All Questions ⁺⁰235702 Questions

0

55

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+1678

Constant term

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

wiseowl Oct 29, 2023

0

50

0

+1678

real numbers

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

wiseowl Oct 29, 2023

0

57

0

+1678

coefficient

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

wiseowl Oct 29, 2023

0

42

0

+1678

binomial theorem

Expand (x^2 + 1/x)*(x + x^4)^3.

wiseowl Oct 29, 2023

0

55

0

+1678

binomial theorem

Expand (sqrt(t) + t^3)^4*(sqrt(t) - t^3)^4*(t - sqrt(t))^4.

wiseowl Oct 29, 2023

0

62

0

+1678

binomial theorem

Fill in the blanks with positive integers:
(3 + sqrt(5))*3*(5 + 3*sqrt(5))^3 = ___ + ___* sqrt(5)

wiseowl Oct 29, 2023

0

56

0

+1678

coefficient

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

wiseowl Oct 29, 2023

0

23

1

+1678

hard probabililty

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both have read more ..

wiseowl Oct 29, 2023

0

44

0

+1678

rolls

Catherine rolls a standard 6-sided die eight times. If the product of her rolls is 2700, then how many different sequences of rolls could there have been? (The order of the rolls matters.)

wiseowl Oct 29, 2023

0

56

0

+1678

Help probability

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

wiseowl Oct 29, 2023

0

57

1

+1678

Probability

Three cards are randomly drawn from a standard deck of $52$ cards, without replacement. Find the probability that the first card is a king, the second card is hearts, and the third card is red.

wiseowl Oct 29, 2023

0

19

2

+660

Easy Fractions; Need Help

A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is $4/7$ times the probability that a freshman is elected. Everyone on the junior varsity swim read more ..

Keihaku Oct 29, 2023

0

16

2

+660

Franklin the fly starts at the point $(0,0)$ in the coordinate plane.

Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After $12$ steps, how many different points could Franklin end up at?
The answer read more ..

Keihaku Oct 29, 2023

0

29

1

+817

counting help

You are given the $4 \times 4$ grid below. Find the number of ways of placing $4$ counters in the squares (at most one counter per square), so that each row contains exactly one counter, and each column contains exactly one counter. read more ..

maximum Oct 29, 2023

0

42

1

+817

help plz

Find the number of positive integers that satisfy both the following conditions:
* Each digit is a $1$ or a $3$ or a $5$
* The sum of the digits is $10$

maximum Oct 29, 2023

0

52

1

+817

need help

A baking club wants to form an executive committee. There are $18$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people?
A baking club wants to form read more ..

maximum Oct 29, 2023

0

22

1

+817

help counting

In how many ways can $4$ balls be placed in $8$ boxes if the balls and boxes are both distinguishable?
In how many ways can $4$ balls be placed in $8$ boxes if neither the balls nor the boxes are distinguishable?
In read more ..

maximum Oct 29, 2023

0

36

1

+817

counting

I run a book club with $n$ people, not including myself. Every day, for $100$ days, I invite $14$ members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of $14$ members read more ..

maximum Oct 29, 2023

0

45

1

+16

geometry similarity

in the diagram m is the midpoint of AB
find mn

mariaB16 Oct 29, 2023

Oct 28, 2023

-1

33

0

+1443

Equation

Fill in the blanks so that the resulting equation has no solutions.
___ + ___ = ___ + ____
p 2p 3p 4p 5p 6p 7p 8p 0 1 2 3 4 5 6 7 8

blackpanther Oct 28, 2023

-1

41

0

+1443

Equation

Find all values of $a$ that satisfy the equation
\[\frac{a}{3} + 1 = \frac{a + 3}{a} - \frac{a^2 + 2}{a}.\]

blackpanther Oct 28, 2023

-1

59

1

+1443

Word problem

Five times a number is divided by $2$ more than that number. If the result is $6,$ then what was the original number?

blackpanther Oct 28, 2023

-1

65

0

+1443

Word problem

If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $10$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

blackpanther Oct 28, 2023

-1

55

0

+1443

Help algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $214$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

blackpanther Oct 28, 2023

0

51

0

+1443

Algebraic Expressions

Consider the two expressions $1$ and $\frac{2x+3}{2x+3}.$
a) Show that the two expressions represent equal numbers when $x=10.$
b) Explain why these two expressions do not represent equal numbers when $x=-\dfrac32.$
c) Show that these read more ..

blackpanther Oct 28, 2023

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