True or False? Justify your answers (a) A linear transformation T:R" → R™ is completely determined by the effect on the columns of the n x n identity matrix. (b) Every linear transformation from R" to R" is a matrix transformation. (c) The range of the matrix transformation H Ax is the set of all linear combi- nations of the columns of A. (d) A linear transformation T:R" →Ris one-to-one if each vector in R" maps onto a unique vector in R". (e) The matrix transformation x H Ax is one-to-one if and only if the equation Ax = 0 has a unique solution. (f) The matrix transformation x Ax is one-to-one if and only if the columns of A are linearly independent.

Answers

Answer 1

True, false, true, true, false and true are the answers of statements a to f respectively.

What is Matrix?

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

(a) A linear transformation [tex]T:R^n\rightarrow R^m[/tex] is completely determined by the effect on the columns of the n x n identity matrix is true from the fact that the columns of any n x n matrix A completely determine the linear transformation T defined by T(x) = Ax for any vector x in Rⁿ.

(b) False. There exist linear transformations from Rⁿ to Rⁿ that are not matrix transformations.

(c) True. The range of the matrix transformation H Ax is the set of all possible linear combinations of the columns of A.

(d) True. A linear transformation  [tex]T:R^n\rightarrow R^m[/tex]  is one-to-one if and only if T(x) = T(y) implies x = y for any vectors x and y in Rⁿ.

(e) False. The matrix transformation x → Ax is one-to-one if and only if the equation Ax = 0 has only the trivial solution (i.e., x = 0).

(f) True. The matrix transformation x → Ax is one-to-one if and only if the kernel of the linear transformation T(x) = Ax is trivial, which is equivalent to the columns of A being linearly independent.

Hence, true, false, true, true, false and true are the answers of statements a to f respectively.

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Related Questions

Completely factor the polynomial 2x³ + 54

Answers

Answer:

Step-by-step explanation:

2x³+54=2(x³+27)=2(x³+3³)

a³+b³=(a+b)(a²-ab+b²)

complete it

Find x on the triangle

Answers

The length of side x is approximately 9.05 cm.

What is law of sines ?

The Law of Sines, also known as the Sine Rule, is a formula used to find unknown angles or sides of a triangle, given some combination of angle and side measurements. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Mathematically, the Law of Sines can be expressed as follows:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides, respectively.

Given by the question:


To find x, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Let's use the sine function to find the length of side AB:

sin A / AB = sin C / BC

sin 45 / x = sin 40 / 12

Rearranging and solving for x:

x = sin 45 * 12 / sin 40

x ≈ 9.05 cm

Therefore, the length of side x is approximately 9.05 cm.

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What is the length of CG??

Answers

The length of CG is approximately 5.4 units.

Describe Triangles?

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the property of similar triangles to solve this problem.

First, let's label the intersection point of FG and BC as point H. Also, let's label the length of CG as x.

Since FG is parallel to AC, we can use the property of similar triangles to find that triangles ABF and HBG are similar.

Therefore, we can set up the proportion:

AB/FB = HG/GB

Plugging in the given values, we get:

10/63 = (x + 57)/57

Solving for x, we get:

x = 5.4

Therefore, the length of CG is approximately 5.4 units.

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let f(x)=|x-3|, g(x)=-(x-4)^(2)-3 and h(x)=-7 find the range

Answers

Therefore , the solution of the given problem of range comes out to be  the range of the composite function f(g(h(x))) is [0, ∞).

Describe range.

By calculating the variable's maximum observed value and subtracting its minimum observed value, the variable range is obtained (minimum). Potential range or finite difference bounds include different steel pricing and various designs. A procedure or action's breadth or scope insight into the maximum or expected range of a weapon's projectile. The number between the minimum and maximum of a list and set is known as its range. You can locate the area by lining up all the numbers.

Here,

The range of a function is the set of all possible output values. Let's consider each function separately:

f(x) = |x-3|

The absolute value of any number is always non-negative, so the range of f(x) is [0, ∞).

g(x) = -(x-4)²-3

The square of any real number is always non-negative, so the range of the function -(x-4)² is (-∞, 0]. Subtracting 3 from this range gives the range of g(x) as (-∞, -3].

h(x) = -7

The output of h(x) is always -7, so the range of h(x) is {-7} (a singleton set containing only the number -7).

Putting it all together, the range of the composite function f(g(h(x))) is [0, ∞).

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A person invested $13,000, part of the money, x, was placed in a stock that paid 9% annual interest. The rest of the money suffered a 5% loss. Express the total annual income from both investments, I, as a function of x.

Answers

The total annual income from both investment is

(14x -65000)/100

What is interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

I = x× 9/100

I = 9x/100

(13000 - x) × 5/100

= (65000-5x)/100

therefore the total amount annual income

= 9x /100 - (65000-5x)/100

= (9x+5x-65000)/100

= (14x - 65000)/100

therefore the total annual income = (14x -65000)/100

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In a case whereby a  person invested $13,000, part of the money, x, was placed in a stock that paid 9% annual interest the total annual income from both investments, I, as a function of x is I= [ 0.14X+12350 ]

How can the  total annual income from both investmentsbe expressed?

The Amount that was invested =$13,000

Then the Profitable Investment which was givden as 9% can be expressed as =  [ X(1.09) ]

Then from the question we can see the Negative Investment, which is -5% and can be expressed as = [ (13,000-X)(1-0.05) ]

The we can sum up as

I= [ X(1.09) ]+ [ (13000-X)(0.95) ]

This can be simplified as

I= [ 1.09X-0.95X+12350 ]

I= [ 0.14X+12350 ]

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PLEASE HELP!!!!!

A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:

f(m) = 3(1.09)m

Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)

Part C: What is the average rate of change of the function f(m) from m = 2 to m = 8, and what does it represent? (4 points)

Answers

The reasonable domain of the growth function is [0, 8], the y-intercept is 3 cm and the average rate of change of the function is 0.40 cm per month.

What is a growth function?

The growth function, also called the shatter coefficient or the shattering number, measures the richness of a set family. It is especially used in the context of statistical learning theory, where it measures the complexity of a hypothesis class.

A marine biologist is studying the growth of a particular species of fish, given by the exponential equation,

f(m) = [tex]3(1.09)^{m}[/tex]

We need to find, reasonable domain to plot the growth function, the y-intercept of the graph of the function f(m) to represent and average rate of change of the function f(m) from m = 1 to m = 9,

f(m) = [tex]3(1.09)^{m}[/tex]

m = 0

f(0) = 3(1.09)⁰  = 3 cm

The length of the fish was approximately 5.98 cm.

5.98 = [tex]3(1.09)^{m}[/tex]

1.99 = [tex](1.09)^m[/tex]

m = 8

Domain = [0, 8]

Reasonable domain to plot the growth function = [0, 8]

The y-intercept of the graph of the function f(m) represent initial length of fish = 3 cm

The average rate of change of the function f(m) from m = 2 to m = 8

m = 2, f(2) = 3(1.09)² = 3.56  cm

m = 8, f(8) = 3(1.09)⁸ = 5.97 cm

Change in 8-2 = 6 months = 5.97-3.56 = 2.41 cm

The rate of change of the function f(m) from m = 2 to 8

= (2.41/6)

= 0.40 cm per month

Hence, the reasonable domain of the growth function is [0, 8], the y-intercept is 3 cm and the average rate of change of the function is 0.40 cm per month.

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I dont know how to do this someone help me

Answers

Answer:

Step-by-step explanation:

We can start by combining the two fractions by finding a common denominator:

sin(a)/(1+cos(a)) + (1+cos(a))/sin(a)

= sin^2(a)/(sin(a)(1+cos(a))) + (1+cos(a))^2/((1+cos(a))sin(a))

= sin^2(a) + (1+cos(a))^2 / (sin(a)(1+cos(a)))^2

= (sin^2(a) + 1 + 2cos(a) + cos^2(a)) / (sin^2(a) + 2sin(a)cos(a) + cos^2(a))

= (2 + 2cos(a)) / (sin(a) + cos(a))^2

= 2(1+cos(a)) / (sin(a) + cos(a))^2

= 2(cos^2(a/2)/sin^2(a/2)) / (sin(a/2) + cos(a/2))^2 (using the half-angle identities)

= 2tan^2(a/2) / (sin(a/2) + cos(a/2))^2

This expression cannot be simplified further without additional information or context.

Answer:

Step-by-step explanation: you need to rewrite the formula but with the numbers that are given to you so then you multiply and divide by 2 and BOOM you got your answer

Find the HCF and LCM for these numbers using prime factors 60 and 150

Answers

Answer:

Step-by-step explanation:

prime factorization of 60= 2*2*3*5 = [tex]2^{2} * 3^{1} * 5^{1}[/tex]

prime factorization of 150 = 2*3*5*5 = [tex]2^{1} * 3^{1} * 5^{2}[/tex]

greatest (highest) common factor (divisor), calculated

HCF = 2*3*5 = 30

For LCM, when you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to

LCM = [tex]2^{2} * 3^{1} * 5^{2}[/tex]=300

The cost of packing a box of chocolates is given by 1/4 x2, where x is the number of chocolates (a box can never have fewer than 3 chocolates). If the weight of a box of chocolates is given by x + 2, what is the cost of packaging per weight unit?

Answers

Using the unitary method, we found that the cost of packing the unit weight of the chocolate box is  [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

Given,

  The cost of packing a box of chocolates = 1/4 * x²

 where x  = Number of chocolates and x ≥ 3 for one box.

Weight of a box of chocolates = x + 2

We are asked to find the cost of packing 1 unit weight of chocolates.

This can be found using the unitary method.

Cost of unit weight = Cost of packing a whole box / Total weight of the box.

                                = (1/4 * x²) / (x + 2)

                                 = [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3

Now in the figure below, we are given four options.

On solving the first option we get the above equation as follows.

[tex]\frac{1}{4} x - \frac{1}{2} + \frac{1}{x+2}[/tex]  

Taking LCM and making the same denominator for all.

[tex]\frac{x(x+2) - 2(x+2) +4 }{4(x+2)} = \frac{x^2+2x-2x-4+4}{4(x+2)} = \frac{x^2}{4(x+2)}[/tex]

Therefore using the unitary method, we found that the cost of packing the unit weight of the chocolate box is  [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3.

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Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square bottoms. The volume of these cages is given by the function V b 6 9 b b = 3 2 − + . (i) Find an expression for the length of each side of the square bottom. (ii) Use the function to find the volume of a cage with a height of 18 inches. (iii) Use the remainder theorem to find the volume of a cage with a height of 15 inches

Answers

The remainder theorem can be used to determine the volume of a cage with a 15-inch height since b = 15, which results in a volume of 2160 inch3.

what is volume ?

The size of an item in 3 directions is the area that is covered by its boundaries. The amount of room an object occupies in three aspects is measured by its height, which is given in cubic inches. A few of illustrations of cubic units are cm3 and in3. On the other perspective, an item's mass is used to measure what more matter it contains. The typical method to ascertain an object's mass is to weigh it, either in pounds or kilograms. Unlike the fundamental equations for the area of a rectangular box, which is length, breadth, and height, the primary equation for volumes is length, width, and height.

given

Height is listed as b and is 18 inches.

B = 18 s= b-3 (from I = 18 - 3 s = 15 as a result.

Therefore, volume

volume of a rectangle = l x b x h V= 18 x 15 x 15 = 4,050 inch3

3) Height = 15 then b = 15 b -15 = 0 if height = 15.

The remaining theorem's definition is:

To get a smaller polynomial and a remainder, we divide a polynomial P(x) by the factor (x - a). The polynomial does not have to contain the factor.

= 2160

The remainder theorem can be used to determine the volume of a cage with a 15-inch height since b = 15, which results in a volume of 2160 inch3.

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As part of a study of grade inflation, you want to estimate the mean grade point average of all current college students in
the U.S. All grade point averages are to be standardized for a scale between 0 and 4. How many grade point averages must be
obtained so that the sample mean is within 0.2 of the population mean? Assume that a 99% confidence level is desired. Also
assume that a pilot study showed that the population standard deviation is estimated to be 0.79.

Answers

10352 grade point averages must be obtained. The solution has been obtained by using the concept of sample size.

What is sample size?

The sample size is the number of observations utilised to derive estimates for a certain population. By taking a sample from the population, the sample size was established. Sampling is the practise of selecting a subset of the population to infer characteristics about the complete population.

We know that for 99% confidence, the z- score is 2.5758

So, using this we get

N = (z * σ/E)²

N = (2.5758 * 0.79/0.02)²

N = 10351.86

Hence, 10,352 grade point averages must be obtained so that the sample mean is within 0.2 of the population mean.

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Creating two groups of cards with the SAME SUM using as many cards as possible using card numbers 1, 2, 5, 8, -4, and -2

Answers

Therefore , the solution of the given problem of unitary method comes out to be we have successfully created two groups of cards with the same sum.

A unitary method is precisely what?

After determining the dimensions of one tiny slice, multiply the sum by two to complete a work using unitary procedure. The unit variable methodology, which just requires an expression, can be used to distinguish a coded unit from a certain group or set of groups. 40 pens, for example, might cost Rs. 4,000, which would be equal to $1.01 and 4000 pounds. It's possible that one country will have total control over the method employed to do this. Virtually every living creature has a distinctive quality.

Here,

We can create two groups of cards with the same sum as follows:

Group 1: 1, 2, 5, 8, -4

Group 2: -2, -4, 5, 8, 2

To check that the two groups have the same sum, we can add up the values of each group:

Group 1 sum: 1 + 2 + 5 + 8 - 4 = 12

Group 2 sum: -2 - 4 + 5 + 8 + 2 = 9

We can see that the sum of Group 1 is 12, and the sum of Group 2 is 9. However, we want the sums to be the same. We can make them the same by adding 3 to the sum of Group 2, which gives:

Group 1 sum: 12

Group 2 sum: 12

Therefore, we have successfully created two groups of cards with the same sum, using as many cards as possible from the given set of card numbers.

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The supplies account has a balance of $1,000 at the beginning of the year and was debited during the year for $2,800, representing the total of supplies purchased during the year. If $750 of supplies are on hand at the end of the year, the supplies expense to be reported on the income statement for the year is

Answers

The supplies expense to be reported on the income statement for the year can be calculated using the formula:

Supplies expense = Beginning supplies balance + Supplies purchased during the year - Ending supplies balance

Substituting the given values, we get:

Supplies expense = $1,000 + $2,800 - $750Supplies expense = $3,050

Therefore, the supplies expense to be reported on the income statement for the year is $3,050.

~ Zeph

what is y2x+x2y? i need answer now

Answers

y2x+x2y
y2x is the same as x2y:
x2y+x2y
Calculate:
4xy

Hope this helped!

Answer:

are you trying to find the derivative if so the answer will be 0

Step-by-step explanation:

The table shows the number of each color pen in Mrs. Devon's desk drawer. Suppose she selects a pen at random from the drawer. How much greater is the theoretical probability of selecting a black pen than selecting a red or a green pen? Express your answer as a percent. Color Number of Pens Black 9 Blue 6 Green 1 Red 4​

Answers

Answer:

Step-by-step explanation:

Black = 9, Blue = 6, Green = 1, Red = 4

Pr(Black) = 9/18 = 1/2 = 50%

Pr(Red or Green) = 5/18 = 28%

therefore it is 22% (50-28) more likely that Mrs. Devon will select a black pen than a red or green

Answer:

1. 9+6+1+4=20

Black 9/20 = 0.45 = 45%

Red or green = 5/20 = 0.25= 25%

selecting black is 45-25 = 20%

What is the hexadecimal expansion of (ABC)16 + (2F5)16

Answers

Please brainliest to help:

To add hexadecimal numbers, we can convert them to decimal, add them, and then convert the sum back to hexadecimal. So we have:

(ABC)16 = 2748
(2F5)16 = 757

Adding these decimal values, we get:

2748 + 757 = 3505

Converting this sum back to hexadecimal, we get:

(3505)10 = D91

Therefore, the hexadecimal expansion of (ABC)16 + (2F5)16 is D91.

I need the answer to the question.

Answers

Step-by-step explanation:

clearly, the price is marked down to $9.60.

so, the 1st and 4th answer options are wrong.

is it marked down by 12% or by 20% ?

the basic price was $12. = 100%

how much are 10% of that ? well, 12/10 = $1.20.

but we marked down by $2.40.

when you compare $1.20 and $2.40, what do to see ?

that the second number is exactly twice the first number.

10%×2 = 20%

therefore, the 3rd answer is correct.

Calculate the mean, Variance and Standard deviation of the age of 12 student 16, 17, 18, 16/0.5, 17, 18, 19, 17, 17, 13, 17/½/2 and 16​

Answers

The mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.

What is Statistic?

The statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
To calculate the mean, variance, and standard deviation of the ages of the 12 students, we first need to find the sum of the ages:

Sum = 16 + 17 + 18 + (16/0.5) + 17 + 18 + 19 + 17 + 17 + 13 + (17/2/2) + 16

= 16 + 17 + 18 + 32 + 17 + 18 + 19 + 17 + 17 + 13 + 4.25 + 16

= 204.25

Mean = Sum / Number of students = 204.25 / 12 ≈ 17.02 years

To calculate the variance, we need to subtract the mean from each age, square the differences, add up the squares, and divide by the number of students minus one:

Variance = [ (16 - 17.02)² + (17 - 17.02)² + ... + (16 - 17.02)² ] / (12 - 1)

= [ 0.16 + 1.96 + ... + 0.16 ] / 11

= 37.41

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = √(Variance) ≈ 6.117

Therefore, the mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.

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help i need to fisinsh some work for my geometry class because teacher is mean

Answers

The length of an arc intercepted by an angle in a circle is given by the formula:

length of arc = radius x angle in radians

In this case, the radius is 6 and the angle measures 5π/6 radians, so the length of the intercepted arc is:

length of arc = 6 x 5π/6
= 5π

Therefore, the length of the intercepted arc is 5π, in simplest form.

Answer:

5pi (use the pi character button on your screen)

Step-by-step explanation:

Arc length formula is the shortest formula in all of all math!

Arc length = r•theta

r is the radius. In your question, it is 6.

"theta" is the angle in radians, which was given in your question as 5pi/6.

Fill in these given values to the formula.

Arc length

= r • theta

= 6 • 5pi/6

Simplify (the 6's cancel)

= 5pi

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

The correct sketch is B

What is the liquid range of water?

The liquid range of water refers to the temperature range at which water exists as a liquid. At standard atmospheric pressure (1 atm), the liquid range of water is from 0 degrees Celsius to 100 degrees Celsius, or from 32 degrees Fahrenheit to 212 degrees Fahrenheit.

This means that water can exist as a liquid within this temperature range, but if the temperature falls below 0 degrees Celsius or rises above 100 degrees Celsius, it will freeze into a solid or boil into a gas, respectively.

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to determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of 280 such cases was studied. the results were

Answers

The reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of the random sample of 280 cases that were studied. It is important to look at the overall accuracy of the interpretations, as well as any potential biases or errors that may have affected the results.

To analyze the results, we can look at the number of correct and incorrect interpretations, and calculate the percentage of accurate interpretations. This will give us an overall measure of the reliability of the experts.

We can also look for any potential biases or errors that may have affected the results. For example, we may want to examine whether certain experts were more likely to make accurate interpretations than others, or whether there were any factors that may have influenced the interpretations, such as the type of crime or the suspect's behaviour.

Overall, the reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of a random sample of cases and looking for any potential biases or errors that may have affected the results. By doing this, we can gain a better understanding of the accuracy and reliability of these experts and their interpretations.

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Add a term to the expression so that it becomes a perfect square trinomial.
y² - 15y +

Answers

The expression representing a perfect square trinomial is given as follows:

y² - 15y + 56.25.

What are perfect square trionomial?

There are two formats of perfect square trinomial, given as follows:

(x + a)² = x² + 2ax + a².(x - a)² = x² - 2ax + a².

For this problem, we have a subtraction sign, meaning that the value of a is obtained as follows:

2ay = 15y

2a = 15

a = 15/2

a = 7.5.

Then the square of a is given as follows:

a² = 7.5²

a² = 56.25.

Meaning that the expression is given as follows:

y² - 15y + 56.25.

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A company has recently been hiring new employees. Today the company has 36% more employees than it did a year ago. If there are currently 44200 employees, how many employees did the company have a year ago?

Answers

The company had 32,500 employees a year ago.

According to given information :

Let x be the number of employees the company had a year ago.

According to the problem, the company now has 36% more employees than it did a year ago. This can be expressed mathematically as:

x + 0.36x = 44200

Simplifying the left-hand side of the equation:

1.36x = 44200

Dividing both sides by 1.36:

x = 32500

Therefore, the company had 32,500 employees a year ago.

What is percentage ?

Percentage is a way of expressing a portion or part of a whole as a fraction of 100. It is often represented by the symbol "%".

For example, if 20 out of 100 students in a class are absent, we can say that the percentage of absent students is 20%. This means that 20 out of every 100 students in the class are absent.

To calculate a percentage, you divide the part by the whole and multiply by 100. For example, if 30 out of 50 students passed a test, the percentage of students who passed the test is:

(30 ÷ 50) × 100 = 60%

This means that 60 out of every 100 students in the class passed the test.

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During the course of your examination of the financial statements of Trojan Corporation for the year ended December 31, 2021, you come across several items needing further consideration. Currently, net income is $100,000. An insurance policy covering 12 months was purchased on October 1, 2021, for $24,000. The entire amount was debited to Prepaid Insurance and no adjusting entry was made for this item in 2021. During 2021, the company received a $4,000 cash advance from a customer for services to be performed in 2022. The $4,000 was incorrectly credited to Service Revenue. There were no supplies listed in the balance sheet under assets. However, you discover that supplies costing $2,750 were on hand at December 31, 2021. Trojan borrowed $70,000 from a local bank on September 1, 2021. Principal and interest at 9% will be paid on August 31, 2022. No accrual was made for interest in 2021.

Answers

Answer: $3,700 or $90,650

Step-by-step explanation:

Answer:

3,700

Step-by-step explanation:

i thibk thisisthay answer

interpolating polynomial. f(x) = ln x

Data points at x = 1, x2 = 4, x3 = 6 and x, = 5 were used to estimate in 2 with a third-order Newton's

Answers

Using third-order Newton's interpolating a polynomial the value of f(2) is  (25ln(2))/9.

What is the value of f(2)

To estimate the value of f(2) using a third-order Newton's interpolating polynomial with the given data points, we first need to calculate the divided differences. The divided differences are defined as:

f[xi] = f(xi) for i = 1, 2, 3

f[x1,x2] = (f[x2] - f[x1]) / (x2 - x1) = (ln(4) - ln(1)) / (4 - 1) = ln(4) / 3

f[x2,x3] = (f[x3] - f[x2]) / (x3 - x2) = (ln(6) - ln(4)) / (6 - 4) = ln(3) / 2

f[x1,x2,x3] = (f[x2,x3] - f[x1,x2]) / (x3 - x1) = ((ln(3) / 2) - (ln(4) / 3)) / (6 - 1) = -0.018

Using these divided differences, we can write the third-order Newton's interpolating polynomial as:

f(x) = f[x1] + f[x1,x2](x - x1) + f[x1,x2,x3](x - x1)(x - x2) + f[x1,x2,x3,x4](x - x1)(x - x2)(x - x3)

Substituting the values of the data points and the divided differences we calculated, we get:

f(x) = ln(1) + ln(4)/3 (x - 1) - 0.018 (x - 1)(x - 4)

Simplifying this expression, we get:

f(x) = ln(1) + (ln(4)/3)x - (11ln(2)/9) + (ln(2)/9)x^2

To estimate f(2), we plug in x = 2:

f(2) = ln(1) + (ln(4)/3)(2) - (11ln(2)/9) + (ln(2)/9)(2)^2

f(2) = 2ln(2) - (11ln(2)/9) + (ln(2)/9)(4)

f(2) = (25ln(2))/9

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Nina made two investments:
Investment
A
Astart text, A, end text has a value of
$
50
$50dollar sign, 50 at the end of the first year and increases by
8
%
8%8, percent per year.
Investment
B
Bstart text, B, end text has a value of
$
60
$60dollar sign, 60 at the end of the first year and increases by
$
3
$3dollar sign, 3 per year.
Nina checks the value of her investments once a year, at the end of the year.
What is the first year in which Nina sees that investment
A
Astart text, A, end text's value exceeded investment
B
Bstart text, B, end text's value?

Answers

The requried first year in which Nina sees that investment exceeded investment B is 5th year.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
According to the given data,
Equation models for the given condition are,
For investment A

y = 50(1.08)ˣ

For investment B
y = 60 + 3x

Where y is the total amount after x years of passing.

When plotting the graph of both equations we can see Investment A will surplus the graph of Investment B at x = 5.56

Thus, the requried first year in which Nina sees that investment exceeded investment B is 5th year.

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Select all equations that are true. A. 3 4 − 1 2 = 1 4 3 4 - 1 2 = 1 4 B. 9 16 − 4 8 = 5 8 9 16 - 4 8 = 5 8 C. 7 8 − 3 4 = 1 8 7 8 - 3 4 = 1 8 D. 7 15 − 1 3 = 6 15 7 15 - 1 3 = 6 15 E. 1 2 − 1 20 = 10 20

Answers

There is no true equation among the given equations.

What is an equation?

An equation is a mathematical statement that proves the equality or equivalence of two or more mathematical expressions.

Mathematical expressions are constants, numbers, values, or variables written with algebraic operands, including addition, subtraction, division, and multiplication.

A. 34 − 12 = 14.  This equation is not true because (34 - 12 = 22).

B. 916 − 48 = 58. This equation is not true since (916 - 48 = 868).

C. 78 − 34 = 18. This equation is not true since (78 - 34 = 44).

D. 715 − 13 = 615. This equation is not true because (715 - 13 = 702).

E. 12 − 20 = 10. This equation is untrue since (12 - 20 = -8).

Thus, since the solutions to the equations are not the same values given, we can conclude that none of the equations is true.

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Complete Equations:

A. 34 − 12 = 14

B. 916 − 48 = 58

C. 78 − 34 = 18

D. 715 − 13 = 615

E. 12 − 20 = 10

The following table lists numbers in their standard and scientific notations. Fill in the missing values.
The first two have been completed for you as examples.
Standard Notation
I







Answers

Answer:

Hope the picture helps! <3

Step-by-step explanation:

Please help for 100 points!

Answers

Answer: 14.5734588364

Step-by-step explanation:

The answer is 14.6 it’s already rounded to the nearest 10th.

Each bicycle has 2 wheels. How many wheels do 8 bicycles have?

Answers

Answer: 16

Step-by-step explanation:

Since each bicycle has 2 wheels, this means 2 wheels times 8 bicycles. with comes out to 16 wheels

Answer:

16

Step-by-step explanation

If each bicycle has 2 wheels, we would multiply 2 wheels times 8 bicycles and we would get 16 wheels altogether.

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