Which expression is equivalent to the number 144?

Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speake

nataly862011 [7]

Answer:

D

Step-by-step explanation:

If you ask questions while their speaking it shows that you are paying attention to them. Avoiding eye contact could mean your thinking about something else or you aren't interested. Interrupting them is just being disrespectful. Leaning towards them doesn't really do anything other than you moving.

7 0

3 years ago

In a highway building project, 32 miles of a new highway have been

pychu [463]

Answer: 105 miles

Step-by-step explanation:

You can write an equation for this problem and solve it.

32 miles=1/3x-3, where x is equal to the total length of the highway.

35=1/3x, and then you multiply by 3, to get x=105

7 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

3 years ago

Paige has 1 ½ feet of rope for a project. She only needs 2/3 of it. How much rope does she need?

Grace [21]

Answer:

1 foot

Step-by-step explanation:

1 1/2 = 3/2

2/3*3/2 = 1

4 0

3 years ago

Read 2 more answers

Write the equation of an ellipse with a major axis of length 8 and co-vertices (0,3) and (0,-3)

alexandr1967 [171]

If the co-vertices are (0, 3) and (0, -3) where x is 0 and y has a value, then y is the minor axis. That means that the x axis is the major axis. Because of what the co-vertices are, the center of the ellipse is at the origin. The formula for an ellipse that has a horizontal major axis is $\frac{(x-h)^2}{a^2}+ \frac{(y-k)^2}{b^2}=1$ . The a value will always be larger than the b value, therefore, the a value goes under the coordinate that is the major axis. Here, its the x-axis. a is the distance that the outer edge of the ellipse is from the center. It's 8 units away from the center along the x axis and 3 units along the y axis from the center. So a = 8 and a^2 = 64; b = 3 and b^2 = 9. Our formula then is $\frac{x^2}{64}+ \frac{y^2}{9}=1$

8 0

4 years ago