Answer:
The general term of the sequence is given by
T
n
=
a
n
2
+
b
n
+
c
The general term of the sequence is given by
T
n
=
a
n
2
+
b
n
+
c
Calculate a,b and c
Determine the 12th term of the sequence.
grade12 general-term sequence series
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1 Answer
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T3 - 6=6
T3=12
then T2-T1=4
6-T1=4
T1=2
T4-T3=8
T4-12=8
T4=20
Therefore terms= 2,6,12,20
1st difference= 4,6,8
2nd difference= 2,2,....
2a=2
a=1
3a+b=4
3(1) + b=4
b= 1
a+b+c= 2
c= 2-1- 1= 0
giving Tn= n^2 + n
T12 = 12^2 + 12 = 156
triangle BCD is a right triangle the length of the hypotenuse is 20 cm the length of one of the legs is 15 cm what is the length of the other leg
Answer:
13.22
Step-by-step explanation:
The eqtn is
hypotenuse^2 = leg^2 + leg^2
20^2 = 15^2 + L^2
400 = 225 + L^2
L^2 = 400 - 225 = 175
L = √175 = 13.22
5c. Solve the differential equations using Laplace transforms
y"+y' - 2y = e-³x, y(0) = 0 and y'(0) = 0
Answer:
[tex]y(x)=\frac{1}{2}e^{-3x}-\frac{2}{3}e^{-2x}+\frac{1}{6}e^{x}[/tex]
Step-by-step explanation:
[tex]y''+y'-2y=e^{-3x},\: y(0)=0,\: y'(0)=0\\\\\mathcal{L}\{y''\}+\mathcal{L}\{y'\}-2\mathcal{L}\{y\}=\mathcal{L}\{e^{-3x}\}\\\\s^2Y(s)-sy(0)-y'(0)+sY(s)-y(0)-2Y(s)=\frac{1}{s+3} \\ \\s^2Y(s)+sY(s)-2Y(s)=\frac{1}{s+3}\\ \\(s^2+s-2)Y(s)=\frac{1}{s+3}\\ \\Y(s)=\frac{2}{(s+3)(s^2+s-2)}\\ \\Y(s)=\frac{2}{(s+3)(s+2)(s-1)}[/tex]
Perform the partial fraction decomposition
[tex]\frac{2}{(s+3)(s+2)(s-1)}=\frac{A}{s+3}+\frac{B}{s+2}+\frac{C}{s-1}\\ \\2=(s+2)(s-1)A+(s+3)(s-1)B+(s+2)(s+3)C[/tex]
Solve for each constant
[tex]2=((-2)+2)((-2)-1)A+((-2)+3)((-2)-1)B+((-2)+2)((-2)+3)C\\\\2=-3B\\\\-\frac{2}{3}=B[/tex]
[tex]2=(1+2)(1-1)A+(1+3)(1-1)B+(1+2)(1+3)C\\ \\2=12C\\\\\frac{2}{12}=C\\ \\\frac{1}{6}=C[/tex]
[tex]2=((-3)+2)((-3)-1)A+((-3)+3)((-3)-1)B+((-3)+2)((-3)+3)C\\ \\2=4A\\\\\frac{2}{4}=A\\ \\\frac{1}{2}=A[/tex]
Take the inverse transform and solve for the IVP
[tex]Y(s)=\frac{\frac{1}{2}}{s+3}+\frac{-\frac{2}{3}}{s+2}+\frac{\frac{1}{6}}{s-1}\\\\y(x)=\frac{1}{2}e^{-3x}-\frac{2}{3}e^{-2x}+\frac{1}{6}e^{x}[/tex]
Solve 3x^3 - 12x = 0 by factoring
Please help me I can’t solve it. Please!!
Answer:
x = 0, 2, -2
Step-by-step explanation:
3x^3 - 12x = 0
3x ( x^2 - 4 ) = 0
3x = 0
x = 0
x^2 - 4 = 0
( x -2 ) ( x + 2 ) = 0
x -2 = 0
x = 2 , x + 2 = 0
x = -2
Which expression is equivalent to 5( 9 + 7)
Answer:80
Step-by-step explanation: Distribute the 5 to the 9 and 7 to get 35+45 and add to get 80
Find the value of x that will make A||B
Answer:
x = 20
Step-by-step explanation:
When two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent.
5x + 20 = 3x + 60
Now subtract 3x form both sides
5x - 3x + 20 = 3x - 3x + 60
2x + 20 = 60
Subtract 20 from both sides
2x + 20 -20 = 60 - 20
2x = 40
Divide both sides by 2
x = 40/2
x = 20
Find the total surface area of the following cone. Leave your answer in terms of a. 2V3 cm 2 cm SA = [ ? ] cm Hint: Surface Area of a Cone = tre + B Where e = slant height, and B = area of the base
Answer: the answer is
90
Answer:
12
Step-by-step explanation:
A pair of jeans originally cost $48, but its price decreased by 25%. What is the new price?
Answer:
$36
Step-by-step explanation:
$48 × (100 - 25)% = $36
Jabari owns 100 shares of Stock A and 45 shares of Stock B. For the past month, his stocks have been
fluctuating inversely. Stock A decreased by m cents per share and Stock B increased by n cents per share.
Which equation can be used to find the total change in value of Jabari's shares per month?
A V = (100.-m)+(45.n)
B V = (100-m)+(45.-n)
V = 100(4.-m)+45(4.n)
D V=145(-mºn)
Answer:
Answer is A
(100*-m)+(45*n)
Step-by-step explanation: because stock a decreases per sock so your going to multiply 100 times -m because it is decreasing so it will be negative
Then it will be 45*n because it increase per number of stocks so you multiply 45 which is the number of stocks times n
Step-by-step explanation:
A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 vears and making monthly payments. What would their monthly payment be?
Answer:
a) payment: $1082.84
b) interest: $194,822.40
Step-by-step explanation:
The monthly payment on the mortgage can be found using the given formula with the given values of principal (P=195000), interest rate (r=0.053), and time period (t=30). The value of n is 12, corresponding to the number of months in a year.
a)The monthly payment is ...
[tex]k=\left(1+\dfrac{r}{n}\right)^{nt}=\left(1+\dfrac{0.053}{12}\right)^{12\cdot30}\approx 4.88661119\\\\\text{monthly payment}=\dfrac{P\cdot\dfrac{r}{n}\cdot k}{k-1}=\dfrac{195000\cdot0.0044166667\cdot4.88661119}{4.88661119-1}\\\\\boxed{\text{monthly payment}=\$1082.84}[/tex]
__
b)The interest owed is the difference between the total of monthly payments and the principal of the loan:
interest owed = (360)(1082.84) -195000 = 194,822.40
The interest owed over 30 years is $194,822.40.
Find the value:
cos -1 ( - √3/2 )
Answer:
The value is undefined.
Rectangle with l = 4f ft, w = 1 ft (show work)
Answer:
if it's 41 and 1 then the answer is 41 but if it's 4 and 1 then the answer is 4
Step-by-step explanation:
you take length times with and so 4 times 1 which is 4 or 41 times 1 which is 41
1 Solve for the variable. 3x + 8 = 44
Answer:
x=12
Step-by-step explanation:
3x12=36
36+8=44
Answer:
x = 12
Step-by-step explanation:
3x + 8 - 8 = 44 - 8
3x = 36
simplify to get 12
Round 47,250 to nearest thousand
Answer:
your answer will be 47000
Answer:
The correct answer is 47,000.
social media influence communication
Answer:
what whats the question so I can answer
Can someone please answer this it would mean the world to me cause im failing right now
Answer:
Alright, for question 7, the angle pair relationship is that they are corresponding angles.
So, 17x - 34 = 13x - 14. This means that 4x = 20, and x = 5 :)
For question 8, the angles are a linear pair. They are supplementary (adding to 180) :)
So, 37x - 17 + 33x - 13 = 180
This means taht 4x = 210, and x = 52.5? (I'm not sure if I screwed up on the arithmetic on this one, please correct if you find any mistakes!)
What is the slope of the line on the graph
Answer:
slope = -3
Step-by-step explanation:
slope = -3
Answer:
-1/3
Step-by-step explanation:
we know ,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}- x_{1} }[/tex]Here , m= slope
(x1,y1) , (x2,y2) are point of the slope
[tex]m=\frac{6-2}{-6-6 }[/tex]
or, [tex]m=\frac{4}{-12 }[/tex]
so , m= -1/3
the price of a 2-pack shopkin should not be more then 4$. choose an inequality for this situation
The required inequality for the price of a 2-pack shopkin should not be more than $4 is ≤ 4.
The price of a 2-pack shopkin should not be more than $4. Inequality in the situation is to be determined.
What is inequality?Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
The price of a 2-pack shopkin should not be more than $4.
Let the price of 2 - pack shopkin is x and it should not be more than $4 it impise the price of 2 pack shopkin canno be set up more than 4 but it could be 4 or less so, Inequality for 4 or less of price of 2 pack shopkin is given by,
x ≤ 4.
