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The probability is 3/10.

By Inclusion-Exclusion, there are 5 people who do all three activities.

Add

L   to both sides

then multiply both sides by 2/3

Given $z=-3+5i$, what is the conjugate $\overline{z}$ of $z$?  Plug in $-3+5i$ for $z$ and the value of the conjugage $\overline{z}$ into the formula $z + \overline{z}$ then simplify to get the answer.
 

Since $f(x)-f(x-2)=5x+1$, a linear function, $f$ must be a quadratic function.  Let $f$ be defined by $f(x)=px^2+qx+r$ for some constants $p$, $q$, $r$.  By substituting $x$ and $x-2$ into the formula for $f(x)$ we get $f(x)-f(x-2)=4px-4p+2q=5x+1$ for all $x$.  This gives two equations $4p=5$ and $-4p+2q=1$.  Solve for $p$ and $q$ and substitute them into $p+q$.
 

The above answer works for all $x$.  If we know that $x<5$, we have
$8x+5-|x-5|= 8x+5 - (5-x) = 8x+5-5+x= 9x$.
 

Yep...add all of the faces....     yep 75 cm^3

No....I do not want to 'Answer it ' .

W = 3T_u

  T = 5W = 5 (3T_u)

T_u  + 3T_u  + 5 (3 T_u) = 152

  19 T_u = 152

      T_u = 8    W = 24    T = 120 cards

Wait!  The question is not asking for how many 5-digit palindromes there are.  It wants the sum of all those palindromes instead.   For example, were I to change the 5 to a 2, the situation would be like this.   There are nine 2-digit palindromes: 11, 22, 33, 44, 55, 66, 77, 88, and 99, but the sum of all the 2-digit palindromes is $11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495$.
 

Angle = 48 degrees

The answer is the harmonic mean of 45 and 63.

Angle EFD = 180 - [1/2(180-69) + 1/2(180-78)]

Hi Melody, I make the transformed area 10.

The scaling on length is \(\sqrt{\sqrt3^2+1^2}=2\)  so the scaling on area is 2² = 4. 

(Note: there's no guarantee that I know what I'm talking about either!)

Let $a$ be the number of students in class A;
$b$ be the number of students in class B;
and $c$ be the number of students in class C.
The assumptions give you three equations in 3 unknowns $a$, $b$, and $c$.
\begin{eqnarray*}
a+b &=& 75 \\
a+c &=& 61 \\
b/c &=& 5/3
\end{eqnarray*}
The answer is $a$ after you solve this system of equations.
 

X-30 = 0.2x - 14

0.8 x  = 16

x = 20

20+40= 60

Double the money, double the rolls.  24 rolls 

(8/4)*12 = 2 *12= 24

In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle?  

There's probably some formula that could be set up, but I'm not that good.  I have to try brute force. 

All I know is, is that the sum of the lengths of two sides of a triangle must exceed the length of the third side. 

33, as above, is good if we assume that 17 is the longest side.  But what if it's not? 

Here are some other triangles.  I'll list 17 first in each case, since that side remains constant:

17, 5, 15   okay  

17, 6, 18   okay  

17, 7, 21   okay  

17, 8, 24   okay  

17, 9, 27   NOPE that won't work because 9 + 17 is not greater than 27.  

So my conclusion is that the greatest possible perimeter is 49 units, in the 17, 8, 24 triangle.  

_.

Let 
\begin{eqnarray*}
f_1 &=& 1+x+x^2+\dots+x^{68}+x^{69} \\
f_5 &=& 1+x^5+x^{10}+\dots+x^{60}+x^{65} \\
f_{10} &=& 1+x^{10}+\dots+x^{50}+x^{60} \\
f_{25} &=& 1+x^{25}+x^{50}.
\end{eqnarray*}
Find the term for $x^{69}$ in the expansion of $f_1f_5f_{10}f_{25}$.  The answer is the coefficient of the term for $x^{69}$.
 

The answer can be written out as an expression in terms of $a$ alone or $b$ alone.    You need to know either the value of $a$ or $b$ in order to know the exact value of $a^2-b^2+2a$.
 

Multiply the expression $(6x-12)(x-8)$ out to a form $ax^2+bx+c$ where $a$, $b$, and $c$ are explicit constants.  Then substitute the values of $a$ and $b$ into the expression $-b/(2a)$ to get the answer.
 

https://web2.0calc.com/questions/ratios_29

Hugo sells handmade key chains online. Yesterday, he made 6 keychains in 30 minutes. Hugo wants to make 9 keychains today. If Hugo works at the same rate today, how long will it take him to make the keychains?

maximum height occurs at t = 0        54 feet