an online retailer has determined that the average time for credit card transactions to be electronically approved is 1.5 seconds. (round your answers to three decimal places.)(a) use an exponential density function to find the probability that a customer waits less than a second for credit card approval.(b) find the probability that a customer waits more than 3 seconds.(c) what is the minimum approval time for the slowest 5% of transactions? sec

Answers

Answer 1

a) The probability that a customer waits less than a second for credit card approval is approximately 0.498.

b) The probability that a customer waits more than 3 seconds for credit card approval is approximately 0.049.

c) The minimum approval time for the slowest 5% of transactions is approximately 2.545 seconds.

How to find probability and minimum time?

a) To find the probability that a customer waits less than a second for credit card approval, we can use the exponential density function. The exponential distribution is characterized by a single parameter, which is the average (or mean) waiting time.

In this case, the average waiting time for credit card approval is 1.5 seconds. Let's denote this parameter as λ (lambda), where λ = 1 / average.

λ = 1 / 1.5 = 0.6667 (approximately)

The exponential density function is given by:

f(x) = λ * e^(-λx)

To find the probability that a customer waits less than a second (x < 1), we need to integrate the density function from 0 to 1:

P(x < 1) = ∫[0, 1] λ * e^(-λx) dx

Solving this integral, we get:

P(x < 1) = 1 - e^(-λx) = 1 - e^(-0.6667 * 1) ≈ 0.498

Therefore, the probability that a customer waits less than a second for credit card approval is approximately 0.498.

b) To find the probability that a customer waits more than 3 seconds, we can again use the exponential density function.

P(x > 3) = 1 - P(x < 3)

Using the same value of λ (0.6667), we can calculate:

P(x > 3) = 1 - (1 - e^(-0.6667 * 3)) ≈ 0.049

Therefore, the probability that a customer waits more than 3 seconds for credit card approval is approximately 0.049.

c) To find the minimum approval time for the slowest 5% of transactions, we need to find the corresponding value of x.

We can use the quantile function of the exponential distribution. For the slowest 5% of transactions, the quantile is denoted as q, where P(x < q) = 0.05.

q = -ln(1 - 0.05) / λ ≈ -ln(0.95) / 0.6667 ≈ 2.545

Therefore, the minimum approval time for the slowest 5% of transactions is approximately 2.545 seconds.

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Related Questions

If an item has an original price of $65, but is discounted 20%. What is the total cost after sales tax (.0825)?

Answers

Answer:56.29$

Step-by-step explanation:

65 x .80 = 52

52 x 1.0825 = 56.29

Answer:

$56.29

Step-by-step explanation:

Original price = $65

discount = 20%

hence discounted price = 100% - 20% = 80% of the original price

discounted price = 80% x $65 = $52

sales tax rate = 0.0825 (i.e 8.25%)

amount of sales tax paid

= 0.0825 x discounted price

= 0.0825 x $52

= $4.29

Final cost

= discounted price + sales tax

= $52 + $4.29

= $56.29

In ΔMNO, m = 8.5 inches, m∠N=52° and m∠O=23°. Find the length of o, to the nearest 10th of an inch.

Answers

Answer:

3.4 inches

Step-by-step explanation:

You want the length of side o in ∆MNO with N = 52°, O = 23°, and m = 8.5 inches.

Law of Sines

The law of sines tells you the side lengths of a triangle are proportional to the sine of the opposite angle:

o/sin(O) = m/sin(M)

In order to make use of this relationship, we need the value of angle M.

M +N +O = 180°

M =52° +23° = 180°

M = 105° . . . . . . . . . . subtract 75°

Now, we can find the length o:

o = m·sin(O)/sin(M) = (8.5 in)·sin(23°)/sin(105°) ≈ 3.4384 in

The length of o is about 3.4 inches.

In MNO, m = 8.5 inches, mN=52 and mO=23. Find the length of o, to the nearest 10th of an inch.

the Robersons are planning to re-pave their driveway. The length of the driveway is 7 feet longer than the width. The total area of the driveway is 144 ft.² write an equation to represent the dimensions of the driveway. now find the dimensions of the driveway.

