Russ James is a sales representative for a chemical company and is paid a commission rate of 5% on all sales. Find his commission if he sold $100,000 worth of chemicals last month.

The area of the largest circular rug that she can buy to fit the space is given as follows:

B. 30.2 ft².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The side length of the square is of 6.2 ft, which is equivalent to the diameter of the circle, hence the radius is given as follows:

r = 0.5 x 6.2

r = 3.1 ft.

Hence the area of the rug is obtained as follows:

A = 3.14 x 3.1²

A = 30.2 ft².

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a) To find the transition matrix from C to the standard ordered basis E, we can express the vectors in C as linear combinations of the vectors in E.

Let's represent the vectors in C as C1 and C2, and the vectors in E as E1 and E2.

C1 = -2E1 - 4E2

C2 = -E2

The transition matrix TEC can be obtained by arranging the coefficients of E1 and E2 as columns:

TEC = [[-2, 0], [-4, -1]]

b) To find the transition matrix from B to E, we need to express the vectors in B as linear combinations of the vectors in E. Let's represent the vectors in B as B1 and B2.

B1 = 4E1 - 7E2

B2 = 3E1 - 5E2

The transition matrix TEB can be obtained by arranging the coefficients of E1 and E2 as columns:

TEB = [[4, 3], [-7, -5]]

c) The transition matrix from E to B can be obtained by finding the inverse of the transition matrix from B to E:

TBE = (TEB)^(-1)

d) To find the transition matrix from C to B, we can express the vectors in C as linear combinations of the vectors in B. Using the same approach as before:

C1 = -2B1 - 4B2

C2 = -B1 - B2

The transition matrix TBC can be obtained by arranging the coefficients of B1 and B2 as columns:

TBC = [[-2, -1], [-4, -1]]

e) To find the coordinates of u = (1, 2) in the ordered basis B, we can use the equation [u]B = TBE[u]E:

[u]B = TBE * [1, 2]^T

f) To find the coordinates of v in the ordered basis B if the coordinate vector of v in C is [v]C = (1, 2), we can use the equation [v]B = TBC * [v]C:

[v]B = TBC * [1, 2]^T

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Answer:

Step-by-step explanation:

To the 4th power means that all the items in the parenthesis is mulitplied 4 times

(9m)⁴

=9*9*9*9*m*m*m*m*m  or

= (9m)(9m)(9m)(9m)

Answer:

\(A=4.5 square feet\)

Step-by-step explanation:

1. The missing side of triangle (a) is calculated:

\(a=3^{2} +3^{2} +2(3)(3)cos140^{0}\)

\(a=18-13.7889\)

\(a=4.2112\)

2. The semi-perimeter (s) is calculated:

\(s=\frac{a+b+c}{2} =\frac{4.2112+3+3}{2}\)

\(s=5.106\)

3. The area is determined:

\(A=\sqrt{s(s-a)(s-b)(s-c)} =\sqrt{5.106(5.106-4.2112)(5.106-3)(5.106-3)}\)

\(A=\sqrt{5.106(0.894)(2.106)(2.106)}\)

\(A=\sqrt{20.26}\)

\(A=4.5\)

Hope this helps.

Answer:

Step-by-step explanation:

Sides r and q form the angle P.

We need to find the value of side p.

According the the information, we have 2 sides and the included angle known and need to find the missing side.

This is possible using the law of cosines:

Correct choice is B

Answer:

Law of Cosines, two sides, and the included angle are known

Step-by-step explanation:

Law of Cosines

\(c^2=a^2+b^2-2ab \cos C\)

where:

This rule can be used to find:

Law of Sines

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

where:

This rule can be used to find:

Therefore, as sides r and q are given and the included angle ∠P is known, we can use the Law of Cosines to find side p:

\(\implies p^2=r^2+q^2-2rq \cos P\)

\(\implies p=\sqrt{r^2+q^2-2rq \cos P}\)

Answer:

A

Step-by-step explanation:

Rewritten as decimals, the numbers are 3.66, 3.50, 3.25, 3.20

Answer:

102.3

Step-by-step explanation:

Convert 1.023 x \(10^{2}\) from scientific notation.

The system stable with P(1)=1.7 and P(-1)=2.7. The correct answer is b.

To test the stability of a discrete control system with an open loop transfer function, we need to examine the roots of the characteristic equation, which is obtained by setting the denominator of the transfer function equal to zero.

The characteristic equation for the given transfer function G(z) is:

z^2 - 1.2z + 0.2 = 0

We can find the roots of this equation by factoring or using the quadratic formula. In this case, the roots are complex conjugates:

z = 0.6 + 0.4i

z = 0.6 - 0.4i

For a discrete control system, stability is determined by the location of the roots in the complex plane. If the magnitude of all the roots is less than 1, the system is stable. If any root has a magnitude greater than or equal to 1, the system is unstable.

In this case, the magnitude of the roots is less than 1, since:

|0.6 + 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

|0.6 - 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

Therefore, the system is stable.

The correct answer is:

b. Stable with P(1)=1.7 and P(-1)=2.7

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the Pearson product moment correlation measures the linear relationship between two interval- and/or ratio-scaled variables (scale variables) such as those depicted conceptually by scatter diagrams: True.

A measure of the degree and direction of relationship between two variables assessed on at least an interval scale is the Pearson product-moment correlation coefficient, or Pearson's correlation.

