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Look here:  https://web2.0calc.com/questions/help-math-problem_8

I know this is a troll question, but here you go :)

I am guessing a lot of stuff since you didn't put them in (work distance, etc.) Also, the answer will be a rough estimate in years.

35, 757, 093 minutes to get to the store-----> roughly 697.01 years

Since your father is slow in the head, it will take him about 5 minutes to realize he doesn't have enough money to buy the milk. Going to

work, guessing about 30 miles from the store in the opposite direction of your house, it takes him, with the given 0.05 mph, about 600 hours or 0.07 years, to get to his work.

That is if, and only if, a cop does not pull over your father for the 200th time for diving immensely slow. It would be a usual sentence of fewer than 30 days. However, your father has been there a lot and the judge has had enough of your father being a public nuisance. This makes the judge sentence your father to jail time for 50 years. Worst-case scenario, your father is sentenced to a lifetime jail residence so make that infinite years.

However, let's not think that way. He gets to work and has to work for the listed 950, 000 days (roughly 2666.67 years). Getting back to the store will take another 0.07 years, buying the milk will take about 50 more years with the state your father's mind is in. Finally, it will take another 697.01 years to get home. 

Totaled up, this is an approximate 4160.83 years for your father to come back home with the milk. Unfortunately, the milk is spoiled by the time he gets home, unless it's the special "Never Go Bad Milk" brand, which is probably not the case since your father probably read the label wrong and got the "Goes Bad in 3 Seconds Milk" brand instead. Thus repeating the never-ending cycle.

sumfor(n, 13, 213, 2*n)==45,426 - sum of all EVEN numbers between 25 and 427

How many ways can you arrange 2 boys and 3 girls in a line, if the 2 boys must stand next to each other?  

B1B2  G1  G2  G3        G1  B1B2  G2  G3        G1  G2  B1B2  G3        G1  G2  G3  B1B2 

B1B2  G1  G3  G2        G1  B1B2  G3  G2        G1  G3  B1B2  G2        G1  G3  G2  B1B2 

B1B2  G2  G1  G3        G2  B1B2  G1  G3        G2  G1  B1B2  G3        G2  G1  G3  B1B2 

B1B2  G2  G3  G1        G2  B1B2  G3  G1        G2  G3  B1B2  G1        G2  G3  G1  B1B2 

B1B2  G3  G1  G2        G3  B1B2  G1  G2        G3  G1  B1B2  G2        G3  G1  G2  B1B2 

B1B2  G3  G2  G1        G3  B1B2  G2  G1        G3  G2  B1B2  G1        G3  G2  G1  B1B2 

So far, we've found 24 ways to arrange these people, with the boys standing Boy 1 Boy 2. 

Now change the position of the boys, to B2B1, and do the same thing for another 24 ways. 

Total possible arrangements, 48 ways.  

_.

Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial.

x^2 + 48x + ___    

This one is easy because the coefficient of the squared term is one. 

When you have (x + n)², multiplied out is x² + 2nx + n²    

In this example, 2nx = 48x therefore n = 24   

So n² = 24², which works out to 576  

Put 576 in that blank.     

_.

9.81477439992×10^-43==0.6309297536^ m/n, solve for m

m==200,   n==101

m  +  n ==200  +  101 ==301

Note: there maybe other integer solution for m and n.

In which number is the value of the 7 ten times the value of the 7 in the number 1,273?  

Were you supposed to give a list to choose from? 

You said "which" number, not "what" number.  

In 1,273 the 7 is in the 10's position.  

So, the answer is the number that has the 7 in the 100's position,

i.e., the one that has the 7 as the third digit going left from the decimal point.  

_.

Ohhhh. This makes sense! I don't really remember how to solve these problems because I missed one class on this topic and didn't fully understand it. Thanks alot!

b² – 4ac = 105  

25 – (4)(1)(c) = 105  

–4c = 80 

    c = –20  

_.

Let the son's age ==S

Father's age ==9S

9S + 3 ==6 [S + 3], solve for S

9S + 3 == 6S + 18

9S - 6S ==18  -  3

3S == 15

S ==15 / 3 == 5 years - the son's age.

Hints:

1-Think about the general form of a "Rotation Matrix" (Something to do with cos(theta),sin(theta),-sin(theta),cos(theta), arranged in a 2x2 matrix).

2-A 2x2 matrix that dilates by scale factor of k must have two elements out of the four as "k"  and the other two elements are 0, as it is centered about the origin.

3-BA means multiply matrix A by matrix B, and order matters (B first then A). Use (1) and (2) to find BA.

4-You are given BA, compare each element you got from (3) with the corresponding given element.

5-Look for the desired system of equations.

6-Solve the system (Further hint: Think of tan(theta)=sin(theta)/cos(theta))

7-It seems there exists two answers for theta... Are both valid? Why? Why not?
8-Hint: k is positive! 

Solution:

Ok, if A is a rotation matrix then it must be:

\(A=\begin{bmatrix} cos\theta && -sin\theta \\ sin\theta && cos\theta \end{bmatrix}\)

and If B is a matrix that dilates then it must be: \(\begin{bmatrix} k && 0 \\ 0 && k \end{bmatrix}\)

So given: \(BA=\begin{bmatrix} -1 && -1 \\ 1 && -1 \end{bmatrix}\)  \(=\)    \(\begin{bmatrix} k && 0 \\ 0 && k \end{bmatrix}\) * \(\begin{bmatrix} cos\theta && -sin\theta \\ sin\theta && cos\theta \end{bmatrix}\)

\(\begin{bmatrix} kcos\theta && -ksin\theta \\ ksin\theta && kcos\theta \end{bmatrix}\)

and just comparing each element of the matrix yields a system with sufficient equations to find both k and theta.

\(-1=kcos\theta \text{ And, }1=ksin\theta\)

Divide the latter by the former:

\(\frac{ksin\theta}{kcos\theta}=-1 \iff tan\theta=-1\), therefore, \(\theta=135,315\) Now, which one of these is the answer depends on the previous system of equations.

Well, since k is positive, then \(\frac{-1}{cos\theta},\frac{1}{sin\theta}\) must be positive. If \(\theta=135\), this is satisfied. But, If \(\theta=315\) 1/sin(theta) will be negative! Hence k is negative, but we are given k>0. Thus we reject \(\theta=315\).

Therefore, \(\theta=135\) only, yielding: \(k=\sqrt{2}\)

Area of rectangle A = 1 * b

                 = 2 * 7 

                 = 14 m2

Area of triangle B

                = 1/2 * b * h

                = 1/2 * 4² * 3

                = 6 m2

Area of triangle C = 1 * b

                             = 9 * 2

                             = 18 m2

Total area = (14 + 6 + 18)m2

                    = 38 m2

Might as well make this easier for others to read.

Suppose that \(\frac{\log_3 2}{\log_2 9} \cdot \frac{\log_3 4}{\log_2 27} \cdot \frac{\log_3 8}{\log_2 81} \cdots \frac{\log_3 2^{100}}{\log_2 3^{101}} = \frac{(\log_3 2)^m}{n}\), where m and n are integers. Find m+n.

That's wrong!!!

I don't know the answer

900/4x3-20=-8

Thanks for the explanation!

A palindrome is a number that reads the same forward as backward. If a three-digit palindrome is randomly chosen, what is the probability that it is a multiple of  8?

1*1     none

2*2        132      172      

3*3     none

4*4        

5*5      none

6*6        816

7*7       none

8*8        808

9*9      none

808, 616, 424, 232,  848, 656,  464,  272,  888, 696

there 10 of them. ar mulples of 8

1*1    10 of those

2*2      10 of those

...

9*9    10 of those

90     3 digit palindromes

P(3 digit palindrome is multiple of 8) =    10/90  = 1/9

As always, you need to check.

Theta is the 8th letter of the Greek alphabet.

Your queston is incomplete.

Future Population==17,000 x 1.03^7 ==20,908 - population of the town after 7 years.

Or more accurately, since population growth is a "continuous process", the following is more accurate:

Future Population==17,000  x  e^(0.03*7) ==20,973 - population of the town after 7 years.

There are 90 3-digit palindromes as follows:

(101 , 111 , 121 , 131 , 141 , 151 , 161 , 171 , 181 , 191 , 202 , 212 , 222 , 232 , 242 , 252 , 262 , 272 , 282 , 292 , 303 , 313 , 323 , 333 , 343 , 353 , 363 , 373 , 383 , 393 , 404 , 414 , 424 , 434 , 444 , 454 , 464 , 474 , 484 , 494 , 505 , 515 , 525 , 535 , 545 , 555 , 565 , 575 , 585 , 595 , 606 , 616 , 626 , 636 , 646 , 656 , 666 , 676 , 686 , 696 , 707 , 717 , 727 , 737 , 747 , 757 , 767 , 777 , 787 , 797 , 808 , 818 , 828 , 838 , 848 , 858 , 868 , 878 , 888 , 898 , 909 , 919 , 929 , 939 , 949 , 959 , 969 , 979 , 989 , 999)==90 Palindromes.

There are 10 palindromes that are multiples of 8 as follows:

(232, 272, 424, 464, 616, 656, 696, 808, 848, 888) >>Total = 10 palindromes.

Therefore, the probability is: 10 / 90 == 1 / 9

Hello MobiusLoops,

When a matrix is applied on a region, the determinant of the matrix is the scale factor of the enlargement that occurs.

That is, the determinant of the matrix: \(\begin{bmatrix} 2 && 1 \\ 3 && -7 \end{bmatrix}\) is: \(2(-7)-1(3)=-17\)  

(In general, the determinant of: \(\begin{bmatrix} a && b \\ c && d \end{bmatrix} \) is \(ad-bc\) )

So, \(3(-17)=-51\), since It is an area, then we take the absolute value of this number, giving the answer to be 51, which is the area of R'.

(The determinant of 3x3 matrix, will be the "Volume scale factor" and the determinant of 2x2 matrix will be "Area scale factor (as above).")

Find the value of sin 2A.

Hello Guest!

cos A = w

\(w^2+w-1=0\\ w=-0.5\pm \sqrt{0.25+1}=-0.5\pm 0.5\sqrt{5}\\ w\in \{{\color{red}-0.5(1+\sqrt{5})},\ \color{blue}-0.5(1-\sqrt{5})\}\\ sin\ 2A=2sin\ A\cdot cos\ A\\ sin\ A=\sqrt{1-cos^2\ A}\)

\(sin\ 2A=\pm 2\sqrt{1-w^2}\cdot w\\ sin\ 2A=\pm 2\sqrt{1-(-0.5(1-\sqrt{5}))^2}\cdot (-0.5(1-\sqrt{5}))\\ \color{blue}sin\ 2A\in \{0.9717,\ -0.9717\}\)

  !

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