Suppose we are given a series [=1(-1)+1 9n(x), where for each fixed x € R, we have 91() > 92(x) > 93(x) > ..0. Assume furthermore that 91(2) is bounded on R, and that the In(x) converge pointwise to 0. Prove that the series converges uniformly on R.

Answers

Answer 1

|In(x)| < ε/M for all x ∈ R, we can bound the above expression by:|91(n+1)(x) + 91(n+2)(x) + ...| ≤ 91(n+1)ε/M + 91(n+2)ε/M + ... = ε.This shows that the series converges uniformly on R.

We must demonstrate that for any given  > 0, there exists a positive integer N such that the difference between the partial sum Sn(x) and the limit L(x) for all x  R is less than to demonstrate that the series converges uniformly on R.

Since 91(2) is limited on R, let M be an upper headed for 91(2). Since the In(x) unite pointwise to 0, for any ε > 0, there exists a positive number N with the end goal that for all n > N, |In(x)| < ε/M for all x ∈ R.

Presently, for n > N and for all x ∈ R, we have:

|Sn(x) - L(x)| = |(∑ i=1 to n 91(i)(x)) - 0| = |91(n+1)(x) + 91(n+2)(x) + ...|

Since |In(x)| < ε/M for all x ∈ R, we can bound the above articulation by:

|91(n+1)(x) + 91(n+2)(x) + ...| ≤ 91(n+1)ε/M + 91(n+2)ε/M + ... = ε

This shows that the series combines consistently on R.

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Related Questions

A store owner offers a discount of 20% off the regular price of all jackets. Jessica has a coupon that gives her an additional 5% off the discounted price. The original price of the jacket Jessica buys is $84. What is the price of the jacket after the discount and Jessica's coupon? ​

Answers

Answer:

21

Step-by-step explanation:

I haven't done this in a long time but this is what I know: the discount would overall be 25%. So, you set it up by .25(84) = 21. Therefore the jacket would cost $21.

I hope this is right and helps!

Assume that females have pulse rates that are normally distributed with a mean of u=72.0 beats per minute and a standard deviation of a 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 70 beats per minute The probability is (Round to four decimal places as needed.) b. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 307 OA. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size OB. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size OC. Since the onginal population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. OD. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute The probability is (Round to four decimal places as needed.) b. I 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 309 O A Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. OB. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size OC. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample site OD. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size

Answers

The probability that a randomly selected adult female has a pulse rate less than 70 beats per minute is about 0.4371.

What is the probability

a. To find the probability that a randomly selected adult female has a pulse rate less than 70 beats per minute, one have to calculate the z-score and use the standard normal distribution.

The z-score can be calculated as:

z = (x - μ) / σ

where:

x =  the value (70 beats per minute)

μ = the mean (72.0 beats per minute)

σ = the standard deviation (12.5 beats per minute).

So putting it into the formula, it will be:

z = (70 - 72.0) / 12.5

z = -0.16

One can know probability using the z-score.

Check z-score in the standard normal distribution table, and the value will be 0.4371 (rounded to four decimal places).

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A poker hand consists of 5 cards. A flush is a hand for which all cards are the same suit,but not of consecutive denominations (where Ace can be high or low.For example,2,3,4,5,7 of Hearts is a flush,but 2,3,4,5,6 of Hearts is not a flush. Find the probability that a poker hand from a well-shuffled deck is a flush. b Anne and Barney are playing poker. On each hand, Anne has a 20% chance of bluffing and Barney has a 30% chance of bluffing; the two players bluff in- dependently. What is the probability that Anne is bluffing,given that at least one player is bluffing?

Answers

The probability that a poker hand from a well-shuffled deck is a flush is 0.00198.

The probability that Anne is bluffing, given that at least one player is bluffing is 1.95.

a) Probability that a poker hand from a well-shuffled deck is a flush:

Consider the following points for a poker hand from a well-shuffled deck is a flush:

There are 4 suits in a deck of cards.

There are 13 denominations in each suit.

When choosing a flush hand, any of the suits can be selected.

Therefore, the probability of choosing a suit is: P(Suit) = 4/4 = 1.

Therefore, the probability of selecting a suit is 1.The first card may be of any denomination. Therefore, the probability of selecting any denomination is 1.

