a relation r is called circular if arb and brc imply that cra. if r is an equivalence relation, then would r be circular?

The correct option is that C. Carmen disagreed and said, "No, the answer is 72x^12"

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

It should be noted that when dividing exponents with same base, we will subtract the powers and when multiplying them, we will add the powers.

Here, the study team was discussing how to multiply 6x^10 by 12x^2. Therefore, this will be:

= 72 × x^(10 + 2)

= 72x^12.

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The probability that it is British is 0.6164 if the Venn diagram shows the information about a stamp collection. f = 100 stamps in the collection A = stamps in the 20th century B = British stamps A B. X(X - 6) х 2x + 32 28 A stamp is chosen at random.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

We have:

f = 100 stamps in the collection

A = stamps in the 20th century

B = British stamps

We can make a linear equation to solve for x as the total stamps are 100 in the collection.

\(\rm x(x-6)+x+2x+32= 100\\\\\rm x^2-6x+x+2x+32 = 100\\\\\rm x^2-3x-68 = 0\)

After solving x = 9.88, or x = -6.88

Probability can't be negative so neglecting the negative ones

x = 9.88

The probability that it is British:

\(=\rm \frac{x +2x + 32}{100}\)  

\(=\rm \frac{9.88 +2(9.88) + 32}{100}\)

= 61.64/100

= 0.6164

Thus, the probability that it is British is 0.6164 if the Venn diagram shows the information about a stamp collection. f = 100 stamps in the collection A = stamps in the 20th century B = British stamps A B. X(X - 6) х 2x + 32 28 A stamp is chosen at random.

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Answer:

The 95% confidence interval is  \( 10.91  <  \mu <11.28  \)  

The 99% confidence interval is \( 10.85  <  \mu <11.33  \)  

Step-by-step explanation:

From the question we are told that

    The sample  mean is  \(\= x = 11.09 \ tons\)

     The standard deviation is  \(\sigma = 0.73 \ tons\)

      The sample size is  n =60

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>    \(E = 1.96 *  \frac{ 0.73  }{\sqrt{n60 }\)    

=>    \(E = 0.1847 \)  

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=>    \( 11.09  - 0.1847  <  \mu <11.09  + 0.1847 \)  

=>    \( 10.91  <  \mu <11.28   \)  

From the question we are told the confidence level is  99% , hence the level of significance is    

      \(\alpha = (100 - 99 ) \%\)

=>   \(\alpha = 0.01/tex]

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  2.58 \)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>    \(E = 2.58 *  \frac{ 0.73  }{\sqrt{n60 }\)    

=>    \(E = 0.2431 \)  

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=>    \( 11.09  - 0.2431<  \mu <11.09  + 0.2431 \)  

=>    \( 10.85  <  \mu <11.33  \)  

The confidence limits for the mean of the maximum loads of all cables produced by the company are: for 95%, it is [10.935,11.245]. For 99%, it is [10.87 ,11.309].

Suppose that we have:

Then the margin of error(MOE) is obtained as

Margin of Error = \(MOE = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\)

\(MOE = Z_{\alpha/2}\dfrac{s}{\sqrt{n}}\)

where \(Z_{\alpha/2}\) is critical value of the test statistic at level of significance

The confidence interval for specific level of significance \(\alpha\) is:

\([\overline{x} - |MOE|, \overline{x} + |MOE|]\)

where \(\overline{x}\) is the sample mean.

For this case, we are given that:

Calculating the confidence limits of given confidence level:

The level of significance = \(\alpha = 100 - 95\% = 5\% = 0.05\)

The critical value of Z at this level of significance is \(Z_{\alpha/2} = Z_{0.05/2} = \pm 1.645\)

Thus, the confidence interval is:

\([\overline{x} - |MOE|, \overline{x} + |MOE|] = [11.09 - 1.645 \times \dfrac{0.73}{\sqrt{60}}, 11.09 + 1.645 \times \dfrac{0.73}{\sqrt{60}}]\\\\\approx [11.09 - 0.155, 11.09 + 0.155] = [10.935,11.245]\)

Thus, the confidence interval at 95% is  [10.935,11.245]

The level of significance = \(\alpha = 100 - 99\% = 1\% = 0.01\)

The critical value of Z at this level of significance is \(Z_{\alpha/2} = Z_{0.05/2} \approx \pm 2.33\)

Thus, the confidence interval is:

\([\overline{x} - |MOE|, \overline{x} + |MOE|] = [11.09 - 2.33 \times \dfrac{0.73}{\sqrt{60}}, 11.09 + 2.33 \times \dfrac{0.73}{\sqrt{60}}]\\\\\approx [11.09 - 0.1847, 11.09 + 0.1847] = [10.87 ,11.31]\)

Thus, the confidence interval at 99% is  [10.87 ,11.309]

Thus, the confidence limits for the mean of the maximum loads of all cables produced by the company are: for 95%, it is [10.935,11.245]. For 99%, it is  [10.87 ,11.309].

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Answer:

6.1 inches

Step-by-step explanation:

You need to find the square root of 38 which is 6.1 when rounded to the nearest ten

In the probability variables the pair that are in independent variable is B. C and D

Independent variable is a term used in probability refer to the fact that the probability of one of the events happening do not rely on the other

If two terms considered in probability are say x and y. If the probability of the two variables are independent, it is usually represented using the symbol

Similarly, in the given problem, the probability of C and D are represented with same symbol and this tells that the variable C is independent to variable D

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Answer:

So what's the Question Because to me it looks like something random

Answer:

yes

Step-by-step explanation:

1/4 = 0.25

The graph of the function is attached below.

The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.

Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.

We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.

In the given problem;

The graph of the function f(x) = 1 + x / x² - 1 is attached below;

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Answer:

The answer is f^-1(x)=0^3\(\sqrt{x}\)+2

Step-by-step explanation: Now we just change y back to f(x) and add a 0−1 to write it in inverse notation We begin with f(x)= x 3−2 . To find the inverse of any equation, just switch x and y No, before we do that, I'm going to change the equation. I'm going to rename f(x) to y , just so that I don't have to deal with the parentheses or anything. Now, all I have to do is change what f (x) is called, not it's actual value. Anyways, we have y = x 3 − 2 Now we switch x and y and then solve for y Now we've got x = y 3−2 If we add 2 on both sides we have x + 2 = y 3 Now we just need to get y as simple as possible, which we'll do by cube rooting both sides of the equation. That leaves us with y=0 3√x+2 Now we just change y back to f(x) and add a 0−1 to write it in inverse notation

Answer:

The 2nd,3rd,5th and the 6th

Step-by-step explanation:

got it right on edmentun/plato

Answer: The probability is that you will get one two times.

Step-by-step explanation: The probability of getting a one when you roll a dice is 1/6. 1/6 of 12 is 2.

9514 1404 393

Answer:

Step-by-step explanation:

In order for the total displacement to be zero, the amount of forward displacement must be equal and opposite to the amount of backward displacement. Since the steps are the same length, they must be equal in number.

Half of the 10 steps were forward, and the other half were backward.

  5 steps forward; 5 steps backward.

_____

Additional comment

Math develops from an effort to model the real world. It would probably give you some insight into this problem if you were to physically take some steps to see how many forward and backward you would need to end where you start.

Answer:

4=No

-3=No

2=Yes

0=No

Step-by-step explanation:

enter enter all the factors into the equation and see which one equals -28 on both sides at the end.

Answer:

D

Step-by-step explanation:

The ratios below that are equivalent to 2:1 is 8:4, 10:5 and 6:3. That is options B, C, and E.

To find the ratio of a given two quantities how many times one quantity is greater or smaller than the other.

Therefore in option B, when 8:4 is simplified by division,

8/4 = 2/1 = 2:1

Therefore, in option C, when 10:5 is simplified by division,

10/5 = 2/1 = 2:1

Therefore, in option E, when 6:3 is simplified by division, 6/3 = 2/1 = 2:1

Therefore, the ratios below that are equivalent to 2:1 is 8:4, 10:5 and 6:3.

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Answer:

There were 12 cookies at the start

Step-by-step explanation:

Since Maximo likes to eat 2 cookies per day, after three days, he would have eaten 6 cookies. There are 6 cookies left after 3 days, so 6(amount he ate) + 6(amount of cookies left) is 12.

Answer: ( - 1, - 1) with center (-1, - 4). (x + 1) 2 + (y + 4) 2 = 9

Step-by-step explanation: I hope this is right :)

Answer:

That first part equals 12.40  which is the answer to part B

Now for Part A

B and C equal 12.4

A, D and E equal 11.4

Step-by-step explanation:

Answer:

True mean/population mean

Step-by-step explanation:

The standard error in this case gives an estimate on how far the values observed during the course of the experiment ate likely to be from the true mean/population mean.

Answer:

b .3

Step-by-step explanation:

every thing else is even and if u add them up u will get to 32 eventually

Answer:

B.) 3

Step-by-step explanation:

To do this problem, we should find out what factors can equal 32. So let's start with finding out. This problem is going to require multiplication and division.

Letter A is a multiple of 32, because:

32 ÷ 2 = 16, which means that 16 x 2 = 32.

Because 2 can be divided equally into 32, this answer is wrong.

_________________

Letter C is a multiple of 32, because:

32 ÷ 4 = 8, which means that 8 x 4 = 32.

Because 4 can be divided equally into 32, this answer is also wrong.

_________________

And, because the last answer equaled 8, that means that:

32 ÷ 8 = 4, which means that 4 x 8 = 32.

Which is also wrong.

_________________

This leaves us with 32 ÷ 3 = 10.6666666667. This answer cannot be multiplied evenly into 32, so it is correct.

I hope that this helps.

Answer:

Step-by-step explanation:

The angle of depression is the downward angle the air traffic controller

looks down from in the tower.  It also equals the angle of elevation which is the angle formed by the runway and the line of sight.

With this information you can find the remaining angle:

180 - (90 + 18)

180 - 108 = 72

Let Angle B = 72°

Angle A = 18°

Angle C =90°

We have one side - 140 feet - this is side a - it is across from angle A.

There is a right triangle formed by the runway (side b) the tower, side a, and the line of sight (side c)

Using the law of sines:

sin A/a = sinB/b

sin 18°/a = sin72°/b

.3090/140 = .9510/x

cross multiply and then divide

140 × .9510/.3090

133.14/.3090

430.873 ft

round to a tenth = 430.9 ft

Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.

To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:

Assumptions:

Tax depreciation is straight-line over five years.

Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.

Tax on salvage value is 30% of the difference between salvage value and book value of the investment.

The cost of capital is 12%.

Given:

Initial investment cost = $50,000

Useful life of the equipment = 5 years

To calculate the depreciation expense each year, we divide the initial investment by the useful life:

Depreciation expense per year = Initial investment / Useful life

Depreciation expense per year = $50,000 / 5 = $10,000

Now, let's calculate the book value at the end of each year:

Year 1:

Book value = Initial investment - Depreciation expense per year

Book value \(= $50,000 - $10,000 = $40,000\)

Year 2:

Book value = Initial investment - (2 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (2 \times$10,000) = $30,000\)

Year 3:

Book value = Initial investment - (3 \(\times\) Depreciation expense per year)

Book value = $50,000 - (3 \(\times\) $10,000) = $20,000

Year 4:

Book value = Initial investment - (4 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (4 \times $10,000) = $10,000\)

Year 5:

Book value = Initial investment - (5 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (5 \times $10,000) = $0\)

Based on the assumptions, the salvage value is $10,000 in Year 5.

If the asset is scrapped in Year 4, the salvage value is $15,000.

To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:

Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)

For Year 5:

Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)

For Year 4 (if scrapped):

Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)

Now, let's calculate the after-tax cash flows for each year:

Year 1:

After-tax cash flow = Depreciation expense per year - Tax on salvage value

After-tax cash flow = $10,000 - $0 = $10,000

Year 2:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 3:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 4 (if scrapped):

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $15,000 - $1,500 = $13,500

Year 5:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $10,000 - $3,000 = $7,000

Now, let's calculate the net present value (NPV) using the cost of capital of 12%.

We will discount each year's after-tax cash flow to its present value using the formula:

\(PV = CF / (1 + r)^t\)

Where:

PV = Present value

CF = Cash flow

r = Discount rate (cost of capital)

t = Time period (year)

NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment

Let's calculate the NPV:

PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)

PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)

PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)

PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)

PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)

NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000

NPV = $22,954.24 - $50,000

NPV = -$27,045.76

The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.

Therefore, the investment may not be favorable.

Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.

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The complete question may be like :

Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.

You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.

Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.

Answer:

\(\huge\boxed{6x-7y=21}\)

Step-by-step explanation:

The slope-intercept form of an equation of a line:

\(y=mx+b\)

\(m\) - slope

\(b\) - y-intercept (0, b)

We have:

\(y=\dfrac{2}{3}x-3\to m=\dfrac{2}{3};\ b=-3\)

From answers:

\(6x-7y=21\qquad|-6x\\\\-7y=-6x+21\qquad|:(-7)\\\\y=\dfrac{6}{7}x-3\to m=\dfrac{6}{7};\ \boxed{b=-3}\)

\(-\dfrac{2}{3}x+3y=6\qquad|+\dfrac{2}{3}x\\\\3y=\dfrac{2}{3}x+6\qquad|:3\\\\y=\dfrac{2}{9}x+2\to m=\dfrac{2}{9};\ b=2\)

\(\dfrac{2}{3}x+3y=-3\qquad|-\dfrac{2}{3}x\\\\3y=-\dfrac{2}{3}x-3\qquad|:3\\\\y=-\dfrac{2}{9}x-1\to m=-\dfrac{2}{9};\ b=-1\)

\(x+4y=12\qquad|-x\\\\4y=-x+12\qquad|:4\\\\y=-\dfrac{1}{4}x+3\to m=-\dfrac{1}{4};\ b=3\)

Answer:

6x-7y=21

Step-by-step explanation: :)

The width of the new phone will be 4.37 inches

Two quantities are compared to form a ratio. An equality of two ratios is a proportion. How to format a ratio Analyze the ratio to determine whether it is part to part or part to whole. Calculate the whole and the parts as necessary.

The ratios between the two variables should be considered in order to determine whether a relationship is proportional. The relationship is proportional if the ratio remains constant. The relationship is not proportional if the ratio shifts.

A direct proportion is a relationship where the ratio of the two variables has a fixed value.

A cell phone's initial dimensions were L=1.2 inches and 4.6 inches, respectively.

A new cell phone will be produced with a proportionately larger size than the previous model.

The new phone's length is specified as L'=1.14 inches. 1,2/1.14=1.053 is the lengths to width ratio.

W'=4.6/1.053=4.37 inches should be the new width.

The next phone will be 4.37 inches wide.

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Answer:

I think this may be the answer. (I got this same question on a test so it probably is the same answer)

Commonsense rules should be stated for any numerical answers.

No questions should be misleading.

Questions should be worded in a clear, concise, and unbiased manner.

Since some items might be sensitive information, design a data form that can be filled out anonymously.

Step-by-step explanation:

Answer:

1,296 miles

Step-by-step explanation:

to answer this question, we have to apply the next formula:  

Distance = Speed rate x time

speed rate = 54 miles per hour

time = 24 hours

Replacing with the values given and solving for D (distance)

D = 54 mph x 24 h = 1,296 m

The car traveled 1,296 miles

Hope this helped! :)

The solution to the simultaneous equations is x = 2 and y = -4. To obtain these values,  18 = 7x - y  is rearranged to y = 7x - 18, and then substituted into 3x + y = 2  to obtain the value of x and y.

Rearranging equation (1) to make y the subject

18 = 7x - y

Add y to both sides

18 + y = 7x

Subtract 18 from both sides

y = 7x - 18

Using the answer to part a) to solve the simultaneous equations

Substitute the expression for y from equation (1) into equation (2)

3x + (7x - 18) = 2

Simplify

10x - 18 = 2

Add 18 to both sides

10x = 20

Divide both sides by 10

x = 2

Substitute x = 2 into equation (1) to find y

18 = 7(2) - y

18 = 14 - y

Subtract 14 from both sides

4 = -y

Multiply both sides by -1

-4 = y

Therefore, the solution to the simultaneous equations is x = 2 and y = -4.

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Step-by-step explanation:

48 hope this helps you out

Answer:

452.4 feet3

452.4 feet

3