(Chapter 13) If |r(t)| = 1 for all t, then |r'(t)| is a constant.
Answers
If |r(t)| = 1 for all t, then r(t) lies on the surface of a unit sphere centered at the origin. The magnitude of the tangent vector r'(t) represents the speed of motion along this surface at time t.
Since r(t) lies on the surface of the unit sphere, it follows that r(t) is a constant distance away from the origin, namely 1. Therefore, any motion along this surface must conserve the distance of the point to the origin, meaning that the magnitude of the tangent vector r'(t) is constant.
In other words, we have:
|r(t)| = 1 -> r(t) dot r(t) = 1
Differentiating both sides with respect to t, we obtain:
2r(t) dot r'(t) = 0
Taking the magnitude of both sides, we get:
2|r(t)||r'(t)|cos(θ) = 0
where θ is the angle between r(t) and r'(t).
Since |r(t)| = 1 for all t, we have cos(θ) != 0, which implies that |r'(t)| must be constant in order to satisfy the equation. Therefore, we can conclude that if |r(t)| = 1 for all t, then |r'(t)| is a constant.
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Related Questions
what is the equation in slope intercept form of the line that passes through the point (2,-5) and is parallel to the line represented by 8x+2y=14
Answers
Answer: y = -4x + 3
Step-by-step explanation:
First, we will write 8x+2y=14 in slope-intercept form.
8x+2y=14
2y = -8x + 14
y = -4x + 7
Next, we will take this new slope-intercept form equation, y = -4x + 7, and use the slope from it to substitute the coordinate point given to find the y-intercept of the equation we are trying to find.
y = -4x + b
(-5) = -4(2) + b
-5 = -8 + b
b = 3
Lastly, we will write our equation with a slope of -4 and a y-intercept of 3.
y = -4x + 3
who used this poem as a little kid i ate and i ate till i fell on the floor so eight times eight is 64
Answers
Like it was pretty catchy ig
Got stuck in my head so I didn’t forget it lol
A local dog show features 8 Portuguese water dogs. The weights of the dogs are 38, 40, 42, 46,
45, 39, 42, 40. What are the mean and median weights of the Portuguese water dogs in the dog
show?
Answers
Answer:
\( \boxed{ \bold{ \sf{Mean \: = 41.5}}}\)
\( \boxed{ \bold{ \sf{Median = \: 41}}}\)
Step-by-step explanation:
Given weights of the dogs :
38 , 40 , 42 , 46 , 45 , 39 , 42 , 40
Find the sum of the whole data:
sum of all items ( Σx ) = 38 + 40 + 42 + 46 + 45 + 39 + 42 + 40 = 332
Number of items ( n ) = 8
To find mean, divide the sum by the total number of data.
Finding the mean weights:
\( \boxed{ \sf{Mean = \: \frac{ Σx}{n}}} \)
⇒\( \sf{ \frac{332}{8} }\)
⇒\( \sf{41.5}\)
Mean weights = 41.5
-----------------------------------------------------------------------
Finding the median
To find the median, arrange the given data in ascending order.
Given data : 38, 40 , 42 , 46 , 45 , 39 , 42 , 40
Arranging the data in ascending order :
38 , 39 , 40 , 40 , 42 , 42 , 45 , 46
Total number of observation ( n ) = 8
Finding the position of median
\( \boxed{ \sf{Position \: of \: median = ( \frac{n + 1}{2} ) ^{th} item}}\)
⇒\( \sf{( \frac{8 + 1}{2} ) ^{th} item}\)
⇒\( \sf{( \frac{9}{2} ) ^{th} item}\)
⇒\( \sf{ {4.5}^{th} item}\)
4.5 th item is the average of 4 th and 5th items .
Here, 4 th item = 40
5 th item = 42
Finding the median
\( \boxed{ \sf{Median = ( \frac{{4}^{th} \: item + {5}^{th} item}{2}) }}\)
⇒\( \sf{ \frac{40 + 42}{2} }\)
⇒\( \sf{ \frac{82}{2} }\)
⇒\( \sf{41 }\)
Hope I helped!
Best regards!!