Since all 5 cards must have the same suit, the second card must be of the same suit as the first card. Therefore, the probability of selecting the second card of the same suit is:

P(Same Suit) = 12/51

The third card must also be of the same suit as the first card and second card. Therefore, the probability of selecting the third card of the same suit is:

P(Same Suit) = 11/50

The fourth card must also be of the same suit as the first card, second card, and third card. Therefore, the probability of selecting the fourth card of the same suit is:

P(Same Suit) = 10/49

The fifth card must also be of the same suit as the first card, second card, third card, and fourth card. Therefore, the probability of selecting the fifth card of the same suit is:

P(Same Suit) = 9/48

Multiplying all probabilities together, we have:

P(Suit) × P(Same Suit) × P(Same Suit) × P(Same Suit) × P(Same Suit)= 1 × 12/51 × 11/50 × 10/49 × 9/48= 0.00198

Therefore, the probability that a poker hand from a well-shuffled deck is a flush is 0.00198.

Ans: 0.00198.

b) Probability that Anne is bluffing, given that at least one player is bluffing:

Consider the following points for the probability that Anne is bluffing, given that at least one player is bluffing:

Anne has a 20% chance of bluffing.

Barney has a 30% chance of bluffing.

The two players bluff independently.

P(Anne is bluffing) = 20/100 = 1/5P(Barney is bluffing) = 30/100 = 3/10

Let A be the event that Anne is bluffing and B be the event that Barney is bluffing.

Let C be the event that at least one player is bluffing.

P(C) = 1 - P(none is bluffing) = 1 - (1 - P(Anne is bluffing)) × (1 - P(Barney is bluffing))= 1 - (1 - 1/5) × (1 - 3/10)= 1 - (4/5) × (7/10)= 1 - 28/50= 22/50= 11/25

Now, P(A ∩ C) = P(A) × P(C|A)

Where P(C|A) is the probability that at least one player is bluffing given that Anne is bluffing.= (3/10 + 7/10 × 4/5) / (1 - 4/5)= (3/10 + 28/50) / (1/5)= (15/50 + 28/50) / (1/5)= 43/50 × 5= 215/50

Therefore, P(A|C) = P(A ∩ C) / P(C)= 215/50 × 25/11= 1.95

Therefore, the probability that Anne is bluffing, given that at least one player is bluffing is 1.95. Ans: 1.95.

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Select the simplification that accurately explains the following statement.

Answers

Under C, I believe. When we have the same base (2 in this case), 2^1/4*2^1/4 can be written as 1/4+1/4 since it’s the same base. And 1/4+1/4+1/4+1/4 is 4/4 and that is 1 so 2^1 is 2.

Answer:

look below I got it right

Step-by-step explanation:

look carefully, for some people it’s a, for some it’s different so just look and compare to the answers

Solve the system with the addition method: S-60 8y * + 5y - 24 26 Answer: (x,y) Preview 2 Preview y Enter your answers as integers or as reduced fraction(s) in the form A/B.

Answers

The solution to the system of equations is (x, y) = (-4, 6).

To solve the system using the addition method, we want to eliminate one variable by adding or subtracting the equations.

Let's solve it step by step:

First, let's multiply the second equation by 6 to make the coefficients of x in both equations equal:

6(x + 5y) = 6(26)

6x + 30y = 156

Now, we can add the modified second equation to the first equation:

(-6x - 8y) + (6x + 30y) = -24 + 156

The -6x and 6x terms cancel each other out:

-8y + 30y = 132

Simplifying the equation further:

22y = 132

To solve for y, divide both sides of the equation by 22:

y = 132 / 22

y = 6

Now that we have the value of y, we can substitute it back into either of the original equations.

Let's use the second equation:

x + 5(6) = 26

x + 30 = 26

x = 26 - 30

x = -4

Therefore, the solution to the system of equations is (x, y) = (-4, 6).

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Complete question =

Solve the system with the addition method:

-6x - 8y = - 24

x + 5y = 26

Answer: (x,y)

Which investment choice carries the greatest price risk?

Common stocks
Preferred stocks
Corporate bonds
Government bonds

Answers

The investment choice that carries the greatest price risk is common stocks. (Option-A)

Common stocks are shares of ownership in a company and their price can be very volatile, changing rapidly depending on market conditions and factors affecting the company. Their prices can be influenced by factors such as overall economic conditions, company financial performance, and investor sentiment.

On the other hand, preferred stocks and corporate bonds are typically less risky than common stocks. Preferred stocks are a type of stock that pays a fixed dividend and has a priority claim on company assets in the event of bankruptcy, while corporate bonds are debt instruments that pay a fixed interest rate.

