When X has the pdf: f(x) = λe^{-λx}λe^(-λx)λe^-λx for x>0
P(X>x) =
A. 1-λe^{-λx}λe^(-λx)λe^-λx
B. 1-λe^{-λx}λe^(-λx)e^-λx
C. λe^{-λx}λe^(-λx)λe^-λx
D. λe^{-λx}λe^(-λx)e^-λx

The letter represented by the star symbol is 1.

We can start by using the rules of arithmetic. Since each symbol represents a different digit, we can represent the symbols with the numbers 0 to 9. Then we can write the equation as an algebraic expression and solve for the star symbol.

Let's assign the value of the letter represented by the star symbol to x.

A + B = 10x + x = 11x

We know that the maximum value for the result of the addition (C) is 18 (9 + 9) and that the maximum value for 11x is 990 (90 * 11), so x cannot be greater than 9.

Let's try the lowest value for x, which is 0.

A + B = 10 * 0 + 0 = 0

Since 0 cannot be a digit in A or B, x cannot be 0.

Let's try the next value for x, which is 1.

A + B = 10 * 1 + 1 = 11

Since 11 is a valid result of the addition, x = 1 is a solution.

Therefore, the letter represented by the star symbol is 1.

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The complete question is:

In the following addition problem, different letters represent different digits, and equal letters represent equal digits. Find the value of the letter represented by the star symbol. A + B = C

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Miles and meters both are units of length. To change a mile's value to meters, you simply multiply it by 1609.344.

What is 1 mile?

A mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is also referred to as the international mile or the statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 meters, establishing a standard between the British Commonwealth and the United States.

To convert 1 mile to meters, multiply  1609.344 by the mile.

The model equation is y = 1609.344x

Where x is in the mile and y is in meters.

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Answer:

Step-by-step explanation:

if a carton of eggs is 4.30 then 1 egg is then 1 egg is 75 cents

The value for the Equation x- 6 = 53 is 59.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x- 6 = 53

Now, make as the subject of formula and solve for x

So, add 6 on both side

x- 6+ 6= 53 + 6

x = 59

Hence, the value of x is 59.

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'a' = 'a' and 'b' < 'd' are correct an rest are incorrect.

'a' = 'a' is correct. In programming and computer science, single quotes are used to denote a string literal, and equality between strings is determined by their lexicographical order. In this case, 'a' and 'a' are the same string, so they are equal.

0 = '0' is incorrect. In programming, 0 is a numerical value, while '0' is a string literal. They cannot be directly compared as equal, unless you cast the string to a numerical type, like this:

python

0 == int('0')

'b' < 'd' is correct. In the lexicographical order of strings, 'b' comes before 'd', so 'b' is considered to be less than 'd'.

'x' > 'y' is incorrect. In the lexicographical order of strings, 'x' comes after 'y', so 'x' is considered to be greater than 'y'.

Therefore, 'a' = 'a' and 'b' < 'd' are correct an rest are incorrect.

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He owed $14,983.85 at the end of 4 years.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Given:

P = $8000

R= 16%

T= 4 years

Now, The equation that models this situation is:

A(t) = P [tex](1 + r/n)^{nt[/tex]

where:

A is the amount he owes at any time (t)

P, is the initial amount borrowed (the amount owed at time t = 0)

n is the number of times the loan is compounded annually

r is the interest rate in decimal form

So,  A(4) = 8000[tex](1 + 0.16/4)^{4.4[/tex]

A(4) = 8000[tex](1 + 0.04)^{16[/tex]

A =  $14,983.85

Hence, the amount is  $14,983.85.

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Hope it helps u

Refer to the image below

Step-by-step explanation:

They are corresponding angle

The length of the other leg is 14.14 cm rounded to two decimal places.

Given data :

Given, The hypotenuse of a right triangle measures 15 cm, and one of its legs measures 5 cm.

We know,

Hypotenuse² = Base² + Adjacent².

Therefore,

15² = 5² + Adjacent².

Adjacent = √(225 - 25).

Adjacent = √200.

Adjacent = 14.14.

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No, the independence condition is not met. The conditions for a binomial setting have not been met in this scenario because the names were pulled and not replaced in the hat, which violates the independence condition.

In a binomial setting, the trials must be independent, meaning that the outcome of one trial does not affect the outcome of any other trial.

Since the names were not replaced in the hat, the outcome of each draw is not independent, and the conditions for a binomial setting have not been met.

Permutation refers to the arrangement of objects in a specific order. For example, if we have three objects A, B, and C, there are six possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA. The number of permutations of n objects is given by n!

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If McKenzie pays $150 per month, she will have paid a total of $92.832 in interest when she pays off her credit card. This is $36.224 more than she would have paid if she had paid $250 per month.

APR stands for Annual Percentage Rate, which is the interest rate associated with a loan, credit card, or other type of borrowing. It is expressed as a percentage and is typically higher than the interest rate because it includes additional costs associated with the loan such as origination fees, processing fees, and other costs.

