Answer:
4x² + 6x + 2
Step-by-step explanation:
Solve by factoring.
4x · x = 4x²
4x · 1 = 4x
2x · 1 = 2x
2 · 1 = 2
Combine like terms.
4x² + 4x + 2x + 2
= 4x² + 6x + 2
Hope this helps.
Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice. Set A Set B The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 42.8 with standard deviation of about 1.86. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set A’s low temperatures have a greater variability than Set B temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set B is about 41.56 with standard deviation of about 6.07. The mean for Set A is about 43.8 with standard deviation of about 14.8. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set A means that Set A’s low temperatures have a greater variability than Set B temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.4. The mean for Set B is about 41.5 with standard deviation of about 6.7. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set B’s low temperatures have a greater variability than Set A temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 43.8 with standard deviation of about 14.8. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set B’s low temperatures have a greater variability than Set A temperatures.
Answer:
Explained below.
Step-by-step explanation:
The question is:
Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.
Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}
Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}
The five-number summary is:
MinimumFirst Quartile Median Third Quartile MaximumThe five-number summary for set A is:
Variable Minimum Q₁ Median Q₃ Maximum
Set A 36.00 38.25 44.00 50.75 54.00
The five-number summary for set B is:
Variable Minimum Q₁ Median Q₃ Maximum
Set B 22.00 28.75 48.00 58.50 65.00
Compute the mean for both the data as follows:
[tex]Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6[/tex]
Both the distribution has the same mean.Compare mean and median for the two data:
[tex]Mean_{A}>Median_{A}\\\\Mean_{B}>Median_{B}[/tex]
This implies that set A is positively skewed whereas set B is negatively skewed.Compute the standard deviation for both the set as follows:
[tex]SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6[/tex]
The set B has a greater standard deviation that set A. Implying set B has a greater variability that set B.Determine whether the lines L1:x=25+7t,y=17+6t,z=t and L2:x=−12+8ty=−17+8tz=−11+4t intersect, are skew, or are parallel. If they intersect, determine
Answer: The lines are skew.
Step-by-step explanation: Two lines can only be parallel OR skew Or intersect each other. To determine that:
1) If the lines are parallel, divide the coefficient that precedes the variable of each equation and compare:
[tex]\frac{7}{8} \neq \frac{6}{8} \neq \frac{1}{4}[/tex]
Since they are not equal, L1 and L2 are not parallel.
2) If the lines intersect, when you equal the equations the variable is a valid statement:
25 + 7t = - 12 + 8t (1)
17 + 6t = - 17 + 8t (2)
t = - 11 + 4t (3)
Using (3) to solve the system:
t - 4t = - 11
3t = 11
t = [tex]\frac{11}{3}[/tex]
Substituing t in (1):
25 + 7(11/3) = -12 + 8(11/3)
25 + 77/3 = - 12 + 88/3
[tex]\frac{152}{3} = \frac{52}{3}[/tex]
Which is not true, so, the lines does NOT intersect.
As they are none of the other options, it can be concluded that the lines L1 and L2 are skew.
Which shapes have the same volume as the given rectangular prism?
How many gallons of fuel costing $1.15 a gallon must be mixed with a fuel costing $0.85 per gallon to get 40
gallons of a fuel that costs $1 per gallon? Formulate an equation and then solve it in order to determine how
many gallons of fuel costing $1.15.
Answer:
multiply 0.85x40
Step-by-step explanation:
helpppppppppp give bralienst
Answer:
1
Hope that helps.
Answer:
1
Step-by-step explanation:
16/16=1
Hope this helps, if you have any questions, feel free to ask
Have a good day! :)
Please answer this correctly
Answer:
1/4
Step-by-step explanation:
The probability of landing on an odd number is 2/4.
The probability of landing on a number greater than 5 is 2/4.
2/4 × 2/4
4/16 = 1/4
The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president. In how many ways can this promotion be made?
Answer:
720 ways
The number of ways in which the promotion can be made is 720 ways
Step-by-step explanation:
Given that;
The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president.
This is a permutation problem because the order of selection is relevant. They will be promoted to various positions.
N = nPr = n!/(n-r)!
n = 10, r = 3
Substituting the values;
N = 10P3
N = 10!/(10-3)! = 10!/7!
N = 720 ways
The number of ways in which the promotion can be made is 720 ways
Functions f(x) and g(x) are shown below: f(x) = x2 g(x) = x2 + 8x + 16 In which direction and by how many units should f(x) be shifted to obtain g(x)? (1 point) Left by 4 units Right by 4 units Left by 8 units Right by 8 units
Answer: left 4 units
Step-by-step explanation: use the formula -b/2a to find the new x value. Or use a graphing calculator and compare the position of g(x) to f(x)
Answer:
Answer: left 4 units
Step-by-step explanation:
Parker wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 3 2% and the other bank is offering a rate of 3%
compounded annually. If Parker decides to deposit $7,000 for 25 years, which bank would be the better deal?
A.)a simple interest rate of 3.2%
B.)a compound interest rate of 3%
Answer:
The better deal would be simple interest rate of 3.2%
Step-by-step explanation:
In order to calculate which bank would be the better deal If Parker decides to deposit $7,000 for 25 years, we would have to make the following calculation:
A. simple interest rate of 3.2%.
Therefore, FV= P*r*t
=$7,000*3.2%*25
=$5,600.
B. compound interest rate of 3%
Therefore, FV=PV(1+r)∧n
FV=$7,000(1+0.03)∧25
FV=$14,656
The better deal would be simple interest rate of 3.2%
Find the distance from point X to line p. An image of a point X, a line p, and three segments joining the point and the line. Question 12 options:
A. 2 √34 units
B. √85 units
C. 2 √17 units
D. √17 units
Answer:
Step-by-step explanation: Answer is 2√17 units
Distance =√ (−2−0) ^2−(5−(−3)) ^2
=√ (−2) ^2−(5+3) ^2
=√4+64
=√68
=2√17 units
V’s Warehouse has a market value of $880,000. The property in V’s area is assessed at 35% of the market value. The tax rate is $58.90 per $1,000 of assessed value. What is V’s property tax?
Answer:
$18,141.20
Step-by-step explanation:
The assessed value is $880,000 × 0.35.
The tax will be ...
(58.90/1000) × (0.35 × $880,000) = $18,141.20
Finally, you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight. Which are knights
Answer:
w and y are knights
Step-by-step explanation:
Of the six natives, W and Y are the knights.
What is the reasoning?In mathematics, reasoning entails making logical deductions from data or presumptions. Making sense of something can be defined as gaining comprehension of a situation, setting, or idea by relating it to what is already known or has already happened.
Given that you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight.
From the given data it is concluded that W and Y are the knights because their statement is W says: At most three of us are knights and Y says: Exactly two of us are knights.
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I NEED HELP PLEASE, THANKS! :) A commercial passenger jet is flying with an airspeed of 185 miles per hour on a heading of 036°. If a 47-mile-per-hour wind is blowing from a true heading of 120°, determine the velocity and direction of the jet relative to the ground. 186.1 mph, 021° 188.5 mph, 021° 195.6 mph, 069° 186.1 mph, 069°
We are given that the passenger's jet is flying at a speed of 185 miles per hour, with a direction of 36 degrees, and the wind speed being 47 mph with a direction of 120 degrees. From this, you could create a diagram is shown in the attachment.
[ 185 cos 36, 185 sin 36 ]
+ [ 47 cos 120, 47 sin 120 ]
_______________________
[ 185 cos 36 + 47 cos 120, 185 sin 36 + 47 sin 120 ]
√( 4263 + 33988 )^2
= ( About ) √38251 = 195.57 mph
Solution = 195.6 mph, 069°
I NEED HELP PLEASE, THANKS! :)
Answer:
D. No solution
Step-by-step explanation:
Instead of solving everything I just plugged the numbers on equations and saw that for some of them the numbers satisfied one or two equation but not all. Also for some I saw that a number set makes the equation have no solution. For eg, I plugged option B into equation 3 and got 1305=756 which is never true so it is no solution.
Hope you understand :)
On Wednesday and Thursday
a total of 32 records were sold.
The number of records sold on
Thursday was 3 times the number
of records sold on Wednesday.
c) How many records were (2)
sold on Wednesday?
d) How many records were (1)
sold on Thursday?
