In a hatch chemical process, two catalysts arc being compared for their effect on the output of the process reaction. A sample of 12 batches was prepared using catalyst 1 and a sample of 10 batches was obtained using catalyst 2. The 12 batches for which catalyst 1 was used gave an average yield of 85 with a sample standard deviation of 4, and the second sample gave an average of 81 and a sample standard deviation of 5. Find a 90% confidence interval for the difference between the population means, assuming that the populations are approximately normally distributed with equal variances
Answer:
The 90% confidence interval, C.I = (0.693, 0.7307)
Step-by-step explanation:
Catalysts 1 and catalyst 2 have the following statistical data;
Catalyst 1
The number of batches in the sample, n₁ = 12
The average yield by the 12 batches of catalyst 1, [tex]\overline x_1[/tex] = 85
The sample standard deviation, s₁ = 4
Catalyst 2
The number of batches in the sample, n₂ = 10
The average yield, [tex]\overline x_2[/tex] = 81
The standard deviation, s₂ = 5
F-test = s₂²/s₁² = 5²/4² = 1.5625
The degrees of freedom, df = n₁ + n₂ - 2
∴ df = 12 + 10 - 2 = 20
The critical-t at 90% confidence level = 1.725
The F-test < The critical-t, we pool the variance
The 90% confidence interval with the assumption of equal variance is given as follows;
[tex]The \ 90\% \ confidence \ interval= \left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2} \times (s_p) \times \sqrt{\dfrac{1^{2}}{n_{1}}+\dfrac{1^{2}}{n_{2}}}[/tex]
[tex]s_p =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]
Therefore;
[tex]s_p[/tex] = √((12 - 1)×4² + (10 - 1)×5²)/(12 + 10 - 2)) ≈ 4.48
Therefore, we get;
[tex]C.I. = \left (85- 81 \right )\pm 1.725 \times 4.48 \times \sqrt{\dfrac{1}{12}+\dfrac{1}{10}}[/tex]
The 90% confidence interval, C.I = 0.693 < μ₁ - μ₂ < 7.307 = (0.693, 0.7307).
The tile showen are placed in a bag you randomly select one of the tiles return it to the bag and randomly selecting Lo tile what is the probability that the first number divided by the second number is greater than zero
Answer:
15
Step-by-step explanation:
The probability that the first number divided by the second number is greater than zero is 1/3
What is probability?Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Tiles are numbered -2,-1,1,2
So, possibility first number divided by the second number is greater than zero
-2/-1=2
-2/1=-2
-2/2=-1
-1/-2= 0.5
-1/1=-1
-1/2=-0.5
1/-2=-0.5
1/-1=-1
1/2=0.5
2/-2=-1
2/-1=-2
2/2=1
Probability the first number divided by the second number is greater than zero = 4/12=1/3.
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what is the sum of the interior angle in a kite
Answer:
the sum of the interior angles = 360°
A kite has 4 sides.
This is the formula for the sum of the interior angles of any polygon:
N = number of sides
the sum of the interior angles = (N x 180°) - 360°
so, N = 4, then:
(4 x 180°) - 360° = 360°
PLEASE HELP WILL GIVE BRAINLIEST:) If S (0,2) is the midpoint of RT and the coordinates of T are (3,5), find the coordinates of R.
Answer:
(-3,-1)
Step-by-step explanation:
So we need to find a number, x=a, such that when we average that number and x=3, we get x=0.
Since we want x=0 to be middle and x=3 is 3 units right of 0, then we are looking for number 3 units left of 0 which is x= -3.
Since we want y=2 to be the middle and y=5 is 3 units above 2, then we are looking for a number 3 units below 2 which is y=-1.
The other endpoint is (-3,-1).
Let's average (-3,-1) and (3,5).
(-3+3)/2=0/2=0
(-1+5)/2=4/2=2.
Check mark.
What two number add up to 10 multiply by 24
Answer:
the two numbers are six and four
Step-by-step explanation: 6+4=10 6x4=24
Someone plsss HELP ME
Answer:
[tex]2,8,6,18[/tex]
Step-by-step explanation:
Coordinates are written in [tex](x,y)[/tex] form. In a function, this translates to (input, output). Therefore, in these four coordinates, the four outputs are 2, 8, 6, and 18.
A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Two marbles are chosen from the bag. What expression would give the probability that one marble is yellow and the other marble is red?
P(Y and R) = StartFraction (8 P 1) (5 P 1) Over 25 P 2 EndFraction
P(Y and R) = StartFraction (8 C 1) (5 C 1) Over 25 C 2 EndFraction
P(Y and R) = StartFraction (1 C 8) (1 C 5) Over 2 C 25 EndFraction
P(Y and R) = StartFraction (1 P 8) (1 P 5) Over 2 P 25 EndFraction
Answer:
The answer is B! P(Y and R) = StartFraction (8 C 1) (5 C 1) Over 25 C 2 EndFraction
Answer:
The Second Option
Step-by-step explanation:
Edge '21
Find the volume of the prism below.
3 ft
8 ft
6 ft
Answer:
3: 27
8; 512
6; 216
Step-by-step explanation:
no wonder why u lookin all aids
Answer:
cuz im Not very smarttt
Step-by-step explanation:
at all
the measures of the angles of a triangle are shown in the figure below. solve for x
Answer:
67 degrees
Step-by-step explanation:
All angles in a triangle add up to 180 degrees. So...
23 + x + 90 = 180
113 + x = 180
x = 67 degrees
PLEASE PLEASE PLEASE HELP ME!!!!!!!!!!
Point (4, –5) is mapped onto ________ when rotated 90° clockwise about the origin.
A)
(5, –4)
B)
(–5, 4)
C)
(5, 4)
D)
(–5, –4)
Answer:
D. (-5, -4)
Step-by-step explanation:
When making a rotation 90° clockwise, the coordinates will swap places. However, the x value will be the opposite and the y value will stay the same.
90° clockwise rule:
(x, y) ---> (y, -x)
(4, -5) ---> (-5, -4)
Hope this helps!!
Phil melange 0.2L de jus de pomme teneur en fruit 25% et 0.1L de jus d'orange teneur de fruit 50% quel est la teneur en fruit de son cocktail
Answer:
10%
Step-by-step explanation:
La teneur en fruits de son cocktail est calculée comme suit:
25% de jus de pomme 0.2L + 50% de jus d'orange 0.1L
0.25 × 0.2 + 0.5 × 0.1
0.05 + 0.05
= 0.10
Conversion en pourcentage
= 0.10 × 100%
= 10%
Par conséquent, la teneur en fruits de son cocktail est de 10%
Answer choices
a
b
c
d
Answer:
Either A or D
Step-by-step explanation:
I got It right Hope it helps this you guys
The Tennis Club decided to buy T-shirts for its members. Action Sports Apparel quoted the following prices for the T-shirts
Number of T-Shirts Total Cost (dollar)
12
156
17
211
22
266
Which equation best describes the relationship between the total cost, c(t), and the number of T-shirts, t?
ok
Answer:
12
Step-by-step explanation:
hi
Equation which describe relationship between total cost and number of t-shirt is [tex]c(t)=75.93e^{0.06t}[/tex].
Data given are ,
Number of t-shirt (t) total cost c(t)
12 156
17 211
22 266
According to above table, exponential function best describes the relationship between the total cost, c(t), and the number of T-shirts, t.
Let, [tex]c(t)=Ae^{kt}[/tex]
Substitute , t=12 and c(t) = 156
We get, [tex]156=Ae^{12k}.......(1)[/tex]
Substitute , t=17 and c(t) = 211
We get, [tex]211=Ae^{17k} ........(2)[/tex]
After solving above equations.
We get, A = 75.93 and k = 0.06
Thus, [tex]c(t)=75.93e^{0.06t}[/tex]
Learn more:
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(10a⁵b⁴-15a⁴b⁵+5a³b³)÷(-5a³b³)
Answer:
[tex]\bold{-2a^2b+3ab^2-1}[/tex]Step-by-step explanation:
[tex](10a^5b^4-15a^4b^5+5a^3b^3)\div(-5a^3b^3)=\dfrac{10a^5b^4-15a^4b^5+5a^3b^3}{-5a^3b^3}=\\\\\\=\dfrac{10a^5b^4}{-5a^3b^3}+\dfrac{-15a^4b^5}{-5a^3b^3}+\dfrac{5a^3b^3}{-5a^3b^3}=-2a^2b+3ab^2-1[/tex]
Which angles are adjacent angles?
