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Math Problems
Precalculus
Mean, variance, and standard deviation of binomial distributions
Two rental car companies are running specials this month. At Rob's Rentals, customers will pay
$
50
\$50
$50
to rent a mid-sized car for the first day, plus
$
4
\$4
$4
for each additional day. At Washington Rent-a-Car, the price for a mid-sized car is
$
60
\$60
$60
for the first day and
$
3
\$3
$3
for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How many additional days would that take?
\newline
Write a system of equations, graph them, and type the solution.
\newline
____ additional days
\newline
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Mr. Johnston is contemplating which chauffeured car service to take to the airport. The first costs
$
30
\$30
$30
up front and
$
2
\$2
$2
per mile. The second costs
$
20
\$20
$20
plus
$
3
\$3
$3
per mile. For a certain driving distance, the two companies charge the same total fare. What is the total fare?
\newline
Write a system of equations, graph them, and type the solution.
\newline
_
_
_
_
\_\_\_\_
____
dollars
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Ken and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Ken starts with
10
10
10
points, and his little brother starts with
30
30
30
points. Ken gets
2
2
2
points for every successful shot, and his brother, since he is younger, gets
1
1
1
point for each successful shot. Eventually, the brothers will have a tied score in the game. How many additional shots will each brother have made?
\newline
Write a system of equations, graph them, and type the solution.
\newline
____ shots
\newline
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For his parents' anniversary party, Alvin is considering using one of two venues. A hotel in Lancaster will cost
$
80
\$80
$80
for a reservation, plus
$
10
\$10
$10
per person. A restaurant in the same city will cost
$
25
\$25
$25
per person, in addition to
$
50
\$50
$50
for the reservation. In order to make the best decision, Alvin figures out how many attendees it would take to have the venues cost the same amount. What would the total cost be?
\newline
Write a system of equations, graph them, and type the solution.
\newline
_
_
_
_
\_\_\_\_
____
dollars
\newline
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Megan recorded the temperature in her garden each morning for
6
6
6
days.
\newline
The mean of her six recorded temperatures was
\newline
2.
1
∘
C
2.1^{\circ}C
2.
1
∘
C
. The temperature on one of the days was
\newline
4.
1
∘
C
4.1^{\circ}C
4.
1
∘
C
.
\newline
What was the mean of her other
5
5
5
recorded temperatures? Give your answer as a decimal.
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Jennifer just got a job teaching sewing classes at In Stitches sewing center. In the classroom, there is a big bag with spools of thread for students to use. Before teaching her first class, Jennifer randomly picked some spools of thread from the bag. She got
7
7
7
blue,
4
4
4
black,
8
8
8
brown,
9
9
9
white,
5
5
5
green, and
2
2
2
yellow spools of thread.
\newline
Based on the data, what is the probability that the next spool of thread Jennifer picks will be green?
\newline
Write your answer as a fraction or whole number.
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Dave coaches a roller hockey team and has a big bin of hockey pucks he uses at practice sessions. He randomly grabs some pucks from the bin and throws them onto the rink for the upcoming practice. So far, he's grabbed
4
4
4
red,
3
3
3
orange,
1
1
1
yellow,
2
2
2
pink, and
2
2
2
green pucks.
\newline
Based on the data, what is the probability that the next puck Dave grabs will be green?
\newline
Write your answer as a fraction or whole number.
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Al released his balloon from the
10
10
10
-yard line, and it landed at the
16
16
16
-yard line. If the ball reached a height of
27
27
27
yards, what equation represents the path of his toss?
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Which event is most likely to occur?
\newline
Rolling a multiple of
3
3
3
on a six-sided die, numbered from
1
1
1
to
6
6
6
.
\newline
Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on red or blue or green.
\newline
Winning a raffle that sold a total of
100
100
100
tickets, if you buy
91
91
91
tickets.
\newline
Reaching into a bag full of
7
7
7
strawberry chews and
33
33
33
cherry chews without looking and pulling out a strawberry chew.
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Which event is most likely to occur?
\newline
Rolling an odd number on a twelve-sided die, numbered from
1
1
1
to
12
12
12
.
\newline
Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on red or blue or green.
\newline
Winning a raffle that sold a total of
100
100
100
tickets, if you buy
41
41
41
tickets.
\newline
Reaching into a bag full of
33
33
33
strawberry chews and
7
7
7
cherry chews without looking and pulling out a strawberry chew.
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Which event is most likely to occur?
\newline
Rolling a multiple of
3
3
3
on a eight-sided die, numbered from
1
1
1
to
8
8
8
.
\newline
Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on red or blue or purple.
\newline
Winning a raffle that sold a total of
100
100
100
tickets, if you buy
88
88
88
tickets.
\newline
Reaching into a bag full of
1
1
1
strawberry chews and
39
39
39
cherry chews without looking and pulling out a strawberry chew.
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Which event is most likely to occur?
\newline
Rolling a number greater than or equal to
3
3
3
on a eight-sided die, numbered from
1
1
1
to
8
8
8
.
\newline
Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on yellow or red.
\newline
Winning a raffle that sold a total of
100
100
100
tickets, if you buy
83
83
83
tickets.
\newline
Reaching into a bag full of
36
36
36
strawberry chews and
44
44
44
cherry chews without looking and pulling out a strawberry chew.
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Which event is most likely to occur?
\newline
Rolling a number greater than
4
4
4
on a twelve-sided die, numbered from
1
1
1
to
12
12
12
.
\newline
Spinning a spinner divided into five equal-sized sections colored red/green/yellow/blue/purple and landing on red or blue or yellow or green.
\newline
Winning a raffle that sold a total of
100
100
100
tickets, if you buy
40
40
40
tickets.
\newline
Reaching into a bag full of
16
16
16
strawberry chews and
44
44
44
cherry chews without looking and pulling out a strawberry chew.
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Which event is most likely to occur?
\newline
Rolling a number greater than or equal to
3
3
3
on a eight-sided die, numbered from
1
1
1
to
8
8
8
.
\newline
Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on blue or green.
\newline
Winning a raffle that sold a total of
100
100
100
tickets, if you buy
80
80
80
tickets.
\newline
Reaching into a bag full of
3
3
3
strawberry chews and
57
57
57
cherry chews without looking and pulling out a strawberry chew.
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0.30
P
+
0.25
G
=
57
0.30 P+0.25 G=57
0.30
P
+
0.25
G
=
57
\newline
A homeowner uses
G
G
G
hours of natural gas heat and
P
P
P
hours of heat from a pellet stove to heat her house one month, with a total of
57
57
57
therms of output. How many therms per hour does the pellet stove output?
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Four times a number decreased by
4
4
4
is between
−
40
-40
−
40
and
88
88
88
.
\newline
Find the interval for valid values. (The answer should be in interval notation.)
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