Use the formula for the sum of a geometric series to calculate the given sum. (Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the series diverges.) 72 73 74 A 75 7 + ... = 123 * 126 Use the formula for the sum of a geometric series to find the sum. (Use symbolic notation and fractions where needed. Enter DNE if the series diverges.) 3 C 19 t 4 - t + - + .. = DNE 934

About 50 percent of its former width.

Now, According to the question:

Let's assume that our parameter of interest is given by θ and in order to construct a confidence interval we can use the following formula:

θ = ± ME(θ vector)

Where θ vector is an estimator for the parameter of interest and the margin of error is defined usually if the distribution for the parameter is normal as:

ME = [tex]z_\alpha[/tex]SE

Where [tex]z_\alpha /2[/tex]  is a quantile from the normal standard distribution that accumulates [tex]\alpha /2[/tex] of the area on each tail of the distribution. And SE represent the standard error for the parameter.

If our parameter of interest is the population proportion the standard of error is given by:

SE =[tex]\frac{p(1-p)}{n}[/tex]

And if our parameter of interest is the sample mean the standard error is given by:

SE = [tex]\frac{1}{\sqrt{n} }[/tex]

As we can see the standard error for both cases assuming that the other things remain the same are function of n the sample size and we can write this as:

SE = f(n)

And since the margin of error is a multiple of the standard error we have that

ME = f(n)

Now if we find the width for a confidence interval we got this:

Width = θ + ME (θ) - [θ - ME (θ)]

Width = 2ME(θ)

And we can express this as:

Width = 2f(n)

And we can define the function f(n) = [tex]\frac{1}{\sqrt{n} }[/tex]  since as we can see the margin of error and the standard error are function of the inverse square root of n. So then we have this:

[tex]Width_i[/tex] = [tex]2\frac{1}{\sqrt{n} }[/tex]

The subscript i is in order to say that is with the sample size n

If we increase the sample size from n to 4n now our width is:

[tex]Width_f[/tex] = [tex]2\frac{1}{\sqrt{4n} }[/tex] = [tex]2\frac{1}{\sqrt{n}\sqrt{4} }[/tex] = [tex]\frac{1}{\sqrt{n} }[/tex] = 1/2 [tex]Width_i[/tex]

The subscript f is in order to say that is the width for the sample size 4n.

So then as we can see the width for the sample size of 4n is the half of the with for the width obtained with the sample size of n. So then the best option for this case is:

about 50 percent of its former width.

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This is incomplete question:

Complete question is this :

In constructing a 95 percent confidence interval, if you increase n to 4n, the width of your confidence interval will (assuming other things remain the same) be:

about 25 percent of its former width.

about two times wider.

about 50 percent of its former width.

about four times wider.

The amount of bad debt expense will the company actually record is c)$139500.

So, correct option is c.

We have some details like total account receivable  as $1800000

allowance for doubtful accounts as $40,500

Now, we have also percentage of bad debt expense as 10% of accounts receivable.

So,10% of  of accounts receivable=(10/100)×1800000=$180000

Now, for getting information of bad debt expense we need to subtract allowance for doubtful accounts.

So, bad debt expense=10% of account receivable - allowance for doubtful debts

=>bad debt expense=$180000-$40500=$139,500

Hence, amount of bad debt expense is $139,500

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(Complete question) is:

Sheffield Corp. unadjusted trial balance includes the following balances (assume the normal balances): Accounts receivable as $1800000. Allowance for doubtful accounts as $40500. Bad debts are estimated to be 10% of the outstanding receivables. What amount of bad debt expense will the company actually record?

a)$137370

b)$182500

c)$139500

d)$177130

Excess capacity (e.g., factories can make more than the optimal industry production quantity) within the industry is not a deterrent to entry into an industry

Barriers to entry is an economics and business term describing factors that can prevent or impede newcomers into a market or industry sector, and so limit competition. Barriers to entry may be caused naturally, by government intervention, or through pressure from existing firms

Common barriers to entry include special tax benefits to existing firms, patent protections, strong brand identity, customer loyalty, and high customer switching costs.

According to the question,

Prevalence of learning curves in the industry , Production that requires expensive machinery that can be resold and High economies of scale in the industry are all deterrent or barriers to entry

But Excess capacity (e.g., factories can make more than the optimal industry production quantity) within the industry is not a deterrent to entry into an industry because when there is excess capacity in the industry , existing firms can cut the prices making it harder for new entrant to make a profit.

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The diameter of the Ferris wheel is equal to 95 ft.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a function that models the height of a seat on a Ferris wheel after [t] minutes.

We have the following function -

f(t) = 95 cos(π/10)t

The diameter of the Ferris wheel would be the maximum height reached by the wheel. We have -

f(t) = 95 cos[(π/10)t]

df/dt = 95 x - sin[(π/10)t] x (π/10)

df/dt = -(95π/10) sin[(π/10)t]

For maximum height -

df/dt = 0

- (95π/10) sin[(π/10)t] = 0

sin[(π/10)t] = 0

sin[(π/10)t] = sin (0)

(π/10)t = 0

t = 0

Put t = 0, in f(t) = 95 cos[(π/10)t], we get -

f(max) = 95 cos(0) = 95 ft

Therefore, the diameter of the Ferris wheel is equal to 95 ft.

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Answer: Option C (190 ft)

Step-by-step explanation:

Answer:

Original = (8,-6) New = (0,1)

Step-by-step explanation:

Arrange the adjustments like this in the parenthesis of the original point

(8 - 8, -6 +7)

Then do the math and get (0,1)

The inverse of the functions are f⁻¹(x) = 2/[3(x + 4)], f⁻¹(x) = √[(x + 1)/2] and f⁻¹(x) = 1/x + 1

Function (a)

This function is given as

f(x)=2/(3x) - 4

The function needs to be represented as an equation

So, we have

y = 2/(3x) - 4

Swap the positions of x and y

x = 2/(3y) - 4

So, we have

2/(3y) = x + 4

Take the reciprocal of both sides

3y/2 = 1/(x + 4)

Multiply both sides by 2/3

y = 2/[3(x + 4)]

So, the inverse function is

f⁻¹(x) = 2/[3(x + 4)]

The inverse is a function with the domain x ≠ -4 and range of f(x) ≠ 0

See attachment 1 for the graphs

Function (b)

This function is given as

f(x) = 2x² - 1

The function needs to be represented as an equation

So, we have

y = 2x²- 1

Swap the positions of x and y

x = 2y² - 1

So, we have

2y²= x + 1

Divide both sides by 2

y²= 1/2(x + 1)

Take the square roots

y= √[(x + 1)/2]

So, the inverse function is

f⁻¹(x) = √[(x + 1)/2]

The inverse is a function with the domain x ≥ -1 and range of f(x) ≥ 0

See attachment 2 for the graphs

Function (c)

This function is given as

f(x) = 1/(x - 1)

The function needs to be represented as an equation

So, we have

y = 1/(x - 1)

Swap the positions of r and y

x = 1/(y - 1)

So, we have

y - 1 = 1/x

Add 1 to both sides

y = 1/x + 1

So, the inverse function is

f⁻¹(x) = 1/x + 1

The inverse is a function with the domain x ≠ 0 and range of f(x) ≠ 1

See attachment for the graphs

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Answer:

The answer to that question is 8

Step-by-step explanation:

2/3 times 12 = 8

The net present value of the machine is rounded to the nearest dollar is $-76,447.56.

Net gift fee is the prevailing fee of after-tax coins flows from an funding much less the quantity invested.

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The perimeter of the rectangle is: 2⅙ yd

The area of the rectangle is: 1/4 yd².

Given the following:

Length of rectangle = 3/4 yd

Width of rectangle = 1/3 yd

The perimeter of rectangle = 2(3/4 + 1/3) = 2(13/12)

Perimeter = 2⅙ yd

The area of the rectangle = (3/4)(1/3)

Area = 3/12

Area = 1/4 yd²

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Answer:

the third opinion: [tex]y = \frac{1}{4}x - 1[/tex] (or as you put it, y equals one fourth times x minus 1)

This is because it's written in slope-intercept form: y = mx + b . m is the slope, which is 1/4, and b is the y-intercept, -1

This is the binomial probability distribution.

n = 10, p = 0.4965 and q = 0.5035

In a binomial probability distribution, the possible outcomes is two that is either success or failure

Here , we are determine the probability of a male,

so here success is male and failure is female

And in selecting ten texans at random, the outcome of one individual is independent of th eother

so it is an binomial probability.

Therfeore, the given experiment is an binomial probability distribution.

n = 10 (the number of randomly selected Texans)

p = 0.4965 (the probability that randomly selected Texan will be male)

q = 0.5035 (the probability that randomly selected Texan will be female)

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The discriminant of the given quadratic equation is 17.

The discriminant is defined as the part of the quadratic formula underneath the square root symbol: b²-4ac. Thus, the discriminant usually tells us whether there are two solutions, one solution, or no solutions in a quadratic equation.

Now, the given quadratic equation is √2x² — 5x + √2 = 0.

This equation is of the general quadratic form of ax² + bx + c = 0.

Where,

a = √2

b = —5

c = √2

Now, discriminant is gotten as;

D = (b² - 4ac)

D= {(-5)² - (4 × √2 × √2)}

D = 25 - (4 × √4)

D = 25 - (4 × 2)

D = 25 - 8

D = 17

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Hi, your answer is b. (1, 2)

Hope this helps.

The area of grass that the horse has access to is 314 square-foot

From the question, we are to determine how much grass the horse have access to.

From the given information,

"A horse is tied with a 10 -foot-long rope to a pole"

This means the horse has access to a circular area of radius 10 feet.

Now, we will calculate the area of a circle with radius 10 feet.

Using the formula for calculating the area of a circle,

A = πr²

Where A is the area of the circle

and r is the radius of the circle

Substitute r = 10 into the equation,

A = π × 10²

A = 100π

Take π = 3.14

Then,

A = 100 × 3.14

A = 314 square foot

Hence, the area is 314 square foot

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Step-by-step explanation:

Let's say that the you have to found the mean of 5, 2, and 8

first you would have to add up all of the number 5+2+8 which equals to 15

now you would have divide 15 by the amount of the data points which is 3, so your mean in this problem is 5.

here is an example by only using numbers:

(5+2+8) ÷ 3 = 5

The journal enetry,

Debit cash is $67,000

Debit discount on payable is $670

Credit bonds payable is $66,330

(Recorded on bonds )

Debit Interest expense is $46,90

Debit discount on bonds payable is $46.9

credit cash is $4643.1..

Bonds payable

Bonds issued when the market price equals the standard rate are issued at face value. In other words, the cash received is face value.

Interest paid on the par Bond includes only the indicated. Interest rate calculated based on the number of annual payments.

We have given that

face amount, F = $67,000

Annually paid interest= $67,000

rate of bond, r = 7%

time bond, n = 10 year

market bond of interest= 7%

Coupon ammount = 7% of 67000 =$ 4690

we have to calculate bond issue and first interest payment .

bond price= C×[1 - (1 + r)⁻ⁿ] /r + F/(1+r)ⁿ

= 4690[ 1 - (8)¹⁰]/7 + 67000/(8)¹⁰

=669.99 + 0.000062 = 669.9901 ~ 670

Interest Expense = Principal * Rate * Time

=> Interest Expense = $67,000×7% ×1

= $46,90

discount or primum on bond payable

= interest expense - $66,330×7% × 1

= $46,90- $4643.1 = $46.9

date General

General journal debit credit

January, cash $67,000 $66,330

2024 Bonds

payable

Discount on

bond $670

payable

December

31, cash $4643.1

2024 interest

expense $46,90

Discount on

bond $46.9

payable

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Complete Question:.Pretzelmania, Inc., issues 7%, 10-year bonds with a face amount of $67,000 for $67,000 on January 1, 2024. The market interest rate for bonds of similarrisk and maturity is 7%. Interest is paid annually on December 31.Record the bond issue and first interest payment on December 31 . (If no entry is required for a transaction/event, select "No journal entry required" in thefirst account

If the customer makes a purchase and pays $5,500 on account and $6,600 cash, the total ammount he paid is $ 12100

The customer makes a purchase

He pays $5500 on account

He also pays 6600 in cash

We need to find the total amount he used to purchase

The total amount can be calculated by adding the price he paid in accound and in cash

The total amount is 5500 + 6600 = 12100

Therefore, if the customer makes a purchase and pays $5,500 on account and $6,600 cash, the total amount he paid is $ 12100

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The length of SR will be 15 units, using Pythagoras' theorem

What is Pythagoras' theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Remember that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Triangle SRT and triangle TRQ can be compared using the image. Since both triangles have equal sides and right angles (T), they are both triangles (RT)

Using Pythagoras theorem,  

RQ² = TQ² + TR²

20² = TR² + 16²

TR = 12

SR/RQ = TR/TQ

SR / 20 = 12 / 16

SR = 15 units

Hence the length of SR will be 15 units.

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The equation of the line in slope intercept form is y = 4/3x - 10/3.

What is a line in slope-intercept?

The equation of a line with a slope of m and a y-intercept of (0, b) is y = mx + b. To graph a slope-intercept line, do the following: On the coordinate plane, draw the y-intercept. Find another point on the line using the slope.

We have,

the line that passes through (2,6) and (-4,-2).

We know that the formula to find the slope of two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

m = (-2 - 6) / (-4 - 2)

m = -8/ -6

m = 4/3

Now using the slope and the point (2, 6) the y-intercept is

y = mx + b

6 = 4/3 (2) + b

6 = 8/3 + b

By further calculation,

b = 6 - 8/3

Taking LCM

b = (18 - 8)/3 = 10/3

By writing the equation in slope intercept form

y = mx + b

y = 4/3x - 10/3

Therefore, the equation of the line in slope intercept form is y = 4/3x - 10/3.

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To graph an inequality, consider the < or > sign to be a = sign and graph the equation. If the inequality is < or >, draw a dotted line to represent the equation.

Graph the equation as a solid line if the inequality is ≤ or ≥, This line divides the xy-plane into two regions: one that meets the inequality and one that does not.

When inequalities are graphed on a coordinate plane, the solutions are found in a region of the plane that is shaded. If the points on the line satisfy the inequality, as in the case of and, the boundary line for the inequality is drawn as a solid line.

Linear inequalities are not the same as linear equations, but what you know about equations can help you understand inequalities. Equations and inequalities are both mathematical statements that compare two values. 

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( π=3,14 , r= d/2= 7.6/2= 3,8m )

C= 2πr
C= 2·π·3.8
C≈23.87m

The probability that a randomly chosen subject completes at least three puzzles in the 5 minute period while listening to soothing music is 0.4.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. The probability of a random variable can be given by,

                                ⇒    f ( x ) p ( x )    =   P ( X = x )

As per the question,

        P ( X = 1 )   =   0.2

        P ( X = 2 )   =   ?

        P ( X = 3 )   =   0.3

        P ( X = 4 )   =   0.1

⇒   P ( X ≥ 3 )   =   P ( X = 3 ) + P ( X = 4 )

                         =   0.3 + 0.1

      P ( X ≥ 3 )   =   0.4  

Therefore, 0.4 is the probability that a randomly chosen subject completes at least three puzzles in the 5-minute period while listening to soothing music.

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The complete question is

The required an equation for the perpendicular bisector of the line segment joining (1,2) and (-5,12) is y = 3x/5 + 41/5.

Equation of the lines which are even or lined up with the X-pivot is y = a, where an is the y - direction of the focuses on the line. Essentially, the condition of a straight line which is vertical or lined up with the Y-hub is x = a, where an is the x-direction of the focuses on the line.

Mid point of the line passing through the points (1,2) and (-5,12).

mid point = [tex](\frac{1-5}{2} , \frac{2+12}{2} )[/tex] = (-2, 7)

So, the line perpendicular to given line is passing through  (-2, 7)

Slope of line of points (1,2) and (-5,12).

Slope(m) = [tex]\frac{12-2}{-5-1}=-\frac{5}{3}[/tex]

Then slope of perpendicular bisector of this line is negative and reciprocal of Slope(m).

slope of perpendicular bisector(n)  = 3/5

Now, equation of line is

[tex](y-y_{1})=n(x-x_{1})[/tex]

(y - 7) = 3/5(x + 2)

y = 3x/5 + 41/5

Thus required equation of perpendicular bisector is y = 3x/5 + 41/5

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A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits.

In the given question we have to explain about 2-digit special number.

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits.

Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.

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The average of numbers from 8 to 49 will be 21.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The numbers 8 to 49.

Now,

The average of numbers from 8 to 49 is calculated as;

⇒ Average = (n + 1) / 2

Where, n is the numbers in between 8 to 49.

Hence, n = 49 - 8

               = 41

Thus, We get;

⇒ Average = (n + 1) / 2

                  = (41 + 1) / 2

                  = 42/2

                  = 21

Therefore, The average of numbers from 8 to 49 will be 21.

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From the four possible outcomes for signal detection theory exhibited in the given example is miss.

Signal detection theory refers to an approach of differentiating an individual ability to discriminate the presence and absence of a stimulus (or different stimulus intensities) from the individual’s criterion (physical/psychological state) to responses to those stimuli. It is a measure of the ability to differentiate between information-bearing patterns and random patterns that distract from the information. The four possible outcomes defined by the theory are hit (signal present and observer respond), miss (signal present and observer did not respond), false alarm (signal absent and observer respond), and correct rejection (signal absent and observer did not respond). As the brother is hiding under a pillow but the sister comes into the room and looks at the sofa, but seeing nothing, she leaves, it is a miss outcome.

Note: The question is incomplete. The complete question probably is: A brother and sister are playing hide and seek and the brother has hid under a pillow on the sofa. His sister comes into the room and looks at the sofa, but seeing nothing, she leaves. What signal detection theory potential outcome is shown in the example.

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The feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

With the constraint that x and y are both non-negative, the second constraint has only one point in common with each of the first and third constraints; and those two points are different.

The feasibility region is empty; so nothing can be optimized.

Plots x + 2y = 30 (red),  2x + 2y = 30 (green)  and  2x+y = 30 (blue)

The feasibility area, according to the condition, is the area of the first quadrant

   - above the red line,

   - below the green line,

   - above the blue line.

It can be seen from the plot that this set is empty.

Therefore, the feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

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Disclaimer

The question given by you is incomplete, so the above solution is of a similar question, and the question is

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT

Maximize p = x + y subject to

x + 2y ≥ 30

2x + 2y ≤ 30

2x + y ≥ 30

x ≥ 0, y ≥ 0.

p=

(x, y)=

The area of the region cut from the first quadrant by the cardioid is 3π/8 +1

A cardioid is a two-dimensional plane figure that has a heart-shaped curve. The equation of cardioid is r = a(1 ± sinθ) .

The area of the polar function can be calculated if the boundary condition that form the reason is given or can be found from the given information now we use the formula using the polar formula of the area as:

[tex]A = \int\limits^b_a {\frac{r^{2}}{2}} d\theta[/tex]

The Area of the region cut from the first quadrant by cardioid,

[tex]A = \int\limits^\frac{\pi}{2}_0 {\frac{r^{2}}{2}} d\theta[/tex]

Substituting r = 1 + sin ∅

[tex]A = \int\limits^\frac{\pi}{2}_0 {\frac{(1+ sin\theta)^{2}}{2}} d\theta[/tex]

Opening square ,

[tex]A = \frac{1}{2}\int\limits^\frac{\pi}{2}_0 {1 +2sin\theta + sin^{2}\theta d\theta[/tex]

=> [tex]A = [ \frac{1}{2} (\theta - 2cos\theta + \frac{1}{2} (\theta - \frac{1}{2}sin2\theta))]^\frac{1}{2}_{0}[/tex]

=> 3π / 8 - (-1)

=> 3π/8 +1

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