Thus, the required inequality for the price of a 2-pack shopkin should not be more than $4 is ≤ 4.
Learn more about inequality here:
brainly.com/question/14098842
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WILL MARK YOU BRAINLIEST!!
Bananas are 3 for a dollar. Jen has $3. How many bananas can Jen buy?
1 dollar for 3 bananas
so with
3 dollars we will get 3x3 = 9 bananas
If her income is 210 marks, how many bananas can she buy if ... is 4 dollars each and the cost of bananas is 3 dollars per bunch.
Step-by-step explanation:
The following is an excerpt from a paper published in BMJ (formerly the British Medical Journal) in 1994:
Charig et al undertook a historical comparison of success rates in removing kidney stones. Open surgery had a success rate of 78% (273/350) while a minimally invasive procedure called percutaneous nephrolithotomy had a success rate of 83% (289/350), an improvement over the use of open surgery. However, the success rates looked rather different when stone diameter was taken into account. This showed that, for stones of <2 cm, 93% (81/87) of cases of open surgery were successful compared with just 83% (234/270) of cases of percutaneous nephrolithotomy. Likewise, for stones of >/=2 cm, success rates of 73% (192/263) and 69% (55/80) were observed for open surgery and percutaneous nephrolithotomy respectively.
The main reason why the success rate reversed is because the probability of having open surgery or percutaneousnephrolithotomy varied according to the diameter of the stones. In observational (nonrandomized) studiescomparing treatments it is likely that the initial choice of treatment would have been influenced by patients'characteristics such as age or severity of condition; so any difference between treatments could be accounted for bythese original factors. Such a situation may arise when a new treatment is being phased in over time. Randomizedtrials are therefore necessary to demonstrate any treatment effect.
This is an example of Simpson's paradox because:
a. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).
b. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them).
c. when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).
d. when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them).
Answer: a. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).
Step-by-step explanation: Simpson's Paradox happens when a group of data shows a relationship in each group but it is reversed when the group is combined.
In the BMJ paper, percutaneous nephrolithotomy had a bigger successful rate than open surgery. But, the rates are reversed when the diameter (size) of the stone is included in the research. So, an individual group of data had a relationship and a factor reversed the relationship. This is an example of Simpson's Paradox.
Excerpt form the paper in BMJ.
The excerpt is taken from the paper that got published in the british medical journal of 1994. Ths journal was understand for a historical comparison of the success rates in kidney stone removal. As the success rate of the surgery was about 83%.
Hence the answer is lurking variable is introduced, the conclusions are reversed.
As per the excerpt of the Simpsons paradox the such as rate of 78% and minimal invasive procedure called the percutaneous has a success rate of 83% thus better over open surgery.Thus the option A is correct. The variable size of stone and conclusion was the opposite.Learn more about the undertook a historical.
brainly.com/question/12653054.
solve the equation..
Answer:
y=252/5=50.4
Step-by-step explanation:
[tex](A)\ 9y-252=4y\\(B)\ 5y=252\\(C)\ y= \frac{252}5 = 50.4[/tex]
In step A we multiplied both sides by the least common multiple of the denominators, in order to deal with only integers for as long as possible.
In step B you subtract 4y and add 252 to both sides ("moving them on the other end of the equal sign").
In step C you finally divide by 5 to isolate y.
A cylinder has a base diameter of 8 centimeters and a height of 7 centimeters. What is its volume in cubic centimeters, to the nearest tenths place
Answer:
Step-by-step explanation:
Answer: 351.9 cm^3
d = diameter = 8 cm
r = radius = diameter/2 = 4 cm
h = height = 7 cm
volume = (pi)r^2h
volume = (3.14159)(4 cm)^2(7 cm)
volume = 3.14159(16 cm^2)(7 cm)
volume = 351.858 cm^3
Answer: 351.9 cm^3
Answer:
Step-by-step explanation:
Answer: 351.9 cm^3
d = diameter = 8 cm
r = radius = diameter/2 = 4 cm
h = height = 7 cm
volume = (pi)r^2h
volume = (3.14159)(4 cm)^2(7 cm)
volume = 3.14159(16 cm^2)(7 cm)
volume = 351.858 cm^3
Answer: 351.9 cm^3
(5x7) + (5x9) = 5x (7+?
Answer:
9
Step-by-step explanation:
this is because it is 9 and it could be 9
Answer:
First let's find what (5x7) + (5x9) equals;
(5x7) + (5x9)
35 + 45
= 80
Now 80 has to equal to;
5 x (7 + y) ( where 'y' is our unknown number)
So we set up the equation:-
80 = 5 x (7 + y)
80 = 35 + 5y
-35 -35
45 = 5y
/5 /5
9 = y
Let's double check:
80 = 5 x (7 + y)
80 = 5 x (7 + 9)
80 = 35 + 45
80 = 80, we are correct.
I need help on this problem
Answer:
D
Step-by-step explanation:
which of the following statements is not true about reflections?
a. The image faces the same direction as the pre-image
b. The image is the same shape as the pre-image
c. The image is the same size as the pre-image
d. Points on the pre-image are the same distance from the line of reflection as the corresponding points on the image
Answer:I’m pretty sure it would be A!
Step-by-step explanation:
Answer:
Should be A
Step-by-step explanation:
But it all depends on the mirror
simplificar cada expresion numerica. -24+(-65)÷5
Answer:
-37
Step-by-step explanation:
-24+(-65) /5
-24 + (-13)
-37
Answer:
-37
Step-by-step explanation:
-24+(-65)/5
-24+(-65/5)
-24 - 13
-37
please help MEEE i need this to be done
Answer:
NO
Step-by-step explanation:
There is an odd number of students so one team would have 7 students while the other would have only 6
Answer:
Step-by-step explanation:
No she can't divide them equally because the total of the both classes is 13 which is an odd number and it is not possible to divide an old number equally.
Hope this helps
Write an inequality that represents the verbal expression.
3 more than a number tis greater than or equal to 21.
Answer:
3x≥21
Step-by-step explanation:
hello help me with this question thanks in advance
[tex]\bold{\huge{\underline{ Solution \: 1 }}}[/tex]
Basic theorems on similarity of trianglesTheorem 1 :- SSS Similarity
When all the three sides of one triangle are in proportion to the other three sides of the another triangle then those 2 triangles are similar by SSS similarity .Theorem 2 :- AA similarity
When the two corresponding angles of one triangle are congruent to other two corresponding angles of another triangle then both the triangles are similar by AA Similarity .Theorem 3 :- SAS similarity
When the two sides of one triangle are in proportion to the other two sides of another triangle and the one of the angles of both the triangles that lie between two corresponding sides are equal then both the triangles are similar by SAS similarity.Theorem 4 :- AAA similarity
When all the three angles of one triangle are equal to other three angles of another triangle then both the triangles are similar by AAA similarity. Let's Begin :-Here, We have given statement that
" If an angle of one triangle is congruent to an angle of another triangle and the corresponding sides including those angles are in proportion, then the two triangles are similar . "From above theorem, we can conclude that
Both the triangles are similar by SAS similarityHence, Option C is correct
[tex]\bold{\huge{\underline{ Solution \: 2 }}}[/tex]
The given statement is proved by using Pythagorean theorem.
Pythagorean theorem states that the square of hypotenuse that is longest side is equal to the sum of the squares of base and perpendicular height that is the smallest sides of the given triangle.That is,
[tex]\sf{\red{ (Hypotenuse)^{2} = ( Perpendicular)^{2} + ( Base) ^{2}}}[/tex]
Hence, Option D is correct that is Pythagorean theorem.
How many bags can you purchase with 20$
Answer:
The answer is 3/5=x/20
If you can buy 3 bags for $5 then you can buy 12 bags with $20
Step-by-step explanation:
Basically divide 20 by 5
Then you multiply the answer to 20/5 which is 4 by 3 to get x
Which would be 12
Find the weight of pure gold in 10 grams of 20 carat. It is given that 24 carat gold is cent-percent pure gold.
Answer:
The weight of pure gold in 10 grams of 20 carat it is given that 24 carat gold is cent percent pure gold is 83.33 grams
hope this is helpful
Answer:
The weight of pure gold in 10 grams of 20 carat it is given that 24 carat gold is cent percent pure gold is 83.33 grams.
Step-by-step explanation:
To find : The weight of pure gold in 10 grams of 20 carat it is given that 24 carat gold is cent percent pure gold ?
Solution :
The percentage of pure gold in 10 grams can be measured of 24 carat gold.
In fact, this is equal to 100 percentage of pure gold in 10 grams of 1 carat.
The pure gold in 10 grams of 24 carat gold is
\frac{10}{24}\times 100=4.16
24
10
×100=4.16
The pure gold in 10 grams of 20 carat gold is
4.16\times 20=83.334.16×20=83.33
Therefore, The weight of pure gold in 10 grams of 20 carat it is given that 24 carat gold is cent percent pure gold is 83.33 grams.