BO is double that of DO. In other words, BO is two times longer than DO. The answer is choice B
For example, if DO were 3 units long, then BO would be 6 units long (2*3 = 6). This works because the triangles DCO and BAO are similar triangles. The corresponding sides are in the same ratio or proportion to one another. The larger triangle (BAO) has sides that are twice as long as the smaller triangle's (DCO) corresponding sides.
Side note: we can prove the triangles to be similar using the AA (angle angle) similarity theorem. The first pair of angles are the vertical angles DOC and BOA which are congruent to each other.The second pair is CDB and ABD which are congruent by the alternate interior angle theorem. Check out the attached image for a visual.
Answer: one solution
Step-by-step explanation:
CONCEPT:
- One solution is when the final variable would be able to find a solution.
- Infinite solution is when the equations result in 0=0, meaning any number will fit
- No solution is when the equation results in both sides on equal.
SOLVE:
Given
3/4x-7=3(1/6x+1)
Expand Parenthesis
3/4x-7=1/2+3
Multiply both sides by the LCM of fractions (Least Common Multiple)
4(3/4x-7)=4(1/2x+3)
3x-28=2x+12
Subtract both sides by 2x
3x-28-2x=2x+12-2x
x-28=12
Add both sides by 28
x-28+28=12+28
x=40
Since we are able to get exactly one solution, there is only one solution.
Hope this helps!! :)
Please let me know if you have any quesionts
Answer:
The 95% confidence interval for the proportion of corporations preferring a nonsmoking candidate is (0.2328, 0.2872)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
For this problem, we have that:
95% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the proportion of corporations preferring a nonsmoking candidate is (0.2328, 0.2872)
Answer:
x=13
Step-by-step explanation:
3(x-2)-3=30
3x-6-3=30
3x-9=30
3x=30+9
3x=39
x=39/3
x=13
Answer:
90 of the students are girls.
Step-by-step explanation:
Boys : Girls
B : G
4 : 3
120 : ?
(120 ÷ 4 = 30) so 4 × 30 = 120
(Do this to the other side) 3 × 30 = 90
B : G
120 : 90 [90 girls out of 210 total students]
Hope this helps. :)
