Resuelve la siguiente ecuación lineal: 13-4(5x+1)=3(7-5x)-15
1 answer:
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For number 4, we'll need a few facts to answer our question:
- Two supplementary angles add up to 180°, forming a straight angle (the angle formed by a straight line)
- The interior angles of a triangle add up to 180°
Given those, we notice that the one unlabeled angle in the figure shares a line with 156°. In fact, this angle is <em>supplementary</em> to 156°, which means that the two add up to 180°. To find the measure of this mystery angle, we can subtract 156 from 180 to obtain 180 - 156 = 24°.
Now, let's look at the triangle. We already know the measure of one of the angles is 24°, and the other two are x°. What else do we know about the angles of a triangle? From the two facts listed at the beginning, we know their interior angles add up to 180°, so let's use that fact to solve for x.
We have:
, or 
Solving for x:
So, x = 78°.
For question 5, the <em>definition</em> of a pair of parallel lines is a pair of lines which <em>never intersect</em>, so "always" would be the appropriate answer.
- Two supplementary angles add up to 180°, forming a straight angle (the angle formed by a straight line)
- The interior angles of a triangle add up to 180°
Given those, we notice that the one unlabeled angle in the figure shares a line with 156°. In fact, this angle is <em>supplementary</em> to 156°, which means that the two add up to 180°. To find the measure of this mystery angle, we can subtract 156 from 180 to obtain 180 - 156 = 24°.
Now, let's look at the triangle. We already know the measure of one of the angles is 24°, and the other two are x°. What else do we know about the angles of a triangle? From the two facts listed at the beginning, we know their interior angles add up to 180°, so let's use that fact to solve for x.
We have:
Solving for x:
So, x = 78°.
For question 5, the <em>definition</em> of a pair of parallel lines is a pair of lines which <em>never intersect</em>, so "always" would be the appropriate answer.
Answer:
And if we solve for a we got
So the value of height that separates the bottom 10% (Fastest 10%) of data from the top 90% is 393.2.
so if the time is 393.2 or lower a boy would earn a certificate of recognition from the fitness association
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the time for this event of a population, and for this case we know the distribution for X is given by:
Where and
NOTE: For this case the fastest 10% is on the lower tail of the distribution
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 10% (Fastest 10%) of data from the top 90% is 393.2.
so if the time is 393.2 or lower a boy would earn a certificate of recognition from the fitness association