Answer:
(0.102, -0.062)
Step-by-step explanation:
sample size in 2018 = n1 = 216
sample size in 2017 = n2 = 200
number of people who went for another degree in 2018 = x1 = 54
number of people who went for another degree in 2017 = x2 = 46
p1 = x1/n1 = 0.25
p2 = x2/n2 = 0.23
At 95% confidence level, z critical = 1.96
now we have to solve for the confidence interval =
<h2>
</h2>
= 0.02 ± 1.96 * 0.042
= 0.02 + 0.082 = <u>0.102</u>
= 0.02 - 0.082 = <u>-0.062</u>
<u>There is 95% confidence that there is a difference that lies between - 0.062 and 0.102 on the proportion of students who continued their education in the years, 2017 and 2018.</u>
<u></u>
<u>There is no significant difference between the two.</u>
Factor?, if so
if in ax^2+bx+c form then
multiply a and c together
result=z,
find 2 numbers that multiply to get z and add up to get b
so
14=a
-17=b
-6=c
14 times -6=-84
factor to find what 2 numbers add up to -17
-84=
-2, 42
-3,28
-4,21
-6,14
-7,12
add each up
-2, 42=40 nope
-3,28=25 nope
-4,21=17 yes, becase if -21 and 4 then answer
-6,14=8 nope
-7,12=5 nope
split up -17 into -21 and 4
14x^2-21x+4x-6
group
(14x^2-21x)+(4x-6)
undistribute
(7x)(2x-3)+(2)(2x-3)
revesres undistribute (ab+ac=a(b+c) or (a+b)(c)+(a+b)(d)=(a+b)(c+d))
(7x+2)(3x-3) is factore out form
then set it to zero and do th emath because if xy=0 then assume x and/or y=0 so
7x+2=0
subtract 2
7x=-2
divide by 7
x=-2/7
3x-3=0
add 3
3x=3
divide 3
x=1
x=-2/7 or 1
Answer:
a. Z = 2.6667
b.
c. Upper limit = 3.39
Step-by-step explanation:
Part a
We are given
Population mean = 3
Population standard deviation = 0.3
Sample mean = 3.2
Sample size = n = 16
Level of significance = 0.05
Null hypothesis: H0: µ = 3
Alternative hypothesis: Ha: µ > 3
The test statistic formula is given as below:
Z = (sample mean – population mean) / [SD / sqrt(n)]
Z = (3.2 – 3)/[0.3/sqrt(16)]
Z = 2.6667
Part b
Type I error is the probability of rejecting the null hypothesis that the population mean is 3 ppm when actually it is 3 ppm. Type II error is the probability of do not rejecting the null hypothesis that the population mean is 3 ppm when actually it is exceeding 3 ppm. Type II error is the serious in this scenario.
Part c
We are given
Population mean = 3
Population standard deviation = 0.3
Sample mean = 3.2
Sample size = n = 16
Confidence level = 90%
Critical z value = 2.3263
Formula is given as below:
Lower limit =sample mean – z*SD/sqrt(n)
Upper limit = sample mean + z*SD/sqrt(n)
Lower limit = 3.2 – 2.5758*0.3/sqrt(16)
Lower limit = 3.01
Upper limit = 3.2 + 2.5758*0.3/sqrt(16)
Upper limit = 3.39
Answer:
x = -5
Step-by-step explanation:
Solve for x:
3 x + 1 = -14
Subtract 1 from both sides:
3 x + (1 - 1) = -14 - 1
1 - 1 = 0:
3 x = -14 - 1
-14 - 1 = -15:
3 x = -15
Divide both sides of 3 x = -15 by 3:
(3 x)/3 = (-15)/3
3/3 = 1:
x = (-15)/3
The gcd of -15 and 3 is 3, so (-15)/3 = (3 (-5))/(3×1) = 3/3×-5 = -5:
Answer: x = -5
The transformations which can lead to the red square image of the blue Square are; Translation, Reflection, Rotation.
<h3>What transformations lead to the image?</h3>
- Translation is when we slide a figure in any direction. The translation of the shape can be by moving the blue leftward or rightward and the then downward.
- Reflection is when we flip a figure over a line. The reflection involves reflect the blue Square over the line; y = x.
- Rotation is when we rotate a figure a certain degree around a point. The rotation is by rotating the blue Square over 180⁰.
Read more on transformations;
brainly.com/question/4289712