Part A:

To calculate how long it will take McKenzie to pay off her credit card, we need to use the formula:

T = (B x i) / P

Where T is the total number of payments, B is the initial balance, i is the interest rate (in decimal form) and P is the amount of the payments.

In this case, B = 936, i = 0.01396 (13.96% expressed as a decimal) and P = 250. So, substituting these values into the formula, we get:

T = (936 x 0.01396) / 250

T = 3.784

Since payments are made monthly, we can round this to 4 payments. Therefore, it will take McKenzie 4 months to pay off her credit card if she makes payments of $250 per month.

Part B:

To calculate the amount of interest McKenzie will have paid when she pays off her credit card, we can use the formula:

I = B x i x T

Where I is the total amount of interest paid, B is the initial balance, i is the interest rate (in decimal form) and T is the total number of payments.

In this case, B = 936, i = 0.01396 and T = 4 (since we calculated this in Part A). So, substituting these values into the formula, we get:

I = 936 x 0.01396 x 4

I = 56.608

Therefore, McKenzie will have paid a total of $56.608 in interest when she pays off her credit card.

Part C:

To calculate how much more interest McKenzie will pay if she only pays $150 per month, we first need to calculate how long it will take her to pay off the credit card using this lower payment amount.

Using the same formula from Part A, we get:

T = (936 x 0.01396) / 150

T = 6.576

Since payments are made monthly, we can round this to 7 payments. Therefore, it will take McKenzie 7 months to pay off her credit card if she makes payments of $150 per month.

Now, to calculate the amount of interest McKenzie will have paid if she pays $150 per month, we can use the same formula from Part B:

I = B x i x T

Where I is the total amount of interest paid, B is the initial balance, i is the interest rate (in decimal form) and T is the total number of payments.

In this case, B = 936, i = 0.01396 and T = 7. So, substituting these values into the formula, we get:

I = 936 x 0.01396 x 7

I = 92.832

Therefore, if McKenzie pays $150 per month, she will have paid a total of $92.832 in interest when she pays off her credit card. This is $36.224 more than she would have paid if she had paid $250 per month.

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The solution is, 2 is the greatest common factor.

and,  10x^2 + 28x − 6=0 has solutions, x = -3, 0.2  a simplified version of the equation.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Simplifying :

10x^2 + 28x − 6=0

Rearrange the terms so that -6+28x+10x^2 =0

Figuring out the value of the variable "x".

Subtract out the number "2", which is the GCF.

2(-3+14x+5x^2)=0

To factor a trinomial

2(5x^2+15x-x-3)=0

(5x-1)(x+3)= 0

i.e. x= -3

or, x= 1/5

      =0.2

Hence, The solution is, 2 is the greatest common factor.

and,  10x^2 + 28x − 6=0 has solutions, x = -3, 0.2  a simplified version of the equation.

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The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil multiplied by height of the tank.

Work = 41 lb/ft3 x (height of the tank)

For example, if the height of the tank is 6 ft,

Work = 41 lb/ft3 x 6 ft = 246 lb-ft

The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil multiplied by the height of the tank.

The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil (which is typically measured in pounds per cubic foot) multiplied by the height of the tank in feet. Thus, the work required can be expressed as: Work = (Weight of olive oil) x (Height of tank in feet). For example, if the olive oil has a weight of 41 pounds per cubic foot and the height of the tank is 6 feet, the work required to pump the olive oil to the rim of the tank would be 246 lb-ft (41 lb/ft3 x 6 ft).

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Answer:

The last graph shows a line.

Step-by-step explanation:

In order, from top to bottom, you have an Angle, a Point, a Ray, and a Line.

The Ray (the one you have marked as the answer) is NOT correct because is has an endpoint and continues in only one direction.

The last image IS correct, it is a Line as it goes on forever in both directions. Honestly, they should have put arrows at each end.

Hope this helps!

Answer:

110° and 215°

Step-by-step explanation:

the bearing of D from C is the angle from the north line at C measured in a clockwise direction from C to D

(a)

bearing of D from C is the purple angle, that is 110°

(b)

bearing of D from C is the blue angle , that is 215°

It does not always take the same time to serve every customer. Option A is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
From the table,
For every order, the pair compare the unit rate of serving the customer.
1
unit rate = 2 / 8
unit rate = 1 / 4
unit rate = it took 4 minutes to serve a customer.

2.
unit rate = 4 / 16
unit rate = 1 / 4
unit rate = it took 4 minutes to serve a customer.

3
unit rate = 7 / 21
unit rate = 1 / 3
unit rate = it took 3 minutes to serve a customer.

Thus, It does not always take the same time to serve every customer. Option A is correct.

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Answer:

Step-by-step explanation:

To find the cost of a 33-minute taxi ride, we first need to determine the cost per minute of the taxi ride. We can do this by dividing the cost of a 14-mile taxi ride ($11.20) by the time it took (16 minutes):

$11.20 ÷ 16 minutes = $0.70 per minute

Now that we know the cost per minute, we can find the cost of a 33-minute taxi ride by multiplying the cost per minute by 33:

$0.70 x 33 minutes = $23.10

So a 33-minute taxi ride at this vacation spot would cost $23.10.

Answer:

7.3

Step-by-step explanation:

a = 2

b = 7

we can use the Pythagorean Theorem

c^2 = a^2 + b^2

c^2 = 4+49

c^2 = 53

c = sqrt(53)

c = 7.3

by solving this equation, the value of y = (x²+1)/(1-x²)

Equation can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make y the subject of the equation x = √((y-1)/(y+1)),

x = √[(y-1)/(y+1)]

we can square both sides:

x² = (y-1)/(y+1)

Next, we can multiply both sides by (y+1) to get rid of the fraction:

x² × (y+1) = y-1

x²y + x² = y - 1

Rearranging the terms:

x² + 1 = y - x²y

x² + 1 = y(1 - x²)

Divide both side by (1-x²) we get

y = (x²+1)/(1-x²)

So, y is the subject of the equation is y = (x²+1)/(1-x²)

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a) The slope of the graph is of $0.75, meaning that each lemon costs $0.75.

b) The intercept of the graph is of $0, meaning that there is not an additional fixed fee.

c) The equation of the line is given as follows: y = 0.75x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at the origin, hence the intercept b is given as follows:

b = 0.

When x increases by 8, y increases by 6, hence the slope m is given as follows:

m = 6/8

m = 0.75.

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The minimum rate of gasoline consumption is typically 0.5 gallons per day, which occurs after five days of vehicle inactivity. This is because the fuel system needs time to dissipate the fuel in the lines and the evaporative system.

The minimum rate of gasoline consumption is the amount used when a vehicle is not in use. This is typically 0.5 gallons per day and occurs after five days of a vehicle being inactive. This is because the fuel system needs time to dissipate the fuel in the lines and the evaporative system. When the vehicle is not used, the fuel system is not under pressure and the fuel in the lines and evaporative system is able to dissipate. This occurs gradually over a period of five days and once this has happened, the minimum rate of gasoline consumption is reached. The fuel system needs to dissipate the fuel in order to prevent it from becoming stale or evaporating, and this is the reason why the minimum rate of gasoline consumption is reached after five days of inactivity.

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The General Multiplication Rule in probability states that the probability of the intersection (occurrence) of two events, A and B, is equal to the product of their individual probabilities. The formula can be written as follows:

p(A and B) = p(A) * p(B | A)

where p(A) represents the probability of event A occurring, and p(B | A) represents the probability of event B occurring given that event A has already occurred.

The formula reflects the idea that the probability of both events occurring is equal to the probability of one event occurring, multiplied by the probability of the other event occurring given that the first event has already happened.

For example, let's say we have two events: "rolling a 6 on a dice" (A) and "choosing a spade from a deck of cards" (B). The probability of rolling a 6 on a dice is 1/6, and the probability of choosing a spade given that a 6 was rolled is 13/52. Using the general multiplication rule, the probability of both events occurring would be (1/6) * (13/52) = 13/312.

In summary, the general multiplication rule is a fundamental concept in probability that helps us calculate the probability of the intersection of two events.

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The coordinates for point B are 7 = √(x - 5)² + (y - 4)².

What is the distance formula?

The distance formula is used to calculate the length of the line which joins the two points in an x−y plane. The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line.

Here, we have

Given: Segment AB Has point A located At (5, 4). If The Distance from A To B Is 7 units.

To find the distance between any two the following formula is used.

D = √(x₂ - x₁)² + (y₂ - y₁)²

7 = √(x - 5)² + (y - 4)²

Hence, the coordinates for point B are 7 = √(x - 5)² + (y - 4)².

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Answer:

m = (d+2)/5

Step-by-step explanation:

d=5m-2

d+2 = 5m

m = (d+2)/5

The equation for the length of the legs is:

0.5*(x + 2)*x = 24

Remember that the area of a right triangle is equal to the product between the lengths of the legs over 2.

Then, if here the area is 24ft.

And the legs measure x and (x + 2), then the area equation will be:

x*(x + 2)/2 = 24

We can rewrite the 1/2 as 0.5, so we will get.

0.5*(x + 2)*x = 24

That is the equation on the first option.

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By using the equation of the trend line, it can be estimated that the​ hiker's elevation after 140 minutes will be, 1919.8 feet

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

The equation of a trend line for the​ hiker's elevation is,

y = 9.27x + 622​

x represents the number of minutes

y represents the​ hiker's elevation in feet

Elevation after 140 minutes = ?

Now, putting value of x as 140 in the given equation,

y = (9.27 x 140) + 622​

  =  1297.8 + 622

  =   1919.8

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Answer:

A. Positive Correlation

Step-by-step explanation:

The dots seem to be going upward throughout the graph, therefore making it a [positive correlation]

Answer: $ 495. 41

Step-by-step explanation:

First, multiply $32 by 3 days and get $96.

Then multiply .69 and 289 and get $ 199.41

Lastly, add those to get and get your answer.

(32 x 3) + .69 x 289 = 495. 41