Answer:
7/36
Step-by-step explanation:
It is given that we have two dice numbered from 1 to 6 . The maximum sum that can be obtained by rolling two dice is 6+6 = 12 and the minimum sum that can be obtained by rolling is 1+1 = 2 .
Now between 2 and 12 , the numbers which are perfect square are 4 and 9 .
Getting a sum of 4 :-
We can get a sum of four from two dice as ,
1 on first dice, 3 on other.2 on first dice , 2 on other.3 on first dice , 1 on other.Getting a sum of 9 :-
3 on first dice, 6 on other.6 on first dice, 3 on other.4 on first dice, 5 on other.5 on first dice, 4 on other.So there are a total of 7 possibilities by which we can can get a perfect square number by rolling two dices .
Now total number of possible outcomes = 6*6 = 36 .
Henceforth the required probability would be ,
[tex]\rm\implies P( getting \ a \ square\ number) =\dfrac{Total \ number\ of \ favourable\ outcomes}{Total \ number \ of \ possible \ outcomes} [/tex]
[tex]\rm\implies \underline{\underline{\red{ P( getting \ a \ square\ number)=\dfrac{7}{36}}}}[/tex]
Hence the required probability is 7/36 .
The probability of getting a square number as the sum is therefore 7/36.
WHAT IS PROBABILITY ?
Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves analyzing the likelihood of an event occurring, given the conditions or circumstances that surround it. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is widely used in many fields, including statistics, physics, finance, engineering, and social sciences, to name a few.
There are 36 possible outcomes when two dice are thrown since each die has 6 possible outcomes.
Let's find the possible outcomes where the sum of the numbers on the dice is a square number. The only possible sums that are squares are 4, 9 and 16.
To get a sum of 4, the dice must land on 1 and 3 or 3 and 1. There are two possible ways of doing this, so there are 2 outcomes.
To get a sum of 9, the dice must land on 3 and 6, 4 and 5, 5 and 4, or 6 and 3. There are four possible ways of doing this, so there are 4 outcomes.
To get a sum of 16, the dice must both land on 6. There is only one possible way of doing this, so there is 1 outcome.
Therefore, there are 2 + 4 + 1 = 7 outcomes where the sum of the numbers on the dice is a square number.
The probability of getting a square number as the sum is therefore 7/36.
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Suppose Winston's annual salary as an accountant is $60,000 and his financial assets generate $4,000 per year in interest. One day, after deciding to be his own boss, he quits his job and uses his financial assets to establish a consulting business, which he runs out of his home. He outlays $8,000 in cash to cover all the costs involved with running the business and earns revenues of $150,000. What is Winston's economic profit?
$138,000
$150,000
$142,000
$78,000
Winston's economic profit based on the forgone salary of $60,000, and the revenue of $150,000 is $78,000. The correct option is therefore;
$78,000
What is an economic profit?An economic profit is a profit that accounts for both the explicit and implicit costs of a business. The economic profit is obtained from the difference between the total revenue and the costs including the opportunity costs.
The annual salary of Winston as an accountant = $60,000
The amount Winston's financial asset generates = $4,000 per year
The cost of running the business = $8,000
The amount Winston earns as revenue = $150,000
Therefore;
Winston's opportunity cost which is the forgone alternative, is the amount he earns as an accountant = $60,000
The interest of $4,000, earned from the financial asset = The cost of using the financial asset for the business
The cost of running the business = $8,000
The total cost = Opportunity cost + Cost of making use of the financial asset + The business running cost
The total cost = $60,000 + $4,000 + $8,000 = $72,000
The economic profit = The total revenue - The total cost
Therefore;
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Create a list of 3 numbers in which the mean is 15
Fred hires Trident Electrik Company to install a new light fixture. The electric company will charge an initial fee for the service call. In addition, the total cost of the job includes an installation fee that will depend on how long the job takes. This situation can be modeled as a linear relationship. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 $25 $50 $75 $100 $125 $150 $175 $200 $225 $250 x y Time (hours) Total cost What does the y-intercept of the line tell you about the situation?
Answer:
Step-by-step explanation:
your mom
Use the trapezoid shown to mark each statement below as true or false. If false, rewrite the statement correctly in the space below the statement.
1. The length of line AB can be found using 3^2 + b^2 = 4^2.
2. The perimeter of the trapezoid shown is 22 units.
True. The length of AB can be gotten by 3^2 + b^2 = 4^2.
True. The perimeter of the trapezoid shown is not 22 units.
How to solve for the perimeterThe length of AB can be gotten by 3^2 + b^2 = 4^2.
9 + b^2 = 16
b^2 = 16 + 9
b = 5
Then we have to count the boxes to get the length of the other sides
CD = 4
AD = 8
BC = 5
AB = 5
Then the perimeter would be be 5 + 5 + 8 + 4
= 22
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To solve using square roots, your quadratic must be in which format?
Answer:
0=-ax^2+bx+c
Step-by-step explanation:
Using the digits 1 to 9, without repeating, fill in the blanks to create a system of equations that intersect at x=1
The exponential function system that intersects as x = 1, is [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].
What is an exponential function?The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The d Here are two different exponential functions of the required form that intersect at x = 1 -
[tex]y = 3(1)^x[/tex]
[tex]y = \frac{6}{8} \times (4)^x[/tex]
In the first equation, a = 3, and b = 2.
Plugging in x = 1, we get -
[tex]y = 3(1)^1[/tex]
y = 3 × 1
y = 3
So the point of intersection of this equation with the x-axis is (1, 3).
In the second equation, a = 6/8 , and b = 4.
Plugging in x = 1, we get -
[tex]y = \frac{6}{8} \times (4)^1[/tex]
y = 3/4 × 4
y = 3
So the point of intersection of this equation with the x-axis is also (1, 3).
So, both of these equations intersect at x = 1 and are of the form [tex]y = a \times b^x[/tex].
Therefore, the equations are [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].
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Complete reference question:
6x^2 + 60x + c what is c so to make it a perfect square trinomial
The calclulated value of c to make a perfect square trinomial from 6x^2 + 60x + c is 150
Calculating the value of c to make a perfect square trinomialTo make a quadratic trinomial a perfect square trinomial, we need to add a constant term that is equal to half of the coefficient of the x-term, squared.
In other words, we need to find a value of c such that:
6x^2 + 60x + c = Perfect square trinomial
Divide through by 6
So, we have
x^2 + 10x + c/6 = Perfect square trinomial
Take the coefficient of x
k = 10
Divide by 2
So, we have
k/2 = 5
Square both sides
(k/2)^2 = 25
This means that
c/6 = 25
So, we have
c = 150
Therefore, to make the trinomial 6x^2 + 60x + c a perfect square trinomial, we need to choose c = 150.
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You pick a card at random. 6 7 8 9 What is P(less than 8)?
Answer:
50% chance
ur welcome-ssq
Abe laid three shortest worms together end to end what is the total length of these three worms
Based on the information provided, the total length of the worms would be 6 1/2 inches.
How to calculate the length of the worms?The graph presented shows the length of the worms Abe measured, based on the graph we know that the shortest worm was 2.125 inches, while the longest worm was 2.875 inches. Using this information, let's now add the three shortest worms together:
2.125 inches + 2.125 inches + 2.25 inches = 6.5 inches in total, which can be expressed ad 6 1/2.
Based on this, the total length of the three shortest worms would be 6 1/2.
Note: This question is incomplete; here is the complete question:
Abe measured the lengths of several worms. He made this line plot to display his measurements. Abe laid the three shortest worms together end to end. What is the total length of these three worms?
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Can someone please help me!!!
The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).
What is vertex?Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.
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which of the following values are needed to determine the area of the trapezoid? choose all that apply
A. 5 mm
B. 6 mm
C. 8 mm
D. 10 mm
Six pounds of raisins are distributed equally into five bags to make trail mix. How many pounds of raisins are in each bag
Answer: 1.2 pounds of raisins
Step-by-step explanation:
If six pounds of raisins are distributed equally into five bags, then each bag will have an equal amount of raisins. To find out how many pounds of raisins are in each bag, we can divide the total amount of raisins by the number of bags:
6 pounds ÷ 5 bags = 1.2 pounds per bag
Therefore, each bag will have 1.2 pounds of raisins.
I am struggling to correct numbers 1, 3, 4, 5, and 7. I have been working for hours on this.
Answer:
Step-by-step explanation:
1. sinL = 3/5
3. cosL = 4/5
4. sinN = 4/3
5. cos32 = x/14
x = 14(cos32) = 11.9
7. tan75 = 17/x
x = 17/tan75 = 4.56 ≈ 4.6
What is the quotient of 13 and 0.4
A. 5.2
B. 52
C. 3.25
D. 32.5
Show work please.
Answer:
The quotient of 13 and 0.4 can be found by dividing 13 by 0.4.
13 ÷ 0.4 = (13/1) ÷ (2/5) = (13/1) × (5/2) = 65/2 = 32.5
So the answer is D. 32.5.
Step-by-step explanation:
The quotient of 13 and 0.4 is 32.5. The method involves directly dividing 13 by 0.4, either manually or using a calculator.
Explanation:The student is asking for the quotient of 13 and 0.4. Quotient means the result of a division operation. In this case, we divide 13 by 0.4. Here's how:
Firstly, we divide 13 by 0.4 directly using a calculator or manually.The result is 32.5.So, the quotient of 13 and 0.4 is 32.5. Therefore, the answer is (D) 32.5.
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1. Give the rule for translating a point 4 units left and 8 units up. (2 points)
2. After the translation, where is A located? (2 points)
2. After the translation, where is A located? (2 points) Now reflect the figure over the y-axis. Answer the questions to find the coordinates of A after the reflection. 3. Give the rule for reflecting a point over the y-axis. (2 points)
4. What are the coordinates of A after the reflection? (2 points)
5. Is the final figure congruent to the original figure? How do you know? (2 points)
The image of the original figure after the translation and reflection is congruent to the original figure.
Translation over a point is what?A particular type of transformation on the coordinate plane called translation keeps the size of the point or geometrical shape constant while only changing the position. Along the x-axis and y-axis in the coordinate system, the point or the figure can be moved in any direction, including up, down, right, left, and multiple directions.
1. By taking away 4 from the x-coordinate and adding 8 to the y-coordinate, we can translate a point 4 units left and 8 units up.
2. Point A after translation is situated at (-2, 9).
3. We negate the x-coordinate and leave the y-coordinate unaltered to indicate a point over the y-axis.
4. Point B is obtained by reflecting point A over the y-axis (2, 9).
5. Indeed, the resulting representation is consistent with the original figure since the rigid transformations of translation and reflection maintain angles and distances. As a result, the original figure's picture after translation and reflection corresponds to the original figure.
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Please helpppp it’s urgent!!! Assume you have a balance of $3000 on a credit card with an APR of 24 %, or 2 % per month. You start making monthly payments of $200, but at the same time you charge an additional $100 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. How long does it take to pay off the credit card debt? Round your numbers to the nearest cent?
It will take around 3.72 months to pay off the credit card debt.
Explain about the annual percentage rate APR?The annual rate of interest that a person must pay on a loan or receives on a bank account is known as the annual percentage rate (APR).APR is utilized for everything, including credit cards, auto loans, and mortgages.The formula for APR is:
A = P * [tex](1 + r/n)^{nt}[/tex]
In which,
A = amount after compounding.
P = balance amount
r = rate of interest.
n = number of time compounded.
Initial balance: $30,000.
Payments per month = $200.
Expenses = $100
Balance amount = 30,000 - 12 *(200 - 100)
Balance amount = $28800
So, time taken for paying off credit card debt.
30,000 = 28800 [tex](1 + 0.24/1)^{1*t}[/tex]
[tex](1.24)^{t}[/tex] = 30,000 / 28800
[tex](1.24)^{t}[/tex] = 1.04
Solve by using logarithmic function.
t = ln (1.04) / 1.24
t = 0.31 year
t = 3.72 months
Thus, it will take around 3.72 months to pay off the credit card debt.
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Need help with number 10.
Answer:
Width = 12
Length = 19
Step-by-step explanation:
They multiply to 228 and 19in is 7in larger than 12in.
A tank in the shape of a hemisphere has a radius of 8 feet. If the liquid that fills the tank has a density of 98.9 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
848,775 pounds
Step-by-step explanation:
The volume of a hemisphere with radius 8 feet is:
V = (2/3)πr^3 = (2/3)π(8^3) = 268.08 cubic feet
The weight of the liquid is given by:
W = V * ρ * g
where ρ is the density of the liquid and g is the acceleration due to gravity. Plugging in the values, we get:
W = 268.08 * 98.9 * 32.2 = 848,774.7 pounds
Rounding to the nearest full pound, the total weight of the liquid in the tank is 848,775 pounds.
58 points please urgent super urgent
4x=16
what is x
Answer:4? Think
Step-by-step explanation:
Calculate the length between the points (2, 3)
and (5. 7)
A. 3
B. 4
C. 5
D. 6
144q-15
as a product of two factors
144q-15 can be expressed as a product of two factors: 3 and (48q-5). The greatest common factor between 144q and 15 is 3:144q = 3 x 48q15 = 3 x 5, so we can factor out the common factor.
What is factor of algebraic expression?The number or algebraic expression that divides another number or expression completely or with no remainder is factor of that expression ,1 is a factor of every number. It is also the smallest factor of a number. or we can say a factor of a number is defined as an exact divisor of the given number. example, the factors of 20 are 1, 2, 4, 5, 10, and 20.
Given that an equation 144q-15
express 144q-15 as a product of two factors,
we can use factorization by grouping:
144q-15 = 12*12q - 3*5 = 3(412q - 5)
Therefore, 144q-15 can be expressed as the product of two factors:
3(48q-5)
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Pls help meee!!!
Anybody pls!!
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
what is the solution to this
Answer:
-2
Step-by-step explanation:
Which of the following is equivalent to 0=2x^(2)-16x-18 when completing the square?
Answer:
X=-1 or 9
Step-by-step explanation:
using the quadratic formula:
[tex]X=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
X=-1
X=9
Rewrite the two equations in the form (x−p)^2=q.
0=x^2-10x+10
x^2+26x+167.5=0
Answer:
(x - 5)^2 = 15 and (x + 13)^2 = 3
Step-by-step explanation:
Sure, I can help you with that.
Let's start with the first equation:
0 = x^2 - 10x + 10
To rewrite this equation in the form (x - p)^2 = q, we need to complete the square.
First, let's factor out the coefficient of x^2:
0 = 1(x^2 - 10x + 10)
Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (10/2)^2 = 25:
0 = 1(x^2 - 10x + 25 - 25 + 10)
Now we can rearrange the terms inside the parentheses and simplify:
0 = 1((x - 5)^2 - 15)
Finally, we can rewrite the equation in the desired form by adding 15 to both sides:
15 = (x - 5)^2
So the first equation in the form (x - p)^2 = q is:
(x - 5)^2 = 15
Now let's move on to the second equation:
x^2 + 26x + 167.5 = 0
Again, we need to complete the square to rewrite this equation in the form (x - p)^2 = q.
First, let's factor out the coefficient of x^2:
x^2 + 26x + 167.5 = 1(x^2 + 26x + 167.5)
Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (26/2)^2 = 169:
x^2 + 26x + 167.5 = 1(x^2 + 26x + 169 - 169 + 167.5)
Now we can rearrange the terms inside the parentheses and simplify:
x^2 + 26x + 167.5 = 1((x + 13)^2 - 1.5)
Finally, we can rewrite the equation in the desired form by adding 1.5 to both sides:
1.5 = (x + 13)^2 - 1.5
So the second equation in the form (x - p)^2 = q is:
(x + 13)^2 = 3
Find the next 2 terms in the geometric sequence: 4, 12, 36,
help so i cna get out of class
Based on the given conditions, the lock solution is 205.
How to solve a lock?To solve the lock, to calculate the total score based on the given conditions:
Crocus: + 20
Daffodil: + 25
Snowflake: - 50
Tulip: + 30
Bird-Red: + 25, else + 10
Calculating the scores for each input:
TULIP: +30
CROCUS: +20
DAFFODIL: +25
TULIP: +30
DAFFODIL: +25
TULIP: +30
DAFFODIL: +25
CROCUS: +20
Total score = 30 + 20 + 25 + 30 + 25 + 30 + 25 + 20 = 205
Therefore, the solution for the lock is 205.
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Image transcribed:
SPRING NOW LOADING.
<IF CROCUS, THEN +20>
<IF DAFFODIL, THEN +25>
<IF SNOWFLAKE, THEN -50>
<IF TULIP, THEN +30>
<IF BIRD-RED, THEN +25, ELSE + 10>
TULIP
CROCUS
DAFFODIL
TULIP
DAFFODIL
TULIP
DAFFODIL
CROCUS
Solve Lock
Rachel ran 3 miles when she was training for a race. How many feet did she run?
15,840 feet
5,280 feet
10,560 feet
14,840 feet
To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:
3 miles x 5,280 feet/mile = 15,840 feet
Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.
The customer service department of a company found that the relationship between the number of minutes a customer spends on hold when telephoning and the customer's level of satisfaction on a 10-point scale can be approximated by the equation y=10−0.1x
, where x
is the number of minutes on hold and y
is the level of satisfaction. What does 0.1 represent in the equation?
In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.
Define slopeit represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.
In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.
In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.
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2 1/4-6/7=
2 5/12-blank=2/3
7 1/12-5 3/8=
blank+7/10=2 9/20
To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:
9/4 - 24/28
= 63/28 - 24/28
= 39/28
Therefore, 2 1/4 - 6/7 = 39/28.
To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:
2 5/12 = (2*12 + 5)/12 = 29/12
Then we can subtract 2/3 from both sides:
2 5/12 - 2/3 = blank
To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:
29/12 - 8/12
= 21/12
= 7/4
Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.
To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:
7 1/12 = (712 + 1)/12 = 85/12
5 3/8 = (58 + 3)/8 = 43/8
Then we can subtract:
85/12 - 43/8
= 85/12 - (433)/(83)
= 85/12 - 129/24
= 5/24
Therefore, 7 1/12 - 5 3/8 = 5/24.
To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:
2 9/20 = (2*20 + 9)/20 = 49/20
Then we can subtract 7/10 from both sides:
blank + 7/10 - 7/10 = 49/20 - 7/10
Simplifying the right side:
49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4
Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:
blank = 7/4
Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.