The big smiles portrait studio is conducting a survey among their clients. one of the questions being asked is if they would recommend the studio to a friend. the studio has given the survey to a simple random sample of 65 clients during the past 2 weeks. what is the probability that more than 60 clients in the sample would answer yes on the survey question

The first few coefficients in the power series expansion of f(x) = (1 - 10x)² are: c₀ = 1, c₁ = -20, c₂ = 100, c₃ = -200, c₄ = 100. The radius of convergence (R) is infinite. The series representation of f(x) = (1 - 10x)² is: f(x) = 6 - 120x + 600x² - 1200x³ + 600x⁴ + ...

The first few coefficients in the power series expansion of f(x) = (1 - 10x)² are:

c₀ = 1

c₁ = -20

c₂ = 100

c₃ = -200

c₄ = 100

The radius of convergence (R) of the series can be determined using the formula:

R = 1 / lim |cₙ / cₙ₊₁| as n approaches infinity

In this case, since c₂ = c₃ = c₄ = ..., the ratio |cₙ / cₙ₊₁| remains constant as n approaches infinity. Therefore, the radius of convergence is infinite, indicating that the power series converges for all values of x.

The series representation of f(x) = (1 - 10x)² is given by:

f(x) = 6 - 120x + 600x² - 1200x³ + 600x⁴ + ...

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Answer:

MN║OP

Step-by-step explanation:

From the picture attached,

MP and OP are the two lines and OT is a transversal intersecting these lines at R and S.

Angles on the same side of transversal OT measure the same as 45°

By the converse of corresponding angles theorem,

"If the corresponding angles formed by the transversal with the lines, are equal in measure, then the lines are parallel."

Therefore, MN║OP is the answer.

The graph is an illustration of several linear functions.

These are functions that have a constant rate or slope

Coffee shop C is located at (8,2)

Hence, the coordinates of coffee shop C is (8,2)

Line QP passes through points (5,3.5) and (4.5,4.5)

Start by calculating the slope of the line

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m = \frac{4.5 - 3.5}{4.5 - 5}\)

\(m = -2\)

So, the equation of the line is:

\(y = m(x -x_1) + y_1\)

This gives

\(y = -2(x -5) + 3.5\)

\(y = -2x +10 + 3.5\)

\(y = -2x +13.5\)

Hence, the equation of line QP C is \(y = -2x +13.5\)

The perpendicular bisector of CD is a horizontal line that passes through y = 3.5

Hence, the equation of the perpendicular bisector of CD is y = 3.5

Point P is located at (5,3.5)

Hence, the coordinates of point P is (5,3.5)

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Answer: Thirty-eight thousand two hundred.

Step-by-step explanation: You'd get Thirty-eight thousand two hundred because the standard form is writing out the number using letters. So, we should break this down:

38,000 + 200 is a good strategy to divide big numbers.

So, 38,000 = Thirty-eight thousand

And 200 = two hundred

So, combine it and you get Thirty-eight thousand two hundred or Thirty-eight thousand and two hundred. (it's the same thing)

Answer:

24

Step-by-step explanation:

We can make the equation

225+50x=1425

=

50x=1200

=

x=24

Answer:

x = a, p

Step-by-step explanation:

the solution is at the points of intersection of the parabola and the straight line.

the points of intersection of the two graphs are (a, b ) and (p, q )

with x = a and x = p

thus x = a , p are the values of x that make the statement true

We are given a function f(x,y) = x/y and a point P(8,1). We need to find the gradient of the function, evaluate it at the point P, and find the rate of change of the function at P in the direction of the vector u = 3/5 i + 4/5 j.

Explanation:

(a) The gradient of a function is a vector that points in the direction of the steepest increase of the function at a point and its magnitude gives the rate of increase. The gradient of the function f(x,y) = x/y can be calculated using partial derivatives as follows:

∇f(x, y) = (∂f/∂x)i + (∂f/∂y)j

= (1/y)i - (x/y^2)j

(b) To evaluate the gradient at the point P(8,1), we substitute x=8 and y=1 in the expression for ∇f(x,y) as follows:

∇f(8, 1) = (1/1)i - (8/1^2)j

= i - 8j

(c) The rate of change of the function f(x,y) at the point P(8,1) in the direction of the vector u = 3/5 i + 4/5 j can be found by taking the dot product of the gradient at P with the unit vector in the direction of u as follows:

Duf(8, 1) = ∇f(8,1) . u/|u|

= (i - 8j) . (3/5 i + 4/5 j)/|(3/5 i + 4/5 j)|

= (3/5) - (32/5)

= -29/5

Therefore, the gradient of f is ∇f(x,y) = (1/y)i - (x/y^2)j, the gradient at P is ∇f(8,1) = i - 8j, and the rate of change of f at P in the direction of u is Duf(8,1) = -29/5.

