All Questions ⁺⁰235551 Questions

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25

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+1431

Algebra

Let a_1, a_2, a_3, \dots, a_8, a_9, a_{10} be an arithmetic sequence. If $a_1 + a_3 = 5$ and $a_2 + a_4 = 6$, then find $a_1$.

kittykat Apr 14, 2024

0

15

0

+1431

Algebra

When the same constant is added to the numbers $a,$ $b,$ and $c,$ a three-term geometric sequence arises. If $a = 60,$ $b = 100,$ and $c = 140,$ what is the common ratio of the resulting sequence?

kittykat Apr 14, 2024

0

22

0

+1768

Algebra

A geometric sequence has 400 terms. The first term is 500 and the common ratio is \frac{11}{12}. How many terms of this sequence are greater than $1?$

bader Apr 14, 2024

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24

0

+1768

Algebra

In a geometric sequence, the 23rd term is 26 and the 26th term is 10. What is the 28th term?

bader Apr 14, 2024

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26

0

+1768

Algebra

In an arithmetic sequence, the 23rd term is 2, and the 35th term is 3. What is the 38th term?

bader Apr 14, 2024

0

22

0

+1768

Algebra

Find constants $A$ and $B$ such that
\frac{2x + 11}{x^2 - 1} = \frac{A}{x + 1} + \frac{B}{x - 1}\]
for all $x$ such that $x \neq -1$ and $x \neq 1$.

bader Apr 14, 2024

0

32

0

+2653

Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

LiIIiam0216 Apr 14, 2024

0

26

0

+2653

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

LiIIiam0216 Apr 14, 2024

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32

0

+2653

plz help

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 ..

LiIIiam0216 Apr 14, 2024

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23

1

+355

pls help anyone

I run a book club with n people, not including myself. Every day, for 400 days, I invite 5 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 5 members over all 400 days read more ..

Lilliam0216 Apr 14, 2024

0

20

0

+1839

Counting

The six faces of a cube are painted black. The cube is then cut into $3^3$ smaller cubes, all the same size.
(a) How many of the smaller cubes have exactly one black face?
(b) How many of the smaller cubes do not have any read more ..

ABJeIIy Apr 14, 2024

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23

0

+1839

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 ..

ABJeIIy Apr 14, 2024

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20

0

+1839

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 ..

ABJeIIy Apr 14, 2024

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26

0

+1839

help counting

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $248,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability read more ..

ABJeIIy Apr 14, 2024

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38

0

+1839

Counting

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if everything mathematician must be between two scientists? (Two seatings are considered read more ..

ABJeIIy Apr 14, 2024

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28

1

+1839

Counting

How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel? For example, AF and EN count, but DE and KC do not.

ABJeIIy Apr 14, 2024

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29

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+1234

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

Akhain1 Apr 14, 2024

0

38

0

+1234

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

Akhain1 Apr 14, 2024

0

27

0

+1234

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?

Akhain1 Apr 14, 2024

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18

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+1234

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?

Akhain1 Apr 14, 2024

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17

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+1234

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?

Akhain1 Apr 14, 2024

+1

19

1

+1234

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?

Akhain1 Apr 14, 2024

Apr 13, 2024

0

29

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+1839

Algebra

Find the domain of the function $$f(x) = \frac{\sqrt{x}}{\sqrt{x^2}}.$$ Express your answer as an interval or as a union of intervals.

ABJeIIy Apr 13, 2024

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26

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+1839

Algebra

Find the domain of the function $$f(x) = \frac{1}{x+8} + \frac{1}{\sqrt{x - 8}} + \frac{1}{\sqrt{8 - x}}.$$ Express your answer as a union of intervals.

ABJeIIy Apr 13, 2024

0

26

0

+1839

Algebra

Find the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c+12x+x^2}$ has a domain of all real numbers.

ABJeIIy Apr 13, 2024

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