Answer:
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Step-by-step explanation:
Given that M is a polynomial of degree 3.
So, it has three zeros.
Let the polynomial be
M(x) =a(x-p)(x-q)(x-r)
The two zeros of the polynomial are -4 and 4i.
Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.
Then,
M(x)= a{x-(-4)}(x-4i){x-(-4i)}
=a(x+4)(x-4i)(x+4i)
=a(x+4){x²-(4i)²} [ applying the formula (a+b)(a-b)=a²-b²]
=a(x+4)(x²-16i²)
=a(x+4)(x²+16) [∵i² = -1]
=a(x³+4x²+16x+64)
Again given that M(0)= 53.12 . Putting x=0 in the polynomial
53.12 =a(0+4.0+16.0+64)
=0.83
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Answer:
The mean is 
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:
What is the mean of this normal distribution if the probability of scoring above x = 209 is 0.0228?
This means that when X = 209, Z has a pvalue of 1-0.0228 = 0.9772. So when X = 209, Z = 2.
The mean is
Answer:
5x - 43
Explanation:
Given the below expression;
To simplify the above, we'll go ahead and use the numbers outside the parentheses to multiply the ones inside to clear the parentheses as seen below;
So the answer is 5x - 43
Answer:
The area of the figure is 117m²
Step-by-step explanation:
In this problem, you have two shapes. One shape is a rectangle. The other shape is a triangle.
Area of a rectangle = b*h = 9*7 = 63
Area of a triangle = 
(b*h) =
Since there are two triangles, you will multiply the area of the one triangle in the figure by 2.
27*2 = 54
Now, you add up the areas!
54 + 63 = 117
So, the area of the figure is 117m²
Hello! To find the unit rate in miles per gallon, all you have to do is divide the amount of miles by the amount of gallons. 2½ is 2.5 in decimal form. 50/2.5 is 20. There. The unit rate is 20 miles per gallon.
