Answer:
En matemáticas, especialmente en la teoría de números hay una proposición que vincula tres conceptos: primalidad, factorial de un número entero no nulo y congruencia de números respecto de un módulo.
answer-Wilson's theorem, in number theory, theorem that any prime p divides (p − 1)! ... + 1, where n! is the factorial notation for 1 × 2 × 3 × 4 × ⋯ × n. For example, 5 divides (5 − 1)!
Mr. Shaw graphs the function f(x) = –5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?
y – 12 = –5(x + 2)
y – 12 = 2(x + 2)
y + 12 = 2(x – 2)
y + 12 = –5(x – 2)
Answer:
the answer is A y − 12 = − 5 ( x + 2 )
Step-by-step explanation:
y − 12 = ( − 5 x + 2 ) ⋅ ( x + 2 )
to get this answer you can plug it into point slope equation:
y-y1=m(x+x1)
plug in the given information:
-y and x will stay the same
-y1 will be 12 and x1 will be -2 (remember the given point -2,12)
-m will be the slope given from the y intercept equation
I hope this helps~
Answer:
a
Step-by-step explanation:
Giving BrainleYst. Which Inequality is graphed on the coordinate plane?
O A. y<-2x-1
OB. y>-2x-1
OC. ys-2x-1
OD. y2-2x - 1
Answer:
A. y<-2x-1
Step-by-step explanation:
not C or D because it is a dashed line meaning the linear equation will either have the symbol ≥ or ≤.
when y is less than, you shade below
thus, the answer is A
A certain cosine function has an amplitude of 7. Which function rule could model this situation?
Answer:
y = 7cos bx
Step-by-step explanation:
For a cosine function without pahse shift and vertical shift, but with amplitude given, it will also have period and thus , the formula for the cosine function is;
y = Acos bx
Where;
A is the amplitude
Period = 2π/b
Now, we are told that the amplitude is 7. Thus;
y = 7cos bx
Which of the following have both 2 and -5 as solutions?
X2+3x-10-0
X2-3x-10=0
X2+7x+10=0
X2-7x+10=0
Answer:
X^2 + 3x - 10=0
21-B Book Street Books sells about 700700 books each month. The pie chart displays the most popular book categories, by percentage, each month. Find the number of romance books sold each month. Round your answer to the nearest integer.
Solution :
Given data :
Total number of books sold each month= 700
The charts in the display attached below shows the most popular books category by percentages.
Percentage of romance books sold each = 8.5%
Therefore, the number of romance books sold in each month is given by :
[tex]$=8.5 \% \text{ of }\ 700$[/tex]
[tex]$=\frac{8.5}{100}\times 700$[/tex]
= 59.5
≈ 60 books (rounding off)
You can use the fact that total amount is taken as 100%.
The number of romance books in the given Streets Books is 60
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is [tex]\dfrac{a}{100} \times b[/tex]
How to find the number of Romance books if its given that it is 8.5% of the total books present in that book collection?Since the total amount of books is 700, and its 8.5% books are romance books, thus we have:
[tex]\text{Number of Romance books} = \dfrac{700}{100} \times 8.5 = 59.5 \approx 60[/tex]
The number of romance books in the given Streets Books is 60
Learn more about percentage here:
https://brainly.com/question/11549320
Which value of a in the exponential function below would cause the function to stretch?
f(x) = (1)
O 0.3
O 0.9
O 1.0
O 1.5
Answer:
1.5
Step-by-step explanation:
Took the test already.
The value of a for which the exponential function below would cause the function to stretch is a > 1 Or 1.5.
What are some rules for function transformations?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over y axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
We know an exponential function f(x) = [tex]e^x[/tex].
Now if we multiply f(x) by some number 'a' which is greater than 1 let it be g(x) = [tex]ae^x[/tex] the function would stretch horizontally for a > 1.
learn more about function transformations here :
https://brainly.com/question/13810353
#SPJ6
Question 24… please someone help thank you!
Answer:
72 in^2
Step-by-step explanation:
The area of the square in the middle is
A = s^2 = 6^2 = 36
The area of the triangle on the left is
A =1/2 bh = 1/2 ( 6*6) = 18
The area of the triangle on the right
A = 1/2 bh = 1/2(6*6) = 18
Add the areas together
36+18+18 = 72
Area of the middle square = 6 x 6 = 36
Area of a triangle is 1/2 x base x height:
Area = 1/2 x 6 x 6 = 18
Both triangles have a base of 6 and height of 6 so both triangles have the same area.
