Four-pack of 16-oz cans of soup contains 16*4=64 oz with a price of \(\dfrac{3,20}{64}=0,05\left(ounce\right)\). 

Three-pack of 24-oz cans of soup contains 24*3=72 oz with a price of \(\dfrac{3,60}{72}=0,05\left(ounce\right)\).

The difference is 0 cent.

Cause there is a 2/3 chance of rain for each of three days. So 1/3 chance it will not rain.

The probability that it will rain on none of the three days is \(\dfrac{1}{3}\cdot\dfrac{1}{3}\cdot\dfrac{1}{3}=\dfrac{1}{27}\)

The sum of Anthony after 5 tests is \(85\cdot5=425\)

Cause the median is 87 and unique mode is 92. So the points of five tests are : x,y,87,92,92.

So x+y = 154. Cause 92 is the unique mode so x (or y) is the greatest < 87 is 86.

So the lowesr score Anthony could have is 68.

The closing price on Wednesday was \(\dfrac{72000}{10}=7200\)$

The closing price on Tuesday was \(\dfrac{7200}{3}=2400\)$

The closing price on Monday was \(\dfrac{2400}{2}=1200\) $

Just do backward :))

The radius has point (3,7) and (1,4).

So its slope is \(\dfrac{7-4}{3-1}=\dfrac{3}{2}\)

Cause Line m is tangent to a circle so the slope of line m is \(-\dfrac{2}{3}\)

We know the length of the shorter leg in each triangle is x = 9.

So y and z will present the longer leg and the hypotenuse.

Using Pythagorean : \(9^2+y^2=z^2\Rightarrow81=\left(z-y\right)\left(z+y\right)\)

Now we find (z-y) and (z+y) when multiply we have 81.

We have 81 = (9*9),(3*27),(1*81).

Cause \(\left(z-y\right)\ne\left(z+y\right)\) so (9*9) don't satisfy.

So apply the (3*27) and (1*81) to (z-y) and (z+y) we have :

+) \(\left\{{}\begin{matrix}z-y=3\\z+y=27\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}z=15\\y=12\end{matrix}\right.\) satisfy cause it gives us the triple (9;12;15) Pythagorean Triple triange.

+) \(\left\{{}\begin{matrix}z-y=1\\z+y=81\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}z=41\\y=40\end{matrix}\right.\)satisfy cause it gives us the triple (9;40;41) Pythagorean Triple triange.

So the sum of the lengths of the longer legs of these two triangles are 12 + 40 = 52.

The odds against the Patriots playing in the championship game are 4:1 => the probability that they won't play is 4/5 , the probability that they play is 1/5.

The odds against the Texans playing in the championship game are 7:1 => the probability that they won't play is 7/8 , the probability that they play is 1/8.

The probability that those two teams will play each other in the championship game is \(\dfrac{1}{5}\cdot\dfrac{1}{8}=\dfrac{1}{40}\)

\(FACT\left(144\right)=2^4\cdot3^2\)

So we have \(\left(4+1\right)\cdot\left(2+1\right)=15\) positive pairs of intergers (x;y) and also 15 negative pairs of intergers (x;y).

So there are 15 + 15 = 30 pairs of (x;y) satisfy \(xy=144\)

The answer is 140 yards.

The boat must cross the river 7 times, each time 20 yards so the answer is 20.7=140 (yards).

Following the thread we can know that Michael Cresta must draw a T and an Y or an Y and a T.

And 3 Ts , 1 Y were taken from 56 tiles all.

So the probability will be \(\dfrac{3}{56}\cdot\dfrac{1}{55}+\dfrac{1}{56}\cdot\dfrac{3}{55}=\dfrac{6}{3080}=\dfrac{3}{1540}\)

When using only the 5-gallon and the 20-gallon jugs we can obtain 5,10,15,20,25 gallons of water.

The sum is 5+10+15+20+25=75 gallons.

I have had a calculation and here is my final answer :

Noah has a monthly sales quota to sell : 2+4+8+16+32+64 = 126 cars.

Ohh i have a mistake :((

Finalists can be choosen by \(51\cdot50\cdot49=124950\) ways so that means it can occur in 124950 ways.

We know that \(\dfrac{12+v+w+x+y+z}{6}=20,75\)

So the sum of these six numbers must be \(20,75\cdot6=124,5\)

In \(\dfrac{51\cdot50\cdot49}{3\cdot2\cdot1}=20825\)ways can the three finalists be chosen.

The ratio is : \(\dfrac{4950000}{49500000}=\dfrac{1}{10}\) (equal the Sum of four-digit palindromes/the Sum of five-digit palindromes).

a) \(x^4-x^3+x^2-x=0\)

\(\Leftrightarrow x^3\cdot\left(x-1\right)+x\cdot\left(x-1\right)=0\)

\(\Leftrightarrow\left(x^3+x\right)\left(x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

b) \(x^2-8^2=0\)

\(\Leftrightarrow\left(x-8\right)\left(x+8\right)=0\Rightarrow\left[{}\begin{matrix}x=-8\\x=8\end{matrix}\right.\)

c) \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+10\right)=55\)

\(\Leftrightarrow10x+55=55\)

\(\Rightarrow x=0\)

The number of odd three-digit natural numbers less than 523 is :

\(\dfrac{521-101}{2}+1=211\left(numbers\right)\)

From 521 to 101 we have 67 numbers that contain 5 in its.

So 211 - 67 = 144 (odd numbers) less than 523 contain no 5.

We have :

3 complete pages ----------------- 40 seconds.

x complete pages ----------------- 180 seconds (= 3 minutes).

So we get \(x=\dfrac{3\cdot180}{40}=13,5\), So there will be 13 complete pages it print in 3 minutes.

3 Less than half : \(\dfrac{x}{2}-3\)

Her brother give response 9, the number that is : \(9=\dfrac{x}{2}-3\Rightarrow x=24\)

The number that Connie said is 24.