The solution is : n = 9
What is multiplication?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.
Explanation:
To find the answer we need to check at what point the running time of algorithm A is equal the running time of B:
1000*n*n = n*n*n*n*n
1000 = n*n*n = n^3
n = ∛(1000) = 10 (when n equals ten A equal B)
For any integer greater than ten B > A and for any integer smaller than ten B < A.
The greatest integer for which B < A is nine, therefore nine is our answer.
A B
1000n^2 n^5
n = 8 64000 < 32768
n = 9 81000 < 59049
n = 10 100000 = 100000
n = 11 121000 > 161051
n = 12 144000 > 248832
therefore nine is our answer.
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For [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex], Algorithm A (which runs in [tex]\( 2n \)[/tex] steps) beats Algorithm B (which runs in [tex]\( 5\sqrt{n} \)[/tex] steps).
To determine for which values of [tex]\( n \)[/tex] Algorithm A beats Algorithm B in terms of running time, we compare their complexities:
Algorithm A runs in [tex]\( 2n \)[/tex] steps.
Algorithm B runs in [tex]\( 5\sqrt{n} \)[/tex] steps.
Algorithm A beats Algorithm B if [tex]\( 2n < 5\sqrt{n} \)[/tex].
Let's solve this inequality step by step:
1. Square both sides to eliminate the square root (valid since [tex]\( n \geq 0 \)[/tex]):
[tex]\[ (2n)^2 < (5\sqrt{n})^2 \][/tex]
[tex]\[ 4n^2 < 25n \][/tex]
2. Bring all terms to one side to form a quadratic inequality:
[tex]\[ 4n^2 - 25n < 0 \][/tex]
3. Factorize the quadratic inequality if possible:
[tex]\[ n(4n - 25) < 0 \][/tex]
4. Find the values of [tex]\( n \)[/tex] that satisfy the inequality:
[tex]\( n(4n - 25) < 0 \)[/tex] holds when one factor is negative, and the other is positive:
[tex]\( n < 0 \)[/tex] and [tex]\( 4n - 25 > 0 \)[/tex]: No valid solutions since [tex]\( n \geq 0 \)[/tex].
[tex]\( n > 0 \)[/tex] and [tex]\( 4n - 25 < 0 \)[/tex]:
[tex]\[ 4n < 25 \Rightarrow n < \frac{25}{4} = 6.25 \][/tex]
[tex]\( n < 0 \) and \( 4n - 25 < 0 \)[/tex]: All [tex]\( n \geq 0 \)[/tex] satisfy this condition.
5. Determine the integer values of [tex]\( n \)[/tex]:
Since [tex]\( n \)[/tex] must be non-negative, the integer values of [tex]\( n \)[/tex] that satisfy [tex]\( 4n^2 - 25n < 0 \)[/tex] are [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex].
solve this system of linear equations. separate the x- and y- values with a coma. 6x+20y=-62
3x-9y=-12
To solve the system of linear equations, use the method of substitution by solving for one variable and substituting it into the other equation.
Explanation:To solve the system of linear equations:
6x + 20y = -62
3x - 9y = -12
We can use the method of substitution:
From the first equation, solve for x: x = (-62 - 20y) / 6Substitute the value of x into the second equation: 3((-62 - 20y) / 6) - 9y = -12Simplify and solve for y:After finding the value of y, substitute it back into the first equation to solve for x. The solution is: x = -2, y = 4.
20 points! Suppose you find six articles related to the topic of your research paper. In how many ways can you choose four articles to read
a.720
b.30
c.360
d.15
A local little league has a total of 85 players, of whom 80% are left-handed. How many left-handed players are there?
The question is asking us to find out how many players are left-handed from a total of 85 players, given that 80% of the players are left-handed. For this, we perform a simple calculation by finding 80% of 85, which equals 68. So, there are 68 left-handed players in the league.
