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This is a computer code in C++:

d=0; if(d==0, goto Begin, goto End);

Begin:d=0;a=listfor(i,10000,99999,i);c=sumforeach(x, a, x%10==d or (x div 10)%10==d and x>9 or (x div 100)%10==d and x>99  or (x div 1000)%10==d and x>999 or (x div 10000)%10==d and x>9999;print"Total(0)=",c;return;

Total= 30,951 - this is the number of integers with at least 1 zero.

Hello, hope this helps! I just expanded the given expression and got this:
 

\(729 y^{12} + 2916 y^{11} - 2430 y^{10} - 19980 y^9 + 135 y^8 + 59976 y^7 + 6364 y^6 - 99960 y^5 + 375 y^4 + 92500 y^3 - 18750 y^2 - 37500 y + 15625\)

As posted before:

ab^4 = 48     then a = 48/b^4

sub into the second equation

48/b^4  * b = 72

48/72 = b^3 

b = .87358      then    a = 82.4194

Let x be the number of $10-notes. The total value of the $2-notes is 2 * 8x = 16x. The total value of the $5-notes is 5 * 3x = 15x. The total value of the $10-notes is 10x. The total value of all the notes is 16x + 15x + 10x = 41x. After 58 $2-notes and 10 $5-notes are taken out, the remaining notes are worth 41x - 2 * 58 - 10 * 5 = 223. Solving for x, we get x = 11. Therefore, there are 11 pieces of $10-notes. So the answer is 11

-2, -4/3

If the area of the circumcircle around triangle OYZ with center X is 1, then the area of triangle XYZ is 1/6.

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We can divide the number line into 4 equal segments, each of length 1/4. If the second number chosen is in the same segment as the first number, then it will not exceed the first number by a distance greater than 1/4 unit. If the second number chosen is in one of the adjacent segments, then it will exceed the first number by a distance greater than 1/4 unit. Therefore, the probability that the second number chosen will exceed the first number by a distance greater than 1/4 unit is 3/4.

Using the information given we can form an equation: 5x = 7+x. Now we solve for x:

5x = 7+x

5x-x = 7+x-x (subract x from both sides)

4x = 7 (combine the like terms)

x = \(\frac{7}{4}\) (divide by 4 to isolate x)

Now let's check our answer by plugging in the value of x to the question:

\(5 \cdot x = 5 \cdot \frac{7}{4} = \frac{35}{4} \)

\(\frac{7}{4}+7 = \frac{7}{4} + \frac{28}{4} = \frac{35}{4}\)

\(\frac{35}{4} - \frac{35}{4} = 0 \)

How many ".............students are 8th graders with brown eyes" ??

a + 2b + 3c + 4d + 5e = 41

2a + 3b + 4c + 5d + e = 15

3a + 4b + 5c + 1d + 2e = 34

4a + 5b + 1c + 2d + 3e = 68

5a + 1b + 2c + 3d + 4e = 57

Use eliminations and substitutions to get:

a==91/15,  b==76/15,  c== - 59/15,  d== - 14 / 15,  e==121/15

1 - 243 - reverse the digits at both ends

2 - It becomes: 324

3 - Take its square root.

4 - sqrt(324) ==18 - reverse the two digits and it becomes: 81

5 - Take its square root.

6 - Sqrt(81) ==9 - the original number that Thea entered into her calculator.

g = grogg age now     d = dad age now 

(g-7) *6  = d- 7     <====given     re-arrange to   g = (d+35)/6

(g-4) * 4 = d- 4   or    4g -16 = d-4     or    4g = d+12       sub in the vlaue of g above 

                                                         4 (d +35) / 6  = d + 12 

                                                          4d +140 = 6d + 72 

                                                                            2d = 68 

                                                                               d = 34 y/o 

sumfor(n, 21, 40, n^2)==19,270 

The sum of the angles in a triangle sum to 180 degrees.

So, we have 
p + 2q + 6p - 8q + 17p + 2q = 180
24p - 4q = 180

6p - q = 180
 

P can equal many numbers, assuming you want integers

F==Full tank

1/2F  -  1/6F ==1/3F

1/3F ==2

F ==2 x 3 ==6 gallons - full capacity of the tank.

 What is the total capacity of the aquarium tank, in gallons?  

Hello Guest!

\(\frac{x}{2}+2\ gallons=x\\ \color{blue}x=4\ gallons\)

The total capacity of the aquarium tank is 4 gallons.

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a + ab = 250

a - ab = -240

Enter all possible values

Hello Guest!

\(a + ab = 250\\ a=\frac{250}{1+b}\\ a - ab = -240\\ \frac{250}{1+b}-\frac{250b}{1+b}=-240\\ 250-250b=-240(1+b)\\ -250b+240b=-240-250\\ -10b=-490\\ \color{blue}b=49\\ a=\frac{250}{1+49}\\ \color{blue}a=5\)

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P(-2,1), P(3,3) Find an equation of the line.

Hello Guest!

\(f(x)=m(x_P-x)+y_P\\ m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-1}{3-(-2)}\\ m=\dfrac{2}{5}\\ f(x)=\dfrac{2}{5}(x-3)+3=\dfrac{2}{5}x+\dfrac{9}{5}\\or\\ f(x)=\dfrac{2}{5}(x+2)+1=\dfrac{2}{5}x+\dfrac{9}{5}\\ \color{blue}f(x)=\dfrac{2}{5}x+\dfrac{9}{5}\)

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The given space is a cube with sides of length 2 centered at the origin. The condition x2+y2+z2≤1 represents a sphere with a radius of 1 centered at the origin. The two regions intersect in a four-sided pyramid with vertices at (1, 1, 1), (1, -1, -1), (-1, -1, 1), and (-1, 1, -1). The volume of the cube is 8, and the volume of the pyramid is 1/3 * 2 * 2 * 2 = 8/3. Therefore, the probability that a randomly selected point in space satisfies the condition x2+y2+z2≤1 is 8/3 / 8 = 1/3.

Oh ok! Thank you! This really helps!!

B mixture has:

5 / 0.2 ==25 g of pepper - so that: 25 g * 0.20 ==5 g of pepper
2/0.4 ==5 g of Ginger     - so that:   5 g * 0.40 ==2 g of Ginger
2 /0.4 ==5 g of Turmeric - so that:   5 g * 0.40 ==2 g of Turmeric

B mixture =25 + 5 + 5 ==35 grams

The area of triangle ABC is 

\(A_{ABC}=\dfrac{(\overline {BX}+\overline {XC})\cdot \overline {AX}}{2}=\dfrac{(10+10)\cdot 13}{2}=130\)

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I wrote a computer code and it gives the answer as: 1023 - not including the empty set - as the number of sets that contain only composite numbers. So: 1023 + 1 =1024 subsets. I hope that helps.

The coefficient of y^4 is 375.

\((2y-5+3y^2)^6\\= 15625 - 37500 y - 18750 y^2 + 92500 y^3 + 375 y^4 - 99960 y^5 + 6364 y^6\\+ 59976 y^7 + 135 y^8 - 19980 y^9 - 2430 y^{10} + 2916 y^{11} + 729 y^{12}\)

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