We are given these three people age below:
- Jim's age
- Carla's age
- Tomy's age
We define the age of Jim as any variable, because the problem doesn't give any specific age. I will define Jim's age as x.
Next, Carla is 5 years older than Jim. That means if Carla is 5 years older, her age would be x+5.
Then Tomy is 6 years older than Carla. That means the age would be 6+(x+5).
The sum of their three ages is 31 years old. That means we add all these ages and equal to 31.
![\large{x + x + 5 + 6 + x + 5 = 31}](https://tex.z-dn.net/?f=%20%5Clarge%7Bx%20%2B%20x%20%2B%205%20%2B%206%20%2B%20x%20%2B%205%20%3D%2031%7D)
Combine like terms and solve for x.
![\large{3x + 16 = 31} \\ \large{3x = 31 - 16} \\ \large{3x = 15} \\ \large{x = 5}](https://tex.z-dn.net/?f=%20%5Clarge%7B3x%20%2B%2016%20%3D%2031%7D%20%20%5C%5C%20%20%5Clarge%7B3x%20%3D%2031%20-%2016%7D%20%5C%5C%20%20%5Clarge%7B3x%20%3D%2015%7D%20%5C%5C%20%20%5Clarge%7Bx%20%3D%205%7D)
Then we substitute the value of x in ages to find these three people ages.
- Jim's age = x = 5
- Carla's age = x+5 = 5+5 = 10
- Tomy's age = 6+(x+5) = 6+(5+5) = 6+10 = 16.
Answer
- Jim's age = 5
- Carla's age = 10
- Tomy's age = 16
Given:
n = 27, sample size
df = n-1 = 26, degrees of freedom
xb = 11.8, sample mean
s = 2.3, sample standard deviation.
Because population statistics are not known, we should use the Student's t-distribution.
At 99% confidence interval, the t-value = 2.779 (from tables).
The confidence interval is
11.8 +/- 2.779*(2.3/√(27)) = 11.8 +/- 1.23 = (10.57, 13.03)
Answer: (10.6, 13.0) to the nearest tenth
Answer:
Step-by-step explanation:
I'll show you how to do the first one; the other are exactly the same, so pay attention.
The formula for arc length is
where θ is the central angle's measure. It just so happens that the measure of the central angle is the same as the measure of the arc it intercepts. Our arc shows a measure of 40°; this measure is NOT the same as the length. Measures are in degrees while length is in inches, or cm, or meters, etc. Going off that info, our central angle measures 40°. Filling in the formula and using 3.1415 for π:
. I'm going to reduce that fraction a bit (and I'll use the same reduction in the Area of a sector coming up next):
which makes
AL = 2.09 units. Now for Area of the Sector. The formula is almost identical, but instead uses the idea that the area of a circle is πr²:
where θ is, again, the measure of the central angle (which is the same as the measure of the arc it intercepts). Filling in:
which simplifies a bit to
. As you can see, the 9's cancel each other out, leaving you with
units²
Answer for this question: X < -20