I have one fair 6-sided die and one unfair 6-sided die. On the unfair die, the probabilities of rolling numbers 2,…,6 are equal and the probability of rolling a 1 has a different value. I roll each die once.
If the probability of rolling one 3 and one 4 is 1/24, what is the probability of rolling two 1’s?
Answer:
[tex]\dfrac{1}{16}[/tex]
Step-by-step explanation:
Probability Distribution Table for X
Where X is the score on a fair, six-sided dice:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(X=x) \phantom{\dfrac11}&\frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} \\\cline{1-7}\end{array}[/tex]
Probability Distribution Table for Y
Where Y is the score on an unfair, six-sided dice, and the probabilities of rolling numbers 2, 3, 4, 5 and 6 are equal, and the probability of rolling a 1 has a different value:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&1-5k&k&k&k&k&k\\\cline{1-7}\end{array}[/tex]
Note: The probabilities of all the possible values that a discrete random variable can take add up to 1.
The outcomes of rolling one 3 and one 4 are:
Rolling a 3 with the first die and a 4 with the second die, ORRolling a 4 with the first die and a 3 with the second die.Given the probability of rolling one 3 and one 4 is ¹/₂₄:
[tex]\implies \text{P}(X=3)\; \text{and} \; \text{P}(Y=4) \; \text{or} \; \; \text{P}(X=4) \; \; \text{and} \; \; \text{P}(Y=3)=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{1}{6} \times k +\dfrac{1}{6} \times k=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{k}{6} + \dfrac{k}{6}=\dfrac{1}{24}[/tex]
[tex]\implies \dfrac{2k}{6}=\dfrac{1}{24}[/tex]
[tex]\implies 24(2k)=6[/tex]
[tex]\implies 48k=6[/tex]
[tex]\implies k=\dfrac{1}{8}[/tex]
Therefore:
[tex]\implies 1-5k=1-\dfrac{5}{8}=\dfrac{3}{8}[/tex]
Hence, the probability distribution table for the unfair 6-sided dice is:
[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} y & 1 & 2 & 3 & 4 & 5 & 6\\\cline{1-7} \text{P}(Y=y) \phantom{\dfrac11}&\frac{3}{8} & \frac{1}{8} & \frac{1}{8}& \frac{1}{8} & \frac{1}{8}& \frac{1}{8} \\\cline{1-7}\end{array}[/tex]
There is only one possible outcome of rolling two 1's, so the probability of rolling two 1's is:
[tex]\implies \text{P$(X=1)$ and P$(Y=1)$}=\dfrac{1}{6}\times\dfrac{3}{8}=\dfrac{3}{48}=\dfrac{1}{16}[/tex]
Note: Please see attachment for the sample-space diagram showing the possible outcomes of rolling two dice. The possible outcomes of rolling one 3 and one 4 are highlighted in yellow. The possible outcome of rolling two 1's is highlighted in blue.
Using the given sample data, calculate the following measures of dispersion, to one decimal place.
Range = 15
Variance = 24.5Explanations
Standard deviation = 5.0
The formula for calculating the range is expressed as:
Range = Highest value - Lowest value
Range = 24 - 9
Range = 15
Calculate the variance
The formula for calculating the variance is expressed as:
[tex]Variance=\frac{\sum(x-\overline{x})^2}{n-1}[/tex]Find the mean
[tex]\begin{gathered} mean=\frac{9+13+15+18+19+20+24}{7} \\ mean\text{ }\overline{x}=\frac{118}{7}=16.9 \end{gathered}[/tex]Determine the variance
[tex]\begin{gathered} S^2=\frac{(9-16.9)^2+(13-16.9)^2+(15-16.9)^2+(18-16.9)^2+(19-16.9)^2+(20-16.9)^2+(24-16.9)^2}{7-1} \\ S^2=\frac{146.9}{6} \\ S^2\approx24.5 \end{gathered}[/tex]Determine the standard deviation
[tex]\begin{gathered} S=\sqrt{variance} \\ S=\sqrt{24.5} \\ S\approx5.0 \end{gathered}[/tex]Can anyone please help me?
Answer:
the answer is 60
Step-by-step explanation:
7x2 – 5x + 10x – 8x2
Answer:
-1(x - 5)x
Step-by-step explanation:
7x2 - 5x + 10x -8x2
7x2 + 5x -8x2
7x2 + 5x - 8x2
-1x2 + 5x
-1x2 + 5x
-x2 + 5x
7x2 - 5x + 10x - 8x2
-1 (x2 - 5x)
-1 (x2 - 5x)
-1(x - 5)x
-1(x - 5)x
find the common difference of thr arithmetic sequence -19 -14 -9
-5 is the common difference of the arithmetic sequence.
What is arithmetic sequence?A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15. The nth term of an arithmetic progression is determined using the arithmetic sequence formula. The series where the common difference between any two next words stays constant is known as an arithmetic sequence.
Given Data
Arithmetic sequence
-19, -14, -9
Common difference = a₂ - a₁
Common difference = -14 - (-19)
Common difference = -14 + 19
Common difference = -5
-5 is the common difference of the arithmetic sequence.
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SOMEONE HELP! I NEED THIS QUICKLY! WILLING TO GIVE 45 POINTS!!! At 1 P.M., the total snowfall is 2 centimeters. At 4 P.M., the total snowfall is 7 centimeters. What is the mean hourly snowfall? Write your answer in simplest form as a fraction or mixed number.
The mean hourly snowfall is (5/3) centimeters per hour, which means that each hour there are 5/3 centimeters more of snow.
What is the mean hourly snowfall?The mean hourly snowfall is given by the quotient between difference between the total snowfall at the two given times and the total time.
Here we have:
Initial snowfall = 2cm
Final snowfall = 7cm
Difference = 7cm - 2cm = 5cm
And that happens between 1 P.M. and 4 P.M., so we have 3 hours.
Then the mean hourly snowfall is:
M = 5cm/3h = (5/3) centimeters per hour.
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Help pls math is not my thing
Answer: 2.25 x 10^18
Step-by-step explanation:
When dividing with exponents you subtract
56-38= 18
10 cancels out
(9 x 10^18) / 4
= 2.25 x 10^18
what is 12 root divided by 3 root (simplify)
Answer:
Дсдслсьмтстстсьсьалалла =4
Answer: 2
Step-by-step explanation:
1. Simplify the expression
[tex]sqrt(12)/sqrt(3)\\3.464/sqrt(3)\\3.464/1.732[/tex]
2. Perform any multiplication or division, from left to right:
[tex]3.464/1.732[/tex]
[tex]2[/tex]
5.) Claire deposited $32 each week for 8 weeks. How much money did she deposit after 8
weeks?
O $256
O-$256
O-$40
O $40
The sum of three consecutive numbers is thirty-three. What is the middle number
Answer:
The first number is 10
The middle number is 11
The last number is 12
Consider the relation R = {(4,7), (5,3), (6,2), (7, 7)}. What is the inverse of R? Enter your answer as a set of ordered pairs.
Check the picture below.
Abdul runs 8 miles in 60 minutes
How many miles does he run per minute
Answer:
2/15 mile per minute
Step-by-step explanation:
8 miles in 60 minutes is equivalent to 8/60 miles per minute
= 2/15 mile per minute
Answer:
Step-by-step explanation:
60/8=7.5
Factor the expression using the GCF 6y + 3
[tex]3(2y+1)[/tex] I believe is the solution you seek.
You factor 3 out of 6y + 3, leaving you with the solution.
Hope this helps!
Samuel was absent for the last biology test. For those who took the test, the mean was 84.6, the median was 82, and the mode was 88. When Samuel took the test, the class mean went down to exactly 84. His score was different from every other students’ score. What effect, if any, did Samuel’s score have on the class mode?
A: None; the mode stayed the same.
B: It decreased the mode by exactly 1 point.
C: It increased the mode by exactly 1 point.
D: It increased the mode by greater than 1 point.
E: The effect of Samuel’s score on the mode cannot be determined from the given information.
The correct option is A: None; the mode stayed the same.
What is Mode?Mode of a data set is the value that occur most frequently in a data set.
There may be no mode, one mode or more than one mode for a data depending on the number of times values are repeating.
Given that before Samuel taking a test,
Mean = 84.6
Median = 82
Mode = 88
After Samuel took the test,
Mean = 84
Also given that, his score was different from every other students’ score.
This means that from the data of scores, Samuel's score is not repeating.
Mode is the most repeating element.
So Samuel's score does not effect the mode and thus stayed the same.
Hence the mode stayed the same.
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Calculate the value of 1 3/5 x 2/5
As a fraction in its simplest form
Answer:
16/25
Step-by-step explanation:
1 3/5 = 8/5
8/5 x 2/5 = 16/25
SOMEONE PLEASE HELPPPP!!! LOOK AT THE PICTURE!
Answer:
x+2=3
collect like terms
x=3-2
x=1
x-12=x+30
collect like terms
x-x=30-12
=18
2(x+6)=2x+12
open bracket
2x+12=2x-12
collect like terms
2x-2x=-12+12
=0
3(x-2)=3x-2
open bracket
3x-6=3x-2
collect like terms
3x-3x=-2+6
=4
what is the answer to Abdul drinks 1 1/2 pints of milk a day. How much is this in cups?
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
3 us cups
Step-by-step explanation:
multiply by 2
When x²+x-3 is subtracted from 3x² - 5, the result is
A. -2x² + x + 2
B. 2x² - x - 2
C. 2x² - x + 2
D. 4x²+x-8
Answer:
B 2x² - x - 2
Step-by-step explanation:
When x²+x-3 is subtracted from 3x² - 5
We get (3x² - 5) - (x² + x - 3)
==> step 1 remove parenthesis and change signs
3x² - 5 - x² - x + 3
==> step 2 combine like terms
2x² - x - 2
Remember like terms are terms with the same variable and degree.
For example 3a² and 5a² would be like terms because both terms have a variable of "a" and a degree of 2
You are given that x = 5^m and y = 5^n
Write 5^m+n/2 in terms of x and y.
