All Questions ⁺⁰236167 Questions

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help help

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction \frac{2}{23} is written in base 16?

LiIIiam0216 Jul 31, 2024

0

13

5

+2653

help with number theory

Jon teaches a fourth grade class at an elementary school where class sizes are always at least 100 students and at most 200. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately read more ..

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LiIIiam0216 Jul 31, 2024

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13

1

+2653

need help

What is the fifth smallest prime number greater than 2000?

LiIIiam0216 Jul 31, 2024

0

16

3

+2653

help me

Some of the following integers are prime. Select all the prime integers in the list.
1 2 3 4 5 6 7 8 9 10

LiIIiam0216 Jul 31, 2024

0

15

1

+878

Algebra

For certain values of $k$ and $m,$ the system
a + 2b = -3 - 7a + b,
4a + 2b = k - 5a - mb
has infinitely many solutions $(a,b).$ What are $k$ and $m?$

magenta Jul 31, 2024

Jul 30, 2024

0

7

1

+948

Algebra

Find the ordered pair (s, t) that satisfies the system
(s/2) + 5t =3 - 7t + 8s
3t - 6s = 9 - 2t

Rangcr897 Jul 30, 2024

0

19

1

+948

Algebra

In an arithmetic sequence, the 23rd term is $\frac{1}{4},$ and the $33$rd term is $-\frac{1}{5}$. What is the $43$rd term?

Rangcr897 Jul 30, 2024

0

4

1

+1573

Algebra

A geometric sequence has 400 terms. The first term is 1000 and the common ratio is -\frac{8}{9}$ How many terms of this sequence are greater than 1?

parmen Jul 30, 2024

0

12

1

+1573

help algebra

If x and y are positive integers for which 3x + 2y + xy = 115 + 11x + 2y, then what is x + y?

parmen Jul 30, 2024

0

16

1

+157

Please help asap. Thanks

Allan, Bala and Chee Wee had some cards. The ratio of the number of Allan's cards to the number of Bala's cards was 3:5. After Bala and Chee Wee had both lost 1/2 of their cards, Bala had 75 more cards than Chee Wee. The three chidren read more ..

sugabreaddoughman Jul 30, 2024

0

7

1

+157

Help

In a bookshop, 40% of the stationery were pencils and the rest were erasers and rulers. The number of rulers is 1/4
the number of erasers. There were 120 more erasers than pencils.
(a) What percentage of the stationery read more ..

sugabreaddoughman Jul 30, 2024

0

18

4

+510

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 = 22$ and $a_2 + a_4 = 17$, then find $a_1$.

onyuIee Jul 30, 2024

0

12

1

+510

Algebra

Let x and y be complex numbers. If x + y = 2 and xy = 5 - x^2 - y^2, then what is x^2 + y^2?

onyuIee Jul 30, 2024

0

14

1

+510

Algebra

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

onyuIee Jul 30, 2024

0

18

1

+1839

Geometry

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

ABJeIIy Jul 30, 2024

0

13

1

+1839

Geometry

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

ABJeIIy Jul 30, 2024

0

17

1

+332

Counting

Joanna has six beads that she wants to assemble into a bracelet. Four of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

MEMEG0D Jul 30, 2024

0

17

1

+332

Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $300,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

MEMEG0D Jul 30, 2024

0

9

1

+637

Counting problem

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 ..

cooIcooIcooI17 Jul 30, 2024

0

21

0

+569

Absolute value

Find all $c$ such that $|c + 5| - 3|c + 7| = 10 + 2|c - 8|.$ Enter all the solutions, separated by commas.

Pythagorearn Jul 30, 2024

0

15

1

+948

Logs

Suppose $a\neq 0$. Compute $\log_{8a} b$ in terms of $a$ and $b$.

Rangcr897 Jul 30, 2024

0

14

1

+842

help with 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?

RedDragonl Jul 30, 2024

0

12

0

+510

help me

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

onyuIee Jul 30, 2024

0

14

2

+1351

Geometry

There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is $5$ miles. The distance from Capital City to Mytown is $2$ miles. The distance from Mytown to Yourtown is $3$ read more ..

learnmgcat Jul 30, 2024

0

18

0

+976

Algebra

Let $f(x) = x^2 + bx + 12 - 3x + 10$ for all real numbers $x$. Find the greatest integer value of $b$ such that $-4$ is not in the range of $f(x)$.

Hi6942O Jul 30, 2024

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