Answer:
2sin4y - sin8x = K (C)
Step-by-step explanation:
Given the differential equation
dy/dx= cos(8x)/cos(4y)
This can be solved by using the variable separable method.
Step 1;
Separate the variables
Cos4ydy = cos 8xdx
step 2:
Integrate both sides of the equation
∫cos4y dy = ∫cos8x dx
sin4y/4 = sin8x/8
Step 3:
Add constant of integration to the side containing x variable
sin4y/4 = sin8x/8+ C
Taking sin8x to the other side we have:
sin4y/4-sin8x/8 = C
Multiplying through by 8:
2sin4y - sin8x = 8C
2sin4y - sin8x = K (where K = 8C )
To solve the given differential equation we have apply variable separation method.
The correct option is (c) 2 sin(4y) - sin(8x) = C.
Variable separation:In mathematics, variable separation method used to calculate the partially and ordinary differential function in which we rewrite the equation so that two variable occurs on two side.
Given:
The given differential equation is as follows,
[tex]\dfrac{dy}{dx}=\dfrac{\cos(8x)}{\cos(4y)}[/tex]
How to calculate the Separate the variable?Separate the variable.
[tex]\cos 4y \:dy =\cos 8x\:dx\\[/tex]
Integrate both side of the equation.
[tex]\int \cos4y dy = \int \cos8x dx\dfrac {1}{4}\sin4y = \dfrac {1}{8}\sin8x\\\dfrac {1}{4}\sin4y-\dfrac {1}{8}\sin8x=C\\2\sin4y - \sin8x = 8C[/tex]
Thus, the correct option is (c) 2 sin(4y) - sin(8x) = C.
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At 3 am the temperature was -4°C by midday the temperature had gone up by 11°C from Midday to midnight the temperature went down by 9°C work out the temperature by midnight?
Answer:
-2º
Step-by-step explanation:
First you add 11 to -4 which is +7and the yousubtract 9 equal to -2
Step-by-step explanation:
Temperature at 3 am = -4°C
Temperature at midday = up 11°C
= -4°C + 11°C
= 7°C
Temperature at midnight = down 9°C
= 7°C - 9°C
= -2°C
So, the temperature at midnight is -2°C
Hope it helpful and useful :)
A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games. He displayed the results in the box plots below.
A box plot titled Number of Shots Taken by home team players. The number line goes from 10 to 32. The whiskers range from 16 to 32, and the box ranges from 20 to 23. A line divides the box at 22.
Number of Shots Taken by Home Team Players
A box plot titled Number of Shots Taken by visiting team players. The number line goes from 10 to 32. The whiskers range from 14 to 32, and the box ranges from 16 to 24. A line divides the box at 18.
Number of Shots Taken by Visiting Team Players
Which describes an inference that the coach might make after comparing the medians of the two data sets?
The home team took more shots than the visiting team.
The visiting team took more shots than the home team.
The home team had more variability in the number of shots taken.
The visiting team had more variability in the number of shots taken.
Answer:
the answer is B
Step-by-step explanation:
did the question on test
The visiting team took fewer shots than the home team, as inferred by comparing the medians represented by the line in each box plot.
Explanation:When comparing the medians of the two data sets from the box plots provided by a hockey coach, an inference that can be made is that the visiting team took more shots than the home team. This is determined by comparing the median number of shots, which is indicated by the line dividing the box within each box plot. For the home team, the median is at 22 shots, while for the visiting team, the median is at 18 shots. Since the median represents the middle value of the data set, having a lower median suggests that the visiting team took fewer shots on average than the home team.
The difference between two numbers is 12. Four times the larger number decreased by 25 equals 48 increased by 3 times the smaller number. Find the numbers.
The larger number is 37 and the smaller number is 25.
Explanation:To solve this problem, let's assume that the larger number is x and the smaller number is y.
According to the problem, x - y = 12 and 4x - 25 = 48 + 3y. We can solve this system of equations by substituting the value of x from the first equation into the second equation.
Substituting x = y + 12 into the second equation, we get 4(y + 12) - 25 = 48 + 3y. Simplifying this equation, we have 4y + 48 - 25 = 48 + 3y. By combining like terms, we get 4y + 23 = 48 + 3y. Subtracting 3y from both sides, we obtain y + 23 = 48. Finally, subtracting 23 from both sides, we find y = 25. Plugging this value into the first equation, we can solve for x: x - 25 = 12. Adding 25 to both sides, we get x = 37.Therefore, the larger number is 37 and the smaller number is 25.
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A city counsel is trying to decide to levy an additional gas tax to help with city improvements. A random sample of
400 voters in the city are asked if they favor an additional 4% gasoline sales tax to provide badly needed revenues for
street repairs. The counsel has decided it will implement the tax if at least 60% of the voters favor the tax. The
survey finds 220 out of the 400 favor the tax. Should the counsel proceed?
Answer:
No
Step-by-step explanation:
220/400=?/?
divide 220 and 400 by 4
220/400=55/100
55<60
hope this helps ;)
What is the perpendicular height of an oblique prism with a volume of 144 cubic units and an area of 24 square units
Answer:
Height of the oblique prism is 18 units.
Step-by-step explanation:
Volume of an oblique prism = [tex]\frac{1}{3}(\text{Area of the base})(\text{Perpendicular height})[/tex]
Area of the base of this prism = 24 square units
And volume of the prism = 144 cubic units
By substituting these values in the formula,
144 = [tex]\frac{1}{3}(24)(h)[/tex]
h = [tex]\frac{144\times 3}{24}[/tex]
h = [tex]\frac{432}{24}[/tex]
h = 18 units
Therefore, height of the oblique prism is 18 units.
A cable company wants to find out the average number of hours its customers spend watching cable television. Which group would best represent a sample of the population?
the first 100 people who pass by the company’s office door one week
100 of the company's customers who canceled their subscriptions last year
100 people who are customers of other cable companies
100 of the company's customers chosen from the monthly billing list
Answer:
D. 100 of the company's customers chosen from the monthly billing list
Step-by-step explanation:
what does
1/2 and 2/8 =
[tex]\frac{1}{2} + \frac{2}{8} = \frac{1 * 4}{2 * 4} + \frac{2}{8} = \frac{4}{8} + \frac{2}{8} = \frac{6}{8} = \frac{3}{4}[/tex]
Two triangular pyramids are similar the volume of the large pyramids is 729cm and the volume of the smaller pyramids is 64 cm . If the perimeter of the base of the similar pyramids is 8 cm what is the perimeter of the base of the larger pyramids
Answer:
18 cm for larger base
Step-by-step explanation:
For similar figures, there is a formula regarding volume, area, and length
Large: small = y: x for length
large: small = (y^3) / (x^3) for volume
729 cm cube/ 64 cm cube = large : small
9: 4 = large: small by length
large/ 8cm = 9/ 4
large = 8*(9/4) = 2*9 = 18 cm
It has been decided that 100 people need to be surveyed to decide the publics opinion on a school building project. A student suggests that they survey the first 100 people who enter the school. Do you think that this proposed way of sampling is an unbiased way to perform the survey?
Answer:
The proposed way of sampling is a biased way to perform the survey.
Step-by-step explanation:
Convenience sampling is a kind of non-probability sampling method that comprises of the sample being taken from that portion of the population that is near to hand. In this type of sampling method, all items doesn’t have an equivalent chance of being selected, which doesn’t comprises of random collection of items.
Convenience sampling is where we take in items which are easy to reach.
Convenience sampling consists of selection bias, i.e.e the bias involved in the sample due to inappropriate selection procedures.
For example, randomly selecting 4 people sitting near him to guesstimate the mean age of the class is a convenience sampling example. or gathering information on customer satisfaction by interviewing 6 randomly selected customers from a local store is an illustration of convenience sampling.
In this case, the sample suggested by the students consists of surveying the first 100 people who enter the school, about the public opinion on a school building project.
This is an example of convenience sample.
So, there is a selection bias present in the sample.
Thus, the proposed way of sampling is a biased way to perform the survey.
Easy question, Easy Points
Topic Volume
Focus on question 15
Answer:
738π cm^3
1458π cm^3
Step-by-step explanation:
The volume of a cylinder is V = πr^2 h, where r=radius and h=height.
a) V = πr^2 h
= π6^2 20.5 = 36*20.5π = 738π cm^3
b) V = πr^2 h
For this one, remember that diameter is half of radius. d = 18, r = 9.
V = π9^2 18 = 81*18π = 1458π cm^3
Answer:
738π cm^3
1458π cm^3
Step-by-step explanation:
Check all of the boxes that show the quotient and
remainder of the division.
66.32
66.8
62.32
62 8/25
66 8/25
DONE
Answer:
66.32
66 8/25
Step-by-step explanation:
The quotient and remainder of the divisions are as follows: 66.32 divided by 66 has a quotient of 1 and a remainder of 0.32. 66.8 divided by 66 has a quotient of 1 and a remainder of 0.8. 62.32 divided by 66 has a quotient of 0 and a remainder of 62.32.
Explanation:When dividing numbers, the quotient is the result of the division and the remainder is what is left over. Let's check the quotient and remainder for each of the given numbers:
66.32 divided by 66: Quotient = 1, Remainder = 0.3266.8 divided by 66: Quotient = 1, Remainder = 0.862.32 divided by 66: Quotient = 0, Remainder = 62.3262 8/25 divided by 66: Quotient = 0, Remainder = 62 8/2566 8/25 divided by 66: Quotient = 1, Remainder = 8/25Learn more about Division of Numbers here:https://brainly.com/question/2273245
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The weights of boxes of a certain brand of pasta follow an
approximately normal distribution with a mean of 16 ounces and a standard
deviation of 0.05 ounces.
What percentage of boxes have weights that are more than 1 standard
deviation above the mean? (Use the Empirical Rule 68, 95, 99.7)
a) 15%
b) 14%
c) 20%
d) 16%
Answer:
d) 16%
Step-by-step explanation:
The empirical rule states that for a normal distribution population with a mean (μ) and standard deviation (σ), the following conditions occur:
68% falls within one standard deviation μ ± σ95% falls within two standard deviation μ ± 2σ99.7% falls within three standard deviation μ ± 3σGiven μ = 16 ounce and σ = 0.05 ounce.
68% falls within one standard deviation = μ ± σ = 16 ± 0.05 = (15.95, 16.05)
the number that falls outside one standard deviation = 100% - 68% = 32%
Therefore percentage of boxes have weights that are more than 1 standard deviation above the mean = 32% / 2 = 16%
Approximately 32% of boxes have weights that are more than 1 standard deviation above the mean.
Explanation:To find the percentage of boxes that have weights more than 1 standard deviation above the mean, we can use the Empirical Rule. According to the Empirical Rule, approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.
Since we want to find the percentage of boxes that have weights more than 1 standard deviation above the mean, we can subtract 68% from 100% to get 32%. So, the answer is 32%.
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Two angles form a linear pair. One angle measures 8 less than three times the other. Find the measures of the angles.
Answer:
47⁰, 133⁰
Step-by-step explanation:
Angles : x , 3x - 8
Sum = 180
x + 3x - 8 = 180
4x = 188
x = 47
Angles are 47 , 133
Ben collected data from a group of 12 people. He measured each persons resting heart rate and recorded the average number of hours each person exercised per week. He created a scatter plot to show the data he collected. Based on the scatter plot, what is the best prediction of the resting heart rate, in beats per minute, of a person who exercises an average of 8 hours each week?
To predict the resting heart rate of a person who exercises 8 hours per week, you can find the corresponding point on the scatter plot that represents 8 hours of exercise and read off the corresponding resting heart rate value.
Explanation:A scatter plot is used to show the relationship between two sets of data. In this case, Ben collected data on the resting heart rate and average hours of exercise per week for 12 people. Based on the scatter plot, we can make a prediction of the resting heart rate for a person who exercises an average of 8 hours per week. To do this, we can find the point on the scatter plot that corresponds to an average of 8 hours of exercise per week and then determine the corresponding resting heart rate.
Let's find the point on the scatter plot that represents an average of 8 hours of exercise per week.
Find the x-coordinate of the point on the scatter plot that corresponds to 8 hours of exercise per week (horizontal axis).From the x-coordinate, find the corresponding y-coordinate (vertical axis), which represents the resting heart rate.Once you have the corresponding point, you can read off the resting heart rate value in beats per minute.
A 16,000 ft
B 8000 ft
C 4000 ft
D 150 ft
Answer:
A
Step-by-step explanation:
If all of the dimensions of the tank are doubled, since we live in three dimensions, the volume of the new tank will be [tex]2^3=8[/tex] times as large. [tex]8\cdot 2000=16000[/tex] feet, or answer choice A. Hope this helps!
Answer:
A 16,000 ft³
Step-by-step explanation:
Let's say the dimensions were 2, 10, and 100 now if you double those, it becomes 4, 20, 200 which equals 16,000.
Now let's say the dimensions were 2, 4, 250 double the dimensions again and it becomes 4, 8, 500 which equals 16,000.
So no matter what the dimensions are, the volume will be 16,000.
You roll a fair number cube. Find each probability:
2. P(2, then 2)
1. P(3, then 5)
3. P(4, then odd)
Answer:
P(2, then 2) = [tex]\frac{1}{36}[/tex]
P(3, then 5) = [tex]\frac{1}{36}[/tex]
P(4, then odd) = [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Given: A fair number cube is rolled
To find: P(2, then 2) , P(3, then 5) , P(4, then odd)
Solution:
Probability refers to chances of occurrence of some event.