Answer:
Step-by-step explanation:
108 identical books have a mass of 30 kg.Find
the mass of 150 such books
the number of such books that have mass of 20 kg
Answer:
41.67 kg
72 books
Step-by-step explanation:
mass of 150 books = 150/108 × 30 kg
= 41.67 kg
number of books = 20/30 × 108 books
= 72 books
no links will mark BRAINLIEST
Answer:
1 = natural numbers
2 = 1
3 = 0
4 = -7/5
5 = NO
6 = 1 and -1
7 = 1/5
8 = x
Circle has a circumference of 38 cm
What is the length of the radius,
6 cm
18 om
36 cm
72 cm
[tex]circumference \: of \: circle \: = 2 \: \pi \: r[/tex]
38 = 2πr
r = 38/2π
r = 38÷6.28
r = 6 cm
Help me figure out the two way table
Fill in the given information then calculate the missing parts. See attached picture
Questions and Answers
1.
A is 40% of B. what percentages
Discuss
A
6090
B.
Answer:
yeah thats right good job keep up the good work and keep doing ur thing good job
Step-by-step explanation:
30% of which number is 3?
Answer:
10
Step-by-step explanation:
30/100*x=3
Multiply both sides by 100 and divide both by 30
You get the answer x=10
Answer:
10
Step-by-step explanation:
DO this 3x100/30 and you get 10
Please help 35 points
100 75 50 25
Answer:
50
Step-by-step explanation:
every 50 points it takes 1 hr
Find 2 points
I’ll use (1,75) and (3,175)
Slope = change in y over the change in x
Slope = (175-75)/(3-1)
Slope = 100/2
Slope = 50
This is the beginning of Antoine's construction. What is he trying to construct?
Select the BEST answer choice. (See Photo)
a. Perpendicular bisectors
b. Angle bisectors
c. Inscribed circle
d. Circumscribed circle
Answer:
option C
Step-by-step explanation:
For this problem use 3.14 for , and any non-integer answers should be entered as decimals rounded to the hundredths place. Lannon is designing a carnival game for a school event. She has a large wooden square and she needs to cut out a circle from the middle. The circumference of the circle that she plans to cut out is 56.52 inches. What is the radius
Answer:
Step-by-step explanation:
For this problem use 3.14 for , and any non-integer answers should be entered as decimals rounded to the hundredths place. Lannon is designing a carnival game for a school event. She has a large wooden square and she needs to cut out a circle from the middle. The circumference of the circle that she plans to cut out is 56.52 inches. What is the radius
The formula for circumference of a circle = 2πr
Circumference = 56.52 inches
r = Circumference/2π
r = 56.52/2π
Find the value of x
(2x+12)
Answer:
[tex]2x + 12 = \frac{180}{2} = 90 \\ 2x = 78 \\ x = 39[/tex]
can someone help me pleaseeeeee
AJKL has vertices at the points (2.5,3) K(3.2,- 4.7), and (-6.9.3). Find the slope of side 1
DA
A undefined
B. -11
C. -0.76
D. 0
Answer:
[tex]S_{DA}=-11[/tex]
Step-by-step explanation:
From the question we are told that:
The Vertices points for DAN
[tex]D= (2.5,3)[/tex]
[tex]A=(3.2,- 4.7)[/tex]
[tex]N=(-6.9.3)[/tex]
Generally the equation for slope of DA [tex]S_{DA}[/tex] is mathematically given by
[tex]S_{DA}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]S_{DA}=\frac{-4.7-3}{3.2-2.5}[/tex]
[tex]S_{DA}=-11[/tex]
The question is "FIND THE VALUE OF 7".
the answers are 27, 5,040, 4,480, and 28.
PLS ANSWER FAST I DONT HAVE MUCH TIME!!!!!