The maximum possible side length of the base of the building is; C: 71 feet.
How to determine the maximum side length of a Pyramid?The given parameters of the new building in the shape of a square pyramid that is to be constructed are as follows:
Base is expressed as b
Slant height (l) is expressed as 5b
The lateral surface area of the square pyramid is calculated from the formula given as;
LSA = 2bl
Thus, the lateral surface area is expressed as;
L = 2 * b * 5b
L = 10b²
The total surface area is calculated using the formula:
T = L + b²
Thus, plugging in the value of 10b² for L gives the total surface area as;
T = 10b² + b²
T = 11b²
The maximum surface area is 50,000 square feet and so we can find b from the following expression;
11b² = 50000
Divide both sides of the equation by 11 to get;
b² = 50000/11
b = √(50000/11)
b = 71 feet to the nearest foot.
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I need help on how to solve for Z
Answer:
[tex]z=\frac{t^{2}(m-3) }{4}[/tex] or [tex]z=\frac{1}{4}t^{2} (m-3)[/tex]
Step-by-step explanation:
[tex]t=\sqrt{\frac{4z}{m-3} }[/tex]
[tex]t^{2} =\frac{4z}{m-3}[/tex]
[tex]4z=t^{2} (m-3)[/tex]
[tex]z=\frac{t^{2}(m-3) }{4}[/tex]
Hope this helps
These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
Town B
10 15 20
H
5
ㅏ
20
30
30
40
55
55
05 10 15 20 25 30 35 40 45 50 55 60
Degrees (F)
The correct option regarding the data-sets represented by the box and whisker plots is:
B. The distribution for town A is positively skewed, but the distribution for town B is symmetric.
What does a box-and-whisker plot shows?A box and whisker plot shows three things:
The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.For data-set A, we have that:
The 25th percentile is of 15.The median is of 20.The 75th percentile is of 30.Since 30 - 20 > 20 - 15, the distribution is positively skewed.
For data-set B, we have that:
The 25th percentile is of 20.The median is of 30.The 75th percentile is of 40.Since 40 - 30 = 30 - 20, the distribution is symmetric.
Hence the correct option is:
B. The distribution for town A is positively skewed, but the distribution for town B is symmetric.
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Morgan is designing a rectangular quilt. The quilt will be 1 3/5 meters wide and will have an area of 6m 2 (To the power). How long is the quilt?
Answer:3 3/4 meters
Step-by-step explanation:
6/(1 3/5)=3.75 meters or 3 3/4 meters
What is [tex]\frac{3}{4}[/tex] - [tex]\frac{2}{b}[/tex]
The answer is [tex]\boxed {\frac{3b - 8}{4b}}[/tex].
3/4 - 2/b3(b) - 2(4) / 4(b)3b - 8 / 4bA variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix.
A number line goes from 65 to 115. Crackers's whiskers range from 70 to 100, and the box ranges from 75 to 85. A line divides the box at 80. Cookies's whiskers range from 70 to 115, and the box ranges from 90 to 105. A line divides the box at 100.
Which statement is true about the box plots?
The interquartile range of the trail mix data is greater than the range of the cracker data.
The value 70 is an outlier in the trail mix data.
The upper quartile of the trail mix data is equal to the maximum value of the cracker data.
The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
The statement that is true about the box plots is: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
What is a Measure of Variation?For a data distribution that is displayed by a box plot, the measure of variation that can be used to describe the data distribution is the interquartile range.
What is the Interquartile Range of a Data Distribution?Interquartile range, which is a measure of variation can be determined from a box plot by finding the value of the third quartile and first quartile, the finding their difference. The difference is the interquartile range.
Interquartile range = third quartile - first quartile.
Interquartile range for crackers = 85 - 75
Interquartile range for crackers = 10
Interquartile range for trail mix = 105 - 90
Interquartile range for trail mix = 15.
The bigger the value of the interquartile range, the more variation there is that exist in a data distribution.
