algebra
factorize
4x-x3
x(2-x) x (2+x)
The sum of two nonzero real numbers is 4 times their product. What is the sum of the reciprocals of the two numbers?
1, 2, 4, 8, 12
4
Two coins are tossed 500 times, and we get:
Two heads: 105 times
One head: 275 times
No head: 120 times
Find the probability of each event to occur.
Solution: Let us say the events of getting two heads, one head and no head by E1, E2and E3, respectively.
P(E1) = 105/500 = 0.21
P(E2) = 275/500 = 0.55
P(E3) = 120/500 = 0.24
The Sum of probabilities of all elementary events of a random experiment is 1.
P(E1)+P(E2)+P(E3) = 0.21+0.55+0.24 = 1
What number doesn’t have its own Roman numeral?
0
20/ 5 x (10+5)
60
2x2 +4(x2+3)-2=22
find x
x= -root 2/ root 2
Find the curved surface area of a hemisphere whose radius is 14 cm.
Solution:
Given: Radius = 14 cm.
1232
One card is drawn from a deck of 52 cards, well-shuffled. Calculate the probability that the card will
(i) be an ace,
(ii) not be an ace.
P(F) = 48/52 = 12/13
what are the first 5 digits of pi
3.141592
(5x6)x32/3-8+4
86
7x-11=17
find x
4
What is the area of a circle with a diameter of 16?
64(picm^2)
Two players, Sangeet and Rashmi, play a tennis match. The probability of Sangeet winning the match is 0.62. What is the probability that Rashmi will win the match?
The probability of Sangeet to win = P(S) = 0.62
The probability of Rashmi to win = P(R) = 1 – P(S)
= 1 – 0.62 = 0.38
What is next in the following number series: 256, 289, 324, 361 . . . ?
400
140,368 - 12,439
127929
A= (-20,12)
B= (15,-40)
what is the midpoint of line AB
(-2.5, -14).
By the triangle rule, x lies between 31 – 16 = 15 and 31 + 16 = 47. That is, we have 15 < x < 47. But we are also given that x is the length of the shortest side of the triangle. So x < 16.Therefore we can grid in any number between 15 and 16. For example, we can grid in 15.1.
In a class there are 35 boys and 15 girls. What is the probability of a randomly selected student of the class to be a girl?
0.3, or 30%.
At a Christmas party, everyone shook hands with everyone else. There were a total of 66 handshakes that happened during the party. How many people were present?
12
√169/256
0.0507812
or
13/ 256
n4+2n3+2n2+2n+1
factorize completely
(n+1)2(n2+1)
In rectangle ABCD, both diagonals are drawn and intersect at point E.
Let the measure of angle AEB equal x degrees.
Let the measure of angle BEC equal y degrees.
Let the measure of angle CED equal z degrees.
Find the measure of angle AED in terms of x, y, and/or z.
180 – 1/2(x + z)
11 A bag contains 5 blue (B) and 3 white (W) marbles and two marbles are selected without
replacement.
a Draw a tree diagram showing all outcomes and probabilities.
b Find the probability of selecting:
i a blue marble followed by a white marble (B, W)
ii 2 blue marbles iii) exactly one blue marble
c If the experiment was repeated with replacement, find the answers to each question in part b .
a) The tree diagram for selecting two marbles without replacement from a bag containing 5 blue (B) and 3 white (W) marbles would look like this:
B W
/ \ / \
B W B W
/ \ / \ / \ / \
B W B W B W B W
b)
i) The probability of selecting a blue marble followed by a white marble (B, W) can be calculated by multiplying the probabilities of each event:
P(B, W) = P(B) * P(W after B)
= (5/8) * (3/7)
= 15/56
ii) The probability of selecting two blue marbles can be calculated similarly:
P(2 blue marbles) = P(B, B)
= P(B) * P(B after B)
= (5/8) * (4/7)
= 20/56
= 5/14
iii) The probability of selecting exactly one blue marble can be calculated by considering two cases: selecting a blue marble and then a white marble, or selecting a white marble and then a blue marble. We can add the probabilities of these two cases:
P(exactly one blue marble) = P(B, W) + P(W, B)
= (5/8) * (3/7) + (3/8) * (5/7)
= 15/56 + 15/56
= 30/56
= 15/28
c) If the experiment is repeated with replacement, the probabilities will change because after each selection, the marble is put back into the bag.
i) The probability of selecting a blue marble followed by a white marble (B, W) would be:
P(B, W) = P(B) * P(W)
= (5/8) * (3/8)
= 15/64
ii) The probability of selecting two blue marbles would be:
P(2 blue marbles) = P(B, B)
= P(B) * P(B)
= (5/8) * (5/8)
= 25/64
iii) The probability of selecting exactly one blue marble would be:
P(exactly one blue marble) = P(B, W) + P(W, B)
= (5/8) * (3/8) + (3/8) * (5/8)
= 15/64 + 15/64
= 30/64
= 15/32
An object is thrown into the air. After a while, it falls back to the Earth. The flight path of the object traces what shape?
parabola
3x+1
no answer