Lastly, government bonds are considered the least risky of all of these investment choices because they are backed by the government, which has a reputation for always repaying its debts.

In summary, while all types of investments carry some level of risk, common stocks have the greatest price risk due to their volatility and sensitivity to changing market conditions.(Option-A)

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are all vertical lines parallel?

Answers

Answer: Yes

Step-by-step explanation: All vertical lines have the same slope and because of that they are always parallel.

If an item is on sale for 60% off, that means you actually PAY _____% of the price.

Answers

Answer:

40%

Step-by-step explanation:

100-60=40

Hey guys I really need help please help me

Answers

The answer could be 111? If you need to get 180 but I can’t remember exactly if you need to get to 180

Answer:

I believe x would be 30

Step-by-step explanation: When you add 20+10 it will give you the other triangle side, which is  30, and then 22+11 will be 33. And for the final side 24+12 will give you 36

identify the pattern 3,7,11,15

Answers

Answer:

Step-by-step explanation:

3 7 11 15 19 23 27

2
A = 2.5 km
b= 5 km
h =

Answers

Answer:

First of all, we have to make area km by multiplying 10 then solve, the answer is 5

A cylinder has a height of 16 meters and a diameter of 26 meters. What is its volume? Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answers

Answer:

V= 5224.96

Step-by-step explanation:

To find the volume for a cylinder, you need to use the formula

V=(pi)r^2h.

The question gives is the diameter. The radius is half of the diameter, so you would divide by 2.

16/2 = 8.

Now we plug in the numbers and solve.

V= (pi) 8^2(26)

V= (pi)(64)(26)

V=(pi)(1664)

V= 5224.96

Maths equation need help please

Answers

Answer:

I FIGURED IT OUT!

Step-by-step explanation:

a = 3

b = 3

c = 5

d = 2

give me brainliest

find the volume of the 2 dice if the length of the base of the cube is 4cm

A) 64cm cubed
B) 96cm cubed
C) 108cm cubed
D) 128cm cubed​

Answers

Answer:

I think the answer is A 64cm cubed

3-6 x (34 divided by 30)2

Answers

Answer:

3-6

Step-by-step explanation:

The expression 3⁻⁶ × (3⁴ ÷ 3⁰)² value is 9 which is 3².

To simplify the given expression: 3⁻⁶ × (3⁴ ÷ 3⁰)², let's break it down step by step:

First, let's simplify the exponent expressions within the parentheses:

3⁴ = 81 (because 3⁴ = 3 × 3 × 3 × 3 = 81)

3⁰ = 1 (because any number raised to the power of 0 is 1)

Now, we can rewrite the expression with the simplified exponents:

3⁻⁶ × (81 ÷ 1)²

Next, simplify the division within the parentheses:

81 ÷ 1 = 81

Now, the expression becomes:

3⁻⁶ × 81²

Simplify the exponent:

81² = 6561 (because 81 × 81 = 6561)

Now, the expression becomes:

3⁻⁶ × 6561

1/729 × 6561

6561/729

dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 9:

729/81

We get 9 which is equal to 3².

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BRAINLIST. BRAINLIST. BRAINLIST. PLS HELP.

Answers

I’m sorry I just need points lol

Answer:

Mild- 5x=50 4x=40  

Medium- 90- 48=42, 42/2=21 so, 2x=21    

Spicy- 90-25=65, 65+18=83

Step-by-step explanation:

I'm gonna guess that this is the angle measurement so.....

Find the equation of the exponential function represented by the table below:

Answers

Answer:

[tex]y=0.01(4)^x[/tex]

Step-by-step explanation:

Inspection of a random sample of 24 aircraft showed that 16 needed repairs to fix a wiring problem that might compromise safety (a) How large a sample would be needed to estimate the true proportion of jets with the wiring problem with 90 percent confidence and an error of + 4 percent? (Enter your answer as a whole number (no decimals). Use a z. value taken to 3 decimal places in your calculations.) Sample size (b) Would the airline actually conduct further sampling, or just inspect all the planes? Conduct further sampling Inspect all the planes

Answers

The sample size required to estimate the true proportion of jets with the wiring problem with 90% confidence and an error of +4% is approximately 92 (rounded up to the nearest whole number).