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Answer:

x = 100/13

Step-by-step explanation:

x 169% = 13

x = 13/169%

x = 13/1.69 = 13/169/100

x = 13 × 100/169

x = 100=13

\(\\ \sf\longmapsto 169\%x=13\)

\(\\ \sf\longmapsto 1.69x=13\)

\(\\ \sf\longmapsto x=\dfrac{13}{1.69}\)

\(\\ \sf\longmapsto x=7.69\)

A confidence interval estimate of the population mean rating for Miami is:

Confidence interval:

(Mean - E) ≤ μ ≤ (mean + E)

(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

Now, According to the question:

Given the data:

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Assume a confidence interval of 95%

Using calculator :

The mean of the distribution (m) = 7.52

Standard deviation (s) = 2.314

Sample size),

Obtaining the t score ;

Degree of freedom (df) = (n-1) = 50 - 1 = 49

t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)

Margin of Error :

2.01 * s/√n = 2.01 * 2.314/7.0710678

Margin of Error (E) = 0.6578

Confidence interval:

(Mean - E) ≤ μ ≤ (mean + E)

(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

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The complete question is this:

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Required:

Develop a confidence interval estimate of the population mean rating for Miami.

Answer:

the answer is 720000

Step-by-step explanation:

looked it up

Answer:

to find out if two ratios form a proportion, they have to form a straight line and pass through the origin.

Step-by-step explanation:

Answer:

B) -8

Step-by-step explanation:

Slope is rise/run, or the difference in y over the difference in x, so to solve this:

Take the y value of one of the points and subtract it from the other, and divide it by the same thing with the x values

\(\frac{9-1}{6-7} =\frac{8}{-1} =-8\)

Answer:

\(let \: number \: of \: rides \: be \: \: n \\ let \: cost \: be \: \: c \\ n \: \alpha \: c \\ n = kc \\ k \: is \: a \: costant \: of \: proportionality \\ when \: n = 1. \: \: c = 2 \\ 1 = (k \times 2) \\ k = \frac{1}{2} \\ therefore : \\ n = 0.5c\)

Answer:

\(\huge\boxed{\sf x = 6 + 2y}\)

Step-by-step explanation:

Let the total cost be x and number of rides be y

It costs $2 on each ride. So, the rides' cost will be:

=> Number of rides * One rides' cost

=> y * 2

=> 2 y

So, The total cost will be:

Total cost = Entrance cost + Rides' cost

Total cost = $6 + $2(Number of rides)

x = 6 + 2y

\(\rule[225]{225}{2}\)

Hope this helped!

Hello there. To solve this question, we'll find how many times George's grandpa is older than his grandson.

First, this is also called the ratio of the ages between George and his grandpa.

To find this, we divide their ages in the order Grandpa : Grandson as following:

Simplify the fraction by a factor of 8

This is how many times George's grandpa is older than him.

Answer: 0.90 g/cm3

Step-by-step explanation:

Their ratio is given by the mass density of ice: M/V = Rhoi ~ 0.90 g/cm3 (iceberg ice is more dense than normal ice since it has been compressed by thousands of years of pressure - normal ice is 0.917 g/cm3).

Answer:

Basal melting of floating ice shelves and iceberg calving constitute the two ... of the Southern Ocean free of large icebergs are largely populated by small iceberg  the hidden part, which is the most important in terms of effort and often the most  So this work explores use of NISAR to map surface structures visible on ice

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

dgshdbahdbdbsbdbdbdbdbebdbdhdhd

Answer:

$18.84

Step-by-step explanation:

volume = πr²L = (3.14)(1²)(12) = 37.68 cm³

37.68 cm³ x 0.50 per cm³ = $18.84

Answer:  x= -6

Step-by-step explanation:

It will be a vertical line parallel to the y-axis at -6 on the x-axis. It passes through every y-value, including the given -5 and -2

Answer:

112

Step-by-step explanation:

734/2 = 367

367-255= 112

Answer:

112

Step-by-step explanation:

734 ÷ 2 = 367

367 - 255 = 112

An example of a +f(pxq) with integer coefficients that factors (poly mod nq), but has no roots is (x^2 + 1)(x^2 + 2). This polynomial satisfies the given conditions and demonstrates that it is possible to have a polynomial with integer coefficients that factors modulo n, but has no roots.

Let's consider the polynomial f(pxq) = (x^2 + 1)(x^2 + 2).
1. This polynomial has integer coefficients as both factors have integer coefficients.
2. Now, let's consider taking the modulo n, where n is any positive integer.
3. Since the modulo operation only affects the coefficients, we will still have a polynomial with integer coefficients after taking the modulo.
4. However, there are no integers x for which f(pxq) = 0 (poly mod n), as the factors x^2 + 1 and x^2 + 2 do not have any integer roots.

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An annual payment is found approximately $617.34. The correct option is e.. $617.34.

To find the size of your payments, you can use the formula for calculating the equal installments on a loan.

First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.

Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.

Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.

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Answer

PART A

Final Cost = $325

PART B

Price after this further discount is applied = $292.5

Explanation

PART A

Mia needs a computer that is $500

The computer is 35% for those that purchase on Saturday.

Final Cost = (Original Price) - (Discount)

Original Price = $500

Discount = 35% of $500 = 0.35 (500) = $175

Final Cost = (Original Price) - (Discount)

Final Cost = 500 - 175 = $325

PART B

There is a further 10% discount for those that arrive at 9:00 am

Price after this further discount is applied = 325 - (10% of 325)

= 325 - [(0.1)(325)]

= 325 - 32.5

= $292.5

Hope this Helps!!!

Answer:

Beau buys 7 kg of chicken for $45.50. Helen buys 10 lbs of chicken for $32.50:

To compare the prices of the chicken that Beau and Helen bought, we need to convert both measurements into the same unit. Since 1 kg = 2.20462 lbs, we can convert Beau's chicken into pounds.

7 kg x 2.20462 lbs/kg = 15.43 lb

So Beau bought 15.43 lbs of chicken for $45.50, meaning he paid:

$45.50 / 15.43 lbs = $2.95/lb

We can now compare this price to the price Helen paid for her chicken:

$32.50 / 10 lbs = $3.25/lb

So, Helen paid a higher price per pound of chicken.

Anne burns 150 calories playing 20 minutes of soccer. In 45 minutes of playing double tennis, Anne burns 306 calories:

To calculate the number of calories Anne burns per minute playing soccer and double tennis, we can divide the total number of calories burned by the time spent playing each sport:

Soccer: 150 calories / 20 minutes = 7.5 calories/minute

Double Tennis: 306 calories / 45 minutes = 6.8 calories/minute

So Anne burns slightly more calories per minute playing double tennis than she does playing soccer.

Jennifer took 40 minutes to ride her bike home from school. The distance from her house to school is 10 kilometers. If her speed remained consistent, how long did it take her to ride 8 kilometers:

To find out how long it would take Jennifer to ride 8 kilometers, we can use the formula:

time = distance / speed

We know that Jennifer's speed remained constant, so we can find her speed by dividing the distance she rode by the time it took her to do so:

speed = distance / time = 10 km / 40 minutes = 0.25 km/minute

We can now use this speed to calculate the time it would take Jennifer to ride 8 kilometers:

time = distance / speed = 8 km / 0.25 km/minute = 32 minutes

So it would take Jennifer 32 minutes to ride 8 kilometers at her constant speed.

Step-by-step explanation:

Approximately $1,061.88 is the payment of interest that Khalid should pay today in the bank paying 7% semi-annually.

