To find the number of 2n-digit integers where odd position digits are odd, and even position digits are even and positive, we calculate based on the choices for each position, giving us a result of (5^n) * (4^n).
Explanation:We encounter a combinatory problem in working out how many 2n-digit positive integers can be formed if the digits in odd positions must be odd and the digits in even positions must be even. Before proceeding, it's important to grasp the concept of positional numbering, where the rightmost digit is considered at position 1, and the counting proceeds from right to left.
For a 2n-digit positive integer, i.e., an integer with an even number of digits, there will be n digits at odd positions and n digits at even positions. For the odd positions, the digits can be any one of the five odd integers (1, 3, 5, 7, 9) and for the even positions, the digits can be any one of the four even positive integers (2, 4, 6, 8) because 0 is excluded as the question mentions they should be positive.
Therefore, for each position, we have a choice of five odd integers or four even integers. Since there are n odd positions and n even positions, we end up with (5^n) * (4^n) total possibilities or combinations.
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The total number of valid 2n-digit positive integers, where digits in odd positions must be odd and digits in even positions must be even, is calculated using the formula 5ⁿ * 4ⁿ.
To solve this problem, we need to consider the constraints given: digits in odd positions must be odd and digits in even positions must be even. Let's break down the problem step-by-step:
We have 2n-digit numbers. Therefore, there are n odd positions and n even positions.For the odd positions (1st, 3rd, 5th, ....., 2n-1), each digit can be 1, 3, 5, 7, or 9. So, there are 5 choices for each position.For the even positions (2nd, 4th, 6th, ....., 2n), each digit can be 2, 4, 6, or 8. There are 4 choices for each position.To find the total number of such 2n-digit positive integers, multiply the number of choices for all positions:Total combinations = (Number of choices for odd positions) n * (Number of choices for even positions) n = 5ⁿ * 4ⁿ
This is the formula to calculate the number of valid 2n-digit integers under the given constraints.
Suppose your average, after taking 4 quizzes, is 73(out of 100). What must your average be on the next 5 quizzes to increase your average to 88 out of 100?
x = average of next 5 quizzes
4 * 73 = first 4 quizzes
There will be a total of 4 +5 = 9 quizzes
Average of all quizzes = 88 = (4*73+5x)/9
9*88 = 9*(292 +5x)/9
792 = 292 + 5x
500 = 5x
X = 500/5 = 100
Next 5 quizzes need to average 100
answer this plz
14 students are surveyed about the clothes they are wearing.
8 students are wearing a t-shirt.
2 students aren't wearing jeans or a t-shirt.
3 students are wearing jeans and a t-shirt.
How many students are wearing jeans, but not a t-shirt?
2
3
4
5
Answer:
its
Step-by-step explanation:
Armando has a baseball card that is worth $45. The value of the card is increasing at a rate of 1.5% per year. How much will the card be worth in 15 years?
making use of Archimedes’s Principle, displacements, and buoyancy, explain why some objects float on water, but others do not.
Answer:
If the weight is equal to the buoyant force, it will float. The same is true for if the weight is less than the buoyant force. However, if the weight is greater than the buoyant force, it will sink.
Which expression is the greatest common factor (GCF) of the terms of trinomial 12x^7y^9 + 6x^4y^7 - 10x^3y^5
Answer: 2. [tex]\mathbf{2x^3y^5}[/tex]
Step-by-step explanation:
Greatest common factor of any two or more expression is the largest common expression that divides them.The given expression : [tex]12x^7y^9 + 6x^4y^7 - 10x^3y^5[/tex]
Term 1 : [tex]12x^7y^9[/tex]
Term 2 : [tex]6x^4y^7[/tex]
Term 3: [tex]- 10x^3y^5[/tex]
Lowest power of x = 3
Thus , The highest common power of x = [tex]x^3[/tex] (i)
Lowest power of y = 5
The highest common power of y =[tex]y^5[/tex] (ii)
Greatest common factor of 12, 6 , -10= 2 [Because 2 is the largest number that divides all of them] (iii)
From (i) , (ii) , (iii) , we have
Greatest common expression : [tex]2x^3y^5[/tex]
Hence, the correct answer is 2. [tex]\mathbf{2x^3y^5}[/tex]
Plastic storage bins are designed so they can be nested. The picture shows how each one fits inside another, leaving only the top part showing. The 4 stacked 10-gallon bins shown here measure 29 inches high. The height of the stack grows at the rate of 4 inches for each added bin. Write an equation in the form y = mx + b to describe the relationship between x, the number of nested bins, and y, the height of the stack.
