Answer: It is a scalene triangle.
Step-by-step explanation:
It is scalene because the length between T and V are not equal,the length between T and S is not equal and the length between V and S is also not equal. All the side lengths of the triangle have different measures.
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (f o g)(-5)
3 sides of the triangle are distinct perfect squares. What is the smallest possible perimeter of the triangle?
Answer:
77
Step-by-step explanation:
At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.
Answer:
e
Step-by-step explanation:
e
The alpha level that a researcher sets at the beginning of the experiment is the level to which he wishes to limit the probability of making the error of____________
Answer:
not rejecting the null hypothesis when it is false.
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis.
For making the error, it should not reject the null hypothesis at the time when it should be false.
What is alpha level?It is the level where the probability of rejecting the null hypothesis at the time when the null hypothesis should be true. It is relevant for making the incorrect decision. Also, it is the statistical test that measured the probability of type 1 error.
Therefore, For making the error, it should not reject the null hypothesis at the time when it should be false.
Learn more about error here: https://brainly.com/question/18831983
A quadratic equation of the form 0=ax2+bx+c has a discriminant value of -16. How many real number solutions does the equation have?
Answer: There will be no real solutions
Explanation: If the discriminant (the part under the radical in the numerator of the quadratic equation) is less than 0, there are no real solutions. If positive, there will be two real solutions. If 0, there will be one.
assume that when adults with smartphones are randomly selected 15 use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that at least 4 of them use their smartphones
Answer:
The probability that at least 4 of them use their smartphones is 0.1773.
Step-by-step explanation:
We are given that when adults with smartphones are randomly selected 15% use them in meetings or classes.
Also, 15 adult smartphones are randomly selected.
Let X = Number of adults who use their smartphones
The above situation can be represented through the binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; n = 0,1,2,3,.......[/tex]
where, n = number of trials (samples) taken = 15 adult smartphones
r = number of success = at least 4
p = probability of success which in our question is the % of adults
who use them in meetings or classes, i.e. 15%.
So, X ~ Binom(n = 15, p = 0.15)
Now, the probability that at least 4 of them use their smartphones is given by = P(X [tex]\geq[/tex] 4)
P(X [tex]\geq[/tex] 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
= [tex]1- \binom{15}{0}\times 0.15^{0} \times (1-0.15)^{15-0}-\binom{15}{1}\times 0.15^{1} \times (1-0.15)^{15-1}-\binom{15}{2}\times 0.15^{2} \times (1-0.15)^{15-2}-\binom{15}{3}\times 0.15^{3} \times (1-0.15)^{15-3}[/tex]
= [tex]1- (1\times 1\times 0.85^{15})-(15\times 0.15^{1} \times 0.85^{14})-(105 \times 0.15^{2} \times 0.85^{13})-(455 \times 0.15^{3} \times 0.85^{12})[/tex]
= 0.1773
Which of the following ordered pairs satisfied the inequality 5x-2y<8
A) (-1,1)
B) (-3,4)
C) (4,0)
D) (-2,3)
Answer: A, B, and D
Step-by-step explanation:
Input the coordinates into the inequality to see which makes a true statement:
5x - 2y < 8
A) x = -1, y = 1 5(-1) - 2(1) < 8
-5 - 2 < 8
-7 < 8 TRUE!
B) x = -3, y = 4 5(-3) - 2(4) < 8
-15 - 8 < 8
-23 < 8 TRUE!
C) x = 4, y = 0 5(4) - 2(0) < 8
20 - 0 < 8
20 < 8 False
D) x = -2, y = 3 5(-2) - 2(3) < 8
-10 - 6 < 8
-16 < 8 TRUE!
given sin theta=3/5 and 180°<theta<270°, find the following: a. cos(2theta) b. sin(2theta) c. tan(2theta)
I hope this will help uh.....
