There are 2 triangles here. You have to drop an altitude and determine the length of it. You can use the fact that sin45 = h/5 (h is the height) and get that the height is 3.5. The rule then is if h is smaller than b which is in turn smaller than c, you have 2 triangles. This is the case of the ambiguous triangle, that SSA that you cannot use to prove congruency. The rules are very particular for whether or not 0, 1, or 2 triangles exist. Learn them.
The most appropriate choice of account for Rohan depends on Rohan's money saving period. If he wants to save his money for less than 2 years then he should choose the Bank A's 5% simple interest account. This account gives 10$ interest in 2 years and 15$ interest in 3 years. If he wants to save his money for more than 2 years then he should choose the Bank A's 4.8% compound interest account. This account gives $9.83 interest in 2 years, $15.1 interest in 3 years, and this account gives more interest than the simple interest account in period above the third year.
Answer:
5
Step-by-step explanation:
6a = (a*-3) + 45
then:
6a = -3a + 45
6a + 3a = 45
9a = 45
a = 45/9
a = 5
Check:
6*5 = (5*-3) + 45
30 = -15 + 45
Answer:
standard error = 2.11
Step-by-step explanation:
First we stablish the data that we have for each sample:
<u>Population 1</u> <u>Population </u>2
n₁ = 100 n₂ = 90
x¯1= 95 x¯2 = 75
σ₁ = 14 σ₂ = 15
To calculate the standard error of each sample we would use the formulas:
σ = σ₁/√n₁
σx¯2 = σ₂/√n₂
Now, in order to obtain the standard error of the differences between the two sample means we combine those two formulas to obtain this:
σx¯1 - σ x¯2 = √(σ₁²/n₁ + σ₂²/n₂ )
So as you can see, we used the square root to simplify and now we require the variance of each sample (σ²):
σ₁² = (14)² = 196
σ₂² = (15)² = 225
Now we can proceed to calculate the standard error of the distribution of differences in sample means:
σx¯1 - σx¯2 = √(196/100 + 225/90) = 2.11
This gives an estimate about how far is the difference between the sample means from the actual difference between the populations means.
Since the geometric series is not long we can pair up the number
20 + 29 = 49
21 + 28 = 49
22 + 27 = 49
23 + 26 = 49
24 + 25 = 49
Since we made 5 pairs of 49, the answer is 245. (49 x 5)