You and two friends (Adam and Alana) will only play a game if it is fair for all three of you. The game your friend has proposed is to roll two number cubes (numbered 1-6) and find the sum. If the sum. If the sum is from 1-4 you get the point, 5-8 Adam gets the point, and 9-12 Alana gets the point.
Yes, the game was fair and no one had a better advantage.
Answer:
yes!
Step-by-step explanation:
no one had a better advantage.everyone had the same amount of advantage.
Find the circumference and the area of a circle with diameter
2ft
The circumference of a circle with diameter 2ft is 2π ft and the area is π ft².
Explanation:To find the circumference of a circle, you can use the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 2ft, so the circumference would be C = π(2) = 2π ft. To find the area of a circle, you can use the formula A = πr², where A is the area and r is the radius. Since the radius is half the diameter, the radius would be 2ft/2 = 1ft. Therefore, the area would be A = π(1)² = π ft².
Final answer:
The circumference of a circle with a diameter of 2 feet is approximately 6.28 feet, and the area is approximately 3.14 square feet using the formulas C = πd and A = πr².
Explanation:
To find the circumference and the area of a circle with a diameter of 2 feet, we can use the formulas for circumference and area. The diameter of the circle is given as 2 feet. Therefore, the radius (r) is half of the diameter, which is 1 foot.
The formula for the circumference of a circle is C = πd where C is the circumference, π (pi) is approximately 3.14159, and d is the diameter. Since the diameter (d) is 2 feet, the circumference is:
C = π × 2 feet ≈ 3.14159 × 2 feet ≈ 6.28318 feet
So the circumference is approximately 6.28 feet.
The formula for the area of a circle is A = πr² where A is the area and r is the radius of the circle. Using the radius 1 foot, we find the area as follows:
A = π × (1 foot)² ≈ 3.14159 × 1 foot × 1 foot ≈ 3.14159 square feet
So the area of the circle is approximately 3.14 square feet.
Suppose we select, without looking, one marbles from a bag containing 4 red marbles and 10 green marbles.what is the probability of selecting a green marbles? cours hero
Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (3x + 1) / (x + 1)^3(x^2 + 8)^2
The answers 80kg, 88 divided by 110 then times by 100
The student is completing a two-step mathematical operation to find a percentage by dividing 88 by 110 and then multiplying the result by 100. The '80kg' mention seems to be unrelated. Without more context, it's difficult to relate this to the given references, though they involve calculations and conversions in physics.
Explanation:The student seems to be performing a two-step operation where they are first dividing 88 by 110 and then multiplying it by 100. This is a common way of finding percentages. To get the result first, divide 88 by 110 which equals 0.8. Secondly, multiply 0.8 by 100 to get 80%. The '80kg' seems irrelevant to this operation if no further context is provided, it could be a weight measurement in physics.
In terms of any associations with the provided references, it seems that the question might be related to converting some measurements or calculating kinetic energy ('K'). However, without additional information, it's hard to ascertain the exact nature of the task.
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The data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique. Which of the numbers below is the best measure of the central tendency of the data? {3, 3, 4, 4, 4, 5, 5, 5, 5, 30}
The length of a spring is a linear function of the weight of the object compressing it. For a particular spring, the length decreases by 1.5 inches for every 3 pounds pressing down on it. When 4 pounds are on the spring, the length of the spring is 8 inches long. What is the length of the spring if 15 pounds are pressing down on the spring?
A basketball player makes 39% of her shots from the free throw line. suppose that each of her shots can be considered independent and that she takes 5 shots. let x = the number of shots that she makes. what is the standard deviation for x?
Answer: 1.09
Step-by-step explanation:
Given : A basketball player makes 39% of her shots from the free throw line.
i.e. Proportion of her shots from the free throw line: p= 0.39
We assume that each of her shots can be considered independent .
She takes 5 shots.
i.e. Number of trials : n= 5
Let x = the number of shots that she makes.
Then , the standard deviation for x will be :-
[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{5(0.39)(1-0.39)}\\\\=\sqrt{1.1895}=1.09064201276\approx1.09064201276\approx1.09[/tex]
Hence, the standard deviation for x= 1.09
Final answer:
The standard deviation for the number of shots made by a basketball player who has a 39% success rate and takes 5 shots is approximately 1.09 shots, calculated using the binomial distribution formula.
Explanation:
To find the standard deviation for the number of shots made by a basketball player who makes 39% of her shots, we use the concept of a binomial distribution.
Given that each shot is independent and that she takes 5 shots, with x representing the number of shots made, we can calculate the standard deviation using the formula for a binomial distribution.
The formula for the standard deviation (σ) in a binomial distribution is σ = √[n × p × (1 - p)], where n is the number of trials (in this case, 5 shots), and p is the success probability per trial (in this case, 0.39 for making a shot).
Plugging in the values, we get σ = √[5 × 0.39 × (1 - 0.39)] = √[5 × 0.39 × 0.61] = √[1.1885] ≈ 1.09 shots.
Therefore, the standard deviation for the number of shots made is approximately 1.09 shots.
The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 40.4 meters, how wide must it be?
Evaluate the line integral where f(x,y,z)=3sin(x)i−(cos(y))j−5xzk and c is given by the vector function r(t)=t5i−t4j+t3kr(t)=t5i−t4j+t3k , 0≤t≤10≤t≤1.
Noel reads 90 minutes a day for six days. Tyra reads 60 minutes for eight days. what is the diffrence , in minutes , between the total amount of time Noel read and the total amount Tyra read.
A. 30
B. 40
C.60
D. 80
The difference between the total reading times of Noel and Tyra is 60 minutes. Therefore, the correct option is option C.
The difference in minutes between the total time Noel read and Tyra read can be calculated by adding up the individual reading times for each and then finding the difference.
Calculate Noel's total reading time: 90 minutes/day * 6 days = 540 minutes.Calculate Tyra's total reading time: 60 minutes/day * 8 days = 480 minutes.Find the difference: 540 minutes (Noel) - 480 minutes (Tyra) = 60 minutes.How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between x=1 and x=b is equal to 240?
Which of the following is not one of the three ways to express ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4
The table shows how an elevator 500 feet above the ground is descending at a steady rate. Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending? h(t) = 5t + 500 h(t) = 5t – 500 h(t) = –5t + 500 h(t) = –5t – 500
How many different three digit numbers can be written using digits 1,2,3,4,5 without any repeating digits? Thank you.
We can use the principles of permutation to find out that there are 60 different three-digit numbers that could be formed using the digits 1,2,3,4,5 without repetition.
Explanation:In order to find out how many different three-digit numbers can be formed using the digits 1,2,3,4,5 without repetition, we use the principles of permutation. Firstly, we should determine how many options we have for each digit place in the three-digit number.
There are 5 possible digits for the first place (since none has been used yet).There are 4 remaining digits for the second place.Finally, there are only 3 digits left to fill the third place.We then multiply these options together (5 x 4 x 3) which equals to 60 different three-digit numbers.
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HELP PLEASE
Evaluate the expression.
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
v ⋅ w
a) -41
b) <-20, -36, 15>
c) <-28, 18, -35>
d) -9
Answer:
v . w = <-20, -36, 15>
Step-by-step explanation:
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
To find the dot product of vectors we multiply the numbers
We need to multiply v and w
vectors is in the form of <x,y,z>
Multiply all the x values
4 times -5= -20
6 times -6 = -36
-5 times -3 = 15
So v . w = <-20, -36, 15>
for the function y=-2+5sin(pi/12)(x-2)), what is the minimum value
Answer:
-7
Step-by-step explanation:
We are given that a function
[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]
We have to find the minimum value of y.
We know that range of sin x is [-1,1].
[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]
[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]
[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]
[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]
[tex]-7\leq y\leq 3[/tex]
Maximum value of y=3
Minimum value of y=-7
Hence, the minimum value of given function =-7
Perform the operation and reduce the answer fully.
frac{1}{12}+\frac{5}{9}
An apartment has 1026 square feet of carpeting. How much is this in square meters? Use the following conversion: 1 square meter is 10.8 square feet.
What is the total amount in an account that has had $35 per month added into it for 30 years and grew with an annual interest rate of 7%?
John's goal is to have more than -7 dollars in his bank account by the end of the month. The variable d is the number of dollars in John's bank account at the end of the month. Write an inequality in terms of d that is true only if John meets his monthly goal.
Answer:
d > - 7
Step-by-step explanation:
Here, d represents the number of dollars in John's bank account at the end of the month.
As per statement,
In John's account,
The balance must be more than -7 dollars,
That is, Number of dollars at the end of each month > - 7 ( '>' is used for more than )
⇒ d > - 7
Which is the required inequality.
PLEASE HELP?? EASY 5 POINTS!!! The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.
The product of (n^2-6n+3)and -4 is
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – x = 25
5.52, –4.52
is the correct answer,never forget negatives!