Answer-
[tex]\boxed{\boxed{a_{12}=354294}}[/tex]
Solution-
If there are 2 terms of a Geometric Sequence [tex]a_n[/tex] and [tex]a_k[/tex] where (n > k), then
[tex]a_n=a_k\cdot r^{n-k}[/tex]
where, r = common ration of the G.P.
Here,
[tex]a_4 = 54\\\\a_7=1458[/tex]
Putting in the equation,
[tex]\Rightarrow a_7=a_4\cdot r^{7-3}[/tex]
[tex]\Rightarrow a_7=a_4\cdot r^3[/tex]
[tex]\Rightarrow 1458=54\cdot r^3[/tex]
[tex]\Rightarrow r^3=\dfrac{1458}{54}[/tex]
[tex]\Rightarrow r^3=27[/tex]
[tex]\Rightarrow r=3[/tex]
Again putting the values in the equation,
[tex]\Rightarrow a_{12}=a_7\cdot r^{12-7}[/tex]
[tex]\Rightarrow a_{12}=a_7\cdot r^5[/tex]
[tex]\Rightarrow a_{12}=1458\cdot 3^5[/tex]
[tex]\Rightarrow a_{12}=354294[/tex]
The 12th term of the geometric sequence is 354,294
The nth term of a geometric sequenceThe nth term of a geometric progression is given by the formula:
[tex]a_n = ar^{n-1}[/tex]
For n = 4
[tex]a_4=ar^{4-1}\\\\a_4=ar^3\\\\ar^3=54..................(1)[/tex]
For n = 7
[tex]a_7=ar^{7-1}\\\\a_7=ar^6\\\\ar^6=1458................(2)[/tex]
Divide equation (2) by equation (1)
[tex]\frac{ar^6}{ar^3} =\frac{1458}{54} \\\\r^3=27\\\\r^3=3^3\\\\r = 3[/tex]
Substitute r = 3 into equation (1)
[tex]a(3)^3=54\\\\27a=54\\\\a=\frac{54}{27}\\\\a=2[/tex]
The 12th term of the sequence is therefore calculated below
[tex]a_{12}=ar^{11}\\\\a_{12}=2(3^{11})\\\\a_{12}=354294[/tex]
The 12th term of the geometric sequence is 354,294
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if f (x) =-14x-2, then f^-1 (x) =
Factor this expression. With work please!
Miss broom invested $10,000 into an account with an interest rate of 6% compounded annually which equation models the time it will take for his money to double?
A- logbase2 1.06= T
B- log2 =T
C-log1.06 =T
D= logbase1.06 2=t
whats the normal arm span for these heights? : 4'10,4'11,5'0,5'4,5'5,5,'7,5'8,5'9,5'10,5'11,6'0
In adults, the arm span is approximately 5 cm greater than the height in adult males and 1.2 cm in adult females. To calculate the arm span for the heights given, we add 5cm to their height. The following are the results:
Height Arm Span Length (in cm)
4’10 152.32
4’11 154.86
5’0 157.4
5’4 167.56
5’5 170.10
5’7 175.18
5’8 177.72
5’9 180.26
5’10 182.80
5’11 185.34
6’0 187.88
To add, the total measurement of the length from the furthermost part of an individual's arms to the other end when raised equidistant to the ground at shoulder height at a 90º angle is called the arm span or wingspan.
Can someone please help me with math for college readiness
Joe gave the following argument: Since lim x→0 0 = 0,
(A) and since 0 = −1 x + 1 x ,
(B) we know that lim x→0 ( −1 x + 1 x ) = 0.
(C) But then, since lim x→0 ( −1 x + 1 x ) = lim x→0 ( −1 x ) + lim x→0 ( 1 x ),
(D) we can say that lim x→0 ( −1 x ) + lim x→0 ( 1 x ) = 0, which means that lim x→0 ( −1 x ) = − lim x→0 ( 1 x ).
(E) no error
In which line, if any, has joe made an error?
I'm having trouble finding the answer to this question
what is 15 square root to the nearest tenth
Suppose you are thinking about buying one of two cars. Car A will cost $17,655. You can expect to pay an average of $1230 per year for fuel, maintenance and repairs. Car B will cost about $15,900. Fuel maintenance and repairs for it will average about $1425 per year. After how many years are the total costs for the cars the same? a. 5 years c. 9 years b. 7 years d. 11 years
After 9 years many years are the total costs for the cars the same.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
Given that:-
Car A will cost $17,655. You can expect to pay an average of $1230 per year for fuel, maintenance and repairs. Car B will cost about $15,900. Fuel maintenance and repairs for it will average about $1425 per year. After how many years are the total costs for the cars the same?We can form two-equation for the total cost of the two cars:-
A = 17655 + 1230y,
B = 15900 + 1425y
We wish to know when the cost will become the same for both the cars.
A = B
15900 + 1425y = 17655 + 1230y
Now subtract 15900 from both sides
1425y = 1230y + 1755
Now subtract 1230y from both sides
195y = 1755
Now divide both sides by 195
y = 9 years
Therefore After 9 years, many years are the total costs for the cars the same.
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Rita made $221 for 17 hours of work.At the same rate, how much would she make for 12
hours of work?
Using the concept of proportion, Rita would make $156 for 12 hours of work at the same rate.
We have,
We can use proportions to solve this problem.
Let x be the amount of money Rita would make for 12 hours of work.
We know that Rita made $221 for 17 hours of work,
which can be written as:
221/17 = x/12
To solve for x, we can cross-multiply and simplify:
221(12) = 17x
2652 = 17x
x = 156
Therefore,
Rita would make $156 for 12 hours of work at the same rate.
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Which of the following is a factor of 6x2 + 2x − 21?
4x − 3
2x + 7
6x − 3
None of the above
Find the surface area of the cone to the nearest tenth.
A. 203 cm2
B. 1341.5 cm2
C. 747.7 cm2
D. 213.5 cm2
The surface area of the given cone is 747.32.
What is area of a cone?"The total surface area of a cone is defined as the total area of the cone occupied in a three-dimensional area. It is equal to the sum of the curved surface and the base of the cone. "
Surface area of the cone is [tex]\pi*r(l+r )[/tex]
[tex](22/7)*7*(27+7)[/tex]
= 747.32
The surface area of the cone is 747.32
Hence, option C is correct.
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Find the exact solution to the equation. Show your work for credit. (1 point) four to the power of quantity twelve minus four x equals two hundred and fifty six.
The exact solution to the equation [tex]4^{(12 - 4x)[/tex] = 256 is x = 2. By recognizing that 256 is 4 raised to the fourth power, we equate the exponents and solve for x.
To solve this problem, we need to recognize that 256 is a power of 4. 4⁴ = 256. With this insight, the equation can be rewritten as:
[tex]4^{(12 - 4x)[/tex] = 4⁴
Since the bases are the same, we can equate the exponents:
12 - 4x = 4
Now, we'll isolate the variable x:
Subtract 12 from both sides: -4x = 4 - 12
-4x = -8
Divide both sides by -4: x = 2
Thus, the exact solution to the given equation is x = 2.
A country population in 1991 was 231 million in 1999 it was 233 million . Estimate the population in 2003 using the exponential growth formula. Round you answer to the nearest million
Answer:
population in 2003 is 234 million.
Step-by-step explanation:
A country's population in 1991 was 231 million
In 1999 it was 233 million.
We have to calculate the population in 2003.
Since population growth is always represented by exponential function.
It is represented by [tex]P(t)=P_{0}e^{kt}[/tex]
Here t is time in years, k is the growth constant, and is initial population.
For year 1991 ⇒
233 = [tex]P_{0}e^{8k}[/tex] = 231 [tex]e^{8k}[/tex]
[tex]\frac{231}{233}= e^{8k}[/tex]
Taking ln on both the sides ⇒
[tex]ln(\frac{233}{231})=lne^{8k}[/tex]
ln 233 - ln 231 = 8k [since ln e = 1 ]
5.451 - 5.4424 = 8k
k = [tex]\frac{0.0086}{8}=0.001075[/tex]
For year 2003 ⇒
[tex]P(t)=P_{0}e^{kt}[/tex]
P (t) = 231 × [tex]e^{(0.001075)(12)}[/tex]
= 231 × [tex]e^{0.0129}[/tex]
= 231 × 1.0129
= 233.9 ≈ 234 million
Therefore, population in 2003 is 234 million.
Find the difference- (ab+3a+7)- (-5ab-2)
Simplify:
6( [tex]4/3 \f[/tex] ( 14 ÷ [tex] \frac{1}{7} [/tex] ) ) ÷ [tex] \frac{13}{10} [/tex]
-
I got 603 [tex] \frac{1}{12} [/tex] , but i'm not completely sure it's correct..
write an equation for a line perpendicular to the x-axis that passes through the point (5,1)
The equation of a line perpendicular to the x-axis passing through the point (5,1) is x = 5. This is because a vertical line crossing the x-axis at a specific point will have the same x-coordinate for all its points.
Explanation:In mathematics, a line perpendicular to the x-axis is a vertical line that crosses the x-axis at a specific point. All points on this line will share the same x-coordinate. Therefore, a line that is perpendicular to the x-axis, and passes through the point (5,1) will have the equation x = 5. This equation represents a line that is vertical and intercepts the x-axis at the point where x equals 5. This is because in each point on the line, x remains constant, which is the characteristic of a vertical line in a Cartesian Coordinate System.
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a farmer needs to enclose a section of land in the shape of a parallelogram by using one side of a barn for one side the barn in the side opposite of the barn will be 10 ft long one of the other sides will be 6 feet long what is the length of the last side?
A) 6 feet
B) 16 feet
C) 4 feet
D) 10 feet
Answer: C:6
Step-by-step explanation:
I just got it right on the quiz
In triangle DEF, DG = 10 cm. What is CG?
