What is the value of n in the equation: 8n + 9 = -n +5
Answers
Answer:
n = -4/9
Step-by-step explanation:
8n + 9 = -n +5
Add n to each side
8n+n + 9 = -n+n +5
9n +9 = 5
Subtract 9 from each side
9n+9 - 9 = 5-9
9n /9 = -4/9
Divide each side by 9
n = -4/9
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Answers
Answer:
66 + 1 ( not fully shaded ) squares will be shaded.
66.67% region will be shaded
Step-by-step explanation:
It is given that Marks uses a grid to model percent equivalent of .
Let us assume that Mark uses a model containing 100 grids.
Now, as the grids are divided into region equivalent to i.e. it is divided into 3 parts.
Moreover, 2 out of those 3 parts will be shaded.
As,
i.e. =66.67%
So, it gives us that 66 squares in the grid will be fully shaded and one will not be fully shaded.
Hence, 66 + 1 ( not fully shaded ) squares will be shaded and in percent, 66.67% of the region will be shaded.
Final answer:
To represent the fraction 2/3 on a grid, approximately 67% of the squares on the grid should be shaded. This means such a fraction corresponds to 67 out of 100 squares on a 100-square grid or equivalently 67% shaded.
Explanation:
To determine how many grid squares Mark should shade to model the percent equivalent of the fraction 2/3, we need to understand the relationship between fractions, decimals, and percents. When we convert the fraction 2/3 into a decimal, we get approximately 0.67. To represent this as a percent, we multiply by 100, which gives us 67%. So, about 67 out of 100 squares should be shaded.
Let's say Mark's grid has 100 squares (10 rows by 10 columns). In that case, he would shade about 67 squares to represent 2/3 as a percent. If the grid contains fewer than 100 squares, he would need to adjust accordingly.
In summary, the model would show about 67% shaded.
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Answers
For this case, we have that by definition, the proportions can be expressed in different ways. Example, if we have a dog and three cats:
75%: It's percentage
0.75: In decimal (75% are cats)
: In fraction. (There are
of cats)
: Using ":" to separate sample values. (For every three cats there is a dog)
Care should be taken with the proportions, always multiplying the numbers in the proportion by the same value.
Example:
Answer:
Care should be taken with the proportions, always multiplying the numbers in the proportion by the same value.
Answers
t = 5c
Each car needs 5 tires (4 on it and 1 spare, which add up to five). So for every one car they make they need 5 tires. Two cars would need 10 tires, 3 would need 15 tires, etc, so the number of tires can be found by multiplying the number of cars by 5. Putting this into equation form, you'd get t = 5c
Final answer:
The formula to calculate the number of tires needed in an automobile factory is t = (4c) + c, where t represents the number of tires needed and c represents the number of cars produced per day.
Explanation:
The formula to calculate the number of tires needed in an automobile factory is given by:
t = (4c) + c
Where t represents the number of tires needed and c represents the number of cars produced per day.
For example, if the factory produces 100 cars per day, we can substitute c = 100 into the formula to find that t = (4 * 100) + 100 = 500 + 100 = 600. Therefore, the factory would need 600 tires per day.
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The notation ">=" without quotes means "greater than or equal to"
The upper case "U" means "set union"
Instead of using the intersection symbol, I will use a lower case 'n'
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Problem 1
A = {x | x < 1} which is the set of x values smaller than 1
B = {x | x >= 5} is the set of x values that are equal to 5 or larger
A U B = set of values that are from set A OR they are from set B (or both)
A U B = {x | x < 1 or x >= 5}
we simply connect the two inequalities mentioned with an "or"
note: how there is no overlap between the two regions. The "U" means "set union" which is like a sort of glue to tie the two sets together with an "or".
Answer: {x| x < 1 or x >= 5}
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Problem 2
A = {x | x < 1}
C = {x | x = 5} which is the set of one value only: 5 (x cannot equal any other value)
A U C = {x| x < 1 or x = 5}
So if a number is in set A U C, then this number is either less than 1, OR it is equal to 5
Answer: {x|x < 1 or x = 5}
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Problem 3
B U C = {x | x >= 5} because set C already has the "or equal to" part in there.
Set C is a subset of set B. If an item is in set C, then it is also in set B.
Answer: {x| x >= 5}
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Problem 4
Again recall that I'm using an 'n' to indicate "set intersection" instead of the upside down "U" symbol
A n B is the set of items that are in BOTH sets A and B at the same time. From problem 1, I mentioned there's a gap. There is no x value that is both less than 1 AND greater than or equal to 5. So this means that
A n B = empty set
which we use the "O" with a slash through it. This is a special symbol to indicate "empty set"
Another way to write "empty set" is to use curly braces with nothing inside like so { }
Answer: The "O" with a slash through it
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Problem 5
B n C is the same as {x| x = 5}
Why? Because if an item is in B n C, then it has to be in BOTH set B and set C at the same time. The only way this happens is if x = 5. If x is any other value, then it won't be in set C
Answer: {x| x = 5}
Answers
A regular hexagon has both reflective and rotation symmetry.
It has 6 rotational symmetries with an angle of 60°.
It has 6 reflection symmetries meaning it has 6 lines of axes.
It is easy to see if there is Reflection symmetry because one half of the whole is the reflection of the other half. In a regular hexagon, you can draw 6 lines across it and still have reflection symmetry.
In Rotational symmetry, the image is rotated around a central point and still looks the same. The regular hexagon is rotated 12 times at an angle of 60°.