Total area = 36 + 18 + 18 = 72 square in.
The answer is D. 72
A jewelry box is in the shape of a rectangular prism with an area of 528 cubic inches. The length of the box is 12 inches and the height is 5 1/2 inches. What is the width of the jewelry box? A=LxWxH
please help. :)
Find the sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento to within 6 minutes with 95% confidence. Based on a previous study, arrival delay times have a standard deviation of 39.6 minutes.
Answer:
The sample size necessary is of 168.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Based on a previous study, arrival delay times have a standard deviation of 39.6 minutes.
This means that [tex]\sigma = 39.6[/tex]
Find the sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento to within 6 minutes with 95% confidence.
This is n for which M = 6. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 1.96\frac{39.6}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 1.96*39.6[/tex]
[tex]\sqrt{n} = \frac{1.96*39.6}{6}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*39.6}{6})^2[/tex]
[tex]n = 167.34[/tex]
Rounding up:
The sample size necessary is of 168.
What two things have to be true in order to use the Zero Product Property?
A: Both sides of the equations must be zero.
B: One side of the equation must be a factored polynomial, and the other side must be -1.
C: One side of the equation must be a factored polynomial, and the other side must be 1.
D: One side of the equation must be a factored polynomial, and the other side must be zero.
Wrong answers will be reported. Thanks!
Answer:
D - One side is a factored polynomial and the other side is 0.
A - Incorrect; If each side is 0, the equation would be equal since 0 = 0.
B - Incorrect; It cannot be -1 because the property states Zero product which means 0 should be the product.
C - Incorrect; It cannot be 1 because the property states Zero product which means 0 should be the product.
D - Correct; One side is 0, and the other is a factored polynomial, which correctly displays the correct definition of Zero Product Property.
4. Consider the function g(x) = 2x^2 - 4x+3 on the interval [-1, 2]
A.) Does Rolle's Theorem apply to g(x) on the given interval? If so, find all numbers, s,
guaranteed to exist by Rolle's Theorem. If not, explain why not. (2 pts.)
b.) Does the Mean Value Theorem apply to g(x) on the given interval? If so, find all
numbers, a guaranteed to exist by the Mean Value Theorem. If not, explain why not.
(4 pts.)
Hi there!
A.) Begin by verifying that both endpoints have the same y-value:
g(-1) = 2(-1)² - 4(-1) + 3
Simplify:
g(-1) = 2 + 4 + 3 = 9
g(2) = 2(2)² - 4(2) + 3 = 8 - 8 + 3 = 3
Since the endpoints are not the same, Rolle's theorem does NOT apply.
B.)
Begin by ensuring that the function is continuous.
The function is a polynomial, so it satisfies the conditions of the function being BOTH continuous and differentiable on the given interval (All x-values do as well in this instance). We can proceed to find the values that satisfy the MVT:
[tex]f'(c) = \frac{f(a)-f(b)}{a-b}[/tex]
Begin by finding the average rate of change over the interval:
[tex]\frac{g(2) - g(-1)}{2-(-1)} = \frac{3 - 9 }{2-(-1)} = \frac{-6}{3} = -2[/tex]
Now, Find the derivative of the function:
g(x) = 2x² - 4x + 3
Apply power rule:
g'(x) = 4x - 4
Find the x value in which the derivative equals the AROC:
4x - 4 = -2
Add 4 to both sides:
4x = 2
Divide both sides by 4:
x = 1/2
Which of the SMART criteria are NOT met by this data analytics project goal (pay close attention to whether the options are words the SMART acronym stands for)?
Answer:
Specific
Step-by-step explanation:
The data analytics is defined as the study of analyzing the raw data and information so as to make a proper conclusion about the information. It is a process of inspecting, transforming, and modelling the data with the intention of finding useful information and conclusions.
The acronym for S.M.A..R.T is Specific, Measurable, Attainable, Relevant and Time bounding.
