use induction to prove 1*3*..\.\*(2n-1)=>2*4*6*..\.\*(2n-2) for every n =>2
Answers
Using mathematical induction, it can be proven that 13...(2n-1) <= 24*...*(2n-2) for every n >= 2.
Base Case: For n = 2, we have 13 = 3 and 24 = 8. Since 3 <= 8, the inequality holds true.
Induction Hypothesis: Assume that 13...(2k-1) <= 24*...*(2k-2) holds true for some positive integer k >= 2.
Induction Step: We need to show that the inequality also holds for k+1, i.e., 13...(2k+1) <= 24*...(2k).
To do this, we start with the left-hand side of the inequality:
13*...(2k+1) = (13*...(2k-1))(2k+1) <= (24...(2k-2))(2k+1)
(Using the induction hypothesis and the fact that 2k+1 is greater than or equal to 2).
Next, we simplify the right-hand side:
24...(2k-2))(2k+1) = 2*(24...(2k-2)(k+1))
Finally, we can conclude that:
13...(2k+1) <= 24*...(2k-2))(2k+1) = 2*(24...(2k-2)(k+1)) <= 24...*(2(k+1)-2)
(Since k+1 is greater than or equal to 2, we can use the induction hypothesis again.)
Therefore, by the principle of mathematical induction, we have proven that 13...(2n-1) <= 24*...*(2n-2) for every n >= 2.
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Related Questions
Can someone help me with this question??
Answers
Answer:
rotate it across the Y axis by 90°. it should be in Quad ||
Which event is an example of a physical change?
1. Iron rusting
2. Fireworks exploding
3. Eggs cooking
4.ice melting
Answers
Answer:
Ice melting
Step-by-step explanation:
Think about ice for a moment. After ice melts into liquid water, you can refreeze it into solid ice if the temperature drops. Freezing and melting are physical changes. The substances produced during chemical changes however cannot easily change back into the original substances.
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The coordinates of the vertices of ΔABC are A(−5, 1), B(−5, −1), and C(−1, −1). Find the side lengths and the angle measures.
AB = 4, BC = 2, AC ≈ 4.24
m∠B = 90°, m∠A ≈ 63°, m∠C ≈ 27°
AB = 2, BC = 4, AC ≈ 4.24
m∠B = 90°, m∠A ≈ 27°, m∠C ≈ 63°
AB = 2, BC = 4, AC ≈ 4.47
m∠B = 90°, m∠A ≈ 63°, m∠C ≈ 27°
AB = 4, BC = 2, AC ≈ 4.47
m∠B = 90°, m∠A ≈ 27°, m∠C ≈ 63°
Answers
The given coordinates of the vertices of the triangle ΔABC, which are: A(-5, -1), B(-5, -1), and C(-1, -1), gives the side lengths and the angle measures found using Pythagorean theorem, and the law of cosines as follows:
AB = 2, BC = 4, AC ≈ 4.47
m∠B = 90°, m∠A ≈ 63°, m∠C ≈ 27°
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the sum of the squares of the legs, is equal to the square of the length of the hypotenuse side.
The vertices of the triangle are; A(-5, 1), B(-5, -1), and C(-1, -1)
The length, l, of a line having points (x₁, y₁) and (x₂, y₂) can be found using Pythagorean theorem as follows;
\(l = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
The length of AB = √((-5 - (-5))² + (-1 - 1)²) = 2
Length of BC = √((-1 - (-5))² + (-1 - (-1))²) = 4
Length of AC = √((-1 - (-5))² + (-1 - 1)²) ≈ 4.47
The interior angles can be found using the law of cosines as follows:
a² = b² + c² - 2·b·c·cos(A)
Which gives: 2·b·c·cos(A) = b² + c² - a²
\(\angle A = arccos\left(\dfrac{b^2 + c^2 - a^2}{2\cdot b \cdot c} \right)\)
Where:
a, b, and c are the side lengths of the triangle, and ∠A is the angle opposite side a.
Taking AB = c, BC = a, AC = b, gives:
\(\angle A = arccos\left(\dfrac{4.47^2 + 2^2 - 4^2}{2\times 4.47 \times 2} \right) \approx 63^{\circ}\)
Similarly, we have:
\(\angle B = arccos\left(\dfrac{4^2 + 2^2 - 4.47^2}{2\times 4\times 2} \right) \approx 90^{\circ}\)
Which by the angle sum property of a triangle gives: ∠C = 180° - 90° - 63° = 27°
The option that gives the side lengths and the angle measure is therefore:
AB = 2, BC = 4, AC = 4.47, m∠B = 90°, m∠A = 63°, m∠C = 27°Learn more about the law of cosines here:
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after analyzing the sales data from both curbside pickup and delivery orders, a local pizza joint obtains the following 95% confidence intervals for the mean of pickup orders and delivery orders: pickup orders: between $33 and $51 per order delivery orders: between $21 and $41 per order can you conclude that an average pickup order has higher amount than an average delivery order?
Answers
Based on the information provided, we cannot conclude with certainty that the average pickup order has a higher amount than the average delivery order.
Based on the information given, we can conclude that there is a 95% chance that the true mean for pickup orders falls between $33 and $51, and the true mean for delivery orders falls between $21 and $41. However, we cannot conclude with certainty that the average pickup order has a higher amount than the average delivery order.
To determine if there is a significant difference between the means of the two groups, we need to perform a hypothesis test. We can set up our null hypothesis as "there is no significant difference between the means of the pickup and delivery orders" and our alternative hypothesis as "the average pickup order has a higher amount than the average delivery order."
We can use a two-sample t-test to test this hypothesis. Assuming equal variances, we would calculate the test statistic as
t = (xpickup - xdelivery) / (s / √n)
where xpickup and xdelivery are the sample means for pickup and delivery orders, s is the pooled standard deviation, and n is the sample size for each group.
If our calculated t-value is greater than the critical value at a chosen significance level (e.g. 0.05), we can reject the null hypothesis and conclude that there is a significant difference between the means of the two groups.
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Lauren invested in a project that has the following quarterly
cash flows over the next 1.5 years. If interest is compounded
quarterly, what is the effective annual rate of return for this
project? (Ro
Answers
The effective annual rate of return for this project is 5.68%.
Formula for effective annual rate:R = (1 + i/m)^m - 1
Where,R = Effective annual rate
i = nominal annual interest rate
m = number of compounding periods in a year
Let's calculate the effective annual rate of return using the above formula. First, calculate the interest rate per quarter:
Project's quarterly cash flows: $80,000, $60,000, $70,000, $90,000
Nominal annual interest rate:
i = Ro = ?
Let's assume that the net present value of the project is $0 to solve for the Ro using the following formula:
Ro = (CF1 + CF2 / (1+i)^2 + CF3 / (1+i)^3 + ... + CFn / (1+i)^n) / Cafe
Where,CF1 = $80,000
CF2 = $60,000
CF3 = $70,000
CF4 = $90,000
CF0 = initial cash investment of Lauren
After calculating the sum of the discounted cash flows and equating to zero, i = 5.48%
Let's now substitute the values in the formula for the effective annual rate:
R = (1 + i/m)^m - 1m = 4 (since interest is compounded quarterly)
R = (1 + 0.0548/4)^4 - 1R = 0.0568 or 5.68%
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Name: Date: 6. A biased four-sided die is rolled. The following table gives the probability of each score. Score 1 21 3 Probability 0.28 k 0.15 0.3 a. Find the value of k. (2 marks) b. Calculate the e
Answers
The expected value of the die roll is 2.47. Finding the value of kProbability is the measure of the likelihood of an event taking place. The sum of the probability of all events occurring must equal one, otherwise, the set of events would be incomplete, which is not possible.
Therefore, we have 0.28 + k + 0.15 + 0.3 = 1 where k is the probability of getting 2 on the die.Solving for k:k = 1 - 0.28 - 0.15 - 0.3k = 0.27Therefore, the value of k is 0.27. b. Calculating the expected valueThe expected value of the die roll is the sum of each score multiplied by its probability of occurrence. This is also called the mean of the probability distribution, given by: E(X) = ΣxP(x)where X is the random variable and P(x) is the probability of X being equal to x.Using the given table of probabilities:E(X) = 1(0.28) + 2(0.27) + 3(0.15) + 4(0.3)E(X) = 0.28 + 0.54 + 0.45 + 1.2E(X) = 2.47Therefore, the expected value of the die roll is 2.47.
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Tommy spent $16 on two toys. The cost of each toy was a multiple of $4. What are the possible prices of the toys?
Answers
ok
Possible prices
Toy 1 Toy 2 Total Price
$12 $4 $16
$8 $8 $16
$4 $12 $16
These are the possible prices:
Find the trig ratio. Reduce to
lowest terms.
6
А
8
[?]
sin A =
![Find the trig ratio. Reduce tolowest terms.68[?]sin A =](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/IvJM0LumVQJPJzCgtqxpAxWgIsHZ6B5d.png)
Answers
Answer:
the answer is 3/5
Step-by-step explanation:
What is the surface area of the square pyramid below?
