So a triangle is always 180°.
If one angle is 90° then we can subtract that from the 180° to find out how much the other two will be.
180°-90°=90°
So the other two angles added together will have to equal 90°.
You have troubles with domains only if you have:
- Denominators
- Roots with an even degree
- Logarithms
In this case, you have neither of these three, so you can compute your function wherever you want. The domain is all real numbers.
Answer:
Part A:
A pair of linear equations can only have one solution or infinitely many solutions. In this case, there would only be one solution as they intersection at only one point.
Part B:
The solution would be (3, 4) because it is the point of intersection between the two linear lines.
Answer:
a. t*
b. (22.87, 24.53)
c. yes
Step-by-step explanation:
We have the following data:
mean = m = 23.7
standard deviation = sd = 2.15
x = 20
Thus:
a. The critical value would be t * since the value is m <30
b. whenever the mean is less than 30, the t distribution is used, for 95% confidence interval with degree of freedom = (x - 1) df
= 20 - 1
= 19
now, for this value we look in the table of t, we find that t * = 1.729
m + - t * (sd / x ^ 81/2))
replacing
23.7 + - 1.729 * (2.15 / 20 ^ (1/2))
23.7 + - 0.8312
then the inverval would be:
23.7 + 0.8312 = 24.5312
23.7 - 0.8312 = 22.8688
(22.87, 24.53)
c. yes, the interval is accurate since the mean of 23.7 is within this value
Answer:
10 bugs
Step-by-step explanation:
If last month the spider ate 8 bugs, and this month the spider ate 25% more bugs, we can calculate the amount of bugs the spider ate this month finding how much is 25% of 8 bugs, and them we sum this value to the 8 bugs it ate last month.
25% of 8 = 8 * 25 / 100 = 2
Now we know that the spider ate 2 more bugs, so the amount of bugs it ate this month is 8 + 2 = 10 bugs.
We can also solve this problem multiplying directly 8 by 1.25 (1.25 represents the 25% increase in the bug consumption):
8 * 1.25 = 10 bugs.
