a local retail company wants to estimate the mean amount spent by customers. their store's budget limits the number of surveys to 225. what is their maximum error of the estimated mean amount spent for a 99% level of confidence and an estimated standard deviation of $10.00? 1% $1.72 $10.00 $1.00

it would be the last one bc it makes a little sense i guess

Answer:

\(A=\) $\(966.306\)

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

\(A=P(1+\frac{r}{n})^n^{t}\)

where

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

\(t= 5\) \(years\)

\(P=\) $\(600.00\)  

\(r=10\)% \(=10/100=0.10\)

\(n=1\)

substitute in the formula above

\(A=600(1+\frac{0.10}{1})^1^*^5\)

\(A=600(1.10)^5\)  

\(A=\) $\(966.306\)

Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).

Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.

Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).

Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.

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Answer:

132in²

Step-by-step explanation:

Answer:

$9.61

Step-by-step explanation:

326.74 divided by 34 = 9.61

Same as if you did 9.61 x 34 it would equal 326.74

Answer:

3 5,7,9,11,13,16,17 19,21,23,25,27,29

Wouldnt the answer be anything above 12? Because if Y is unknown, and you're taking 2 away from it, and it still has to be greater than 10, then it should be anything above 12. Unless it's saying that the number is greater than 10, and you are just taking away 2 from a number and it doesn't have to be greater than 10.

Answer:

The distance would be √85

Step-by-step explanation:

Answer:

The item that attaches to the bowstring to improve accuracy by giving a consistent anchor point each time the bowstring is drawn is called a "release aid" or "bow release".

The line integral of a vector around the perimeter of a rectangle with corners (x0, y0), (x1, y1), (x2, y2), and (x3, y3) traversed in that order.

What is perimeter?

A closed path which encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose a yard as well as garden is called the perimeter. How far a wheel or circle will roll inside one revolution is determined by its circumference, or perimeter.

To find the perimeter by adding up the side lengths of various shapes.

The line integral starts from the first corner to the last corner of the rectangle and it shows that both the x and y values.

(x0,y0)-first corner point
(x1,y1)-second corner point
(x2,y2)-third corner point
(x3,y3)-four corner point

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Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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According to the proof, equal difference property is not satisfied by the function f(x).

There are four binary variables, x1, x2, x3, and x4.

The binary format is now converted to hexadecimal format, and the values are stored as A, B, C, and D, accordingly.

Convert every four bits of a binary value to a hexadecimal value.

ex: Split into 4 bits: x1 = 00000000 = 0000 0000 = 0 0 (convert the 4 bits to hex)

A = 00 ( hexadecimal of x1 )

B= 01 ( hexadecimal of x2 ) ( hexadecimal of x2 )

C=02 ( hexadecimal of x3 ) ( hexadecimal of x3 )

D=03 ( hexadecimal of x4 ) ( hexadecimal of x4 )

The function in question is f(x) = BS(x), which means that it performs byte alternation on the input x.

This means that f(x1) = 63, f(x2) = 7C, f(x3) = 77, and f(x4) = 7B.

We must now demonstrate that x1 xor x2 equals x3 xor x4 and that f(x1) xor f(x2) does not equal f(x3) xor f(x4) (x4).

If x1 xor x2 = 00, then xor 02 = 02 xor 01 = 01 x3 xor x4 03 = 01 So, x1 Equals x2 OR x3 OR x4 In the present, f(x1) xor f(x2) = 63 xor 7C = 1f f(x3) xor f(x4) = 77 xor 7B = 0C Due to f(x1) xor f(x2) not being equivalent to f(x3) xor f(x4).

Hence, the equal difference property is not satisfied by the function f(x), which is the Byte Substitution (BS) function of AES, according to the proof.

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question: An investment of $100 is now valued at $149.18 the interest rate is 8% per year, compounded continuously about how long has the money been invested

Answer:

5.2 years

Step-by-step explanation:

Applying

A = P(1+R/100)ⁿ.......................... Equation 1

Where A = amount, P = principle, R = rate, n = time.

From the question,

Given: A = $149.18, P = $100, R = 8%

Substitute these values into equation 1 and solve for n

149.18 = 100(1+8/100)ⁿ

149.18/100 = (1+8/100)ⁿ

1.4918 = (1+0.08)ⁿ

1.4918 = (1.08)ⁿ

Taking the Logarithm of both side

Log(1.4918) = Log(1.08)ⁿ

Log(1.4918) = nLog(1.08)

n = Log(1.4918)/Log(1.08)

n = 0.1737/0.0334

n = 5.2 years.

Answer:

\(6n - 6 = 36 \: d. - - - addition \:property \: of \: equality \\

6n = 42 \: e. - - - division \: property \: of \: equality \: \\ \)

Answer:

142.5 ft^2

Step-by-step explanation:

You need to calculate each figure separately

area of the first rectangle = 5 x 4 = 20

area of the second rectangle = (5+6)x(4) = 44

area of 1/4 circle =  1/4π(10^2) = (1/4) x 3.14 x 100 = 78.5

area of figure: 78.5 + 20 + 44 = 142.5

Answer:

To find the area of this figure, we need to first determine its shape. The lengths given do not form a clear shape, so we need more information to determine the shape.

Assuming that the shape is a trapezoid with the bases of 6ft and 10ft, and a height of 5ft, we can use the formula for the area of a trapezoid:

Area = (b1 + b2) / 2 * h

where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.

Plugging in the values, we get:

Area = (6ft + 10ft) / 2 * 5ft

Area = 8ft * 5ft

Area = 40 sq ft

Area ≈ 3.73 sq m (rounded to two decimal places)

Therefore, the area of this figure is approximately 3.73 square meters.

(If it wasn't in decimals, it would be 40 square feet.)

Hopefully this helped! I'm sorry if it's wrong. If you need more help, ask me! :]

Answer:

7/9

Step-by-step explanation:

To add fractions, you have to have like denominators. First find the LCM (Least Common Multiple) of both denominators. That is 9. The second fraction already has a denominator of 9, so leave it as is. The first fraction doesn't so what will happen is you will be converting it into a fraction with a denominator of 9. Multiply the denominator by 3 to get 9. Then multiply the top by 3 because whatever you do to the bottom you do the top. You will then get 3/9. 3/9+4/9 is equal to 7/9 because you just add the numerators, but keep the denominators the same.

Answer:

C

Step-by-step explanation:

Sum of angles in triangle is 180 degrees.

28°+58°+ x= 180 degrees

x=94 degrees

sum of angles on a straight line is 180 degrees

thus, 94 degrees + ? = 180 degrees

?= 86 degrees

angle TGF is 86 degrees

Answer and Explanation:

Given:

Let's go ahead and chose different values of x and corresponding values of y;

When x = -2;

When x = -1;

When x = 0;

When x = 1;

When x = 5;

With the above values, we can go ahead and graph the function as seen below;

The domain of a function is the set of possible input values(x-values) for which the function is defined. On a graph, it is the set of x-values from left to right.

Looking at the given graph, we can see that the domain is;

The range of a function is the set of possible output values(y-values). It is the set of y-values from the bottom to the top of the graph.

Looking at the given graph, we can see that the range is;

The order should include: 32 chairs, 24 monitors, 14 desks, 25 company orientation bulletins, and 18 hard drives.

To determine what should be ordered based on the given instructions and information provided by the office manager, let's break down each requirement:

1- Number of Chairs: The order for chairs should be based on the increase in headcount. Given that 17 people have left the company and 33 have joined in the past 60 days, the net increase is 33 - 17 = 16 people. Therefore, the number of chairs to be ordered should be double this increase, which is 2 * 16 = 32 chairs.

2- Number of Monitors: The IT department has requested 12 monitors. According to the instructions, we need to order double the number requested. Thus, the number of monitors to be ordered is 2 * 12 = 24 monitors.

3- Number of Desks: The accounting department has requested 40 desks. We are required to order 1/3 of the desks requested, rounding up if necessary. 1/3 of 40 is approximately 13.33, which rounds up to 14 desks.

4- Number of Company Orientation Bulletins: The administrative department requested 20 company orientation bulletins. We need to order 1/4 more than what they requested, which is 1/4 * 20 = 5 additional bulletins. Therefore, the total number of bulletins to be ordered is 20 + 5 = 25.

Number of Hard Drives: The instructions state that 18 hard drives should be ordered.

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Answer and work down below. Let me know if you have any questions

The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.

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We need to demonstrate that its opposite sides are parallel and its angles are right angles.

To establish that quadrilateral ABCD is a rectangle, we need to show that its opposite sides are parallel and its angles are right angles.

First, let's calculate the slopes of the sides AB, BC, CD, and DA. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1).

For side AB: slope = (-4 - 0) / (6 - 2) = -1.

For side BC: slope = (0 - (-4)) / (10 - 6) = 1.

For side CD: slope = (4 - 0) / (6 - 10) = -1.

For side DA: slope = (0 - 4) / (2 - 6) = 1.

Since opposite sides AB and CD have slopes of -1 and opposite sides BC and DA have slopes of 1, we can conclude that they are parallel.

Next, we can calculate the slopes of the perpendicular sides. The slope of a line perpendicular to another line with slope m is -1/m.

For side AB and its perpendicular side CD: -1/-1 = 1.

For side BC and its perpendicular side DA: -1/1 = -1.

The slopes of the perpendicular sides indicate that the angles formed by the sides AB and BC, and sides CD and DA, are right angles.

Therefore, since quadrilateral ABCD has opposite sides that are parallel and angles that are right angles, we can conclude that ABCD is a rectangle.

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Answer:

x = 4√7

Step-by-step explanation:

You can use the pythagorean theorem which is a² + b² = c²

if you plug it in, it would be...

x² + 12² = 16²

x² + 144 = 256, subtract 144 to both sides

x² = 112, square root both sides to make x by itself.

x = 4√7  

The solution to the given question is given below:(a) f(x) = 3x^2+4/x^2+2To differentiate the given function, we will use the quotient rule of differentiation.

which is given by,(f(x)/g(x))'=[f'(x)g(x)-f(x)g'(x)]/[g(x)]2Now, putting the given values into the formula, we get,f(x) = 3x2+4/x2+2Let f(x) = 3x2+4 and g(x) = x2+2Now,f'(x) = d/dx[3x2+4] = 6xg'(x) = d/dx[x2+2] = 2xAfter substituting all the values in the quotient rule, we get,(f(x)/g(x))'=(6x(x2+2)-2x(3x2+4))/(x2+2)2=(-6x^3-8x+12x^3+16x)/[x^4+4x^2+4] = (6x^3+8x)/[x^4+4x^2+4]Hence, f'(x) = (6x^3+8x)/[x^4+4x^2+4].Therefore, the required derivative of the given function is (6x^3+8x)/[x^4+4x^2+4].(b) f(x) = (x2 - 7x)12To differentiate the given function, we will use the chain rule of differentiation which is given by, d/dx[f(g(x))] = f'(g(x)).g'(x)Now, putting the given values into the formula, we get,Let f(x) = x^12 and g(x) = x2-7xThen,f'(x) = 12x^11g'(x) = d/dx[x2-7x] = 2x-7After substituting all the values in the chain rule, we get,d/dx[f(g(x))] = f'(g(x)).g'(x) = 12(x2-7x)11.(2x-7)Therefore, the required derivative of the given function is 12(x2-7x)11.(2x-7).(c) f(x) = x^4√6x+5To differentiate the given function, we will use the product rule of differentiation which is given by, (fg)' = f'g + fg'Now, putting the given values into the formula, we get,Let f(x) = x^4 and g(x) = √6x+5Then,f'(x) = d/dx[x4] = 4x3g'(x) = d/dx[√6x+5] = 3/√6x+5After substituting all the values in the product rule, we get,(fg)' = f'g + fg' = (4x3).(√6x+5) + (x^4).(3/√6x+5)Hence, f'(x) = (4x3).(√6x+5) + (x^4).(3/√6x+5).Therefore, the required derivative of the given function is (4x3).(√6x+5) + (x^4).(3/√6x+5).

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The derivatives of the functions of the differentiation of the given functions has been calculated.

(a) The rule of differentiation applied to

f(x) = 3x²+4/x²+2 is as follows:

f'(x) = [12x(x²+2)-(6x)(4)] / [(x²+2)²]

=> f'(x) = [12x³-24x] / [(x²+2)²]

=> f'(x) = 12x(1-x²)/[(x²+2)²].

(b) The rule of differentiation applied to f(x) = (x² - 7x)^12 is as follows:

f'(x) = 12(x²-7x)^11(2x-7).

We apply the chain rule, which is the following:

[f(g(x))]' = f'(g(x)) * g'(x).(c)

The rule of differentiation applied to f(x) = x⁴√(6x+5) is as follows:

f'(x) = 4x³ * (6x+5)¹∕² + x⁴ * 1/2(6x+5)^-1/2 * 6

=> f'(x) = [24x³(6x+5) + 3x⁴(6)]/[2(6x+5)¹∕²]

=> f'(x) = [3x³(8x²+15)]/[(6x+5)¹∕²].

Thus, the differentiation of the given functions has been calculated.

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Answer:-8, -6, -4, -2 ...

Step-by-step explanation:

An arithmetic sequence consists numbers being added or subtracted in a specific pattern. 2, 4, 8, 16 is multiplying not adding. -2, 4, -6, 8 is not in a specific pattern. Hope this helped :)

An arithmetic sequence is a sequence in which the same number is repeatedly added is called an arithmetic sequence.

So in order for a sequence to be arithmetic, the difference between consecutive terms must remain constant.

Let's look at the second pattern.

Notice that each time, we add 2 to reach the next term.

The other sequences don't have a common difference.

Answer:

The correct option is;

(2·x - y = -2 and 22·x + 10·y = 7)

2 x minus y = negative 2 and 22 x + 10 y = 7

Step-by-step explanation:

2x - y = -2.........(1)

3x + 2y = 5.......(2)

4x - y = 2..........(3)

22x + 10y = 7...(4)

Given that the solution of the system of equation is (-0.3, 1.4), we have;

The system of equations consist of those equations that pass through the point (-0.3, 1.4)

We check as follows;

Equation (1)

2×(-0.3) - 1.4 = -2

Therefore, equation (1) passes through the point (-0.3, 1.4) and is one of the equations

Equation (2)

3×(-0.3) + 2×1.4 = 1.9 ≠ 5

Equation (2) is not part of the system of equations

Equation (3)

4×(-0.3) - 1.4 = -2.6 ≠2

Equation (3) is not part of the system of equations

Equation (4)

22×(-0.3) + 10×1.4 = 7.4 ≈ 7

Therefore, equation (4) approximately passes through the point (-0.3, 1.4) and is one of the equations

The correct option is A. \(2x - y = -2\ and 22x + 10y = 7.\)

Given equations,

\(2x - y = -2.........(1)\)

\(3x + 2y = 5.......(2)\)

\(4x - y = 2..........(3)\)

\(22x + 10y = 7...(4)\)

Since the solution of the system of equation is \((-0.3, 1.4),\)  Hence the system of equation satisfy the above point.

Now check all the equations,

Equation (1),

\(2\times(-0.3) - 1.4 = -2\\-0.6-1.4=-2\\-2.0=-2\)

Hence, equation (1) passes through the point\((-0.3, 1.4)\)  and is one of the equations.

Similarly, Equation (2)

\(3\times (-0.3) + 2\times1.4 = 5\\-0.9+2.8=5\\1.9=5\\\)

Hence the above equation does not satisfy the solution, so it is not the other system of equation.

Now, Equation (3)

\(4\times(-0.3) - 1.4 = -2.6 \neq 2\)

Hence Equation (3) is not part of the system of equations.

Now, Equation (4)

\(22\times (-0.3) + 10\times1.4 = 7.4\)

Hence the above equation approximately passes through the solution\(.(-0.3, 1.4)\) and is one of the equations.

Hence the required system of equation is  \(2x - y = -2\) and \(22x + 10y = 7\).

Therefore the correct option is A.

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A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

In Mathematics, there are different types of functions and these include the following;

In this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.

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Complete Question:

Which of the following best defines an output?

A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.

B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.

D. An output is a set of ordered pairs in which no y-value repeats.

Answer:

0

Step-by-step explanation:

-12 - (-12)

-12 + 12

0