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3 years ago

The sales tax on a sofa that cost $575 was $43.13. What was the percent sales tax?

Mathematics

2 answers:

laiz [17]3 years ago

4 0

$43.13/ $575* 100%= 7.5%

The percent sales tax was 7.5%~

babunello [35]3 years ago

3 0

It is important to look at all details given in the question very carefully.
Amount of sales tax taken on the sofa = $43.13
Actual cost of the sofa = $575
Let us assume the percentage of sales tax taken = x%
Then
(x/100) * 575 = 43.13
5.75x = 43.13
x = 43.13/5.75
= 7.50 percent
So the percentage of sales tax charged for the sofa was 7.50%.I hope the procedure is clear enough for you to understand. Based on this procedure, similar problems can be done with absolute ease.

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An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false

asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let $p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1)$ 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 $p(\lambda)=\det(B-\lambda I)$ . 0 is a root of p, so we have that $p(0)=\det(B-0 I)=\det B=0$ .

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.

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3 years ago

For the following system, use the second equation to make a substitution for y in the first equation.

ICE Princess25 [194]

Answer:

It is A

Step-by-step explanation:

2x + y = 5

y + 3 = 2x

From equation 2:

y = 2x - 3

Substituting in the first equation:

2x + 2x - 3 = 5.

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3 years ago

An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made t

solniwko [45]

Answer:

B) Method 2 will increase the standard deviation of the students' scores.

Step-by-step explanation:

Given that an instructor in a college class recently gave an exam that was worth a total of 100 points.

The average score for his students was 43 and the standard deviation of the scores was 5 points.

And now he is considering two different strategies for rescaling the exam results of which:

Method 1 = Add 17 points to everyone's score.

Method 2 = Multiply everyone's score by 1.7 .

And we have to check what will be the impact of these methods on the standard deviation of the students' scores.

For this let us consider a simple example to understand this:

Firstly, Formula for calculating Standard Deviation = $\sqrt{\frac{\sum (X-Xbar)^{2}}{n-1}}$

Suppose,

X X - Xbar $(X - Xbar)^{2}$

3 3 - 6 = -3 -3 * -3 = 9

5 5 - 6 = -1 -1 * -1 = 1

10 10 - 6 = 4 4 * 4 = 16

Mean of above data, Xbar = $\frac{3+ 5+10}{3}$ = 6

Standard Deviation of data = $\sqrt{\frac{26}{3-1} }$ = 3.6055

Now let us suppose that we multiply each value of above data with 2 so the new data will be:

X X - Xbar $(X - Xbar)^{2}$

3*2 = 6 6 - 12 = -6 -6 * -6 = 36

5*2 = 10 10 - 12 = -2 -2 * -2 = 4

10*2 =20 20 - 12 = 8 8 * 8 = 64

Mean of new data, Xbar = $\frac{6+ 10+20}{3}$ = 12

Standard Deviation of new data = $\sqrt{\frac{104}{3-1} }$ = 7.2111

Hence, we see that when we multiply any value to the data the standard deviation will increase and in other words it will multiplied by that value which value we multiplied with each data value i.e. when we multiply each data value with 2 the standard deviation also get multiplied by as

3.6055 * 2 = 7.2111

Therefore option B is correct that Method 2 will increase the standard deviation of the students' scores.

And on the other hand Similarly by adding any constant to the data the Standard Deviation will remain same. Therefore Method 1 will have no impact on standard deviation of the students' scores.

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Answer:

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