All Answers 352639 Answers

yes, it is

Infinity :)

The probability of the first fish being a catfish is 5 catfish out of 19 total fish \(\Rightarrow \frac{5}{19}\)

The probability of the second fish being a catfish is 4 catfish out of 18 total fish \(\Rightarrow \frac{4}{18} \Rightarrow \frac{2}{9}\)

The total probability is \(\frac{5}{19} \cdot \frac{2}{9} = \frac{10}{171}\)

How much food would the zoo need to provide all five lions a day?

https://prnt.sc/qrd2v8

would it be the second one 

In how many years will the trees be the same height?

Am I correct? ​ Can anyone please help me?ASAP!!! Thank you

Yes, you are correct! 

You can always check for it by substituting n=1, n=2 etc.. and compare it with the geometric sequence. 

How many sequences of length 5 can be formed using the digits 0, 1, 2, . . . , 9 with the property that exactly two of the 10 digits appear, e.g., 05550

Hi Guests,  asker and answerer. 

Here is my take. No promises that I am right though.

There are 10C2 = 45  conbinations of 2 numbers

You can have them in the ratio 1:4    or   2:3

It you have 1 of one of the numbers and 4 of the other then there is 5 ways to do that.

But either can be the single so that is 2 times

so I have   2*5*45 = 450 ways

If I have 2 or 1 and 3 of the other then i have 2*5C2ways = 20       

20*45=900 ways

900+450 = 1350 combinations that meet that requirement. 

Continued here

Hi Heureka,

I've one question why is \(sin(\theta )=sin(180-A)\)

h = 40*0.65^8

h=1.274579252

With its radar, an aircraft spots another aircraft 8000 feet away at a 12 degree angle of depression Determine the vertical distance and horizontal distance between the two aircraft.

Do you make these things up as a challenge to this community ?? I think you do.

The number in question is = 25

2 + 5 =7.

7 x 4 =28

28 - 3 = 25 - which is your number.

25 + 27 = 52 which is 25 with its digits reversed.

Are you happy now?

An engine runs on 0.1 quart of oil for every 3.5 quarts of gasoline. You make 3 quarts of the mixture. How much oil and gasoline do you use?

Hello Guest!

\(x\cdot(3.5+0.1)=1\)

                    \(x=\frac{1}{3.5+0.1}=\color{blue}\frac{1}{3.6}\)

\(\frac{1}{3.6}\cdot(3.5+0.1)=\\ 0,97\overline 2+0,02\overline7=1\\ \times 3=\\ \color{blue}\ 2.91\overline6+0.08\overline3=3\)

gasoline      oil     mixture

  !

Please find the value of x.

sin-rule:

\(\begin{array}{|rcll|} \hline \dfrac{\sin(\theta)}{24} &=& \dfrac{\sin(A)}{3x-3} \\\\ \mathbf{\dfrac{\sin(A)}{\sin(\theta)}} &=& \mathbf{\dfrac{3x-3}{24}} \\ \hline \end{array}\)

sin-rule:

\(\begin{array}{|rcll|} \hline \dfrac{\sin(\theta)}{44} &=& \dfrac{\sin(180^\circ-A)}{5x} \quad | \quad \sin(180^\circ-A) =\sin(A) \\\\ \dfrac{\sin(\theta)}{44} &=& \dfrac{\sin(A)}{5x} \\\\ \mathbf{\dfrac{\sin(A)}{\sin(\theta)}} &=& \mathbf{\dfrac{5x}{44}} \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline \dfrac{\sin(A)}{\sin(\theta)} = \dfrac{3x-3}{24} &=& \dfrac{5x}{44} \\\\ \dfrac{3x-3}{24} &=& \dfrac{5x}{44} \\\\ 44(3x-3) &=& 24*5x \\ 132x- 132 &=& 120x \quad | \quad +132 \\ 132x &=& 120x +132 \quad | \quad -120x \\ 132x-120x &=& 132 \\ 12x &=& 132 \quad | \quad : 12 \\ x &=& 132 \quad | \quad : 12 \\ \mathbf{x} &=& \mathbf{11} \\ \hline \end{array}\)

There are 203 tickets sold for a college basketball game.
Tickets were $4.50 for students and $9 for adults.
The total amount collected was $1485.

How many of each type of ticket were sold?

\(\text{Let tickets for students $= x$ } \\ \text{Let tickets for adults $= y$ } \)

\(\begin{array}{|rcll|} \hline \mathbf{x+y} &=& \mathbf{203~tickets} \\ y &=& 203 - x \\\\ \mathbf{$4.50x + $9y} &=& \mathbf{$1485} \\ 4.50x + 9(203 - x) &=& 1485 \\ 4.50x + 1827 - 9x &=& 1485 \\ -4.50x + 1827 &=& 1485 \\ -4.50x &=& 1485-1827 \\ -4.50x &=& -342 \quad | \quad *(-1) \\ 4.50x &=& 342 \quad | \quad :4.50 \\ \mathbf{x} &=& \mathbf{76~tickets} \\\\ y &=& 203 - x \\ y &=& 203 - 76 \\ \mathbf{y} &=& \mathbf{127~tickets} \\ \hline \end{array}\)

76 tickets for students
127 tickets for adults

Lucinda is a cross-county ski racer. On Saturday she skied twice as many miles as she did on Sunday.
Over the weekend she skied a total of 63 miles. How far did she ski on each day?

\(\text{Let Saturday $= x$ } \\ \text{Let Sunday $= y$ } \)

\(\begin{array}{|rcll|} \hline \mathbf{x + y} &=& \mathbf{63~miles} \\ y &=& 63 - x \\\\ \mathbf{x} &=& \mathbf{2y} \\ x &=& 2(63 - x) \\ x &=& 126 - 2x \\ 3x &=& 126 \quad | \quad : 3 \\ \mathbf{x} &=& \mathbf{42~miles} \\\\ y &=& 63 - x \\\\ y &=& 63 - 42 \\ \mathbf{y} &=& \mathbf{21~miles} \\ \hline \end{array}\)

On Saturday she skied \(\mathbf{42~miles}\)
On Sunday she skied \(\mathbf{21~miles}\)

Jeff can get to any point in the square at (5,5), (5,-5), (-5,-5), (-5,5), so the answer is 100 points.

Truck #1 and Truck #2 left from the same location at the same time, driving in opposite directions.
If Truck #1 traveled at 70 mph and Truck #2 at 65 mph, how many hours was it before they were 1,755 miles apart?

Formula: \(s=v*t\)

\(\begin{array}{|lrcll|} \hline \text{Truck}_1: & s_1 &=& v_1 *t & v_1 = 70~mph \\ & s_1 &=& 70 *t \\\\ \text{Truck}_2: & s_2 &=& v_2 *t & v_2 = 65~mph \\ & s_2 &=& 65 *t \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline s_1+s_2 &=& 1755~ miles \\ 70 *t+65 *t &=& 1755 \\ 135 *t &=& 1755 \quad | \quad : 135 \\ \mathbf{ t } &=& \mathbf{13~h} \\ \hline \end{array}\)