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?
Answers
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.
Related Questions
In the following equation, what would be the most logical first step when solving for z.
Answers
Answer:
Multiply 5/2 to both sides
Step-by-step explanation:
Doing so 'cancels' out the coefficient of (z+1) on the left-hand side.
Does anyone know how to do this? Or tell me how you do these questions?
Answers
The equation of line in slope intercept form can be written as y = mx + c where m is the slope of line and c is the y intercept.
We are given three equations namely y = 2x -2, y = -x + 1 and y = x - 4 and we need to determine the description of equation, slope and y intercept. The equation y = 2x - 2 is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = 2 and c = -2. Thus, slope is 2 and y intercept is -2. The equation y = -x +1 is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = -1 and c = 1. Thus, slope is -1 and y intercept is 1. This equation y = x - 4is the equation of straight line. If we compare this equation with the slope intercept form of line then, m = 1 and c = -4. Thus, slope is 1 and y intercept is -4. The graphs of the equation are attached below.
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What is the solution to the inequality |2x – 3| > 5?
A) x < –1 or x > 4
B)x < 0 or x > 8
C)0 < x < 8
D)–1 < x < 4
Answers
The solution to the inequality |2x - 3| > 5 is: x < -1 or x > 4
Therefore, the correct option is A) x < -1 or x > 4.
Given that we need to find the solution to the inequality |2x – 3| > 5
To solve the inequality |2x - 3| > 5, we can break it down into two cases:
Case 1: 2x - 3 > 5
In this case, we have:
2x - 3 > 5
2x > 5 + 3
2x > 8
x > 4
Case 2: -(2x - 3) > 5
In this case, we have:
-(2x - 3) > 5
-2x + 3 > 5
-2x > 5 - 3
-2x > 2
x < -1 (remember to reverse the inequality when multiplying or dividing by a negative number)
Combining the solutions from both cases, we find that the solution to the inequality |2x - 3| > 5 is:
x < -1 or x > 4
Therefore, the correct option is A) x < -1 or x > 4.
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1) Mrs. Martins deposits $2,650 into a savings account. The account earns 6%
interest per year, and the interest is not compounded. How much amount will
be in the account after 9 years?
Answers
The amount in the savings account of Mrs. Martins after 9 years will be $4081.
According to the question,
We have the following details:
The amount deposited in the savings account or the principal amount = $2,650
Interest per year = 6%
Time = 9 years
(It is given that the interest is not compounded.)
Now, using the formula of simple interest, we will first find the total interest after 9 years,
Simple Interest (S.I.) = (Principal * Rate * Time)/100
S.I. = (2650*6*9)/100
S.I. = (2650*54)/100
S.I. = 143100/100
S..I. = $ 1,431
Now, the total amount in the savings account would be the sum of the principal amount and the total interest.
So, we have:
Total amount = Principal + S.I.
Total amount = $ (2,650+1,431)
Total amount = $ 4,081
Hence, the total amount in Mrs. Martins's savings account is $ 4,081.
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If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the
square?
Answers
Answer:
approximately 31.96 m (you can round to 32m)
Step-by-step explanation:
If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the
square?
find the area with the formula ½ × d ^ 2 Square units, take the square root of the result and find the side, multiply by 4 and you have the perimeter.
AREA1/2 11.3^2 =
1/2 127,69 =
63.845 m²
SIDE√63.845 =
7.99 m
Perimeter7.99 * 4 =
31.96 m
Given m n, find the value of x.
m
(5X-11)°
(6x-7)°
Answers
Answer:
x = 18
Step-by-step explanation:
the angles pictured are supplementary angles.
supplementary angles are angles whose sum equals 180°
ex: <1 + <2 = 180°
[tex]5x - 11 + 6x - 7 = 180[/tex]
[tex]11x - 18 = 180[/tex]
[tex]11x = 198\\x = 18[/tex]
Answer:
[tex]\boxed{\sf{x=18}}[/tex]
Step-by-step explanation:
To find the value of x, you have to use the supplementary angles which is equal to 180°.
Supplementary angles = 180°
5x-11+6x-7=180
Combine like terms.
[tex]\sf{5x+6x-11-7=180}[/tex]
5x+6x=11x
[tex]\sf{11x-11-7=180}[/tex]
Subtract the numbers from left to right.
-11-7=-18
[tex]\sf{11x-18=180}[/tex]
You have to add by 18 from both sides.
11x-18+18=180+18
Solve.
Add the numbers from left to right.
180+18=198
11x=198
Divide by 11 from both sides.
11x/11=198/11
Solve.
198/11=18
[tex]\rightarrow \boxed{\sf{x=18}}[/tex]
Therefore, the final answer is x=18.
A rental company rents a luxury car at a daily rate of $38.48 plus $.50 per mile. Paul is allotted $110 for car rental each day. Write an equation to represent the cost C of renting a car and driving x miles.
How many miles can Paul travel on the $110?
Answers
Answer:
C=38.48+0.5x
about 143 miles
Step-by-step explanation:
$38.48 base cost plus $.50 per mile, so after x miles, it would be 0.5x
so C=38.48+0.5x
to find how many miles Paul can travel
we set 110=38.48+0.5x
then solve
x=143.04
so Paul can travel about 143 miles
Need help on finding the domain and range
Answers
The domain and the range of the graph are x >= 1 and -∝ < y < ∝, respectively
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 1 and it extends indefinitely to the right
This means that the domain is x >= 1
The range
On the graph of the function, we can see that:
The y values extend indefinitely on all sides of the coordinate plane
This means that the range is -∝ < y < ∝
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Solve the inequality. Graph the solution. 3x≤−54
Answers
[tex]x\leq -18[/tex]
Graph Displayed Below
Hope this helps!
The solution to the given inequality [tex]3x \leq -54[/tex] is [tex]x \leq \frac{-54}{3}[/tex] .
Inequality is a fine statement that compares two values, showing if one is lower than, lesser than, or simply not equal to another value. Inequalities are frequently used to represent connections between amounts, similar to the relationship between the height and weight of a person, or the relationship between the speed and time of an object in stir.
We first divide the inequality [tex]3x \leq -54[/tex] by 3 on both sides to obtain:
[tex]x \leq \frac{-54}{3}[/tex] .
Then, we plot the line [tex]x = \frac{-54}{3}[/tex] on the graph. The region left to the line thus obtained is the solution of the given question.
Thus, the line [tex]x \leq \frac{-54}{3}[/tex] is plotted in the graph.
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3x^2 +16x−10=6x−2 algebra 2
Answers
Answer:
x= 2/3 or x= −4
Explanation:
3x2+16x−10=6x−2
Step 1: Subtract 6x-2 from both sides.
3x2+16x−10−(6x−2)=6x−2−(6x−2)
3x2+10x−8=0
Step 2: Factor left side of equation.
(3x−2)(x+4)=0
Step 3: Set factors equal to 0.
3x−2=0 or x+4=0
x=2/3 or x= −4
Find AC (why do questions have to be at least 20 characters LOL)
Answers
Answer:
Step-by-step explanation:
21
Answer: 21
Step-by-step explanation: To solve for AC, you will need to add segments AB and BC together. So, 9+12=21
You earn $100 per month and want to save 10% in a savings account.
How much will your monthly contribution be? (Do not include the $ sign in your
response) PLEASE HELPP
Answers
The cost of a mobile set is Rs 18000. If Mrs Sharma purchased it with 13% VAT,how much did she pay for it.
Answers
To purchase a mobile set with the cost of Rs 18000 and VAT 13% , Mrs Sharma needs to pay Rs 20,340.
As given in the question,
Cost of the mobile set Mrs Sharma purchase = Rs 18000
VAT added on purchasing a mobile set is equal to 13%
Amount of VAT on mobile set is equal to
= 13% of 18000
= (13/100) × 18000
= 13 ×180
= Rs 2340
Mrs Sharma needs to pay amount to purchase a mobile set
=18000 + 2340
= Rs 20,340
Therefore, to purchase a mobile set with the cost of Rs 18000 and VAT 13% , Mrs Sharma needs to pay Rs 20,340.
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Use the point and the slope to graph each line. Write the equation of the line. The line contains point (1,-1) and is perpendicular to a line with slope 1
ANSWER ASAP
20 POINTS AND BRAINLIEST IF FIRST
Answers
the equation of the line will be x + y = 0 and it is being graphed.
Point on the line = (1, -1)
Slope of the perpendicular line = 1
So, the slope of the line will be
m × 1 = - 1
m = - 1
Equation of the line will be given by:
y - y₁ = m (x - x₁)
y - (- 1) = (- 1) (x - 1)
y + 1 = - x + 1
x + y = 0
We have graphed the equation.
Therefore, we get that, the equation of the line will be x + y = 0 and it is being graphed.
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hey! i will give a lot of pts for the answers to these!!
Answers
Answer:X squared =4/9 is c
X to the third power is a
X squared =81/46 is b or d
X to the third power is d or b
2(3x +4) -(x-2)
expand and simplify
Answers
5x + 10 is the simplified form of the expression 2( 3x + 4 ) - ( x - 2 ).
What is the simplified form of the given expression?Given the expression in question;
2( 3x + 4 ) - ( x - 2 )
To expand and simplify, get rid of the first parenthesis using distributive property.
2( 3x + 4 ) - ( x - 2 )
3x( 2 ) + 4 ( 2 ) - ( x - 2 )
6x + 8 - ( x - 2 )
For the second parenthesis, the negative sign before it affects everything inside it, hence;
6x + 8 - ( x ) - ( - 2 )
6x + 8 - x + 2
Collect like terms
6x - x + 8 + 2
Add 6x and -x
5x + 8 + 2
Add 8 and 2
5x + 10
Therefore, the simplified form of the expression is 5x + 10.
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solve the inequlaity 2(4x+1)<3(2x-3)
Answers
The solution to given inequality 2(4x + 1) < 3(2x - 3) is x < -11/2
In this question, we have been given an inequality 2(4x + 1) < 3(2x - 3)
We need to solve given inequality.
2(4x + 1) < 3(2x - 3) ..............(Given inequality)
8x + 2 < 6x - 9 .............(simplify both sides of the inequality)
8x + 2 - 6x < 6x - 9 - 6x ............(subtract 6x from both the sides)
2x + 2 < -9
2x + 2 - 2 < -9 - 2 ............(subtract 2 from each side)
2x < -11
2x/2 < -11/2 ................(Divide each side by 2)
x < -11/2
Therefore, the solution to given inequality 2(4x + 1) < 3(2x - 3) is x < -11/2
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Select all diagrams that have expressions in corresponding angles.
Answers
Answer:
1, 2, 8
Step-by-step explanation:
Corresponding angles lie on the same side of the parallel lines and on the same side of the transversal.
1, 2, and 8 are corresponding angles.
Math easy will give brainly and points
A large container is being filled with water at the rate of 2 3/4 per minute
Answers
Answer:
5 minutes and 20 seconds
Step-by-step explanation:
basically your equation is: (rate of filling container) x (time to fill container)
- (minus)
(rate of leaking from container) x (time to fill container)
=
(the size of the container in gallons)
--------------------
step 1 - so t = the time in minutes to fill14 gallon container
step 2 - convert 2 3/4 to quarters so:
2 • 4 = 8 and it’s in quarters so 8/4 then
8/4 + remaining 3/4 = 11/4
step 3 - so then you fill in the equation:(11/4)•t - (1/8)•t = 14
step 4 - multiply both sides of the equation by 8:
(11/4) = 2.75 • 8 = 22
(1/8) = 0.125 • 8 = 114 • 8 = 112
so the equation is:
22t - t = 112
step 5 - divide both sides of the equation by 22:
22t / 22 = t
112 / 22 = 5.333
so t = 5.333
step 6 - convert
so 5.333 has a repeating decimal of 0.3 which is 1/3. so to convert that to seconds, take 1/3 of 60:
60 / 3 = 20
so it takes 5 minutes and 20 seconds to fill the 14 gallon container
hope this helps :)
If the area of a square shaped rug is 81 in², what is the
measurement
of ONE SIDE of the rug?
Answers
Answer: 9 inches
Step-by-step explanation:
We know that the area of a square can be solved with the following formula when s is the length of one side. We will plug in our known values and solve:
a = s²
(81) = s²
[tex]\sqrt{81}[/tex] = s
9 in = s
One side of the rug is equal to 9 inches.
PLEASE HELP, I will give brainliest! due soon thank you so much and please give explanation
question 1,2 and 3 thank you
Answers
Answer:
8.368, 156.8, 2.52$
Step-by-step explanation:
0.8% of 1,046 is 8.368
to get this first find 80% of 8.368 so you can get 836.8 and then you move it back 2 places to get 8.368
160% of 98 will be 156.8
first split it up into 2 problems for it to be easier
100% of 98
and 60% of 98
100% of 98 = 98
60% of 98 = 9.8*6 = 58.8
98+58.8 = 156.8
For the 3rd one it will be 2.52$ srry gtg soon so can't explain
A group of friends wants to go to the amusement park. They have no more than $170 to spend on parking and admission. Parking is $7.25, and tickets cost $23.25 per person, including tax. Write and solve an inequality which can be used to determine
x, the number of people who can go to the amusement park.
Answers
Answer:
7 People is they all go in the same car and pay only for 1 parking space.
Step-by-step explanation:
23.25x + 7.25 ≤ 170 Subtract 7.25 from both sides of the equation
23.25x ≤ 170 Divide both sides by 23.25
x ≤ 7
Write an equation in point-slope form form for the lines that passes through the given point and has the given slope. (3, 2); m = 5
Answers
Answer:
y=5x-13
Step-by-step explanation:
1. (3,2) = x,y
2. substitute each x and y digit into y=mx+b format
3. 2=5(3)+b
4. solve for 2=5(3)+b which equals b=-13
5. ANSWER IS SOLVED WHEN ANSWERED IN y=mx+b FORMAT
5. y=5x-13
If you have $1400 ).and you spend 1/8of it on school supplies and 1/4 of it on groceries and 5/16 of it on clothes what is the total fraction spent
Answers
Answer: 11/16
Step-by-step explanation:
1/8=2/16
1/4=4/16
5/16=5/16
add it all together
The amount of time Demi spends studying and her test scores have a proportional relationship. Complete the table. __________ Complete the table.
Answers
Both of the blanks given in the table can be filled in by the ratio 18/1.
Here, we are given a table as shown in the image given above.
There is a proportional relationship given between Demi's test scores and her studying time.
When she studies for 3 hours, her test score is 54.
Thus, the ratio of her test score to hours studying is - 54/3
= 18/1
Similarly, when she studies for 4 hours, her test score is 72.
Thus, the ratio of her test score to hours studying is - 72/4
= 18/1
Thus, both of the blanks given in the table can be filled in by the ratio 18/1.
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-2 3/7 - 1 2/3 show ur work!please
Answers
Answer:
-4 2/21
Step-by-step explanation:
-2 3/7 - 1 2/3
Change to improper fraction
-2 3/7 = -17/7
- 1 2/3 =-5/3
-17/7-5/3
L.C.M=21
-51-35/21
= -86/21
= -4 2/21
Hope it helps..
Please mark brainliest
Find the equation of a line that passes through the point (1,-3) and has a gradient of 3.
Leave your answer in the form
a
x
+
b
y
=
c
Where
a
,
b
and
c
are integers.
Answers
Answer:
3x+1y=0
Step-by-step explanation:
the equation of a straight line on a graph is y= mx+c
where m is the gradient and c is the y intercept.
we know that the line passes through (1,-3) and has a gradient of 3, therefore we can substitute these values into the equation.
-3 = 3*1 +c
3 = 3+c
c = 3-3 = 0
therefore the equation of this line is y = 3x+0
now we have to write this in the form ax+by=c
3x+1y=0
Subtract 8 1/6-4 5/6. Simplify the answer and write as a mixed number.
Answers
michael is one-third of keanus age if the sum of their ages is 52 how old is michael
Answers
Answer:
Michael age is 13 and keanus age is 39
Step-by-step explanation:
Michael is 1/3 of keanus age
so Michael is 1 and keanus is 3 so if u add them all up it's 4 so 52 divide by 4 it's 13 so Michael is 13 and if you times three it will be 39, and if u add their age together it adds up to 52 so it's 13
Find all horizontal asymptotes of the following function.
f(x) =3x² - 48/2x+8
Answers
The given function f(x) =3x² - 48/2x+8 has no Horizontal asymptote.
A horizontal asymptote may be defined as a horizontal line at which the graph of the function will appear to meet but will not actually meet. It is a tool to determine the end behavior of the function. We are given the function f(x) = 3x² - 48/2x+8. Now to find horizontal asymptote of this function we first find lim ₓ→∞ f(x) that is
lim ₓ→∞ (3x² - 48)/(2x + 8)
lim ₓ→∞ 3/2(x - 4) = ∞
Now, we calculate lim ₓ→-∞ f(x) that is
lim ₓ→-∞ (3x² - 48)/(2x + 8)
lim ₓ→-∞ 3/2(x - 4) = -∞
Since, both the limits are different therefore function does not have any horizontal asymptote.
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