Explanation:The subject of this question falls under the category of Mathematics, more specifically, it is about percentage calculations. In order to figure out how many left-handed players there are out of the total 85 players, we need to remember that percent means 'per 100'. So, 80% translates to 80 out of 100. Therefore, to find out how many are left-handed, we need to take 80% of 85.
The calculation is as follows:
Left-handed players = 85 * (80/100)
= 85 * 0.80
= 68
So, there are 68 left-handed players in the local little league.
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Find three positive numbers whose sum is 100 and whose product is a maximum. (enter your answers as a comma-separated list.)
Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant.
The area of the plane 5x + 4y + z = 20 in the first octant is calculated using a double integral over the xy-plane. The limits are defined by the intersection of x and y with the xy-plane when z=0, and the solution is approximately 66.67 square units.
Explanation:To solve for the area of the part of the plane that lies in the first octant, we first need to isolate z in our equation. z = 20 - 5x - 4y. The limits for x and y in the first octant are from 0 to positive infinity, but in this case, they will be limited by the plane defined by z = 0 (the xy-plane). x and y will range from 0 to the point where they meet the plane. Therefore, we set z = 0 and solve for both x and y, giving us x = 4 and y = 5.
Now in order to calculate the area, we must interpret this integral on the xyz-plane as a double integral on the xy-plane. Now, we integrate over the region in the xy-plane that x and y range over:
Area = ∫ from 0 to 4 ∫ from 0 to (5 - 1.25x) (20 - 5x - 4y) dy dx
And that is the integral you need to calculate to find the area. Attempting to calculate this integral results in the area ≈ 66.67 square units.
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If two parallel lines are cut by a transversal and corresponding angles measure 10x – 1 and 8x + 21, what is the value of x?
What is 2 2/5 ÷ (- 1/4) And how?
Betty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations mc004-1.jpg and x + 4y = 17. Based on this information, which statement is correct? (–3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17. (–3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17. (–3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7. (–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17
For which real numbers x and y is it true that x + y = x+y?
The speed of the car was 45 mph. A driver noticed that while moving with this speed it took him 40 seconds to cross a bridge. On the way back crossing the same bridge, it took him 30 seconds. What was the speed of the car on the way back?
Answer:
Speed of car on the way back = 30 mph
Step-by-step explanation:
Speed of car on the way = 45 mph = 45 x 1.6 = 72 kmph = 20 m/s
Time taken to cross bridge on the way = 40 seconds
Length of bridge = Speed of car on the way x Time taken on the way = 20 x 40 = 800 m
Time taken to cross bridge on the way back = 30 seconds
Length of bridge = Speed of car on the way back x Time taken on the way back
800 = Speed of car on the way back x 30
Speed of car on the way back = 26.67 m/s =96 kmph = 30 mph
Speed of car on the way back = 30 mph
How long will it take for the object to fall all the way down to the ground? The function for objects dropped from a height where t is the time in seconds, h is the height in feet at time t, and h is the intial height is h(t)=-16t^2+h. The building is 162 feet tall.
Thanks so much!
A laptop computer is purchased for $1300. After each year, the resale value decreases by 35%. What will the resale value be after 3 years?
How to estimate 208 + 569
find the equation in general form of the circle with center at the origin and radius equal 6.
The fifth term of a geometric sequence is 781.25. Each previous term is 1/5 of the value of the current term. Which recursive formula represents the situation?
Answer:
[tex]a_n=5a_{n-1}[/tex]
Step-by-step explanation:
Given fifth term of a geometric sequence is 781.25.
[tex]a_5= 781.25[/tex].
Also, each previous term is 1/5 of the value of the current term.
Therefore, common ratio would be 5.
But we just need to find the recursive formula .
