What is the approximate height of h?

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

Please help help help

mash [69]

Answer:

a, 2 cups of rice bubbles

3/4 cups icing sugar

1 1/2 tablespoons of cocoa

1/2 cup of desiccated coconut

125 g Copha

7 0

3 years ago

Social security tax that is 6.2% of her gross pay medicare tax that is 1.45% of her gross pay state tax that is 21% of her feder

user100 [1]

Marilyn's net pay will increase by $18.15 as her Federal Withholding Allowance increases from 3 to 4.

<h3>What is Federal Withholding Allowance?</h3>

A Federal Withholding Allowance is an exemption that lowers the amount of income tax you must deduct from an employee's paycheck.

Given: The following are the deductible computation:

For federal withholding allowance = 3:

Social Security Tax: 6.2% of $810 = $\frac{6.2\times810}{100}$ = $50.22
Medicare tax : 1.45% of $810 = $\frac{1.45\times810}{100}$ = $11.745
State tax: (21% of 3)% of $810= $\frac{21\times3 }{100} \times\frac{810}{100}$ = 0.63% of $810 = $\frac{0.63\times810}{100}$ = $5.103

Total = $67.068; deducted amount of his gross pay = $810 - $67.068 $742.932 (3 federal withholding).

For Federal Withholding Allowance = 4:

State tax: (21% of 4)% of $810 = $(\frac{21\times4}{100}) \times\frac{810}{100}$ = 0.84% of $810 = $\frac{0.84\times810}{100}$ = $6.8704

Thus, as we can see from the calculations, the State taxes increased from $5.103 to $6.8704. Hence, the net pay increases by $18.15 as the federal allowance increases from 3 to 4.

To learn more about Federal Withholding Allowance, refer to the link: brainly.com/question/1212566

#SPJ4

4 0

1 year ago

Complete the table:<br> 6,000<br> meters<br> kilometers<br> 8,000<br> 9,000<br> 5<br> 7

Alex17521 [72]

Answer:

Remember while answering, 1 kilometer = 1,000 meters

5,000 ⇒ 5

6,000 ⇒ 6

7,000 ⇒ 7

8,000 ⇒ 8

9,000 ⇒ 9

Step-by-step explanation:

1 kilometer is 1,000 meters because "kilo" means 1,000

Knowing this we can make an equation to figure this out

When we know x, or meters, we can do y = x/1,000

When we know y, or kilometers, we can do x = 1,000y

4 0

2 years ago

PLEASE ANSWER ASAP WORTH 100 points get it right please

Trava [24]

Answer:

See below.

Step-by-step explanation:

Part A:

triangle QPR and triangle PSR are similar

Part B:

Triangle QPR is a right triangle with right angle QPR.

Triangle SPR is a right triangle with right angle PSR.

Angle QPR of triangle QPR corresponds to and is congruent to angle PSR of triangle PSR.

Angle R of triangle QSR corresponds to and is congruent to angle R of triangle PSR.

The similar triangles by AA Similarity are

triangle QPR and triangle PSR

Part C:

QR/PR = PR/SR

16/PR = PR/4

PR² = 16 * 4

PR² = 64

PR = 8

8 0

2 years ago

What is the approximate height of h?​

What is the approximate height of h?