Answers

20 length by 7 feet.

If x+4/4 = y+7/7 then x/4 =___.
(Number 9 is the one I need an answer for)

Answers

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

$\sf \frac{x+4}{4} =\frac{y+7}{7}$

Use cross multiplication.

$\sf 7(x+4)=4(y+7)$

Solve the brackets.

$\sf 7x+28=4y+28$

Subtract 28 from both sides.

$\sf 7x=4y+28-28\\\\\sf7x=4y$

Divide both sides by 7.

$\sf x=\frac{4y}{7}$

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

$\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}$

Question 3
Write the ordered pair for the post office.
?
Understand the Coordinate Plane-Quiz - Level E
DONE
10-
2987
7-
6543 N
4-
2
1
O
2 3 4 5 6
6 7
Post
Office
Library
8 9 10
A
X

Answers

Based on the coordinate plane, the ordered pair for the post office is (9, 9).

What is an ordered pair?

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

By critically observing the coordinate plane shown in the image attached below, we can logically deduce that the coordinates of the post office would be located in quadrant I at point (9, 9).

Similarly, the the coordinates of the library is also located in quadrant I and it is represented by the ordered pair (6, 2).

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Question 3Write the ordered pair for the post office.?Understand the Coordinate Plane-Quiz - Level EDONE10-29877-6543

What is 57.9709 divided by 3.456072

Answers

Answer: 16.77363782

Step-by-step explanation:

Higher income Here is the distribution of the adjusted gross income in
thousands of dollars) reported on individual federal income tax returns
in a recent year. Given that a return shows an income of at least
$50,000, what is the probability that the income is at least $100,000?

Answers

Probabilities are used to determine the chances of events

The probability that the income is at least $100,000 is 0.106

How to determine the probability

From the table, we have the following parameters:

Salary 100 - 499 = 0.100

Salary >= 500 = 0.006

The probability that the income is at least $100,000 is then calculated as:

p = 0.100 + 0.006

Evaluate the sums

p = 0.106

Hence, the probability that the income is at least $100,000 is 0.106

Answers

1) The solution to the initial-value problem is y(t) = 2 cos(4t) - (1/2) sin(4t).

2) The solution to the initial-value problem is y(t) = 0.

Let's solve the initial-value problems given.

Initial-Value Problem: y'' + 16y = 0, y(0) = 2, y'(0) = -2

We have a second-order linear homogeneous differential equation. To solve this, we assume a solution of the form y(t) = $e^{rt$, where r is a constant to be determined.

Substituting this assumed solution into the differential equation, we get the characteristic equation:

$r^2$ + 16 = 0

Solving the characteristic equation for r, we have:

r = ±4i

Since the roots are complex (r = 4i and r = -4i), the general solution will involve complex exponentials.

The general solution for the differential equation is:

y(t) = $c_1$ cos(4t) + $c_2$ sin(4t)

To find the particular solution that satisfies the initial conditions, we substitute the initial conditions y(0) = 2 and y'(0) = -2 into the general solution:

y(0) = $c_1$ cos(0) + $c_2$ sin(0) = $c_1$ = 2

y'(0) = -4$c_1$ sin(0) + 4$c_2$ cos(0) = 4$c_2$ = -2

Solving these equations, we find $c_1$ = 2 and $c_2$ = -1/2.

Therefore, the solution to the initial-value problem is:

y(t) = 2 cos(4t) - (1/2) sin(4t)

2) Initial-Value Problem: y'' + y' + 2y = 0, y(0) = y'(0) = 0

We have a second-order linear homogeneous differential equation. To solve this, we assume a solution of the form y(t) = $e^{rt$, where r is a constant to be determined.

Substituting this assumed solution into the differential equation, we get the characteristic equation:

$r^2$ + r + 2 = 0

Solving the characteristic equation for r, we have:

r = (-1 ± √(1 - 4(1)(2)))/2

= (-1 ± √(-7))/2

= (-1 ± i√7)/2

Since the roots are complex, the general solution will involve complex exponentials.

The general solution for the differential equation is:

y(t) = $c_1$ $e^{-t/2$ cos((√7/2)t) + $c_2$ $e^{-t/2$ sin((√7/2)t)

To find the particular solution that satisfies the initial conditions, we substitute the initial conditions y(0) = 0 and y'(0) = 0 into the general solution:

y(0) = $c_1$ = 0

y'(0) = -(1/2)$c_1$ + (√7/2)$c_2$ = 0

Solving this equation, we find $c_1$ = 0 and $c_2$ = 0.

Therefore, the solution to the initial-value problem is:

y(t) = 0

In this case, the zero solution satisfies the initial conditions.

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Damon makes 20 cups of lemonade by mixing lemon juice and water. The ratio of lemon juice to water is shown in the tape diagram.

Answers

Answer:

4 cups

Step-by-step explanation:

( 20 / 5 ) × 1 = 4

cups total lemon

ratio juice

ratio

Which expression is equivalent to (7x+9y)2

Answers

Answer:

$49x^2+126xy+81y^2$

Step-by-step explanation:

Use the square of a binomial theorem

$(a+b)^2$= $a^2+2ab+b^2$

Now expand the given equation:

$(7x+9y)^2=49x^2+126xy+81y^2$

Hope this helps :)

Have a great day!

Which of the following factors does NOT control the stability of a slope?
the angle of repose for intact bedrock
whether the slope is rock or soil
the amount of water in the soil
the orientation of fractures, cleavage, and bedding

Answers

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Which of the following functions represent exponential decay and has a y-
intercept of 2?
O y = {(0.85)*
O y = (2)*+2
O y = 4 (2)*
O y = 2(3)*

Answers

Answer:

Non of the given options

A function that represent an exponential decay and 2 as the y-intercept is y = 0.85ˣ + 1

Step-by-step explanation:

An exponential decay function is a function that reduces in magnitude at a constant percentage rate, r (< 1)

An exponential decay can be represented by the formula, y = a·(1 - r)ˣ

Therefore, the growth factor, (1 - r) = b is less than 1 for an exponential decay

Therefore the function that represent an exponential decay is y = 0.85ˣ, while a function that represent an exponential decay and has a y-intercept of 2 is y = 0.85ˣ + 1. therefore, non of the options

if 7 cosec^2 theta-9 cot^2theta=7 then what is the value of tantheta

Answers

The value of tanθ = ±∞ or tanθ = ±√(7/5)

The question is a trigonometric equation

What is a trigonometric equation?

A trigonometric equation is an equation that has unknowns that contain trigonometric ratios.

How to find the value of tanθ?

Given the trigonometric equation 7cosec²θ - 9cot²θ = 7, we require tanθ.

So, 7cosec²θ - 9cot²θ = 7

using the trigonometric identity 1 + cot²θ = cosec²θ.

Substituting this into the equation, we have

7cosec²θ - 9cot²θ = 7

7(1 + cot²θ)² - 9cot²θ = 7

7(1 + 2cot²θ + cot⁴θ) - 9cot²θ = 7

7 + 14cot²θ + 7cot⁴θ - 9cot²θ = 7

14cot²θ + 7cot⁴θ - 9cot²θ = 7 - 7

14cot²θ + 7cot⁴θ - 9cot²θ = 0

7cot⁴θ + 14cot²θ - 9cot²θ = 0

7cot⁴θ + 5cot²θ = 0

Factorizing out cot²θ, we have

cot²θ(7cot²θ - 5) = 0

⇒ cot²θ = 0 or 7cot²θ - 5 = 0

⇒ cotθ = ±√0 or 7cot²θ = 5

⇒ cotθ = ±0 or cot²θ = 5/7

⇒ cotθ = ±0 or cotθ = ±√(5/7)

⇒ 1/tanθ = ±0 or 1/tanθ = ±√(5/7)

⇒ tanθ = ±1/0 or tanθ = ±√(7/5)

⇒ tanθ = ±∞ or tanθ = ±√(7/5)

So, the value of tanθ = ±∞ or tanθ = ±√(7/5)

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156 divided by 24 and 102 divided by 15 both have the quotient of 6 and the remainder of 12. Are the division expressions equivalent to each other or not

Answers

Yes , the division expressions are equivalent to each other 156/24 = 6.5, 102/15 = 6.8

156 = dividend
24 = divisor
156/24 and 102/15 both have a quotient of 6 and a remainder of 12.

