Together, teammates
Pedro and Ricky got 2673 base hits last season.
Pedro had 279 more hits than Ricky.
How many hits did each player have?
P + R = 2673
P = (R + 279)
(R + 279) + R = 2673
2R + 279 = 2673
2R = 2394
R = 1197
P + 1197 = 2673
P = 1476
.
cosine equals adjacent over hypotenuse
cos(62o) = AB / 12
0.4695 = AB / 12
AB = 12 • 0.4695
AB = 5.634 rounds to 5.6
James is playing an arcade game with tokens. In the firstgame, he hits the jackpot and doubles the number of tokens that he has. In the second game, James wins 12 more tokens. In his third and final game, he loses 4 tokens. James now has 170 tokens. How many tokens did he have before he started playing the game?
Let "x" stand for the original amount
2x + 12 – 4 = 170
2x = 170 – 12 + 4
2x = 162
x = 81
Complementary angles add to 90o
Supplementary angles add to 180o
DBC + EBC = 180 (1.)
ABC + DBC = 90 (2.)
subtract (2.) from (1.) to obtain EBC – ABC = 90
it is given that ABC = (2/5) EBC so EBC – (2/5) EBC = 90
(3/5) EBC = 90
EBC = 150
from (1.) DBC + EBC = 180
DBC + 150 = 180
DBC = 30
If you have a group of 5 men and 4 women and we selected two at random, without replacement then find the probability that they are all men
a) Probability 1st selection is a man 5 / 9
b) Probablilty 2nd selection is a man 4 / 8
Probability both a) and b) happen (5 / 9) • (4 / 8) = 20 / 72
reduces to 5 / 18
You are biking at a speed of 18 miles per hour. You are 3 miles behind your friend, who is biking at a speed of 12 miles per hour. Write and solve an equation to find the amount of time x it takes for you to catch up to your friend.
Distance to make up = 3 miles
Speed differential = 6 miles per hour
Distance = Rate times Time —>> Time = Distance / Rate
3 mi
Time = ––––––– = 0.5 hour
6 mi/hr
Use the distance formula to order AB, CD, and EF from shortest to longest.
AB2 = 52 + 22 = 29 —>> AB = sqrt(29)
CD2 = 42 + 12 = 17 —>> CD = sqrt(5)
EF2 = 52 + 12 = 26 —>> EF = sqrt(26)
CD, EF, AB
A bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km away. Write a formula expressing the dependence of the variable s on t, where s is the distance between the bicyclist and the station in km, t - the duration (time) of his travel in hours. Using the formula, find: t for s=30
Distance = rate • time
30 km = 12 km/hr • t
30 km
t = ––––––––
12 km/hr
t = 2.5 hr
A man has 29 coins in his pocket, all of which are dimes (worth $ 0.10 each) and quarters (worth $ 0.25 each). If the total value of his change is $ 4.85 , how many dimes and how many quarters does he have?
D = number of Dimes
Q = number of Quarters
D + Q = 29 —>> Q = 29 – D (equation 1)
10D + 25Q = 485 (equation 2)
Substitute (29 – D) in
place of Q in (eq 2) 10D + (25)(29 – D) = 485
10D + 725 – 25D = 485
– 15D = – 240
D = 16
D + Q = 29
16 + Q = 29
Q = 13
Logan made 4 stacks of wooden blocks. Number of Blocks Used
The first stack was 6 blocks tall. 6
The second stack was 2 blocks taller than the first. 8
The third stack was 2 blocks shorter than the second stack, 6
and the last stack was 10 blocks taller than the third stack. 16
How many blocks did Logan use in all? 36
Find the y-intercept of the line.
The y-intercept is when x = 0.
It looks like y increases 9 for every time x increases by 12.
So continue the colums in the direction that leads to x = 0.
x y
0 – 26 <<—— the y-intercept at (0, –26)
12 – 17
24 – 8
36 1
48 10
Suppose ten distinct, positive integers have a median of 100. ("Distinct integers" means that no two integers are the same.) What is the smallest the average of those ten integers could be?
Definition: The median is the middle value in a set of numbers when they are arranged in order. It represents the point that divides a dataset in half, with half of the values falling above it and half below it.
Here's my submission: 1 2 3 4 99 101 102 103 104 105
Median = 100
Average = 62.4
A kite is on a 25 m string. The kite is directly above a barn that is 18 m away from the person holding the kite string. What angle does the string make with the ground?
cosine = adjacent over hypotenuse
cosine = 18 / 25
cosine = 0.7200
arccosine (0.7200) = 43.95o
what is the upper and lower bound of 8.31 to 2 decimal places. what is the upper lower bounds or 8.31
The degree of accuracy is determined by the number of decimal places.
The uncertainty is half of the smallest unit of accuracy.
So, the lower and upper bounds of 8.31 are 8.305 and 8.315
Based on the Census, state A has 16 fewer electoral votes for president than state B.
If the total number of electoral votes for these two states is 84, find the number for each state.
A + 16 = B
A + B = 84
A + (A + 16) = 84
2A + 16 = 84
2A = 68
A = 34
34 + B = 84
B = 50
A restaurant has 11.5 litres of juice. It sells juice by the glass. Each glass will hold 275 ml of juice. How many full glasses of juice could the restaurant sell?
11.5 liters = 11.5 x 1000 = 11,500 milliliters
11,500 milliliters / 275 milliliters/glass = 41.8 glasses = 41 full glasses
How many prime numbers less than 100 have a units digit of 7?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
I count five of them.
Find the sum of all solutions to the equation 4x(x-3) = 23 + 3x^2 + 10x.
4x(x – 3) = 23 + 3x2 + 10x
4x2 – 12x = 23 + 3x2 + 10x
x2 – 22x – 23 = 0
(x + 1)(x – 23) = 0
x = +23
x = – 1
their sum: +22
The correct answers are 16, 18, and 20.
The correct answer is 15.
The correct answer is 51.
What real value of t produces the smallest value of the quadratic t^2 -9t - 36 + t^2 - t + 14?
t2 – 9t – 36 + t2 – t + 14
This is a parabola that opens upward
so the smallest value is at the vertex. 2t2 – 10t – 22
Set the first derivitive equal to zero. 4t – 10 = 0
4t = 10
t = 2.5
The question doesn't ask for it, but at t = 2.5 the value of the quadratic is –34.5.
What is the largest number c such that 2x^2 + 5x + c = x^2 - 4x has at least one real solution? Express your answer as a common fraction.
2x2 + 5x + c = x2 – 4x
x2 + 9x + c = 0
For there to be any real solutions,
the discriminant must be positive. b2 – 4ac > 0
92 – (4)(1)c > 0
81 – 4c > 0
4c < 81
c < 81/4
