Answer:
1/2 = r
Step-by-step explanation:
7r + 21 = 49r
Subtract 7r from each side
7r-7r + 21 = 49r-7r
21 = 42r
Divide each side by 2
21/42 = 42r/42
1/2 = r
Answer:
a) 0.96
b) 0.016
c) 0.018
d) 0.982
e) x = 2
Step-by-step explanation:
We are given with the Probability density function f(x)= 2/x^3 where x > 1.
<em>Firstly we will calculate the general probability that of P(a < X < b) </em>
P(a < X < b) =
=
=
{ Because
}
=
=
=
=
a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }
Comparing with general probability we get,
P(1 < X < 5) =
=
= 0.96 .
b) P(X > 8) = P(8 < X < ∞) = 1/
- 1/∞ = 1/64 - 0 = 0.016
c) P(6 < X < 10) =
=
= 0.018 .
d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)
=
+ (1/
- 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982
e) We have to find x such that P(X < x) = 0.75 ;
⇒ P(1 < X < x) = 0.75
⇒
= 0.75
⇒
= 1 - 0.75 = 0.25
⇒
=
⇒
= 4 ⇒ x =
Therefore, value of x such that P(X < x) = 0.75 is 2.
Answer: 40
Step-by-step explanation:
1 hour and 30 min is 15 pages read
If you read for three hours its 30 pages
An hour and a half is three parts of 30 so three parts of 15 is five
But you need a whole hour so its ten
Then you add 10 and 30
Its 40 pages in 4 hours.
Answer:
The y-intercept of the equation is 100 and represents the initial studio-use fee.
Step-by-step explanation:
In this equation, our t variable (time) is the equivalent of the x-variable on a graph. This is because it is the variable that we 'change' to see its impact on y. We see how the amount of hours affects the price. So our P variable (price) is the equivalent of y on a graph. The y-intercept is where the line crosses the y-axis on a graph. At this point, x=0.
Since P is our y, and t is our x, to find the y-intercept, we simply need to make t = 0.
P = 50(0) + 100
P = 100
Therefore the y-intercept is 100.
In this context, t represents time, so even though the studio has been used for 0 hours, the price is still 100. This is because the 100 represents the initial studio-use fee, and using it for certain amounts of time adds onto the initial fee of $100. The hourly fee is represented by 50t so it costs $50 more for each hour of use.
Hope this helped!