Interquartile range for trial mix is the largest, therefore, the statement that is true about the box plots is: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
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What is the independent variable in the following function?
The independent variable of f(c) = -3c + 9 is c
What are variables?Variables in an equation are the unknown parameters of the equation that change in values
There are two types of variables
Dependent variableIndependent variableHow to determine the independent variable?The equation of the function is given as
f(c) = -3c + 9
The dependent variable is the output of the function, while the independent variable is the input of the function
For the function, f(c) = -3c + 9
The input variable is c
Hence, the independent variable of f(c) = -3c + 9 is c
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Select the correct answer what are the solutions of this quadratic equation x^2+8x+3=0
Answer:
x= -4 + radical 13
Step-by-step explanation:
‼️‼️‼️‼️HELP‼️‼️‼️‼️‼️‼️‼️
Michael took a drive down to the beach and drove at a pace of 45mph on the way there. The trip took him 3 hours. He drives the exact same route on the way back, but takes it slow so he can enjoy the sunset. If Henry's return trip took him 4 hours, how fast was he driving on his return?
Michael took the return trip at a velocity 33.75 miles per hour.
How fast did Michael drive in his return trip?
Let suppose that Michael drove in straight line road and at constant velocity. Therefore, the speed of the vehicle (v), in miles per hour, can be defined as distance traveled by the vehicle (d), in miles, divided by travel time (t), in hours.
First trip
45 = s / 3 (1)
Second trip
v = s / 4 (2)
By (1) and (2):
45 · 3 = 4 · v
v = 33.75 mi / h
Michael took the return trip at a velocity 33.75 miles per hour.
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Use the wave equation to find the speed of a wave given by y(x,t) = (9. 13 mm) sin[(6. 65 m-1)x - (5. 52 s-1)t]
The speed of the wave is 0.83 m/s.
According to the statement
we have given that the equation and we have to find the speed of the wave.
So, For this purpose, we know that the
The given equation is y(x,t) = (9. 13 mm) sin [(6. 65 m^-1)x - (5. 52 s^-1)t]
Then we have to find the speed of the wave
So, Comparing y(x,t) = (9. 13 mm) sin[(6. 65 m-1)x - (5. 52 s-1)t]
to the general expression y(x,t)=y m sin(kx−ωt),
Because the general expression is y(x,t)=y m sin(kx−ωt)
we see that k= 6.65 m −1 and ω= 5.52 rad/s.
The speed of the wave is
v=ω/k=(5.52 rad/s)/(6.65 m )= 0.83 m/s
So, The speed of the wave is 0.83 m/s.
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What is the slop of the line?
[tex]3y - 5x = 10[/tex]
Find the gradient of the linear relation
Isolate y
3y=5x+10y=5/3x+10/3Compare to slope intercept form y=mx+b
Slope=m=5/3
Answer:
[tex]\dfrac{5}{3}[/tex]
Step-by-step explanation:
To find the gradient (slope) of the given linear relation, use arithmetic operations to isolate y:
Given relation:
[tex]3y-5x=10[/tex]
Add 5x to both sides:
[tex]\implies 3y-5x+5x=10+5x[/tex]
[tex]\implies 3y=5x+10[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]
[tex]\implies y=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]
Slope-intercept form of a linear equation
[tex]y = mx+b[/tex]
where:
m is the slope (gradient)b is the y-interceptComparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.
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HALP AFAP PLSSS
Figure A is a scale image of figure B. what is the value of x?
Using proportions, it is found that the value of x is of 5.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, since Figure A is a scale of Figure B, the side lengths are proportional, hence the following rule of three is established:
x/12.5 = 2/5
Applying cross multiplication:
5x = 25
x = 5.
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A contractor is excavating a ramp into a trench for a construction project. How much dirt will the crew have to remove? To answer, find the volume of the triangular prism in the figure shown. Opening 4 x 6, ramp 8'deep
Write an expression containing x2-terms, x-terms and constants. The
x2-terms should combine to −2x2 the x-terms should sum to 3x,
and the constants should sum to 3.
[tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
Like terms are terms whose variables (and their exponents such as the 2 in [tex]x^{2}[/tex]) are the same. Like terms can easily be added and substracted. Such questions just need like terms to be bought together and simplified
Infinite number of equations or expressions can be written for the given question. So writing one possibility for the given question,
= [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex]
which sums up to
= [tex]-2x^{2} +3x+3[/tex]
Thus [tex]7x^{2} - 9x^{2} +8x-5x + 10-7[/tex] is the given expression
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In your own words, define the unit rate in an equation of proportional relationship y= kx.
Answer:
hdchyf
Step-by-step explanation:
fhyrb ufgfyg hchybgvtct ugh
A friend of mine believes that the average GPA at KSU is equal to 3.0. In order to test whether he/she is right, I collect some information from the data. Specifically, I use 100 KSU students to form a sample and find that their sample average GPA is equal to 3.3. In addition, suppose that I also know the population standard deviation of GPA at KSU is 1.5. I decide to use 0.05 as the level of significance for my hypothesis testing. Could you help me with Q1-Q10 below? Q1: What should be my null hypothesis? What should be my alternative hypothesis? Q2: Is this a lower-tailed, upper-tailed or two-tailed case? Q3: Show me how to calculate my test statistic.
Q4: If I use the critical value approach, explain how to derive my critical value(s). Q5: If I use the p-value approach, explain how to derive my p-value. Q6: If I use the confidence interval approach, show me how to derive the confidence interval. Q7: How to make my decision, if I use the critical value approach? Q8: How to make my decision, if I use the p-value approach? Q9: How to make my decision, if I use the confidence interval approach? Q10: Are the decisions in Q7, Q8, and Q9 the same?
The solution of the questions is given as
a)
The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)
b)
This is a case with two separate arguments. (This is a two-tailed case)
c)
Test Statistic is given by:
z= 2.00
d)
Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.
e)
, p-value = 0.0455
f)
CI= (3.006, 3.594)
g)
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
h)
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
i) Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.
j)
The choices you choose in Questions 7, 8, and 9 are identical.
What is the null hypothesis?a)
The null hypothesis states that mu equals 3.0. ( the average GPA at KSU is equal to 3.0) (Claim)
The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)
b)
This is a case with two separate arguments.
c)
Test Statistic is given by:
[tex]z=\frac{\barx-u^0}{σ/Vn}\\\\z=33 - 3.0/1.5/V100[/tex]
z= 2.00
d)
[tex]\alpha = 0.05[/tex]
Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.
e)
Z Score = 2.00
reading from table, p-value = 0.0455
f)
Confidence Interval:
[tex]CI= \barx \pm \frac{ZX\sigma }{\sqrt((n)}[/tex]
[tex]CI =3.3 \pm 1.96 x 1.5 / \sqrt{100}[/tex]
CI= (3.006, 3.594)
g)
The disparity is noteworthy given that the computed value of Z = 2.00 is higher than the crucial value of z = 1.96. Cast doubt on the null hypothesis.
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
h)
The difference may be considered statistically significant since the p-value of 0.0455 is lower than the alpha threshold of 0.05. Cast doubt on the null hypothesis.
Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.
i)
The difference is statistically significant since the value of 3.0 is not included in the confidence range (3.006 - 3.594). Cast doubt on the null hypothesis.
Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.
j)
The choices you choose in Questions 7, 8, and 9 are identical.
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If f(x + 1) = x + 2 then f(x - 1) is
Answer: [tex]\Large\boxed{f(x-1)=x}[/tex]
Step-by-step explanation:
Given function
f(x + 1) = x + 2
Isolate [ x + 1 ] on the right-hand side
f(x + 1) = x + 1 + 1
f(x + 1) = (x + 1) + 1
Substitute [ x + 1 ] with x
f(x) = x + 1
Substitute [ x ] with [ x - 1 ]
f(x - 1) = (x - 1) + 1
[tex]\Large\boxed{f(x-1)=x}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Figure 222 is a scaled copy of Figure 111.
