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Probability
Jacob performed an experiment with a weighted die, numbered 1 to 6. He rolled the die 125 times and recorded the results.
Complete the table below.
0.232
37
24
0.176
18
0.048
0.104
22
Result of Roll
Frequency
Experimental
Probability
1
2
13
3
0.144
4
29
5
0.296
6
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Submit
Answers
Answer:
[tex]1 \to 22 \to 0.176[/tex]
[tex]2 \to 13 \to 0.104[/tex]
[tex]3 \to 18 \to 0.144[/tex]
[tex]4 \to 29 \to 0.232[/tex]
[tex]5 \to 37 \to 0.296[/tex]
[tex]6 \to 6 \to 0.048[/tex]
Step-by-step explanation:
Given
[tex]n = 125[/tex]
See attachment for proper table
Required
Complete the table
Experimental probability is calculated as:
[tex]Pr = \frac{Frequency}{n}[/tex]
We use the above formula when the frequency is known.
For result of roll 2, 4 and 6
The frequencies are 13, 29 and 6, respectively
So, we have:
[tex]Pr(2) = \frac{13}{125} = 0.104[/tex]
[tex]Pr(4) = \frac{29}{125} = 0.232[/tex]
[tex]Pr(6) = \frac{6}{125} = 0.048[/tex]
When the frequency is to be calculated, we use:
[tex]Pr = \frac{Frequency}{n}[/tex]
[tex]Frequency = n * Pr[/tex]
For result of roll 3 and 5
The probabilities are 0.144 and 0.296, respectively
So, we have:
[tex]Frequency(3) = 125 * 0.144 = 18[/tex]
[tex]Frequency(5) = 125 * 0.296 = 37[/tex]
For roll of 1 where the frequency and the probability are not known, we use:
[tex]Total \ Frequency = 125[/tex]
So:
Frequency(1) added to others must equal 125
This gives:
[tex]Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125[/tex]
[tex]Frequency(1) + 103 = 125[/tex]
Collect like terms
[tex]Frequency(1) =- 103 + 125[/tex]
[tex]Frequency(1) =22[/tex]
The probability is then calculated as:
[tex]Pr(1) = \frac{22}{125}[/tex]
[tex]Pr(1) = 0.176[/tex]
So, the complete table is:
[tex]1 \to 22 \to 0.176[/tex]
[tex]2 \to 13 \to 0.104[/tex]
[tex]3 \to 18 \to 0.144[/tex]
[tex]4 \to 29 \to 0.232[/tex]
[tex]5 \to 37 \to 0.296[/tex]
[tex]6 \to 6 \to 0.048[/tex]
Related Questions
brainiest exchange give me and I will give you 2+2
Answers
Answer:
4
Step-by-step explanation:
and sure
Answer:
4
Step-by-step explanation:
A rectangle is 64 cm long 40 cm wide find is area and perimeter
Answers
Answer:
Assuming the length to be x and the width to be y.
Since the area is 64cm, hence
x*y = 64 (equation 1)
Since the perimeter is 40cm, hence
x + x + y + y = 40
2x + 2y = 40
2(x + y) = 2(20)
x + y = 20 (equation 2)
Hence by using simultaneous equation,
x = 20 - y (equation 3)
Substituting equation 3 into equation 1, we get
(20-y)*y=64
20y-y^2=64
Tidying up the equation,
y^2 - 20y + 64 = 0
By using factorisation,
(y-16)(y-4)=0
y=16 or y=4
By substituting y=16 into equation 1,
x*16=64
x = 4
By substituting y = 4 into equation 1,
x*4=64
x=16
Therefore,
The length is 4 cm while the width is 16 cm.
OR
The length is 16 cm while the width is 4cm.
Hope this helps!!
Please help I’m stuck
Answers
Answer:
96
Step-by-step explanation:
Its a pattern :) BTW can you help with mine please
y = x2 – 3x + 2
use the discriminant to determine the number of solutions
Answers
Answer:
2 real solutions
Step-by-step explanation:
The formula for determining the discriminant is b² - 4ac.
