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The 2 is given     2 play guitar AND piano       

If a total of 5 play guitar then 5-2 =3   play ONLY guitar

If 6 play piano   then   6-2 = 4 play piano ONLY

The Q states 17 people         17 -(3+2+4) = 8 that play neither.  

Question 2) All of the items must be sold to profit at least $1, so we must choose the cheapest item to make sure that the markup percentage suits all of the items. 

The cheapest item is the Spin Top, costing $1.50  (Man, that is an expensive top!). $1 is 2/3, or 66.6%, of the price of the top, so we must increase the markup price by at least $\boxed{67\%}$ to get at least a $1 profit on all items.

Hope this helps,

- PM 

Question 1) 2 necklaces are $15 without marking up the price, so each necklace is $7.50. If the price is marked up by 15%, we can multiply 15 by $\dfrac{115}{100} \Rightarrow \dfrac{23}{20}$ to get 17.25.

Each individual necklace is $8.625, or $8.63. Each necklace will be sold for $$\boxed{8.63}$, and the profit for each necklace is 8.63 - 7.50 = $\boxed{\$ 1.13}$. 

- PM

94 - 27 = 67, so between the 27th and 94th entries, there are 67-1 = 66 entries. The entries before the 94th entry were probably one greater than the entry after, so entry 93 is 28, entry 92 is 29, etc. This makes sense because the average of E92 and E94 is 28, which is the value in E93. 

If the 27th entry is 94, then the 26th entry must be 95, the 25th entry must be 96, etc. From the 27th entry, there are 26 entries ahead of it, so the finrst entry is 94 + 26 = 120. The first entry is $\boxed{120}$.

Hope this helps, 

- PM

Where did you the 3,2,4,and 8 values ?If u dont mind explaining

Where did you the 3,2,4,and 8 values ?If u dont mind explaining

1. Imagine the side lengths of the square are (s, s, s, s) . The area is the same since s*s=s^2 Now, label the figures correctly and you would see that AC is the diagonal of the square, which is $s\sqrt{2}.$ Now, we have for rectangle AC*CE=$s^2$, but we already know AC, so we have $CE=\frac{s^2}{s\sqrt{2}}$ . Rationalizing the denominator, we get $CE=s\sqrt{\frac{5}{2}}$ . Now, dividing AC by CE, we get an answer of $\frac{2}{\sqrt{5}}$ , which can be changed into   $\boxed{\frac{2\sqrt{5}}{5}}.$

Do you have a diagram for problem 2?

Hope this helped,

tertre.

It is the last one of the choices.....

Imagine a right triangle: We have adjacent/hypotenuse, so 20 cos 72 approx 6.2! Like what EP had said!

2 wavelengths in pi time        2/pi

Let's make a Venn diagram to answer this question. We can put all the information we know into a Venn diagram. Since Andrew has 17 total, we can say that 17-9=8 CD's are Andrew's and not John's. The question is asking how many albums are in either Andrew's or John's collection, but not both? So, we can add up the numbers in only Andrew's and only John's. Then we get 8+6 which is equal to 14 CD's in total.

I got 32. Does that seem right?

Why don't you just count them?

2^10=1024 that is too big  so  1/2^10 is too little

2^9 = 512  that is the biggest power of 2 and 2^-9 is the smallest   So that is 9+9+1=19     

(9 negative, nine positive  the one extra one is 2^0=3^0=1)

Now do the same for powers of 3  

and find the total :)

If you want more help then ask. But show me what you have tried. :)

First find the mean of the list of numbers

5 + 9 + 11 +4 +8 + 9 + 12   /  7    = 8.286   

Now subtract the mean from each number

-3.286    .714    2.714    -4.286   -.286   .714   3.714       Now square all of these numbers   

                                    then add that together   and find the mean

                                               then  take the square root to find

      S.D. = 2.7

well done 

1                                   1

2                 8

3                                 27

4               64

5                                125

6              216

7                                 343

8              512

9                                 729

10            1000

11                              1331

12            1728

Looks like 6

[L - F] / D + 1 = N, where L = Last term, F = First term, D = Common difference, N = Number of terms

[9,999 - 1,002] / 3 + 1 = 3,000 - 4-digit numbers that are multiples of 3.

Probability of green is .2    that means the remaining cabbages represent  0.8 of the total

3:29 is possibly 32 cabbages

32 = .8x   x = 40 total cabbages        

3:29    means there are 3 reds and 29 whites and 8 greens    out of 40

red/40 = 3/40 = .075 chance of picking a red one

Base 6      413 - 215 = 154 in base 6      so   ' 4 ' is in the units place

you are subtracting  5 from 3.....you will have to borrow a '6' from the next column to make the 3  a value of a  9    9-5=4

The ladder is the hypotenuse of a right triangle 

20 cos (72) = 6.18 ft ~~ 6.2 ft

20,000 (1-.15)^x  =  10440

.85^x = 10440/20000

x log(.85) = log(10440/20000)

x = 4.00 years

thank you