Two dice are rolled. Let X and Y denote, respectively, the largest and the smallest values obtained a. Compute the conditional probability mass function of Y-i given X-1, for i-1,2, ..., 6 b. Are X and Y independent? Why or why not?
The conditional PMF of Y=i given X=1 is 1 if i=1 and 0 otherwise and X and Y are not independent because the value of X affects the possible range of values for Y.
a. To compute the conditional probability mass function (PMF) of Y=i given X=1, we need to find the probability of Y=i when X=1. Since X=1, the only possible outcome is (1,1), and Y can only be 1. Hence, the conditional PMF of Y=i given X=1 is:
P(Y=i | X=1) = 1, if i=1; 0, otherwise.
b. X and Y are not independent. If they were independent, the outcome of one die roll would not provide any information about the other die roll. However, given that X is the largest value and Y is the smallest value, we can see that X directly affects the possible range of values for Y. If X is 6, then Y cannot be greater than 6. Therefore, the values of X and Y are dependent on each other, and they are not independent.
Therefore, The conditional PMF of Y=i given X=1 is 1 if i=1 and 0 otherwise and X and Y are not independent because the value of X affects the possible range of values for Y.
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11. angle MLN and angle JLK are complementary, m angle MLN=7x-1 and m angle JLK=4x+3 . a. Solve for x b. Find m angle MLN and m angle JKL .
a. Solve for x
Since angle MLN and angle JKL are complementary, the value of x = 8
Since angle MLN and angle JKL are complementary, their sum equal 90°.
Since angle MLN = 7x - 1 and angle JKL = 4x + 3, we have that
7x - 1 + 4x + 3 = 90
Collecting like terms, we have
7x + 4x - 1 + 3 = 90
Simplifying, we have
11x + 2 = 90
Subtracting 2 from both sides, we have
11x = 90 - 2
11x = 88
Dividing through by 11, we have
x = 88/11
x = 8
So, Since angle MLN and angle JKL are complementary, the value of x = 8
b. Find m angle MLN and m angle JKL .
Since angle MLN=7x-1 and angle JLK=4x+3 thus, angle MLN = 55° and angle JKL = 35°
Since angle MLN = 7x - 1 and x = 8, we have
angle MLN = 7x - 1
angle MLN = 7(8) - 1
angle MLN = 56 - 1
angle MLN = 55°
Since angle JKL = 4x + 3 and x = 8, we have
angle JKL = 4x + 3
angle JKL = 4(8) + 3
angle JKL = 32 + 3
angle JKL = 35°
So, Since angle MLN=7x-1 and angle JLK=4x+3 thus, angle MLN = 55° and angle JKL = 35°
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Find the midpoint of the line segment with end coordinates of:(0,2) and (8,8)
HELPPP PLSSS IF YOUR A BOT I WILL REPORT !! A(b) is a function
A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. a. Find a 95% confidence interval for the mean score on the test. Be sure to write out what you entered in your calculator. (3 points) b. Interpret the interval you found in part a. (2 points) • For parts c-e, calculations are not necessary. c. Suppose the standard deviation of the tests had been 42.8 instead of 21.4. What would the larger standard deviation do to the width of the confidence interval? (1 point) d. If the confidence level were reduced to 90%, will the interval be wider or narrower? (1 point) e. If the sample size was increased to 75 subjects, will the interval be wider or narrower? (1 point)
a) Entering this into a calculator gives us:CI = (63.876, 88.524) b) test for the population is between 63.876 and 88.524 c) If the standard deviation of the test scores had been 42.8 instead of 21.4, the width of the confidence interval would increase. d) . If the confidence level were reduced to 90%, the interval would be narrower. e) If the sample size was increased to 75 subjects, the interval would be narrower.
a. To find a 95% confidence interval for the mean score on the test, we can use the formula:
To find the confidence interval, we need to estimate the population standard deviation with the sample standard deviation. So:
CI = 76.2 ± 1.96 * (21.4/√27)
Entering this into a calculator gives us:
CI = (63.876, 88.524)
b. The confidence interval we found tells us that we are 95% confident that the true mean score on the test for the population is between 63.876 and 88.524. In other words, if we were to take many random samples of 27 people and compute a 95% confidence interval for each one, then about 95% of those intervals would contain the true population mean.
c. If the standard deviation of the test scores had been 42.8 instead of 21.4, the width of the confidence interval would increase. This is because a larger standard deviation means that the data are more spread out, which makes it more difficult to estimate the population mean accurately.
d. If the confidence level were reduced to 90%, the interval would be narrower. This is because a higher confidence level requires a larger z-score, which widens the interval. Conversely, a lower confidence level requires a smaller z-score, which narrows the interval.
e. If the sample size was increased to 75 subjects, the interval would be narrower. This is because a larger sample size decreases the standard error (σ/√n), which makes it easier to estimate the population mean accurately and results in a narrower confidence interval.
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squaring a number is raising that number to a power of
Step-by-step explanation:
2
Example, 2*2=2^2
Hope it helped❤️
Answer:
to the power of 2
for example you can be asked to find the square number of 5 which is the same as 5²= 25
Today the population of a city is 250,000 and is growing at a rate
of 4% per year. When or how many years will the population reach
850,000
Step-by-step explanation:
Principal = 250,000
Rate = 4%
Simple interest = 850,000
Time = ?
\(t = \frac{100 \times interest}{principal \times rate} \\ t = \frac{100 \times 850000}{250000 \times 4} \\ t = \frac{100 \times 85}{25 \times 4} \\ t = \frac{8500}{100} \\ t = 85years\)
Write an equation involving absolute value for the following graph:
Answer:
|x+3|=2
Step-by-step explanation:
We need to make the equation so that -5 and -1 both work, so this equation is one of many that we can construct.
Answer: i cant see
Step-by-step explanation:
I need to know this now please
Answer + Step-by-step explanation:
\(\begin{matrix}x&y\\ -2&2(-2) +3=-1\\ 0&2(0)+3=3\\ 1&2(1)+3=5\\ 3&2(3)+3=9\end{matrix}\)
Check the illustration I provided
Solve the inequality. Graph the solution.
−8 ≤ z + 6.4
Answer:
Solve for z- by simplifying both sides of the inequality, then isolating the variable.
Inequality Form:
z≥−14.4
Step-by-step explanation:
The solution of the inequality −8 ≤ z + 6.4 is z ≥ 14.4.
What are open and closed circles?A closed circle on a point represents including(less than or equal to or greater than or equal to) the point and an open circle on a point represents we are not including(strictly less than or greater than) that point.
The solution of the inequality −8 ≤ z + 6.4 is,
z ≥ 6.4 + 8.
z ≥ 14.4.
∴ The graph of the inequality z ≥ 14.4 will be a line denoted by a closed circle at 14.4 to infinity or a region greater than or equal to 14.4.
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if the major arc is 218 degrees, what is the measurement of the minor arc
To answer this question, we must be familiar with the relationship between a major and minor arc in a circle.
In a circle, if the measure of the major arc is known, the measurement of the minor arc can be found by subtracting the major arc from 360°.For example, given a major arc measuring 218°, the minor arc would be 360° - 218°.
Therefore, the measurement of the minor arc would be 142°.Hence, the correct option is A) 142 degrees.
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Which of the following is the graph of 6x – 4y ≤ 20
Answer:
It should be something like that :
A lighthouse flashes a beam of light once every 3/5 of a minute. How many times does it flash a beam of light in half an hour?
Answer:
Total number of flash = 50 flash
Step-by-step explanation:
Given:
Time taken of a flash = 3/5 minute = 3/5 × 30 = 36 sec
Total time = 30 minute = 30 × 60= 1800 sec
Find:
Total number of flash in 30 minutes
Computation:
⇒ Total number of flash = Total time / Time taken of a flash
⇒ Total number of flash = 1800 / 36
⇒ Total number of flash = 50 flash
(q13) Evaluate the definite integral.
The definite integral in this problem has the value given as follows:
B. 42.
How to solve the definite integral?The definite integral in the context of this problem is given as follows:
\(\int_0^2 (x^7 + 5) dx\)
Applying the power of x integral rule, the result of the integral is given as follows:
\(\frac{x^8}{8} + 5x\)
At x = 2, the numeric value of the integral is given as follows:
\(\frac{2^8}{8} + 5(2) = 42\)
At x = 0, the numeric value of the integral is given as follows:
0.
(as both terms involve a multiplication by x and x = 0).
Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:
42 - 0 = 42.
Hence option B is the correct option in the context of this problem.
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define a relation p on ℤ as follows: for every ordered pair (m, n) is in ℤ ✕ ℤ, m p n ⇔ m and n have a common prime factor. (a) is 10 p 35?
If for every ordered pair (m,n) is in ℤ×ℤ, "m P n" ⇔ m and n have a common prime factor , then yes "10 P 35" because 10 and 15 share a common prime factor of 5.
The Relation "P" on ℤ is defined as follows: For every ordered pair (m, n) in ℤ ✕ ℤ, "m P n" if and only if m and n have a common prime factor.
To determine whether 10 P 15, we need to check if 10 and 15 have a common prime factor.
The prime factors of 10 are 2 and 5, whereas the prime factors of 15 are 3 and 5.
So , 10 and 15 share a common prime factor of 5.
Therefore , we can conclude that "10 P 15".
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The given question is incomplete , the complete question is
Define a relation "P" on ℤ as follows: for every ordered pair (m, n) is in ℤ×ℤ, "m P n" ⇔ m and n have a common prime factor. Is "10 P 35"?
Can you have an 'All Real Numbers' solution for inequalities? If so, give an example.
Answer:
yes
Step-by-step explanation:
x+7>x+3
6 unit squares each have 3/5 of their area shaded. What is 3/5 of 6?
Answer: 3.6
Step-by-step explanation:
3/5 is equal to 20% (3 divided by 5 times 100)
1.2 is 20% of 6
So, 3.6 is 3/5 of 6
On a game show, a contestant must guess a secret two-digit number. The secret number is 27. Write an absolute-value inequality that shows that the contestant's guess is more than 14 numbers away from the secret number. Use n as the variable.
Answer:
|n - 27| > 14
Answer:
| n - 27| > 14
Step-by-step explanation:
Triangle RST has vertices R(6, 5), S(9, −4), and T(10, 1). Triangle RST has vertices R′(6, −5), S′(9, 4), and T′(10, −1).
Which transformation of triangle RST produced triangle RST?
a rotation of 90° clockwise around the origin
a rotation of 90° counterclockwise around the origin
a reflection across the y-axis
a reflection across the x-axis
Answer:
Its D :p
Step-by-step explanation:
Answer:
a reflection across the x axis
Step-by-step explanation:
What is the quotient ? -4 /5 divide 2 A . - 1 3/5 B . -2 /5 c. 1/2 D . 1 3/ 5
Answer:
\( \boxed{ - \frac{2}{5} }\)Option B is the correct option.
Step-by-step explanation:
\( \mathrm{ - \frac{4}{5} \div 2}\)
\( \mathrm{dividing \: a \: negative \: and \: a \: positive \: equals \: a \: negative \:. \: ( - ) \div ( + ) = ( - )}\)
\( \mathrm{ - \frac{4}{5} \div 2}\)
\( \mathrm{dividing \: is \: equivalent \: to \: multiplying \: with \: the \: reciprocal}\)
\( \mathrm{ - \frac{4}{5} \times \frac{1}{2} }\)
\( \mathrm{reduce \: the \: numbers \: with \: G.C.F \: 2}\)
\( \mathrm{ - \frac{2}{5} }\)
Hope I helped!
Best regards!
The quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
We have been given that -4 /5 divide 2
Thus, we have to divide the terms as;
-4 /5 ÷ 2
Therefore, -4 /5 x 1/ 2
-2/5
Hence, the quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
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dang. Yall need to stop harrassing a girl for what she asks for. If she asks for perfume, she gets perfume. Nothing wrong with that. Comment if you agrreee/
Answer:
._.
Step-by-step explanation:
If she has money, she gets stuff. If she broke, doesn't work/help, and expects another person to buy it for her, she ain't gonna get anything. Either way, she better work for that perfume.
Answer:
h*ll yes theyre still human i dont know why people care about that stuff
Step-by-step explanation:
if they deserve it then who cares
Graph the solution to this inequality on the number line. 1/2x−3<−1 3/8
The solution to the inequality, 1/2x - 3 < -1 3/8, is x < 13/4. See the graph below.
How to Graph the Solution of an Inequality on a Number Line?Given the inequality, 1/2x - 3 < -1 3/8, solve to find the value of x, which is the solution to the inequality.
1/2x - 3 < -1 3/8 [given]
1/2x - 3 < -11/8
Add 3 to both sides of the equation:
1/2x - 3 + 3 < -11/8 + 3 [addition property of equality]
1/2x < 13/8
Multiply both sides by 2:
1/2x * 2 < 13/8 * 2 [multiplication property of equality]
x < 13/4
The solution to this inequality, x < 13/4 is given in the graph below.
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Consider any conic section and discuss an application of the conic that you find
most interesting. Include an example of a mathematical equation that models
the application. Also, describe why you think this application is relevant and
beneficial to society.
PLEASE HELP ME COME UP WITH AN EQUATION USING A CONIC SECTION! Just one that I could put into a calculator.
Conic sections are shapes that are formed when the surface of a cone intersects with a plane shape
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and divis
Now, Types of conic section are,
The types include
1) Hyperbola
2) Parabola
3) Ellipse
Here, Application of conic section (Parabola) is,
The parabola can be applied in solving quadratic equations, functions and graph.
Hence, The general equation of a parabola is: y = a(x - h)² +k
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Simplify the expression (picture down below)
Answer:
6.75
Step-by-step explanation:
The term 6.75 is within absolute value bars. These bars force any term inside of them to be positive. Since 6.75 is already positive, the bars have no effect.
The term 6.75 is already simplified.
if a, b, and c are integers between -10 and 10 inclusive such that a^3 b^3 = c^3, what is the greatest possible value of a b c?
The greatest possible value of abc, given that a³b³ = c³ and a, b, and c are integers between -10 and 10 inclusive, is 1.
If a, b, and c are integers between -10 and 10 inclusive such that a³b³ = c³, then what is the maximum possible value of abc?We will start with listing the cubes of numbers between -10 and 10. Below is the table of cubes of numbers between -10 and 10 inclusive.
{-1000, -729, -512, -343, -216, -125, -64, -27, -8, -1, 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000}In the table above, the only numbers that occur thrice are 1, -1, and 0.
All the other numbers are either negative or positive and occur once.So, this means that a, b, and c must be either 1, -1, or 0. This is because if a, b, and c are any other numbers, the left side of the equation, a³b³ = c³, is going to be a cube of some number between -10 and 10 inclusive which is not in the table above.
Hence, this would mean that a³b³ ≠ c³. Therefore, a, b, and c must be either 1, -1, or 0.Now, we can determine the largest possible product of abc: abc = (1)(1)(1) = 1 or (1)(1)(0) = 0 or (-1)(-1)(1) = -1. In conclusion, the greatest possible value of abc is 1.
The greatest possible value of abc, given that a³b³ = c³ and a, b, and c are integers between -10 and 10 inclusive, is 1.
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What is the greatest common factor of 36 and 48?
Answer:
The GCF, or greatest common factor, of 36 and 48 is 12.
Step-by-step explanation:
Answer:
The GCF, or greatest common factor, of 36 and 48 is 12.
Answer is 12.
I hope it's helpful!
a circle has a diameter of 8 feet what is its approximate area
Answer:
50.27Ft² should be your answer.
Step-by-step explanation:
A=1 /4πd²=1/ 4·π·8²≈50.26548ft²
Answer:
50.24ft^2
Step-by-step explanation:
3.14x4^2
= 50.24
square root of 10 with work
5. The volume of a cube is 125 cubic centimeters. How many centimeters long iseach edge of the cube?5 centimeters11 centimeters15 centimeters42 centimeters
Answer: 5 cm
Step-by-step explanation:
A cube means all sides have an equal length. therefore you need to find what number times itself 3 times will equal 125
to do this you can also do the cube root(∛) of 125 which will give you 5 cm
to verify your answer, simply do 5 x 5 x 5 which is 125
Which fraction would make this equation true? 4 × ? ? = 6 2 3 2 3 3 3 5 3
The fraction that would make the equation true is 2/3.
We are given the equation 4 × ? ? = 6 2 3 2 3 3 3 5 3. To solve the equation 4 × ? ? = 6, we need to find the value of the missing fraction. We can rewrite the equation as 4 × x = 6, where x represents the missing fraction.
To isolate x, we divide both sides of the equation by 4, resulting in x = 6/4. Simplifying the fraction gives x = 3/2. Therefore, the missing fraction that makes the equation true is 3/2, which can also be written as 2/3 in simplified form.
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