Hurry please!!!!

I know number 13 is right, how do I do 11 and 12?

snow_tiger [21]

11. 43 ; 137
12. 12 ; 102

8 0

3 years ago

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

4 years ago

A demographer wants to measure life expectancy in countries 1 and 2. Let μ1 and μ2 denote the mean life expectancy in countries

Art [367]

Answer:

For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:

Null hypothesis: $\mu_1 \leq \mu_2 -10$

Alternative hypothesis: $\mu_1 > \mu_2 -10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 - \mu_2 >10$

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:

Null hypothesis: $\mu_1 \leq \mu_2 -10$

Alternative hypothesis: $\mu_1 > \mu_2 -10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 - \mu_2 >10$

7 0

3 years ago

Could you help me with number 18

Travka [436]

The better bargain is the 4 quarts

6 0

3 years ago

What are the Slope and the Equation of the Image?

Rama09 [41]

change in y/change in x

y2-y1/x2-x1

-1--5/0-2

-1+5/-2

4/-2

-2

slope is -2

now take one ordered pair and plug it into the equation (for this example i will use the SECOND ordered pair

y = -2x +b

-1 = -2(0)+b

-1 = b

the equation is

5 0

3 years ago