alfred and bonnie play a game in which they take turns tossing a fair coin. the winner of a game is the first person to obtain a head. alfred and bonnie play this game several times with the stipulation that the loser of a game goes first in the next game. suppose that alfred goes first in the first game, and that the probability that he wins the sixth game is m n , where m and n are relatively prime positive integers. what are the last three digits of m n ? (1993,

Answer: The answer would be

Step-by-step explanation:

28/3

in decimal form- 9.3 (3 keeps going)

Mixed Number- 9 1/3

Solving exponential and logarithmic equations requires a strong understanding of the properties of exponents and logarithms, as well as the use of logarithmic identities and inverse operations. It is important to simplify expressions and isolate the variable using basic algebraic operations, logarithmic identities, and inverse functions.

When solving exponential or logarithmic equations, there are several important steps to consider:

Simplify the equation using basic algebraic operations, such as multiplication, division, addition, and subtraction.

Isolate the exponential or logarithmic expression on one side of the equation.

Use the properties of exponents or logarithms to simplify the expression, if possible.

Use logarithmic identities such as logarithmic rules and change-of-base formula to simplify the expression.

Solve for the variable by using inverse operations.

Check your answer by substituting it back into the original equation and verifying that both sides are equal.

Identities and logs can be helpful in solving exponential and logarithmic equations because they provide a set of rules that can be used to simplify expressions. For example, logarithmic identities such as log(a * b) = log(a) + log(b) and log(a/b) = log(a) - log(b) can be used to simplify expressions containing products and quotients.

However, identities and logarithms can also be confusing because they involve complex concepts and require a solid understanding of logarithmic properties. This can make solving exponential and logarithmic equations challenging for some students.

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The total length in feet of the two bulletin boards side by side is 9 feet.

The total length of the bulletin boards when calculated side by side will be done using addition operation. The expression that will form for calculation is -

The total length = length of one bulletin board + length of second bulletin board

Keep the values in formula -

The total length = 1.25 + 1.75

Performing addition on Right Hand Side of the equation

The total length of the two bulletin boards = 3 yards

The total length in feet = 3 × (3 feet)

Performing multiplication

Total length = 9 feet

The total length in feet is 9 feet.

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There are 66 ways to choose two vehicles from the dealer's inventory.

A combination is a grouping of items from a larger set in which the order of the items is irrelevant. In other words, it is a method of selecting a subset of items from a larger set without regard for their order of selection.

The formula C(n, k) = n! / (k! (n - k)!) can be used to calculate the number of combinations.

where n represents the total number of items in the set and k represents the number of items in the combination.

The exclamation mark (!) represents the factorial function, which is the sum of all positive integers up to a certain number.

The number of ways to select two vehicles from 8 cars and 4 trucks is 8 + 4 = 12 vehicles.

To find the number of combinations, we use the formula for combinations, which is:

C(n, k) = n! / (k! (n - k)!)

where n is the total number of vehicles and k is the number of vehicles we want to choose.

So, for n = 12 and k = 2,

we have:

So, putting the value in above formula:

We will get it as:

C(12, 2) = 12! / (2! (12 - 2)!) = (12 * 11) / (2 * 1) = 66

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Answer:

1,500

Step-by-step explanation:

It's preetty fast but it cannot be the record holder of " Lockheed SR-71 Blackbird " Which it's top speed i 2,100 miles per hour !!

Refer to the image attached.

The perimeter of the rectangle  = (6 x + 8) meters. and the Area is  

2x² +10x.

step 1: The first side's length is (x+ 5) metres, while the second side's breadth is (2x+ 1) metres.

Now, the RECTANGLE'S PERIMETER = 2 (LENGTH + WIDTH).

Here, perimeter is equal to 2 ((x+ 5) m + (2x + 1) m) or 2 (x + 5 + 2x +1) = 2(3x + 4) = 6x + 8

Therefore, the rectangle's perimeter is equal to (6 x + 8) metres.

step 2:

Area of a rectangle equals length times breadth

Given:

Size = x+5

Thickness = 2x+1

Area of rectangle = length breadth = (x+5) (2x+1) = 2x (x+5) (2x+1) =2x2+5+4x+1 =2x2+10x, according to the query.

The area is therefore 2x2 + 10x.

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Andy is using wooden boards that are 0. 45 feet wide to build a deck. The number of rows of boards are needed to completely cover a space is 47 rows of boards.

Divide the total width (21 feet) by the width of each board (0. 45 feet):

21 / 0. 45 = 46. 666666

Round the result up to the next whole number:

47 rows of boards

In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

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Answer:

Ariel's plant is 1.6 inches taller than Dyani's.