156/24 = 6.5.

102/15 = 6.8.

Equivalent expressions that are equivalent do the same thing even though they have different appearances. When we enter the same value(s) for the variable, when we plug in the same value(s) for the variable(s).

The remainder is the amount that does not entirely enter the divisor; the quotient is the number that left after a division is fully completed.

For example, 105 divided by 15 is R 1, so 6 is the quotient, and 12 is the remainder.

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can someone help me. i missed todays lesson and kinda having a brain malfunction

Answers

Answer:

x^2 +2 quadratic

1/3x + 3 linear

Find the volume of a cone that has a radius of and a height of 1.

Answers

the volume of the cone would be 2.36 I hope this helps ❤️

A computer originally priced at $850 is on sale for 15% off. What is the sale price of the computer?

Answers

Answer:

Sale price: $722.50

Step-by-step explanation:

Subtract 15% from 100%, obtaining 85%. The computer is sold for 85% off.

Converting this 85% to a mixed decimal, we get 0.85, and then we multiply the original price ($850) by this 0.85: 0.85($850) = $722.50

Which of the following expressions is the GCF of the polynomial
12x³y5-8x²y³ +24x5y¹?

A. 4x²y³
B. 8x5y5
C. 8x²y³
D. 4x^5y^5

Answers

Answer: B. 8x5y5

Step-by-step explanation: i guessed it but it was worth a try

A parabola can be drawn given a focus of (-4,-3) and a directrix of y = 1. Write the equation of the parabola in any form?

Answers

Answer:

Step-by-step explanation:

To plot

(

−

)

, start at the origin

(

)

and move left

units and down

units.

(

−

)

The function f(x) = a^x -4 will never cross the x-axis if a is positive.

Answers

If a is positive, the function f(x) = $a^x$ - 4 will never cross the x-axis.

1. We want to determine whether the function f(x) = $a^x$ - 4 will intersect or cross the x-axis.

2. To find the x-intercepts, we set f(x) = 0 and solve for x. In this case, we have $a^x$ - 4 = 0.

3. Adding 4 to both sides of the equation, we get $a^x$ = 4.

4. If a is positive, raising a positive number to any power will always yield a positive value.

5. Therefore, there are no values of x that will make $a^x$ equal to 4 when a is positive.

6. Since the function f(x) = $a^x$ - 4 cannot equal zero, it will never cross the x-axis when a is positive.

7. In other words, the graph of the function will always remain above the x-axis for positive values of a.

8. However, if a is negative, then there will be values of x where $a^x$ - 4 = 0 and the function crosses the x-axis.

9. Therefore, the statement that the function f(x) = $a^x$ - 4 will never cross the x-axis is true only when a is positive.

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The length of a rectangle in longer than it’s width. If the perimeter of the rectangle is 70 in, find the length and width.

Answers

When the perimeter of the rectangle is 70 in, the length and width are 19 and 16 inches.

How to calculate the length?

It should be noted that the perimeter of a rectangle will be calculated as:

= 2(Length + Width)

In this case, the length of a rectangle is 3in longer than it’s width and the perimeter of the rectangle is 70 in.

Therefore, width = w

length = w + 3

The perimeter will be:

2(w + w + 3) = 70

2(2w + 3) = 70

4w + 6 = 70

Collect like terms

4w = 70 - 6

4w = 64

Divide

w = 64 / 4

w = 16

Width = 16 inches

Length = w + 3 = 16 + 3 = 19 inches.

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Complete question

The length of a rectangle is 3in longer than it’s width. If the perimeter of the rectangle is 70 in, find the length and width.

