All Questions ⁺⁰236027 Questions

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In triangle ABC, cos A=sqrt(7/10) and cos B=sqrt(3/10) Find cos C

In triangle ABC, cos A=sqrt(7/10) and cos B=sqrt(3/10) Find cos C

RedDragon1 May 9, 2024

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13

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+27

Hard Counting and Probability

A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than 10 times? Express your answer as a common fraction.
Thanks read more ..

colinqiu May 9, 2024

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29

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+2653

Algebra

Find all values of a that satsify the equation \frac{a}{3} + 1 = \frac{a + 3}{a} + 1.

LiIIiam0216 May 9, 2024

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21

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+2653

Algebra

Solve for the variable x in terms of y and z, assuming y \neq \frac{1}{2}:
xy + x = \frac{3x + 2y + z + y + 2z}{3}

LiIIiam0216 May 9, 2024

+1

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+35

Help please

Megha has two large cylindrical urns for water, one of which is twice as deep as the other (note that the urns don't necessarily have the same base radius). Initially, the deep urn is full and the shallow urn is empty. At some time in the morning, Megha read more ..

Mather459 May 9, 2024

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18

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+2653

Counting

Find the number of ways of arranging the numbers 1,2 ,3, 4, 5, 6 in a row so that the product of any two adjacent numbers is at least 5.

LiIIiam0216 May 9, 2024

+1

28

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+5

basic question but its tripping me up

Let a, b, c, and d be real numbers such that a > b and c > d. Enter the letters of the statements below that MUST be true.
a) a + c > b + d
b) 2a + 3c > 2b + 3d
c) a read more ..

wowiewowwowwow May 9, 2024

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24

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+2653

Algebra

Compute \log_{1/2} (16*5*1/10).

LiIIiam0216 May 9, 2024

May 8, 2024

+1

15

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+10

help me!

Find the last two digits of $9^{8^7}$. (By convention, exponent towers are evaluated from the top down, so $9^{8^7} = 9^{(8^7)}$.)

capybara111 May 8, 2024

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20

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+2653

Algebra

Find x if \log_2 (\log_3 x) = 2 \log_4 (x).

LiIIiam0216 May 8, 2024

0

15

2

+2653

Algebra

Find all c such that |c + 5| - 3c = 10 + 2|c - 4| - 6|c|. Enter all the solutions, separated by commas.

LiIIiam0216 May 8, 2024

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17

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+2653

Algebra

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{2}}}}.

LiIIiam0216 May 8, 2024

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29

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+2653

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6 + 2ab,$ then what is $a^3 + b^3?$

LiIIiam0216 May 8, 2024

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27

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+2653

Counting

Syd chooses two different primes, and multiplies them. If both primes are greater than 3, and the resulting product is less than 500 , then how many different products could Syd have ended up with?

LiIIiam0216 May 8, 2024

0

35

0

+2653

Counting

How many solutions are there to the equation
u + v + w + x + y + z = 7
where u, v, w, x, y, and z are nonnegative integers, and x is at most 2 or y is at least 3?

LiIIiam0216 May 8, 2024

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22

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+2653

Coefficient

Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.

LiIIiam0216 May 8, 2024

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27

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+2653

System

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab^2 = 4. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)

LiIIiam0216 May 8, 2024

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25

1

+2653

System

Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p read more ..

LiIIiam0216 May 8, 2024

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16

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+2653

Counting

Six children are each offered a single scoop of any of $3$ flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five c read more ..

LiIIiam0216 May 8, 2024

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24

1

+2653

Counting

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)

LiIIiam0216 May 8, 2024

0

31

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+2653

Counting

In how many ways can the numbers through be entered once each into the five boxes below so that all the given inequalities are true?
___ > ___ > ___ > ___ < ___

LiIIiam0216 May 8, 2024

0

24

0

+2653

Counting

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

LiIIiam0216 May 8, 2024

May 7, 2024

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18

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+2653

Counting

A baking club wants to form an executive committee. There are $20$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $7$ people, including Mark?

LiIIiam0216 May 7, 2024

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28

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+2653

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

LiIIiam0216 May 7, 2024

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