To determine the sample size needed to estimate the true proportion of jets with the wiring problem, we can use the formula for sample size calculation for proportions:

n = ([tex]Z^2 * p * q[/tex]) / [tex]E^2[/tex]

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of 1.645)

p = estimated proportion (16/24 = 0.6667)

q = 1 - p

E = maximum error tolerance (4% = 0.04)

Let's calculate the sample size:

p = 0.6667

q = 1 - p = 0.3333

E = 0.04

Z = 1.645

n = ([tex]1.645^2[/tex] * 0.6667 * 0.3333) / [tex]0.04^2[/tex]

n ≈ 91.62

Regarding the decision to conduct further sampling or inspect all the planes, it depends on the context and resources available. If inspecting all the planes is feasible and does not require excessive time or cost, it might be preferred to ensure the safety of all aircraft.

However, if conducting further sampling is a practical and reliable way to estimate the proportion while saving time and resources, the airline might choose to conduct additional sampling.

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4x + 14 = 4x + 24 its to hard for me

Answers

Answer:

x=10

Step-by-step explanation:

i think the answer is x = 10

The volume of a cube is 216 cubic feet. What is the length of each side of the cube?

side = ? ? ? feet

Answers

Answer:

find the cube root of 216 to get the length of one side as you get the volume of a cube by length x length x length

Step-by-step explanation:

the the cube root of 216 is 6

so the length of one side is 6 inches

Hope This Helps :)

Answer: I think it is 54 because there are four sides of a cube. So I just did 216/4 and got 54.

Step-by-step explanation:

Might be wrong but this is what I think the answer is.

Consider the points A (-1, 1), B (1,5) and C (5, 1). M is the midpoint of AB, and N is the
midpoint of BC.
Show that MN is parallel to AC

Answers

Step-by-step explanation:

IN ΔAMN ΔABC

Since MN∣∣BC

∠AMN=∠ABC (Corresponding angles)

∠ANM=∠ACB (Corresponding angles)

∴ΔAMN∼ΔABC(By $$AA similarity criterion)

AB

AM

=

AC

AN

=

BC

MN

(CPST)

Since, M is mid-point of AB,

AM=

2

1

AB,or,

AB

AM

=

2

1

or,

AB

AM

=

AC

AN

=

2

1

AC

AN

=

2

1

5

AN

=

2

1

[∵AC=5cm]

AN=

2

5

cm=2.5cm

Also,

AB

AM

=

BC

MN

=

2

1

7

MN

=

2

1

[∵BC=7cm]

MN=

2

7

=3.5

Ans=AN=2.5cm and MN=3.5cm

solution

Which expression represents the area of the shaded region?

Answers

Given:

A circle of radius r inscribed in a square.

To find:

The expression for the area of the shaded region.

Solution:

Area of a circle is:

[tex]A_1=\pi r^2[/tex]

Where, r is the radius of the circle.

Area of a square is:

[tex]Area=a^2[/tex]

Where, a is the side of the square.

A circle of radius r inscribed in a square. So, diameter of the circle is equal to the side of the square.

[tex]a=2a[/tex]

So, the area of the square is:

[tex]A_2=(2r)^2[/tex]

[tex]A_2=4r^2[/tex]

Now, the area of the shaded region is the difference between the area of the square and the area of the circle.

[tex]A=A_2-A_1[/tex]

[tex]A=4r^2-\pi r^2[/tex]

[tex]A=4r^2-\pi r^2[/tex]

[tex]A=r^2(4-\pi )[/tex]

Therefore, the correct option is (a).

Michael Scott, regional manager at Dunder mifflin Scranton, bought a coin from a magic shop that is designed to flip heads much often than tails. Dwight Schrute, his employee, wants to estimate the proportion of all glips of this coin that will be heads. In 400 flips of the coin Dwight flipped 312 times. Construct and interpret the 90% confidence interval for the population proportion of flips that will be heads. show at least 2 decimal digits in your endpoints.

Answers

The 90% confidence interval for the  population proportion of flips that will be heads is given as follows:

(0.746, 0.814).

The interpretation is that we are 90% sure that the true proportion of all tosses with this coin is between these two bounds.

What is a confidence interval of proportions?