PLEASE HELP
Identify the side in Figure 222 that corresponds to side \overline{CD}
CD
start overline, C, D, end overline in Figure 111.
Choose 1 answer:
Choose 1 answer:
! What are modern numbers? and how are they used?
Modern numbers are the ten numerical digits used in constructing other numbers.
What are modern numbers?Modern numbers are also called Arabic numerals. They are the ten numerical digits:
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Uses of modern numbers;
They are used as symbols to write decimal numbers.They are used in writing numbers in other systems like the octal, and for writing identifiers such as computer symbols, trademarks, or license plates.They are used in constructing other numbers.Hence, modern numbers are the ten numerical digits used in constructing other numbers.
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Which of the following linear equations corresponds to the table above?
O A. y = 4x - 3
O B. y=¹/4 x-3
OC. y=1/4x+3
OD. y = 4x + 3
The linear equations that corresponds to the table is y = 4x + 3
How to determine the linear equation?The missing table of values in the complete question is given as:
x y
0 3
3 15
7 31
10 43
Start by calculating the slope of the equation using
m = (y2 - y1)(x2 - x1)
Substitute the values on the table in the above equation
m = (15 - 3)/(3 - 0)
Evaluate the difference
m = 12/3
Evaluate the quotient
m = 4
The linear equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 4(x - 0) + 3
Evaluate the expression
y = 4x + 3
Hence, the linear equations that corresponds to the table is y = 4x + 3
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HELP Given the set of all odd integers from 1 to 81, what is the probability
of choosing a number that is a multiple of 9?
If you enter your answer as a decimal, round to the thousandths place.
Using it's concept, the probability of choosing a number that is a multiple of 9 is of 0.111.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
From 1 to 81, there are 81 numbers, of which 81/9 = 9 are multiples of 9, hence, considering that 81 is the number of total outcomes and that 9 is the number of desired outcomes, the probability is given the following division:
p = 9/81 = 1/9 = 0.111.
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if y=mx+b, find m and use the formula for the previous question to find m when the coordinates are (4,7) and b=12
Answer:
m = -5/4
Step-by-step explanation:
In the slope-intercept form formula, y = mx + b, substitute 4 for x, 7 for y, and b for 12 to solve for m.
y = mx + b
7 = 4m + 12
-5 = 4m
m = -5/4
How many lattice points (points with integer coordinates) are on the line segment whose endpoints are $(3,17)$ and $(48,281)
Any line through the points [tex](a,b)[/tex] and [tex](c,d)[/tex] has
[tex]\gcd(c-a,d-b)+1[/tex]
lattice points. In this case, the count is GCD(45, 264) + 1.
Using Euclid's algorithm, we have
264 = 5•45 + 39
45 = 1•39 + 6
39 = 6•6 + 3
6 = 2•3 + 0
so that GCD(45, 264) = 3. Then there are 3 + 1 = 4 lattice points.
PLEASE HELP ME QUICKLY!! IM BEING TIMED
The sum of 2 numbers is 36. The first number is twice the second number. Find the second number
Answer: 24+12=36
Step-by-step explanation:
36= _+_
2x(2 times)
x
X+2x=36
3x=36
12
12+2(12)=36
12+24=36
Answer:
The value of the second number is 24 and the first no 12.Step-by-step explanation:
Greetings !From, the given word explanation try to create your own equation like
x + y = 36... (1) let the two numbers be x and y respectively.2x = y ....(2) let x be the first no and it's twice that of the second number.From, equation (1) solve for x
x + y = 36x = 36-y... (3)Substitute, equation (3) to equation (2).
