Answer: IX - 4I ≤ 4
Step-by-step explanation:
In the numer line we can see that our possible values of x are in the range:
0 ≤ x ≤ 8
And we want to find an absolute value equation such that this set is the set of possible solutions.
An example can be:
IX - 4I ≤ 4
To construct this, we first find the midpoint M of our set, in this case is 4.
Then we write:
Ix - MI ≤ IMI
Notice that i am using the minor and equal sign, this is because the black dots means that the values x = 0 and x = 8 are included, if the dots were empty dots, it would be an open set and we should use the < > signs.
Answer: The value of x in trapezoid ABCD is 15
Step-by-step explanation: The trapezoid as described in the question has two bases which are AB and DC and these are parallel. Also it has sides AD and BC described as congruent (that is, equal in length or measurement). These descriptions makes trapezoid ABCD an isosceles trapezoid.
One of the properties of an isosceles trapezoid is that the angles on either side of the two bases are equal. Since line AD is equal to line BC, then angle D is equal to angle C. It also implies that angle A is equal to angle B.
With that bit of information we can conclude that the angles in the trapezoid are identified as 3x, 3x, 9x and 9x.
Also the sum of angles in a quadrilateral equals 360. We can now express this as follows;
3x + 3x + 9x + 9x = 360
24x = 360
Divide both sides of the equation by 24
x = 15
Therefore, in trapezoid ABCD
x = 15
Answer:
3 hours 20 minutes
Step-by-step explanation:
Together, the workers can assemble 9 + 6 = 15 products per hour. So the assembly of 50 products will take ...
(50 products)/(15 products/hour) = 50/15 hours = 3 1/3 hours
The two workers can assemble 50 products in 3 1/3 hours.
Answer:
The mean is the better method.
Step-by-step explanation:
The best way to meassure the average height is throught mean. The mean of a sample is the average of that sample's height, and it will be a good estimate for the population's average height.
The mode just finds the most frequent height. Even tough the most frequent height will influence the average height, knowing only what height is the most frequent one doesnt give you enough informtation about how the height is centrally distributed.
As for the median, it is fine to use the median of a sample to estimate the median of the population, but if you use the median to estimate the average height you may have a few issues. For example, if you include babies in your population, the babies will push the average height down a lot and they are far below te median height. This, as a result, will give you a median height of a sample way above the average height of the population, becuase median just weights every person's height the same, while average will weight extreme values more, in the sense that a small proportion of extreme values can push the average far from the median.
Answer:
A: C = 2: 1
Step-by-step explanation:
Please see the attached pictures for the full solution.
Further explanantion (2nd image):
The reason why the ratio of A: C is equal to the ratio if 2A: 2C is that the number of parts of A and C is equal, which is 2 parts. If I were to divide both 2A and 2C by 2 to find the ratio of A: C, I would obtain 15: 15/2. However, ratios are expressed as whole numbers and thus, we would multiply the whole ratio by 2 again and the answer would still be 30: 15. This ratio is not in the simplest form since both can be divided by 15. Thus, dividing both sides of the ratio by 15 will leave us with the final answer of
A: C= 2: 1.
☆ An alternative method is to simplify the ratio 3B: 2C at the beginning.
3B: 2C
= 36: 15
= 12: 5
Multiply the first ratio by 2 so 3B has 12 parts in both ratios:
2A: 3B
= 10: 12
Combining the 2 ratios together,
2A: 3B: 2C
= 10: 6: 5
2A: 2C
= 10: 5
= 2: 1
A: C= 2: 1