So, let's identify our variables.
a = 1
b = 3
c = 2
Now, we can plug in our values.
3² - 4(1)(2)
9 - 8
1
1 is the discriminant of this function, and since 1 is positive, this indicates that there are two distinct real number solutions.
89.5, 71, 75, 76, 74, 87, 89, 71, 85
mode = ?
Answers
Answer:
mode of this question is 71
Answer:
71
Step-by-step explanation:
because mode is the number that occurs most frequently
Pls help
If a varies jointly as b and c, find a when b = 4 and c = -3.
a = -96 when b = 3 and c = -8
a=
Answers
Answer:
a=4bc
a=4(4)(-3)=-48
a= - 48 when b equals to 3 is equals to - 8
The required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
When a variable varies jointly as two other variables, it means that the relationship between the variables can be expressed using direct variation. In this case, we have that "a varies jointly as b and c."
To find the value of a when b = 4 and c = -3, we can set up the proportion based on the direct variation relationship:
a/bc = k
where k is the constant of variation.
Substituting the given values:
a/(4)(-3) = k
Simplifying, we have:
a/-12 = k
Now, we can find the value of a when b = 4 and c = -3 by substituting these values into the equation and solving for a:
a/(-12) = k
a/(-12) = -96/-12 (since k = -96 when b = 3 and c = -8)
a = 96
Therefore, the required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
Learn more about direct variation here:
https://brainly.com/question/29150507
#SPJ2
u = 63 cm, t = 34 cm and ∠T=158°. Find all possible values of ∠U, to the nearest 10th of a degree.
Answers
Answer:
{}
Step-by-step explanation:
Thats actually the answer believe it or not :)
14. A boy completes a 100 m circular track race in 5 min. Another boy runs in the same
time
completes the race in 6 minutes. If they start from the same point then after how many
will they meet at the starting point
Find the smallest 3-digit number which is exactly divisible by 5.10 and 20
Answers
Answer:
ee
Step-by-step explanation:
An investor wants to invest up to $100,000 as follows:
X amount into a Certificate of Deposit (CD) that yields an expected annual return of 1% with a risk index of 1,
Y amount into a Bond with an expected annual return of 3% and a risk index of 4,
Z amount into a Stock with an expected annual return of 7% and a risk index of 8.
The investor’s objective is to maximize the total expected annual return of the investment.
However, to be prudent, the investor requires that:
The fraction of the total investment in X must be at least 20%.
The fraction of the total investment in Z must not exceed 50%.
The combined portfolio risk index must not exceed 5.
Required:
a. Set up this investment problem as a linear program, which has 3 variables, 3 basic constraints, and 4 special constraints.
b. Use an LP software to find the maximum expected annual return in dollars and the dollar values of X, Y, and Z for this best investment.
c. From the software solution, show the values of the dual variables for the four special constraints.
Answers
Answer:
a-The Linear Model is as follows:
[tex]X+Y+Z\leq 100,000\\{0.001X}\geq 20\\{0.001Z}\leq 50\\0.00001X+0.00004Y+0.00008Z\leq5\\X\geq0\\Y\geq0\\Z\geq0[/tex]
b-The values are
X=$33,333.33
Y=$16,666.67
Z=$50,000.00
Leading to a total expected return of $4333.33.
c-The values of constraints are as follows
X+Y+Z=33333.33+16666.67+50000=100,000
X=33%, Y is 16.67% and Z is 50%
Risk component of X is 0.33
Risk component of Y is 0.66
Risk component of Z is 4.00
Step-by-step explanation:
a
From the conditions, the first special constraint is the total amount which is that the sum of investments must not be more than the total available amount of $100,000 so
[tex]X+Y+Z\leq 100,000[/tex]
The second special constraint is that the percentage of X must be at least 20% So
[tex]\dfrac{X}{100,000}\times100 \geq20\\\dfrac{X}{1000} \geq20\\{0.001X}\geq 20[/tex]
The third special constraint is that the fraction of total investment of Z must not exceed 50% So
[tex]\dfrac{Z}{100,000}\times100 \leq50\\\dfrac{Z}{1000}\leq 50\\0.001Z\leq50[/tex]
The fourth special constraint is that the combined portfolio risk index must not exceed 5 so
[tex]\dfrac{X}{100,000}\times1+\dfrac{Y}{100,000}\times4+\dfrac{Z}{100,000}\times8\leq5\\0.00001X+0.00004X+0.00008Z\leq5[/tex]
As the investments cannot be negative so three basic constraints are
[tex]X\geq0\\Y\geq0\\Z\geq0[/tex]
The maximization function is given as
[tex]f(X,Y,Z)=\dfrac{X}{X+Y+Z}\times1\%+\dfrac{Y}{X+Y+Z}\times3\%+\dfrac{Z}{X+Y+Z}\times7\%\\f(X,Y,Z)=\dfrac{X}{X+Y+Z}\times0.01+\dfrac{Y}{X+Y+Z}\times0.03+\dfrac{Z}{X+Y+Z}\times0.07[/tex]
b
By using an LP solver with BigM method the solution is as follows:
X=$33,333.33
Y=$16,666.67
Z=$50,000.00
Leading to a total expected return of $4333.33.
c
The values of constraints are as follows
X+Y+Z=33333.33+16666.67+50000=100,000
X=33%, Y is 16.67% and Z is 50%
Risk component of X is 0.33
Risk component of Y is 0.66
Risk component of Z is 4.00
a cylinder shaped water pitcher has a radius of 5 inches and a height of 12.5 inches find the surface area of the pitcher
A.5495 in² B. 54.95 in²
C.549.5 in² D. 5.495 in²
Answers
A cylinder shaped water pitcher has a radius of 5 inches and a height of 12.5 inches. Find the surface area of the pitcher.
Answer:-Given:-[tex] \bullet [/tex] Radius (r) of a cylinder shaped water pitcher = 5 inches.
[tex] \bullet [/tex] Height (h) of a cylinder shaped water pitcher = 12.5 inches.
To Find:-The surface area of the pitcher.
Solution:-We know,
Formula of Surface area of a cylinder is 2πr(r + h) sq. units.
So,
Surface area of the pitcher = 2 × 3.14 × 5(5 + 12.5)
Surface area of the pitcher = 31.4 × 17.5
Surface area of the pitcher = 549.5 in²
[tex] \therefore [/tex] The surface area of the pitcher is 549.5 in².
Hence, the option (C) 549.5 in² is correct. [Answer]
The surface area of the cylinder is 549.50 in².
What is the surface area of the cylinder?A cylinder is a three-dimensional object. It is made up of a prism with a circular base. The total surface area is the sum of the areas of the faces or surfaces of a 3-dimensional object
Total surface area = 2πr(r + h)
Where:
π = 3.14r = 5 h = height2 x 3.14 x 5 (5 + 12.5) = 549.50 in²
if f(x)= 3x+16 what is f(2)
Answers
Answer:
22
Step-by-step explanation:
Reason:
3x2=6
6+16=22
So the answer is 22
jam brought three shirts for $3900 what is the cost of five shirts
Answers
Answer:
6,500
Step-by-step explanation:
Answer:
6500
Step-by-step explanation:
3900 divided by 3 is 1300 which is the cost of 1 shirt, so 1300 times 5 is 6500
Find the coefficient of the x^3 in the expansion of (2x-9)^5
Answers
Use the binomial theorem:
[tex]\displaystyle (2x-9)^5 = \sum_{k=0}^5 \binom5k (2x)^{5-k}(-9)^k = \sum_{k=0}^5 \frac{5!}{k!(5-k)!} 2^5 \left(-\frac92\right)^k x^{5-k}[/tex]
The x ³ terms occurs for 5 - k = 3, or k = 2, and its coefficient would be
[tex]\dfrac{5!}{2!(5-2)!} 2^5 \left(-\dfrac92\right)^2 = \boxed{6480}[/tex]
You invest $25,000 at 12% for 30 years, find the total balance
Answers
Answer:
115000
Step-by-step explanation:
25000 x .12 = 3000
3000 x 30 = 90000
90000 + 25000 = 115000
A pair of weak earthquakes is modeled by a system of inequalities. One earthquake occurred roughly 20 km east and 14 km north of the center of Columbia, NC. The quake could be felt from 25 km away. A couple days later, another earthquake occurred 8 km west and 3 km north of the center of Columbia and could be felt from 14 km away. If Columbia is located at (0, 0) on a coordinate grid, the system of inequalities represents this scenario.
