All Questions ⁺⁰235711 Questions

0

3

1

+1533

Sum

If $S$ is a nonempty set, $P(S)$ is defined to be the product of the elements in $S.$ What is the sum of the values of $P(S)$ over all the nonempty subsets $S$ of {1, -1, 0}? Express your answer as a common fraction.

parmen Feb 9, 2024

+2

4

1

+0

Help ASAP

Let D be the circle x^2 + 2x + y^2 = 10. No point on D has integer coordinates (meaning x and y can’t both be integers). What is the distance from D to the nearest point with integer coordinates? Explain please

Curry30shivank Feb 9, 2024

+2

44

1

+0

Please help ASAP

What’s the smallest n > 1 such that n! is divisible by n^4 ? Explain please

Curry30shivank Feb 9, 2024

Feb 8, 2024

0

21

1

+1533

Counting question

Amos counts out loud by six beginning with $0.$ Sarah counts out loud by three also beginning with $0.$ Between $0$ and $100$ inclusive, how many of the numbers do both Sarah and Amos say out loud?

parmen Feb 8, 2024

+2

17

2

+1632

Could I get some help on pre-calc?

What is the maximum possible length of the vector resulting from the following linear combination?
read more ..

proyaop Feb 8, 2024

0

17

2

+1533

Sums

Consecutive positive even integers are sorted into $100$ groups. Group $1$ includes $2,$ $4$ and $6.$ Group $2$ includes $8,$ $10,$ $12$ and $14.$ Group $3$ includes $16,$ $18,$ $20,$ $22$ and $24.$ Each successive group has one additional number in it read more ..

parmen Feb 8, 2024

0

13

1

+1533

Partitions

If $n$ is a positive integer, a $3$-partition of $n$ is a list of powers of $3$, arranged in order from greatest to least, whose sum is $n.$ For example, there are three $3$-partitions of $6,$ namely $3-3, 3-1-1-1$ and $1-1-1-1-1-1.$ How many different read more ..

parmen Feb 8, 2024

-2

42

0

+400

Prism

The three-dimensional figure shown is a right rectangular prism. What is the area of triangle PQR? Express your answer in simplest radical form.

omgitsrne Feb 8, 2024

-1

18

1

+400

Probability

A machine randomly generates one of the nine numbers 1, 2, 3, \dots, 9 with equal likelihood. What is the probability that when Tsuni uses this machine to generate four numbers their product is divisible by 2?
Express your answer as a common fra read more ..

omgitsrne Feb 8, 2024

-2

28

1

+400

Circle area

The figure shows circle $O$ with diameter $AB$ and inscribed angle $ABC$ with $AB = 8$ and $BC = 4.$ When the area of the shaded region, in square units, is expressed in the form $a + b\pi$, what is the value of $ab\,?$

omgitsrne Feb 8, 2024

0

30

1

+692

Sums

How many unique sums can be formed by adding any three different numbers from the set {4,6,8,10,12,...,154}?

booboo44 Feb 8, 2024

0

18

1

+692

Rectangle in Circle

A rectangle is inscribed in a circle of radius $5$ cm. If the area of the rectangle is equal to 24, what is the perimeter of the rectangle? Express your answer as a decimal to the nearest tenth.

booboo44 Feb 8, 2024

0

3

1

+692

Rate question

Tanzi and Maeve each have brand new $1200$ mL bottles of soap. They use soap at different constant rates. When Tanzi's bottle is completely empty, she asks Maeve to add soap from Maeve's bottle, which is still one-third full. How many milliliters of soap read more ..

booboo44 Feb 8, 2024

-1

16

1

+1911

Triangle Area

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

tomtom Feb 8, 2024

+1

14

1

+0

Semicircles

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

Vxrtate Feb 8, 2024

0

20

1

+0

Geometry question

In the diagram, ABCD is a square. Find sin PAQ.

Vxrtate Feb 8, 2024

0

29

2

+1768

Decimal notation

Convert 0.038\overline{146} to a fraction in simplest form.

bader Feb 8, 2024

0

44

1

+0

Help with geometry

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

Vxrtate Feb 8, 2024

0

37

1

+1768

Decimal notation

Convert $0.\overline{296841}$ to a fraction in simplest form.

bader Feb 8, 2024

+1

29

2

+0

External tangent intersecting a point between Radi???

So I'm not sure if the book has the definitions wrong, but aren't external tangents not supposed to intersect the radi? I understand PQ is 20 and and how to calculate say the external tangent (19.6)
But If I were to imagine an "internal" tangent read more ..

LioLaeus504 Feb 8, 2024

0

3

1

+1768

Digits

Find the six-digit number abcdef such that
0.\overline{abcdef} = \frac{1}{7},
without a calculator.

bader Feb 8, 2024

0

4

1

+1768

Digits

Find the first ten digits after the decimal point in the decimal expansion of \frac{7}{11}=0.abcdefghij\ldots without a calculator.
(Express your answer as a ten digit number.)

bader Feb 8, 2024

0

27

1

+0

Circles

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB. read more ..

Vxrtate Feb 8, 2024

0

27

1

+400

Maximum

Let x, y, and z be positive real numbers. Find the largest possible value of
sqrt((3x + 4y)/(6x + 5y + 4z)) + sqrt((y + 2z)/(5x + 6y + 4z)) + sqrt((2z + 3x)/(x + 2y + 3z))

omgitsrne Feb 8, 2024

3 Online Users