Answer:
X + e^(Y-5)/2
Step-by-step explanation:
X = 5^m
Y = 5^n
e^Y = n*e^5
n = e^(Y-5)
6 kg rice is enough for 20 people. How much rice is required for 100 people
Answer:
30.
Step-by-step explanation:
Apologies if I am late, but I believe this is the answer!
In general, the air temperature decreases 12°F for every
4,000 feet increase in altitude. If a hiker climbs 3,000 feet, by how
much can she expect the temperature to decrease?
Answer: 9
Step-by-step explanation:
Aaron Rodgers' yearly salary is 2.2 x 10' dollars. The yearly salary of one of his backup
quarterback's is 6.3x105 dollars. How many times greater is Aaron Rodgers' salary than his
backup's salary?
Aaron Rodgers salary is 2.19×[tex]10^1^1[/tex] greater than his backups.
To find how many times a quantity x is greater than y we do subtraction. That is we do [tex]x-y[/tex].
So, here Aaron's salary is given to be $ 2.2× [tex]10^1^0[/tex]
And his quarterback's salary is $ 6.3×[tex]10^5[/tex].
Thus the difference between salaries= 2.2×[tex]10^1^0[/tex] - 6.3 × [tex]10^5[/tex]
= 2.19×[tex]10^1^1[/tex]
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Write a formula for each rule, and graph the formula for each one.
1.The perimeter P of an equilateral tri-angle equals three times the length of a side s.
2.The number of tablespoons T is equal to the number of teaspoons x divided by 3.
The proportional relationships that model each relation are given as follows:
1. P = 3s.2. T = x/3.What is a direct proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the equation below:
y = kx.
Both items in this problem are represented by direct proportional relationships, we just have to identify the constants then graph the relations.
For item 1, the constant is of 3, as the perimeter is of three times the side length of the triangle.For item 2, the constant is of 1/3, as a division by 3 is equivalent to a multiplication by 1/3.The graph of a proportional relationship is linear with slope given by the constant and intercept at 0, hence the graphs for each item are given at the end of the answer.
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A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $40 million after 4 years, while profits increased $30 million per year. Select the linear function in slope-intercept form that models this situation (in millions).
Group of answer choices
y = 160x + 30
y = 40x + 4
y = 30x - 40
y = 30x - 80
BRAINIEST AND A LOT OF EXTRA POINTS FOR A SURE AND CORRECT ANSWER
Using the arithmetic operations, the total change in her monthly electric bill over 5 months is +$10.58
For the past 5 months,
The change in her July electric bill = +$18.02
The change in her August electric bill = +$1.03
The change in her September electric bill = -$0.44
The change in her October electric bill = -$6.84
The change in her November electric bill = -$1.19
The total change in her monthly electric bill over 5 months = Sum of all changes in her electric bill over 5 months
= +18.02+1.03-0.44-6.84-1.19
= +$10.58
Hence, the total change in her monthly electric bill over 5 months is +$10.58
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You can use this rule to work out the total cost, in pounds, of hiring a carpet cleaner. Multiply the number of days by 7.8 and then add 12
Andy hires a carpet cleaner.
The total cost is £82.20
(a) Work out the number of days Andy hires the carpet cleaner for.
Andy hired the carpet cleaner for 9 days, bringing the total cost to £82.20.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Dependent variables depend on other variable while an independent variable .
Let y represent the amount of money paid to the carpet cleaner for working x days. Multiply the number of days by 7.8 and then add 12, Hence:
y = 7.8x + 12
For a total cost of 82.20
82.2 = 7.8x + 12x = 9.
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Please SIMPILFY these
Answer:
a) 81
b) 16807
c) 100
d) 78125
PLEASE GIVE ME A BRAIN
[tex]\sqrt{3(\sqrt{3}-1)^2 }[/tex]
Answer:
3-[tex]\sqrt{3}[/tex] is the exact form
Question 2 of 10
Question 2
"If two lines intersect, then the lines are coplanar."
Identify the following statements as the contrapositive, converse, or inverse of the
statement above.
• If two lines do not intersect, then the lines are not coplanar. inverse
+
• If two lines are coplanar, then the lines intersect. converse
• If two lines are not coplanar, then the lines do not intersect.
contrapositive
C
The inverse of the conditional statement is : if two lines do not intersect, then the lines are not coplanar.
Conditionals are commands used in programming languages to handle decisions.
Conditional statements are those that have both a hypothesis and a conclusion. It is also known as a "If-then" statement. If the conclusion and the hypothesis are both true, the conditional statement is untrue.They include conditional statements, conditional expressions, and conditional constructions. Particularly, conditionals carry out various calculations or actions according on whether a boolean condition set by the programmer evaluates to true or false. The decision is always made in terms of control flow by selecting changing the control flow based on some situation.The contrapositive statement is : If two lines are not coplanar, then the lines do not intersect.
The converse statement is : If two lines are coplanar, then the lines intersect.
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The points (3, – 1) and (2,s) fall on a line with a slope of – 9. What is the value of s?
giving free brainlist!
Answer:
8
Step-by-step explanation: