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X is hard to solve but you can draw a perpendicular line from E to meet the diameter of the circle and name the intersection point F. Then you can prove that triangle BEF is congruent to triangle BED. Then BD = \(\sqrt{11}\) and BC²= \((\frac{\sqrt{11}}{2})^2 = \frac{11}{4}\)

Therefore X = 11+4 = 15.

For Y, the source of cashew. I don't think it's a fruit but I think it's a country. India? China? we will figure out.

India = 9 + 14 + 4 + 9 + 1 = 37

China = 3 + 8 + 9 + 14 + 1 = 35

As the clue of Z stated that all of the digits in the combination are unique. So we'll use India which is 37.

For Z, 8 not necessarily distinct prime factors for all digits...... the hardest of all. Now the number's 1537**  

Using a website factorizing numbers, the number is 153720 = 2³ × 3² × 5 × 7 × 61

geno3141 : However, if the ratios are not that nice: if you assume that the ratio of Lev's age to Mina's age is a / b and you assume that the ratio of Mina's age to Naomi's age is c / d, then: since a / b = a·c / b·c and c / d = b·c / c·d, the three-way ratio is: a·c : b·c : c·d.

You did the last part wrong. c / d = b·c / b·d So the three-way ratio is a·c: b·c: b·d

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables.

Source: Wolfram Mathworld

5(x+3)-3(x+2)

= 5x+15-3x-6

= 2x+9

1, 16 , 49 , 100 , 169

6em+5e+\(\frac{7}{6}\)

most simplified form.

slope-intercept form means ' in the form of y=ax+b ' and the answer for this is \(y=-\frac{2}{5}x+\frac{6}{5}\) 

I need some help with part b too. Both the above answers are wrong.

If you assume that the ratio of Lev's age to Mina's age is  L / M

and you assume that the ratio of Mina's age to Naomi's age is  M / N,

then the three-way ratio is:  L : M : N.

However, if the ratios are not that nice:

if you assume that the ratio of Lev's age to Mina's age is  a / b

and you assume that the ratio of Mina's age to Naomi's age is  c / d,

then:  since  a / b  =  a·c / b·c

            and  c / d  =  b·c / c·d,

the three-way ratio is:  a·c : b·c : c·d.

We need to know the ratios involved......

5 < 2n ≤ 20   divide each term by 2

5/2 < n  ≤ 10

So.......the the possible values for n   exist in the interval  (5/2, 10 ]

We obviously can't write down ALL the possible values for n, since there are infinite values in the interval that would satisfy the inequality....!!!

Correct !!!

10 / 20    =  20  / 40          because the cross-products are equal....that is.....

40 *10    = 20 * 20

400   = 400

What is the smallest interval that will produce a complete graph of r=3sin(5x)?

Normally, it takes  360^o  or  2pi  to produce one complete cycle of sin; however, because the function has  5x  instead of just  x, the graph travels "five times as fast" or it takes only "one-fifth the amount of time to make one full cycle"; thus the smallest interval will be  360^o / 5  or  72^o; in radians this is  2pi/5.

The '3' in the equation affects the amplitude; the graph's maximum value will be 3 instead of the usual 1; also, the graph's minimum value will be -3 instead of the usual -1.

I for one am going to need a better clue regarding these cashews.

Suppose it were rational, then you could write it as the ratio n/m where n and m are relatively prime integers (ie  they don't have any factors in common), and m>n.Then by squaring both sides you would get

n^2/m^2 = 2/3.  So 3n^2 = 2m^2

The right hand side must be an even integer (because multiplied by 2), so therefore the left hand side must be as well. Since 3 is odd, n^2 must be even, which means n must be even (the square of an odd number is odd).  If n is even we can write n = 2p, where p is another integer. Hence we would have. 3*4p^2 = 2m^2. or

2*3p^2 = m^2

Now the left hand side is clearly even, so therefore m^2 must also be even, hence m must be even. 

But if m and n are both even, they can both be divided by 2. This contradicts our original assumption that n and m are relatively prime. We cannot have a contradiction, hence our original assumption that sqrt(2/3) is rational must be wrong.

sqrt(2/3) is irrational

.

Set 4 = 2x - 1

2x = 5 

x = 2.5

so P is at (2.5, 4)

Strictly, as C is written, guest #1 is correct.  However, if C were written as 2^(2-8), then guest #2 would be correct.

The n'th term can be written as (3n - 2)^2 where n is 1, 2, 3, etc.

Substitue n=3 to find the missing number.

Which is equivalent to:            2^2/2^8

   2^2/2^8 =2^(2 - 8)=2^-6. The answer is "C".

9 x 250,000,000 =2.25 x 10^9

E. None of the above

correct: 1/2^6

The maximal number of intersection points inside the circle occurs when no three of our segments pass through the same point inside the circle. Now consider one of the intersection points and the two segments which meet at it. These two segments are the diagonals of a quadrilateral which has the endpoints of the two segments as its vertices. This is true for every intersection point inside the circle. Moreover, it is true that if we select any four of the nine given points on the circle, connecting them will form a quadrilateral whose diagonals provide one intersection point inside the circle. Therefore, our problem becomes one of counting the number of ways to pick 4 of the 9 points, which can be done in \({9\choose 4} = \boxed{126}\) ways.

2.25

5/2 < n < =10

n=3, 4, 5, 6, 7

14,000,000 =1.4 x 10^7

12,500,000 =1.25 x 10^7