in a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 47 and a standard deviation of 5. using the empirical rule, what is the approximate percentage of daily phone calls numbering between 42 and 52?

[tex]10 + 9 + 2 + 4 = 25[/tex] possible outcomes

[tex]25 - 4 = 21[/tex] outcomes that are not green

[tex]\dfrac{21}{25}[/tex] chance that you don’t choose green

[tex]\frac{21}{25}=\bold{84\%}[/tex]

a) The power series representation of f(x) = 1/5 + x f(x) centered at x = 0 is f(x) = sigma^infinity_n = 0 ((x/5)^n)

b) The interval of convergence is (-5, 5)

To find the power series representation of f(x), we can use the formula for the geometric series

1 / (1 - r) = sigma^infinity_n = 0 (r^n)

where r is a constant.

In this case, we have

f(x) = 1/5 + x f(x)

We can solve for f(x) to get

f(x) = 1/5 / (1 - x)

Using the formula for the geometric series with r = x/5, we have

f(x) = sigma^infinity_n = 0 ((x/5)^n)

Multiplying both sides by 5, we get

5f(x) = sigma^infinity_n = 0 (x^n

So the power series representation of f(x) centered at x = 0 is

f(x) = sigma^infinity_n = 0 ((x/5)^n)

To determine the interval of convergence, we can use the ratio test

| (x/5)^(n+1) | / | (x/5)^n | = |x/5|

The series converges if the limit of |x/5| as n approaches infinity is less than 1. This is true when |x| < 5, so the interval of convergence is (-5, 5).

Learn more about power series here

brainly.com/question/17193241

#SPJ4

Answer:

Step-by-step explanation:

Answer:

There are 13 hearts in a deck of cards, so the probability of drawing a heart on the first draw is 13/52. After the first heart is drawn, there are 12 hearts left in the deck out of a total of 51 cards, so the probability of drawing another heart is 12/51. This process continues until we have drawn 4 hearts and 1 spade. Therefore, the total number of ways to draw 5 cards with 4 hearts and 1 spade is:

(13/52) x (12/51) x (11/50) x (10/49) x (13/48) x 5!

The factor of 5! accounts for the fact that the 5 cards can be drawn in any order. Simplifying the expression above, we get:

(13/52) x (12/51) x (11/50) x (10/49) x (13/48) x 120 = 0.000495 or approximately 1 in 2,020 ways.

Therefore, there are approximately 2020 ways to draw 5 cards from a regular deck of cards and get 4 hearts and 1 spade.

There are 54,145,200 ways to draw 5 cards and get 4 hearts and 1 spade from a regular deck of cards.

There are 13 hearts in a deck of cards, so the probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing another heart on the second draw, given that one heart has already been drawn, is 12/51. The same goes for the third and fourth draws. The probability of drawing a spade on the fifth draw is 13/50.

To calculate the number of ways to draw 4 hearts and 1 spade, we need to multiply the number of ways to choose 4 hearts from 13 (13 choose 4 or 715) by the number of ways to choose 1 spade from 13 (13 choose 1 or 13) and then multiply that by the number of ways to arrange those 5 cards (5!). So, the total number of ways is:

715 * 13 * 5! = 54,145,200

Therefore, there are 54,145,200 ways to draw 5 cards and get 4 hearts and 1 spade from a regular deck of cards.

Learn more about Cards

brainly.com/question/7570270

#SPJ11

Answer:

[tex]\frac{\sqrt{202} }{9}[/tex] OR ≈ 1.57919

Step-by-step explanation:

tanθ = opp/adj

opp/adj = 11/9

hyp = [tex]\sqrt{202}[/tex]

secθ = 1/cosθ

cosθ = [tex]\frac{9}{\sqrt{202} }[/tex]

1/cosθ = [tex]\frac{1}{\frac{9}{\sqrt{202} } }[/tex]

= [tex]\frac{\sqrt{202} }{9}[/tex] or ≈ 1.57919

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

1) We know that there is a total of 24 hours in a day.

therefore, 7/8 hours of Wednesday =

number of hours in a day = 24

number of hours every Wednesday = 7/8

= 7/8 x 24 hours

= 7 x 3 hours

= 21 hours

7/8 hours every Wednesday means 21 hours every Wednesday.  

2) We know that there are a total of 24 hours in a day;

therefore, 3/8 hours of Friday =

number of hours in a day = 24

number of hours every Friday = 3/8

= 3/8 x 24 hours

= 3 x 3 hours

= 9 hours

3/8 hours every Friday means 9 hours every Friday.

therefore, the total number of hours = 21 + 9 = 30

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

To learn more about sum, click here:

brainly.com/question/29034036

#SPJ4

Answer:

I'm pretty sure it's C. isnnxixiab

Answer:

The answer should be 20,365.714 but I am not sure

Step-by-step explanation:

Answer:

m = 50 + 6

m= 56

lol easy ques

This one is easy. All you have to do is add 6 to both sides to get the value of m

m-6=50

m=50+6

m=56

The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines.

