All Answers 356003 Answers

1) \(1 \frac{2}{3} \cdot 1 \frac{1}{4} = \frac{5}{3} \cdot \frac{5}{4} = \boxed{\frac{25}{12} = 2 \frac{1}{12}}\)

2) \(N \cdot \frac{3}{8} = \frac{5}{3}\)

To isolate N, multiply both sides by the reciprical of 3/8, which is 8/3.

\(N = \frac{5}{3} \cdot \frac{8}{3} = \boxed{\frac{40}{9}}\)

3) \(2 \frac{3}{4} \div \frac{1}{8} = 2 \frac{3}{4} \cdot 8 = \frac{11}{4} \cdot 8 = \boxed{22}\)

4) \(\text{cashew nuts mass}= \frac{2}{5} \cdot 2 \frac{1}{2} = \frac{2}{5} \cdot \frac{5}{2} = 1\)

\(\text{total mass} = 2 \frac{1}{2} + 1 = 3 \frac{1}{2} = \frac{7}{2}\)

\(\text{mass per packet} = \frac{7/2}{8} = \boxed{\frac{7}{16}}\)

\(\sqrt{64} = \sqrt{8^2} = 8^{2 \cdot \frac{1}{2}} = \boxed{8}\)

The equation y = -4.2t^2 + 42t + 18.9 describes the height (in meters) of a ball tossed up in the air at 42 meters per second from a height of 18.9 meters from the ground, as a function of time in seconds. In how many seconds will the ball reach maximum height?

This is a concave down parabola, the max will be when t = axis of symmetry

max height will be reached when t = -42/-8.4 = 5seconds

Just as BuilderBoi already said  

CONGRATULATIONS!

I am really pleased to hear that BuilderBoi.

Maths people, anD many others too, like to see their numbers grow.  

It is not a tangible reward but it certainly is an emotional one.    

I hope you stay with us well into the future and continue to have fun while you learn !     

Yes I believe it means you can only use the blocks given, the question is misworded. 

I also imagine that the blocks are lined up, not added

0,1,10,11,100,101,110,1001,1010,1100     That is 10 numbers.

\((1 + i\sqrt{3})^6\\ =\binom{6}{0}(i\sqrt3)^0+\binom{6}{1}(i\sqrt3)^1+\binom{6}{2}(i\sqrt3)^2 +\binom{6}{3}(i\sqrt3)^3+\binom{6}{4}(i\sqrt3)^4+\binom{6}{5}(i\sqrt3)^5+\binom{6}{6}(i\sqrt3)^6\\ =1+6*(i\sqrt3)^1+15(i\sqrt3)^2+20(i\sqrt3)^3+15(i\sqrt3)^4+6(i\sqrt3)^5+(i\sqrt3)^6\\ =1+(6\sqrt3)i-15(\sqrt3)^2-20(\sqrt3)^3i+15(\sqrt3)^4+6(\sqrt3)^5i-(\sqrt3)^6\\ =1+(6\sqrt3)i-15*3-60(\sqrt3)i+15*9+6*9\sqrt3 i-27\\ =1+6\sqrt3i-45-60\sqrt3i+135+54\sqrt3 i-27\\ =1-45+135-27+(6\sqrt3-60\sqrt3+54\sqrt3) i\\ =1-45+135-27+(6\sqrt3-60\sqrt3+54\sqrt3) i\\ =64\)

You need to check my working.   there may also have been a simpler path.

LaTex

(1 + i\sqrt{3})^6\\
=\binom{6}{0}(i\sqrt3)^0+\binom{6}{1}(i\sqrt3)^1+\binom{6}{2}(i\sqrt3)^2
+\binom{6}{3}(i\sqrt3)^3+\binom{6}{4}(i\sqrt3)^4+\binom{6}{5}(i\sqrt3)^5+\binom{6}{6}(i\sqrt3)^6\\
=1+6*(i\sqrt3)^1+15(i\sqrt3)^2+20(i\sqrt3)^3+15(i\sqrt3)^4+6(i\sqrt3)^5+(i\sqrt3)^6\\
=1+(6\sqrt3)i-15(\sqrt3)^2-20(\sqrt3)^3i+15(\sqrt3)^4+6(\sqrt3)^5i-(\sqrt3)^6\\
=1+(6\sqrt3)i-15*3-60(\sqrt3)i+15*9+6*9\sqrt3 i-27\\
=1+6\sqrt3i-45-60\sqrt3i+135+54\sqrt3 i-27\\
=1-45+135-27+(6\sqrt3-60\sqrt3+54\sqrt3) i\\
=1-45+135-27+(6\sqrt3-60\sqrt3+54\sqrt3) i\\
=64

What is the measure of the smallest angle?

Hello Guest!

The measure of the smallest angle is 180 degrees - 128 degrees = 52 degrees.

The difference is d = (128 - 52) degrees / 3 .

d = 25 degrees 20 angular minutes.

 !

I COULDN'T WRITE ALL THE ENTIRE Chart,

but its asking for the comparison of prices between Europe and france

A) This forum is not meant to do your homework for you

B) We need the image to solve this problem

When it means "without using each digit more than once", I think it means that you can't use each block more than once. Although, it doesn't make sense why they would give you 2 blocks of each. 

In this case, the only possible answers would be \(\color{brown}\boxed{0, 1, 10 }\).  

324 / 162 = 2

105 * 5 2^2 = 105 * 4 = 420

The population of bacteria will have 420

Tom has 9 balls

and also n/2 + n/4 balls 

so n/2 + n/4 = 9

   (2n + n)/4 = 9

   2n + n = 36

    3n = 36

      n = 12

Jack has n balls

      n = 12

        12 balls

According to the problem we can know that:

We can define that: {Celia has x pears

                                {Eliot has y pears

So we get: { (x + 21)/y - 21 = 3/1    {

                                                =>  {
                 { (x - 12)/y + 12 = 3/2     {
So Celia has 144 - 76 = 68 pears

x/2 + x/4 = 9

= 3/4

9 * 4/3

= 12

He would have 12 balls 

please help?

The maximum value is \(18.9 - {1764\over-16.8} = 123.9\). Subsitute the equation like this:\(123.9=-4.2t^2+42t+18.9\). Solve for \(t\), and you get \(\color{brown}\boxed 5\)

Thank you I got it from here!

I got

sum = 10n

soo

(10n+50)/(n+2)=12

cross multiplying we get

10n+50 = 12n+24

therefore we get n= 18

For the original sequence: \({\text {sum}\over n } = 10\)

When you add the terms \(20\) and \(30\), we have the equation: \({{\text{sum} + 50}\over{n+2}} = 12\)

These two are a equations form a system, and you can solve for \(n\) from here.

Good Luck!

4C3 = 4

4/16   = 1/4

\({1 \over 2^3} \times {1 \over 2} \times {4 \choose 1} = {4 \over 16} = \color{brown}\boxed {1\over 4}\)

Explanation:

There is a \({1 \over 2} \times {1 \over 2} \times {1 \over 2} \) chance of the successes (\(3\) tails)

There is a \(1 \over 2\) chance of failure (\(1\) head)

There are \(4 \choose 1\) ways to order the failure (the same as \(4 \choose 3\), which counts the ways to order the successes.)

\({1 \over 3} \times 24 = \color{brown}\boxed 8\) 

After 162 hours, there will be \(105 \times 2 = 210\) bacteria.

After 324 hours, there will be \(210 \times 2 = \color{brown}\boxed{420}\) bacteria

oh ok!