If a fair coin is flipped n times, the number of head/tail arrangements follows a geometric sequence. In the figure, if the coin is flipped 1 time, there are two possible outcomes, H or T . If the coin is flipped 2 times, then there are four possible outcomes: HH, HT, TH , and TT . a. Write a formula for the nth term of a sequence representing the number of outcomes if a fair coin is flipped n times. b. How many outcomes are there if a fair coin is flipped 10 times?
If a fair coin is flipped n times, the number of head/tail arrangements follows a geometric sequence. In the figure, if the coin is flipped 1 time, there are two possible outcomes, H or T . If the coin is flipped 2 times, then there are four possible outcomes: HH, HT, TH , and TT . a. Write a formula for the nth term of a sequence representing the number of outcomes if a fair coin is flipped n times. b. How many outcomes are there if a fair coin is flipped 10 times?
Solution Summary: The author explains the formula for the nth term of a sequence representing the number of outcomes, if the coin is flipped 1 times.
If a fair coin is flipped
n
times, the number of head/tail arrangements follows a geometric sequence. In the figure, if the coin is flipped
1
time, there are two possible outcomes,
H
or
T
. If the coin is flipped
2
times, then there are four possible outcomes:
HH, HT, TH
, and
TT
.
a. Write a formula for the nth term of a sequence representing the number of outcomes if a fair coin is flipped
n
times.
b. How many outcomes are there if a fair coin is flipped
10
times?
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
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