Answer:
5 cm is the correct answer it would be half of DG
Step-by-step explanation:
Please help me to do this one
Answer is 4
1. Multiple 29 by both side to get N by itself
2. solve 29/7.25 on a calculator, because it's easier
3. answer is 4.
4. Check your answer. Plug in 4 to see if you get the same answer on both sides. You should get .138 aprox. on both side.
Which graph represents the function f(x) = x2 + 3x + 2?
graph 1
graph 2
graph 3
graph 4
Answer:
Graph 1
Step-by-step explanation:
Here, the given equation is,
[tex]f(x)=x^2+3x+2-----(1)[/tex]
For x-intercept, f(x) = 0
[tex]x^2+3x+2=0[/tex]
[tex]x^2+2x+x+2=0[/tex]
[tex]x(x+2)+1(x+2)=0[/tex]
[tex](x+1)(x+2)=0[/tex]
[tex]\implies x=-1\text{ or } -2[/tex]
So, the x-intercept of the function are (-1,0) and (-2,0)
Since, the line must has at least one x-intercept.
⇒ Graph 2 and Graph 4 can not be the graph of the given function,
Also, for y-intercept,
Put x = 0 in equation (1),
We get, f(x) = 2,
Hence, the y-intercept of the given function is (0,2),
But in Graph 3 the y-intercept of the function = (0,1)
⇒ Graph 3 can not be the graph of the given function,
Therefore, Graph 1 is the correct graph of the given function.
The measure of ∠B is (3x – 4 )° and the measure of ∠D is (2x – 6)°. What are the measures of angles B and D?
The measures of angles B and D are 110° and 70° respectively.
What is cyclic quadrilateral?The rule of cyclic quadrilateral states that, the sum of the opposite is supplementary i.e 180°
Therefore, applying this rule, Angle B and D are supplementary
Then, B+D=180°
Given that, B=3x-4 and D= 2x-6
Thus, (3x-4)+(2x-6)=180°
3x-4+2x-6=180°
3x+2x-4-6=180°
5x-10=180°
5x=180°+10
5x=190°
Then, x =190/5
x=38°
Then solving for B and D;
B=3x-4
B=3(38)-4
B=114-4
B=110°
Also, D=2x-6
D=2(38)-6
D=76-6
D=70°
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how close are a meter and a yard? convert 1 meter into yards by using the fact
that there are 100 centimeters in a meter, 2.53 centimeters in a inch, 12 inches in a foot, and 3 feet in a yard.
Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2
***PLEASE HELP**
800x200 I know the answer is 160000 but I want to see how quick you guys answer...
Simplify the expression: -3(4a-5b)
Karen is trying to determine how long her 4-year-old daughter should sit in time-out for deliberately pouring her juice on the floor. if she uses the suggested estimate, her daughter will be in time-out for:
A good rule of thumb is one minute per year of your child's age. So Karen’s child is 4 years old, she would get four minutes of time-out. If you find that the shorter time-outs aren't having the wanted result, increase the length by half the time (so your 4-year-old would get an extra two minutes, for a total of six minutes).
Which system is the only inconsistent system?
Select one:
a.
y
y
=
=
x+4
2x+4
y=x+4y=2x+4
b.
y
y
=
=
x
−x
y=xy=−x
c.
y
y
=4
=
x−3
4x+3
y=4x−3y=4x+3
d.
y
2y
=2
=
x−3
4x−6
y=2x−32y=4x−6
Option (c) represents an inconsistent system of equations, as the constant terms are not proportional, while the coefficients of x are. This system (y=4x-3, y=4x+3) has no solutions.
Explanation:In mathematics, specifically in algebra, an inconsistent system is a system of equations that has no solutions. To check which system is inconsistent from the options you've given, we need to compare the coefficients of each equation within a system. An inconsistent system will have proportional coefficients of x and y between the two equations, but the constant terms will not be proportional.
Looking at each option:
Option (a): y=x+4 and y=2x+4
Option (b): y=x and y=−x
Option (c): y=4x−3 and y=4x+3
Option (d): y=2x−3 and 2y=4x−6
From here, we can see that option (c): y=4x-3, y=4x+3 is inconsistent. In this system, the coefficients of x are proportional (4), but the constant terms (-3 and +3) are not proportional.
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How can the average rate of change be found using a discrete graph?
The average rate of change can be found using a discrete graph by calculating the slope between two points on the graph. This provides insight into how the dependent variable changes as the independent variable varies.
Explanation:The average rate of change can be found using a discrete graph by calculating the difference in the y-values of two points and dividing it by the difference in the x-values of those same points. This will give you the slope of the line connecting the two points, which represents the average rate of change between those two points. For example, if you have two points (x1, y1) and (x2, y2), the average rate of change can be calculated as:
(y2 - y1) / (x2 - x1)
By finding the average rate of change at different intervals on the graph, you can analyze how the dependent variable changes in relation to the independent variable.
What is the equation of the line perpendicular to 5x − 2y = −18 that contains the point (10, 4)?
y=-2/5x
y=-2/5x+8
y=-5/2x+29
y=5/2x-29