All Answers 356457 Answers

There are 4! =24 such numbers:

1234 , 1243 , 1324 , 1342 , 1423 , 1432 , 2134 , 2143 , 2314 , 2341 , 2413 , 2431 , 3124 , 3142 , 3214 , 3241 , 3412 , 3421 , 4123 , 4132 , 4213 , 4231 , 4312 , 4321 >>Total =  66,660 - Their total sum

x = $1 bills            value = (1)(x) = x

14-x = $ 5 bills      value = 5(14-x)               summed, they equal $ 50

x + 5 (14-x) =50    solve for x (the number of $1 bills)   then $5's = 14-x

t

f = 3t

t = 2s-5        s = (t+5)/2       all three sides sum to 52

t + 3t + (t+5)/2 = 52     solve for t        then f = 3t      and s = (t+5)/2

question hide because of copyright claim: "This is a problem from the current round of USAMTS: https://www.usamts.org/Tests/Problems_32_1.pdf"

Find the dervative of y with respect to the given independent variable .
y=log₂r . Log₄r

Hi Jenny,

2 are correct and one is wrong.

I think it may be just a careless mistake.

See if you can work out which one is wrong and why it is wrong   

BD = 15/2 = 7.5 

You say " Thank you very much! But 9420 is incorrect "!, But the answer given to you is 9240 and NOT 9420 ?!.

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Of the 60 people in a room, three-fourths (3/4) of the people are men, and two-fifths (2/5) of the people have blonde hair. What is the least number of men in the room who could have blonde hair?

Of the 60 people,  (3/4) or 45 are men             ( I guess 15 are women)

Of the 60 people (2/5) or 24 have blonde hair

If all 15 women have blonde hair, then only 9 men have blonde hair. 

angle b = 48 degrees

angle c = 46 degrees

This is toooooooooooo easy

1/   angle ABD = arcsin(4 / 8)

2/   BD = sqrt( 8² - 4²)

3/    CD = BD / sin(ABD)

4/   AC = CD + 4

The possible values of a are 3 and -7.

The solution is (x,y,z) = (-1,3,4).

m^2 + 1/m^2 + 4 = 88.

When trying to find combinations, we multiply the numbers of things we can add to it. There are 6 different types of bread, 4 different types of meat, and 7 different types of condiments plus the no condiment. Since for the meat and condiment, there's another possible outcome than having just 1 type of meat and no condiment, we multiply by two twice.

This means we have 6*4*2*7*2=672 different sandwiches.

n = -2.

The number of square inches of waste is 36.

We can break this figure up into 3 rectangles. The 3x6 one, the 6x9 one, and the 15x12 one. Then, to find the area of the figure all we need to do is multiply and add them up. 3*6=18, 6*9=54, and 15*12=180. Then, we do 18+54+180= 252 sqaure inches, so your answer would be the first option. 

I figured it out! It's actually 217, but thank you! 

Let triangle XOY be a right-angled triangle with XOY being 90 degrees. Let M and N be the midpoints of legs OX and OY respectively. Given that XN=24 and YM=31, find XY (aka the hypotenuse).

OX => a       OY => b

24² = (b/2)² + a²

576 - (b/2)² = a²

^{~~~~~~~~~~~~~~~~}

(a/2)² = 31² - b²

a² / 4 = 961 + b²

a² = 3844 - 4b²                   a² = 358.13333333

~~~~~~~~~~~~~~

576 - b² / 4 = 3844 - 4b²

b² = 13072 / 15                  b² = 871.4666667

XY = sqrt( a² + b² ) = 35.0656527   

If you draw a line through the two given lines, you will find the second line is parallel the graphed line

   so    There is no solution to the system of equations

Thanks!

Also, I just came up with a proof due to your VERY USEFUL desmos grapher I don't know how you did it but it is amazing ANYWAYS

Because the diagonals of a regular polygon radiating from the same side intersect, if drawn a line through, will be the median line of the side they share or one of the vertices' sides independent from the other vertex's side. For example, if we have a hexagon ABCEDF, diagonal EA and FB will intersect at a point with a median line of side AF going through that point. Notice AF doesn't include E, but does include the other endpoint of diagonal EA.

Thus we can make a generalization that there will be--for a polygon with n sides-- n intersections of this sort. This is because there are n possibilities to order each of the letters ABCDEF in ascending order in the alphabet. AB, BC, CD, DE, EF, and FA=6 ways, in a hexagon. These intersections of diagonals form n triangles. Congruent triangles. Mirror image each of these, and they will form your shape with n bases as sides! And because these are congruent, this is a regular shape, similar to your mother shape!

First, do 0.7*0=0.315? This is obviously not 'and' probability, but I don't know if I am missing something so I will do it the way I would without any mistakes in the problem...

P(A U B) = 0.45 + 0.7 – 0.65 = 0.5= 1/2

Also, U is the 'or' sign in probability.

This is P(A)+P(B)-P(A and B), the formula for 'or' probabilities.

Your answer is 0.5