Since this is a problem in exponential growth/decay, y = ab^x is the formula that will be used to solve this problem.
The initial value, "a", is the value you start out with and in this case, it is $2000.
The growth/decay factor is what "b" represents, and it is 4%. We need to change the percentage into a decimal, so we will take the percent symbol, change it into a decimal, and move it two places to the left. This is make it 0.04. The problem also mentions interest, implying an exponential growth. Therefore, you will add 0.04 by 1: 1+0.04 = 1.04.
The "x" represents an amount of time. It is 5 years. The equation should be written like this:
y = 2000(1.04)^5
y = 2433.30. When rounded to the nearest dollar, it is $2433.
Answer:
First angle = 30°
Second angle = 60°
Third angle = 90°
Step-by-step explanation:
x + y + z = 180
y + z = 5x
z = y + 30
then:
y + (y+30) = 5x
2y + 30 = 5x
x = (2y+30)/5
then:
x + y + z = 180
{(2y+30)/5} + y + y+30 = 180
{(2y+30)/5} + 2y + 30 = 180
{(2y+30)/5} = 180 - 30 - 2y
{(2y+30)/5} = 150 - 2y
2y+30 = 5(150-2y)
2y+30 = 5*150 + 5*-2y
2y+30 = 750 - 10y
2y + 10y = 750 - 30
12y = 720
y = 720/12
y = 60°
x = (2y+30)/5
x = (2*60 + 30)/5
x = (120+30)/5
x = 150/5
x = 30°
z = y + 30
z = 60 + 30
z = 90°
Check:
x + y + z = 180°
30° + 60° + 90° = 180°
Answer:
And we can find the individual probabilities using the probability mass function
And replacing we got:
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest "number of automobiles with both headligths working", on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And for this case we want to find this probability:
And we can find the individual probabilities using the probability mass function
And replacing we got:
Answer: 65 kmh
Step-by-step explanation:
70 kmh for 2 hours = 140 km.
63 kmh for 5 hours = 315 km
140 + 315 = 455/7 total hours = 65 kmh