It doesn't seem that you can multiply the measurement of Dyani's plant anymore than Ariel's. So I believe that would be 0 inches.

Step-by-step explanation: You can multiply Dyani's measurement with number like 1.0, 1.2, etc. You still wouldn't be able to multiply it anymore.

I hope this helps!

Answer:

ch.1 = 12x1.2=14.4

ch.2=10.5x1.2=12.6

ch.3=39.3x1.2=47.16

Step-by-step explanation:

You just have to multiply all the chapters by 1.2

i think if im wrong im sorry

Answer: 14.4, 12.6, 49.16

Step-by-step explanation:

Multiply each number by 1.2

12x1.2=14.4

10.5x1.2=12.6

39.3x1.2=49.16

chapter 1 : 14.4

chapter 2: 12.6

chapter 3: 49.16

A sentence constructed up of variables, numbers, or both is known as an expression in mathematics.

A mathematical expression is a sentence with at least two numbers or variables, at least one mathematical operation, and at least single mathematical operation. Math allows for addition, subtraction, multiplication, and division.

Using variables, numbers, or both, a mathematical expression is a phrase. A symbol in an expression can never be equal. Examples include these expressions. Equations are mathematical statements that demonstrate the equality of two expressions.

Let the equation be 2x + 10

Where, x = 15

substitute the values in the above equation, we get

= 2(15) + 10

= 40

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Using the expression you found in part a, how many minutes will it take to make and pack an order for 15 parts? Show your work.

Given expression is:

2x + 10

Answer:

(-1,2)

Step-by-step explanation:

Recall the midpoint formula:

[tex]\frac{x^1+x^2}{2}[/tex] to solve for the X coordinate and [tex]\frac{y^1+y^2}{2}[/tex] to solve for Y.

Replace the variables with their appropriate numbers.

[tex]X(\frac{-9+7}{2})[/tex]  [tex]Y(\frac{-4+8}{2})[/tex]

[tex]X(\frac{-2}{2} )[/tex]      [tex]Y(\frac{4}{2} )[/tex]

[tex]X(-1)[/tex]       [tex]Y(2)[/tex]

Therefore, the answer is (-1,2)

Answer:

  305 miles

Step-by-step explanation:

You want to know how far Dylan travelled if he drove 50 mph for 3.5 hours and 65 mph for 2 hours.

Distance is the product of speed and time. The total distance Dylan travelled will be the sum of lengths of the legs of his trip.

  distance = speed · time

  total distance = speed1 · time1 + speed2 · time2

  = (50 mi/h)(3.5 h) +(65 mi/h)(2 h) = 305 mi

Dylan travelled a total of 305 miles.

Nasim have to pay for 3 pounds of coffee is  $10.75.

The  expression for p pounds of coffee is 4.75p - 3.5.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

The price per pound of the coffee is $4.75 per pound and he has a coupon for $3.50 off the final amount.

and, Nasim have to pay to buy 3 pounds of coffee.

So, Nasim have to pay for 3 pounds of coffee.

= 3 x 4.75 - 3.50

= 14.25 - 3.5

= $10.75

and, the expression for p pounds of coffee is

= 4.75p - 3.5

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Answer:

-72

Step-by-step explanation:

Assuming it is -x^2 - x and not (-x)^2, then you simply plus in -9 for x:

-(-9)^2-(-9) = -72

Answer: by putting some clothes on

Step-by-step explanation:

comon man put some clothes on man do it for the kids

The piece of pasta he started with was 34 inches long.

Defining a problem, identifying its underlying cause, locating, ranking, and selecting potential solutions, as well as putting those ideas into practice, are all steps in the issue-solving process. Diagnose the circumstance to keep your attention on the issue and not merely its symptoms.

Let x be the length of the original piece of pasta.

After taking bites, he has (x - 3) pieces of pasta, each 17/10 inches long.

So, the total length of all pieces of pasta is (x - 3) * 17/10 = 17 inches.

Therefore, x = 10 * 17/7 + 3 = 34 inches.

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[tex]\sqrt[9]{-512}\qquad \begin{cases} -512=-2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\cdot -2\\ \qquad 2^9 \end{cases} \\\\\\ \sqrt[9]{(-2^9)}\implies -2[/tex]

The circumference of the circles are 25.12 cm and 29.516 in

From the question, we have the following parameters that can be used in our computation:

(a) D = 8 cm and (b) R = 4.7 inches

Given the diameter, the circumference is

C = πD

So, we have

C = 3.14 * 8 cm = 25.12 cm

Given the radius, the circumference is

C = 2πR

So, we have

C = 2 * 3.14 * 4.7 in = 29.516 in

Hence, the circumference is 29.516 in

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Complete question

What is the circumference of the circle given its diameter (D) of its radius (R)

(a) D = 8 cm and (b) R = 4.7 inches

Answer: x = 33°

Step-by-step explanation: 2x° + 24°-24 = 90°-24 2x/2 = 66/2 x = 33°

The inequality to represent the constraints will be:

x + y ≥ 325

x + 2y = 600

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Let x = number of vegetarian meals

Let y = number of meats.

The inequality to represent the constraints will be:

x + y ≥ 325

x + 2y = 600

In this case, the daily budget is 600.

Subtract the equations

y = 275

Number of meats = 275

Number of vegetarian meals = 325 - 275 = 50

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Constants are fixed values that never change, whereas variables are values that can change but are often initialized to “0” or another default value because the program's user will supply the actual values.

In programming, a variable is a value that may vary depending on outside variables or data that has been provided to the program. A program normally consists of instructions that tell the computer what to do and data that it utilizes while running.

The correct values for the variables x and y are 8 and 5, respectively.

[tex]3 \times 8 + 2 \times 5=34[/tex]

[tex]24 + 10 =34[/tex]

[tex]\frac{1}{2}\times 8+2 \times 5=14[/tex]

[tex]4 + 10 =14[/tex]

Constants and variables are typically categorized as certain data kinds. Each data type specifies and restricts the data's shape.

An integer expressed as a decimal number or a string of text characters with a set maximum length are examples of data types. Each object in object-oriented programming includes the data variables of the class of which it is an instance.

Therefore, The methods of the object are made to deal with the actual values that are presented to it when it is utilized.

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Answer:

x = 40 and y = 100

Step-by-step explanation:

random number 100

40% of 100 = 0.40 * 100 = 40

It will take 48 hours, to fill the tank if both pipes are left open simultaneously.

We are given the following data -

The time taken to fill the tank by inlet pipe = 12 hrs

so, the rate of filling = 1/12

The time taken to empty the tank by drain pipe = 16 hrs

so, the rate of emptying = - 1/16

Therefore, the total work done by both pipes can be given by the following formula -

(1/rate of filling) + (1/rate of emptying) = (1/rate of net change)

1/12 + (-1/16) = (1/Rn)

Therefore, (1/Rn) = 1/12 - 1/16 = 1/48

To find how long it will take to fill the tank, we need to find the reciprocal of the rate of net change:

1/Rn = 1/(1/48)

Rn = 48

So it will take 48 hours, to fill the tank if both pipes are left open.

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Answer:

1480

Step-by-step explanation:

To the nearest 10, is the 10s place. 76 is closes to 80, so round 1476 to 1480. Hope this helps!

The function after transformation is G(x) = -5 ln (x+6) is the correct answer.

The correct answer is an option (C)

Here, the function is f(x) = ln x

A function f(x) is stretched vertically by a factor of 5.

As we know for a vertical stretch, we need to multiply the whole function by the factor of stretching.

If the stretching factor is m, then after stretching the function becomes

⇒ m × f(x)

Here, stretching factor m = 5

So the transformed function would be,

G(x) = 5 f(x)

⇒ G(x) = 5 ln x

Now, function is reflected across the x-axis, so the function becomes

⇒ G(x) = -5 ln (x+6)

Then the function is shifted by 6 units left, so after translation the function becomes

⇒ G(x) = -5 ln (x+6)

Thus, we can conclude that the function f(x) = ln x after transformation would be G(x) = -5 ln (x+6) is the correct answer.

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Suppose the prediction of an annual drop in magazine subscriptions of 8% is correct. In that case, the number of subscribers that a magazine with 85,630 subscribers will have in 8 years, using an exponential function, is 43,947.

The exponential function is an expression in the form of f(x) = bˣ, where the b constant is called the base and the x variable is called the exponent.

Exponential functions may describe exponential growth or exponential decay.

Exponential decay refers to a decrease or drop, where the decay rate is known.

The annual drop in magazine subscriptions = 8%

The number of current magazine subscribers = 85,630

The number of years for the prediction = 8 years

Decay factor = (1 - 8%) = 0.92

The number of magazine subscribers in 8 years = 85,630 x 0.92^8

= 85,630 x 0.5132189

= 43,947

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Answer: $115

Step-by-step explanation:  

92 is the price after a 20% discount, so it is 80% of the original value.

So, solve, 92÷0.80=115

So the original price was $115