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Phoenix [80]
3 years ago
11

Select each set of events that are independent.

Mathematics
1 answer:
sashaice [31]3 years ago
3 0

Answer:

Options A, B and C are all independent events while the rest are all dependent events.

Step-by-step explanation:

Please kindly check the attached files for explanation.

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Share £480 in the ratio 2:3:7
aleksandr82 [10.1K]
£480

2:3:7 =  2+3+7  = 12

 2
--- 0f £480 = £80
12


 3
--- of £480 = £120
12

 7
--- of £480 = £280
12


answer =  £80 : £120 : £280
5 0
3 years ago
Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.
irina1246 [14]
Lagrange multipliers:

L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)

L_x=y^2z^2+\lambda=0
L_y=2xyz^2+\lambda=0
L_z=2xy^2z+\lambda=0
L_\lambda=x+y+z-5=0

\lambda=-y^2z^2=-2xyz^2=-2xy^2z

-y^2z^2=-2xyz^2\implies y=2x (if y,z\neq0)

-y^2z^2=-2xy^2z\implies z=2x (if y,z\neq0)

-2xyz^2=-2xy^2z\implies z=y (if x,y,z\neq0)

In the first octant, we assume x,y,z>0, so we can ignore the caveats above. Now,

x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of f(1,2,2)=16.

We also need to check the boundary of the region, i.e. the intersection of x+y+z=5 with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force f(x,y,z)=0, so the point we found is the only extremum.
4 0
3 years ago
What is the correct letter? (Giving brainliest)
vampirchik [111]

Answer:

d is the answer

Step-by-step explanation:

perimeter of rect = 2(7+3) = 20

perimeter of square = 4 a =20

a = 5

3 0
2 years ago
Which statements are true about the rules of multiplication for signed numbers? Check all that apply.
Mekhanik [1.2K]

Answer:

i think that 1, 3 and 4 are correct !!

Step-by-step explanation:

youre welcome, have a nice day!

NOTE: next time please provide the list of choices so it can be easier to help you

4 0
3 years ago
there are 5 pounds of apples in one bag make a table to show how many pounds of apples are in 6 bags. how do you know your answe
Dmitrij [34]
You can make a table like this:


If 1 bag=5 pounds
Then 6 bags must equal six times the weight of the first bag
5 times 6=30
Your answer is reasonable because 5+5+5+5+5+5=30

a.k.a
=5 =30


3 0
3 years ago
Read 2 more answers
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