If you want to determine whether there is a linear relationship between two quantitative variables, you may use Pearson's correlation. The expectation of a linear relationship between those variables is the sole part of the study hypothesis.

This approach finds the precise amount or degree of correlation between any two variables and tells if there is or is not any correlation between them.

Thus, the given statement is true.

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Answer:

E

Step-by-step explanation:

Irrational means cannot be put into a fraction. Or random repeating decimals is how I remember it.

√48 can be simplified to equal 4√3. √3 cannot be put into fraction form.

Answer:

20 % discount

Step-by-step explanation:

Lilian got 4 dollars off of the original price    (20 - 16 = 4 )

4 / 20  * 100% = 20% off

The percentage of discount that Lillian gets because of sale is 20%.

Percentage is a measurement to find value of given number out of hundred.

Given that,

The price of phone on tag = $20.

Lillian paid for phone = $16.

To find the percent discount on phone,

First find amount of discount = 20 - 16 = $4.

The percentage of discount = (4 / 20) x 100 = 20 %

Lillian gets 20% discount on new mobile.

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Answer:blue

Step-by-step explanation:

Volume of the  rectangular prism is 2048  cm^3

volume of a rectangular prism is V=lwh

where l= length of rectangular prism

w= width of rectangular prism

and

h=height of rectangular prism

now length is 8 times of heigth. Thus l=8h

width is 4 times of the heigth.Thus w=4h

V=24h^3

Given that AG=36

we know from Pythagorean theorem that AG^2=AC^2+CG^2

again AC^2=AB^2+BC^2=(8h)^2+(4h)^2=80h^2

Thus 1296=80h^2+h^2=81h^2

h^2=16

h=4

V=lwh= 8*4*4*4*4 cm^3= 2048  cm^3

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So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

We can use the formula for the area of a triangle, which is A = (1/2)bh, where b is the length of the base and h is the height. In this case, we know that the base has length 2a, so we need to find the height.

Let's call the third side of the triangle, which is not given, b. We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, so we have:

a + 2a > b

3a > b

We can rearrange this to solve for b:

b < 3a

Now, let's use the formula for the area of a triangle:

A = (1/2)bh

We want to maximize A, so we want to maximize h. We know that h is the height of the triangle, which is perpendicular to the base, so it forms a right angle. We can use the Pythagorean theorem to find h in terms of a and b:

\(h^2 = b^2 - a^2\)

We can substitute our inequality for b:

\(h^2 < (3a)^2 - a^2\)

\(h^2 < 8a^2\)

h < √(8\(a^2\))

h < 2 √(2)a

Now we can use the formula for the area of the triangle again:

A = (1/2)bh

A < (1/2)(2 √(2)a)(a)

A < \(a^2\) √(2)

So we have shown that the largest possible area of the triangle is \(a^2,\)which occurs when the third side has length 3a and the height is a.

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Answer:

A

Step-by-step explanation:

Congruent angles are angles that have the same angle.

Those red squares in the corner of ∠DFE and ∠BFC mean they are 90°

I hope this helps you! :)

The value of x is 13.85.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

(7x + 1)° and (6x - 1)° makes a straight angle.

This means,

(7x + 1) + (6x - 1) = 180

7x + 1 + 6x - 1 = 180

13x = 180

x = 180/13

x = 13.85

Thus,

x is 13.85°

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What expression is equivalent to -2 (5x - 4) + 13x

=3x+8

Answer: it’s b

Step-by-step explanation:

Answer: Carrots cost(s) the most per pound

Step-by-step explanation:

The correct option is option (C) .

Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .

Sampling :

Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.

Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.

There are two main types of sampling:

i) probability sampling

ii) Non-probability sampling

A) probability sampling:

It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.

The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.

Probability Samples:

1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.

2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.

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Answer:

1) 9

2)5.85

Step-by-step explanation:

Answer:

Step-by-step explanation:

Mark gave 1.80 tip which was 20% of the meal

1.80...................20%

? ........................100%

the meal was 9 dollars ,  1.80*5=9

second problem

finance charge was 15% which amounts 39.00 dollars

if 15% is 39 dollars

5% is 39/3=13

100% is 13*20=260

260 was the original price

we can estimate the MAD to be around 22.5.

To find the mean of the scores, we add up all the scores and divide by the total number of scores. However, we are given a range of scores rather than the actual scores themselves. To find an estimate of the mean, we can use the midpoint of the range, which is (40 + 85)/2 = 62.5.

                                                   Therefore, we can estimate the mean to be around 62.5.

b. The MAD (mean absolute deviation) measures the average distance of each data point from the mean. Again, we do not have the actual scores, but we can estimate the MAD using the range. The range is 85 - 40 = 45. Half of the range is 22.5.

                                    Therefore, we can estimate the MAD to be around 22.5.

These estimates are rough and assume a uniform distribution of scores within the given range. Without actual data points, we cannot calculate the exact mean and MAD.

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Answer:

52, 60, 68, 76..

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Use the Law of Sines to find a:

Since both a and the angle A are unkowns, we need to find the measure of the angle opposite to the side A first. Notice that two of the interior angles of the triangle are given. Remember that the sum of the internal angles of every triangle must add up to 180º.

Then:

Then, the angle opposite to the side with length a has a measure of 50º.

Isolate a from the equation of the law of sines and replace A=50º to find the length a:

Therefore, to the nearest tenth, the length of a is equal to 44.1cm.