How many playlists can we make with 38 songs if we can repeat 5 songs in each playlist? Use the permutation or combination formula if applicable.
Final answer:
The number of playlists that can be created with 38 songs allowing for the repetition of 5 songs is calculated using combinations with repetition, resulting in a total of 850,668 possible playlists.
Explanation:
The question relates to the number of different ways we can create playlists from 38 songs, with the possibility of repeating 5 songs in each playlist. To calculate the number of different playlists that can be made by repeating songs, we need to use combinations with repetition. This is a concept in combinatorics which allows for the selection of items with replacements.
We can represent the problem with a formula used for combinations with repetition: (n + r - 1) choose r, where n is the total number of options (in this case, 38 songs) and r is the number of choices to make (in this case, repeating 5 songs). The formula becomes (38 + 5 - 1) choose 5, which simplifies to 42 choose 5. Using the combination formula, we can compute the total number of possible playlists as follows:
C(42, 5) = 42! / (5!(42-5)!) = 42! / (5!37!) = 850,668
This number represents the total number of playlists we can create with 38 songs, allowing for the repetition of 5 songs on each playlist.
the floors of houses in japan are traditionally covered by tatami. tatami are rectangle shaped straw mats that measure about 6 feet by 3 feet. if a room is 48 feet by 24 feet, how many tatami are needed to cover the floor
Oh yikes, this one hasn't been answered in 4 years..
Let's get the area of one tatami, then the one of the floor.
Tatami area: 6*3 = 18 sq. feet
Floor area: 48*24 = 1152 sq. feet
To know how many tatami are needed, we need to divide the floor area by the tatami area:
1152/18 = 64
You'd need 64 tatami to cover the floor
find the value of A E B C and D please
I'll give brainliest to whoever shows there work to the answer. Plz answer quickly.
Which point best approximates the square root of 3?
A
B
C
D
find the solution x = 3 + y 21x + 8y = -24
A paleontologist uncovers a fossil of a saber-toothed cat in California. He analyzes the fossil and concludes that the specimen contain 15% of its original carbon-14. Carbon-14 has a half-life of 5730 years. Use carbon-14 dating to determine the age of the fossil.
Carbon-14 dating is used to determine the age of fossils by comparing the amount of carbon-14 in the specimen to the amount in the atmosphere. The half-life of carbon-14 is 5730 years, and by analyzing the percentage of carbon-14 remaining, the age of the fossil can be calculated.
Explanation:Carbon-14 dating is used to determine the age of fossils. Carbon-14 (14C) is a radioisotope that is present in living organisms while they are alive, and it starts to decay after they die. The half-life of carbon-14 is 5730 years, which means that after this time period, half of the original carbon-14 will have decayed.
In the case of the saber-toothed cat fossil, the paleontologist analyzed the specimen and found that it contained 15% of its original carbon-14. By comparing this percentage to the amount of carbon-14 in the atmosphere, which is known, they can determine the age of the fossil.
Since carbon-14 dating is accurate up to about 50,000 years, this method is suitable for dating the fossil. The age of the fossil can be calculated by considering the amount of carbon-14 remaining and the known half-life of the isotope.
Given that the points (-3, 2) and (1, 2) form one leg of a right triangle, which point could be another vertex of the triangle?
A) (7, 2)
B) (-1, 4)
C) (-3, -2)
D) (-1, -2)
The possible vertices of the right triangle are (-3, -2) and (-1, -2).
Option C and D are the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The points (-3, 2) and (1, 2) have the same y-coordinate, which means that they lie on a horizontal line.
The distance between these two points is 4 units, which is the length of the leg of the right triangle that they form.
The only way to form a right triangle using these points is to choose a third point on a vertical line passing through one of these two points.
Option B)
(-1, 4) does not lie on a vertical line passing through either of the given points.
Option C)
(-3, -2) lies on a vertical line passing through the point (-3, 2), so it could be a vertex of the right triangle.
Option D)
(-1, -2) lies on a vertical line passing through the point (1, 2), so it could be a vertex of the right triangle.
Therefore,
The possible vertices of the right triangle are (-3, -2) and (-1, -2).
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how is adding and subtracting decimals similar to and different from adding and subtracting whole number
There isn't any real difference in adding and subtracting decimals from whole numbers but there is just a decimal point in front of the number to make it a decimal.
For example, 2 is a whole number but adding a .0 will make it 2,0 which makes it a decimal.
Sophie bikes at a speed of s miles per hour. Her friend Rana is slower, her biking speed is only r miles per hour.
Rana's yesterday's trip was m miles long. How long did Rana bike yesterday?
How many times greater is the value of 5 in 3,590 than the value of 5 in 359 ?
Answer:
10 times greater is the value of 5 in 3,590 than the value of 5 in 359.
Step-by-step explanation:
To find : How many times greater is the value of 5 in 3,590 than the value of 5 in 359 ?
Solution :
The place value stem is
Thousand Hundred Tens Ones
1000 100 10 1
The value of 5 in 3,590 is at hundred place
So, [tex]5\times 100=500[/tex]
The value of 5 in 359 is at tens place
So, [tex]5\times 10=50[/tex]
Number of time greater is the value of 5 in 3,590 than the value of 5 in 359 is given by,
[tex]n=\frac{500}{50}[/tex]
[tex]n=10[/tex]
Therefore, 10 times greater is the value of 5 in 3,590 than the value of 5 in 359.
Final answer:
The value of 5 in 3,590 is 10 times greater than the value of 5 in 359 because the 5 in 3,590 represents 500 while in 359 it represents 50.
Explanation:
The question asks how many times greater the value of 5 in 3,590 is compared to the value of 5 in 359. In the number 3,590, the 5 is in the hundred's place, meaning it has a value of 500 (5 x [tex]10^2[/tex]). In the number 359, the 5 is in the ten's place, meaning it has a value of 50 (5 x [tex]10^1[/tex]). To find out how many times greater one value is than the other, we divide the larger by the smaller
So, 500 divided by 50 equals 10. This means the value of 5 in 3,590 is 10 times greater than the value of 5 in 359.
which phrase correclty describe the location on thr number line of opposite of -8? A a point 8 unit tot he left of -8. B a point 8 unit to the right of -8 C.a point 8 unit to the left of 0 D.a point 8 unit to the right of 0
Which expression is equivalent to log w (x2-6)4
The measure of angle KMN = ?? degrees
can someone help me with this question?
1. Suzette ran and biked for a total of 34 mi in 3.5 h. Her average running speed was 6 mph and her average biking speed was 12.5 mph. How many hours did suzette run
Final answer:
To find out how many hours Suzette ran, we used a system of equations with the total distance and total time for running and biking. Solving the system, we determined that Suzette ran for 1.5 hours.
Explanation:
To determine how many hours Suzette ran, we can use the total distance and the total time given for running and biking activities, alongside her average speeds for each activity. We will then set up a system of equations that account for the distances and times and solve for the time Suzette spent running.
Let r be the time spent running and b be the time spent biking. We are given:
Total time: r + b = 3.5 hours
Total distance: 6r + 12.5b = 34 miles (6 mph is the running speed, 12.5 mph is the biking speed)
Now we'll solve this system of equations:
Substitute b from the first equation into the second equation: 6r + 12.5(3.5 - r) = 34.
Simplify and solve for r: 6r + 43.75 - 12.5r = 34.
This simplifies further to -6.5r = -9.75, hence r = 1.5.
Suzette ran for 1.5 hours.
Write the following as a whole number:
19 thousands + 46 hundreds + 32 tens + 57 ones
The figure shows two parallel lines AB and DE cut by the transversals AE and BD:
AB and DE are parallel lines, and AE and BD are transversals. The transversals intersect at C. Angle CAB is labeled 1, angle ABC is labeled 2, angle ACB is labeled 3, angle ACE is labeled 4, angle CDE is labeled 6, and angle CED is labeled 5.
Which statement best explains the relationship between Triangle ABC and Triangle EDC ?
Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5
Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
9514 1404 393
Answer:
Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5
Step-by-step explanation:
Nothing indicates any triangle sides are congruent, a necessary condition for the triangles to be congruent.
In triangles ABC and EDC, angles 1 and 5 are corresponding. They are "alternate interior angles" with respect to the transversal AE, so are congruent. Angles 2 and 6 are congruent for a similar reason. The vertical angles at C are congruent, so the triangles are similar.
Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5.
The temperature is 9 degrees below zero
The mathematical expression for the temperature measured can be obtained as -9°.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity knows units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
The given measure of the temperature is 9°.
Since, the convention to take measured figures with the values below zero is negative.
The given temperature can be written as -9°.
Hence, the given temperature can be written as -9°.
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Three consecutive even integers add to −6. What are these integers?
Let's consider the smallest even integer = x.
then second even integer = (x + 2).
and third even integer = (x + 4).
So three consecutive even integers would be x, (x + 2), and (x + 4).
The sum of these numbers is -6. Its equation would be as follows :-
x + (x + 2) + (x + 4) = -6
3x + 6 = -6
3x = -6 - 6
3x = -12
x = -4
So first number = x = -4
second number = (x + 2) = -2
third number = (x + 4) = 0
Hence, three consecutive even integers are -4, -2, and 0
Answer:
-4, -2, and 0
Step-by-step explanation:
The diameter of a small gear is 16cm. This is 2.5cm more than 1/4 of the diameter of a larger gear. What is the diameter of the larger gear?
To find the diameter of the larger gear, we set up an equation based on the information that the smaller gear's diameter is 2.5cm more than a quarter of the larger gear's diameter. Solving this, the diameter of the larger gear is found to be 54cm.
The student has asked for the diameter of a larger gear when given that the diameter of a smaller gear is 16cm, which is 2.5cm more than one quarter of the larger gear's diameter. To find the diameter of the larger gear, we can set up an equation where d represents the diameter of the larger gear.
According to the question:
16cm = 1/4d + 2.5cm
To solve for the diameter d, we subtract 2.5cm from both sides and then multiply by 4:
The diameter of the larger gear is therefore 54cm.
A supermarket conducts a survey to find the approximate number of its customers who like apple juice. What is the population of the survey?
In a survey conducted by a supermarket to find out how many customers like apple juice, the population of the survey would be all customers of the supermarket. The population in a survey defines the group the research wants to gain information about and determine the applicability of the findings.
Explanation:In the context of survey research, a population refers to the entire group about which information is wanted. In your scenario, where a supermarket is conducting a survey to find out how many customers like apple juice, the population of the survey would be all customers of the supermarket. It's important to identify the population in a survey because it helps determine the scope of the study and how broadly the findings can be applied.
For example, if you were a marketing manager for an electronics chain store wanting information about the ages of its customers, the population would also be all customers of the store. Similarly, if a radio station wants to know its listeners' preferences, the population would be all listeners of that station. The aim is to collect data that is representative of this population, be it through sampling or other data collection methods.
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The population of the supermarket survey is the entire customer base, including individuals with varying shopping frequencies, aimed at determining the approximate number of customers who like apple juice through representative insights from the diverse customer demographic.
The population of a survey refers to the entire group that the survey aims to represent or provide insights into. In this case, the supermarket is conducting a survey to find the approximate number of its customers who like apple juice. The population of the survey, therefore, is the entire customer base of the supermarket.
To determine the population, the supermarket would ideally want to include all its customers who may have preferences or opinions about apple juice. This could include individuals who have shopped at the supermarket recently or regularly. The population might also encompass a broader range, considering both frequent and occasional customers to ensure a more representative sample of the supermarket's clientele.
In summary, the population of the survey is the entire customer base of the supermarket, encompassing individuals who may have opinions or preferences regarding apple juice.
In 1900, there was an Olympic underwater swimming event. The score was calculated by giving one point for each second the swimmer stayed under water and two points for each meter that the swimmer traveled. Charles de Vendeville from France earned a gold medal by staying under water 68.4 seconds while traveling 60.2 meters. How many points did Charles de Vendeville earn to place first? Express the answer to the nearest tenth of a point.
The points for the swimming event are calculated as :one point for each second the swimmer stayed under water and two points for each meter that the swimmer traveled.
Charles de Vendeville stayed under water for 68.4 seconds.
Points earned for staying under water = 68.4 (1)= 68.4
Vendeville from France travelled 60.2 meters
Points earned for traveling 60.2 meters = 60.2(2)= 120.4
Total points earned = 68.4+120.4=188.8
Suppose MyBook has roughly 1,000,000 users, and as each member signs up for an account, he or she is assigned a number. Which of these would result in the smallest sample size using systematic sampling?
A. Surveying every 25,000th number
B. Surveying every 250th number
C. Surveying every 25th number
D. Surveying every 2500th number
In systematic sampling, a higher n-value (every nth number) means fewer members are selected, thus smaller sample size. Therefore, surveying every 25,000th number results in the smallest sample size.
Explanation:In systematic sampling, every nth member of a population is chosen for sampling. The smaller the value of n, the larger the sample size will be, because you're selecting a member more frequently. When we compare the options given: A. 25,000, B. 250, C. 25, and D. 2500, we see that option A (the 25,000th member), will result in the smallest sample size. In this scenario, for a total user base of 1,000,000, selecting every 25,000th member would produce approximately 40 samples (1,000,000 / 25,000 = 40), which is less than what you'd get with the other options.
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type the correct answer in the box.use numeral instead of words. if necessary, use / for the fraction bar.
HELP ASAP PLEASE HELP ASAP PLEASE HELP ASAP
The rental car holds 25 gallons of gas and gets 18 miles per gallon. The trip to Yarrow City is 1350 miles. How many times will the car need to be filled up to make the trip?
A. 2
B. 3
C. 4
D. 5
A rectangular prism measures 2 2/5 inches by 3 1/5 inches by 2 inch. Priya said, it takes more cubes with edge length 2/5 inch cubes than cubes with edge length 1/5 to pack the prism. Do you agree?
No, she is not correct.
The volume of cubes with side 2/5 inches is : [tex](\frac{2}{5}) ^{3}[/tex] = 8/125 [tex]in^{3}[/tex]
and the volume of cubes with side 1/5 inches is : [tex](\frac{1}{5} )^{3}[/tex] = 1/125 [tex]in^{3}[/tex]
The cubes with sides 1/5 inches have 8 times lesser volume than that of the cubes with sides 2/5 inches.
So, to fill up the same volume, we would require 8 times more cubes of side 1/5 inches than cubes of side 2/5 inches.
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Find x and fill in the angle values. Could you also explain how it works? Please and thank you.
What is the square root of 1,563?
Maggie wants to buy 4 roses, 6 carnations, and 9 tulips. She estimates that she will spend about 14 dollars on these flowers. Do you agree?
Helpppp!!!!Im not sure what this is, isn’t the square root of 144 a rational number and the square root of 34 a rational number, too?