How many solutions does the following system of linear equations have?
1 answer:
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The right answer is -2/3
please see the attached picture for full solution
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The pyramid is shown in the diagram below.
The pyramid is built from four congruent triangles and one square as the base
We have the side of the square, so the area is = 10×10 = 100
We need the height of the triangle to work out its area. We can find out by using the height of the pyramid and half of the length of the side of the square.
Using the Pythagoras rule
Height of triangle =
Area of one triangle = 1/2×10×12=60
Surface area of the pyramid = 100 + (4×60) = 340 square inches
The pyramid is built from four congruent triangles and one square as the base
We have the side of the square, so the area is = 10×10 = 100
We need the height of the triangle to work out its area. We can find out by using the height of the pyramid and half of the length of the side of the square.
Using the Pythagoras rule
Height of triangle =
Area of one triangle = 1/2×10×12=60
Surface area of the pyramid = 100 + (4×60) = 340 square inches
Answer:
And if we solve for a we got;
So the value of height that separates the bottom 95% of data from the top 5% is 11.64
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 certain lifetime of a population, and for this case we know the distribution for X is given by:
Where and
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 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05
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 95% of data from the top 5% is 11.64