Answer:
B. No, because the probability of success is different for each trial.
The experiment is not binomial.
Step-by-step explanation:
The trials are not independent because they are chosen without replacement.
There are successes and failures but the trials are dependent.
So it is not binomial.
When the balls are not replaced the probability of success becomes different for each ball.
Suppose we have 10 balls and we pick out 1 so the p1 = 1/10
but when we again pick out another without replacement the p2= 1/9
This explains why it is not binomial. In binomial the n is fixed.
A racecar is traveling at a constant speed of 150 miles per hour. How many feet does it travel in 5 seconds? Remember that 1 mile is 5280 feet.
Answer:
distance covered in 5 seconds
= 1.4283 *10^10 feet
Step-by-step explanation:
A racecar is traveling at a constant speed of 150 miles per hour.
One mile = 5280 feet
150 miles= 5290*150
150 miles= 793500 feet
A racecar is traveling at a constant speed of 793500 feet per hour.
Converting 793500 feet per hour to feet per seconds .
793500 feet per hour
= 793500*60*60 feet per seconds
=2856600000 feet per second
In 5 seconds , distance covered
= 2856600000 *5
distance covered in 5 seconds
= 1.4283 *10^10 feet
Solve for x: 3(x + 1)= -2(x - 1) + 6.
Answer:
x=1
Step-by-step explanation:
3(x + 1)= -2(x - 1) + 6.
Distribute
3x+3 = -2x+2+6
Combine like terms
3x+3 = -2x+8
Add 2x to each side
3x+3+2x = 8
5x+3 = 8
Subtract 3 from each side
5x =5
Divide by 5
x =1
Use mathematical induction to prove the statement is true for all positive integers n. The integer n3 + 2n is divisible by 3 for every positive integer n.
Answer:
Prove:
Using 1
n³+2n = (1)³+2(1) = 1+2= 3 ---> 3/3= 1 ✔
Using 2
n³+2n = (2)³+2(2)= 8+4=12 --> 12/3=4✔
Using 3
n³+2n= (3)³+2(3)= 27+6= 33 --> 33/3=11✔
So it is proven that n³+2n is divisible by 3 for every positive integer.
I hope this helps
if u have question let me know in comments
I NEED HELP ASAP
FUND THE VALUE OF X
Answer:
2 sqrt(41) = x
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 10 ^2 = x^2
64+ 100 = x^2
164 = x^2
Take the square root of each side
sqrt(164) = sqrt(x^2)
sqrt(4) sqrt(41) = x
2 sqrt(41) = x
1
Drag and drop the
labels to the correct
sides using Angle A
as a reference.
A
boy
3
4
hypotenuse
adjacent
opposite
5
6
hypotenuse goes to the line across from the right angle. adjacent is the bottom one. lastly opposite is the left one.
Step-by-step explanation:
Hi, there!!
According to the question, we should find the hypotenuse, adjacent, and opposite to the refrence angle A ,right.
so, let's simply work with it,
hypotenuse (h)= AC {side opposite to the 90° is always a hypotenuse}.
opposite (p)= BC { as the side opposite to the refrence angle is always perpendicular or opposite}
adjacent (b)= AB { as remaining side is always base or adjacent}
Hope it helps....
Choose the correct ray whose endpoint is B.
Answer:
The second option.
Step-by-step explanation:
The first option consists of a line that extends at both opposite sides to infinity, with no precise end.
The third option is a ray that has an endpoint of A, and extends to infinity towards B.
The fourth option is a line segment. It has two endpoints, B and A.
The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.
The answer is the 2nd option.
The top speed of this coaster is
128 mph. What is the tallest peak
of this coaster?
** Hint... convert mph into m/s.*
To convert miles per hour to meters per second divide by 2.237
128 miles per hour / 2.237 = 57.22 meters per second.
Using the first equation:
57.22 = sqrt(2 x 9.81 x h)
Remove the sqrt by raising both sides to the second power:
57.22^2 = (2 x 9.81 x h)
Simplify Both sides:
3274.1284 = 19.62h
Divide both sides by 19.62:
H = 3274.1284/ 19.62
H = 166.88 meters
3 With 72 million bicycles, correct to the
nearest million, Japan is at the top of the list
of countries with most bicycles per person.
On average, Japanese people travel about
2 km by bicycle, correct to the nearest km,
each day. Calculate the upper bound for the
total distance travelled by all the bicycles in
Japan.
Answer:
181 million km
Step-by-step explanation:
"Correct to the nearest unit" means the actual value might be 1/2 unit larger (or smaller) than the reported value.
