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zheka24 [161]
2 years ago
5

An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is

programmed to go on at a randomly selected time after the subject clicks "Start." The density curve models the amount of time the subject has to wait for the light to flash. a. What height must the density curve have? Justify your answer. b. About what percent of the time will the light flash more than 3.75 seconds after the subject clicks "Start"? c. Calculate and interpret the 38th percentile of this distribution.
Mathematics
1 answer:
Ganezh [65]2 years ago
4 0

Answer:

(a) 0.20

(b) 31%

(c) 2.52 seconds

Step-by-step explanation:

The random variable <em>Y</em> models the amount of time the subject has to wait for the light to flash.

The density curve represents that of an Uniform distribution with parameters <em>a</em> = 1 and <em>b</em> = 5.

So, Y\sim Unif(1,5)

(a)

The area under the density curve is always 1.

The length is 5 units.

Compute the height as follows:

\text{Area under the density curve}=\text{length}\times \text{height}

                                          1=5\times\text{height}\\\\\text{height}=\frac{1}{5}\\\\\text{height}=0.20

Thus, the height of the density curve is 0.20.

(b)

Compute the value of P (Y > 3.75) as follows:

P(Y>3.75)=\int\limits^{5}_{3.75} {\frac{1}{b-a}} \, dy \\\\=\int\limits^{5}_{3.75} {\frac{1}{5-1}} \, dy\\\\=\frac{1}{4}\times [y]^{5}_{3.75}\\\\=\frac{5-3.75}{4}\\\\=0.3125\\\\\approx 0.31

Thus, the light will flash more than 3.75 seconds after the subject clicks "Start" 31% of the times.

(c)

Compute the 38th percentile as follows:

P(Y

Thus, the 38th percentile is 2.52 seconds.

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Assoli18 [71]

Answer:

-3/2

Step-by-step explanation:

y=mx +b

where m is the slope and b is the y intercept

we just need to rewrite 3x+2y+18=0 to look like that

We need to get y by itself

3x+18= -2y

we need y to be positive and to have no number in front of it (no coeficcent)

y= -3/2x-9

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2 years ago
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Find the output (y) of the function y=6x+4 if the input (x) is 2
Dmitry_Shevchenko [17]

Answer:

f(2) = 16

or

y = 16

Step-by-step explanation:

Step 1: Write out function

y = 6x + 4

Step 2: Define variable for problem

<em>x</em> = 2

Step 3: Plug into function f(x)

f(2) = 6(2) + 4

f(2) = 12 + 4

f(2) = 16

Step 4: Change f(2) to y

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Triangle A B C is reflected across line m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated
Helga [31]

Answer:

  1. reflection across line m
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Step-by-step explanation:

The problem statement tells you exactly what the transformations are.

The first transformation is reflection across line m.

The second transformation is rotation about point A'.

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2 years ago
A rectangular field is 95 meters long and 65 meters wide. Give the length and width of another rectangular field that has the sa
Lena [83]

Answer:

There are a ton of answers. For instance, 1m by 159m.

Step-by-step explanation:

The formula for the area is a=l*w, where l and w are constants.

The formula for perimeter is p=2l+2w

The question wants another rectangle that has the same perimeter, but a smaller area.

The perimeter of the two fields has to be:

p=(2*95)+(2*65)\\p=190+130\\p=320

Thankfully, the question never specified how much smaller the area has to be. So let's go to the logical extreme and make it 1 meter wide. To conserve the perimeter, we'd have to add the removed 64 meters to the original 95 meters of length, resulting in a rectangle with a width of 1m and a length of 159m. This results in an area of exactly 159 m^{2}. The original rectangle had an area of 6175m^{2}. Mission accomplished!

But why stop there? Let's go even further down this rabbit hole!

Instead of 1, why don't we take it several steps further and use 0.0000001? At that point, the length would end up being  159.9999999m.

The area would be 0.00001599999999 m^{2}.

Let's go further!!

Width: 0.00000000000000000001

Length: 159.99999999999999999999

Area: 0.00000000000000000001599999999999999999999 (approximate).

One more, for old time's sake.

Width: 0.00000000000000000000000000000000000000000000000001m

Length: 159.99999999999999999999999999999999999999999999999999m

Area: 0.00000000000000000000000000000000000000000000000015999999999999999999999999999999999999999999999999999 m^{2}

At that point, there's so little area in the plot of land that you could claim it has no area!

5 0
2 years ago
Hay guys can you plz help
snow_tiger [21]

We can notice from the figure that : Area of the home plate is equal to sum of the Area of the rectangle ( 8 in x 15 in) and Area of the triangle with height 6 in and base 15 in.

Area of the rectangle : Length x Width

⇒  Area of the rectangle = 15 x 8 = 120 in²

Area of the triangle : 1/2 x Base x Height

⇒  Area of the triangle = 1/2 x 15 x 6 = 45 in²

Area of the home plate = Area of rectangle + Area of triangle

⇒ Area of the home plate = 120 in² + 45 in² = 165 in²

<u>Answer</u> : D

3 0
2 years ago
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