Use all the information below to find the missing x-value for the point that is on this line. m = - 1 / 3 b = 7 ( x, 4 )
Answer:
[tex]\boxed{x = 9}[/tex]
Step-by-step explanation:
m = -1/3
b = 7
And y = 4 (Given)
Putting all of the givens in [tex]y = mx+b[/tex] to solve for x
=> 4 = (-1/3) x + 7
Subtracting 7 to both sides
=> 4-7 = (-1/3) x
=> -3 = (-1/3) x
Multiplying both sides by -3
=> -3 * -3 = x
=> 9 = x
OR
=> x = 9
Answer:
x = 9
Step-by-step explanation:
m = -1/3
b = 7
Using slope-intercept form:
y = mx + b
m is slope, b is y-intercept.
y = -1/3x + 7
Solve for x:
Plug y as 4
4 = 1/3x + 7
Subtract 7 on both sides.
-3 = -1/3x
Multiply both sides by -3.
9 = x
A drawer contains 3 white shirts, 2 blue shirts, and 5 gray shirts. A shirt is randomly
selected from the drawer and set aside. Then another shirt is randomly selected from the
drawer.
What is the probability that the first shirt is white and the second shirt is gray?
Answer:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Given that
3 white, 2 blue and 5 gray shirts are there.
To find:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?
Solution:
Here, total number of shirts = 3+2+5 = 10
First of all, let us learn about the formula of an event E:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
[tex]P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}[/tex]
[tex]P(First\ White) = \dfrac{3}{10}[/tex]
Now, this shirt is set aside.
So, total number of shirts left are 9 now.
[tex]P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }[/tex]
So, the answer is:
Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = [tex]\frac{1}{4}[/tex]
an auto dealer offers a compact car, a midsize, a sport utility vehicle, and a light truck, each either in standard, custom, or sport styling, a choice of manual or automatic transmission, and a selection from 7 colors. How many ways of buying a vehicle from this dealer are there?
Answer: 168
Step-by-step explanation:
First, let's count the types of selection:
We can select:
Type of car: a compact car, a midsize, a sport utility vehicle, and a light truck (4 options)
Pack: standard, custom, or sport styling, (3 options)
type of transmission: Manual or automatic (2 options)
Color: (7 options)
The total number of combinations is equal to the product of the number of options in each selection:
C = 4*3*2*7 = 168
Rewrite the equation in =+AxByC form. Use integers for A, B, and C. =−y6−6+x4
Answer:
6x + y = -18
Step-by-step explanation:
The given equation is,
y - 6 = -6(x + 4)
We have to rewrite this equation in the form of Ax + By = C
Where A, B and C are the integers.
By solving the given equation,
y - 6 = -6x - 24 [Distributive property]
y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]
y = -6x - 18
y + 6x = -6x + 6x - 18
6x + y = -18
Here A = 6, B = 1 and C = -18.
Therefore, 6x + y = -18 will be the equation.
Dimitri is solving the equation x2 – 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
Answer:
[tex]\boxed{\sf \ \ 25 \ \ }[/tex]
Step-by-step explanation:
Hello,
we can see that
[tex]x^2-10x = x^2-2*5x[/tex]
is the beginning of
[tex]x^2-2*5x+5^2=(x-5)^2[/tex]
so we must add 5*5=25 to both sides of the equation to make the left side a perfect square trinomial
hope this helps
Answer:
25.
Step-by-step explanation:
To find the value that will make the left side a perfect-square trinomial, you need to find (b/2)^2. In this case, b = -10.
(-10 / 2)^2
= (-5)^2
= (-5) * (-5)
= 25
Once you add 25 to both sides, the left side becomes x^2 - 10x + 25, which is equal to (x - 5)^2.
Hope this helps!
A machine fills containers with 35 ounces of raisins
The correct graph will be the first one (A)
Which transformation should be applied to the graph of the function y=cot(x) to obtain the graph of the function y=6 cot(3x-pi/2)+4
Answer:
The correct answer is the first one.
Step-by-step explanation:
Let's analyse the effect of each modification in the function.
The value 6 multiplying the cot function means a vertical stretch.
The value of 3 multiplying the x inside the function is a horizontal compression, which causes the period to be 3 times lower the original period.