Answer:
A local dog show features 8 Portuguese water dogs. The weights of the dogs are 38, 40, 42, 46,
45, 39, 42, 40. What are the mean and median weights of the Portuguese water dogs in the dog
show?
Step-by-step explanation:
Find the slope of (2 , -7 ) and ( -1 , 6 )
A. 4
B. -6
C. -1/6
D. 6
Answers
Answer:
-13/3
Step-by-step explanation:
y2 - y1 / x2 - x1
6 - (-7) / -1 - 2
13 / -3
= -13/3
Hello !
Answer:
\( \boxed{\sf None \: of \: the \: options \text{:} \: \: m =- \dfrac{13}{3}} \)
Step-by-step explanation:
The slope m of a line passing through two points can be calculated using the following formula:
\( \sf m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1} \)
\( \\ \)
Let (x₁ , y₁) = (2 , -7)
Let (x₂ , y₂) = (-1 , 6)
Substitute these values into our formula:
\( \sf m =\dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{6 - (-7) }{-1 - 2 } = \dfrac{13}{-3}\\ \\ \implies \boxed{\sf m = -\dfrac{13}{3}} \)
Have a nice day ;)
For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.
Answers
a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.
b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.
c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.
(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.
(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.
(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.
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public class BinarySearch \{ public static void main(Stringll args) f int [1]yl ist ={1,2,3,7,10,12,20}; int result = binarysearch ( inylist, 20); if (result =−1 ) System, out, println("Not found:"); else System.out.println("The index of the input key is " + result+ ". "): y public static int binarysearch(int]l List, int key) \{ int low =0; int high = iist. length −1 while (high >= low) \& int mid =( low + high )/2; if (key < List [mid] high = mid −1; else if (key =1 ist [ mid ] ) return inid; else low = mid +1; return −1; // Not found \} l TASK 4: Binary Search in descending order We have learned and practiced the implementation of the binary search approach that works on an array in ascending order. Now let's think about how to modify the above code to make it work on an array in descending order. Name your new binary search method as "binarysearch2". Implement your own code in Eclipse, and ensure it runs without errors. Submit your source code file (.java file) and your console output screenshot. Hint: In the ascending order case, our logic is as follows: int mid =( low + high )/2 if ( key < list [mid] ) else if (key = ist [mid]) return mid; In the descending order case; what should our logic be like? (Swap two lines in the above code.)
Answers
The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.
The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.
To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.
The modified code for binary search in descending order would look like this:
public static int binarysearch2(int[] list, int key) {
int low = 0;
int high = list.length - 1;
while (high >= low) {
int mid = (low + high) / 2;
if (key > list[mid])
high = mid - 1;
else if (key < list[mid])
low = mid + 1;
else
return mid;
}
return -1; // Not found
}
By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.
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the mean sustained wind velocity, v, can be determined by the equation , where p is the air pressure, in millibars, at the center of the hurricane. what is the approximate air pressure at the center of a hurricane when the mean sustained wind velocity is 64 meters per second? 103 millibars
Answers
The approximate air pressure at the center of a hurricane is 910 millibars.
Given,
The mean sustained wind velocity equation, v = 6.3 × √(1013 - p)
p is the air pressure in millibars
The mean sustained wind velocity - 64 meters per second.
We have to find the approximate air pressure.
Here,
The equation for wind velocity ;
v = 6.3 × √(1013 - p)
v is given 64
Then substitute;
64 = 6.3 × √1013 - p
64/6.3 = √1013 - p
10.16 = √1013 - p
Square both sides
(10.16)² = (√1013 - p)²
We get,
103.23 = 1013 - p
p = 1013 - 103.33 = 909.67 ≈ 910 millibars
That is,
The approximate air pressure at the center of a hurricane is 910 millibars.
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John rode his dirt bike 45 miles in two hours. At this rate, how many miles will he travel in 1/2 an hour?
Answers
Answer:
11.25 miles
Step-by-step explanation:
To figure out how many miles John will travel in 1/2 an hour, we can use the following formula:
distance = rate x time
We know the rate, which is the number of miles John can travel per hour. We can find this by dividing the total distance by the total time:
rate = distance / time
rate = 45 miles / 2 hours
rate = 22.5 miles per hour
Now we can use this rate and the given time of 1/2 an hour to find the distance:
distance = rate x time
distance = 22.5 miles per hour x 1/2 hour
distance = 11.25 miles
Therefore, John will travel 11.25 miles in 1/2 an hour at this rate.
17. P(-6, 16), Q(2, -4), R(-6, 14), S(-2, 4)Slope of PQ Slope of RSTypes of Lines
Answers
The formula for finding slope is expressed as
slope = (y2 - y1)/(x2 - x1)
where
y2 and y1 are final and initial values of the y coordinates respectively
x2 and x1 are final and initial values of the x coordinates respectively
Considering line PQ,
x1 = - 6, y1 = 16
x2 = 2, y2 = - 4
Slope = (- 4 - 16)/(2 - - 6) = - 20/8
Slope = - 2.5
Considering line RS,
x1 = - 6, y1 = 14
x2 = - 2, y2 = 4
Slope = (4 - 14)/(- 2 - - 6) = - 10/4
Slope = - 2.5
If the slope of two lines are equal, it means that they are parallel. We can see that the slopes of PQ and RS are equal. Thus,
Line PQ is parallel to line RS
2
Plzz help 15 points
Which of the following graphs show
f(x) =
x + 1, when x < 1
4, when ≥ 1
Answers
Answer:
I think its C if I'm wrong, sorrryyy
Determine f(4) for the function f(x)=2/5x+11
Answers
Answer:
63/5 in improper form and 12 and 3/5 in mixed form
Step-by-step explanation:
f(x) = 2/5x + 11
Substitute in value of x for the equation
f(4) = 2/5(4) + 11
f(4) = 8/5 + 11
f(4) = 8/5 + 55/5
f(4) = 63/5 or 12 and 3/5
So, the answer should be 63/5 in improper form and 12 and 3/5 in mixed form.
Answer:
Step-by-step explanation:
f(x) = \(\frac{2}{5}x + 11\)
f(4) = \(\frac{2}{5}*4 +11\\\)
\(=\frac{8}{5}+11\\\\=\frac{8}{5}+\frac{11*5}{1*5}\\\\=\frac{8}{5} + \frac{55}{5}\\\\=\frac{63}{5}\\\\=12\frac{3}{5}\)
(L1) Given: ∠DEF; point I in the interior of the angle;m∠DEF=46∘;IG=IH=5 in; IG¯⊥EG¯;IH¯⊥EH¯.What is the measure of ∠DEI?By which Theorem?
Answers
Angle DEI is equal to the sum of angles DEF and EIG. therefore, the measure of DEI is 136°. The theorem used to solve this problem is the Angle Addition Postulate.
Based on the given information, we can determine the measure of angle EIG and angle EIH as follows:
Since IG ⊥ EG, we know that angle EIG is a right angle. Therefore, angle DEI is equal to the sum of angles DEF and EIG:
∠DEI = ∠DEF + ∠EIG = 46° + 90° = 136°
Similarly, since IH ⊥ EH, we know that angle EIH is a right angle.
The theorem used to solve this problem is the Angle Addition Postulate, which states that the measure of an angle formed by two adjacent angles is equal to the sum of the measures of the two adjacent angles.
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according to a survey of adults, 64% have money in a regular savings account. if we plan on surveying 50 randomly selected adults, find the mean number of adults who would have regular savings accounts.
Answers
By using Binomial probability distribution, the mean number of adults who would have bank savings accounts is 32.
For every survey, there are only two possible outcomes.
First- they have bank savings accounts,
second- they do not.
So, by using the binomial probability distribution we can solve this problem.
Probability of exactly Y successes in ‘n’ repeated trials, with ‘p’ probability.
Probability = p
Successes repeated = n times
The value of the binomial distribution is:
E(Y) = n x p
In this problem, we have that:
p = 0.64
If we were to survey among 50 randomly selected adults, the mean number of adults who would have bank savings accounts is,
E(Y) when, n = 50
So,
E(Y)= n x p
= 50 x 0.64
= 32
Hence ,our required answer is 32 adults who would have bank savings accounts
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Determine whether the given statements are equivalent and why.a) If she attends the meeting, she will become the secretary.b) If she does not become the secretary, then she did not attend the meeting.
Answers
No, the statements a) If she attends the meeting, she will become the secretary b) If she does not become the secretary, then she did not attend the meeting are not equivalent.
The statement "a" says that if she attends the meeting, then she will become the secretary. This is a sufficient condition for her to become the secretary.
The statement "b" says that if she does not become the secretary, then she did not attend the meeting. This is a necessary condition for her not attending the meeting.
So, while the statements are related, they don't represent the same relationship between the events of attending the meeting and becoming the secretary.
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Salem has 150 cookies to sell. Each cookie is one of four types. . 1/6 of cookies are oatmeal raisin. . 1/4 of cookies are sugar cookie. . 5/12 of cookies are chocolate chip. The rest are double chocolate. How many of the cookies are double chocolate?
Answers
Answer: 22 double chocolate cookies
Step-by-step explanation:
25 oatmeal raisin
38 sugar cookie
65 chocolate chip
22 double chocolate
The length of the hypotenuse of an isosceles right triangle is 14. What is the length of each leg of the triangle?
Answers
Answer:
leg = √7 units (approximately 2.65 units)
Step-by-step explanation:
Given a right isoceles triangle with a hypotenuse of 14 units, the two other legs must be congruent in length. Because this is a right triangle, the pythagorean theorem a^2 + b^2 = c^2, can be used.
Since the two legs are congruent, side a = side b. This means that
2leg^2 = hypotenuse.
_____________
2leg^2 = 14 units
÷ 2. ÷2
_____________
leg^2 = 7 units
√ √
____________
leg = √7 units
At a concert, the organizer ditributed out 1050 paper fan, 1575 glow tick and 3150 ticker to the participant. All the participant had the equal number of each of the item. Find the larget number of participant for the concert
Answers
The largest number of participants at the concert was 4.
To determine the largest number of participants at the concert, we need to find the least common multiple (LCM) of 1050, 1575, and 3150. The LCM is the smallest positive integer that is a multiple of all three numbers.
The prime factorization of 1050 is 2 * 3 * 5 * 5 * 7.
The prime factorization of 1575 is 3 * 5 * 5 * 11.
The prime factorization of 3150 is 2 * 3 * 5 * 5 * 7 * 11.
The LCM of 1050, 1575, and 3150 is therefore 2 * 3 * 5 * 5 * 7 * 11 = 31500.
Since each participant received one of each item, the largest number of participants at the concert was
31500 / (1050 + 1575 + 3150) = 31500 / 7775 = 4.
Therefore, the largest number of participants at the concert was 4.
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Samantha paid $26.25 for three books that all cost the same amount. What was the cost per book?
Answers
Answer:
$8.75 per book
Step-by-step explanation:
26.25/3 = 8.75
Answer:
$8.75
Step-by-step explanation:
26.25 divided by 3 = 8.75
m<3+m<5=180 true or false
Answers
Answer:
False.
Step-by-step explanation:
Help please? 10 points
Answers
Answer:
277 cm^2
Step-by-step explanation:
Two of the triangular faces will have areas of ...
A = 1/2bh = (1/2)(8 cm)(11 cm) = 44 cm^2
and the other two will have areas of ...
A = 1/2bh = (1/2)(9 cm)(13 cm) = 58.5 cm^2
The base will have an area of ...
A = LW = (9 cm)(8 cm) = 72 cm^2
So, the total area will be ...
2(44 cm^2) +2(58.5 cm^2) +72 cm^2 = 277 cm^2
_____
Comment on the problem
You could not actually build this pyramid. The height of the peak above the 8-cm edges must be ...
√(11^2 -(4.5)^2) = 10.04 cm
The height of the peak above the 9-cm edges must be ...
√(13^2 -4^2) = 12.37 cm.
The peak cannot be in two places at once. This geometry is impossible.
Help pls find the area
Answers
Answer: 112 ft²
Step-by-step explanation:
The area of a triangle can be found with the equation
\(A=\frac{1}{2} bh\), where b is the base (bottom line of the triangle) and h is the height (the distance of the line from the peak of the triangle that forms a right angle with the base).
In this problem we are given the base and height: the base is 16 feet, and the height is 14 ft.
Therefore, the area is \(\frac{1}{2} *16*14\), which is 112 ft²
An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion who are not satisfied.
(a) Past studies suggest that this proportion will be about 0.17. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015. (You will need a critical value accurate to at least 4 decimal places.) Sample size:
(b) Using the sample size above, when the sample is actually contacted, 25% of the sample say they are not satisfied. What is the margin of the error of the confidence interval? MoE:
Answers
The margin of error for the confidence interval is approximately 0.014, indicating that the estimate of the proportion of dissatisfied customers could be off by approximately plus or minus 0.014. This means that we can be 95% confident that the true proportion of dissatisfied customers falls within the range of the estimated proportion ± 0.014.
(a) To find the sample size needed to achieve a margin of error of about 0.015 with a 95% confidence level, we can use the formula for sample size calculation for proportions:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = critical value (corresponding to the desired confidence level)
p = estimated proportion of the population
E = margin of error
In this case, the estimated proportion of dissatisfied customers is 0.17, and the desired margin of error is 0.015. Since we want a 95% confidence level, the critical value can be obtained from a standard normal distribution table. The critical value for a 95% confidence level is approximately 1.96.
Plugging these values into the formula, we have:
n = (1.96^2 * 0.17 * (1-0.17)) / 0.015^2
n ≈ 1901.63
Therefore, the sample size needed is approximately 1902.
(b) If 25% of the sample say they are not satisfied, we can calculate the margin of error using the following formula:
MoE = Z * sqrt((p * (1-p)) / n)
Where:
MoE = margin of error
Z = critical value (corresponding to the desired confidence level)
p = proportion of the sample
n = sample size
Using the same critical value of 1.96 for a 95% confidence level and plugging in the values:
MoE = 1.96 * sqrt((0.25 * (1-0.25)) / 1902)
MoE ≈ 0.014
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These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
Help
simplest terms.
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.
Answers
The probability of drawing two yellow balls if they're not replaced exists 1/45.
What is probability?
The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.
Number of yellow marbles be 2
Number of pink marbles be 3
Number of blue marbles be 5
Total number of marbles = 2+3+5 = 10
The probability of removing the first yellow ball = 2/10
Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.
Probability of drawing the second yellow ball = 1/9.
Probability of drawing two yellow balls if they're not replaced
= 2/10 × 1/9
= 2/90
= 1/45
The probability of drawing two yellow balls if they're not replaced exists 1/45.
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Consider random variables X, Y with probability density f(x,y) = C(x+y), x € [0, 1], y E [0, 1]. Assume this function is 0 everywhere else. Find the value of C, compute covariance Cov(X,Y) and correlation p(X,Y). Are X, Y independent?
Answers
We can find the marginal densities as follows: f_X(x) = integral from 0 to 1 of f(x,y) dy = integral from 0 to 1 of (2/3)(x + y) dy
To find the value of C, we need to use the fact that the total probability over the region must be 1. That is,
integral from 0 to 1 of (integral from 0 to 1 of C(x + y) dy) dx = 1
We can simplify this integral as follows:
integral from 0 to 1 of (integral from 0 to 1 of C(x + y) dy) dx = integral from 0 to 1 of [Cx + C/2] dx
= (C/2)x^2 + Cx evaluated from 0 to 1 = (3C/2)
Setting this equal to 1 and solving for C, we get:
C = 2/3
To compute the covariance, we need to first find the means of X and Y:
E(X) = integral from 0 to 1 of (integral from 0 to 1 of x f(x,y) dy) dx = integral from 0 to 1 of [(x/2) + (1/4)] dx = 5/8
E(Y) = integral from 0 to 1 of (integral from 0 to 1 of y f(x,y) dx) dy = integral from 0 to 1 of [(y/2) + (1/4)] dy = 5/8
Now, we can use the definition of covariance to find Cov(X,Y):
Cov(X,Y) = E(XY) - E(X)E(Y)
To find E(XY), we need to compute the following integral:
E(XY) = integral from 0 to 1 of (integral from 0 to 1 of xy f(x,y) dy) dx = integral from 0 to 1 of [(x/2 + 1/4)y^2] from 0 to 1 dx
= integral from 0 to 1 of [(x/2 + 1/4)] dx = 7/24
Therefore, Cov(X,Y) = E(XY) - E(X)E(Y) = 7/24 - (5/8)(5/8) = -1/192
To compute the correlation, we need to first find the standard deviations of X and Y:
Var(X) = E(X^2) - [E(X)]^2
E(X^2) = integral from 0 to 1 of (integral from 0 to 1 of x^2 f(x,y) dy) dx = integral from 0 to 1 of [(x/3) + (1/6)] dx = 7/18
Var(X) = 7/18 - (5/8)^2 = 31/144
Similarly, we can find Var(Y) = 31/144
Now, we can use the definition of correlation to find p(X,Y):
p(X,Y) = Cov(X,Y) / [sqrt(Var(X)) sqrt(Var(Y))]
= (-1/192) / [sqrt(31/144) sqrt(31/144)]
= -1/31
Finally, to determine if X and Y are independent, we need to check if their joint distribution can be expressed as the product of their marginal distributions. That is, we need to check if:
f(x,y) = f_X(x) f_Y(y)
where f_X(x) and f_Y(y) are the marginal probability densities of X and Y, respectively.
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A library receives 413 boxes of books and 125 boxes of magazines. There are 18 books in each box of books. How many total books did the library receive?
? x 18 = ?
Answers
Answer: 7434 books
Step-by-step explanation:
413 x 18= 7434
_____ is the tendency to emit repeatedly the same verbal or motor response to varied stimuli.
Answers
Answer:
perseveration
Step-by-step explanation:
The term you are looking for is "perseveration."
How do you find the angles of a 5/12/13 triangle?
Answers
The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.
What is Law of cosines formula?In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ
where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.
To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.
a² = b²+ c²– 2bc cos αb²= a² + c²– 2ac cos βc²= b² + a² – 2ba cos γWe have , a = 5 , b = 12 , c= 13
cos α =( 12² + 13² - 5² )/2×12×13= 288/312
=> α = cos⁻¹(0.923 ) = 22.63°
cos β = (5² + 13² - 12² )/2×13×5 = 50/130
=> β = cos⁻¹(5/13) = 67.38°
cos γ = (12² + 5² - 13² )/2×12×5= 0
=> γ = cos⁻¹(0) = 90°
Hence, the required angles are 90°, 22.63°, 67.38°.
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Let L = {w € {a + b}" | #b(w) is even}. Which one of the regular expression below represents L? pt) (a) (a*ba*b)* (b) a*(baba")" (c) a* (ba*b*)*a* (d) a*b(ba*b)"ba
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The regular expression that represents the language L is option (c) a* (bab)a. This regular expression matches strings that consist of zero or more 'a's followed by zero or more occurrences of the pattern 'bab', and ending with zero or more 'a's. This pattern ensures that the number of 'b's in the string is always even.
To understand why option (c) is the correct regular expression for representing the language L, let's break down the components of the regular expression:
a* - Matches zero or more occurrences of 'a'.
(bab)* - Matches zero or more occurrences of the pattern 'bab', where 'b' can be followed by zero or more 'a's. This pattern allows for an arbitrary number of 'b's to occur, as long as the count is even.
a* - Matches zero or more occurrences of 'a'.
By combining these components, the regular expression ensures that any string in L will start and end with zero or more 'a's and have an even number of 'b's in between.
The other options (a), (b), and (d) do not correctly represent the language L. Option (a) allows for any number of 'b's, including odd counts.
Option (b) requires a specific pattern of 'baba' to appear in the string, which may not satisfy the condition of having an even number of 'b's. Option (d) allows for an arbitrary number of 'b's without enforcing an even count.
Therefore, option (c) is the correct choice for representing the language L.
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4 times what eqwals 20
Answers
Answer: 5
Step-by-step explanation:
4 times 5 equals 20.
I hope this helps!
So your answer should be 5
Ken planted 10 flowers and 8 shrubs in his garden.
He ran out of fertilizer before he finished and
3 flowers and 2 shrubs were planted without
fertilizer. What percentage of plants were planted
without fertilizer?