An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.

For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.

Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.

To determine the double inequalities that define the shaded region, we need to find the equations of the two boundary lines that form the sides of the shaded region.

The two vertical lines are x=-4 and x=3. The two horizontal lines are y=1 and y=6.

The shaded region is enclosed by these four lines, so the double inequalities that define it are:

-4 ≤ x ≤ 3 and 1 ≤ y ≤ 6

The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines. Together, they define the rectangular shaded region with vertices (-4,1), (-4,6), (3,6), and (3,1).

To know more about equations visit:

https://brainly.com/question/30289958

#SPJ1

The inverse function for the given function F(x)=1/x² -3x +1  is given by

f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.

Function f(x) is equals to,

F(x)=1/x² -3x +1

Inverse of a function, we need to swap the positions of the x and y variables and then solve for y.

Let's start with the original function

f(x) = 1/x^2 - 3x + 1

Now we will swap x and y,

⇒ x = 1/y^2 - 3y + 1

Next, Solve for y in terms of x

⇒ x = 1/y^2 - 3y + 1

⇒ x - 1 = 1/y^2 - 3y

⇒ 1/(x - 1) = y^2 - 3y

⇒ 1/(x - 1) = y(y - 3)

⇒ y(y - 3) = 1/(x - 1)

⇒ y^2 - 3y - 1/(x - 1) = 0

Using the quadratic formula, solve for y to get inverse function we have,

y = (3 ± √(9 + 4/(x - 1))) / 2

Therefore, the inverse function of f(x) is equal to f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.

Learn more about inverse function here

brainly.com/question/29157071

#SPJ4

The above question is incomplete, the complete question is:

F(x)=1/x squared -3x +1 then Find the inverse

Answer:

i don't know i haven't done integers in a long time

Step-by-step explanation:

Answer:

Density = number of books over volume of box

Step-by-step explanation:

The formula that can be used to calculate the density of books in the box is:

Density = number of books / volume of box

This formula relates the number of books in the box to the volume of the box, and calculates the density of books per unit volume.Therefore, the correct formula to calculate the density of books in the box is the first one given in the options:

Density = number of books over volume of box

Answer:

Density = number of books over volume of box

Step-by-step explanation:

Coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. The side chains of the tetraalkylammonium are modified with the ethylene glycol ether, which is a highly polar solvent, allowing for better solubility in nonaqueous electrolyte solutions. Additionally, the ethylene glycol ether has the ability to modify the stability of the ionic species, preventing aggregation and ensuring the longevity of the battery. This increases the redox capacity and enhances the performance of the flow battery.

The ethylene glycol ether-tetraalkylammonium coupling has been proven to be an effective method for improving the solubility and stability of anthraquinone-based ionic species. For example, it has been observed that the coupling of ethylene glycol ether to anthraquinone-based ionic species enhanced the current density of the battery by more than 3 times. Furthermore, the coupling process has also been found to improve the energy efficiency and storage capacity of the nonaqueous redox flow battery.

Overall, coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method for enabling highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. This process has been proven to improve the performance of the battery, including current density, energy efficiency, and storage capacity.

for such more questions on solubility

https://brainly.com/question/23946616

#SPJ11

Answer: 1 1/12

Step-by-step explanation:

so you would subtract 2-1=1

Then you do 1/3-1/4=1/12

The answer would be 1 1/12

UR WELCOME

The missing dimension of the cone is its height, which is approximately 2.5 m when rounded to the nearest tenth.

We can use the formula for the volume of a cone, which is:

Volume = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

We are given the volume of the cone as 13.4 m³ and the radius as 3.2 m. Substituting these values into the formula, we get:

13.4 = (1/3)π(3.2)²h

Multiplying both sides by 3 and dividing by π(3.2)², we get:

h = 3 × 13.4 / π(3.2)²

h ≈ 2.5 m

Find more about volume of the cone

brainly.com/question/1578538

#SPJ4

The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.

A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]

The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.

The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.

for such more question on resistance

https://brainly.com/question/28135236

#SPJ11

As per the combination concept, there are 735,471 ways to choose 16 shows from a set of 24.

To find the number of ways to choose 16 shows from a set of 24, we can use the formula for combinations, which is:

ⁿCₓ = n! / x!(n-x)!