StartLayout Enlarged left-brace first row (x minus 20) squared + (y minus 14) squared less-than-or-equal-to 625 second row (x + 8) squared + (y minus 3) squared less-than-or-equal-to 196 EndLayout
Which location relative to Columbia felt both earthquakes?
4 km west and 12 km south
6 km west and 4 km north
2 km east and 10 km north
6 km east and 8 km north
Answers
Answer:
2 km east and 10 km north
Step-by-step explanation:
I did the activity and got the right answer.
By evaluating the inequalities, we will see that the correct option is: 2 km east and 10 km north
Which location will feel both earthquakes?
Here we have the inequalities:
(x - 20)^2 + (y - 14)^2 ≤ 625
(x + 8)^2 + (y - 3)^2 ≤ 196
Where, x is the distance due east, and y is the distance due north.
So we just need to find which of the given options makes both inequalities true, for example, for the first one we have:
x = -4
y = -12
Replacing that on the first inequality we get:
(-4 - 20)^2 + (-12 - 14)^2 ≤ 625
1,252 ≤ 625
This is false, so this option is not correct.
Now we just need to check the other options. Particularly for the third we have:
x = 2
y = 10
Replacing that in both inequalities we get:
(2 - 20)^2 + (10 - 14)^2 ≤ 625
340 ≤ 625 (true).
(2 + 8)^2 + (10 - 3)^2 ≤ 196
149 ≤ 196 (true)
So at 2km east and 10km north of Columbia, the two earthquakes can be felt.
If you want to learn more about inequalities, you can read:
https://brainly.com/question/18881247
Ann races her bicycle for 58m. A wheel of her bicycle turns 29 times as the bicycle travels the distance. What is the diameter of the wheel
Answers
Answer:
0.637 m or 63.7 cm
Step-by-step explanation:
Formula
d = n * pi di
Givens
di = diameter and is unknown
n = 29 times
d = 58 meters
Solution
58 = 29 * 3.14 * di
2 = 3.14 * di
2/3.14 = di
d = 0.637 meters
or
d = 63.7 cm
A quarter has a diameter of 24 mm.
Which measurement is closest to the
circumference of the quarter in
millimeters?
A. 452.39 mm
B. 37.7 mm
C. 75.4 mm
D. 150.8 mm
Answers
Answer:
C or D
Step-by-step explanation:
help meh pwase explain how ur answer is plz
Answers
Answer: for question 2
B
Step-by-step explanation:
23.15
+12.67
------------
35.82
40.00
- 35.82
---------
4.18
What is the mode of this
data?
5, 3, 3, 6, 7, 9, 10
uh help
Answers
Answer:
3
Step-by-step explanation:
3 appears the most (twice)
The rest of the numbers only appear once
what is:
k/3 + 17 = 12?
Answers
k/3 + 17 = 12?
k = -15
Answer:
-15
Step-by-step explanation:
yan po ang answer thank you na lang po
Help 16-18 thank you
Answers
Answer:
16. (80)(60) = 4800
17. (500)(600) = 300000
18. (700)(800) = 560000 a). high
Step-by-step explanation:
10h + hx=d-5 solve for h
Answers
Answer:
Hey!!
Step-by-step explanation:
h = d − 5 /10 + x
Hope this helps!
Have a nice day<3
Please helppp!!!
what is the perimeter of the triangle?
what is the area or the triangle?
Answers
Answer:
The perimeter is 27 km
The area is 21 km^2
Step-by-step explanation:
The perimeter of a triangle will just be all of the sides added up.
12 + 9 + 6 = 27 km
The area of a triangle is:
A = 1/2 * base * height
The base is 6 km, and the height is 7 km. Substituting the values in and solving, we get:
A = 1/2 * 6 * 7
A = 3 * 7
A = 21 km^2
please help me I've been asking for this question for a while and I keep getting those spam messages please help me 15pts
How would you go about finding the confidence interval of say 90% or 95% for any given distribution scenario?
