All Questions ⁺⁰233683 Questions

0

13

0

+2115

Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10}

LiIIiam0216 May 18, 2024

0

10

1

+2115

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{9} + \frac{7}{12} + \dotsb.

LiIIiam0216 May 18, 2024

0

12

0

+2115

Help Algebra

Let S be the set of all real numbers of the form
a1/3 + a2/3^2 + a3/3^3 + ....
where a_i \in {0, 1, 2} for all i.
(a) Is the number 1/7 in the set S?
(b) Is the number 1/4 in the set S? read more ..

LiIIiam0216 May 18, 2024

0

3

1

+311

Expected value

The grid below is made up of line segments, like the line segment in red.
[asy] unitsize(1 cm); int i; for (i = 0; i <= 3; ++i) { draw((i,0)--(i,2)); } for (i = 0; i <= 2; ++i) { draw((0,i)--(3,i)); } draw((3,1)--(3,2), linewidth(2*bp) + red);read more ..

Lilliam0216 May 18, 2024

0

4

1

+311

6 and 5

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probability that all three resulting pieces are shorter than 5 units?

Lilliam0216 May 18, 2024

0

7

1

+2115

Algebra

All members of our painting team paint at the same rate. If $40$ members can paint a $100$ square foot wall in $50$ minutes, then how long would it take the $40$ members to paint a $480$ square foot wall, in minutes?

LiIIiam0216 May 18, 2024

0

9

0

+2115

Algebra

All members of our painting team paint at the same rate. If $45$ members can paint a specific wall in $60$ minutes, then how long would it take $12$ members to paint the same wall, in minutes?

LiIIiam0216 May 18, 2024

0

12

0

+2115

Algebra

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

LiIIiam0216 May 18, 2024

May 17, 2024

0

10

0

+2115

Algebra

Compute the unique positive integer $n$ such that
2 \cdot 2^2 + 3 \cdot 2^3 + 4 \cdot 2^4 + \dots + n \cdot 2^n = 32.

LiIIiam0216 May 17, 2024

0

6

0

+2115

Algebra

Find the value of $k$ so that
3 + \frac{3 + k}{4^2} + \frac{3 + 2k}{4^4} + \frac{3 + 4k}{4^6} + \dotsb = 8.

LiIIiam0216 May 17, 2024

0

2

2

+13

help pls

Problem:
Report Error
Lizzie came up with a divisibility test for a certain number :
Break a positive integer into two-digit chunks, starting from the ones place. (For example, the number would break into the two-digit chunks ) read more ..

Dysoncloud May 17, 2024

+1

11

0

+34

Quadratics

A rocket is launched with a velocity of 1200 ft/sec from the ground. How long until it hits the ground?
Hint: Use

jilin73 May 17, 2024

0

7

0

+2115

Algebra

Let $r$ be the positive real solution to $x^3 + \frac{2}{5} x - 1 = x^3 - 3x + 7.$ Find the exact numerical value of
r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb.

LiIIiam0216 May 17, 2024

0

7

1

+2115

Algebra

Our badminton team has finished $75\%$ of its season. So far, we have won $35\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

LiIIiam0216 May 17, 2024

0

8

0

+2115

Algebra

The system of equations
\[\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 5\]
has exactly one solution. What is $z$ in this solution?

LiIIiam0216 May 17, 2024

0

9

0

+2115

Algebra

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $10$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $4$ times as much money as read more ..

LiIIiam0216 May 17, 2024

0

4

1

+311

Stick and probability

A stick is broken at two points, chosen at random. If the length of the stick is 6 units, then what is the probability that all three resulting pieces are shorter than 5 units?

Lilliam0216 May 17, 2024

0

12

0

+729

Algebra

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. read more ..

eramsby1O1O May 17, 2024

0

4

2

+729

Algebra

Solve the inequality 2x - 5 <= -x + 12 - 7x + 18.

eramsby1O1O May 17, 2024

0

6

1

+2115

Coordinates

Fill in the blanks with integers, and select the correct operator ($+$ or $-$), to give an equation whose graph is the line that passes through the point $(-1,8)$ and is parallel to the graph of $4x + 3y = -8 - x - 15y.$

LiIIiam0216 May 17, 2024

0

6

1

+2115

Coordinates

Line $\ell_1$ represents the graph of $3x + 2y = -14 - 8x + 5y$. Line $\ell_2$ passes through the point $(5,-6)$, and is perpendicular to line $\ell_1$. Write the equation of line $\ell_2$ in the form $y=mx +b$.

LiIIiam0216 May 17, 2024

0

9

0

+2115

Algebra

Here is a summary of some inequality rules.
Fill in the blanks to complete the rules. (The first rule is already complete.)

You can add or subtract the same quantity from both sides.
You can multiply/divide both sides by read more ..

LiIIiam0216 May 17, 2024

0

8

1

+2115

Algebra

All members of our painting team paint at the same rate. If $50$ members can paint a $3600$ square foot wall in $20$ minutes, then how long would it take for $25$ members to paint a $4000$ square foot wall, in minutes?

LiIIiam0216 May 17, 2024

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