Where n is the total number of objects in the set (in this case, 24), and x is the number of objects we want to choose (in this case, 16). The exclamation mark (!) denotes the factorial function, which means multiplying the number by all positive integers less than itself.

Plugging in the numbers, we get:

²⁴C₁₆ = 24! / 16!(24-16)! = 735471

To know more about combination here

https://brainly.com/question/28998705

#SPJ4

1. The amount of medication to be given is 99.25 mg.

2.The amount of 1.985 mL medication should be injected.

To answer the given question, let's follow the steps mentioned below.

1. Convert the weight of the patient from pounds to kilograms.
    175 pounds = 79.4 kilograms

2. Multiply the patient's weight in kilograms by the ordered dosage.
    1.25 mg/kg × 79.4 kg = 99.25 mg

Therefore, 99.25 mg of medication is required

1. Find the number of milliliters (mL) required to deliver the medication dosage.
      The concentration of the drug is 100 mg/2 mL.
      100 mg/2 mL ÷ 1 = 50 mg/m

2. Divide the total amount of medication required by the concentration of the drug.
      99.25 mg ÷ 50 mg/mL = 1.985 mL

Therefore, 1.985 mL of the medication should be injected.

Note:

For similar question on medication.

https://brainly.com/question/28978561

#SPJ11

the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.

To calculate the surface area of a triangular prism, you need to find the area of each of the faces and add them up.

First, let's find the area of the two triangular faces. To do this, we need to find the base and height of each triangle. Since the prism is isosceles, the base of each triangle is 6 inches (the length of one of the sides of the equilateral triangle). The height of each triangle can be found using the Pythagorean theorem. We have two sides of the triangle: 4 inches and 5 inches. Using the Pythagorean theorem, we can find the height:

[tex]h^2 = 5^2 - 4^2\\h^2 = 25 - 16\\h^2 = 9\\h = 3[/tex]

So the height of each triangular face is 3 inches. Now we can find the area of each triangular face:

Area of one triangular face = (1/2) x base x height

= (1/2) x 6 x 3

= 9 square inches

Since there are two triangular faces, the total area of the triangular faces is:

Total area of triangular faces = 2 x 9 = 18 square inches

Next, let's find the area of the three rectangular faces. We have two rectangles with sides of 6 inches by 8 inches, and one rectangle with sides of 4 inches by 8 inches. The area of each rectangular face is:

Area of rectangular face = length x width

So the area of the rectangular faces are:

Area of rectangular face 1 = 6 x 8 = 48 square inches

Area of rectangular face 2 = 6 x 8 = 48 square inches

Area of rectangular face 3 = 4 x 8 = 32 square inches

Therefore, the total surface area of the triangular prism is:

Total surface area = 18 + 48 + 48 + 32 = 146 square inches

So the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.

To know more about Pythagorean theorem click here:

brainly.com/question/28361847

#SPJ4

The inequality that represents Miguel's spending limit is $16.00 ≤ x.

Let x represent the total amount of money Miguel wants to spend. We know he spent $10.49 on popcorn and can spend up to $5.51 on a drink.

To find the inequality, we can add these two amounts together and set it less than or equal to x, since x represents the maximum amount he wants to spend. Mathematically, we can write:

$10.49 + $5.51 ≤ x

Simplifying this inequality, we get:

$16.00 ≤ x

This means that Miguel can spend up to $16.00 in total on the popcorn and drink combined. If he spends more than $16.00, he will have exceeded his limit.

To know more about inequality here

https://brainly.com/question/28823603

#SPJ4

There are a total of 32 different possible footwear choices that we can make.

Given, The number of pairs of socks = 4

The number of pairs of shoes = 4

We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.

So, We can wear any pair of socks with any pair of shoes including a mismatch.

Thus, for each pair of socks, there are 4 possible pairs of shoes.

And for each pair of shoes, there are 4 possible pairs of socks.

Therefore, we can form,

Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.

For similar question on combination.

https://brainly.com/question/24306044

#SPJ11

Answer:

x = 8

y = 12

Step-by-step explanation:

m∠A = sin⁻¹(9/15) = 36.87⁰

cos36.87 = y/15

y = 15(cos36.87) = 12

sin36.87 = 12/(12+x)

12 + x = 12/(sin36.87)

x = 12/(sin36.87) - 12 = 8

Ronaldo's family drove a total of 6.90 kilometres to get from their house to the store.