Answers
Answer:
You'd want to divide.
Step-by-step explanation:
Let's say you got a 9/10 on a test.
You'd do 9 divided by 100 and multiply it by 10 to get 90%
That is how you solve a percentage problem
FORMAT IN LESS DETAILED EXPLANATION:
9/100x10=90%
Nine divided by one-hundred times ten equals ninety percent
work out the value of (6-2.5)( 8+4)
Answers
Answer:
42
Step-by-step explanation:
Uh, I'm guessing what is being asked here is to solve, so, time to distribute.
(6 - 2.5)(8 + 4)
48 + 24 - 20 - 10
42
Would greatly appreciate the help
Answers
Answer:
Answer is E but not 100%
Step-by-step explanation:
Answer:
A is correct
E shows an error as the first two values are identical so one cannot be greater than the other.
Step-by-step explanation:
A shows 2.69 is equal to 2.696 which is more than 2.696 which is more than 2.696 which is more than 2.696
As when;
2.696 repeats in bold = 2.696969696 1st greatest
2.696 repeats in bold = 2.696696696 2nd in highest value so 2nd in order.
2.696 repeats in bold = 2.696666666 3rd in highest value so 3rd in order.
2.696 does not repeat = 2.696 so is the least greatest from the list.
Based on your understanding of the ideas of external consistency and fruitfulness, which of the following statements best describes the relevance of these ideas to the acceptance of hypotheses?
1. A fruitful hypothesis is considered stronger because fruitful hypotheses are always externally consistent with previously held theories
2. A fruitful hypothesis is considered stronger because fruitful hypotheses promote scientific progress by revealing new avenues of research and analysis
3. An adequate theory is always a fruitful theory
4. AB internally coherent theories are fruitful.
Which of the following scenarios best demonstrates the idea of fruitfulness?
1. The fundamental rules of quantum mechanics were established during the first half of the twentieth century by numerous scientists to deal with atomic and subatomic systems. Today, quantum mechanics provides the underlying mathematical framework of many fields of physics, including condensed matter physics, solid state physics, and nuclear physics
2. While both Einstein's theory of general relativity and quantum theory are indisputably supported by empirical evidence, scientists have as yet been unable to incorporate both of them within one cohesive model
3. The predictions of quantum mechanics correspond to the predictions of the classical theories of physics when the quantum theory is used to describe the behavior of systems that can be successfully described by classical theories
4. Ordinantly, quantum mechanics is used to describe the behavior of bodies that are so smal that they cannot be seen under an optical microscope, while the theories of classical physics we used to analyze the behavior of large-scale bodies.
Answers
Answer:
Based on your understanding of the ideas of external consistency and fruitfulness, which of the following statements best describes the relevance of these ideas to the acceptance of hypotheses?
2. A fruitful hypothesis is considered stronger because fruitful hypotheses promote scientific progress by revealing new avenues of research and analysis
Which of the following scenarios best demonstrates the idea of fruitfulness?
4. Ordinantly, quantum mechanics is used to describe the behavior of bodies that are so smal that they cannot be seen under an optical microscope, while the theories of classical physics we used to analyze the behavior of large-scale bodies.
Step-by-step explanation:
What is the area of this polygon? Im really bad a geometry so can I have help please.
Answers
Explain the importance of putting your data set in order from least to greatest.
Answers
Answer:
In order to make it easier for you to understand and helps in making problems more easier and faster to do
the ratio of the corresponding sides of two similar triangles is 2:5 the sides of the smaller triangle is 6mm 8mm and 12mm what is the perimeter of the larger triangle?
Answers
Answer:
65
Step-by-step explanation:
using the ratio we can find the side lengths of the other triangle.
since it is 2:5
6:x=2:5
so x = 15(first side)
8:x=2:5
so x = 20(second side)
12:x=2:5
x=30(third side)
so then we add them up
15+20+30
65
hope this was helpful
