What is the volume of a triangular prism that is 10cm long, 7 cm wide and 4 cm high

For each $n \in \mathbb{N}$, let $A_n = [n] \times [n]$. Define $B = \bigcup_{n \in \mathbb{N}} A_n$. Does $B = \mathbb{N} \time

andre [41]

Answer:

No, it is not.

Step-by-step explanation:

The set $C = \mathbb{N} \times \mathbb{N}$ contains every ordered pair of Natural numbers, while B only contains those pairs in which both values in each entry are the same. Therefore, C is a bigger set than B, but B is not equal to C because for example C contains $[1] \times [2]$ and B doesnt because 1 is not equal to 2.

4 0

3 years ago

a cooler contains 50 bottles; 30 bottles of water, which 8 are lemon flavored and 20 bottles of tea, of which 5 are lemon flavor

xenn [34]

Answer:

The required probability is $\dfrac{13}{50}$

Step-by-step explanation:

Total number of bottles = 50

Total number of water bottles = 30

Total number of lemon flavored water bottles = 8

Total number of tea bottles = 20

Total number of lemon flavored tea bottles = 5

Probability of selecting a lemon flavored water bottle = Probability of selecting a water bottle $\times$ Probability of selecting a lemon bottle out of water bottles.

Probability of selecting a lemon flavored tea bottle = Probability of selecting a tea bottle $\times$ Probability of selecting a lemon bottle out of tea bottles.

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$