Suppose you have a random variable that is uniformly distributed between 80 and 667. What is the probability of observing a random draw greater than or equal to 314? Answer to three decimal place if necessary.


Answer 1


P(x>=314) = 354/588 = 0.602

Step-by-step explanation:

At first, we will find the sample space S

S = 667-80+1.  i.e 80 and 667 are included

S= 588, so we have total of 588 numbers in the series

now comes the number greater or equal to 314

we will get total of 354 number greater than or equal to 314

x = 667-314+1 = 354

p( number >= 314) = (numbers >= 314)/total sample space

p= 354/588

p= 0.602

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The distance a vehicle travels can be found by using the formula d = rt, where d is the total distance traveled, r is the rate of speed, and t is the amount of time spent traveling. Grace drives her truck a distance of 80 miles at a steady speed of 50 miles per hour. To the nearest hour, how many hours does she spend driving?



She spends 2 hours driving.

Step-by-step explanation:

The formula given is:

d = rt

In which d is the distance traveled, r is the rate of speed, and t is the amount of time spent traveling.

Grace drives her truck a distance of 80 miles at a steady speed of 50 miles per hour.

This means that d = 80, r = 50

To the nearest hour, how many hours does she spend driving?

We have to find t. So

d = rt

50t = 80

t = (80)/(50)

t = 1.6

Rounding to the nearest hour

She spends 2 hours driving.

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1479 g

Step-by-step explanation:

The volume of the bar is

V = l*w*h

  = 10*3*5

  = 150 cm^3

Now multiply by the density

150 cm^3 * 9.86 g/ cm^3 =1479 g

What are the coordinates of point b on ac such that ab=2/5ac




Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = (mx_2+nx_1)/(m+n)

and y = (my_2+ny_1)/(m+n)

where (x_1, y_1) and (x_2,y_2) are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = (2* 2+(-8)* 5)/(2+5)

  = -(36)/(7)

y = (2* 5+5* 6)/(2+5)

  = (40)/(7)

Therefore, coordinates of pint B will be,


Final answer:

The coordinates of B on segment AC such that AB=2/5AC are given by line segment division theorem as ((2x2 + 5x1) / 7 , (2y2 + 5y1)/ 7), where A is (x1, y1) and C is (x2, y2).


The question is asking for the coordinates of point B on line segment AC such that the length of AB is 2/5 times the length of AC.

Since we don't have any specific coordinates for points A, B and C, we can't determine exact coordinates for point B. However, we can describe how to find B based on given points A and C.

If A and C have coordinates (x1, y1) and (x2, y2), respectively, then the coordinates of B can be found using the theorem of line segment division. This theorem says that the coordinates of the point dividing a line segment in the ratio m:n are given by:

((mx2 + nx1) / (m+n) , (my2 + ny1)/ (m+n))

Given the ratio is 2:5, m is 2 and n is 5, substitute the values into the formula:

((2x2 + 5x1) / (2+5) , (2y2 + 5y1)/ (2+5))

So, point B is at ((2x2 + 5x1) / 7 , (2y2 + 5y1)/ 7).

Learn more about Coordinates finder here:


Help please points and brainlest!!



0.20m + 650 < 755

Step-by-step explanation:

So you know that m is the total amount of miles that he travelled, so the cost of these miles would have been 0.20m. The total also included 650 and it has to be less than 755. Thus the equation would be 0.20m + 650 < 755 which means that the sum of 0.20m (cost of miles) and 650 (night cost) is less than (< means less than something else on the right) 755.

Which procedure would you use to convert a fraction to a decimal?1
Convert to a decimal.
to a decimal?


Answer: Since 1 is a natural number, there is a decimal in every number in history. It is invisible, but that is only because we don't put decimals if it is not needed. But the decimal on the number always exists. Therefore, 1 in a decimal is 1.0. Same with 5. 5 is also written as 5.0.

Hope this helps!

99 Points + Brainliest answer to first person.Which is the focus of a parabola with equation y^2 = 4x?
A). (–1, 0)
B). (0, –1)
C). (0, 1)
D). (1, 0)



  D).  (1, 0)

Step-by-step explanation:

The parabola opens to the right, so the focus will be to the right of the vertex at (0, 0). The only answer choice with a positive x-value is D.


The equation of a parabola with vertex (0, 0) can be written as

  y^2 = 4px

where p is the distance from the vertex to the focus. Here, that distance is 1.


D). (1, 0)  this is the only positive answer

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