Answer:
The degree of freedom = 16
Step-by-step explanation:
In conducting hypothesis tests where the population standard deviation isn't known, the t-distribution is used to obtain critical value and p-value of the distribution.
To use the t-distribution, the degree of freedom of the test is usually required.
The degree of freedom refers to the maximum number of independent variables, values or parameters, that are allowed to vary in the sample data.
The degree of freedom for a paired test with the same sample size for the two pairs, is given mathematically as
df = n - 1
where n = Sample size = 17
df = 17 - 1 = 16
Hope this Helps!!!
The mean of 3 numbers is 4
The two numbers are 1,9
what is the missing number?
Answer:
2
Step-by-step explanation:
1+9+2 = 12
12/3= 4
Answer:2
Step-by-step explanation:9+2+1=12
So 12/3=4
ANSWER=2
The base diameter and the height of a cone are both equal to
x units.
Which expression represents the volume of the cone, in
cubic units?
pix2
2pix3
1/3pix2
1/12pix3
Answer:
[tex]\frac{\pi x^3}{3}[/tex]
Step-by-step explanation:
[tex]V=\pi r^2h\frac{1}{3}[/tex]
[tex]V=\pi x^2x\frac{1}{3}[/tex]
[tex]V=\pi x^3\frac{1}{3}[/tex]
[tex]V=\frac{\pi x^3}{3}[/tex]
[tex]V=1.047198x^3[/tex]
Answer:
Step-by-step explanation:
1/12 pi x ^3
— 3х + 7 < 19 ?
Help plz
Answer:
x > -4
Step-by-step explanation:
— 3х + 7 < 19
Subtract 7 from each side
— 3х + 7-7 < 19-7
-3x < 12
Divide each side by -3, remembering to flip the inequality
-3x/-3 > 12/-3
x > -4
Just like any of your two-step equations, in this inequality,
start by isolating the x term which in this case is -3x by
subtracting 7 from both sides.
This gives us -3x < 12.
Solving from here, we divide both sides by -3.
However, when solving inequalities, you need to watch out.
When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when dividing both sides of an inequality by a negative.
So we end up with x > -4.
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
In the attached file
The relationship between the number of pencil sharpener a company can sell each week and the price of each sharpener p is given by the equation x = 2300 − 100 p At what price should the sharpeners be sold if the weekly revenue is to be $ 12000
Answer:
The price p could be any of $8 or $15 .
Step-by-step explanation:
The equation is a relationship between the numbers of pencil sharpener x can sell each week and the price of each sharpener p.
x = 2300 - 100p
xp = 12000
therefore,
x = 12000/p
insert the value of x in the equation
x = 2300 - 100p
12000/p = 2300 - 100p
12000/p + 100p - 2300 = 0
multiply through by p
12000 + 100p² - 2300p = 0
100p² - 2300p + 12000 = 0
divide through by 100
p² - 23 + 120 = 0
Find the number that we can multiply to give 120 and add to give - 23. The number are -15 and - 8.
p² - 8p - 15p + 120 = 0
p(p - 8) - 15(p - 8) = 0
(p - 8)(p - 15)
p = 8 or 15
x = 2300 - 100p
x = 2300 - 100(8)
x = 2300 - 800
x = 1500 pencil sharpener sold
or
x = 2300 - 100(15)
x = 2300 - 1500
x = 800 pencil sharpener sold
The price could be any of $8 or $15 .
Please select the word from the list that best fits the definition
a leader of a group of people
Answer:
a sultan
Step-by-step explanation:
i looked it up on quizlet after thinking it was sultan and i was right
anyways the answer is sultan and its correct
have a good day!
Answer
the answer is sultan
Step-by-step explanation:
y = -9x - 2; (4, -37)
A. Yes it satisfies the equation
B. No the ordered pair does not satisfy the equation
Answer:
B. No the ordered pair does not satisfy the equation
Step-by-step explanation:
y = -9x - 2
Substitute the point in and see if it is true
-37 = -9(4) -2
-37 = -36 -2
-37 = -38
This is not true so the point is not a solution
Eliminate the variable t from the set of parametric equations. Graph the equation X=5cost Y=5sint Please explain this, I need to know how to do these kinds of equations for my trig final
Answer:
x^2 + y^2 = 25
Step-by-step explanation:
x = 5 cos t
cos t = x/5
y = 5 sin t
sin t = y/5
cos^2 t + sin^2 t = 1
(x/5)^2 + (y/5)^2 = 1
x^2/25 + y^2/25 = 1
(x^2 + y^2)/25 =1
x^2 + y^2 = 25
The Gleason family has a monthly budget of $4,500. Mr. Gleason has a full-time job and takes home $900 each week. Mrs. Gleason works part time and brings home $9 each week. For every hour she works. How many hours per month must Mrs. Gleason work to make sure that she and Mr. Gleason have met their monthly budget?
Answer:
The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month.
Step-by-step explanation:
To answer this item, we let x be the number of hours per month that Mrs. Gleason should work. The total budget is equal to sum of the amount acquired by Mr. Gleason and Mrs. Gleason. The equation that would express this is,
4,500 = 900(4) + 9x
The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month.
I am sorry if you get this wrong.
Dan buys a car for £2300. It depreciates at a rate of 0.2% per year. How much will it be worth in 6 years? Give your answer to the nearest penny where appropriate.
9514 1404 393
Answer:
£2272.54
Step-by-step explanation:
An equation for the value is ...
v = £2300(0.998^t)
Then for t=6, the value is ...
v = £2272.54
_____
Additional comment
The growth factor (0.998) is (1 - decay rate) = (1 -0.002).
Answer:
the answer is 2272.54
Step-by-step explanation:
:))
Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. Select all that apply.
{f(x) = 2(3)^x
{g(x) = 10log(x+3)
(-1.9, 15.9)
(-2, 0.2)
(1.9, -15.9)
(2, -0.2) (1.9, 15.9)
Answer:
closest choice: (-2, 0.2)
Step-by-step explanation:
The attached image from a graphing calculator shows the solutions (to the nearest tenth) to be ...
(-1.9, 0.2)
(1.0, 6.0)
The closest of the offered choices is (-2, 0.2). None are actually correct.
Darnell spends $100 dollars a week
eating out. His sister told him that if he
would reduce this spending by $50 a
week, he could increase his credit card
payment to $300 per month. How much
will he save if he takes his sister's advice?
ent?
How much will Darnell save by increasing
his monthly payment by $200?
Answer:
$200
$100
Step-by-step explanation:
Darnell spends $100 dollars a week, if he reduces this spending by $50 a week, he will be able to save
$50 x 4 weeks in a months = $200
This, in a month he will be able to save $200.
Increasing his credit card payment by $200 to a total of $300...
since he now spends $50 per week now,
in a month he will spend $50 x 4 weeks = $200 and be able to save $100.
Aunit cube is shown.
Select the true statements
A unit cube can have a length of 1 inch, a width of 1 inch, and a height of 2 inches
A unit cube has one cubic unit of volume.
Another unit cube with the same length, width and height as the unit cube shown would have
the same volume
Aunit cube can be used to measure the weight of a rectangular prism.
A unit cube can be used to measure the volume of a rectangular prism.
Aunit cube can have a length of 4 feet, a width of 4 feet, and a height of 4 feet.
A unit cube can be used to determine the angle measures of a rectangular prism,
4 of 10 Answered
Session Timer: 11:03
Session Score: 259
Answer:
A unit cube has one cubic unit of volume.
Another unit cube with the same length, width and height as the unit cube shown would have the same volume
Step-by-step explanation:
A cube is a shape formed from the combination of a square.
A cube has equal sides.
But a unit cube has equal sides and equal volume to be equal to one, i.e unity.
Sally earns $12.50 an hour cleaning houses. If she works from 8:00am to 6:00pm, how much money will she make?
Answer:
She will make 125 dollars
Step-by-step explanation:
First figure out how many hours are in between 8 AM and 6PM
Second multiply that number by the salary she makes per hour. In this case its 12.50*10
Lastly Get the answer and add a dollar sign :D
1. Use limit comparison test to determine whether the series converges or diverges:
Σ[infinity]_n=1 n^2 + 1 / 2n^3 - 1
2. Use limit comparison test to determine whether the series converges or diverges:
Σ[infinity]_n = 1 n / √n^5 + 5
3. Use direct comparison test to determine whether the series converges or diverges:
Σ[infinity]_n = 1 4 + 3^n / 2^n
Answer:
1. Diverges
2. Converges
3. Diverges
Step-by-step explanation:
Solution:-
Limit comparison test:
- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ). Then the following three conditions are applicable for the limit:
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = c
Where,
1) If c is finite: 0 < c < 1, then both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] either converges or diverges.
2) If c = 0, then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges.
3) If c = ∞ or undefined, then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges.
a) The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{n^2+1}{2n^3-1} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{n^2( 1 + \frac{1}{n^2} )}{n^3 ( 2 - \frac{1}{n^2} ) } ] = [ \frac{( 1 + \frac{1}{n^2} )}{n( 2 - \frac{1}{n^2} ) } ][/tex]
- Apply the limit ( n - > ∞ ):
(n = 1) ∑^∞ [tex][ \frac{1}{2n}][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )
- Both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.