Total marks: 5
Answer:
8 records were sold on Wednesday, and 24 records were sold on Thursday
Step-by-step explanation:
Let's call the number of records sold on Wednesday w, and the number sold on Thursday t.
t+w=32
t=3w
Substituting:
(3w)+w=32
4w=32
w=8
t=3w=3(8)=24
Hope this helps!
O número inteiro positivo, cujo produto de seu antecessor com seu sucessor é igual a 8, é
A) 5
B) 4
C) -3
D) 3
El 2
Answer:
Olá!
`~~~~~~~~~~~~~~~~~~
3 (número inteiro positivo)
2 (antessor)
4 (sucessor)
Para provar isso, simplesmente multiplicamos entre 4 e 2:
4 x 2 = 8
Espero que isso tenha ajudado! Também seria bom se você me desse Brainliest!
Flag question
You buy halibut at $30 per
pound,
One portion of seared
halibut requires 6 ounces of
halibut.
How much does the halibut
for one portion cost? Round
to the nearest cent.
Answer:
$11.25
Step-by-step explanation:
price = $30/lb
16 oz = 1 lb
1 portion = 6 oz = 6/16 lb = 3/8 lb
$30/lb * 3/8 lb = $11.25
Two particles travel along the space curves r(t) and u(t). A collision will occur at the point of intersection if both particles are at P at the same time. (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list.)
r(t) = t^2i + (9t - 20)j + t^2k u(t) = (3t + 4)i + t^2j + (5t - 4)k point of intersection (x, y, z) =
1. Do the particles collide?
a. Yes
b. No
2. Do their paths intersect?
a. Yes
b. No
Answer:
Point of intersection (x, y, z) = (16, 16, 16)
1. a. Yes
2. a. Yes
Step-by-step explanation:
In order for the particles to colide (and therefore have their paths intersect), the values for the i, j, and k coordinates must be equal for a given 't':
For the i coordinate:
[tex]i_{r(t)} =i_{u(t)}\\t^2=3t+4\\t=\frac{3\pm\sqrt{9-4*1*(-4)} }{2}\\t=4\ or\ -1[/tex]
For the j coordinate:
[tex]j_{r(t)} =j_{u(t)}\\9t-20=t^2\\t=\frac{9\pm\sqrt{81-4*1*20} }{2}\\t=4\ or\ 5[/tex]
For the k coordinate:
[tex]k_{r(t)} =k_{u(t)}\\t^2=5t-4\\t=\frac{5\pm\sqrt{25-4*1*4} }{2}\\t=4\ or\ 1[/tex]
As we can see, for t =4, both paths have the same coordinates and therefore they intersect and the particles will colide.
[tex]r(4) = 4^2i + (9*4 - 20)j + 4^2k \\r(4)=16i+16j+16k\\u(4) = (3*4 + 4)i + 4^2j + (5*4 - 4)k\\u(4)=16i+16j+16k[/tex]
Point of intersection (x, y, z) = (16, 16, 16)
Which of the following is false? Correlation coefficient and the slope always have the same sign (positive or negative). If the correlation coefficient is 1, then the slope must be 1 as well. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation measures the strength of linear association between two numerical variables.
Answer:
If the correlation coefficient is 1, then the slope must be 1 as well.
Step-by-step explanation:
Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.
If the correlation coefficient is 1, then the slope must be 1 as well.
The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.
Correlation coefficient and the slope both quantify the direction and strength of the relationship between two numeric variables. When the correlation (r) is negative, the regression slope (b) will be negative. When the correlation is positive, the regression slope will be positive.If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them.
So, the false statement is:
If the correlation coefficient is 1, then the slope must be 1 as well.
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Suppose you draw a single sample of size 64 from a large population and measure its sample proportion. What is the margin of error for 95% confidence?
(a) 5% (b) 6.25% (c) 12.5% (d) 95%
Answer:
(b) 6.25%
Step-by-step explanation:
Margin of error is the chances of percentage deviation that may differ from original population data. The margin of error for 95% confidence interval can be 6.25%. To find this we divide population standard deviation with square root of sample size. The margin of error is the estimate of the deviation from actual and real value of population.
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not have the disease. Round to three decimal places as needed.
Yes - Have the disease No - Do not have the disease
Positive 142 6
Negative 7 145
Answer:
0.505 = 50.7% probability of a negative test.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
142 + 6 = 148 people tested positive. Of those, 142 had the disease and 6 did not.
