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Katena32 [7]
3 years ago
12

A bag contains both 10 blue and 10 red objects. There are 5 blue circles, 5 red circles, 5 blue squares and 5 red squares. If I

draw out two objects from the bag what is the probability that both of them are circles?
A) 1/10
B) 1/4
C) 5/19
D) 9/38
Mathematics
2 answers:
-BARSIC- [3]3 years ago
8 0

Answer:

P(red or a circle) = 4⁄16 + 7⁄16 - 4⁄16 = 7⁄16 = 43.8%

Step-by-step explanation:

Levart [38]3 years ago
6 0

B) 1/4 because there are 4 groups and with those groups you can pick any of them








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A coordinator will select 6 songs from a list of 9 songs to compose an event's musical entertainment lineup. How many different
g100num [7]

Answer:

84 different lineups are possible

Step-by-step explanation:

The order in which the songs are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

6 musics from a set of 9. So

C_{9,6} = \frac{9!}{6!(9-6)!} = 84

84 different lineups are possible

4 0
3 years ago
How do you find a vector that is orthogonal to 5i + 12j ?
Rashid [163]
\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\
slope=\cfrac{a}{{{ b}}}\qquad negative\implies  -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\
-------------------------------\\\\

\bf \boxed{5i+12j}\implies 
\begin{array}{rllll}
\ \textless \ 5&,&12\ \textgreater \ \\
x&&y
\end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5}
\\\\\\
slope=\cfrac{12}{{{ 5}}}\qquad negative\implies  -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12}
\\\\\\
\ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}

if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.

so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.

so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.

or using a unit vector for those above, then

\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}}&#10;\\\\\\&#10;\cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}}&#10;\\\\\\&#10;\cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}
4 0
3 years ago
Please help me with these questions. Thank you.
Bas_tet [7]

Answer:

36 x⁸y⁶

 √2/2

Step-by-step explanation:

Factor 1296 into its prime factors

           1296 = 24 • 34 

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

           1296 = 24 • 34 

No factors remain inside the root !!

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

           36 = 22 • 32 

At the end of this step the partly simplified SQRT looks like this:

         36 √(x¹⁶y¹²)

STEP2:Simplify the Variable part of the SQRT

Rules for simplifing variables which may be raised to a power:

   (1) variables with no exponent stay inside the radical

(2) variables raised to power 1 or (-1) stay inside the radical

   (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

      √(x⁸)=x⁴

     √(x^-6)=x^-3

 

 Applying these rules to our case we find out that

      SQRT(x¹⁶y¹²) = x⁸y⁶

Combine both simplifications

      sqrt (1296x¹⁶y¹²) =  36 x⁸y⁶

Simplified Root : 36 x⁸y⁶ 

number 2)

3√2/3√4=

=3√2/3×2

=3√2/6

=3√2/6 ×3/3

=1√2/2

=√2/2

3 0
2 years ago
Find the length of the radius for this circle.(x - 3)² (y - 5)² = 8
viva [34]
The standard formula of circle is x^2 +y^2 = r^2 

hope this will help you getting the length of radius sure right easy 

r = sqrt8 = 2sqrt2 

hope this will help you  
6 0
3 years ago
Read 2 more answers
Fine the slope of the line that passes through (9,3) (2,2)
Charra [1.4K]
Just substitute it into the gradient formula which is: y2 - y1 / x2 - x1. So 2-3/2-9 = -1/-7 = 1/7
4 0
3 years ago
Read 2 more answers
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