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Helen [10]
3 years ago
14

Each day the wildlife commission releases 100 fish into the Durkee River in the following proportions: 55 brown trout and 45 rai

nbow trout.All of the fish swim through a watch station, one at a time,on the way upstream.which of the following expression represents the way to calculate the probability of a passing fish being a rainbow trout? 1. 45/55 2. 45/ 100 3. 55/100 4. 55-45/100 5. 45 +55 /100
Mathematics
1 answer:
bazaltina [42]3 years ago
6 0
45/100 so, 45 of every 100 fish should be rainbow trout.
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1. Prove or give a counterexample for the following statements: a) If ff: AA → BB is an injective function and bb ∈ BB, then |ff
Fantom [35]

Answer:

a) False. A = {1}, B = {1,2} f: A ⇒ B, f(1) = 1

b) True

c) True

d) B = {1}, A = N, f: N ⇒ {1}, f(x) = 1

Step-by-step explanation:

a) lets use A = {1}, B = {1,2} f: A ⇒ B, f(1) = 1. Here f is injective but 2 is an element of b and |f−¹({b})| = 0., not 1. This statement is False.

b) This is True. If  A were finite, then it can only be bijective with another finite set with equal cardinal, therefore, B should be finite (and with equal cardinal). If A were not finite but countable, then there should exist a bijection g: N ⇒ A, where N is the set of natural numbers. Note that f o g : N ⇒ B is a bijection because it is composition of bijections. This, B should be countable. This statement is True.

c) This is true, if f were surjective, then for every element of B there should exist an element a in A such that f(a) = b. This means that  f−¹({b}) has positive cardinal for each element b from B. since f⁻¹(b) ∩ f⁻¹(b') = ∅ for different elements b and b' (because an element of A cant return two different values with f). Therefore, each element of B can be assigned to a subset of A (f⁻¹(b)), with cardinal at least 1, this means that |B| ≤ |A|, and as a consequence, B is finite.

b) This is false, B = {1} is finite, A = N is infinite, however if f: N ⇒ {1}, f(x) = 1 for any natural number x, then f is surjective despite A not being finite.

4 0
3 years ago
Construct parallelogram PQRS<br>with |PQ|=10cm, |ps|=8cm and<br>&lt;QPS = 120​
IgorC [24]

Find sketch of parallelogram attached

Answer and explanation:

A parallelogram is a quadrilateral which is wider than it is long. A parallelogram has two sides parallel to the other. From the above, we are told the parallelogram PQRS has an angle QPS 120, with sides 10cm and 8cm, we use this to sketch the parallelogram

We find that angle QPS is 120 degrees hence angle RSP is 60 degrees since angle on straight line is 60 degrees from 180-120 in angle QPS and alternate angles are equal. Also opposite angles of a parallelogram are equal

4 0
3 years ago
How do I simplify the following to "a+bi" form: (1+2i)^3
damaskus [11]

Answer:

Expand it.

(1+2i)^3 is equal to (1+2i)(1+2i)(1+2i).

Multiply everything out (being sure to multiply <em>every</em> term. (1+2i) * (1+2i) = 1+2i+2i+4i^2.

i is the square root of negative one, so i^2 is just -1. 1+2i+2i-4 is what you get from the first two, so now simplify that:

1-4 + 2i+2i = (-3+4i) and now multiply that by (1+2i):

(-3+4i) * (1+2i) = -3 - 6i +4i +8i^2.

Simplify again, and the answer is: -11-2i

Step-by-step explanation:

I hope this helps - really my only tip is don't spend time thinking about what i is, that just hurts your brain. Just remember that i^2 is equal to negative one, and treat it like regular multiplication and you will be fine.

7 0
1 year ago
You earn $18 for watching three cars how much do you earn to Washing 2 cars
Sever21 [200]

Answer:

$12

Step-by-step explanation:

3 cars divide that by $18 and u get $6 per car. multiply that by two cars nd you get $12.

6 0
2 years ago
-3x+3y=3<br> -5x+y=13<br> Solve for substitution
vladimir1956 [14]
Take -5x + y =13 and rearrange for y:
y=13+5x

Substitute into other equation for y:
-3x+3(13+5x)=3

Multiply out brackets:
-3x+39+15x=3

Simplify:
12x+39=3

Rearrange for x:
12x=-36
x=-3

Substitute back into y=13+5x:
y=13+5(-3)
y=13-15
y=-2

8 0
3 years ago
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