PLS HELP!! PThe tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days. How do the functions in the table compare?Since x-intercepts indicate the amount of eachbacteria at the start of the experiment, there wasmore of bacteria B than bacteria A at the start.O Since y-intercepts indicate the amount of eachbacteria at the start of the experiment, there wasmore of bacteria B than bacteria A at the start.O Since the maximum value in the table for bacteria Ais greater than the maximum value in the table forbacteria B, bacteria A has a faster growth rate thanbacteria B.O Since the minimum value in the table for bacteria Ais less than the minimum value in the table forbacteria B, bacteria A has a slower growth rate thanbacteria B

Answers

Solution

The answer

Since y-intercepts indicate the amount of each

bacteria at the start of the experiment, there was

more of bacteria B than bacteria A at the start.

Fill in the blank to make the statement true: -18 ___ -19

<

=

>

Answers

Answer: -18 > -19

Step-by-step explanation:

ANWSER:-18>-19

I hope this helped

Kelly got a part time job and had to pay $150 worth of taxes, which was 10% of her monthly payment. How much money did she make before paying taxes?

Answers

Answer:

$1,500

Step-by-step explanation:

To find how much money she made before paying taxes, divide 150 by 0.1:

150/0.1

= 1500

So, Kelly made $1,500 before taxes

Answer:

$1,500

Step-by-step explanation:

Turn 10% into a decimal: To turn a percent into a decimal, you move the decimal twice to the left.

10%=.1

Divide: $150 divided by .1=1500

$1,500

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Good luck!

Brainliest?!?!

Alyssa’s extended family is staying at the lake house this weekend for a family reunion. She is in charge of making homemade pancakes for the entire group. The pancake mix requires 2 cups of flour for every 10 pancakes.

1. Write a ratio to show the relationship between the number of cups of flour and the number of pancakes made.

2. Determine the value of the ratio.

3. Use the value of the ratio to fill in the following two multiplicative comparison statements.

a. The number of pancakes made is ________ times the amount of cups of flour needed.

b. The amount of cups of flour needed is ________ of the number of pancakes made.

4. If Alyssa has to make 70 pancakes, how many cups of flour will she have to use?

Answers

Answer:

1. 2:10 or 1:5

2. 20%

3a. 5

3b. 1/5

4. 14 cups. If you multiply the ratio by 7 to get 70 total pancakes, the other value will be 14.

2:10 * 7 = 14:70

Which function has a greater slope? Function 1 Function 2 or both

Answers

Answer:

Function 2!

Step-by-step explanation:

the slope is longer

helllllllllllllllllpppppp meeeeeeeeeeee please i really need this Sabastian wanted to compare how much time his neighbors spend on the Internet to how much mail they receive in a week. He gathered data by surveying his neighbors. [ NOTE: He gathered data, so He Has it Already, do not go back in time...] Explain the steps Sabastian should take in order to analyze the data.

Answers

Answer:

Step-by-step explanation:

Step 1: Create a Survey

Step 2: Administer the Survey

Step 3: Collect responses.

Step 4: Organize responses - Since the data is bivariate I'd like to see them explain that they would maybe use a frequency table to organize this data.

Step 5: Analysis

Then he can look at how to explain the organization of their data - can we use a chart? If I am using a scatter plot, how do I find the line of best fit? How do I correlate data, etc?

The step to analyze the collected data include plotting the data on an histogram

How to determine the steps?

From the question, we understand that the data has already been gathered.

The next step is to analyze the collected data.

This can be done in several ways.

One of them is as follows:

Sort the data in ascending orderDetermine the mean, median, mode and rangeDetermine the standard deviation and variancePlot the data on a chart (e.g. histogram)

Answers

Answer:

117

Step-by-step explanation:

Given the expression

r³ - 2s ← substitute given values into the expression

= 5³ - 2(4)

= 125 - 8

= 117

Hey there! $\bold{r = 5 ; s =4}$$\bold{5^3 -2(4)}\\ \\ \bold{5^3=5\times5\times5 \rightarrow 25\times5 = \underline{125}}\\\\\bold{2\times4=\underline{8}}\\\\\\\bold{125-8 = \underline{117}}\\\\\\\\\boxed{\boxed{\bold{Answer: \underline{117}}}}\huge\checkmark$Good luck on your assignment and enjoy your day!~$\frak{LoveYourselfFirst:)}$

i need an answer for this question please help 75x4000