- Compute the limit:
Lim ( n-> ∞ ) [tex][ \frac{n^2 + 1}{2n^3 - 1} * 2n ] = [ \frac{2n^3 + 2n}{2n^3 - 1} ][/tex]
Lim ( n-> ∞ ) [tex][ \frac{2n^3 ( 1 + \frac{1}{n^2} ) }{2n^3 ( 1 - \frac{1}{2n^3} ) } ] = [ \frac{ 1 + \frac{1}{n^2} }{ 1 - \frac{1}{2n^3} } ][/tex]
- Apply the limit ( n - > ∞ ):
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = [tex][ \frac{1 + 0}{1 + 0} ][/tex] = 1 ... Finite
- So from first condition both series either converge or diverge.
- We check for ∑[tex]b_n[/tex] convergence or divergence.
- The ∑[tex]b_n[/tex] = ( 1 / 2n ) resembles harmonic series ∑ ( 1 / n ) which diverges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 1 ≤ 1. Hence, ∑
- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also diverges.
Answer: Diverges
b)
The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{n}{n^\frac{5}{2} +5} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{n( 1 )}{n ( n^\frac{3}{2} + \frac{5}{n} ) } ] = [\frac{1}{( n^\frac{3}{2} + \frac{5}{n} )} ][/tex]
- Apply the limit ( n - > ∞ ) in the denominator for ( 5 / n ), only the dominant term n^(3/2) is left:
(n = 1) ∑^∞ [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )
- Both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.
- Compute the limit:
Lim ( n-> ∞ ) [tex][ \frac{n}{n^\frac{5}{2} +5} * n^\frac{3}{2} ] = [ \frac{n^\frac{5}{2}}{n^\frac{5}{2} +5} ][/tex]
Lim ( n-> ∞ ) [tex][ \frac{n^\frac{5}{2}}{n^\frac{5}{2} ( 1 + \frac{5}{n^\frac{5}{2}}) } ] = [ \frac{1}{1 + \frac{5}{n^\frac{5}{2}} } ][/tex]
- Apply the limit ( n - > ∞ ):
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = [tex][\frac{1}{1 + 0}][/tex] = 1 ... Finite
- So from first condition both series either converge or diverge.
- We check for ∑[tex]b_n[/tex] convergence or divergence.
- The ∑[tex]b_n[/tex] = ( [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] ) converges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 3/2 > 1. Hence, ∑
- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also converges.
Answer: converges
Comparison Test:-
- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ).
-Then the following conditions are applied:
1 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) < 0 , then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges
2 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≤ 0 , then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges
c) The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{4 + 3^2}{2^n} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{3^n ( \frac{4}{3^n} + 1 )}{2^n} ][/tex]
- Apply the limit ( n - > ∞ ) in the numerator for ( 4 / 3^n ), only the dominant terms ( 3^n ) and ( 2^n ) are left:
(n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex] ... The comparative series ( ∑[tex]b_n[/tex] )
- Compute the difference between sequences ( [tex]a_n[/tex] - [tex]b_n[/tex] ):
[tex]a_n - b_n = \frac{4 + 3^n}{2^n} - [ \frac{3^n}{2^n} ] \\\\a_n - b_n = \frac{4 }{2^n} \geq 0[/tex], for all values of ( n )
- Check for divergence of the comparative series ( ∑[tex]b_n[/tex] ), using divergence test:
∑[tex]b_n[/tex] = (n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex] diverges
- The first condition is applied when ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≥ 0, then ∑diverges only if ∑[tex]b_n[/tex] diverges.
Answer: Diverges
The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answer: first answer choice
Step-by-step explanation:
They give us that f(0) and g(0) = 4 and f(2) = g(2) = 0, so the answer is simply the first one. When x=0, y=4 for both and when x=2, y=0 for both.
Hope that helped,
-sirswagger21
Answer:
A
Step-by-step explanation:
on edge
Consider the homogeneous second-order linear differential equation y′′+4y′−12y=0. Which of the following pairs gives two solutions to this equation? A. y1=e2x,y2=e−6x B. y1=e3x,y2=e1x C. y1=e2x,y2=e−2x D. y1=e−12x,y2=xe−12x E. y1=cos(−12x),y2=sin(−12x) F. y1=e−4x,y2=e−12x Then for these solutions find a particular solution of the form y=c1y1+c2y2 that satisfies the initial conditions y(0)=−5,y′(0)=0. y = y1 + y2.
perimeter.
6) A quadrilateral can have 2
reflex angles.
Answer:
False
Step-by-step explanation:
Answer:
A quadrilateral can't have 2 reflex angles
Step-by-step explanation:
A quadrilateral can't have 2 reflex angles because reflex angles > 180° so if you add two together, it is > 360°
If the figures below are similar, find the scale factor of Figure B to Figure A.
48
27
60
А
16
B
20
9
Answer:
The scale factor is 3.
Step-by-step explanation
Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.
In a survey of students, 60% were in high school and 40% were in middle school. Of the high school students, 30% had visited a foreign country. If a surveyed student is selected at random, what is the probability that the student is in high school and has visited a foreign country?
Answer:
The probability that the student is in high school and has visited a foreign country is 0.18.
Step-by-step explanation:
We are given that in a survey of students, 60% were in high school and 40% were in middle school.
Of the high school students, 30% had visited a foreign country.
Let the Probability that students were in high school = P(H) = 60%
Probability that students were in middle school = P(M) = 40%
Also, let F = event that students had had visited a foreign country
So, Probability that high school students had visited a foreign country = P(F/H) = 30%
Now, probability that the student is in high school and has visited a foreign country is given by = Probability that students were in high school [tex]\times[/tex] Probability that high school students had visited a foreign country
= P(H) [tex]\times[/tex] P(F/H)
= 0.60 [tex]\times[/tex] 0.30
= 0.18 or 18%
Can someone please help me with this I’m stuck and I need to finish but I don’t understand
Answer:
28
Step-by-step explanation:
Because the lines are parallel:
[tex]\dfrac{m}{21}=\dfrac{8}{6} \\\\m=\dfrac{8}{6}\cdot 21=28[/tex]
Hope this helps!
According to a survey of business executives, 78% received a pay raise when they asked for one. A random sample of four executives was selected. The probability that all four received a raised when they asked for one is ________. 0.056 0.127 0.237 0.370
Answer:
The probability that all four received a raised when they asked for one is 0.370.
Step-by-step explanation:
Let the random variable X represent the number of business executives who received a pay raise when they asked for one.
The probability that a business executives received a pay raise when they asked for one is, p = 0.78.
A random sample of n = 4 executives was selected.
The events of any executive receiving a pay raise when they asked for one is independent of the others.
The random variable X follows a Binomial distribution with parameters n = 4 and p = 0.78.
The probability mass function of X is:
[tex]P(X=x)={4\choose x}\ (0.78)^{x}\ (1-0.78)^{4-x};\ x=0,1,2,3...[/tex]
Compute the probability that all four received a raised when they asked for one as follows:
[tex]P(X=4)={4\choose 4}\ (0.78)^{4}\ (1-0.78)^{4-4}[/tex]
[tex]=1\times 0.37015056\times 1\\\\=0.37015056\\\\\apporx 0.370[/tex]
Thus, the probability that all four received a raised when they asked for one is 0.370.
What is the square root of -1?
Answer:
i
Step-by-step explanation:
Why is i the square root of negative one?
The term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.
Angle 6= (11x+8) and angle 7=(12x-4) what is the measure of angle 4
Answer:
Answer is m∠4=40
Step-by-step explanation:
take note that m∠6 & m∠7 are vertical angles. Vertical angles are equal to each other, therefore m∠6 is equal to m∠7.
m∠6 = m∠7 (vertical angles)
11x + 8 = 12x – 4
12x - 11x = 8 + 4
x = 12
so
m∠6 = 11x + 8
m∠6 = 11(12) + 8
m∠6 = 132 + 8
m∠6 = 140
m∠4 = 180 - m<6
m∠4 = 180 - 140
m∠4 = 40
Answer:
A
Step-by-step explanation: Took test
What is 1.036 that add up to 4
Answer:
2.964
Step-by-step explanation:
Bonita said that the product of 5/6 x 1 2/3 is 7/3. How can you tell that her answer is wrong.
Answer:=
1 7/18
Step-by-step explanation:
Turn the improper fraction into a mixed fraction.
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
According to theorem, "the measure of central angle of minor Arc of a circle is doubleto that of the angle subtended by the corresponding major Arc."
So
m<AOB = 2(m<AZB)
m<AZB = M<AOB / 2
m<AZB = 68/2
m<AZB = 34°
Answer:
34° is right answer
Step-by-step explanation:
correct answer is 34
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Diameter = 11 inches.
Radius = D/2 = 5.5 inches
Volume = 4/3πr³
= 4/3(3.14)(5.5)³
= 696.6 in.³
Can someone please please help me
Answer:
The answer is None
Step-by-step explanation:
Multiply 6 2 and 1 and also multiply 12 4 and 2 separately now divide 96 with 12 and you get 8 which is none of the answer choices
Joseph places $5,500 in a savings
account for 30 months. He earns $893.75
in interest. What is the annual interest
rate?
Answer: About 6.2%
Step-by-step explanation:
He starts with 5500 and gains 893.75 in 2.5 years.
The equation is then 5500*(x)^2.5 = 5500+893.75, or
5500*x^2.5 = 6393.75.
x is about 1.0621, or about 6.2% because it's interest.
Hope that helped,
-sirswagger21
Answer: 137.5%
Step-by-step explanation
