Using the z-distribution, as we are working with a proportion, it is found that the margin of error for the 90% confidence interval is of 0.0524 = 5.24%.
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:
In which:
is the sample proportion.
The margin of error is given by:
In this problem, the critical value is given as z = 1.645, and since 26 out of 80 students said they would be willing to pay extra:
Then, the <em>margin of error</em> is of:
More can be learned about the z-distribution at brainly.com/question/25890103
Answer:
10/3
3.3reaping
3 1/3
Step-by-step explanation:
Answer:
Option A is correct because sum of m<2 and m<3 are complementary. So m<2+m<3 =90° .
Step-by-step explanation:
Given: <2 and <3 are complementary angles.
Definition of complementary angles says if two angles sum is equal to 90 degrees then they are called complementary angles.
Statement Reason
1.<2 and <3 are complementary 1. Given
2. m<2+m<3 =90° 2. Definition of complementary <s
3. m<1= m<3 3. Given
4. m<1+m<2= 90° 4.Substitution property of =
5. <1 and <2 are complementary 5. Definition of complementary <s.
Option A matches with the given. We can not use addition properties of equality for statement 2 so, other options are incorrect.
So, according to the given options A is correct.
You can learn more about complementary angles at brainly.com/question/21400774
Answer:
9. (7a + 6b – 9c) – (3a – 6c)
=7a+6b-9c-3a+6c
=7a-3a+6b-9c+6c
=4a+6b-3c
10. (x2 – 9) – (-2x2 + 5x – 3)
= x^2-9+2x^2-5x+3
=x^2+2x^2-5x-9+3
=3x^2-5x-6
11. (5 – 6d – d2) – (-4d – d2)
=5-6d- d^2+4d+ d^2
=5-6d+4d-d^2+ d^2
=5-2d
12. (-4x + 7) – (3x – 7)
=-4x+7-3x+7
= -4x-3x+7+7
=-7x+14
13. (4a – 3b) – (5a – 2b)
=4a-3b-5a+2b
=4a-5a-3b+2b
= -a-b
14. (2c + 3d) – (-6d – 5c)
=2c+3d+6d+5c
=2c+5c+3d+6d
=7c+9d
15. (5x2 + 6x – 9) – (x2 – 3x +7)
=5x^2+6x-9- x^2+3x-7
=5x^2- x^2+6x+3x-9-7
=4x^2+9x-16
16. (3y – 6) – (8 – 9y)
=3y-6-8+9y
=3y+9y-6-8
=12y-14
17. (3a2 – 2ab + 3b2) - (-a2 – 5ab + 3b2)
=3a^2-2ab+3b^2+ a^2+5ab-3b^2
=3a^2+ a^2-2ab+5ab+3b^2- 3b^2
=4a^2+3ab
18. 5c – [8c – (6 – 3c)]
=5c-[8c-6+3c]
=5c-8c+6-3c
=5c-8c-3c+6
= -6c+6
19. 10x + [3x – (5x – 4)]
=10x+[ 3x-5x+4]
=10x+3x-5x+4
=8x+4
20. 3x 2 – [7x- (4x – x2) + 3]
=3x^2-[7x-4x+ x^2+3]
=3x^2-7x+4x- x^2-3
=3x^2-x^2-7x+4x-3
=2x^2-3x-3
21. x2 – [ - 3x+ ( 4 – 7x)]
= x^2-[ -3x+4-7x]
= x^2+3x-4+7x
= x^2+3x+7x-4
= x^2+10x-4
<span>To get the bigger number, divide by 2 the sum of the given sum of the numbers and their difference. In this case-
(226 + 200)/2 = 426/2 = 213.
To get the smaller number, divide by 2 the difference of the given sum of the numbers and their difference. In this case -
(226 - 200)/2 = 26/2 =13.
The two numbers are 213 and 13.
The bigger number is 213</span>