To determine the total distance Ronaldo's family drove, we need to add the distance from their house to the gas station and the distance from the gas station to the store. We can write this as:

[tex]4 6/10 km + 2 30/100 km[/tex]

To add these two distances, we need to find a common denominator for the fractions. The smallest common denominator for 10 and 100 is 100, so we can convert the first distance to an equivalent fraction with a denominator of 100:

[tex]4 6/10 km = 4 60/100 km = 4.60 km[/tex]

Then we can add the two distances:

[tex]4.60 km + 2.30 km = 6.90 km[/tex]

Therefore, Ronaldo's family drove a total of 6.90 kilometres to get from their house to the store.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ9

Alexis has 12 quarters and 8 dimes.

Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.

We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:

10d + 25q = 380

To make things easier, let's divide both sides of the equation by 5:

2d + 5q = 76

Now we can use the first equation to solve for d in terms of q:

d + q = 20

d = 20 - q

Substituting this into the second equation gives:

2(20 - q) + 5q = 76

Expanding the parentheses and simplifying, we get:

40 - 2q + 5q = 76

3q = 36

q = 12

Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:

d + q = 20

d + 12 = 20

d = 8

The total value of 12 quarters and 8 dimes is:

12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80


To know more about quarters and dimes refer here:

https://brainly.com/question/6500943#

#SPJ11

Answer:

x = 3, y = 4

Step-by-step explanation:

Substitute 4x - 8 in for y and then solve for x:

4x + 2(4x - 8) = 20

Then, 4x + 8x - 16 = 20 --> 12x = 36 --> x = 3.

Once you have x, you can solve for y.

y = 4x - 8 = 4(3) - 8 = 12 - 8 = 4

So, x = 3, y = 4

To solve this problem, we need to convert the hexadecimal numbers (20cba)16 and (a02)16 to decimal form, add them together, and then convert the result back to hexadecimal form.

(20cba)16 = 2x16^4 + 12x16^3 + 11x16^2 + 10x16^1 = 131402

(a02)16 = 10x16^2 + 0x16^1 + 2x16^0 = 256

Adding the two decimal numbers together gives us:

131402 + 256 = 131658

To convert this decimal number back to hexadecimal form, we can use the repeated division method.

131658 / 16 = 8228 remainder 10 (A)

8228 / 16 = 514 remainders 4 (4)

514 / 16 = 32 remainder 2 (2)

32 / 16 = 2 remainder 0

2 / 16 = 0 remainder 2

Therefore, (20cba)16 + (a02)16 = (131658)10 = (2002A)16.

To find their product, we can multiply the two decimal numbers together and then convert the result to hexadecimal form.

131402 x 256 = 33559552

Converting this decimal number to hexadecimal form gives us:

33559552 / 16 = 2097472 remainder 0

2097472 / 16 = 131092 remainder 0

131092 / 16 = 8193 remainder 4 (4)

8193 / 16 = 512 remainders 1 (1)

512 / 16 = 32 remainder 0

32 / 16 = 2 remainder 0

2 / 16 = 0 remainder 2

Therefore, the product of (20cba)16 and (a02)16 is (33559552)10 = (2011004)16.

For more questions like numbers (20cba)16, visit the link below:

https://brainly.com/question/9713995

#SPJ11

The correct interpretation of the 99 percent confidence interval (22.5, 28.7) is B: We are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.

This does not indicate that the mean level of the contaminant in all the water in the region is necessarily between 22.5 ppb and 28.7 ppb.

Confidence intervals provide an estimate of the population mean based on a sample. In other words, they indicate the range of values that are likely to include the true mean of the population. Therefore, the interval (22.5, 28.7) indicates that we are 99 percent confident that the mean of the sample (which is used to estimate the true population mean) lies between 22.5 ppb and 28.7 ppb. However, this does not guarantee that the true population mean (i.e., the mean of all the water in the region) lies between 22.5 ppb and 28.7 ppb.

The other answers are incorrect because they do not reflect the fact that the interval provides an estimate of the population mean based on a sample.

Answer A is incorrect because it states that all of the water in the region must contain a level of the contaminant between 22.5 ppb and 28.7 ppb, which is not necessarily true.

Answer D is incorrect because it states that there is a 0.99 probability that the mean of the sample is between 22.5 ppb and 28.7 ppb, when in reality the interval indicates that we are 99 percent confident that the mean of the sample is between 22.5 ppb and 28.7 ppb. Finally,

Answer E is incorrect because it states that there is a 0.99 probability that the true population mean (i.e., the mean of all the water in the region) is between 22.5 ppb and 28.7 ppb, which is not necessarily true.

In summary, the correct interpretation of the 99 percent confidence interval (22.5, 28.7) is that we are 99 percent confident that the mean level of the contaminant in the sample is between 22.5 ppb and 28.7 ppb.

See more about confidence interval at: https://brainly.com/question/16742675

#SPJ11