We know in these kind of triangles that have a 90 degrees angle, we can do:
so the first question:
and then:
so , when you want to rationalize , usually you must multiply the irrational factor as 1:
so , now multiply:
in the next question,we know negative numbers in radical don't have any solution so 2 is correct,
Answer:
Step-by-step explanation:
Answer:
4.1 years.
Step-by-step explanation:
We have been given that The Lisbon’s new heat pump cost $4,500. They bought it to replace their old furnace and air conditioner which cost about $2,800 a year to run. The heat pump will save them approximately 39% a year.
Yearly cost was 2800 at first and the pump will save 39% of 2800. So annual saving with new heat pump will be:
Let x be the number of years in which heat pump will pay for itself, so saving in x years will be:
Now let us equate the savings by new heat pump with cost of heat pump to find the number of years (x).
Therefore, the heat pump will pay for itself in 4.1 years.
Answer: the probability of getting a number less than 3 and tails is P 1/6
Step-by-step explanation:
Assuming that the dice and the coin are normal ones, we can expect that the probability for each outcome is about the same.
For the coin we have 2 outcomes, heads and tails, then each outcome has a probability of 1/2
The dice has 6 outcomes, and each outcome has a probability of 1/6.
Then the probability of rolling a number less than 3 is equal to the probability of rolling a 1 plus the probability of rolling a 2.
P1 + P2 = 1/6 + 1/6 = 2/6 = 1/3.
The probability of getting tails with the coin is 1/2.
Now, the joint for both events is equal to the product of the probabilities of each event, this is:
P = (1/3)*(1/2) = 1/6
24 is the LCD of 5/12 and 3/8
