The total number of possible outcomes when rolling a six-sided number cube twice is 36. This is calculated by multiplying the 6 possible outcomes from the first roll with the 6 possible outcomes from the second roll.
When you roll a six-sided number cube two times, you create a series of possible outcomes that can be categorised by understanding that each roll is independent of the other. On the first roll, you have 6 possible outcomes (1, 2, 3, 4, 5, or 6), and for the second roll, regardless of what the first number was, you again have 6 possible outcomes. To find the total number of outcomes possible when rolling a cube twice, you multiply the number of outcomes for each event. So, we calculate the total outcomes with 6 (for the first roll) times 6 (for the second roll), which equals 36 possible outcomes.
This means that rolling two dice can lead to one of thirty-six different combinations, where the first number of the pair corresponds to the result of the first roll and the second number to the result of the second. For instance, if you first roll a 4 and then a 3, one possible outcome is (4,3).
It is important to note that when calculating probabilities for specific sums of the two dice, such as the probability of rolling a seven, the outcomes are not all equally likely. If we consider the sum of the dice, rolling a two is less likely than rolling a seven because there's only one combination (1,1) for a sum of two, while there are six combinations (1,6; 2,5; 3,4; 4,3; 5,2; 6,1) for a sum of seven.
determine the number of solutions for the system 6x+9y=9 and -6x+6y=1
Answer:
one solution
Step-by-step explanation:
the numbers aren't the same, the variables don't repeat
Is the system of equations consistent and independent, consistent and dependent, or inconsistent? y = -x + 1 2y = -2x + 2
Answer:
Step-by-step explanation:
y = -x + 1
2y = -2x + 2......reduce by divide everything by 2 and u get y = -x + 1
same line......infinite solutions....CONSISTENT and DEPENDENT
Final answer:
The system of equations represented by y = -x + 1 and 2y = -2x + 2 is both consistent and dependent, as the equations are essentially the same, representing the same line with infinitely many solutions.
Explanation:
To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, we need to assess if they have one unique solution, infinitely many solutions, or no solutions at all. The two equations given are y = -x + 1 and 2y = -2x + 2.
Consistency: To see if the equations are consistent, they must at least have one solution. By looking at the second equation, we can simplify it by dividing every term by 2, yielding y = -x + 1, which is identical to the first equation. This implies that both equations actually represent the same line.
Dependence: Given that both equations are the same, they have an infinite number of solutions where the two lines would intersect if they were different. Since they are the same line, the system is considered dependent.
Therefore, the system of equations is both consistent and dependent, as both equations are the same, representing the same line and thus having infinitely many solutions.
A metalworker has a metal alloy that is 20% copper and another alloy that is 70% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 50% copper alloy?
40 kilograms alloy of 20 % copper and 60 kilograms of alloy of 70 % copper is combined to get 100 kg of 50 % copper alloy
Solution:
Th final alloy is 100 kg
Let "x" be the alloy of 20 % copper
Then, (100 - x) is the alloy of 70 % copper
Therefore,we can say,
"x" kilograms alloy of 20 % copper and (100 - x) kilograms of alloy of 70 % copper is combined to get 100 kg of 50 % copper alloy
Therefore, we frame a equation as:
[tex]x \times 20 \% + (100-x) \times 70 \% = 100 \times 50 \%\\\\x \times \frac{20}{100} + (100-x) \times \frac{70}{100} = 100 \times \frac{50}{100}\\\\0.2x + (100-x) \times 0.7 = 0.5 \times 100\\\\0.2x + 70 - 0.7x = 50\\\\-0.5x = -20\\\\x = 40[/tex]
Thus 40 kilograms of 20 % copper
Then, 100 - x = 100 - 40 = 60
60 kilograms of 70 % copper is used
The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s) to f(x)=g(x)? Explain your answer(s).
x –3 –2 –1 0 1 2
f(x) 81 27 9 3 1 1⁄3
g(x) 6 7.5 9 10.5 12 13.5
Answer:
x = -1
Step-by-step explanation:
Both tables show a function value of 9 for x = -1.
x = -1 is the solution to f(x) = g(x), since f(-1) = 9 = g(-1).
The points (9,9) and (10,k) fall on a line with a slope of -1. What is the value of k?
The value of k is 8
Solution:
Given that, points (9, 9) and (10, k) fall on a line with a slope of -1
To find: value of "k"
The slope of a line with points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here given that,
slope = m = -1
[tex](x_1, y_1) = (9, 9)\\\\(x_2, y_2) = (10, k)[/tex]
Substitute the values in formula, and solve to get value of k
[tex]m = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{10-9}\\\\-1 = \frac{k-9}{1}\\\\k-9 = -1\\\\k = -1+9\\\\k = 8[/tex]
Thus the value of k is 8
Help ASAP
What is the 5th term in the geometric sequence described by this explicit
formula?
an=40 • (-2)^(n-1)
A. 1280
B. -640
c. -1280
D. 640
The fifth term of the geometric sequence is 640, so the correct option is D.
How to get the fifth term of the given geometric sequence?
Here we have a geometric sequence, such that the terms are given by:
[tex]A_n = 40*(-2)^{(n-1)}[/tex]
To get the 5-th term, we just need to replace n by 5 on the above rule, so we can write:
[tex]A_5 = 40*(-2)^{(5-1)} = 40*(-2)^4 = 640[/tex]
Then the value of the 5-th term is 640, which means that the correct option is D.
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(6x - 4) + (-4x + 8)
the number 1 is an example of an element in the set of natural numbers. true or false
Your answer is True!
Some other examples of an element in the set of natural numbers are 2, 3, 4, 5, etc.
Hope this helps you!
~sofia
A 2-pound box of candy cost $8.00. What was the cost per ounce (1 pound= 16 ounces)
A) $0.25
B) $0.50
C) $0.80
D) $0.20
Answer:
A: $0.25
Step-by-step explanation:
8 Jack bought 4 bagels for $3.00. How many ba
. How many bagels can he buy for $4.50?
Answer:
5 3.00 for 4 is 1.50 each so add 3.00 +1.50 is 4.50
Four times a number minus twice another number is -16 the sum of the two numbers is -1 find the numbers
The numbers are -3 and 2
Step-by-step explanation:
Let x be the first number and y be the second number
then according to given statements the linear equations will be:
"Four times a number minus twice another number is -16"
[tex]4x-2y = -16\ \ \ Eqn1[/tex]
"The sum of the two numbers is -1"
[tex]x+y = -1\ \ \ Eqn2[/tex]
From equation 2:
[tex]y = -x-1[/tex]
Putting y = -x-1 in equation 1
[tex]4x-2(-x-1) = -16\\4x+2x+2 = -16\\6x +2 = -16[/tex]
Subtracting 2 from both sides
[tex]6x+2-2 = -16-2\\6x = -18[/tex]
Dividing both sides by 6
[tex]\frac{6x}{6} = \frac{-18}{6}\\x = -3[/tex]
Putting x = -3 in equation 2:
[tex]x+y = -1\\-3+y = -1\\y = -1+3\\y = 2[/tex]
Hence,
The numbers are -3 and 2
Keywords: Linear equations, variables
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what is the answer to: 2.15, 15% markup
An equilateral triangle has a perimeter of 54 ft. What is the length of one side? Answer:____ft.
Answer: 18 ft
Step-by-step explanation:
The length of one side is 18 feet.
What is perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
An equilateral triangle has a perimeter of 54 feet.
Let x be the side of an equilateral triangle.
Then,
3x = 54
x = 54/3
x = 18
Therefore, 18 feet are the length of one side.
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there are 16 different colored markers in the bucket. how many ways can kelly choose five of them?
Answer:
80
Step-by-step explanation:
you multiply 16 x 5 = 80
The solution is 4368 ways
The number of ways 16 colored markers in bucket can be arranged by Kelly if she chose 5 of them is 4368 ways
What are Combinations?
The number of ways of selecting r objects from n unlike objects is:
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the equation be represented as A
Now , the value of A is
The number of colored markers n = 16 markers
The number of markers Kelly chooses x = 5 markers
The number of ways Kelly can choose 5 markers from 16 markers is calculated by Combinations
And , the combination is given by
¹⁶C₅ = 16! / ( 16 - 5 )! ( 5! )
On simplifying the equation , we get
¹⁶C₅ = 16! / 11! x 5!
¹⁶C₅ = ( 16 x 15 x 14 x 13 x 12 ) / ( 5 x 4 x 3 x 2 x 1 )
The value of ¹⁶C₅ = 4368 ways
Therefore , the value of A is 4368 ways
Hence , The number of ways 16 colored markers in bucket can be arranged by Kelly if she chose 5 of them is 4368 ways
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At bright minds learning , 75% of employees work as instructors . If there are 300 employees at bright mind Learning , how many of them work as instructors
Answer:
225
Step-by-step explanation:
75/100×300=225
What is the value of the expression below? (9 divided by 3) + 4 (6 minus 7)
Answer:
-1
Step-by-step explanation:
9/3+4(6-7)
3+4(-1)
3+(-4)
3-4
-1
Answer:
-1
Step-by-step explanation:
Just did the test
Rachel earned $34 in four hours at her job today. She wants to know how much she could earn Tomorrow if she work 10 hours at the same hourly rate. How much will Rachel earn in 10 hours
first you should find the hourly rate so you take 34 and divide it by 4 to get 8.5 which will be the hourly rate
then you take 8.5 and multiply it by 10 to get how much she'll earn for 10 hours of working
the answer for how much will she earn in 10 hours is $85.
1. Suppose you have a spinner that is evenly
divided showing all the days of the weck, You
also have a bag of papers that list the months
of the year, Are you more likely to spin the
current day of the week or pull out the paper
with the current month?
a) What is the probability of spinning a Monday
b) What is the probability of pulling November?
c) Compare the two fractions, decimals, and
percentages.
4% of what amount of money is $19?
Estimate 432 divided by 9
Answer:
48
Step-by-step explanation:
Answer:48
Step-by-step explanation:
Round 7,492 to the nearest hundreds
I need help please and thank you
Add the two equations 2x+6 and 6x-1
Answer:
The sum of the two equations is 8x + 5 and the value of x is -5/8
Step-by-step explanation:
Let's add these two equations and solve for x:
2x + 6 + 6x - 1 = 0
8x + 5 = 0
8x = -5
x = -5/8
The sum of the two equations is 8x + 5 and x = -5/8
Answer:
Sum = 8x + 5
Step-by-step explanation:
It is required to add the following equations
2x+6 & 6x-1
So, the sum of the equations
= (2x + 6) + ( 6x - 1 ) ⇒ Combine like terms.
= ( 2x + 6x ) + ( 6 - 1 )
= 8x + 5
So, the result of adding the equations 2x+6 and 6x-1 is 8x + 5
A bike shop charges X dollars to rent a bike for half a day. It charges X+ $40 to rent a bike for a full day. One on that day the shop made a total of $600 from the bike rentals. Half day x(5). Full day (x+40)3. How much the the cost to rent a bike for a full day? Please help
Answer:
The cost for full day car rental will be $100.
Step-by-step explanation:
A bike shop charges x dollars to rent a bike for half a day. It charges (x + 40) dollars to rent a bike for a full day.
On that day the shop made a total of $600 from the bike rentals. If there were 5 half day and 3 full day rental, then we can write
5x + 3(x + 40) = 600
⇒ 8x = 600 - 120
⇒ 8x = 480
⇒ x = $60
Therefore, the cost for full day car rental will be $(x + 40) = $100. (Answer)
Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method.
Note: interest rate is given as a monthly rate.
Previous balance = $410.22
Payments/credits = $160.00
Unpaid balance = $
Monthly rate = 1.25%
Finance charge = $
New purchases = $95.25
New balance = $
Answer:
Unpaid balance = $ 250.22
Finance charge = $ 3.13
New balance = $ 348.60
Step-by-step explanation:
Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method.Note: interest rate is given as a monthly rate.
Previous balance = $410.22
Payments/credits = $160.00
subtract 410-160 to get unpaid balance
Unpaid balance = $ 250.22
Monthly rate = 1.25%
multiply 250 by monthly rate (decimal) .0125 to get finance charge
Finance charge = $ 3.13
New purchases = $95.25
add unpaid balance and finance charge and new purchases to get new balance
New balance = $ 348.60
Final answer:
To calculate the unpaid balance, finance charge, and new balance using the unpaid balance method, subtract the payments/credits from the previous balance, add the finance charge, add the new purchases, and calculate the new balance.
Explanation:
To calculate the unpaid balance, finance charge, and new balance using the unpaid balance method, follow these steps:
Start with the previous balance.
Subtract the payments/credits.
Add the finance charge.
Add the new purchases.
Calculate the new balance.
For example, with a previous balance of $410.22, payments/credits of $160.00, and new purchases of $95.25, the equation would be: unpaid balance = previous balance - payments/credits = $410.22 - $160.00 = $250.22. The finance charge would then be calculated by multiplying the unpaid balance by the monthly interest rate. Finally, the new balance would be the unpaid balance plus the finance charge and new purchases.
a rope is 24 feet long. it is cut into two pieces such that one piece is half the length of the other. find the lengths of the two pieces of rope
Answer:
16 ft and 8 ft
Step-by-step explanation:
x + 1/2 x=24
2/2 x + 1/2 x= 24
3/2 x=24
3 x= 48
x=16
1/2x=16/2=8
Complete the equation of the line whose slope is 5 and y intercept is (0,4)
y = 5x + 4 is the equation of the line whose slope is 5 and y intercept is (0,4)
Solution:
Given that we have to write the equation of the line whose slope is 5 and y intercept is (0,4)
The equation of line in slope intercept form is given as:
y = mx + c -------- eqn 1
Where, "m" is the slope of line and "c" is the y - intercept
Given that,
Slope = m = 5
Also, y intercept is (0,4)
Therefore, c = 4
Substitute c = 4 and m = 5 in eqn 1 to get equation of line
y = 5x + 4
Thus the equation of line is found
What would m equal if -6.85+m/4=-11
Hope this will help u..............
river c is 100 miles longer than river d.if the sum of the rivers is 5500 miles then what is the length of both rivers?
Answer:
river c is 2850 and river d is2650
Step-by-step explanation:
Answer:
Step-by-step explanation:
I would look at it by taking the 100 off of the 5500. Leaving you with 5400 you would then Divide that by two since there is two rivers being described. So River d is 2700 miles long and then river c is 2800. Hope it helps :)
Clara’s teacher asked her to draw a polygon with vertices (–2, 4), (5, 4), (3, –3), and (–2, 0) and to identify the polygon. Clara drew the polygon below and identified it as a quadrilateral.
Which explains whether Clara is correct?
Clara drew the figure correctly and correctly identified the four-sided figure as a quadrilateral.
Clara drew the figure with the wrong coordinates, but she correctly identified the four-sided figure as a quadrilateral.
Clara drew the figure correctly, but she should have identified the figure as a pentagon.
Clara drew the figure with the wrong coordinates, and she should have identified the figure as a pentagon.
Answer:
Clara drew the figure correctly and correctly identified the four-sided figure as a quadrilateral.
Step-by-step explanation:
To plot the vertices of the figure, Clara needs to take the first coordinate of each point and mark it on the x-axis and the second coordinate should be marked on the y-axis. Then she has to draw vertical and horizontal lines through the x-coordinate and y-coordinate. These two lines intersect at the point which has those coordinates. Following these steps, Clara drew the figure correctly.
Connecting all consecutive vertices, she got a figure with four sides - this is exactly the quadrilateral.
Hence, Clara drew the figure correctly and correctly identified the four-sided figure as a quadrilateral.
Answer:
A
Step-by-step explanation: