Find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer below.
A.682
B.2044
C.2048
D.678
Answer: The correct option is (B) 2044.
Step-by-step explanation: We are given to find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024.
We know that
the n-th term of a geometric sequence with first term a and common ratio r is given by
[tex]a_n=ar^{n-1}.[/tex]
According to the given information, we have
[tex]a=4[/tex]
and
[tex]ar^{9-1}=1024\\\\\Rightarrow 4\times r^8=1024\\\\\Rightarrow r^8=\dfrac{1024}{4}\\\\\Rightarrow r^8=256\\\\\Rightarrow r^8=2^8\\\\\Rightarrow r=2.[/tex]
Therefore, the sum of the 9-term geometric sequence is given by
[tex]S_9\\\\\\=\dfrac{a(r^9-1)}{r-1}\\\\\\=\dfrac{4\times(2^9-1)}{2-1}\\\\\\=\dfrac{4\times(512-1)}{1}\\\\=4\times511\\\\=2044.[/tex]
Thus, the required sum of the 9-term sequence is 2044.
Option (B) is CORRECT.
Help with math please.
Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3).
Question 1 options:
The rate of change is –3, and the y -intercept is 18.
The rate of change is 3, and the y -intercept is –6.
The rate of change is 1/3, and the y intercept is 4 2/3
The rate of change is -1/3, and the y intercept is 7 1/3
2.What is the correct equation of the line shown below ?
The equation of the line shown is y = (3/2)x + 3.
What is the equation of line?The general equation of a straight line is
y = mx + c,
where m is the gradient or slope, and
y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Now given points from the line passes are (0,3) and (-4,-3)
Therefore we have,
x₁ = 0
y₁ = 3
x₂ = -4
y₂ = -3
Now since the slope of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
⇒ m = (-3 - 3)/ (-4-0)
⇒ m = -6/(-4)
⇒ m = 6/4
or, ⇒ m = 3/2
Now, for intercept c we can put any of points in the equation of line.
So, put (0,3)in the equation of line
3 = m(0) + c
3 = 0 + c
⇒ c = 3
Hence the required equation of line is given as,
y = mx + c
put the values of m and c,
y = (3/2)x + 3
which is the required equation of the line shown
Hence,the equation of the line shown is y = (3/2)x + 3.
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A rectangular picture frame measures 83 cm by 42 cm What is the perimeter or distance around the picture frame in meters
Write the next two terms in the pattern. 3, 10, 17, 24, . . .
10-3 =7
each term increases by 7
so 24 +7 = 31
31+7 = 38
next 2 terms are 31 & 38
Let r1 and r2 be relations on a set a represented by the matrices mr1 = ⎡ ⎣ 0 1 0 1 1 1 1 0 0 ⎤ ⎦ and mr2 = ⎡ ⎣ 0 1 0 0 1 1 1 1 1 ⎤ ⎦. find the matrices that represent
a.r1 ∪ r2.
b.r1 ∩ r2.
c.r2 ◦r1.
d.r1 ◦r1.
e.r1 ⊕ r2.
The operation results on the matrices representing relations r1 and r2 are beautiful illustrations of how relations are manipulated in set theory. Given the limitations imposed by the data available, only three of the five stipulated operations can be carried out.
Explanation:In the given question, the student needs to perform different operations on the matrices that represent relations r1 and r2. Here is the solution:
r1 ∪ r2 (Union of r1 and r2): It's obtained by taking the union of the corresponding elements in the two matrices. If either or both of the matrices have a 1 in a position, then put a 1, else 0. So the matrix for r1 ∪ r2 is ⎡ ⎣ 0 1 0 1 1 1 1 1 1 ⎤ ⎦ r1 ∩ r2 (Intersection of r1 and r2): It's obtained by taking the intersection of the corresponding elements in the two matrices. If both of the matrices have a 1 in a position, then put a 1, else 0. So the matrix for r1 ∩ r2 is ⎡ ⎣ 0 1 0 0 1 1 1 0 0 ⎤ ⎦ r2 ◦r1 (Composition of r2 and r1): If there exists an element in the set such that (a, b) is in r1 and (b, c) is in r2, then put a 1 in A[ac] else put a 0. Due to this, the matrix comprehension is studied in higher mathematics, and it can't be calculated from the given matrices. r1 ◦r1 (Composition of r1 and r1): Same as the previous operation but with both relations being r1. It also requires the full set of elements to calculate and can't be derived from the given matrices. r1 ⊕ r2 (Symmetric difference of r1 and r2): It is obtained by taking the XOR of each element in the matrices. So if the two elements are the same, put a 0, else put a 1. So the matrix for r1 ⊕ r2 is ⎡ ⎣ 0 0 0 1 0 0 0 1 1 ⎤ ⎦ Learn more about Matrix Operations here:
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On average, how many times must a 6-sided die be rolled until a 6 turns up twice in a row?
Ronald walks from home to Taco Bell to eat everyday. It takes him 30 minutes to walk the 2 mile distance. A) write a function for Ronald’s wall. Let x be the number of minutes he walks.
B) what should the domain of the function be?
Which transformation is not isometric?
8 less than one third of x is y
How is an emulsion different from a solution?
:The components are mixed unevenly instead of evenly within the emulsion.
:Insoluble instead of soluble particles are suspended within the emulsion.
:Two liquids that normally are not mixable are mixed in the emulsion.
:The components of an emulsion are single elements or compounds instead of a mixture of compounds.
Six students measure the acceleration (in meters per second per second) of an object in free fall. The measured values are: 10.56, 9.52, 9.73, 9.80, 9.78, 10.91.The students want to state that the absolute deviation of each measured value xfrom the mean is at most
d. Find the value of
d.
a pyramid with a square base of length 3cm and height 16cm
Deidre is 5 feet 4 inches tall and her weight is 135 pounds. her bmi is closest to _____ kg/m2.
Find the volume of the composite solid. Round your answer to the nearest hundredth.
A.239.24cm^3
B.246.08cm^3
C.294.03cm^3
D.308.78cm^3
A new truck that sells for $25,000 depreciates (decreases in value) 11% each year. What will be the value of the truck in 2 years
Answer:
Price of Truck after 2 year = $ 19802.50
Step-by-step explanation:
Given: Price of truck = $ 25,000
Price depreciate at rate of 11% in a year
To find: Price of truck after 2 years
If we let Price of truck to be P = $ 25000
And Rate of deprecation to be R = 11%
And time to be n = 2
now by using formula of deprecation, we get
[tex]A=P\times(1-\frac{R}{100})^n[/tex]
[tex]A=25000\times(1-\frac{11}{100})^2[/tex]
[tex]A=25000\times0.7921[/tex]
A = $ 19802.50
Therefore, Price of Truck after 2 year = $ 19802.50
What is the average of 5.24,6.875,3.298,5.7,4.98? Round the answer to 2 decimal points
The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x) • g(x).
A. 2x3 − x2 + 4x − 3
B. x2 − 4x + 3
C. 2x3 − x2 − 4x + 3
D. 2x3 − 4x2 + 3
in 2003, a gallon of gas cost $1.75. In 2013 a gallon of gas cost $3.25. Write an equation to model this situation.
To model the situation of the gas prices in 2003 and 2013, we can use a linear equation. The equation to model this situation is y = $0.15x - $298.70.
Explanation:To model the situation of the gas prices in 2003 and 2013, we can use the equation of a linear relationship between the year (x) and the cost of gas (y). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m):
The change in cost of gas is $3.25 - $1.75 = $1.50The change in years is 2013 - 2003 = 10Therefore, the slope (m) is $1.50 / 10 = $0.15.
Next, let's find the y-intercept (b):
Using the point (2003, $1.75), we can substitute the values into the equation and solve for b:$1.75 = $0.15(2003) + b
b = $1.75 - $0.15(2003)
b = $1.75 - $300.45
b = -$298.70
Therefore, the equation to model this situation is y = $0.15x - $298.70, where x is the year and y is the cost of gas.
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Sharon needs 64 credits to graduate from her community college. So far she has earned 24 credits. What percent of the required credits does she have?
A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. Hence, Sharon has [tex]12.5[/tex]% of the credits required.
What is the percentage?
A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. It is often denoted using the percent sign, "%".
Here given information:-
Sharon needs [tex]64[/tex] credits and he earned [tex]24[/tex] credits.
So,
[tex](\frac{24}{64})[/tex]×[tex]100[/tex][tex]=\frac{1}{8}[/tex]×[tex]100[/tex]
[tex]=0.125[/tex]×[tex]100[/tex]
[tex]=12.5[/tex]%
Hence, Sharon has [tex]12.5[/tex]% of the credits required.
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14-3x=4x solve and explain
The african bush elephant weighs between 4.4 tons and 7.7 tons. What are its least and greatest wieghts rounded to the nearest ton
based on the pattern of the drawings which conjecture is reasonable to make?
A. when a pair of parallel lines is intersected by a third line, the corresponding angles are complementary
B. when a pair of parallel lines is intersected by a third line, all of the angles formed are congruent.
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
D. when a pair of parallel lines is intersected by a third line, the corresponding angles are supplementary.
the 2 angles in each picture are the same - meaning they are congruent,
so the answer is:
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
Conjectures are simply opinions from a given information.
The conjecture that can be formed is: C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
From the three diagrams, we can see that:
[tex]\mathbf{30^o = 30^o}[/tex][tex]\mathbf{35^o = 35^o}[/tex][tex]\mathbf{50^o = 50^o}[/tex]From the figures above, we have the following observations
The angles are congruentThe angles are correspondingThe congruence of the angles is based on parallel lines, intersected by a third line (i.e. the transversal)Hence, the conjecture that can be formed is: option (c)
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The relative frequency of a car travelling through a road junction having exactly two occupants is 0.26.If 5,000 cars are observed passing through the junction, how many of the cars could be expected to have only two occupants?
A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each representing a different lake. The points are widely dispersed on the scatterplot with no pattern of grouping. Interpret what the results of the scatterplot tell you about the relationship between the two variables.
Answer:
Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.
Step-by-step explanation:
Bill Payne visits his local bank to see how long it will take for $1,000 to amount to $1,900 at a simple interest rate of 12 ½%. Provide Bill with the solution to his problem in years. A. 6.5 years B. 7.2 years C. 12.5 years D. 10.2 years
What is the surface area of a cylinder whose radius is 3 inches and whose height is 10 inches? Round to the nearest tenth.
SA = 2π r2 + 2π rh
A. 226.1 square inches
B. 241.8 square inches
C. 244.9 square inches
D. 543.3 square inches
PLEASE HELP
Solve for x.
−32>−5+9x
Enter your answer, as an inequality, in the box.
Inequality is a statement of an ordered relationship
The value of x as inequality is less than -3.
x < -3 is our answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
Example:
x > 3
y < 5
x ≤ 6
y ≥ 2
We have,
-32 > -5 + 9x
Add 5 on both sides.
-32 + 5 > -5 + 9x + 5
[ -32 + 5 = -27 ]
-27 > 9x
Divide both sides by 9.
-27/9 > 9x/9
-9 x 3 / 9 > 9x / 9
-3 > x
This can be written as:
x < -3
Thus,
The value of x as inequality is less than -3.
i.e x < -3
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Help me i hate word problems
Which statement is true about the equations –3x + 4y = 12 and x – y = 1?
The system of the equations has exactly one solution at (–8, 3).
The system of the equations has exactly one solution at (–4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
Answer:
C
Step-by-step explanation:
Its C just did the test