Is −10 − 5 equal to −10 + (−5)? Explain in terms of additive inverses.

Mathematics

1 answer:

Gelneren [198K]3 years ago

5 0

Yes!
Because -10 - 5 is -15 and -10 + (-5) is also -15 so they’re equal!

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3 years ago

A bag contains 6 red apples and 5 yellow apples. 3 apples are selected at random. Find the probability of selecting 1 red apple

tester [92]

Answer: The required probability of selecting 1 red apple and 2 yellow apples is 36.36%.

Step-by-step explanation: We are given that a bag contains 6 red apples and 5 yellow apples out of which 3 apples are selected at random.

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Let S denote the sample space for selecting 3 apples from the bag and let A denote the event of selecting 1 red apple and 2 yellow apples.

Then, we have

$n(S)=^{6+5}C_3=^{11}C_3=\dfrac{11!}{3!(11-3)!}=\dfrac{11\times10\times9\times8!}{3\times2\times1\times8!}=165,\\\\\\n(A)\\\\\\=^6C_1\times^5C_2\\\\\\=\dfrac{6!}{1!(6-1)!}\times\dfrac{5!}{2!(5-2)!}\\\\\\=\dfrac{6\times5!}{1\times5!}\times\dfrac{5\times4\times3!}{2\times1\times3!}\\\\\\=6\times5\times2\\\\=60.$

Therefore, the probability of event A is given by

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Read 2 more answers

What is the focus of the parabola? y=−1/4x^2−x+3

Delvig [45]

We know that
the equation of the parabola is of the form
y=ax²+bx+c

in this problem
y=−1/4x²<span>−x+3
where
a=-1/4
b=-1
c=3

</span><span> the coordinates of the focus are
</span>
(-b/2a,(1-D)/4a)
where
D is the discriminant b²-4ac
D=(-1)²-4*(-1/4)*3-----> D=1+3---> D=4
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> -2

y coordinate of the focus
(1-D)/4a------> (1-4)/(-4/4)---> 3

the coordinates of the focus are
(-2,3)

5 0

4 years ago