C
By subtracting 18 to both sides you are separating the 3x because you are not ready to isolate the variable (x) in step 1
Answer:
27 degrees
Step-by-step explanation:
The easy way is by remembering the formula (a-b)/2=c, where a is the larger angle, and b is the smallest angle. (90-36)/2=27.
The longer, more drawn out answer goes as follows. See the image to understand the notation I use:
- AOE + BOD + BOA + DOE = 360
- AOE + BOD = 90 + 36 = 126
- BOA + DOE = 360 - AOE - BOD = 234
- Since the sum of a triangle's angles is 180, ODE = (180 - DOE) / 2
- Likewise, OBA = (180 - BOA) / 2
- Since CDE is 180, CDO = 180 - ODE = 180 - (180 - DOE) / 2
- Likewise, CBA is 180, so CBO = 180 - OBA = 180 - (180 - BOA) / 2
- The interior angles of the irregular polygon CBOD add up to 360, so CBO + CDO + BOD + BCD = 360.
- Substituting what we already found, 180 - (180 - BOA)/2 + 180 - (180 - DOE)/2 + 36 + BCD = 360
- Cleaning it all up, we get 180 + (BOA + DOE)/2 + 36 + BCD = 360
- As we found in line 3, BOA + DOE = 234, so substituting that in, 180 + 117 + 36 + BCD = 360
- Finally, solving for BCD (360 - 36 - 117 - 180) we get our answer, 27
Note: The long drawn out method shown above is a way to derive the formula for the secant theorem. You do not need to use this method every time. Just remember, large angle minus small angle, all divided by 2. That is it.
The area of a rectangle is length times width. Since a square's length is equal to its width, a square's area is equal to the length of one side times itself. So, reversed, the square root of the square's area gives the length of one side. In this case, the square root of 36 square centimeters is 6 centimeters. Again, since all four sides of a square are the same, its perimeter is equal to the length of one side times four. For a square with one side equal to 6 centimeters, the perimeter equals 24 centimeters.
Answer:
2.6
Step-by-step explanation:
4 squared - 3 squared =7
Square root 7 equals 2.6 to the nearest tenths
Answer:
Assuming ages are normally distributed, the 98% confidence interval for the population average age is [26.3, 35.7].
Step-by-step explanation:
We have to construct a 98% confidence interval for the mean.
The information we have is:
- Sample mean: 31
- Variance: 49
- Sample size: 15
- The age is normally distributed.
We know that the degrees of freedom are

Then, the t-value for a 98% CI is t=2.625 (according to the t-table).
The standard deviation can be estimated from the variance as:

The margin of error is:

Then, the CI can be constructed as:
