Add 4 to both sides
x - 4 < -3
x-4+4 < -3+4
x < 1
To graph this on a number line, plot an open circle at 1 on the number line. Do not fill in the open circle. Shade to the left of the open circle. The shaded region represents all x values smaller than 1.
The graph is shown below.
Answer:
1.778 times more or 16/9 times more
Step-by-step explanation:
Given:
- Mirror 1: D_1 = 8''
- Mirror 2: D_2 = 6"
Find:
Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?
Solution:
- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:
LGP ∝ A
- Whereas, Area is proportional to the squared of the diameter i.e an area of a circle:
A ∝ D^2
- Hence, LGP ∝ D^2
- Now compare the two diameters given:
LGP_1 ∝ (D_1)^2
LGP ∝ (D_2)^2
- Take a ratio of both:
LGP_1/LGP_2 ∝ (D_1)^2 / (D_2)^2
- Plug in the values:
LGP_1/LGP_2 ∝ (8)^2 / (6)^2
- Compute: LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more
Answer:
17.5%
Step-by-step explanation:
First of all, see this situation as a cumulative binomial distribution. You have isolated trials with a probability of success. This makes it binomial. The wording of the question "what is the probability of at least half..." makes this cumulative.
There are a few ways to calculate this, and I'm not quite sure which way you're familiar with. I'll show the cumbersome way and use wolfram to make the calculation.
First, I'll calculate the probability for 15 success, given 30 trials.
30c15*0.4^15*0.6^15
Since the question asks for the probability of at least 15 success, I'll have to make a calculation for the probability of 16 successes, then 17, and so on. Then I'll have to add all the probabilities together. So, I'll use wolfram for that (see attached)
Answer:
see explanation
Step-by-step explanation:
Let c represent the number of children, then
number of men = 4c and number of women = 2c
Sum the numbers of each and equate to 266
4c + 2c + c = 266, that is
7c = 266 ( divide both sides by 7 )
c = 38
Thus
4 × 38 = 152 and 2 × 38 = 76
The group consists of 38 children, 152 men and 76 women
Thats means angle BEC is 63. By the vertical angle theorem AED is the same. 3x-27 when x=30 is also 63.
