All Answers 356462 Answers

10080 , 12600 , 15120 , 17640 , 20160 , 22680 , 25200 , 27720 , 30240 , 32760 , 35280 , 37800 , 40320 , 42840 , 45360 , 47880 , 50400 , 52920 , 55440 , 57960 , 60480 , 63000 , 65520 , 68040 , 70560 , 73080 , 75600 , 78120 , 80640 , 83160 , 85680 , 88200 , 90720 , 93240 , 95760 , 98280 , Total =  36 such numbers

Note: Each number is divisible by 7 and by 8 and by 9 and by 10.

Mary gets an oil change for her car every 3750 miles and a tire rotation every 5000 miles. What is the mileage of the car at the first time she gets both an oil change and a tire rotation at the same time?     

3,750 x 4  =  15,000  

5,000 x 3  =  15,000  

First term =2

Second term =2^2 * (2 - 1) = 4

Third term =4^2 * (4 - 1) =48

Fourth term =48^2 * (48 - 1) =108,288

Fifth term =108,288^2 * (108,288 - 1) =1,269,804,867,452,928.......and so on.

The cost of the television is $740.

If it is on sale for 40% off, multiply the original cost of the television by 0.6. The price of the television when it is on sale will be $444. 

Joeseph will be paying 30% of $444. Multiply 444 by 0.3. Which gets to the final answer of $133.20.

(-2, -4)

Good job! I also got the 1st digit of 20! is 2.

1) By computer, the first sum is 1/(sin(3)), so n = 3.

2) By computer, n = 16384, so the answer is 384.

-3          -108          -234          -384          -564          -783          -1053 

   ×2-102      ×2-18      ×2+84        ×2+204       ×2+345    ×2+513 

ow my thumbs

Yay!

20! is 2432902008176640000

The first digit of 20! is 2

Yay!

So sorry, my answer was wrong. Great job!

It's fine. Thanks I think I get it now. Brb I'm going to try to solve it

The favorable possibilities will be 1 choice out of 5, a 1/5 probability of getting a question right, 4/5 for getting a question wrong. Thus by the binomial probability distribution, 

P(8 correct; 2 wrong)

$(1/5)^8 \cdot (4/5)^2 \cdot {10 \choose 8}$

Make sure you see why this works! This is an AND (U) Probability! What is the formula and be sure to include the unfavorable attempts too!!

This gives you a result of $\frac{144}{1953125}$, or $0.000073728,$ or in standard form, $7.3728 \times 10^{-5}$, or $0.0073728$%

For what value of b will this equation have only one real root: (2b−5)x^2−2(b−1)x+3=0.

7/ (7+3) x      -3    = 5/(5+3) x

solve for x = total amount = 40

7 / 10   * 40 = 28

3/10 * 40    = 12      initially

A/H =7/3,   

(A - 3) / (H + 3) =5 / 3, solve for A, H

Alia had 28 and Huda had 12 initially.

There are 12 digaonals that have a length of P_1 P_2, which from the Sine Law, is sin (15 degrees).  There are 12 diagonals that have a legnth of P_1 P_3, which from the Sine Law, is sin (30 degrees).  We can appy the same reasoning to the other diagonals, which gives us a total sum of

(12 sin 15)^2 + (12 sin 30)^2 + (12 sin 45)^2 + (12 sin 60)^2 + (12 sin 75)^2 + (12 sin 90)^2 + (12 sin 105)^2 + (12 sin 120)^2 + (12 sin 135)^2 + (12 sin 150)^2 + (12 sin 175)^2 = 864.

Since we have double-counted, the answer is 864/2 = 432.

What is the area in square units of the convex quadrilateral with vertices (-1, 0), (0, 1), (2, 0) and (0, -3)?

NO!  THAT IS NOT TRUE !!!!  I gave you the answer of 1,256 because:

1256 mod 9 = 5

1256 mod 7 = 3

1256 mod 5 = 1

Your answer of 1561 DOES NOT balance the congruences, because:

1561 mod 9 =4 NOT 5

1561 mod 7 =0 NOT 3

1561 mod 5 = 1

The smallest possible value of N is 1561.

48 birds were transferred on the last day.

You don't understand the answer given under your first post? if so, why?

SOLVED
ANS=5

2 - There are 576 three-digit numbers. Their sum: 5 + 7 + 6 =18. The sum of 18 = 1 + 8 =9. So:

576 + 18 + 9 =603 mod 9 =0.

The discriminant of the quadratic formula must = 0 to have only one root

b^2 - 4ac = 0

b in the quadratic formula for this case is -2b+2      a is 2b-5     c is 3  

Plug these values into the red equation to find  b = 4