values of y (the output) that the function can take.

To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between

x = 0 and x = 300

So, the domain is [0,300].

To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between

y = 0 and x = 250

So, the range is [0,250].

The slope of a function in a certain range is given by

$m=\frac{\Delta y}{\Delta x}$

where

$\Delta y$ is the change in the y-coordinate

$\Delta x$ is the change in the x-coordinate

For the initial climb (pink line), we have:

$\Delta y = 250 - 0 = 250\\\Delta x = 70 - 0 = 70$

Therefore, the slope in this part is

$m=\frac{250}{70}=3.57$

We can now write the equation of the line in the form

y = mx + b

where b is the y-intercept: since it is zero, the line has simply the form

$y=mx \rightarrow y = 3.57 x$

Again, to calculate the slope of the hill, we use:

$m=\frac{\Delta y}{\Delta x}$

where

$\Delta y$ is the change in the y-coordinate

$\Delta x$ is the change in the x-coordinate

For the green hill, we have:

$\Delta y = 60-200 = -140$

$\Delta x = 300-200 = 100$

So the rate of change is

$m=\frac{-140}{100}=-1.4$

As before, the rate of change of the hill is

$m=\frac{\Delta y}{\Delta x}$

For the blue hill, we have:

$\Delta y = 30-230 = -300$

$\Delta x = 200-60 = 140$

So the rate of change is

$m=\frac{-300}{140}=-2.1$

To know which hill is steeper, we need to compare the magnitude of their rate of change.

In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.

For the green hill:

$|m| = 1.4$

For the blue hill:

$|m|=2.1$

We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.

A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).

This means that a function cannot have multiple values of y for the same x (the input).

By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.

Learn more about functions:

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5 0

4 years ago

Read 2 more answers

Serena makes $9 per hour cutting lawns. Each day, she earns about $15 in tips. If Serena made no less than $110 on Monday, which

Serhud [2]

The total amount Serena earns is the sum of her regular wage and the tips. The amount she earns from the wage is equal to 9h. This total should be more than or equal to $110. This is mathematically expressed as,
9h + 15 ≥ 110

3 0

3 years ago

Read 2 more answers

The equation of the line passing through the points (3, 16) and (5, 10) can be expressed as y = mx + b. Give the value of b

Alenkinab [10]

we are given two points as

(3, 16) and (5, 10)

firstly , we will find slope

slope is m

so, we can use formula

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug points

$m=\frac{10-16}{5-3}$

$m=\frac{-6}{2}$

$m=-3$

we can plug it in y=mx+b

we get

$y=-3x+b$

now, we can select any one points

and find b

(3,16)

x=3 and y=16

$16=-3*3+b$

we can find b

$b=25$

now, we can plug back b

and we get

$y=-3x+25$

so, equation is

$y=-3x+25$

and

$b=25$ ...............Answer

8 0

3 years ago

Did the scale factor of 0.75 enlarge reduce or stay the same?

elixir [45]

Answer:

$\huge\boxed{\sf Reduces}$

Step-by-step explanation:

Since the scale factor of 0.75 is less than 1, So the dilated image is a reduced image.

Thus the scale factor of 0.75 reduces the dilated image.

$\rule[225]{225}{2}$

Hope this helped!

<h3>~AnonymousHelper1807</h3>

6 0

3 years ago

Read 2 more answers

If a = 5^x, b = 5^y and a^y×b^x = 25 then prove that: xy =1

avanturin [10]

$a = {5}^{x} \\ b = {5}^{y} \\ {a}^{y} \times {b}^{y} = 25 \\ prove \: ( {5}^{x} )^{y} \times ( {5}^{y} ) ^{x} = 25 \\ {5}^{xy} \times {5}^{yx} = {5}^{2} \\ {5 }^{xy + yx} = 5^{2} \\ 5^{2xy} = {5}^{2} \\ is \: \: 2xy = 2 \\ xy = \frac{2}{2} \\ xy = 1$

3 0

3 years ago