All Questions

479

help counting

A state requires that all boat licenses consist of the letter A or M or P or S followed by any five digits. What is the number of groups of letters and numbers available for boat licenses?

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Guest Aug 13, 2021

424

Algebra

For what value of x will (3 + x)/(5 + x) and (1 - x)/(2 + x) be equal?

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Guest Aug 13, 2021

Aug 12, 2021

378

Counting

The product of the digits of 3214 is 24. How many distinct four-digit positive integers are such that the product of their digits equals 24?

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Guest Aug 12, 2021

411

help coordinates

You connect the points (0, 0) and (9, 6) with a line segment. Starting at (0, 0), you move 1/2 of the way along the segment. What is the sum of the coordinates of the point you land upon?

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Guest Aug 12, 2021

730

(a) Simplify \[\dfrac{\dbinom{n}{k}}{\dbinom{n}{k - 1}}.\]

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Guest Aug 12, 2021

281

help complex numbers

If z is a complex number satisfying z+(1/z)=1, calculate z^2+ (1/z^2).

Guest Aug 12, 2021

430

mathematics

Lawrence had some money. He spent 3/5 of it on 4 similar highlighters. With the rest of his money, he bought another 2 such highlighters and 10 rulers.
(a) What fraction of his money was spent on buying 10 rulers? Give read more ..

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Guest Aug 12, 2021

289

mathematics

Eddy had some round and square magnets in a box. 1/3 of the round magnets and 7/11 of the square magnets were blue. 1/2 of the total number of magnets in the box were blue. There were 6 more square magnets than round magnets in the box. How many magnets read more ..

Guest Aug 12, 2021

282

Brichcy

Rina had a box of red, blue and green counters. The ratio of red counters to blue counters was 5:2. The ratio of blue counters to green counters is 3:5.
A) what is the ratio of red to blue to green counters ?
B) After Rina took out 126 read more ..

Guest Aug 12, 2021

608

Inequality

Solve the inequality x^3 + 4x > 5x^2 + 4x.

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Guest Aug 12, 2021

523

investment rates

An investment of $24,000 is made in a government bond that will pay 1% bi-monthly interest (meaning that the investment will increase by 1% every two months). At the end of five years, what is the total number of dollars in this investment?
Express read more ..

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Guest Aug 12, 2021

524

Inequality

Solve the inequality x(x + 6) > 16 + 2x.

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Guest Aug 12, 2021

620

help pls!!

What is the smallest positive multiple of $23$ that is $4$ more than a multiple of $89$?

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Guest Aug 12, 2021

387

help 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. We read more ..

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Guest Aug 12, 2021

627

pls help

The distance light travels in one year is known as a light year. A light year is equal to 5.87 × 10^12 miles. The closest that Earth ever gets to Jupiter is 3.65 × 10^8 miles. What is a correct representation of the number of years it will take light to read more ..

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SenseiBungeeGum Aug 12, 2021

484

help plz

Simplify the following:
(2y + 1)(4y^10 + 2y^9 + 4y^8 + 2y^7 + 2y^6 + 4y^5)
Express your answer as a polynomial with the degrees of the terms in decreasing order.

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Guest Aug 12, 2021

344

+12

function

a function f is defined on the positive integers. it is given that f is non-decreasing, that f(2) = 2, and that f(mn) = f(m)f(n) for m and n relatively prime. prove that f(4) f(13) >= [f(7)]^2

Vaishali Aug 12, 2021

501

+12

prove that (3+2√2)^2n-1 + (3-2√2)^2n-1 - 2 is a perfect integral square

prove that (3+2√2)^2n-1 + (3-2√2)^2n-1 - 2 is a perfect integral square for every positive integer n.

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Vaishali Aug 12, 2021

397

+12

sum of three positive real numbers by the sum of their reciprocals is always atleast 9

Show that the product of the sum of three positive real numbers by the sum of their reciprocals is always atleast 9. When can the product be exactly 9?

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Vaishali Aug 12, 2021

449

Coordinates

A segment with endpoints at A(2, -2) and B(14, 4) is extended through B to point C. If BC = 3*AB, what are the coordinates for point C? Express your answer as an ordered pair.

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Guest Aug 12, 2021

471

Counting

How many subsets of the set {1,2,3,4,5,...,10} contain the number 5?

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Guest Aug 12, 2021

606

The owners of a house that is assessed at $\$120,\!000$ pay $\$3,\!000$ in taxes. At the same rate, what is the tax, in dollars, for a house

The owners of a house that is assessed at $\$120,\!000$ pay $\$3,\!000$ in taxes. At the same rate, what is the tax, in dollars, for a house assessed at $\$160,\!000$?

Bulbous ●

Guest Aug 12, 2021

449

help counting

A group of 10 Caltech students go to Lake Street for lunch. Each student eats at either Chipotle or Panda Express. In how many different ways can the students collectively go to lunch?

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Guest Aug 12, 2021

499

+54

Help

A snail fell into a well which is 3 m deep. It would climb 1/4 m up the all in the day and slide 1/10 m in the night. How many days would the snail take to get out of the well?

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mitgliedd1 Aug 12, 2021

472

mathematics

Three boys had 144 erasers together. Alan gave some of his erasers to Bill and Bill's erasers doubled. Bill then gave some of his erasers to Charlie and Charlie's erasers doubled. In the end, the three boys had and equal number of erasers read more ..

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Guest Aug 12, 2021

All Questions ⁺⁰237807 Questions

help counting

Algebra

Counting

help coordinates

(a) Simplify \[\dfrac{\dbinom{n}{k}}{\dbinom{n}{k - 1}}.\]

help complex numbers

mathematics

mathematics

Brichcy

Inequality

investment rates

Inequality

help pls!!

help algebra

pls help

help plz

function

prove that (3+2√2)^2n-1 + (3-2√2)^2n-1 - 2 is a perfect integral square

sum of three positive real numbers by the sum of their reciprocals is always atleast 9

Coordinates

Counting

The owners of a house that is assessed at $\$120,\!000$ pay $\$3,\!000$ in taxes. At the same rate, what is the tax, in dollars, for a house

help counting

Help

mathematics

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