The original period of the cotangent function is pi, so the horizontal compression will make the period be pi/3.
The value of -pi/2 inside the cotangent function normally causes a horizontal shift of pi/2 to the right, but the x-values were compressed by a factor of 3 (horizontal stretch), so the horizontal shift will be 3 times lower: (pi/2) /3 = pi/6
And the value of 4 summing the whole equation is a vertical shift of 4 units up.
So the correct answer is the first one.
Answer:
option 1
Step-by-step explanation:
f(x)=x^2+12x+7 f(x)=(x+_)^2+_ Rewrite the function by completing the square
Answer:
f(x) = (x + 6)² - 29
Step-by-step explanation:
Given
f(x) = x² + 12x + 7
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² + 12x
x² + 2(6)x + 36 - 36 + 7
= (x + 6)² - 29, thus
f(x) = (x + 6)² - 29
answers are 6, and -29
The General Social Survey (GSS) is a sociological survey used to collect data on demographic characteristics and attitudes of residents of the United States. In 2010, the survey collected responses from over a thousand US residents. The survey is conducted face-to-face with an in-person interview of a randomly-selected sample of adults. One of the questions on the survey is "For how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?" Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010. Given this information, which of the following statements would be most appropriate to make regarding the true average number of days of "not good" mental health in 2010 for US residents? 1 point For these 1,151 residents in 2010, we are 95% confident that the average number of days of "not good" mental health is between 3.40 and 4.24 days. There is not sufficient information to calculate the margin of error of this confidence interval. For all US residents in 2010, based on this 95% confidence interval, we would reject a null hypothesis stating that the true average number of days of "not good" mental health is 5 days.
The most appropriate statement is the one that correctly reflects the confidence interval obtained from the survey data, as stated above.
The most appropriate statement to make regarding the true average number of days of "not good" mental health in 2010 for US residents, based on the given information, is:
"For these 1,151 residents in 2010, we are 95% confident that the average number of days of 'not good' mental health is between 3.40 and 4.24 days."
The 95% confidence interval of 3.40 to 4.24 days is obtained from the survey data, and it provides an estimate of the range within which the true average number of days of "not good" mental health falls for the entire population of US residents.
Regarding the provided options:
There is not sufficient information to calculate the margin of error of this confidence interval: This statement is not accurate since the margin of error can be calculated using the formula Margin of Error = (Upper Limit - Lower Limit) / 2.
For all US residents in 2010, based on this 95% confidence interval, we would reject a null hypothesis stating that the true average number of days of "not good" mental health is 5 days: This statement is not supported by the given information. The confidence interval provides an estimate of the range within which the true average lies, but it does not involve a comparison to a specific value such as 5 days.
for such more question on confidence interval
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Based on the provided information and the 95% confidence interval of 3.40 to 4.24 days for "not good" mental health in 2010,
The most appropriate statement to make regarding the true average number of days of "not good" mental health for US residents in 2010 is:
"For these 1,151 residents in 2010, we are 95% confident that the average number of days of 'not good' mental health is between 3.40 and 4.24 days."
This statement accurately represents the confidence interval obtained from the survey data.
It indicates that the true average number of "not good" mental health days for the entire US population in 2010 is likely to fall within this range with a 95% level of confidence.
It's important to note that this statement only applies to the specific sample of 1,151 US residents surveyed in 2010.
To make inferences about the true average number of "not good" mental health days for all US residents in 2010, a different sample with a larger representative size would be required.
Learn more about confidence intervals here:
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show all work!! Plus this is the same question as my last one so you get a total of 25 points if you answer both! Just copy the answer you got from this one and paste it in the other question (the same question)
Answer:
increase of 30
Step-by-step explanation:
1255- 1075 = 180
This is an increase of 180
Divide by the number of numbers which is 6
180 /6 = 30
The mean will increase by 30
Answer:
+30
Step-by-step explanation:
1255- 1075 = 180
180 /6 = 30
(I NEED HELP) The data below shows the scores of some students on a test: 23, 27, 21, 20, 25, 31, 22 Which box-and-whisker plot represents the data?
Answer:
B
Step-by-step explanation:
Answer:
the 2nd one
Step-by-step explanation:
because the Minimum is 20
the Maximum is 31
the median is 23
20, 21, 22, 23, 25, 27, 31,
21, 22, 23, 25, 27
22, 23, 25,
23
convert 1000m to kilometres
Answer:
1km
Step-by-step explanation:
1000m=1km
Ez Money
Answer:
1000m= 1km
if you convert 1m to km is 0.001km times it by 1000, you get 1km.
What is the measure of A? (solve to the nearest WHOLE DEGREE)
Answer:
A = 0.507 or 29 degrees
Step-by-step explanation:
5 = tanA * 9
inv tan = 5/9
angle A = 0.507
angle A = 29 degrees
which quadratic function in standard form has the value a= -3.5, b=2.7, and c= -8.2?
Answer:
y = -3.5x² + 2.7x -8.2
Step-by-step explanation:
the quadratic equation is set up as a² + bx + c, so just plug in the values
Answer:
[tex]-3.5x^2 + 2.7x -8.2[/tex]
Step-by-step explanation:
Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].
So, we can use your values of a, b, and c, and plug them into the equation.
A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].
B is 2.7, so the second term is [tex]2.7x[/tex]
And -8.2 is the C, so the third term is [tex]-8.2[/tex]
So we have [tex]-3.5x^2+2.7x-8.2[/tex]
Hope this helped!
PLEASE HELP HOW DO I TRANSLATE IT TO A PROPORTION!!
Answer:
See below.
Step-by-step explanation:
A proportion is setting two ratios equal to each other.
Look at the info you are given for price in $ and area in sq ft:
$385 for 70 sq ft
That allows you to write a ratio. The ratio of dollars to square feet is
385/70 (notice it's dollars divided by sq ft)
Now you look at the part of the problem that has an unknown, and you set up the same type of ratio (dollars to sq ft) using x for the unknown.
x dollars to 200 sq ft
The ratio is
x/200 (notice that, again, it's dollars divided by sq ft)
In both cases the ratios are dollars to sq ft.
To set up a proportion, you just set the ratios equal to each other.
385/70 = x/200
Now we solve the proportion. We can cross multiply.
385/70 = x/200
70x = 385 * 200
70x = 77,000
x = 1100
They would charge $1100 to install 200 sq ft of tile.
The unit price is obtained by dividing a cost by the corresponding area in sq ft. you can use either ratio.
unit price = ($385)/(70 sq ft) = $5.5/sq ft
($1100/200 sq ft also works since it is also equal to $5.5/sq ft)
The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order bold x1 and bold x2
1 7
-4 -7
0 -6
1 1
The orthogonal basis produced using the Gram-Schmidt process for W is:__________. (Use a comma to separate vectors as needed.)
Answer:
[tex]y_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex] , [tex]y_2 = \left[\begin{array}{ccc}5\\1\\-6\\-1\end{array}\right][/tex]
Step-by-step explanation:
[tex]x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex] and [tex]x_2 = \left[\begin{array}{ccc}7\\-7\\-6\\1\end{array}\right][/tex]
Using Gram-Schmidt process to produce an orthogonal basis for W
[tex]y_1 = x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]
Now we know X₁ , X₂ and Y₁
Lets solve for Y₂
[tex]y_2 = x_2- \frac{x_2*y_1}{y_1*y_1}y_1[/tex]
see attached for the solution of Y₂
A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (
This question is incomplete
Complete Question
A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.)
(a) Greater than 64
(b) Less than 57
Answer:
(a) Greater than 64 = 0.1788
(b) Less than 57 = 0.1094
Step-by-step explanation:
To solve the above questions we would be using the z score formula
The formula for calculating a z-score :
z = (x - μ)/σ,
where x is the raw score
μ is the population mean = 61
σ is the population standard deviation = 13
(a) Greater than 64
z = (x - μ)/σ,
where x is 64
μ is the 61
σ is the 13
In the above question, we are given the number of samples = 16
Sample standard deviation = popular standard deviation/ √16
= 13/√16
z = 64 - 61 ÷ 13/√16
z = 3/3.25
z = 0.92308
Approximately, z values to 2 decimal places ≈ 0.92
Using the z score table of normal distribution to find the Probability (P) value of z score of 0.92
P(z = 0.92) = 0.82121
P(x>64) = 1 - P(z = 0.92)
= 1 - 0.82121
= 0.17879
Approximately , Probability value to 4 decimal places = 0.1788
(b) Less than 57
z = (x - μ)/σ,
where x is 57
μ is the 61
σ is the 13
In the above question, we are given the number of samples = 16
Sample standard deviation = popular standard deviation/ √16
= 13/√16
z = 57 - 61 ÷ 13/√16
z = -4/3.25
z = -1.23077
Approximately, z values to 2 decimal places ≈ -1.23
Using the z score table of normal distribution to find the Probability (P) value of z score of -1.23
P(z = -1.23) = P(x<Z) = 0.10935
Approximately , Probability value to 4 decimal places = 0.1094
The area of an Equilateral triangle is given by the formula A= 3pi squared/4(s)Squared. Which formula represents the length of equilateral triangle’s side S?
Answer:
The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is [tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex] .
Step-by-step explanation:
We are given the area of an Equilateral triangle which is A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex] . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).
So, the area of an equilateral triangle = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]
where, s = side of an equilateral triangle
A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]
Cross multiplying the fractions we get;
[tex]4 \times A = \sqrt{3} \times \text{s}^{2}[/tex]
[tex]\sqrt{3} \times \text{s}^{2}= 4\text{A}[/tex]
Now. moving [tex]\sqrt{3}[/tex] to the right side of the equation;
[tex]\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }[/tex]
Taking square root both sides we get;
[tex]\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]
[tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]
Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).
In a cinema, there are eight seats in a row. Four of the seats in one row are occupied. What fraction of seats are available in that row?
Answer:
[tex] \frac{1}{2} [/tex]Step-by-step explanation:
Given,
There are 8 seats in a row.
There are 8 seats in a row.4 seats are occupied.
Available seats = 8 - 4 = 4 seats
Fraction of seats available:
[tex] \frac{number \: of \: seats \: available}{total \: number \: of \: seats} [/tex]
[tex] = \frac{4}{8} [/tex]
Reduce the fraction with GCF 4
[tex] = \frac{1}{2} [/tex]
Hope this helps..
Best regards!!
Answer:
Your correct answer is that there are 4 seats available. The fraction version is 1/2
Step-by-step explanation:
Since there are 8 in a row and 4 are taken, subtract 8 by 4.
8 - 4 = 4 seats that are available.
Use the Limit Comparison Test to determine whether the series converges.
[infinity]∑ from k = 1 StartFraction 8/k StartRoot k + 7 EndRoot EndFraction
Answer:
The infinite series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} \frac{8/k}{\sqrt{k + 7}}[/tex] indeed converges.
Step-by-step explanation:
The limit comparison test for infinite series of positive terms compares the convergence of an infinite sequence (where all terms are greater than zero) to that of a similar-looking and better-known sequence (for example, a power series.)
For example, assume that it is known whether [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] converges or not. Compute the following limit to study whether [tex]\displaystyle \sum\limits_{k = 1}^{\infty} a_k[/tex] converges:
[tex]\displaystyle \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}[/tex].
If that limit is a finite positive number, then the convergence of the these two series are supposed to be the same.If that limit is equal to zero while [tex]a_k[/tex] converges, then [tex]b_k[/tex] is supposed to converge, as well.If that limit approaches infinity while [tex]a_k[/tex] does not converge, then [tex]b_k[/tex] won't converge, either.Let [tex]a_k[/tex] denote each term of this infinite Rewrite the infinite sequence in this question:
[tex]\begin{aligned}a_k &= \frac{8/k}{\sqrt{k + 7}}\\ &= \frac{8}{k\cdot \sqrt{k + 7}} = \frac{8}{\sqrt{k^2\, (k + 7)}} = \frac{8}{\sqrt{k^3 + 7\, k^2}} \end{aligned}[/tex].
Compare that to the power series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] where [tex]\displaystyle b_k = \frac{1}{\sqrt{k^3}} = \frac{1}{k^{3/2}} = k^{-3/2}[/tex]. Note that this
Verify that all terms of [tex]a_k[/tex] are indeed greater than zero. Apply the limit comparison test:
[tex]\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}\\ &= \lim\limits_{k \to \infty} \frac{\displaystyle \frac{8}{\sqrt{k^3 + 7\, k^2}}}{\displaystyle \frac{1}{{\sqrt{k^3}}}}\\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{k^3}{k^3 + 7\, k^2}}\right) = 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\end{aligned}[/tex].
Note, that both the square root function and fractions are continuous over all real numbers. Therefore, it is possible to move the limit inside these two functions. That is:
[tex]\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\\ &= \cdots \\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\\ &= 8\left(\sqrt{\frac{1}{\displaystyle 1 + \lim\limits_{k \to \infty} (7/k)}}\right) \\ &= 8\left(\sqrt{\frac{1}{1 + 0}}\right) \\ &= 8 \end{aligned}[/tex].
Because the limit of this ratio is a finite positive number, it can be concluded that the convergence of [tex]\displaystyle a_k &= \frac{8/k}{\sqrt{k + 7}}[/tex] and [tex]\displaystyle b_k = \frac{1}{\sqrt{k^3}}[/tex] are the same. Because the power series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] converges, (by the limit comparison test) the infinite series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} a_k[/tex] should also converge.
Two similar data sets are being compared. The standard deviation of Set A is 4.8. The standard deviation of Set B is 6.5.
Answer:
The spread of the data in Set B is greater than the spread of the data in Set A.
Step-by-step explanation:
Just took the test :3
(very urgent) will gave 20 pts
Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that
a) the bit string has exactly two 1s;
b) the bit string begins and ends with 0;
c) the bit string has the sum of its digits equal to seven;
d) the bit string has more 0s than 1s;
e) the bit string has exactly two 1s, given that the string begins with a 1.
Answer:
a. 45/1024
b. 1/4
c. 15/128
d. 193/512
e. 9/256
Step-by-step explanation:
Here, each position can be either a 0 or a 1.
So, total number of strings possible = 2^10 = 1024
a) For strings that have exactly two 1's,
it means there must also be exactly eight 0's.
Thus, total number of such strings possible
10!/2!8!=45
Thus, probability is
45/1024
b) Here, we have fixed the 1st and the last positions, and eight positions are available.
Each of these 8 positions can take either a 0 or a 1.
Thus, total number of such strings possible
=2^8=256
Thus, probability is
256/1024 = 1/4
c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string.
Also, it means there must also be exactly three 0's
Thus, total number of such strings possible
10!/7!3!=120
Thus, probability
120/1024 = 15/128
d) Following are the possibilities :
There are six 0's, four 1's :
So, number of strings
10!/6!4!=210
There are seven 0's, three 1's :
So, number of strings
10!/7!3!=120
There are eight 0's, two 1's :
So, number of strings
10!/8!2!=45
There are nine 0's, one 1's :
So, number of strings
10!/9!1!=10
There are ten 0's, zero 1's :
So, number of strings
10!/10!0!=1
Thus, total number of string possible
= 210 + 120 + 45 + 10 + 1
= 386
Thus, probability is
386/1024 = 193/512
e) Here, we have fixed the starting position, so 9 positions remain.
In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.
Thus, total number of such strings possible
9!/2!7!=36
Thus, probability is
36/1024 = 9/256
Rotate the figure 90 counterclockwise about the origin. Determine the orientation of the rotated figure and place it in the correct position (PLS HELP)
Answer:
see below
Step-by-step explanation:
The rotated location of D' is (-2, 1). The "arrow" points to the left. The attached figure is the best I could do with your distorted image.
You have to rotate the figure 90 counterclockwise about the origin.