Recursive formula of a geometric sequence is given by
[tex]a_n=ra_{n-1}[/tex]
Plugging value of r in above formula, we get
[tex]a_n=5a_{n-1}[/tex]
Therefore, recursive formula would be [tex]a_n=5a_{n-1}[/tex] represents the situation.Answer: c
Step-by-step explanation:
buddy beneath me is blabbin to much
"assume that josh throws the discus 36 times. let y denote the sum of the lengths of the 36 throws.
a. what is the expected value of y
A student has three mangos, two papayas, and two kiwi fruits. if the student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed
There are 210 different ways for the fruits can be consumed.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A student have 3 mangos, 2 papayas, and 2 kiwi fruits.
And, The student eats one piece of fruit each day, and only the type of fruit matters.
Now,
Total number of fruits = 3 + 2 + 2
= 7
And, There are 3 mangos, 2 papayas, and 2 kiwi fruits.
So, Number of ways for the fruits can be consumed, is calculated as;
= 7! / 3! 2! 2!
= 7 x 6 x 5 x 4 x 3! / 3! 2! 2
= 7 x 6 x 5 x 4 / 2 x 1 x 2 x 1
= 7 x 6 x 5
= 210
Thus, There are 210 different ways for the fruits can be consumed.
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Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 2x − sin(2x) 2x − tan(2x)
Using the L'Hospital's Rule, we differentiate the numerator and denominator of the given function separately, substitute these derivatives back into the function, and then attempt to evaluate the limit as x approaches 0.
Explanation:To find the limit of the given function as x approaches 0, we will use the L'Hospital's Rule since the function gets an indeterminate form 0/0 as x approaches 0. L'Hospital's Rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.
First, we differentiate the numerator and the denominator separately. For the numerator, the derivative of 2x is 2, and the derivative of sin(2x) is 2cos(2x). So the derivative of the numerator is 2 - 2cos(2x).
For the denominator, the derivative of 2x is 2, and the derivative of tan(2x) is 2sec²(2x), since the derivative of tan(x) is sec²(x) and because of the chain rule, we multiply by 2. So, the derivative of the denominator is 2 - 2sec²(2x).
Now, we substitute these derivatives back into the original function and take the limit as x approaches 0: lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x)).
After further simplifying the above expression, you can evaluate the limit.
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The limit is 0.
We need to find the limit:
lim x→0 (2x − sin(2x)) / (2x − tan(2x))
Both the numerator and the denominator approach 0 as x approaches 0, which means it is in the indeterminate form 0/0. This suggests that we can use L'Hôpital's Rule.
According to L'Hôpital's Rule, we can differentiate the numerator and the denominator and then take the limit of the resulting fraction.
First, let's compute the derivative of the numerator:
Numerator: 2x - sin(2x)Derivative: 2 - 2cos(2x)Next, let's compute the derivative of the denominator:
Denominator: 2x - tan(2x)Derivative: 2 - 2sec²(2x)Now, we apply L'Hôpital's Rule:
lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x))
As x approaches 0, cos(2x) approaches 1 and sec²(2x) also approaches 1, so:
lim x→0 (2 - 2(1)) / (2 - 2(1)) = 0 / 0
This fraction again gives an indeterminate form. Applying L'Hôpital's Rule a second time will be helpful. We need to differentiate the numerator and the denominator again:
Second derivative of the numerator: d/dx [2 - 2cos(2x)] = 4sin(2x)
Second derivative of the denominator: d/dx [2 - 2sec²(2x)] = -8sec²(2x)tan(2x)
Applying L'Hôpital's Rule once more, we get:
lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x))
Substitute x = 0:
lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x)) = 0
Therefore, the limit is 0.
What is the area of a regular polygon with 100 sides and a perimeter of 100 units?
One hundred pounds of co2 is contained in a 10:0-ft3 tank. the safety limit of the tank is 1600 psig.
Final answer:
To answer the question, we need to convert the mass from pounds to kilograms, use the ideal gas law equation to calculate the pressure in atmospheres, and then convert atmospheres to psig.
Explanation:
In this question, we are given that 100 pounds of CO2 is contained in a 10.0-ft3 tank and the safety limit of the tank is 1600 psig. To convert pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms. So, 100 pounds of CO2 is equal to 45.36 kilograms. Now, we can use the ideal gas law equation PV = nRT to find the pressure in bar. Rearranging the equation, we have P = (nRT) / V. Plugging in the values given, n = mass / molar mass, R = 0.0821 atm L / mol K, T = 273 + degrees Celsius, and V = 10.0 ft3 converted to liters, we can calculate the pressure in atmospheres. Finally, we can convert atmospheres to psig by multiplying by 14.7.
Find the distance the point p(0,0,−4)p(0,0,−4) is to the line through the two points q(−4,1,−2q(−4,1,−2 ), and r(−2,0,−5r(−2,0,−5 ).
What are the values of the mean and standard deviation after converting?
In 2015, in Buffalo, New York, there were 8,625 arrests, 2,678 robberies, 865 assaults, and 20 murders. The population of Buffalo is 258,959. What is the ratio of the number of assaults to the number of robberies in simplest form?
Answer:
The simplest form of the ratio is: [tex]\dfrac{865}{2678}[/tex]
Step-by-step explanation:
We are given information about the buffalo in New york in the year 2015 as:
Number of arrests= 8,625
Number of robberies=2678
Number of assaults= 865
Number of murders= 20
The population of Buffalo is 258,959.
he ratio of the number of assaults to the number of robberies in simplest form is given by:
[tex]\dfrac{865}{2678}[/tex]
As the number in the numerator and the denominator do not have a common factor. hence the simplest form of the ratio is:
[tex]\dfrac{865}{2678}[/tex]
Mira has breakfast at a restaurant. She leaves a 20% tip of $1.80. What is the price of Mira’s breakfast,before tip?
If 300 cm2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters
What is the third term of the sequence defined by the recursive rule f(1)=2, f(n)=2f(n-1) +1
The ice cream Palace received 3 gallons of strawberry ice cream, 5 pints of mocha ice cream, and 1 quart of vanilla ice cream today. How many pints of ice cream did they receive?
Fraction 4 over 5n = Fraction 2 over 3. n = ___? Fraction 2 over 15 Fraction 5 over 6 1Fraction 1 over 5 1Fraction 7 over 15
Answer:
what?
Step-by-step explanation:
What happens to the average kinetic energy of water molecules as water freezes? A. It decreases as the water releases energy to its surroundings.
B. It increases as the water releases energy to its surroundings.
C. It increases as the water absorbs energy from its surroundings.
D. It decreases as the water absorbs energy from its surroundings.
Answer: Option (A) is the correct answer.
Explanation:
Kinetic energy is defined as the energy possessed by an object because of it's motion.
Whereas average kinetic energy is the sum of kinetic energy of all the particles of a substance.
Therefore, when water freezes then there will decrease in kinetic energy of particles and thus, particles will gain potential energy.
Hence, we can conclude that when water freezes average kinetic energy of water molecules decreases as the water releases energy to its surroundings.
The average "kinetic-energy" of water molecules decreases as water freezes, because water releases energy to its surroundings, option (a) is correct.
When water freezes, it undergoes a phase transition from a liquid to a solid state. During this process, water molecules lose energy and slow down, causing decrease in their average kinetic energy.
As temperature decreases, water molecules arrange themselves into a more structured pattern due to the formation of hydrogen bonds.
In order for water to freeze, it needs to release energy to its surroundings, in form of heat. This release of energy is necessary to facilitate transformation from a higher-energy liquid state to lower-energy solid state. As a result, average kinetic energy of water molecules decreases as water freezes.
Therefore, the correct option is (a).
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The distance from Talamunda to Velcratia is 700 miles. The train takes 5 hours to travel the distance. At what unit rate is the train traveling?
Answer: 140 miles per hour
Step-by-step explanation: