Answers
From your earlier questions, we found
[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]
so the wave has amplitude √29. The weight's maximum negative position from equilibrium is then -√29, so you are solving for t in the given interval for which
[tex]\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac{\sqrt{29}}2[/tex]
Divide both sides by √29:
[tex]\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac12[/tex]
Take the inverse sine of both sides, noting that we get two possible solution sets because we have
[tex]\sin\left(\dfrac{7\pi}6\right)=\sin\left(\dfrac{11\pi}6\right)=-\dfrac12[/tex]
and the sine wave has period 2π, so [tex]\sin x=\sin(x+2\pi)=\sin(x+4\pi)=\cdots[/tex].
[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{7\pi}6+2n\pi[/tex]
OR
[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{11\pi}6+2n\pi[/tex]
where n is any integer.
Now solve for t :
[tex]t=\dfrac{\frac{7\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]
OR
[tex]t=\dfrac{\frac{11\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]
We get solutions between 0 and 0.5 when n = 0 of t ≈ 0.196946 and t ≈ 0.363613.
Related Questions
A train leaves the station traveling north at 75 mph 2 hours later a second train leaves on a parallel track and travels north at 125 mph how far from the station will they meet
Answers
Answer:
At 3 hours, the trains will be equidistant from the station.
Step-by-step explanation:
The first train leaves at 75 miles per hour and has a 2 hour head start. This will put the first train at mile marker 150 (75 * 2) when the second train leaves the station at 125 mph.
To solve when they will be near each other, we set up an equation to solve for t.
150 + 75t = 125t
150 = 50t
3 = t
So given this value, we know the trains will be equidistant from the train station on parallel tracks after 3 hours.
Cheers.
In a frequency distribution of 290 scores, the mean is 99 and the median is 86. One would expect this distribution to be:
Answers
Answer:
positively skewed to the right
Step-by-step explanation:
The measure of the central tendency is a profound way to describe the mean, median and mode. The measure of central tendency indicates where the center of distribution tends to be. The measure of central tendency provide a validity and answers whether the scores are high or generally low.
In this measure,The mean is usually pulled to the tail. The skewed is determined by where the tail goes, to the right side , it is positively skewed and to the left side , it is known as negatively skewed distribution.
Given that:
In a frequency of distribution of 290 scores,
the mean = 99
the median = 86
One would expect this distribution to be; positively skewed to the right since the mean value is greater than the median value.
The margin of error ________ (increases or decreases) with an increased sample size and ________ (increases or decreases) with an increase in confidence level.
Answers
With such a larger sample size, the margin of error lowers (grows or decreases), whereas, at a higher confidence level, it increases (increases or declines).
The margin of error:
A margin of error increases as the confidence level rises, resulting in a larger interval. A margin of error is reduced as confidence is increased, resulting in a narrower interval.By increasing sample size and confidence level, the margin of error lowers and grows.
Margin of error [tex](E) = Z_c * {\frac{\sigma}{\sqrt{n}}}[/tex]
Here [tex]Z_c[/tex] denotes the confidence level's critical value.Whenever it comes to sample size, n is the number of people who take part in the study.As a result, the margin of error lowers as the sample size grows, and the margin of error increases as the confidence level grows.Find out more about the margin of error here:
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Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the distribution of the population is normally distributed. 150 150 180 170
a. State the null and alternative hypotheses.
b. Using a critical value, test the hypothesis at the 10% level of significance.
c. Using a p-value, test the hypothesis at the 10% level of significance.
d. Using a confidence interval, test the hypothesis at the 10% level of significance.
e. Could a Type II error have been committed in this hypothesis test?
Answers
Answer:
a; H0: u= 140 Ha: u ≠ 140 two tailed test.
b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or
3 > t ( ∝/2) (n-1) =2.353
c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05 therefore reject H0.
d. Again reject H0 as 140 < 150.163
e. A type II error has not been committed as H0 is rejected.
Step-by-step explanation:
We formulate the null and alternative hypotheses as
a; H0: u= 140 Ha: u ≠ 140 two tailed test.
For a two tailed test the significance level ∝= 0.1 the critical region is given by
t ≤ t ( ∝/2) (n-1) and t > t ( ∝/2) (n-1)
So the critical region will be
t≤ t ( ∝/2) (n-1) =2.353
where
t= x` - u / s/ √n
Sr. No X X²
1 150 22500
2 150 22500
3 180 32400
4 170 28900
∑ 650 106,300
X`= ∑x/n = 650/4= 162.5
s²= 1/n-1 (x-x`)²= 1/n-1 [ ∑x² -(∑x)²/n ]
= 1/3[106,300 -650²/4] = 225
s= 15
Putting the values in the above equation
t= 162.5- 140/ 15/ √4
t= 3
So calculated value of t= 3
b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or
3 > t ( ∝/2) (n-1) =2.353
c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05 therefore reject H0.
d. a 90% confidence interval based on the calculated values will be
x`± 1.645 (s)/ √n
Putting the values
162.5 ±1.645 ( 15/2)
162.5 ±12.3375
174.84 , 150.163
d. Again reject H0 as 140 < 150.163
e. A type II error has not been committed as H0 is rejected.
The company charges $5 per sq ft, AND has a minimum charge of 3 sq ft per order (meaning if a customer orders something SMALLER than 3 sq ft they still are charged as if they ordered 3 sq ft, never less - but if they order something larger than 3 sq ft they just pay regularly by the sq ft). What would you charge someone who orders a piece of glass 12in X 12in
Using the same sq ft charge ($5 per sq ft) and remembering the rule about when to use the minimum charge, what would you charge someone ordering a piece of glass 48in X 48in? *
Answers
Answer:
12 inches by 12 inches = 15 dollars
48 inches by 48 inches = 80 dollars
Step-by-step explanation:
12 inches = 1 ft
so 12 inch by 12 inches is 1 ft * 1 ft
1 ft* 1 ft
1 ft^2
This is smaller than 3 ft^2 so they will get charged for 3 ft^2
3 ft^2 = 3 ft^2 * $5 / ft^2 = 15 dollars
48 inches = 48/12 = 4 ft
4ft * 4 ft = 16 ft^2
16 ft^2 = 16 ft^2 * $5 / ft^2 = 80 dollars
For any real number r, which of the following must be greater than r?
Answers
An expression is a set of numbers, variables, and mathematical operations. The correct option is C, r² + 1.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Since real numbers contain positive integers, negative integers, positive decimals, negative decimals, and zero.
Therefore, For any real number r, the expression that will be always greater than r will be (r²+1). This is because,
√r :- If r=2, then √r will be 1.4142, therefore, √r will be lesser than r.2r :- If r is negative then 2r will also be negative and will be a smaller number than that.r² + 1 :- Irrespective of r is negative or positive, decimal or integer, the given expression will be always greater than r.r³ + 1 :- If the value of r is negative, then the expression will return a smaller negative number.Hence, the correct option is C, r² + 1.
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. One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is 16, what is the value of Cohen’s d?
Answers
Answer:
Cohen's d : 1.00
Step-by-step explanation:
We know that M₁ = 18, and M₂ = 14. Given that the pooled variance for the these two samples are 16, S²Pooled = 16, and therefore S - pooled = 4.
The formula to solve for the value of Cohen's d is as follows,
d = M₁ - M₂ / S - pooled,
d = 18 - 14 / 4 = 4 / 4 = 1
Therefore the value of Cohen's d = 1
A researcher was interested in whether a new sports drink could change people's running endurance. For one week, 6 participants continued with their normal routine and then their endurance was measured. The following week, the same participants were instructed to drink the new sports drink an hour before their endurance was measured. Below are your data.
Week I 90 100 110 110 85 95
Week 2 100 110 110 120 95 95
What type of analysis would be used on the above data?
a. Z-test
b. One sample t-test
c. Independent samples t-test
d. Dependent samples t-test
Answers
Answer:
The correct option is (d).
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
We use the paired t-test if we have 2 measurements on the same item, person or thing. We should also use this test if we have 2 items that are being measured with a unique condition.
For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.
In this case, the same participants are selected for both the trials.
And the difference between the endurance before and after the usage of the new sports drink are noted.
Thus, the analysis that would be used on the data is the Dependent samples t-test.
-36 4/9 - (-10 2/9) -(18 2/9)
Answers
Answer: [tex]-44\dfrac{4}{9}[/tex]
Step-by-step explanation:
The given expression: [tex]-36\dfrac{4}{9}-(-10\dfrac{2}{9})-(18\dfrac{2}{9})[/tex]
Here, [tex]36\dfrac{4}{9}=\dfrac{36\times9+4}{9}=\dfrac{328}{9}[/tex]
[tex](10\dfrac{2}{9})=\dfrac{92}{9}\\\\(18\dfrac{2}{9})=\dfrac{9\times18+2}{9}=\dfrac{164}{9}[/tex]
That is
[tex]-36(\dfrac{4}{9})-(-10\dfrac{2}{9})-(18\dfrac{2}{9}) = -\dfrac{328}{9}-(-\dfrac{92}{9})-\dfrac{164}{9}\\\\=-\dfrac{328}{9}+\dfrac{92}{9}-\dfrac{164}{9}\\\\=\dfrac{-328+92-164}{9}\\\\=\dfrac{-400}{9}\\\\=-44\dfrac{4}{9}[/tex]
Determine which is the appropriate approach for conducting a hypothesis test. Claim: The mean RDA of sodium is 2400mg. Sample data: n150, 3400, s550. The sample data appear to come from a normally distributed population.
Answers
Answer:
Use the student t distribution
Step-by-step explanation:
Here is the formula
t = (x - u) ÷(s/√N)
From the information we have in the question:
n = 150
s = 550
x = 3400
u = mean = 2400
= 3400 - 2400÷ 500/√150
= 1000/44.9
= 22.27
At 0.05 significance level, df = 149 so t tabulated will be 1.65.
We cannot use normal distribution since we do not have population standard deviationWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceThe parametric or bootstrap method cannot be used either.Which is an infinite arithmetic sequence? a{10, 30, 90, 270, …} b{100, 200, 300, 400} c{150, 300, 450, 600, …} d{1, 2, 4, 8}
Answers
Answer:
C
Step-by-step explanation:
An arithmetic sequence has a common difference d between consecutive terms.
Sequence a
30 - 10 = 20
90 - 30 = 60
270 - 90 = 180
This sequence is not arithmetic
Sequence b
200 - 100 = 100
300 - 200 = 100
400 - 300 = 100
This sequence is arithmetic but is finite, that is last term is 400
Sequence c
300 - 150 = 150
450 - 300 = 150
600 - 450 = 150
This sequence is arithmetic and infinite, indicated by ........ within set
Sequence d
2 - 1 = 1
4 - 2 = 2
8 - 4 = 4
This sequence is not arithmetic
Thus the infinite arithmetic sequence is sequence c
In order to purchase a new backyard patio in 3 years, the Robinsons have decided to deposit $1,700 in an account that earns 6% per year compounded monthly for 3 years. How much money will be in the account in 3 years?
Answers
Answer: A = 2,034.356 ≈ $2,034.36
$2,034.36 will be in the account in 3 years
Step-by-step explanation:
Given that ;
P = $1,700
Rate r = 6%
Time period (t) = 3 years
now to find how much money will be in the account in 3 years
we say;
A = P ( 1 + r/n )^nt
A = 1,700 ( 1 + 0.06/12) ¹²ˣ³
A = 1,700 ( 1.19668)
A = 2,034.356 ≈ $2,034.36
Look at parallelogram below d1 and d3 Are both 35 degrees what is the measurement of d2
Answers
Answer:
145 degrees
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary.
d2 = 180° -d1 = 180° -35°
d2 = 145°
Help please
I don’t know what it is and I need to find the value of x please HELP
Answers
Answer:
[tex]\large \boxed{x\° = 130}[/tex]
Step-by-step explanation:
The triangle is an isosceles triangle. The base angles are equal.
Angles in a triangle add to 180 degrees.
[tex]y+65+65=180\\y+130=180\\y=50[/tex]
Angles on a straight line add up to 180 degrees.
[tex]x+50=180\\x=130[/tex]
Answer:
[tex]\huge\boxed{\sf x = 130\ degrees}[/tex]
Step-by-step explanation:
The measure of exterior angle is equal to the sum of non-adjacent interior angles.
So,
x = 65 + 65
x = 130 degrees
Find f(x) and g(x) so the function can be expressed as y = f(g(x) y = [tex]\frac{8}{x^2}[/tex]+4
Answers
Answer:
Step-by-step explanation:
Hello,
[tex]f(g(x))=\dfrac{8}{x^2}+4[/tex]
So if we take
[tex]f(x)=\dfrac{8}{x}+4 \ \ and \\\\g(x)=x^2\\ \\f(g(x))=\dfrac{8}{g(x)}+4=\dfrac{8}{x^2}+4[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the error in this problem
Answers
Answer:
12). LM = 37.1 units
13). c = 4.6 mi
Step-by-step explanation:
12). LM² = 23² + 20² - 2(23)(20)cos(119)°
LM² = 529 + 400 - 920cos(119)°
LM² = 929 - 920cos(119)°
LM = [tex]\sqrt{929+446.03}[/tex]
= [tex]\sqrt{1375.03}[/tex]
= 37.08
≈ 37.1 units
13). c² = 5.4² + 3.6² - 2(5.4)(3.6)cos(58)°
c² = 29.16 + 12.96 - 38.88cos(58)°
c² = 42.12 - 38.88cos(58)°
c = [tex]\sqrt{42.12-20.603}[/tex]
c = [tex]\sqrt{21.517}[/tex]
c = 4.6386
c ≈ 4.6 mi
The accompanying summary data on total cholesterol level (mmol/l) was obtained from a sample of Asian postmenopausal women who were vegans and another sample of such women who were omnivores.
Diet Sample Size Sample Mean Sample SD
Vegan 85.00 5.20 1.08
Omnivore 91.00 5.65 1.10
Calculate a 99% CI for the difference between the population mean total cholesterol level for vegans and population mean total cholesterol level for omnivores. (Use μvegan−μomnivore). Round to three decimal places.)
Interpret the interval.
a. We are 99% confident that the true average cholesterol level for vegans is less than that of omnivores by an amount within the confidence interval.
b. We are 99% confident that the true average cholesterol level for vegans is greater than that of omnivores by an amount within the confidence interval.
c. We are 99% confident that the true average cholesterol level for vegans is greater than that of omnivores by an amount outside the confidence interval.
d. We cannot draw a conclusion from the given information.
Answers
Answer: hey
Step-by-step explanation:
The cost, C, in United States Dollars ($), of cleaning up x percent of an oil spill along the Gulf Coast of the United States increases tremendously as x approaches 100. One equation for determining the cost (in millions $) is:
Answers
Complete Question
On the uploaded image is a similar question that will explain the given question
Answer:
The value of k is [tex]k = 214285.7[/tex]
The percentage of the oil that will be cleaned is [tex]x = 80.77\%[/tex]
Step-by-step explanation:
From the question we are told that
The cost of cleaning up the spillage is [tex]C = \frac{ k x }{100 - x }[/tex] [tex]x \le x \le 100[/tex]
The cost of cleaning x = 70% of the oil is [tex]C = \$500,000[/tex]
Now at [tex]C = \$500,000[/tex] we have
[tex]\$ 500000 = \frac{ k * 70 }{100 - 70 }[/tex]
[tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]
[tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]
[tex]k = 214285.7[/tex]
Now When [tex]C = \$900,000[/tex]
[tex]x = 80.77\%[/tex]
simplify each expression 17x + 4 - 3x
Answers
Answer:
14x+4
Step-by-step explanation:
17x-3x=14x
Consider the distribution of exam scores graded 0 from 100, for 79 students. When 37 students got an A, 24 students got a B and 18 students got a C. How many peaks would you expect for distribution?
Answers
Answer:
Three
Step-by-step explanation:
Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores
Find the value of x that will make L || M
Answers
Answer:
x = 7
Step-by-step explanation:
L and M would be parallel if angle 2x -3 and the angle x + 4 are equal.
Thus, 2x - 3 = x + 4, so that x = 7
A hypothesis test is the following:
a. a descriptive technique that allows researchers to describe a population
b. an inferential technique that uses information about a population to make predictions about a sample
c. a descriptive technique that allows researchers to describe a sample
d. an inferential technique that uses the data from a sample to draw inferences about a population
Answers
Answer:
c
Step-by-step explanation:
c. a descriptive technique
the length of a mathematical text book the is approximately 18.34cm and its width is 11.75 calculate ?
the approximate perimeter of the front cover?
the approximate area of the front cover of the book?
Answers
Answer:
Perimeter=60.18cm
Area=215.495cm^2
Step-by-step explanation:
Given:
Length of book=18.34cm
Breadth=11.75cm
Solution:
Perimeter=2(l +b)
P=2(18.34+11.75)
P=2 x 30.09
P=60.18cm
Area=l x b
A=18.34 x 11.75
A=215.495 cm^2
Thank you!
Find the value of x.
Answers
x=2.86
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {24}^{2} + {32}^{2} = 40[/tex]
[tex]c = 40[/tex]
[tex]6x + 6 + 9x - 9 = 40[/tex]
[tex](6x + 9x) + (6 - 9) = 40[/tex]
[tex]15x - 3 = 40[/tex]
[tex]15x = 43[/tex]
[tex]x = 2.866[/tex]
[tex]23.16 + 16.74 = 39.9[/tex]
the
[tex]6(2.86) + 6 = 23.16[/tex]
[tex]9(2.86) - 9 = 16.74[/tex]
Please help me out!! (the question and answer choices are all in the image). Please include all work!! <3
Answers
Answer:
bgd=cgd+cgb
agf=cgd
50=cgd
cgd=50
bgd=90
so cgd=50
bgc=40
bgd=90
Answer:
C 90-degrees
Step-by-step explanation:
Using alternate interior angles, you can say m<CGD = 50 degrees.
From here, using the fact that line BE is a bisector of line CF, we know that the sum of degrees of the line BE would be 180 degrees.
So we can say m<EGD + m<CGD + m<BGC = 180. Plug in our known values.
90 + 50 + m<BGC = 180
m<BGC = 40
And we can see that m<BGD = m<BGC + m<CGD
Thus, m<BGD = 40 + 50 = 90.
So the m<BGD = 90 degrees.
Cheers.
At a baby shower, 15 guests are in attendance and 4 of them are randomly selected to receive a door prize. If all 4 prizes are identical, in how many ways can the prizes be awarded?
Answers
Answer:
1365
Step-by-step explanation:
We figure out combinations using this formula: n!
r!(n-r)!
n=15
r=4
So n!= 15x14x13x12x11x0x9x8x7x6x5x4x3x2x1
r! = 4x3x2x1 times 15-4!, which is 11! = 11x10x9x8x7x6x5x4x3x2x1
Put this together and you have 15x14x13x12/4x3x2x1=
There are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
What are the Combinations?Combinations are the procedures used in mathematics to pick k things from n different items without replacement.
The following formula computes the combinations of k items from n:
(n, k) = n! / k!×(n-k)!
The number of ways to award the 4 door prizes to 4 guests out of a group of 15 guests is a combinatorial problem that can be calculated using the formula.
Here, n = 15 (the total number of guests) and k = 4 (the number of prizes to be awarded).
So, the number of ways to award the prizes is:
C(15, 4) = 15! / (4! (15 - 4)!)
= 15! / (4! 11!)
= 15 x 14 x 13 x 12 / (4 x 3 x 2 x 1)
= 1365.
Therefore, there are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
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Solve for x in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. 12-8x=5
Answers
x=7/8 ≈ 0.88
0.88
Answer:
x = 0.88Step-by-step explanation:
[tex]12-8x=5\\\\Collect\:like\:terms\\\\-8x =5-12\\\\-8x = -7\\\\Divide\:both\:sides\:by -8\\\frac{-8x}{-8} \\=\frac{-7}{-8} \\\\x = 0.875\\\\x = 0.88[/tex]
Renting a car costs $30 per day, or $600 per month. Renting daily is cheaper for a few days, but after how many days are the two options equal (after which renting monthly is cheaper)?
Answers
Answer:
20 days
Step-by-step explanation:
Renting a car costs $30 per day.
y = 30x
Renting a car costs $600 per month
y = 600
Set the two equations equal to each other.
30x = 600
(30x)/30 = (600)/30
x = 20
After 20 days, the two options have an equal cost.
Which of the following expression is equal to X^2+9
Answers
Answer:
(x + 3i) * (x - 3i) = x^2 + 3xi - 3xi - 9(i^2) = x^2 + 9
Step-by-step explanation:
3a-27=0
How to solve
Answers
Answer:
a = 9
Step-by-step explanation:
3a - 27 = 0
3a = 27
a = 27/3
a = 9
3*9 - 27 = 0
27 - 27 = 0
Answer:
a = 9
Step-by-step explanation:
3a-27=0
Add 27 to each side
3a = 27
Divide by 3
3a/3 = 27/3
a = 9
