Evaluate 2x-2 + y 2 / 3 for x = 1.5 and y = 3. Show all of your work.

With a perfectly balanced roulette wheel, in the long run, red numbers should turn up 18 times in 38. To test its wheel, one cas

topjm [15]

Answer:

a) more than 18/38

b) The null says that the percentage of reds in the box is 2842.105. The alternative says that the percentage of reds in the box is -0.933521

c) z= -0.933521 , p≤ z= 17.105%

d) p-value is 17%

Step-by-step explanation:

1. We are counting the number of reds, so we have a box with "1" s for reds and "0"s for others. The question is what proportion of 1's and 0' are in the box.

a) The null hypothesis is that the wheel is balanced, so the box contains 18 "1"s and 20 "0"s. Or you might state this in terms of the proportion of 1's (18/38) and 0's (20/38). The alternative hypothesis if that the wheel favors reds, so the proportion of 1's is more than 18/38.

b) Under the null hyp., we expect 6000*(18/38)= 2842.105 Reds. The SE is sqrt(6000)* SD(Box)= Sqrt(6000)*(1-0)*sqrt((18/38)*(20/38))= 38.67615. We observed2806, which is fewer than we expected. The question is , is it much fewer that we suspect foul play, or it is the usual sort of variation we expect due to chance? The test statistic is z=(obs-expected)/SE =(2806-2842.105)/38.67615= -0.933521.

c) The p-value is the probability of gettinga test statistic as extreme or morer extreme than this, which in this case means seeing a test statistic less than or equal to - 0.933521. The closest value gives a probability of (100-65.79)/2 = 17.105%

d) If we reject H0 and claim the roullette wheel is unfair, then there's a 17.105% chance we are wrong. This is a large probability of making a serious mistake, and it would be reasonable to not reject and conclude that there is insufficient evidence to suspect the wheel is unfair. (we would reject H10 if the p-value were less than 5%. Since it is 17%, we won't reject)

6 0

2 years ago

It takes 12 minutes to fill an entire bathtub using both the cold and hot water. If just the cold water is used, it takes 18 min

Kipish [7]

Answer:

<h2>It takes 36 minutes to fill the bathtub using just hot water.</h2>

Step-by-step explanation:

We are gonna name V the complete volume of the bathtub, which is filled a certain amount of minutes. Each filling rate or speed is gonna be expressed as: $\frac{V}{t}$ .

So, if we apply this consideration to each case we have:

Using cold and hot water: $\frac{V}{12}$

Using only cold water: $\frac{V}{18}$

Using only hot water: $\frac{V}{x}$ ; because we don't knot the time it takes to fill the bathtub with hot water.

Now, as you can see, Cold and Hot water is a sum of cold water only and hot water only:

$\frac{V}{12}=\frac{V}{18}+\frac{V}{x}$

Solving the equation for x:

$\frac{V}{12}=\frac{xV+18V}{18x} \\\frac{V}{12}=\frac{(x+18)V}{18x}\\\\\frac{18xV}{V}=12(x+18)\\18x=12x+216\\18x-12x=216\\6x=216\\x=\frac{216}{6}=36$

Therefore, it takes 36 minutes to fill the bathtub using just hot water.

7 0

2 years ago

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How do you do solve for this again? Picture above

Goshia [24]

Answer:

Step-by-step explanation:

Do you remember the formula so that you can solve this problem??

4 0

2 years ago

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Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and th

White raven [17]

Let

t--------> the time in hours

d-------> the distance in miles

we know that

$d=16t$

this is a linear equation that represent the scenario

in this equation the independent variable is the time t and the dependent variable is the distance d

The distance's equation in function notation is equal to

$f(t)=16t$

Using a graph tool

see the attached figure

The domain of the function is the interval----------> [0,∞)

$t\geq0$

The range of the function is the interval-------> [0,∞)

$f(t)\geq0$

Statements

a) The independent variable, the input, is the variable d, representing distance

The statement is false

Because the independent variable is the variable t

b) The distance traveled depends on the amount of time Marlene rides her bike

The statement is true

Because the distance's equation in function notation is equal to

$f(t)=16t$

c) The initial value of the scenario is 16 miles per hour

The statement is false

Because $16$ represent the rate or the slope of the linear equation

d) The equation t = d + 16 represents the scenario

The statement is false

Because, the scenario is represented by the function $f(t)=16t$

e) The function f(t) = 16t represents the scenario

The statement is true

8 0

2 years ago

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Point T, the midpoint of segment RS, can be found using the formulas x = (6 – 2) + 2 and y = (4 – 6) + 6. What are the coordinat

Fiesta28 [93]

Question:

Point T, the midpoint of segment RS, can be found using the formulas x = (1/2) (6 – 2) + 2 and y = (1/2) (4 – 6) + 6. What are the coordinates of point T?

Answer:

$T(4,5)$