All Answers 355974 Answers

What is the largest value of k such that the equation 6x-x^2=k has at least one real solution?

Rearrange as    x^2 - 6x + k = 0

If this has at least one real solution, the discriminant must be ≥ 0

So

(-6)^2 -   4(1)(k) ≥ 0

36 - 4k ≥ 0

36 ≥ 4k 

9 ≥ k

So .....the max value  of k that produces at least one real solution is when k = 9

x^2-6x+k=0

Factor the equation into (x+a)(x+b)=0

We know that a+b=-6 and the maximum value of ab is 9

:D

There are b-1 choices for the first digit, b-1 choices for the second, and b-2 choices for the third. That means (b-1)(b-1)(b-2)=180 so b=7.

:D

Let's use complementary counting. The only way for no girls to be next to each other is if they sit b-g-b-g-b-g-b. There are 4!=24 ways to arrange the boys and 3!=6 ways to arrange the girls in this case. That makes 144 cases. There are 7!=5040 ways to organize the people with no restrictions so the answer is 5040-144=4896.

:D

Because the circumcenter is the intersection of perpendicular bisectors, we can graph two perpendicular bisectors from two lines. Then we know the circle's center, (-4,2). Once we get the radius, we can use the formula (x-a)^2+(y-b)^2=r^2 where a and b are the coordinates of the circles center.

:D

So we know (n-2)(n+18)=n(2n-4). Simplifying gets us n^2+16n-36=2n^2-4n so n^2-20n+36=0. We can factor this equation into (n-2)(n-18) so n=18.

:D

I don't think you quite got it. There are 9*10^4 5 digit numbers and 6*7^4 that have no 2's, 3's, or 4's. Using complementary counting, the answer is 75594.

:D

There are 6choose2 or 15 ways to paint two faces. There are two ways to get a product of 6. (6,1) and (3,2). 15-2=13

:D

10*9*8*7*6*5*4*3*2*1 turns into 10/9/8*7*6/5*4*3/2*1 so 4 *'s were replaced.

:D

You have to go right 8 times and up 2 times. We can write this as RRRRRRRRUU. There are 10!/(8!*2!) ways to arrange it so the answer is 45

:D

the question didn't ask for the odds, it asked for the number of 5 digit numbers satisfying the statement.

Instead of counting the number of 5 digit numbers satisfying the statement, count the ones that don't satisfy the statement and subtract from the total number of possibilities.

For the first digit, there are 9-3=6 possibilities, and for the rest of the digits, there are 10-3=7 possibilities. Therefore the total of numbers that don't satisfy the statement is equal to 6*7*7*7*7 = 14406.

The total number of possibilities is just 9*10*10*10*10=90000.

Subtracting, we get the answer:

75594 5-digit numbers.

How many 5 digit numbers are there

99999-10000+1= 90000     or

9*10*10*10*10=90000

How many are there that do not have a 2 or 3 or 4 as any digit.

6*8^4 = 24576

So how many of them DO have at least one 2 or one 3 or one 4 

90000-24576 = 65424

LOL, i did not know that.... i was just curious when you said good night gracie, and i was not sure if you where talking to me :P LOL

-Grace

There are 10 different number 0-9. There are three digits and you want at least one to appear. That means the odds are 3/10.

Solution 1. 5÷10000 = 0.0005= 1/2000 

Solution 2. 5÷99999 = 0.000050000500005= 10000100001/20000000000000

not sure which one it is...... Can somebody please check me......?

( I think solution to makes more sense because if it's a 5 digit lock combination and all the highest possible numbers to have would be 99,99, the highest possible numbers to have would be 99,999 and there are five digit, so you would 99999÷5 

-Grace

A is true because a constant (which can be of any value ) is involved when you do the 'anti-derivative'  

   Example  Anti derivative   x²  +3             x^2 +12            x^2 +19 

                 all have derivative    of   2x  

                        so, in other words , the 'anti-derivative' of   2x     can be     any of the red equations (or more)   

The empty space will be equal to the volume of container B  (that was removed from A)

pi r^2 h   for container B 

 pi (5^2)(18) = 25*18*pi = ~ 1413.7  ft³

So for the beginning number we have 3 possibilities and the second number have 4 possibilities, the 3rd one have 3, the 4th one have 2, and there is only one possibility for 5, so there is 3*4! arrangements, however, since there is two 8s and two 0s, we have to divide by 2!*2!, which gets the final answer of 18. Hope this helped :)

G(x)=145+13.50x. Since 145 is needed to even open the GYA booth and 13.50 is the hourly wage. Hope this helped :)

circumferance= pi*diameter, so the radius is 8, 8*8=64, 64pi is the area for base, 192pi/64pi=3, and 3*3=9, the ratio of the heights are 9/30, which is 3/10. If you're confused just search up how to calculate the column of a cone. Hope this helped.

Thanks

Correct me if I'm wrong, I think the answers are just factors of 90, which are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. so there are 12 possible measurements. Hope this helped