A general contractor is constructing a building that requires A concrete foundation that is to be 15 feet by 12 feet and 24 inch
1 answer:
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In the given diagram, the traingles USW and UTV are similar triangles and thus the following ratio equality applies to them.
..........(Equation 1)
Checking the diagram given, we see that:
VT=y, WS=22, VU=8, ST=x-2
WU=WV+VU=12+8=20
TU=5
SU=ST+TU=(x-2)+5=x+3
Thus, substituting the required values in (Equation 1) we get:
Now, as can be clearly seen, to find y we will use the first two ratios as:
In a similar manner, to find the value of x we can use the last two ratios:
After cross multiplication we get:
Which can be simplified as:
Thus,
Therefore, the required answer is:
x=9.5 and y=8.8
Answer:
Step-by-step explanation:
First we can determine the x value of our vertex via the equation:
Note that in general a quadratic equation is such that:
In this case a,b and c are the coefficients and so a=1, b=6 and c=13.
Therefore we can determine the x component of the vertex by plugging in the values known and so:
Now we can determine the y-component of our vertex by plugging in the x-component to the equation and so:
Therefore our vertex is (-3,4). Now in vertex our x component determines is the axis of symmetry so the equation for axis of symmetry is:
x=-3
Similarly, the y-component of our vertex is the minimum or maximum. In this case it is the minimum you can determine this because a is positive meaning that the parabola will point up, and so the equation for the minimum is:
y=4
The range of the formula is the smallest y-value meaning the minimum y=4 and all real numbers that are more than 4, mathematically:
Range = All real numbers greater than or equal to 4.
Answer:
The minimum score of those who received C's is 67.39.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?
This is X when Z has a pvalue of 1-0.695 = 0.305. So it is X when Z = -0.51.
The minimum score of those who received C's is 67.39.