7 + 145 = 152 people tested negative. Of those, 7 had the disease and 145 did not.
Find the probability of getting someone who tests negative, given that he or she did not have the disease.
This is the probability of a negative test.
152 negative tests out of 148 + 152 = 300
152/300 = 0.507
0.505 = 50.7% probability of a negative test.
If a carpenter nails a 15-ft brace to the wall 9 feet above the floor, how far (in ft) from the base of the wall should he nail the brace to the floor? ___________________________________ ft.
Answer:
c = 12ft
Step-by-step explanation:
Given that the wall is 9ft from the ground.
Brace nailed to the wall is 15ft.
Note that the brace to the wall will be slant hence it will look like the hypotenus side of a triangle.
The question requires the solution to the distance from the base of the wall to the brace.
Note from Pythagoras theorem
a^2 = b^2+c^2
Where a = 15ft
b = 9ft
Hence, from the base of the wall, the brace will be nailed 9ft
c = ?
15^2 = 9^2+c^2
225 = 81+c^2
225-81 = c^2
144 = c^2
c =√144
c = 12ft
Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 49 days and a standard deviation of 10.2 days. Find the probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days.
Answer:
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
Step-by-step explanation:
In this case, we have a population lifetime normally distributed with mean 49 and standard deviation 10.2.
We take a sample of size n=64.
Then, we can calculate the z-score for a sample mean M=54, in order to calculate P(M>54):
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{54-49}{10.2/\sqrt{64}}=\dfrac{5}{1.275}=3.922\\\\\\P(M>54)=P(z>3.922)=0.00004[/tex]
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
In a book the characters are trying to determine whether the Poisson probabilistic model can be used to describe the locations that rockets landed in a city. They divided the city into 0.25-kmsquared regions. They then counted the number of rockets that landed in each region, with the results shown in the table below. Complete parts (a) through (e). Number of rocket hits 0 1 2 3 4 5 6 7 Observed number of regions 228 214 94 32 7 0 0 1 (a) Estimate the mean number of rocket hits in a region by computing mu equals Summation from nothing to nothing xP left parenthesis x right parenthesis.
Answer:
The estimated mean number of rockets hits in the region is 533.
Step-by-step explanation:
We are given the following information,
Number of rocket hits | Observed number of regions
0 | 228
1 | 214
2 | 94
3 | 32
4 | 7
5 | 0
6 | 0
7 | 1
We are asked to estimate the mean number of rocket hits in the region.
The mean or expected value is given by
[tex]\mu = \sum (x \cdot P(x)) \\\\\mu = (0 \cdot 228) + (1 \cdot 214) + (2 \cdot 94) + (3 \cdot 32) + (4 \cdot 7) + (5 \cdot 0) + (6 \cdot 0) + (7 \cdot 1) \\\\\mu = 0 + 214 +188+ 96 +28 +0+ 0 + 7 \\\\\mu = 533[/tex]
Therefore, the mean number of rockets hits in the region is 533.
A tank contains 40 lb of salt dissolved in 500 gallons of water. A brine solution is pumped into the tank at a rate of 5 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 5 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t)
Answer:
[tex]A(t)=500C_{in}(t)+[40-500C_{in}(t)]\cdot e^{-\frac{t}{100}}[/tex]
Step-by-step explanation:
Volume of water in the Tank =500 gallons
Let A(t) be the amount of salt in the tank at time t.
Initially, the tank contains 40 lbs of salt, therefore:
A(0)=40 lbs
Rate of change of the amount of Salt in the Tank
[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]
Rate In=(concentration of salt in inflow)(input rate of brine)
[tex]=(C_{in}(t))( 5\frac{gal}{min})\\=5C_{in}(t)\frac{lbs}{min}[/tex]
Rate Out=(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{500})( 5\frac{gal}{min})=\frac{A}{100}[/tex]
Therefore:
[tex]\dfrac{dA}{dt}=5C_{in}(t)-\dfrac{A}{100}[/tex]
We then solve the resulting differential equation by separation of variables.
[tex]\dfrac{dA}{dt}+\dfrac{A}{100}=5C_{in}(t)\\$The integrating factor: e^{\int \frac{1}{100}}dt =e^{\frac{t}{100}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{100}}+\dfrac{A}{100}e^{\frac{t}{100}}=5C_{in}(t)e^{\frac{t}{100}}\\(Ae^{\frac{t}{100}})'=5C_{in}(t)e^{\frac{t}{100}}[/tex]
Taking the integral of both sides
[tex]\int(Ae^{\frac{t}{100}})'=\int [5C_{in}(t)e^{\frac{t}{100}}]dt\\Ae^{\frac{t}{100}}=5*100C_{in}(t)e^{\frac{t}{100}}+C, $(C a constant of integration)\\Ae^{\frac{t}{100}}=500C_{in}(t)e^{\frac{t}{100}}+C\\$Divide all through by e^{\frac{t}{100}}\\A(t)=500C_{in}(t)+Ce^{-\frac{t}{100}}[/tex]
Recall that when t=0, A(t)=40 lbs (our initial condition)
[tex]A(t)=500C_{in}(t)+Ce^{-\frac{t}{100}}\\40=500C_{in}(t)+Ce^{-\frac{0}{100}}\\C=40-500C_{in}(t)\\$Therefore, the amount of salt in the tank at any time t is:\\\\A(t)=500C_{in}(t)+[40-500C_{in}(t)]\cdot e^{-\frac{t}{100}}[/tex]
–735 = 15(m + 929) m = _______
Answer:
-978
Step-by-step explanation:
1.) Use Distributive property (by multiplying 15 by the values in parentheses): -735=15m + 13935
2.) Subtract 13,935 on both sides, to move that value to the left side, to further isolate the variable m.
-735-13935=15m + 13935 - 13935
3.)-Simplify/Combine Like Terms
-14,670=15m
4.) Divide both sides by 15 to isolate and solve for m
-14,670/15=15m/15
5.) Simplify
-978=m
6.) Rearrange so m is on left side and value is on right side
m=-978
Skylar has 4 times as many books as Karen. If Skylar has 164 books, how many books does Karen have?
Answer:
41
Step-by-step explanation:
If Skylar has 4 times as many books as Karen, that means that you have to do a division problem to figure out how books Karen has. Because Skylar has 4 times as many books, and she has 164 books, the division problem is 164÷4=41 books.
The number of books Karen has will be 41.
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
Let,
Skylar has x number of books
Karen has y number of books = 164
Given condition;
y=4x
164=4x
x=41 books
Hence Karen has 41 books.
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The height of a projectile launched upward at a speed of 32 feet/ second from a height of 128 feet is given by the function h(t)=-16t^2+32t+128. How long will it take the projectile to hit the ground?
Answer:
8.51 seconds
Step-by-step explanation:
Time to reach maximum height
=( Usin90)/2g
= 32/2*9.81
= 32/19.62
= 1.63 s
Max height = U²Sin²tita/g
= 32²/9.81
= 1024/9.81
= 104.38ft
Total height=104.38 + 128= 232.38
Time to fall back to the ground using the formula
h = ut+(1/2)gt²
U= 0
H= 232.38
g = 9.81
(232.38 *2 )/9.81= t²
47.376= t²
t = 6.88 s
Total time taken to hit ground
= 6.88 + 1.63
= 8.51 seconds
What is 62 in expanded form?
A. 2 x 2 x 2 x 2 x 2 x 2
B. 6 x 6
C. 12
D. 36
Answer:
I think so you meant to write 62 as 6^2
If this is the question , then the answer is 6 x 6
HOPE THIS HELPS AND PLS MARK AS BRAINLIEST
THNXX :)
Answer:
B. 6 × 6
Step-by-step explanation:
6²
The square of a number means that the number is multiplied by itself.
6 × 6 (expanded form)
Find the third term in a geometric sequence if a = 8 and r = -1. Use the formula a(subscript n) = arⁿ⁻¹
Answer:
[tex]a_{3} = 8[/tex]
Step-by-step explanation:
=> [tex]a_{n} = ar^{n-1[/tex]
Where n = 3, a = 8 and r = -1
=> [tex]a_{3} = (8)(-1)^{3-1}[/tex]
=> [tex]a_{3} = (8)(1)[/tex]
=> [tex]a_{3} = 8[/tex]