Answer:
The correct option is (a) 0.9780.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
As the sample selected is quite large, i.e. <em>n</em> = 110 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:
Compute the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 as follows:
*Use a <em>z</em>-table.
Thus, the probability that the sample proportion of students living in the dormitories falls in between 0.60 and 0.80 is approximately equal to 0.9780.
The correct option is (a).
Answer:
Your answer would be 4! Or if you want it in fraction form then it would be 7/3!
7x-1/2(8x+2)=6
We simplify the equation to the form, which is simple to understand
7x-1/2(8x+2)=6
Simplifying:
7x-0.5*(8x+2)=6
Reorder the terms in parentheses
7x+(-4x-2)=6
Remove unnecessary parentheses
+7x-4x-2=+6
We move all terms containing x to the left and all other terms to the right.
+7x-4x=+6+2
We simplify left and right side of the equation.
+3x=+8
We divide both sides of the equation by 3 to get x.
x=7/3
The value of the investment of $2500 for 3 years will be $3703.86.
<h3>What is compound interest?</h3>
Compound interest is applicable when there will be a change in principle amount after the given time period.
For instance, if you give someone $500 at a 10% yearly rate, $500 is considered your primary sum. After a year, the interest will be $50, making the principle amount $550. Moving forward, the interest will be $550 rather than $500.
Given,
Principle amount (P) = $2500
Rate of interest (R) = 14%.
Time period (T) = 3 years.
Compound interest formula
A = P
So,
A = 2500[1 + 14/100]³
A = $3703.86
Hence the investment of $2500 at a rate of 14% for 3 years will be $3703.86.
For more information about compound interest
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150 + 0.14(6050) = 150 + 847 = 997 <== total pay
** the 14% commission pay is calculated by taking 14% of the sales....so by turning the percent to a decimal (0.14) and multiplying it by the total sales, u arrive at how much the commission pay was
Answer:
Only d) is false.
Step-by-step explanation:
Let be the characteristic polynomial of B.
a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)
b) Remember that . 0 is a root of p, so we have that .
c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.
d) det(B)=0 by part c) so B is not invertible.
e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.