The SMAR criteria which do not meet the data analytics project goal in the question is "Specific".
pls help me in this question it is really needed
Answer:
6 1/8 ×10 2/7= 60
60÷2 1/3= 30
The answer:
30
how to construct angle 30°
Answer:
Angle ABC = 30°
Step-by-step explanation:
Construct a ray AB, horizontally.Take a compass, keep the pointy edge on the origin of the ray and make an arc passing through AB.Mark the point where the arc cuts AB as XPlace the pointy edge of the compass on X, draw another arc through the existing arc.Mark the point where on arc cuts the other arc as Y.Now from the origin of AB through the point Y draw a straight line.The angle thus formed is 60°.Now make arcs keeping the compass on X and Y.Mark the point where these two arcs meet as Z.Now from the origin of AB through the point Z draw a straight line.The angle formed in this process is a 30°.4)In order to set rates, an insurance company is trying to estimate the number of sick daysthat full time workers at an auto repair shop take per year. A previous study indicated thatthe standard deviation was2.2 days. a) How large a sample must be selected if thecompany wants to be 92% confident that the true mean differs from the sample mean by nomore than 1 day
Answer:
A sample of 18 is required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.92}{2} = 0.04[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.04 = 0.96[/tex], so Z = 1.88.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
A previous study indicated that the standard deviation was 2.2 days.
This means that [tex]\sigma = 2.2[/tex]
How large a sample must be selected if the company wants to be 92% confident that the true mean differs from the sample mean by no more than 1 day?
This is n for which M = 1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.88\frac{2.2}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 1.88*2.2[/tex]
[tex](\sqrt{n})^2 = (1.88*2.2)^2[/tex]
[tex]n = 17.1[/tex]
Rounding up:
A sample of 18 is required.
Determine whether the series is convergent or divergent by expressing the nth partial sum sn as a telescoping sum. If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)
Answer: Hello attached below is the complete question
answer :
It is convergent , sum = 7/12
Step-by-step explanation:
Sn = 1/3 + 1/4 - 1/n - 1/n+1
It is convergent and the sum = 7/12
attached below is the remaining part of the solution
Pls solve x it’s urgent
Answer:
1. 55 degree
2. 50 degree
3. 88 degree
4. 50 degree
Step-by-step explanation:
1.
Angle AE interior 180-120 = 60
Angle CD interior 180-112 = 68
x = 180- (60+68) = 180-128 = 52 degree
2.
interior 180 -120= 40
interior 180- 110 = 90
x = 180 - (40+90) = 180-130 = 50 degree
3.
exterior 90-52= 38
exterior 90-40 = 50
x = 180-(52+40)= 180-92 = 88 degree
4.
interior 180- (45+50) = 180-95 = 85 degree
interior adjoining triangle 180 - 85 = 95
all angles add up to 180
interior 180- (35 + 95)= 180-130 = 50 degree
x = 50 degree
If three times a number added to 8 is divided by the number plus 7, the result is four thirds. Find the number.
9514 1404 393
Answer:
4/5
Step-by-step explanation:
The wording is ambiguous, as it often is when math expressions are described in English. We assume you intend ...
[tex]\dfrac{3n+8}{n+7}=\dfrac{4}{3}\\\\3(3n+8)=4(n+7)\qquad\text{multiply by $3(n+7)$}\\\\9n+24=4n+28\qquad\text{eliminate parentheses}\\\\5n=4\qquad\text{subtract $4n+24$}\\\\\boxed{n=\dfrac{4}{5}}\qquad\text{divide by 5}[/tex]
The number is 4/5.
the fraction a/24reduced by a factor 4, and the result is 5/b. Find a and b
PLEASE HELP MY SISTER
Answer:
A= 20
B= 6
Step-by-step explanation:
A= 5 times 4= 20
B= 24/4= 6
Let (-5, 2) be a point on the terminal side of 0.
Find the exact values of coso , csco, and tano.
Answer:
Following are the response to this questions:
Step-by-step explanation:
Please find the graph file in the attachment.
Given:
P=2
B=-5
H=?
[tex]H=\sqrt{P^2+B^2}[/tex]
[tex]=\sqrt{2^2+(-5)^2}\\\\=\sqrt{4+25}\\\\=\sqrt{29}\\\\[/tex]
Using formula:
[tex]\to \ cosec \theta \ or\ \ csco \theta =\frac{H}{P}\\\\\to \cos \theta=\frac{B}{H}\\\\\to \tan \theta=\frac{p}{B}\\\\[/tex]
So,
[tex]\to \ cosec \theta \ or\ \ csco \theta =\frac{\sqrt{29}}{2}\\\\\to \cos \theta=\frac{-5}{\sqrt{29}} =\frac{-5}{\sqrt{29}}\times \frac{\sqrt{29}}{\sqrt{29}}=-\frac{5\sqrt{29}}{29}\\\\\to \tan \theta=\frac{2}{-5}= -\frac{2}{5}\\\\[/tex]
What is the simplified expression for the
expression below? 4(x+8)+5(x-3)
Plz answer quick!!! Apx Unit 7
A punch contains cranberry juice and ginger ale in the ratio 5:3. If you require 32 L
of punch for a party, how many litres of cranberry juice and how many litres of ginger
ale are required?
Line segment TV is a midsegment of ∆QRS. What is the value of n in the triangle pictured?
A: 6.5
B: 7.6
C: 15.2
D: 3.2
Answer:
D. 3.2
Step-by-step explanation:
Mid-segment Theorem of a triangle states that the Mid-segment in a triangle is half of the third side of the triangle.
Based on this theorem, we have: TV = ½(RS)
TV = 3n - 2
RS = n + 12
Substitute
3n - 2 = ½(n + 12)
Multiply both sides by 2
2(3n - 2) = (n + 12)
6n - 4 = n + 12
Collect like terms
6n - n = 4 + 12
5n = 16
Divide both sides by 5
5n/5 = 16/5
n = 3.2
What is the following product?
(V12+ V6 (16-V10
6-12-2130+6-2V15
-2 དུ་
6V3-615
31/7- V22+2/3-4
2V3+6-2V15
Answer:
The answer is A: 6√2 - 2√30 + 6 - 2√15
Believe me it right.
A business rents in-line skates and bicycles to tourists on vacation. A pair of skates rents for $5 per day. A bicycle rents for $20 per day.
On a certain day, the owner of the business has 25 rentals and takes in $425.
Write a system of equation to represent this situation, then solve to find the number of each item rented.
Show both the equations and the solution.
Answer:
5x+20y=425
Step-by-step explanation:
Its 5 bucks for x pairs of skates
Its 20 dollars for y bikes
x+y rentals have to equal 25
all of this is equal to 425. All that is left to do is test with number until the statement is true.
try :
5(5)+(20)(20)=425
x + y do equal 25, and the total is equal to 425.
A soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 95% confidence interval with an error of no more than 0.08. A consultant has informed them that a previous study found the mean to be 3.1 soft drinks per week and found the variance to be 0.49. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
Answer:
The minimum sample size required to create the specified confidence interval is 295.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Variance of 0.49:
This means that [tex]\sigma = \sqrt{0.49} = 0.7[/tex]
They want to construct a 95% confidence interval with an error of no more than 0.08. What is the minimum sample size required to create the specified confidence interval?
The minimum sample size is n for which M = 0.08. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.08 = 1.96\frac{0.7}{\sqrt{n}}[/tex]
[tex]0.08\sqrt{n} = 1.96*0.7[/tex]
[tex]\sqrt{n} = \frac{1.96*0.7}{0.08}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.7}{0.08})^2[/tex]
[tex]n = 294.1[/tex]
Rounding up:
The minimum sample size required to create the specified confidence interval is 295.
Area: Change in Dimensions
A rectangle FGHJ has a width of 3 inches and a length of 7 inches
Answer:
A) 21 in²
B) 42 in²
C) 84 in²
D) I) 4 in²
II) 8 in²
III) 16 in²
E) From our calculations, we can see that doubling one part of the dimensions gives an area that is twice the original one while doubling both dimensions gives an area that four times the original one.
Step-by-step explanation:
We are given dimensions of triangle as;
width; w = 3 inches
length; L = 7 inches
A) Area of triangle is;
A = Lw
A = 7 × 3
A = 21 in²
B) If we double the width, then area is;
A = 7 × (2 × 3)
A = 42 in²
Area is twice the original area
C) If we double the width and length, then we have;
Length = 7 × 2 = 14 in
Width = 3 × 2 = 6 in
Area = 14 × 6 = 84 in²
Area is four times the original one
D) Let's try a triangle with base 2 in and height 4 in.
I) formula for area of triangle is;
A = ½ × base × height
A = ½ × 2 × 4
A = 4 in²
II) If we double the width(base) , then area is;
A = ½ × 2 × 2 × 4
A = 8 in²
This is twice the original area.
III) If we double the width(base) and length(height), then we have;
A = ½ × 2 × 2 × 4 × 2
A = 16 in²
This is four times the original area
E) From our calculations, we can see that doubling one part of the dimensions gives an area that is twice the original one while doubling both dimensions gives an area that four times the original one.
- Mariah is looking at her bank account and sees that she is in debt $40. She plans to buy dinner
for several friends on Friday at $5 per meal. On Monday she earns $30.25 babysitting and
$25.75 for tutoring several younger students. On Tuesday, she cleans the apartment for her
mom and earns $11 dollars. She spends $2 of those dollars on a candy bar. How many friends
can she buy dinner for on Friday?
Answer: 5 friends
Note: if Mariah pays for her own meal, then it would drop to 4 friends.
===========================================================
Explanation:
Add up the amount she earns:
30.25+25.75+11 = 67
Now add up the amounts that she's either in debt or that she spends money on. Ignore the dinner portion for now.
40+2 = 42
She earns $67 total and has to spend $42, without including the dinner portion just yet. That means Mariah has 67-42 = 25 dollars left over.
-------------------
Let x be the number of $5 meals she can buy
So she can spend a total of 5x dollars here. Set this equal to 25 (the amount left over) and solve for x.
5x = 25
x = 25/5
x = 5
She can buy dinner for 5 friends. Or if Mariah is paying for herself as well, then she can buy dinner for 4 friends. It's not clear which scenario your teacher is after, but I'll assume the first scenario.
Provided below are summary statistics for independent simple random samples from two populations. Use the pooled t-test and the pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
x1=21, s1=4, n1=12, x2=20, s2=3, n2=15
A. What are the correct hypotheses for a right-tailed test?
b. Compute the test statistic.
c. Determine the P-value.
B. The 90% confidence interval is from ____to ____.
Answer:
(a) [tex]H_o:\mu_1 = \mu_2[/tex] [tex]H_a:\mu_1 > \mu_2[/tex]
(b) [tex]t = 0.74[/tex]
(c) [tex]p =0.2331[/tex]
(d) [tex]CI = (-2.095,4.095)[/tex]
Step-by-step explanation:
Given
[tex]\bar x_1=21,\ s_1=4,\ n_1=12,\\ \bar x_2=20,\ s_2=3,\ n_2=15[/tex]
Solving (a): The hypotheses
The test is right-tailed, means that the alternate hypothesis will contain greater than sign.
So, we have:
[tex]H_o:\mu_1 = \mu_2[/tex]
[tex]H_a:\mu_1 > \mu_2[/tex]
Solving (b); The test statistic (t)
This is calculated as:
[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{s_1^2(n_1 - 1) + s_2^2(n_2 - 1)}{n_1 + n_2 - 2} * (\frac{1}{n_1} + \frac{1}{n_2})}}[/tex]
So, we have:
[tex]t = \frac{21 - 20}{\sqrt{\frac{4^2(12 - 1) + 3^2(15 - 1)}{12 + 15 - 2} * (\frac{1}{12} + \frac{1}{15})}}[/tex]
[tex]t = \frac{1}{\sqrt{\frac{302}{25} * (0.15)}}[/tex]
[tex]t = \frac{1}{\sqrt{12.08 * 0.15}}[/tex]
[tex]t = \frac{1}{\sqrt{1.812}}[/tex]
[tex]t = \frac{1}{1.346}[/tex]
[tex]t = 0.74[/tex]
Solving (c): The P-value
First, we calculate the degrees of freedom
[tex]df = n_1 + n_2 -2[/tex]
[tex]df = 12+15 -2[/tex]
[tex]df = 25[/tex]
Using the t distribution, the p-value is:
[tex]p =TDIST(0.74,25)[/tex]
[tex]p =0.2331[/tex]
Solving (d): The 90% confidence interval
Calculate significance level
[tex]\alpha = 1 - CI[/tex]
[tex]\alpha = 1 - 90\%[/tex]
[tex]\alpha = 0.10[/tex]
Calculate the t value (t*)
[tex]t^* = (\alpha/2,df)[/tex]
[tex]t^* = (0.10/2,25)[/tex]
[tex]t^* = (0.05,25)[/tex]
[tex]t^* = 1.708[/tex]
The confidence interval is calculated using:
[tex]CI = (\bar x - \bar x_2) \± t^* *\sqrt{\frac{s_1^2(n_1 - 1) + s_2^2(n_2 - 1)}{n_1 + n_2 - 2} * (\frac{1}{n_1} + \frac{1}{n_2})}[/tex]
[tex]CI = (21 - 20) \± 1.708 *\sqrt{\frac{4^2(12 - 1) + 3^2(15 - 1)}{12 + 15 - 2} * (\frac{1}{12} + \frac{1}{15})}[/tex]
[tex]CI = 1 \± 1.708 *1.812[/tex]
[tex]CI = 1 \± 3.095[/tex]
Split
[tex]CI = 1 - 3.095 \ or\ 1 + 3.095[/tex]
[tex]CI = -2.095 \ or\ 4.095[/tex]
[tex]CI = (-2.095,4.095)[/tex]
