Answer:
RT = 20
Step-by-step explanation:
Point S is on line segment
R------------S------------T
RS + ST = RT
Given
ST=3x-8
RT=4x
RS=4x-7,
Step 1
We find x
4x - 7 + 3x - 8 = 4x
4x + 3x -7 - 8 = 4x
7x - 15 = 4x
7x - 4x = 15
3x = 15
x = 15/3
x = 5
Step 2
We find RT
RT = 4x
x = 5
RT = 4 × 5
RT = 20
The numerical length of RT is 20
Answer:
Step-by-step explanation:
The expected value is the probability of an event multiplied by the number of times the event happens. And if there is more than 1 event, the expected value is the sum of those.
There are 52 cards in a deck.
There are 12 face cards in a deck. (gain 10)
There are 4 ace in a deck. (gain 20)
Any other card is 36 of them. (lose 5)
The probability of face card is 12/52
The probability of ace is 4/52
The probability of any other card is 36/52
Thus the expected values is:
(12/52)(10) + (4/52)(20) + (36/52)(-5) = $0.38
Answer: A, C, and D
Step-by-step explanation:
A terminating decimal is a decimal that has an end. In other words,
is one, but
is not.
✓ A. 0.032
✗ B. 0.999...
✓ C. 0.525
✓ D. 0.75
The correct answer is x = 1/28y^2
(a) If the particle's position (measured with some unit) at time <em>t</em> is given by <em>s(t)</em>, where

then the velocity at time <em>t</em>, <em>v(t)</em>, is given by the derivative of <em>s(t)</em>,

(b) The velocity after 3 seconds is

(c) The particle is at rest when its velocity is zero:

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

In interval notation, this happens for <em>t</em> in the interval (0, √11) or approximately (0, 3.317) s.
(e) The total distance traveled is given by the definite integral,

By definition of absolute value, we have

In part (d), we've shown that <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √11 as

and by the fundamental theorem of calculus, since we know <em>v(t)</em> is the derivative of <em>s(t)</em>, this reduces to