A. 40 cm^2
B. 200 cm^2
C. 185 cm^2
D. 105 cm^2
Answers
Answer:
A
Step-by-step explanation:
Answer:
D. 105 cm^2
Step-by-step explanation:
Base: 5 * 5 = 25
Sides/Triangles: 8 * 5 * 0.5 = 20
20 + 20 + 20 + 20 + 25 = 105
Solve the equation 6+2x=20
10 points!!!
Answers
Answer:
x=7
Step-by-step explanation:
2x=20-6
2x=14
x=14/2
x=7
See the image below MATHH
Answers
The restricted value on the range of function f(x) is given as follows:
3.
How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.From the horizontal dashed line, the function never assumes a value of y = 3, hence the restricted value on the range of function f(x) is given as follows:
3.
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Answer:
3
Step-by-step explanation:
The range of a function is the set of all possible output values (y-values).
The given diagram shows the graph of a rational function with a horizontal asymptote at y = 3 (indicated by the dashed line).
An asymptote is a line that the curve gets infinitely close to, but never touches.
Therefore, as there is an asymptote at y = 3, the curve of the function will never touch the line y = 3, and consequently the value of y = 3 is restricted from the range of the function.
TRUE OR FALSE Let us observe n coin flips. We record each heads as a 1, and each tails as a 0. If we sum up all of our 1s and 0s, then divide by n (in other words, we calculate the sample mean), we have just calculated the sample proportion p-hat.
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TRUE. We can observe n coin flips, record each heads as 1, and each tails as 0. Then, sum up all of our 1s and 0s, divide by n (in other words, we calculate the sample mean), and we have just calculated the sample proportion p-hat. This is a method used to find the probability of an event.
The sample proportion is known as p-hat. The proportion of successes in the sample is denoted by the p-hat symbol. The sample proportion is a statistic that estimates the actual proportion of the population. The proportion of successes in a sample is referred to as the sample proportion.
When sample proportion represents a percentage, it is indicated as a percentage (x%). So, sample proportion p-hat is a statistical term that provides us with an estimate of the actual proportion of the population from the sample proportion.
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find the measurement of angle G
Answers
Answer:
I want to say it's 60...because if you add up 150 and 90 (the right angle) you get 240 which when subtracted from 360 gives you 120...with both E & G being created with equal lengths you would divide 120 by 2 which gives you 60. Hope this helps :)
Tell me if I’m correct
Answers
Answer:
Yah i think i remember doing this question once, it looks correct, i hope you do well on the test
Have a nice day!! :)
Policies Current Attempt in Progress On May 1, 2021, Sheffield Company sells office furniture for $300000 cash. The office furniture originally cost $746800 when purchased on January 1, 2014. Depreciation is recorded by the straight-line method over 10 years with a salvage value of $80200. What gain should be recognized on the sale? (Hint: Use 7.333333 for years used in calculation.) O $44540. O $22220. O $84080. O $42040. Save for Later -/5 = 1 Attempts: 0 of 1 used Submit Answer
Answers
To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.
First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.
Depreciation per year = (Cost - Salvage Value) / Useful Life
Depreciation per year = ($746,800 - $80,200) / 10 years
Depreciation per year = $66,160
Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.
Accumulated Depreciation = Depreciation per year × Years
Accumulated Depreciation = $66,160 × 7.33 years
Accumulated Depreciation = $484,444.80
Now, we can calculate the book value of the furniture:
Book Value = Cost - Accumulated Depreciation
Book Value = $746,800 - $484,444.80
Book Value = $262,355.20
Finally, we can calculate the gain on the sale:
Gain on Sale = Sale Price - Book Value
Gain on Sale = $300,000 - $262,355.20
Gain on Sale = $37,644.80
Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.
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The gain that should be recognized on the sale of the office furniture is $84,080.
The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.
Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.
For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420
Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.
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aldosterone stimulates the reabsorption of sodium while enhancing potassium secretion.
a. true b. false
Answers
I believe that may be false
Answer:
Step-by-step explanation:
True.
Aldosterone is a hormone produced by the adrenal gland that plays an important role in regulating electrolyte and water balance in the body. It acts on the cells of the distal tubules and collecting ducts of the kidneys to increase the reabsorption of sodium ions and the secretion of potassium ions.
This helps to increase blood volume and blood pressure by retaining more sodium and water in the body while getting rid of excess potassium. Aldosterone release is regulated by the renin-angiotensin-aldosterone system, which is activated in response to low blood pressure or low sodium levels in the blood.