Given, Khalid wants to have BD 30000 in his account by the end of 96 months. Interest rate = 7% (semi-annually)

We have to find how much should he pay interest today in the bank. For calculating this, we have to follow the below steps:

To calculate the payment of interest, we have to use the formula of Present Value of an Annuity or PV(Present value) of an annuity. In this formula, we have to calculate the present value of all the future payments, which he will be paying until the end of 96 months. Using the formula of Present Value of an Annuity or PV(Present value) of an annuity:

PV = PMT * [(1 - (1 + r/n)^-nt)/(r/n)]

Where, PV = Present Value

PMT = Payment amount

r = interest rate

n = number of times interest is compounded per year

t = time in years

For Semi-annually, the compounding period is 2.

PV = PMT * [(1 - (1 + r/n)^-nt)/(r/n)]

PV = Payment * [(1 - (1 + r/n)^-nt)/(r/n)]

PV = Payment * [(1 - (1 + 0.07/2)^-(96*2))/(0.07/2)]

PV = Payment * [(1 - (1.035)^-192)/(0.035)]

PV = Payment * [(1 - 0.000044)/0.035]

PV = Payment * 28.23130

Therefore, the amount Khalid should pay today in the bank paying 7% semi-annually is:

PV = Payment * 28.23130

$30,000 = Payment * 28.23130

Payment = $1,061.88

Approximately $1,061.88 is the payment of interest that Khalid should pay today in the bank paying 7% semi-annually.

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Answer:

(5,1)

is one of infinitely many possible order pairs.

Step-by-step explanation:

There are an infinite amount of x values that give you an answer to this question. You get to choose. But first let's start off with isolating y.

\(-x + 6y = 1\\6y = 1 + x\\y = \frac{1+x}{6}\)

Now the equation is easier to interpret. \(y = \frac{1+x}{6}\)

Now here's the part where you actually get to choose. Take any x, value, I'll choose 5.

I'll sub it into the equation and get my y value, \(y = \frac{1 + (5)}{6}= 1\)

Okay, we get that y = 1, when x = 5. That's an ordered pair:

(5,1)

Remember you could follow this same procedure for any x value you choose.

By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

What does testing your hypotheses mean?

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.

               First, a hazy assumption about the parameter or distribution is made.

What is hypothesis testing, and how can it be used?

A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.

                     The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.

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Answer:

7.76

Step-by-step explanation:

0.22×20=4.4

3.36(base amount ,average of the others)+4.4=7.76

The expression is to be written in complete square method and the value will be equal to  (x + 5/2)² + 7/4.

The expression x² + 5x + 8 is a quadratic polynomial and a quadratic polynomial is one which can be written in the form ax² + bx + c; where a, b and c are constant values and x is the independent variable. Now in order to write the expression by using completing square method we write the polynomial as

x² + 5x + 8

We divide the coefficient of x that is 5 by 2 so we get

x² + (5/2)x + 8

Now, we add and subtract the square of coefficient of x that is 5/2 so we get

x² + (5/2)x + 8 + (5/2)² - (5/2)²

From the above expression we get

(x + 5/2)² + 8 - 25/4

(x + 5/2)² + (32 - 25)/4

(x + 5/2)² + 7/4

Thus we have written the expression in the form (x + p)² + q as (x + 5/2)² + 7/4.

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 The sum is about 3.31227766017..., an irrational number.  3/20 +√10 = 0.15 + 3.16227766017...

To find the sum of 3/20 and √10, we first need to simplify the expression. The square root of 10 (√10) is an irrational number and cannot be simplified further. We can add the rational number 3/20 to √10, but we cannot combine them into a single term. Therefore, the sum of 3/20 and √10 cannot be simplified any further. As for classification, 3/20 is a rational number because it can be expressed as a fraction, whereas √10 is an irrational number because it cannot be expressed as a fraction.

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Answer:

44.10 = 2.1x

x = 21 miles

Step-by-step explanation:

Cost per mile = $2.1

Driver tip = $5

Total amount paid = $49.10

Let

x = number of miles

​Write an equation to determine the distance in miles \left(x\right)(x) between the airport and Anna's home.

Total cost of miles = Total amount paid - Driver tip

= $49.10 - $5

= $44.10

Equation to determine distance in miles

Total cost of miles = cost per mile * number of miles

44.10 = 2.1x

Find the distance between the airport and Anna's home

44.10 = 2.1x

Divide both sides by 2.1

44.10 / 2.1 = 2.1x / 2.1

21 = x

x = 21 miles