The upper bound would be the product of the maximum number of bicycles and the maximum distance each travels:
(72.5 · 10^6 bicycles)(2.5 km/bicycle) = 181.25 · 10^6 km
__
Since the given numbers are good to 2 significant figures (or so), we might reasonably put the upper bound as 180·10^6 km.
A 2-column table with 9 rows. The first column is labeled year with entries 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010. The second column is labeled pounds of trash with entries 3.25, 3.25, 3.66, 3.83, 4.57, 4.52, 4.74, 4.69, 4.44. The table shows the average number of pounds of trash generated per person per day in the United States from 1970 to 2010. Use the statistics calculator to calculate the mean and median. Round the answers to the nearest hundredth. Median = Mean =
Answer:
Median: 4.44
Mean: 4.11
On edge
Step-by-step explanation:
The mean and median of the data is
Mean ≈ 4.1 pounds
Median = 4.44
How to find mean and median of a data?The ratio of the total number of observations to the sum of the observations is known as the mean.
The median is a value for an ordered data collection that has the same amount of observations on its left and right (in either ascending or descending order).
We have the following data:
3.25, 3.25, 3.66, 3.83, 4.57, 4.52, 4.74, 4.69, 4.44
So, Mean of the data is
= sum/number of observations
= (3.25 + 3.25 + 3.66 + 3.83 + 4.57 + 4.52 + 4.74 + 4.69 + 4.44) / 9
= 36.95 / 9
= 4.10555
Now, Arranging the data in ascending order gives
3.25, 3.25, 3.66, 3.83, 4.44, 4.52, 4.57, 4.69, 4.74
Here mid value is the 5th value from both end.
Thus, median of the data set = 4.44
Learn more about mean and median here:
brainly.com/question/16118626
#SPJ6
The one-sample z ‑statistic for Thomas' statistical test has a value of −1.73346 , and Thomas calculates a P-value of 0.0830 . Should Thomas conclude that telephone surveys provide adequate coverage with respect to p ? Why or why not? Select all correct statements about his decision and conclusion.
Answer:
Thomas should not reject the null hypothesis.
Step-by-step explanation:
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. Here in this question the test value is -1.73346 and p-value is 0.0830. The p value is greater than the test value therefore the null hypothesis should be accepted.
h(x) = -x² + 3x + 10
Answer:
x = 5 or x = -2 or 3 - 2 x (derivative)
Step-by-step explanation:
Solve for x over the real numbers:
-x^2 + 3 x + 10 = 0
Multiply both sides by -1:
x^2 - 3 x - 10 = 0
x = (3 ± sqrt((-3)^2 - 4 (-10)))/2 = (3 ± sqrt(9 + 40))/2 = (3 ± sqrt(49))/2:
x = (3 + sqrt(49))/2 or x = (3 - sqrt(49))/2
sqrt(49) = sqrt(7^2) = 7:
x = (3 + 7)/2 or x = (3 - 7)/2
(3 + 7)/2 = 10/2 = 5:
x = 5 or x = (3 - 7)/2
(3 - 7)/2 = -4/2 = -2:
Answer: x = 5 or x = -2
____________________________________
Find the derivative of the following via implicit differentiation:
d/dx(H(x)) = d/dx(10 + 3 x - x^2)
Using the chain rule, d/dx(H(x)) = ( dH(u))/( du) ( du)/( dx), where u = x and d/( du)(H(u)) = H'(u):
(d/dx(x)) H'(x) = d/dx(10 + 3 x - x^2)
The derivative of x is 1:
1 H'(x) = d/dx(10 + 3 x - x^2)
Differentiate the sum term by term and factor out constants:
H'(x) = d/dx(10) + 3 (d/dx(x)) - d/dx(x^2)
The derivative of 10 is zero:
H'(x) = 3 (d/dx(x)) - d/dx(x^2) + 0
Simplify the expression:
H'(x) = 3 (d/dx(x)) - d/dx(x^2)
The derivative of x is 1:
H'(x) = -(d/dx(x^2)) + 1 3
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.
d/dx(x^2) = 2 x:
H'(x) = 3 - 2 x
Simplify the expression:
Answer: = 3 - 2 x
Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Select three options.
Answer:
The answer is "Choice B, C, and F is correct".
Step-by-step explanation:
The following are choices, which is missing in the question, that can be defined as follows:
A) {x| x ≥ 3} is the domain.
B) The set shall be {y| y ≥ –1}.
C) over the interval (–∞, 3), is the function, that decreases.
D) it's over the duration the function increases its value, that is (–1, ∞).
E) The symmetry axis will be x = – 1.
F) vertex is (3, – 1).
In choice A, It is incorrect even though f is the domain, which is all true numbers because it has a quadrant function. In choice B, it is correct. In choice C, It is valid because it was a parable open with vertex so if we exploded view f (3, -1). Because as value opens up, its value with x from-∞ to 3 drops while it goes up from increasing from 3 to ∞. In choice D, It is wrong since we have just said f decreases from-∞ to 3. Therefore, f decreases from -1 to 3, too. Therefore, f doesn't grow from -1 to ∞. In choice E, It is incorrect because the symmetry axis is x = 3. In choice F, it is true.Answer:
the answers are b, c, e
Step-by-step explanation:
i just took the test
Express the quotient of z1 and z2 in standard form given that [tex]z_{1} = -3[cos(\frac{-\pi }{4} )+isin(\frac{-\pi }{4} )][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2} )+isin(\frac{-\pi }{2} )][/tex]
Answer:
Solution : [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
Step-by-step explanation:
[tex]-3\left[\cos \left(\frac{-\pi }{4}\right)+i\sin \left(\frac{-\pi \:}{4}\right)\right]\:\div \:2\sqrt{2}\left[\cos \left(\frac{-\pi \:\:}{2}\right)+i\sin \left(\frac{-\pi \:\:\:}{2}\right)\right][/tex]
Let's apply trivial identities here. We know that cos(-π / 4) = √2 / 2, sin(-π / 4) = - √2 / 2, cos(-π / 2) = 0, sin(-π / 2) = - 1. Let's substitute those values,
[tex]\frac{-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)}{2\sqrt{2}\left(0-1\right)i}[/tex]
=[tex]-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)[/tex] ÷ [tex]2\sqrt{2}\left(0-1\right)i[/tex]
= [tex]3\left(-\frac{\sqrt{2}i}{2}+\frac{\sqrt{2}}{2}\right)[/tex] ÷ [tex]-2\sqrt{2}i[/tex]
= [tex]\frac{3\left(1-i\right)}{\sqrt{2}}[/tex]÷ [tex]2\sqrt{2}i[/tex] = [tex]-3-3i[/tex] ÷ [tex]4[/tex] = [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
As you can see your solution is the last option.
If the errors produced by a forecasting method for 3 observations are +3, +3, and −3, then what is the mean squared error?
Answer:
9
Step-by-step explanation:
The mean squared error (MSE)of a set of observations can be calculated using the formula :
(1/n)Σ(Actual values - predicted values)^2
Where n = number of observations
Steps :
Error values of each observation (difference between actual and predicted values) is squared.
Step 2:
The squared values are summed
Step 3:
The summation is the divided by the number of observations
The difference between the actual and predicted values is known as the ERROR.
(1/n)Σ(ERROR)^2
n = 3
Error = +3, +3, - 3
MSE = (1/3)Σ[(3)^2 + (3)^2 + (-3)^2]
MSE = (1/3) × [9 + 9 + 9]
MSE = (1/3) × 27
MSE = 9
Please help with this
Answer:
A
Step-by-step explanation:
● first one:
The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.
STP is one of them so this statement is true.
● second one:
If ST and PT were equal this would be a square not a rhombus.
● third one:
If SPQ was a right angle, this woukd be a square.
● fourth one:
Again if the diagonals SQ and PR were equal, this would be a square.
g a video game claims that the drop rate for a certain item is 5% according to the game publisher. in online forums, a number of players are complaining that the drop rate seems to be low. in order to test the drop rate claim, 100 players agree to attempt to get the drop, each attempting 10 times. of the 1000 tries, the item only drops 40 times state the null hypothesis needed to test this claim group of answer choices
Answer:
p0 = 0.05
Step-by-step explanation:
Express the product of z1 and z2 in standard form given that [tex]z_{1} = 6[cos(\frac{2\pi }{5}) + isin(\frac{2\pi }{5})][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2}) + isin(\frac{-\pi }{2})][/tex]
Answer:
Solution : 5.244 - 16.140i
Step-by-step explanation:
If we want to express the two as a product, we would have the following expression.
[tex]-6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right]\cdot 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Now we have two trivial identities that we can apply here,
( 1 ) cos(- π / 2) = 0,
( 2 ) sin(- π / 2) = - 1
Substituting them,
= [tex]-6\cdot \:2\sqrt{2}\left(0-i\right)\left(\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right)[/tex]
= [tex]-12\sqrt{2}\sin \left(\frac{2\pi }{5}\right)+12\sqrt{2}\cos \left(\frac{2\pi }{5}\right)i[/tex]
Again we have another two identities we can apply,
( 1 ) sin(x) = cos(π / 2 - x )
( 2 ) cos(x) = sin(π / 2 - x )
[tex]\sin \left(\frac{2\pi }{5}\right)=\cos \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]
[tex]\cos \left(\frac{2\pi }{5}\right)=\sin \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex]
Substitute,
[tex]-12\sqrt{2}(\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}) + 12\sqrt{2}(\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4})[/tex]
= [tex]-6\sqrt{5+\sqrt{5}}+6\sqrt{3-\sqrt{5}} i[/tex]
= [tex]-16.13996 + 5.24419i[/tex]
= [tex]5.24419i - 16.13996[/tex]
As you can see option d is the correct answer. 5.24419 is rounded to 5.244, and 16.13996 is rounded to 16.14.
Find the value of x that will make L || M
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
the rainfall R(t) (inmm) over the course of a year in bali, indonesia as a function of time t(in days) can be modeled by a sinusoidal expression of the form a*sin(b*t)+d. At t=0, in mid april, the expected daily rainfall is 2.3mm, which is the daily average value throughout the year. 1 quarter of the year leter, at t=91.25, when the rainfall is at its minimum, the expected daily value is 1.4mm. find R(t).
[tex]\bold{\text{Answer:}\quad R(t)=-0.96\sin\bigg(\dfrac{\pi}{182.5}t}\bigg)+2.3}[/tex]
Step-by-step explanation:
The equation of a sin function is: y = A sin (Bx - C) + D where
Amplitude (A) is the distance from the midline to the max (or min)Period (P) = 2π/B --> B = 2π/PC/B is the phase shift (not used for this problem)D is the vertical shift (aka midline)D = 2.3
It is given that t = 0 is located at 2.30. The sin graph usually starts at 0 so the graph has shifted up 2.3 units. --> D = 2.3
A = -0.96
The amplitude is the difference between the maximum (or minimum) and the centerline. A = 2.30 - 1.44 = 0.96
The minimum is given as the next point. Since the graph usually has the next point as its maximum, this is a reflection so the equation will start with a negative. A = -0.96
B = π/182.5
It is given that [tex]\frac{1}{4}[/tex] Period = 91.25 --> P = 365
B = 2π/P
= 2π/365
= π/182.5
C = 0
No phase shift is given so C = 0
Input A, B, C, & D into the equation of a sin function:
[tex]R(t)=-0.96\sin\bigg(\dfrac{\pi}{182.5}t-0}\bigg)+2.3[/tex]
Please help me I will mark brainliest! The ratio of the number of boys to the number of girls in a school is 3:4. One-third of the boys and three-eighths of the girls wear spectacles, If there are 612 pupils who do not wear spectacles, a)find the total number of the pupils in the school, and b) how many more girls than boys are there in the school
Answer:
a) 952
b) 136
Step-by-step explanation:
Ratio of b:g = 3:4, based on this we have:
Number of boys = 3xNumber of girls = 4xTotal number of pupils = 3x+4x = 7xNumber of spectacle wearers:
1/3*3x + 3/8*4x = x + 3/2x = 2.5xNumber of those not wearing spectacles:
7x - 2.5x= 4.5xAnd this number equals to 612, then we can find the value of x:
4.5 x = 612x= 612/4.5x= 136a) Total number of pupils:
7x = 7*136 = 952b) The difference in the number of boys and girls:
4x-3x= x = 136Answer:
total number of students: 952
number of girls more than boys :136 more girls
Step-by-step explanation:
1/3 of boys +3/8 girls= spectacles
612 people do not wear spectacles
3:4= boys: girls
total number of students
3+4=7
boys + girls = total ratio
7= total ratio
1/3×3=1 3/8×4=3/2
1+3/2=5/2
7-5/2=9/2 9/2=612 students
If 9/2=612 Then 7=?
7= 7÷ 9/2×612
=952 people
Girls more than boys
if 7= 952
3= 3/7 × 952=408 boys
if 7 = 952
4= 4/7 ×952=544girls
Girls - boys
544- 408 = 136 girls
Consider a pair of random variables X; Y with constant joint density on the quadrilateral with vertices (0; 0), (2; 0), (2; 6), (0; 12). a) Find the expected value E(X). b) Find the expected value E(Y ).
The given quadrilateral (call it Q) is a trapezoid with "base" lengths of 6 and 12, and "height" 2, so its area is (6 + 12)/2*2 = 18. This means the joint density is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac1{18}&\text{for }(x,y)\in Q\\0&\text{otherwise}\end{cases}[/tex]
where Q is the set of points
[tex]Q=\{(x,y)\mid0\le x\le 2\land0\le y\le12-3x\}[/tex]
(y = 12 - 3x is the equation of the line through the points (0, 12) and (2, 6))
Recall the definition of expectation:
[tex]E[g(X,Y)]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty g(x,y)f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy[/tex]
(a) Using the definition above, we have
[tex]E[X]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty xf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac x{18}\,\mathrm dy\,\mathrm dx=\frac89[/tex]
(b) Likewise,
[tex]E[Y]=\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\ifnty yf_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_0^2\int_0^{12-3x}\frac y{18}\,\mathrm dy\,\mathrm dx=\frac{14}3[/tex]
Your friend Stacy has given you the following algebraic expression: "Subtract 20
times a number n from twice the cube of the number. What is the expression that your
friend is saying?
Answer:
Expression = 2n³ - 20n
Step-by-step explanation:
Find:
Expression
Computation:
Assume given number is 'n'
Cube of number = n³
Twice of cube = 2n³
Subtract number = 20n
Expression = 2n³ - 20n
Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about 13% of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York). The resulting relative frequency can be used as an estimate of the true probability of all Americans who can wiggle their ears. The resulting relative frequency can be used as an estimate of the true probability of all Americans who cannot wiggle their ears. The resulting relative frequency is the true probability of all Americans who can wiggle their ears. The resulting relative frequency cannot be used as an estimate of the true probability of all Americans who can wiggle their ears.
Answer:36
Step-by-step explanation:
The equation| x + 4| = x has solution a. X = -2 b. X = 2 c. X = -4 d. X = 4
Answer:
B) 2
/////////////////
I help! solve 12x^2+54x=-42
Answer: Hi!
Let's solve your equation step-by-step.
12x^2 + 54x = −42
Step 1: Subtract -42 from both sides.
12x^2 + 54x − (−42) = − 42 − (−42)
12x^2 + 54x + 42 = 0
Step 2: Factor left side of equation.
6(2x + 7)(x + 1) = 0
Step 3: Set factors equal to 0.
2x + 7 = 0 or x + 1 = 0
You have two answers.
x = −7/2 or x = −1
Hope this helps!
Why is f (x) = (3x + 1/3)^2 + 8/9 not the vertex form of f (x)
not the vertex form of f (x) = 9x^2 +2x +1?
O The expression has a constant outside of the squared term.
O Some of the terms are fractions instead of integers.
O The expression is not the product of two binomials.
O The variable x has a coefficient.
Answer:
The Variable has a coefficient.
Step-by-step explanation:
Please answer this correctly without making mistakes
Answer:
1/8
Step-by-step explanation:
3/8-1/8-1/8=1/8
Suppose that X; Y have constant joint density on the triangle with corners at (4; 0), (0; 4), and the origin. a) Find P(X < 3; Y < 3). b) Are X and Y independent
The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]
where T is the set
[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]
(a) I've attached an image of the integration region.
[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]
(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.
Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:
[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]
[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]
Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.
Find the sum of the even numbers between 199 to 1999
[tex]S_n=\dfrac{n(a_1+a_n)}{2}\\a_1=200\\a_n=1998\\n=?\\\\a_n=a_1+(n-1)d\\d=2\\1998=200+(n-1)\cdot2\\2n-2=1798\\2n=1800\\n=900\\\\S_{900}=\dfrac{900\cdot(200+1998)}{2}=450\cdot 2198=989100[/tex]
The Sum is 989100.
what is sum of Even numbers?The sum of even numbers formula is determined by using the formula to find the arithmetic progression. The sum of even numbers goes on until infinity. The sum of even numbers formula can also be evaluated using the sum of natural numbers formula. We need to obtain the formula for 2 + 4+ 6+ 8+ 10 +...... 2n.
The sum of even numbers = 2(1 + 2+ 3+ .....n). This implies 2(sum of n natural numbers) = 2[n(n+1)]/2 = n(n+1)
Given:
a1 = 200
an= 1998
So, using formula
S= n(a1 + an)/2
now,
d=2
an= a1+(n-1)d
1998= 200 + (n-1) 2
1998-200= (n-1)2
1798/2=n-1
n= 900
S900= 900( 200 + 1998)/2
=450*2198
= 989100
Hence, the sum is 989100.
Learn more about this concept here:
https://brainly.com/question/18837188
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find the perimeter of a square of sides 10.5cm
Answer:
42 cm
Step-by-step explanation:
A square has 4 equal sides. To find the perimeter, add all side lengths together.
1. Set up the equation and solve
10.5 + 10.5 + 10.5 + 10.5 = 42
