All Questions ⁺⁰236341 Questions

0

23

0

+844

Number Theory

How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{10}?$

RedDragonl Jun 26, 2024

0

18

1

+48

Geometry

Chords UV,WX andYZ of a circle are parallel. The distance between chords UV and WX is 2 and the distance between chords WX and YZ is also 2. If UV=64 and YZ=48 then find WX. read more ..

jumbcan Jun 26, 2024

0

19

1

+48

Help inequality

I can't solve this
For an integer n, the inequality x^2 + nx + 15 < -21 - 280
has no real solutions in x. Find the number of different possible values of n.

jumbcan Jun 26, 2024

0

13

1

+844

Counting

In how many ways can 4 balls be placed in 6 boxes if the balls are distinguishable, and the boxes are indistinguishable?

RedDragonl Jun 26, 2024

-2

17

1

+204

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

BRAlNBOLT Jun 26, 2024

-2

16

1

+204

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

BRAlNBOLT Jun 26, 2024

0

22

0

+1839

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

ABJeIIy Jun 26, 2024

0

28

0

+1839

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

ABJeIIy Jun 26, 2024

0

12

1

+9

math

an empty rectangular tank measures 55cm by 35cm by 30 cm.Mr tay emptied 62L of water from another container into the rectangylar tank
How much water overflows from the rectangular tank?
Give your Answers in litres and millilitres.</ read more ..

studywithme513524 Jun 26, 2024

0

25

0

+48

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from read more ..

jumbcan Jun 26, 2024

0

18

0

+48

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
\[0.\overline{0121}_3 = 0.01210121 \dots,\]
which is repeating.
When read more ..

jumbcan Jun 26, 2024

0

25

0

+48

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$.

jumbcan Jun 26, 2024

0

19

0

+48

Number Theory

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
\[a + 3n = b - 2n = \frac{c}{5n},\]
compute the value of $a$.

jumbcan Jun 26, 2024

0

20

0

+868

Number Theory

Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.

eramsby1O1O Jun 26, 2024

0

17

0

+868

Number Theory

On planet Enigma, the residents use a currency called the confusion. There are only 2 confusion bills on Enigma, one worth 2 confusions and the other worth 3 confusions. There are also some coins of smaller value, but each weighs over 10 read more ..

eramsby1O1O Jun 26, 2024

0

20

1

+868

Number Theory

The product of a set of distinct positive integers is $630$. If one of the numbers is 42, what are the other two numbers?

eramsby1O1O Jun 26, 2024

0

14

0

+868

Number Theory

How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{24}?$

eramsby1O1O Jun 26, 2024

0

26

0

+1839

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

ABJeIIy Jun 26, 2024

0

25

0

+1839

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

ABJeIIy Jun 26, 2024

0

20

0

+1839

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

ABJeIIy Jun 26, 2024

0

24

0

+1839

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

ABJeIIy Jun 26, 2024

0

29

0

+1379

Algebra

In a geometric sequence, the 23rd term is 16 and the 24th term is 1/4. What is the 30th term?

learnmgcat Jun 26, 2024

0

15

0

+1379

Algebra

Find the sum of all positive integers less than 1000 ending in 3 or 4 or 6 or 9.

learnmgcat Jun 26, 2024

+1

17

2

+33

Geometry

Chords UV,WX andYZ of a circle are parallel. The distance between chords UV and WX is 2 and the distance between chords WX and YZ is also 2. If UV=38 and YZ=22 then find WX. read more ..

jumbean Jun 26, 2024

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