Step-by-step explanation:
there are 36 (6×6) possible results and number combinations for 2 dice.
a)
to create a sum of 4 we need one of the following combinations :
1 3
2 2
3 1
so, 3 out of the overall possible 36 possibilities.
and that means the probability is 3/36 = 1/12
b)
to create a sum of 7 we need one of the following combinations :
1 6
2 5
3 4
4 3
5 2
6 1
so, 6 out of the overall possible 36 possibilities.
and that means a probability of 6/36 = 1/6
c)
since the possible outcomes in that regard are only 2 (even and uneven), with equal balance the probability is 1/2.
make it more formal ?
to get an even sum, every possible number on one die can be combined with 3 possibilities on the other.
1 can be combined with 1, 3, 5
2 with 2, 4, 6
3 with 1, 3, 5
4 with 2, 4, 6
5 with 1, 3, 5
6 with 2, 4, 6
these are 6×3 = 18 combinations of of the possible 36.
so, the probability is 18/36 = 1/2
d)
not a 6 ?
so, what does that mean ?
we are looking only at 5 possible outcomes per die.
that is 5×5 = 25 combinations out of the possible 36.
that means that probabilty is 25/36.
e)
not a perfect square ?
we have in the range of the possible sums with 2 dice (2 .. 12) only two perfect squares : 4 and 9
so, the sum must NOT be 4 AND NOT be 9.
so, here it might be easier to count the unwanted cases and then deduct the probability from 1 to express the opposite.
the combinations to get 4 we have already under a)
3 combinations with 3/36=1/12 probability.
the combinations to get 9
1 none
2 none
3 6
4 5
5 4
6 3
so, 4 combinations with a probability of 4/36 = 1/9
therefore, we have (3+4) = 7 cases out of the possible 36 we actually want to avoid.
so, the probability to get any one of the other (desired) combinations is therefore (36-7)/36 = 29/36
The probabilities are:
a) 0.083b) 0.167c) 0.5d) 0.861e) 0.806.How to get the probabilities?The probability for a given outcome is given by the quotient between the number of combinations that give that outcome and the total number of combinations.
Here each dice has 6 possible outcomes, so the total number of combinations for the two dice is:
6*6 = 36 combinations.
a) Here we need to count how many combinations add to 4, the notation I will use is:
dice 1 dice 2
1 3
3 1
2 2
There are 3 combinations that add to 4, then the probability of getting a sum equal to 4 is:
P = 3/36 = 0.083
b) Same thing as before, this time we count the combinations that add to 7.
dice 1 dice 2
1 6
6 1
5 2
2 5
4 3
3 4
There are 6 combinations that add to 7, so the probability is:
P = 6/36 = 0.167
c) The possible even numbers are: {2, 4, 6, 8, 10, 12}
A way of doing this, is:
If the first dice is even/odd, then the second also must be even/odd.
Then the probability is just 1/2 = 0.5 (because there are the same number of odd and even numbers in a dice).
d) The sum must not be equal to 6, the combinations that add up to 6 are:
dice 1 dice 2
2 4
4 2
3 3
1 5
5 1
So 5 combinations add up to 6, then there are 31 combinations that do not add up to 6, this means that the probability of not getting a sum equal to 6 is:
P = 31/36 = 0.861
e) The perfect squares are 4 and 9, we already know that 3 combinations add up to 4, now let's find the combinations that add up to 9.
dice 1 dice 2
6 3
3 6
5 4
4 5
So 4 combinations add up to 9, then there is a total of 7 combinations that give a perfect square, then there are 29 combinations that do not add to a perfect square.
The probability is:
P = 29/36 = 0.806
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
There are only 6 blue pens, 5 green pens and 8 red pens in a box.
One pen is taken at random from the box.
Write down the probability that this pen is blue.
Answer:
0.316
Step-by-step explanation:
Probability = (number of outcomes)/(total number of outcomes)
In this case,
the total number of outcomes is 6+5+8 = 19, and
the number of outcomes for getting a blue pen = 6
Hence,
P(blue) = 6/19 = 0.31578947368 ≈ 0.316
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
Isaac wants to play miniature golf. Go Golf charges $2.50 for ball and club rental and $4.25 per game. Golf Games charges $3.25 for ball and club rental and $8.50 for two games. For how many games would the cost be the same? Write and solve an equation to determine the number of games for which the cost would be the same.
The cost would be the same for 47 Go golf and 54 golf games.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
Given data as:
Charges for Go Golf -
Renting a ball and a club costs $2.50.
$4.25 for one game and
Charges for Golf Games -
3.25 for the rental of a ball and a club
$8.50 for two games
We have to determine the number of games would the cost be the same.
Total charges of Go golf per game = $2.50 + $4.25 = $6.75
Total charges of Golf game for 2 games = $3.25 + $8.50 = $11.75
For per game = $11.75 / 2 = $5.875
Let the game would be x for Go golf and
And let game would be y for the golf game
As per the given condition,
6.75 x = 5.875y
27/4 x = 47/8 y
Apply cross multiplication operation,
54x = 47y
x/y = 47 / 54
x = 47
So y = 54.
Hence, the cost would be the same for 47 Go golf and 54 golf games.
Learn more about Multiplication operations here:
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The cost would be the same for 47 games at Go Golf and 54 games at Golf Games.
Total charges of Go golf per game = $2.50 + $4.25 = $6.75
Total charges of Golf game for 2 games = $3.25 + $8.50 = $11.75
Cost per game at Golf Games
= Total charges for 2 games / 2
= $11.75 / 2
= $5.875
Let the number of games be x for Go Golf and y for Golf Games.
As per the given condition,
6.75x = 5.875y
To find the relation between x and y, cross-multiplication can be used:
27/4 x = 47/8 y
54x = 47y
x/y = 47/54
Comparing the value gives
x = 47 and y = 54.
Hence, the cost would be the same for 47 games at Go Golf and 54 games at Golf Games.
Learn more about Ratio here:
https://brainly.com/question/13419413
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Two movies, an action movie and a drama, were released on the same day. The producers of the action movie claimed that their movie would be better received by audiences than the drama. To test the producers' claim, CinemaScore randomly selected 100 people and showed them both movies. Then the viewers were asked whether they liked or disliked each movie. The results are shown in the table.
Answer:
C is the correct answer.
If you need an explanation tell me.
More people like the action movies.
What is comparison of two numbers?
Comparison of two numbers, means to examine the differences between numbers, quantities or values to decide if it is greater than, smaller than or equal to another quantity.
According to the given question
We have a data in which
Number of people who liked action movie = 78
Number of people who liked action movie = 60
Number of people who disliked the action movie = 22
And, number of people who disliked the drama movie = 40
From the given data we conclude, that action movie is liked by more people as compared to drama movie because 78 > 60.
Hence, the action movie is better received by the audience than the drama.
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solve pls brailiest!
Answer:
73,if you need explanation then let me know, always happy to help anyone! btw if you could give me brainliest then that would be great, i also undestand if not because im not the first to answer so dont be shy and hit theirs with brainliest if you want! :))
Step-by-step explanation:
The radius of a circle with centre O is 5 cm. The lengths of the chords AB and BC are 6 cm and 8 cm respectively. The midpoints of the chords are X and Y respectively. Find the perimeter of the quadrilateral OXBY.
Answer:
Step-by-step explanation:
AB=6 cm
BX=1/2 AB=1/2 ×6=3 cm
BC=8 cm
BY=1/2×BC=1/2×8=4 cm
perpendicular bisector of a chord always passes through the center.
so quadrilateral OXBY is a rectangle.
Perimeter=2(BX+BY)=2(3+4)=2×7=14 cm.
Find the sum of −6x^2 −1 and x+9
Answer:
[tex]6 {x}^{2} - 1 + x + 9 \\ = 6 {x}^{2} + x + 8[/tex]
Erin ran 5 km in 25 minutes. What is her speed in km per minute? (Answer as a decimal)
Answer:
what what what what what what what what
Cómo hallar el dominio de una función identidad?
Answer:
Cómo hallar el alcance de una función cúbica? or How to find the scope of a cubic function?
Step-by-step explanation:
Use the Quadratic Formula to solve for x and then determine whether your solution is real or
complex.
y = x2 - 4x + 9
**Remember y = 0**
O Real
o Complex
Answer:
[tex] {x}^{2} - 4x + 9 = 0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-( - 4)\pm\sqrt{( - 4)^2-4(1)(9)}}{2(1)} \\x=\frac{ 4\pm\sqrt{ 16-36}}{2} \\ x=\frac{ 4\pm\sqrt{ - 20}}{2} \\ x=\frac{ 4\pm2i\sqrt{ 5}}{2} \\ x = 2\pm \: i\sqrt{ 5} \\ D = {b^2-4ac} \\D = { 16-36} \\ = - 20 < 0 \rightarrow \: x \in \: \mathbb{C} \: \\ x \: is \: complex [/tex]
need help now if u will
Given f ( x ) = x + 4 and g ( x ) = √ x + 5 , determine the following. Write each answer using interval notation. Domain of f ( g ( x ) ) : Domain of g ( f ( x ) ) :
Answer:
In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
Step-by-step explanation:
Answer:
The answers are f(g(x))=x−7 and g(f(x))=√x2−7. Explanation: This is a composition of functions. f(x)=x2−4. g(x)=√x−3.
Step-by-step explanation:
i used the pemdas treatment
HELP I DONT WANT A 0000
Step-by-step explanation:
=(5+8)hours
=12hours.
At a farm the ratio of cows to horses was 8 : 3. If there were 24 cows at the farm, how many horses were there?
Adrian and his children went into a restaurant where they sell hotdogs for $3 each
and hamburgers for $8 each. Adrian has $80 to spend and must buy no less than 12
hotdogs and hamburgers altogether. If x represents the number of hotdogs
purchased and y represents the number of hamburgers purchased, write and solve a
system of inequalities graphically and determine one possible solution.
need both inequalities and how many hotdogs and burgers he can buy
Answer: 16x + 4y= 80
16 (3) + 4 (8) = 80
The population of a city decreases by 0.9% per year. If this year's population is 338,000, what will next year's population be, to the nearest individual?
Answer:
The population will be 334,958.
Step-by-step explanation:
Multiply 338,000 by 0.009 to get the answer. The reason is to multiply by a percentage, you move the decimal two spots to the left. For example, 0.9 -> 0.009. Another would be 3 -> 0.03.
3.
1. The 20 students on the math team want to raise $490 to buy practice books.
They have already raised $220. If each student raises the same amount, how
much more money must each student raise?
Answer:
Each student must raise $13.50
Step-by-step explanation:
490-220=270 left to raise
270÷20=13.50
In 1993, the moose population in a park was measured to be 4350. By 1999, the population was measured again to be 4890. If the population continues to change linearly: Find a formula for the moose population, P , in terms of t , the years since 1990.
Answer:
P = 90t
t = 31 years
Step-by-step explanation:
The acceleration due to gravity on Earth is 9.8 m/s? What is the weight of a 75 kg person on Earth?
O 9.8 N
O 75 N
O 85 N
O 735 N
Answer:
the answer is 9.8 N you're welcome
I need an answer ASAP besties- I’m currently crying rn
Answer:
126/25 or 5.04
Step-by-step explanation:
The Astronomical Telescope shop plans to introduce a new model based on the following information: Rent and utilities per period are $ {fixed}; variable cost per unit is $ 217; selling price per unit is $ 305; determine the break-even point in units if rent and utilities are increased to $ 5420.
Using the profit concept, it is found that the break-even point is of 61.6 units.
Profit is given by revenue subtracted by cost.The break-even point is when the revenue is the same as the cost, which means that the profit is zero.In this problem:
Variable cost per unit x of $217, fixed cost of $5,420, thus, the cost equation is given by:[tex]C(x) = 217x + 5420[/tex]
Selling price per unit of $305, thus, the revenue equation is given by:
[tex]R(x) = 305x[/tex]
The break-even point is the value of x for which:
[tex]R(x) = C(x)[/tex]
Then
[tex]305x = 217x + 5420[/tex]
[tex]88x = 5420[/tex]
[tex]x = \frac{5420}{88}[/tex]
[tex]x = 61.6[/tex]
The break-even point is of 61.6 units.
A similar problem is given at https://brainly.com/question/4001746
Đề bài sau dùng cho 3 câu từ câu 1 đến 3
Doanh thu (triệu đồng) 830 900 950 1.020 1.200
Số cửa hàng 15 25 30 20 10
1. Doanh thu bình quân của các cửa hàng là:
a. 980,0 b. 958,5 c. 950,0 d. 980,6
2. Trung vị về doanh thu là:
a. 900 b. 950 c. 958 d. 925
3. Mốt về doanh thu là:
a. 900 b. 950 c. 1.020 d.
Answer:
Step-by-step explanation:
Needs to show work.
Find the X intercept and the Y intercept for 2x-6y=12
Answer:
x: (6,0)
y: (0,-2)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y intercept, substitute in 0 for x and solve for y .
Ex -
X : 2x -6(0)=12
2x=12
2 cancels out with 2
12/2 = 6
Y: 2(0 )- 6y =12
-6y=12
negative 6 times negative 6 cancels
12/-6 = -2
Answer:
See Below
Step-by-step explanation:
Given: 2x-6y=12
Plug 0 in the equation for y:
y is zero
2x-6(0)=12
2x=12
The x-intercept: (6,0)
Plug 0 in the equation for x:
x is zero
2(0)-6y=12
−6y=12
The y-intercept: (0,−2)
Translate into an algebraic equation, then solve the equation.
Peter paid $9.75 to go to the movies, which was $46.25 less than he paid to go to a concert. How much did he pay to go to the concert?
Answer:
$56
Step-by-step explanation:
Simply add the two values together, the algebraic equation would be:
9.75 + 46.25 = 56
So he paid $56 to go to the concert.
Hope this helps!
Which is the graph of the following equation?
Square root of x = 4
Answer:
A
Step-by-step explanation:
because 2 times 2 equals 4 and the square root just means what times itself equals this
Find the mass of 250 ml of water. The density of water is 1 g/ml.
D= Density
M=
Volume - 10ml
What is the Mass?
V=
Mass - 70
Density
Alaalam
Answer:
250g
Step-by-step explanation :
250ml x 250g/ml = 250 g
To get the mass (in grams), you need to divide the ml's off and get the g alone.
An inlet pipe on a swimming pool can be used to fill the pool in 15 hours. The drain pipe can be used to empty the pool in 20 hours. If the pool is [tex]\frac{1}{3}[/tex] filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool? Round your answer to two decimal places, if needed.
_____________ hours
Answer:
40 hoursStep-by-step explanation:
Rate of filling is 1/15Rate of draining is 1/20If both lines are open the rate of filling is:
1/15 - 1/20 = 4/60 - 3/60 = 1/60 per hourSince tank is 1/3 full we need to fill the remaining 2/3 of it.
Time required:
2/3 : 1/60 = 2/3*60 = 40 hours(20 Points) What is the value of x?
Solve: sin(11pi/2 +x)= -1/2 for [pi, 2pi]
Step-by-step explanation:
Step-by-step explanation: Given the expression sin(11pi/2 +x) =-1/2. Take the arcsin of both sides. sin⁻¹[sin(11pi/2 +x)]
Which property of multiplication is shown? 3 * (5 * 7) = (3 * 5) * 7
Answer:
the associative property
Answer:
It is the associative property of multiplication
Step-by-step explanation:
It is generally expressed as
(ab)c=a(bc)
3*(5*7)=(3*5)*7
105=105
The owner of a used car dealership is trying to determine if there is a relationship between the price of a used car
and the number of miles it has been driven. The owner collects data for 25 cars of the same model with different
mileage and determines each car's price using a used car website. The analysis is given in the computer output.
Predictor Coef SE Coef t-ratio
р
Constant 2415712 2164.1 2.965
0.046
Mileage
-0.181 0.024 5.377
0.000
s = 3860.7
R-S = 68.0%
R-Sq (Adi) = 69.59
Using the computer output, what is the value of the coefficient of determination?
00.46
0.68
N
0.70
0.82
The value of the coefficient of determination is gives the percentage of the variation which is explained by the regression line. The value of the coefficient of determination is the R² value which is 68%.
The Coefficient of determination is the proportion of change in the regression model caused by the regression line. From the computer output, the coefficient of determination is denoted as R² ; which is given as 0.68 Expressing the value as a percentage ; 0.68 × 100% = 68%Therefore, the coefficient of determination is 0.68
Learn more : https://brainly.com/question/25178853
Answer:
B) .68
Step-by-step explanation:
EDGE
If y varies directly with x which equation describes x = 72 and y = 36?
Answer:
k = 1/2
Step-by-step explanation:
direct variation equation is y = kx where 'k' is the constant of variation
substitute 36 for 'y' and 72 for 'x' to get:
36 = 72k
solve for 'k' to get:
k = 36/72 or k = 1/2