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The parameters for this problem are given as follows:

[tex]n = 400, \pi = \frac{312}{400} = 0.78[/tex]

The lower bound of the interval is given as follows:

[tex]0.78 - 1.645\sqrt{\frac{0.78(0.22)}{400}} = 0.746[/tex]

The upper bound is given as follows:

[tex]0.78 + 1.645\sqrt{\frac{0.78(0.22)}{400}} = 0.814[/tex]

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Bella is going to redecorate her room using wallpaper. Her wall has a large window in the middle. The diagram below shows the wall she is decorating with the window. How many square feet of the wallpaper will she need?
A-42 sq ft
B-82 sq ft
C-104 sq ft
D-130 sq ft

Answers

82sq ftAnswer:

Step-by-step explanation:

I need help with this please lol

Answers

Answer:

360 degrees

Step-by-step explanation:

HHHHHHHHHHHHHELLLLLPPPPPPP ME PLS PLS PLS a school wants to add a new sports team. The school sent out surveys asking for the​ students' favorite sport. seventeen students named swimming. Others named hockey or volleyball . Use pencil and paper. Explain how to use the circle graph and ratios to find the number of students surveyed. Then find this number.

Answers

Answer:

Total 100% or 25 students

Swimming 36%  or 9 students

Lacrosse 48%  or 12 students

Volleyball 16% or 4 students

Step-by-step explanation:

To do a circle graph, you draw a circle and divide it into all sections.

To know the size of each section, you need to know the total number of every category.

You could draw it with percent.

100% is total, and you know the percent of each sport.

They told you 12 students choose lacrosse so, this represents 48%.

Now, you can find the other numbers with cross-multiplication.

48%____12

100%____X=

X=(100x12)/48=25

Total students: 25

Students that named lacrosse: 12 or 48%

100%____25

16%____X=

X=(16x25)/100=4

Students that named Volleyball: 4 or 16%

100%____25

36%____X=

X=(36x25)/100=9

Students that named Swimming: 9 or 36%

To confirm: 12 + 9 + 4 = 25

Brainlist Pls!

Answer:

50

Step-by-step explanation:

Solve: 6x - 13 = 4(x + 10) + 2x

Answers

Answer:

null

Step-by-step explanation:

Answer: 0=53

Step-by-step explanation:

convert (badfaced)16 from its hexadecimal expansion to its binary expansion

Answers

The binary expansion of (badfaced)16 is 10111010111111011010111110101101 2.

In order to convert (badfaced)16 from its hexadecimal expansion to its binary expansion, we need to follow the steps below:

Step 1: Write down the hexadecimal number (badfaced)16

Step 2: Write the binary equivalent of each hexadecimal digit (use the table below)

Step 3: Combine all the binary digits to get the answer

Table showing the binary equivalent of each hexadecimal digit Binary Equivalentb00001011a00001010d00001101f00001111a00001010c00001100e00001110d00001101

Step 2: Writing the binary equivalent of each hexadecimal digit(badfaced)16 = b a d f a c e d

Step 3: Combining all the binary digits to get the answer(badfaced)16 = 10111010111111011010111110101101 2

Thus, the binary expansion of (badfaced)16 is 10111010111111011010111110101101 2.

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Express your answer in scientific notation. 6.4 * 10^5 + 36,000 =

Answers

Answer:

6.76x10^5

^ represents to the 5th power

Step-by-step explanation:

What is the volume of the solid figure?
Enter your answer in the box.

Please help..

Answers

Answer:

188

Step-by-step explanation:

10*5*4 - 6*2

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QN 3:There are two developers interested in buying a piece of land in a busy town. You have been asked to estimate the residual value for each development using the following information: Developers profit: 15% Property management fees: 1.5% of Annual RentalIncome Professional fees: 10% of Building costs Voids & contingencies: 3% of Building costs Advertising, marketing & sales fees: 5% of completed development Site Acquisition fees: 2%a) Developer A wishes to develop an office building 4,000m2 gross external area (with 3,600m2 Net Internal Area). It is estimated that Building costs will be 2,500,000; Rent is 300 per m2; and the development will take 24 months. You also know that the finance rate is 9% and the developer s yield is 8%. (7 Marks)b) Developer B plans to develop luxury flats on the site. The developer is proposing 24 units which are expected to sell at 250,000 each. It is estimated that the development period will be 18 months with development costs reaching 2,100,000. The developer s finance rate is 10%. (7 Marks)c) Discuss the various techniques that can be used to estimate construction costs at the pre-contract stages, including outlining the procedures followed to arrive at fairly accurate cost reports. (6 marks) PARKA MAUR The War an Poverty has been gong on to decades While event spending continues to the are not a Pemprovide samples of new or cativ weys which makes might as they1. The War on Poverty has b for a given quantity, the total profit of a perfectly competitive firm is equal to the vertical distance between the firm's total revenue curve and its total cost curve. T/F Numerical Analysis and differential equation( please help with Q21 the polynomial p2(x) = 1 1 2 x2 is to be used to approximate f (x) = cos x in [1 2 , 1 2 ]. find a bound for the maximum error) John's employment wages are $ 158,000 for 2021. What is theemployee portion of the Social Security tax that will be deductedon this amount?a) $ 9,796.00b) $ 8,853.60c) $ 8537.40d) $ 10,534.05 A cell membrane at 37C is found to be permeable to Ca2+ but not to anions, and analysis shows the inside concentration to be 0.100 M and the outside concentration to be 0.001 M in Ca2+.a. What potential difference in volts would have to exist across the membrane for Ca2+ to be in equilibrium at the stated concentrations? Assume that activity coefficients are equal to 1. Give the sign of the potential inside with respect to that outside.b. If the measured inside potential is +100 mV with respect to the outside, what is the minimum (reversible) work required to transfer 1 mol of Ca2+ from outside to inside under these conditions? Factory Overhead Costs During May, Jernigan Company incurred factory overhead costs as follows: indirect materials, $3,080; indirect labor, $2,910; utilities cost, $1,280; and factory depreciation, $3,640. Journalize the entry to record the factory overhead incurred during May. If an amount box does not require an entry, leave it blank. Consider the following reaction:POCl3(g) POCl(g) + Cl2(g) Kc = 0.450A sample of pure POCl3(g) was placed in a reaction vessel and allowed to decompose according to the above reaction. At equilibrium, the concentrations of POCl(g) and Cl2(g) were each 0.150 M. What was the initial concentration of POCl3(g)?Answer: 0.200 M Answer the questions below using the following information on stocks A, B, and C. Stock ABC Beta 1.822.20.8 Assume the risk-free rate of return is 3% and the expected market return is 12% According to CAPM, what is the required return for stocks A, B, and C? Calculate the definite integral S4 **+2 2 dx, by: +2 a) trapezoidal rule using 6 intervals of equal length. b) Simpson's rule using 6 intervals of equal length. Round the values, in both cases to four decimal points describe and give an example ofTropical xerophytic forests and subtropical rain forests Charlie's Indifference curves have the equation y constant/x, where larger constants correspond to better indifference curves. Charlle strictly prefers the bundle (5, 13) to the bundle O None of the a Minerals can form in all of the following ways EXCEPT:a) Crystallization from a magmab) Metamorphismc) Physical weatheringd) Precipitation from hot springs it destroyed a european coalition of austrian, polish, bavarian, and saxon forces at vienna in 1683 and held the city for ten years. I know how to do part (a); I just need help with part (b). I have the answer, but I can't figure out how to arrive at it. I thought it would just be P(2,2) P(4,4) P(2,2) or 2!4!2!, but that's not working out for me.Here's the problem:At a college library exhibition of faculty publications, two mathematics books, four social science books, and two biology books will be displayed on a shelf. (Assume that none of the books is alike.)(a) In how many ways can the eight books be arranged on the shelf?40,320 ways(b) In how many ways can the eight books be arranged on the shelf if books on the same subject matter are placed together?576 ways Epsilon company is considering investing in Project X or Project Y. Project X generates the following cash flows: year ""zero"" = 339 dollars (outflow); year 1 = 255 dollars (inflow); year 2 = 290 dollars (inflow); year 3 = 335 dollars (inflow); year 4 = 186 dollars (inflow). Project Y generates the following cash flows: year ""zero"" = 230 dollars (outflow); year 1 = 120 dollars (inflow); year 2 = 100 dollars (inflow); year 3 = 200 dollars (inflow); year 4 = 120 dollars (inflow). The MARR is 10%. Compute the External Rate of Return (ERR) of the BEST project. Standing at a location, a person can throw a ball anywhere within a circle of radius 50 yards. A randomly chosen person attempts to throw a ball. What is the average and standard deviation of the distance thrown by any individual? LetA=102111215 and b=317.Define the linear transformation T:R2R2as T(x)=Ax. Find a vector xwhose image under Tis b.x=Is the vector xunique? (enter YES or NO) A new client has just been released from the hospital after intensive treatment for multiple injuries after a motorcycle accident. what type of care will he probably receive? Marks cost does not vary directly with time spent talking because