Probability = Number of favourable outcomes/Total number of outcomes
Sample space = [tex]\left \{ 1,2,3,4,5,6 \right \}[/tex]
Total number of outcomes = 6
P(2, then 2) = P(2)P(2) = [tex]\frac{1}{6}(\frac{1}{6})=\frac{1}{36}[/tex]
P(3, then 5) = P(3)P(5) = [tex]\frac{1}{6}(\frac{1}{6})=\frac{1}{36}[/tex]
Odd numbers out of the sample space = [tex]\left \{ 1,3,5 \right \}[/tex]
P(4, then odd) = P(4)P(odd) = [tex](\frac{1}{6})(\frac{3}{6} )=\frac{1}{12}[/tex]
To calculate the probability of rolling specific numbers on a fair, six-sided die, multiply the probabilities for each individual roll. P(2, then 2) and P(3, then 5) are both 1/36. P(4, then odd) is calculated as P(4) multiplied by the combined probability of rolling an odd number, resulting in 1/12.
Understanding Probability with a Fair Number Cube:
When rolling a fair, six-sided die, each outcome has an equal probability of occurring. Specifically, the probability (P) of any one number, such as a 2 or a 3, is 1/6 since it is a fair die. When considering sequential rolls, we have to calculate the probability of each event happening one after another, which involves multiplying the probabilities of the individual events.
P(2, then 2) = P(2) * P(2) = (1/6) * (1/6) = 1/36.P(3, then 5) = P(3) * P(5) = (1/6) * (1/6) = 1/36.P(4, then odd) involves the probability of rolling a 4 first, and then an odd number, which could be a 1, 3, or 5. The probability for each odd number is 1/6, and since there are three odd numbers, the combined probability of rolling an odd number is 3/6 or 1/2. Therefore, P(4, then odd) = P(4) * P(odd) = (1/6) * (1/2) = 1/12.Thus, to find the probability of rolling specific numbers or combinations on a number cube, you can calculate each probability separately and then combine them as needed using multiplication.
Please help im gonna scream im so confuesed :(
Answer:
[tex]14^{-17}[/tex]
Step-by-step explanation
using the rules of exponents, it would be [tex]14^{10}[/tex]÷[tex]14^{27}[/tex] so then take away 27 from 10 and get -17 meaning that the answer would be A or [tex]14^{-17}[/tex]
Answer: A
Step-by-step explanation:
14^10 is already set.
(14^9)^3 is not set you need to multiply the exponents
14^18
14^10/14^27 = 14
14^-27 or 1/14^27
Each week, Kathy receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 - 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?
A.) Kathy starts each week with 108 phones to fix.
B.) Kathy repairs phones at a rate of 108 per hour.
C.) Kathy repairs phones at a rate of 108 per day.
emily buys 14 balloons. 3 are red, 4 are white, and the rest are blue. what is the ratio of blue balloons to the total number of balloons
Emily bought 14 balloons in total, with 7 balloons being blue. The ratio of blue balloons to total balloons is 1:2.
Explanation:In this numerical problem, Emily bought a total of 14 balloons. Among them, 3 are red and 4 are white. To find out how many balls are blue, subtract the number of red and white balloons from the total which is 14 - 3 - 4 = 7. Therefore, Emily has 7 blue balloons.
The ratio of blue balloons to the total number of balloons can be calculated by dividing the number of blue balloons by the total number of balloons: 7/14. This results in a ratio of 1:2. This means, for every one blue balloon, there are two total balloons.
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Final answer:
Explaining the ratio of blue balloons out of the total in the scenario where Emily buys balloons.
Explanation:
The ratio of blue balloons to the total number of balloons is 7:14 or 1:2.
To calculate this ratio, you add the number of blue balloons (7) to the total number of balloons (14), resulting in a ratio of 7:14, which simplifies to 1:2.
Phillip watched a beach volleyball game from 1 P.M. to 1:20P.M. How many degrees did the minute hand turn?
Answer:
The minute hand covered 120 degrees
Step-by-step explanation:
Minute hand completes 1 round in 60 minutes
1 round =[tex]360^{\circ}[/tex]
So, The minute hand covered degrees in 60 minutes = [tex]360^{\circ}[/tex]
The minute hand covered degrees in 1 minute [tex]= \frac{360^{\circ}}{60^{\circ}}[/tex]
Phillip watched a beach volleyball game from 1 P.M. to 1:20P.M.
So, He watched it for 20 minutes
So,The minute hand covered degrees in 20 minutes =[tex]\frac{360^{\circ}}{60^{\circ}} \times 20 =120^{\circ}[/tex]
Hence The minute hand covered 120 degrees
How many solutions does the system have?2x+3y=-6 6x-4y=-12
Answer:
One solution, which is below
Step-by-step explanation:
2x+3y=-6
6x-4y=-12
Multiply the top equation by 3 to get 6x+9y=-18.
Subtract second equation from first:
13y=-6
y=-6/13
x=-30/13
There is only one solution to this system. Hope this helps!
Solve: g^2x+1=g^3x-2
x=?
Answer:
the answer you will be looking for is g^2x - g^3x = -3
Step-by-step explanation:
as much as I would like to, I'm really not that great at explaining things
Answer:
Solve: 9^2x+1 = 9^3x-2
= 3
Step-by-step explanation:
Henry can build 2 birdhouses in 30 minutes how many birdhouse can he builds in four hours
Answer:
16 birdhouses
Step-by-step explanation:
2 birdhouses = 30 minutes
multiply by 2
4 birdhouses =60 minutes = 1 hour
Multiply by 4
16 birdhouses = 4 hours
Answer: 16.
Step-by-step explanation:
There is 60 minutes in 1 hour, multiply 60 by 4 then divide it by 30. Then multiply by 2.
Help Please geometry Question
The formula a=119e^0.027t models the population of a particular city, in thousands, t years after 1998, when will the population of the city reach 178 thousand
Answer:
By year 2092
Step-by-step explanation:
In this question, we are asked to calculate the year at which the population of the city will reach 178,000
The equation that models the population of the city is given as;
A = 119e^0.027t
Here, we plug A to be 178,000
178000 = 119e^0.027t
we take the natural logarithm of both sides)
ln 178,000 = ln (119e^0.027t)
12.09 = 0.027t ln 119
12.09/ln 119 = 0.027t
2.53 = 0.027t
t = 2.53/0.027
t = 93.7 which is approximately 94 years
Since t is number of years after 1998, the exact time the population will reach 178,000 will be 1998 + 94 years = 2,092
Answer:
The population of the city will reach 178 thousand almost 15 years after 1998, that is, in the last months of 2012.
Step-by-step explanation:
The equation to be solved is:
[tex]178 = 119\cdot e^{0.027\cdot t}[/tex]
Now, the variable is cleared with the help of algebraic handling:
[tex]\frac{178}{119} = e^{0.027\cdot t}[/tex]
[tex]\ln \frac{178}{119} = 0.027\cdot t[/tex]
[tex]t = 37.037\cdot \ln \frac{178}{119}[/tex]
[tex]t \approx 14.913\,yr[/tex]
The population of the city will reach 178 thousand almost 15 years after 1998, that is, in the last months of 2012.
What is the output when the input is 4 for the algebraic rule: 5x-6
Answer:
The output is 14
Step-by-step explanation:
y = 5x-6
Let x = 4
y = 5(4) -6
y = 20-6
y = 14
Did it rain spaghetti more or less than ½ of the month? Explain how you know.
pls explain
Answer:
More and Brainliest PLS
Step-by-step explanation:
there is 20 spaghetti days
half of 30 is 15
20 is greater than 15 so it is more than half of the month
Help plz what is the answer to this question?
Answer
c) (-3/4)pi
Step-by-step explanation:
radians = degrees*(pi/180)
radians = (-135)*(pi/180)
radians = (-135(pi))/180
Simplify to (-3(pi)/4) or (-3/4)pi
Hope this helped!
If a cone with a diameter of 10 m has a surface area of 190.6m2, find its slant height. Round to the nearest tenth.
Slant Height = m
Answer: The slant height of the cone is 65.6 m
Step-by-step explanation:
Given: The diameter of a cone = 10 m
Surface area of cone = 190.6 m²
To find: Slant height
Diameter of cone = 10 m
Therefore Radius of cone = [tex]\dfrac{\text {Diameter }}{2} = \dfrac{10}{2} =5m[/tex]
As we know that surface area of a cone is given by
[tex]S.A. = \pi r(l+r)[/tex]
Where S.A. is surface area , r is the radius of cone and l is the slant height of the cone.
Let Slant height = l
So we have
[tex]190.6 = \dfrac{22}{7} \times 5 ( 5+l)\\\\\Rightarrow 5+l= \dfrac{190.6 \times 7}{22}\\\\\Rightarrow l= \dfrac{1334.2}{22}+5\approx 60.64+5 = 65.64\approx65.6[/tex]
Hence the slant height of the cone is 65.6 m
Can you please find the quotient of 9/18÷ 3/6. I am pretty sure that the answer is 1
Answer:
It is 1
Step-by-step explanation:
Answer:
lol yeah its 1, you're right.
Step-by-step explanation: