So, the last three digits of m*n is 001.
Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.
Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:
p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2
Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.
Therefore, the last three digits of m*n is 001.
To learn more about probability
Visit; brainly.com/question/28525447
#SPJ4
Evaluate the following. 4 x 5 - 18 divided 3 - 8
Answer: The answer would be
Step-by-step explanation:
28/3
in decimal form- 9.3 (3 keeps going)
Mixed Number- 9 1/3
Dylan drove from Liverpool to Sunderland at an average speed of 50 mph for 3 hours and 30 minutes. He then drove from Sunderland to Edinburgh at an average speed of 65 mph for 2 hours. Work out how many miles Dylan travelled in total.
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.
DistanceDistance 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.
Find perimeter and area of the rectangle simplify completely.
The perimeter of the rectangle = (6 x + 8) meters. and the Area is
2x² +10x.
How to find perimeter of rectangle?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.
To learn more about Perimeter and Area refers to;
https://brainly.com/question/13811125
#SPJ1
A publishing industry report predicts that magazine subscriptions will drop by 8% each year,
If this prediction is correct, then how many subscribers will a magazine with 85,630
subscribers have in 8 years?
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.
What is an exponential function?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
Learn more about exponential functions at https://brainly.com/question/2456547
#SPJ1
The Lockheed Martin F-22
Military Raptor can travel
3,000 miles in 2 hours.
What is it's top speed?
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 !!
henry the donkey has a very long piece of pasta. he takes a number of bites of pasta, each time eating 3 inches of pasta from the middle of one piece. in the end, he has 10 pieces of pasta whose total length is 17 inches. how long, in inches, was the piece of pasta he started with?
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.
To learn more about inches here:
https://brainly.com/question/16311877
#SPJ4
an auto dealer has 8 different cars and 4 different trucks. how many ways are there to select two vehicles?
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
For more questions on Permutation and Combination
https://brainly.com/question/28065038
#SPJ4
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.
A sentence constructed up of variables, numbers, or both is known as an expression in mathematics.
What does expression mean?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.
According to the given information:Let the equation be 2x + 10
Where, x = 15
substitute the values in the above equation, we get
= 2(15) + 10
= 40
To learn more about expression refer to:
brainly.com/question/1859113
#SPJ1
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
A tank can be filled by an inlet pipe in 12 hours and emptied by a drain pipe in 16 hours. How long will it take to fill the tank if both pipes are left open?
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.
Read more about pipes and cisterns:
brainly.com/question/27864377
#SPJ4
Can someone help me please? I'm struggling :(
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!
The value of x is 40% of y. What are possible values for x and y? *
Answer:
x = 40 and y = 100
Step-by-step explanation:
random number 100
40% of 100 = 0.40 * 100 = 40
Nasim went to the store to buy some coffee. The price per pound of the coffee is $4.75 per pound and he has a coupon for $3.50 off the final amount. With the coupon, how much would Nasim have to pay to buy 3 pounds of coffee? Also, write an expression for the cost to buy p pounds of coffee, assuming at least one pound is purchased.
Nasim have to pay for 3 pounds of coffee is $10.75.
The expression for p pounds of coffee is 4.75p - 3.5.
What is Expression ?
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:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.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
Learn more about Expression here:
https://brainly.com/question/14083225
#SPJ1
Andy is using wooden boards that are 0. 45 feet wide to build a deck. How many rows of boards are needed to completely cover a space that is 21 feet wide?
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.
To know more about division here
https://brainly.com/question/21416852
#SPJ4
how do i find the square root of a circle
Answer: by putting some clothes on
Step-by-step explanation:
comon man put some clothes on man do it for the kids
Please help!!!
What are some of the important steps to consider when solving an exponential or logarithmic equation? How can identities and logs help you to solve these equations? How are identities and logarithms confusing? Cite examples that help illustrate your ideas, and show steps to solve such equations in your post. Ask clarifying questions about anything you find confusing
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.
To know more on exponential and logarithmic equations
https://brainly.com/question/3181916
#SPJ4
Find x, y, and z. Enter your answer in simplest radical form.
Enter the correct values in the boxes.
x=?
y=?
z=?
Find the indicated real n the root(s) of a. n=9, a=-512
[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]
Dustin’s math classroom has 2 bulletin boards side by side. The teacher said the length of one
board is 1. 25 yards, and the other is 1. 75 yards. What is the total length in feet of the two
bulletin boards side by side?
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.
Learn more about length calculations -
https://brainly.com/question/28108430
#SPJ4
what is D=8 cm and R =4.7 in ,
The circumference of the circles are 25.12 cm and 29.516 in
How to determine the circumference of the circleFrom 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
Read more about circumference at
https://brainly.com/question/3883184
#SPJ1
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
The original price of a salt lamp is $92 after a 20% discount
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
pls help fast it due today
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
solve for x.
2x°
24°
Answer: x = 33°
Step-by-step explanation: 2x° + 24°-24 = 90°-24 2x/2 = 66/2 x = 33°
What is the midpoint of the line segment with the endpoints J(–9, –4) and K(7, 8)? (–5, –1) (–2, 1) (–1, 2) (3, 5)
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)
Write 1476 to the nearest 10
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!
given f(x) = -x2 - x, find f(-9)
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
Question Down Below: (Please i really need to complete this right now) Please anyone :(
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
How to calculate the inequality?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
Learn more about inequalities on;
brainly.com/question/24372553
#SPJ1
What are the x and y for only
3x+2y=34
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.
What is variables?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.
Learn more about variables here:
https://brainly.com/question/17344045
#SPJ1
the feather on an arrow form two congruent parallelograms. the parallelograms are reflection of each other over the line that contains their shared side show that m
Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 5, reflected across the x-axis, and shifted by 6 units left.
A. G(x) = -5ln (x - 6)
B. G(x) = 5ln (x + 6)
C. G(x) = -5ln (x + 6)
D. G(x) = 5ln (x - 6)
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.
Learn more about transformation of function here:
brainly.com/question/12718390
#SPJ4
Pleas answer these questions..
Refer to the image attached.