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Help me find z please
Answers
Answer:
z = 3
Step-by-step explanation:
The triangles are similar by the AAS theorem. That is, ∆ABD ~ ∆EBC.
We notice short side AD is half the length of the longer marked side AB. Then corresponding short side EC will be half the length of corresponding longer side EB.
z = 6/2 = 3
Please help me guys I beg you I will give you lots of credit plz
Answers
Answer:
11m/min
Step-by-step explanation:
slope of the line = velocity of the turtle
slope = y/x
= 55/5
=11
Answer:
11
Step-by-step explanation:
55 meters by 5 minutes, so divide 55 by 5 to find one minute.
55/5 = 11
a cleaning service lets customers decide which way they would like to be charged.
• for choice A, the total cost is $25 dollars per hour of cleaning.
•for choice B, the total cost is $50+$15h, where h is the number of hours of cleaning.
which of the following statements is true?
• Choice A always costs more $10 more than choice B
• Choice B is always more expensive
• Choice A charges less for a cleaning job that takes 5 hours
• Choice B charges more for a cleaning job that takes 3 hours.
Answers
Answer:
the 4th statement
Step-by-step explanation:
subsititute the values for h, use numbers between 1-10 to help find the answer.
A cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius 9 cm. Find the volume of the ring-shaped solid that remains.
Answers
The volume of the ring-shaped remaining solid is 1797 cm³.
The volume is the total space occupied by an object.
The volume of a sphere of radius r units is given as (4/3)πr³.
The volume of a cylinder with radius r units and height h units is given as πr²h.
In the question, we are asked to find the volume of the remaining solid when a sphere of radius 9cm is drilled by a cylindrical driller of radius 5cm.
The volume will be equal to the difference in the volumes of the sphere and cylinder, where the height of the cylinder will be taken as the diameter of the sphere (two times radius = 2*9 = 18) as it is drilled through the center.
Therefore, the volume of the ring-shaped remaining solid is given as,
= (4/3)π(9)³ - π(5)²(18) cm³,
= π{972 - 400} cm³,
= 572π cm³,
= 1796.99 cm³ ≈ 1797 cm³.
Therefore, the volume of the ring-shaped remaining solid is 1797 cm³.
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3 divided by 1/5????
Answers
Answer:
15
Step-by-step explanation:
It helps to think that there are 15 1/5's in the number 3. Hope that helps!
we were told the results are based on a random sample of ann arbor teens. is the following statement about the remaining assumption correct or not correct?we need to have a simple size n that is large enough, namely that the sample size n is at least 25.O CorrectO Incorrect
Answers
Correct. The assumption that the sample size should be at least 25 is correct. This is because, for a sample to be representative of the population, it should have enough observations to provide a reasonable estimate of the population parameters.
A sample size of at least 25 is generally considered the minimum requirement for statistical analysis. The statement about the remaining assumption is correct. In order to make valid inferences from a random sample, it is important to have a large enough sample size (n). A common rule of thumb is that the sample size should be at least 25. This helps to ensure that the sample is representative of the population and increases the accuracy of the results.
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Need help ASAP. For Finals
Answers
Answer:
a. \(50b + 250 \leq 3000\)
b. 55 boxes
c. 5 trips
Step-by-step explanation:
a. Each box weighs 50lbs and the number of boxes is our variable. If you add the worker's weight (180) and the cart's weight (70) you get a constant weight of 250. All of this cannot weigh more than 3000, therefore it can weigh equal to or less than it. Therefore, the equation is \(50b + 250 \leq 3000\).
b. Solve the equation to find the maximum amount of boxes that he can move in one trip, like this:
\(50b + 250 \leq 3000\\50b \leq 2750\\b \leq 55\)
Therefore, the greatest number of boxes that the worker can move is 55 boxes.
c. Divide the total number of boxes (275) by the amount of boxes that can be taken in one trip (55) to find how many trips it will take. Like this:
275/55 = 5
The worker needs to make 5 trips in order to deliver 275 boxes.
I hope this helps!!
- Kay :)
Answer:
a.) 3000 *no more than symbol* 180 + 70 +50b
A seasoning blend is 4\%4%4, percent onion powder, by mass. How much pure onion powder should they include in a 72\,\text{g}72g72, start text, g, end text bottle to make the final blend have 20\ , percent onion powder? khan academy
Answers
They need to put 14.4 grams of onion powder in each bottle.
Given,
The quantity of onion powder in a seasoning blend = 4%
We have to find the quantity of pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder;
How much is a percentage?
A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."
Here,
Let x be the seasoning blend.
Now, 4% of 72=20% of x
⇒ 0.04×72=0.2×x
⇒ 0.2x=2.88
⇒ x=2.88/0.2
⇒ x=14.4 g
Therefore, a container should contain 14.4 grams of onion powder.
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Adult tickets to the fall play cost 6 and student tickets cost 3 . The drama class sold 25 more student tickets than adult tickets to the fall play. If the class collected 660 from ticket sales, how many student tickets were sold?
Answers
Let x be the total number of student tickets sold.
Then, x - 25 is the number of adult tickets sold.
660 = 3x + 6(x - 25)
660 = 3x + 6x - 150
9x = 810
x = 90
Thus, 90 student tickets were sold.
Triangles ABC and DEF are similar.
Side length AB is 2, side length AC is 4, and side length BC is 3
Side length DE is 1.34
What is the length of DF and EF?
Answers
If Triangles ABC and DEF are similar. Side length AB is 2, side length AC is 4, and side length BC is 3 Side length DE is 1.34 then length of DF = 2.68 and length of EF = 2.01
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given,
Triangles ABC and DEF are similar.
AB = 2
AC = 4
BC = 3
DE = 1.34
We need to find the length of DF and EF
Given that ABC and DEF are similar, therefore:
AB/DE = BC/EF = AC/DF
2/1.34=3/EF=4/DF
1.49=3/EF=4/DF
Now,
1.49=3/EF
EF=3/1.49
EF=2.01
1.49=4/DF
DF=4/1.49
DF=2.68
Hence, length of DF = 2.68 and length of EF = 2.01
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Which equation would demonstrate the commutative property?
A. 14(3 + 4) = (14 • 3) + (14 • 4)
B. 37 • 26 = 26 • 37
C. 8 • 1 = 8
D. (8 • 1)• 7 = 8 • (1 • 7)
i will give brainiest
Answers
Answer:
b. 37 • 26 = 26 • 37
commutative property states that the change in the order of numbers in an addition or multiplication operation does not change the sum or the product.
Sally has been measuring the tree in her yard for a science project. The tree has grown 12 of an inch each month and grown a total of 2 inches taller. How many months has Sally been measuring this tree?
Answers
Answer:
Sally has been measuring the tree for 4 months
Step-by-step explanation:
The correct question is as follows;
Sally has been measuring the tree in her yard for a science project. The tree has grown 1/2 of an inch each month and grown a total of 2 inches taller. How many months has Sally been measuring this tree?
.........................................................................................
Solution;
The tree has grown 1/2 of an inch each month and has grown a total of 2 inch taller.
We now need to know the number of months in which the measuring has been taking place.
To know the number of months, we simply need to divide the change in height which is 2 inch by the individual month growth rate which is 1/2 inch
So mathematically, that would be 2/1/2 = 2 * 2 = 4 months
Point-slope form
Complete the point-slope equation of the line through (-2, 6) and (1, 1).
Use exact numbers.
y-6=
Answers
The point slope equation of the line from the given points (-2, 6) and
(1, 1) is 3y+5x = 8 .
What is equation of straight line ?
The equation of straight line as follows , y = mx+b .
where m is the slope .
Given ,
To find the point slope equation of the line
from the given points (-2, 6) and (1, 1).
First we have to find slope,
so slope = y2-y1 / x2-x1
This is (1-6)/(1-(-2)) = -5/3
Now that you know the slope you can use that for the point-slope equation
The point-slope equation is y-y1 = m(x-x1). If we start with y-6, the x value is -2 (from our point (-2,6)
y-6 = -5/3 (x-(-2))
y-6 = -5/3 (x+2)
3(y-6) = -5(x+2)
3y - 18 = -5x -10
3y+5x = 18-10
3y+5x = 8
Hence, The point slope equation of the line from the given points (-2, 6) and (1, 1) is 3y+5x = 8 .
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in a bag of marbles, 1 2 are red, 1 4 are blue, 1 6 are green, and 1 12 are yellow. you pick a marble without looking. what color marble are you most likely to choose?
Answers
The most probable color marble which could be picked up without looking is red colored marble because there quantity is comparatively higher than others.
As per the data given, the probability that the specific colored balls are picked up is given. So depending upon the total number of balls be any number x, then the number of red balls is half of the total balls, blue balls is quarter of total balls, green balls is one sixth of total balls and yellows balls are one twelfth of total balls.
Hence, yellow balls are least in number and red colored balls are higher in number and hence the probability that a red colored ball is picked up first is 1/2*100 = 50%.
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