Step-by-step explanation:
We have got the lines :
Both lines intercept the x-axis in the point :
In all point from x-axis the y-component is equal to 0.
We replace the I point in the lines equations:
From the first equation :
From the second equation :
Then
Finally :
y = ax + b and y = cx + d have the same x-intercept ⇔ad=bc
Answer:
a)
b) 69.764
Step-by-step explanation:
1) 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".
2) Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
3) Part b
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 69.764.
The number of boxes fitted in the larger container is found out by the volume of both boxes.
The number of boxes fitted into the larger container is 480.
<h3>What is the volume?</h3>
The volume can be defined as the space occupied by an object in three dimensions.
Given that the edge of the cube box is 1/4 ft. The dimensions of the larger box are 3 ft long, 1 1/4 ft wide, and 2 ft.
The volume of the cube box is calculated as given below.
Where Vs is the volume of the cube box and s is the edge of the cube box.
The volume of the larger box is calculated as given below.
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Where V is the volume, l is length, w is width and h is the height of the larger box.
The number of cube boxes fitted into the larger box is calculated as given below.
Hence we can conclude the number of boxes fitted into the larger container is 480.
To know more about the volume, follow the link given below.