Answer:
1. ∠1 = 120°
2. ∠2 = 60°
3. ∠3 = 60°
4. ∠4 = 60°
5. ∠5 = 75°
6. ∠6 = 45°
Step-by-step explanation:
From the diagram, we have;
1. ∠1 and the 120° angle are corresponding angles
Corresponding angles are equal, therefore;
∠1 = 120°
2. ∠2 and the 120° angle are angles on a straight line, therefore they are supplementary angles such that we have;
∠2 + 120° = 180°
∠2 = 180° - 120° = 60°
∠2 = 60°
3. Angle ∠3 and ∠2 are vertically opposite angles
Vertically opposite angles are equal, therefore, we get;
∠3 = ∠2 = 60°
∠3 = 60°
4. Angle ∠1 and angle ∠4 an=re supplementary angles, therefore, we get;
∠1 + ∠4 = 180°
∠4 = 180° - ∠1
We have, ∠1 = 120°
∴ ∠4 = 180° - 120° = 60°
∠4 = 60°
5. let the 'x' and 'y' represent the two angles opposite angles to ∠5 and ∠6
Given that the two angles opposite angles to ∠5 and ∠6 are equal, we have;
x = y
The two angles opposite angles to ∠5 and ∠6 and the given right angle are same side interior angles and are therefore supplementary angles
∴ x + y + 90° = 180°
From x = y, we get;
y + y + 90° = 180°
2·y = 180° - 90° = 90°
y = 90°/2 = 45°
y = 45°
Therefore, we have;
∠4 + ∠5 + y = 180° (Angle sum property of a triangle)
∴ ∠5 = 180 - ∠4 - y
∠5 = 180° - 60° - 45° = 75°
∠5 = 75°
6. ∠6 and y are alternate angles, therefore;
∠6 = y = 45°
∠6 = 45°.
Using the t-distribution, it is found that:
a. The <u>margin of error</u> is of 4.7 homes.
b. The 98% confidence interval for the population mean is (19.3, 28.7).
The information given in the text is:
- Sample mean of
. - Sample standard deviation of
. - Sample size of
.
We are given the <u>standard deviation for the sample</u>, which is why the t-distribution is used to solve this question.
The confidence interval is:
The margin of error is:
Item a:
The critical value, using a t-distribution calculator, for a two-tailed <u>98% confidence interval</u>, with 23 - 1 = <u>22 df</u>, is t = 2.508.
Then, the <em>margin of error</em> is:
Item b:
The interval is:
The 98% confidence interval for the population mean is (19.3, 28.7).
A similar problem is given at brainly.com/question/15180581
A biased example: Asking students who are in line to buy lunch
An unbiased example: Asking students who are leaving/going to lunch(<em>NOT buying </em><em>lunch</em><em />).
But in this case, the answer choices can be... confusing.
Don't panic! You're given numbers and, of course, your use of logic.
Answer choice A: 100 students grades 6-8
Answer choice B: 20-30 students any <em>one</em> grade<em></em><em>
</em>Answer choice C: 5 students
<em></em>Answer choice D: 50 students grade 8
An unbiased example would be to choose students from <em>any grade.</em> So we can eliminate choices B and D.
Now, the question wants to <em>estimate how many people at your middle school buy lunch.</em> This includes the whole entire school, and if you are going to be asking people, you aren't just going to assume that if 5 people out of 5 people you asked bought lunch, the whole school buys lunch.
So, to eliminate all bias and/or error by prediction, answer choice A, the most number of students, is your answer.
Answer:
9 shirts
Step-by-step explanation:
12 - 6 = 6
6/2 = 3
3 times 3 = 9
