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I need help on this too! I'm Stumped!

\(a b^4 = 12 \Rightarrow a^5 b^{20} = 248832 \\ b^{15}=\dfrac{a^5 b^{20}}{a^5 b^5} = \dfrac{248832}{7776} = 32 \\ b = 32^{1/15} = 2^{1/3} \\ a b^4 = 12 \\ a \left(2^{1/3}\right)^4 = 12 \\ a 2^{4/3} = 2^2(3) \\ a = 3\cdot 2^{2/3} \)

∑[ i^n, n, 1, 99]=-1, because[i^1 + i^2 +i^3 + i^4]=0 + [i^5+i^6+i^7+i^8]=0+0=0. This pattern continues until i^96, which is a multiple of 4. i^97=i, i^98=-1, i^99=-i. So add the last 3 together:

i + (-1) + (-i) = -1 - the two "i" cancel leaving -1 as the answer.

Let the total =T
Let the pure cotton=C
Let the rest =R
C + R =T 
0.6T x 0.8 =0.48T = 96 of 60% are Pure Cotton
0.6T - 0.48T = 0.12T=24 of 60% are NOT Pure Cotton
T =24/0.12 =200 Total pieces of clothings.
0.7*200 =140 Pure Cotton
R =200 -140 =60 pieces that are NOT Pure Cotton.
140 -96 =44 pieces that need washing are Pure Cotton
80(or 40% of 200) - 44 =36 pieces that need wasing are NOT Pure Cotton.

\(P[\text{2 red plates}]=\dfrac 5 9 \dfrac 4 8 = \dfrac{5}{18}\\ P[\text{2 blue plates}] = \dfrac 4 9 \dfrac 3 8 = \dfrac{1}{6}\\ P[\text{plates are same color}]=\dfrac{5}{18}+\dfrac 1 6 = \dfrac 4 9\)

Jeeze where are you getting these problems?

First off the two spins have the following distribution on the resulting movement.

Movement to the right is positive, movement to the left is negative.

\(P[(-2,~0,~2)] = \left(\dfrac 1 9,~\dfrac 4 9,~\dfrac 4 9\right)\)

Second we note the possible multiples of 3 which are (0, 3, 6, 9, 12)

So with probability 1/9 of ending up on a multiple of 3 we can choose (2,5,8)

With probability 4/9 of ending up on a multiple of 3 we can choose (3, 6, 9)

With probability 4/9 of ending up on a multiple of 3 we can choose (1, 4, 7, 10)

All cards have probability 1/10 of being chosen and we end up with the following probabilities

\(P[\text{ending up on multiple of 3}] = \dfrac{3}{10} \dfrac 1 9 + \dfrac{3}{10}\dfrac 4 9 + \dfrac{4}{10}\dfrac 4 9 = \dfrac{31}{90}\)

hint: remember the formula for a sum of a geometric sequence

Thanks

Combine the terms that are of the same order.  The order is given by the power to which the x’s are raised. So, here, we have:

Order      Terms

5.             x^5

4.             x^4

3.             -x^3-2x^3 → -3x^3

2.             -x^2-2x^2 → -3x^3

1.             4x

0.             3-3 → 0

Result:  x^5 + x^4 - 3x^3 - 3x^2 + 4x

Gilligan is too scrawny, but the Skipper could sustain you for weeks.

Thank you so much for your help! Highly appreciated.

Look at the following sequence of probability tables

We see the answer is 36, choice B.

not a terribly well worded question.  I'm going to assume the stated speeds are with respect to a stationary object on the ground.

Given that the resultant speed of the two cars approach is

s=70+80=150mph

t = d/s = 750miles/150mph = 5hr

choice B

in general the formula for the volume of a cylinder is

\(V = \pi r^2 h\)

looking at #1 we have \(V = \pi (12^2) (8) \approx 3619.115 \)

it looks like you squared the diameter instead of the radius

Looking at #2 \(V = \pi (7.5^2)(4) = 706.858\)

again you used the diameter instead of the radius

You got the 3rd one correct because they gave you the radius, not the diameter, in the diagram.

A gets reflected to B=(3,-4) which then gets reflected to C=(-3,-4)

That gets us a right triangle with legs of length 6 and 8.

Can you figure out the area from that?

Thanks Alan :)

Sounds like a plan     

This means the limit of f(x) as x approaches 2 from below.

In the function graphed below we see that 

\(\lim \limits_{x\to 2^-} = 1 \\ \lim \limits_{x \to 2^+} = 5 \\ \lim \limits_{x\to 2} \text{ does not exist.}\)

Quilly don't be lazy.

Type your question in.

For hard to write question you can learn to use the  insert image button but it is easier for answerers if you type your question in.

This question would be easy for you to type in.

Hint:

Start by multiplying both sides by -2  but remember that when you multiply by a negative number you must turn the inequality around. so the  <  will become >

This is the question

70226 + 40545 sqrt(3) = 70,226 + 70,225.999992880 =~140,452