2(36-y) =y72 - 2y =y72 = y + 2y.... solve for y72 = 3y.... divide both sides by 372/3 = y..y=24 ...simplifiedIf six cans of soda cost nine dollars, how much would it cost for 8 cans.
Answer:
Solution:
here,
6 cans cost = 9 dollars
1 can costs = 9÷6 dollars
= 1.5 dollars
Now,
8 cans cost = 8×1.5 dollars
= 12 dollars
There is 1 pint of liquid in this container. if another pint were added, how much liquid would there be? a) 2 cups b) 1 pint c) 1 quart d) 2 gallons
Answer:
C: 1 Quart
Step-by-step explanation:
2 pints are the equivalent of 1 quart
Answer:1 Quart
Step-by-step explanation: Because 2 pints equals=1 quart
Find the quotient.
18.)97.2
Answer:
540
Step-by-step explanation:
540 =18% of 97.2
Done please
it's quotient it's a synthax error..
Evaluate the following integral (Calculus 2) Please show step by step explanation!
Answer:
[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x=-\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle \int \dfrac{\ln x}{x^8}\:\:\text{d}x[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
Using Integration by parts:
[tex]\textsf{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]
[tex]\textsf{Let }\dfrac{\text{d}v}{\text{d}x}=x^{-8} \implies v=-\dfrac{1}{7}x^{-8+1}=-\dfrac{1}{7}x^{-7}=-\dfrac{1}{7x^7}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x^{-8}\ln x\:\:\text{d}x & = -\dfrac{1}{7x^7}\ln x- \int -\dfrac{1}{7x^7} \cdot \dfrac{1}{x}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7x^8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}+ \int \dfrac{1}{7}x^{-8}\:\:\text{d}x\\\\& = -\dfrac{\ln x}{7x^7}-\dfrac{1}{7 \cdot 7}x^{-8+1}+\text{C}\\\\& = -\dfrac{\ln x}{7x^7}- \dfrac{1}{49x^7}+\text{C}\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Differentiating $\ln x$}\\\\If $y=\ln x$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
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Substitute [tex]y=\ln(x) \iff e^y = x[/tex] and [tex]dy=\frac{dx}x[/tex] to get
[tex]\displaystyle \int \frac{\ln(x)}{x^8} \, dx = \int ye^{-7y} \, dy[/tex]
Integrate by parts with
[tex]u = y \implies du = dy[/tex]
[tex]dv = e^{-7y} \, dy \implies v = -\dfrac17 e^{-7y}[/tex]
Then
[tex]\displaystyle \int u\,dv = uv - \int v\,du \\\\ \implies \int y e^{-7y} \, dy = -\dfrac17 ye^{-7y} + \frac17 \int e^{-7y} \, dy + C \\\\ ~~~~~~~~~~~~ = -\frac17 ye^{-7y} - \frac1{49} e^{-7y} + C \\\\ ~~~~~~~~~~~~ = \boxed{-\frac{\ln(x)}{7x^7} - \frac1{49x^7} + C}[/tex]
URGENT!!! What happens to the graph of y=−x6−6x5+50x3+45x2−108x−108 as x heads toward ∞ and −∞?
A. as x→∞, y→−∞ as x→−∞, y→−∞
B. as x→∞, y→∞ as x→−∞, y→∞
C. as x→∞, y→∞ as x→−∞, y→−∞
D. as x→∞, y→−∞ as x→−∞, y→∞
Using limits, the correct option regarding the end behavior of the function is given by:
A. as x→∞, y→−∞ as x→−∞, y→−∞.
How to find the end behavior of a function f(x)?The end behavior is found calculating the limit of f(x) as x goes to infinity.
For this problem, the equation is given by:
[tex]f(x) = -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108[/tex]
Since x goes to infinity, we consider only the term with the highest exponent, hence the limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow -\infty} -x^6 = -(-\infty)^6 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow \infty} -x^6 = -(\infty)^6 = -\infty[/tex]
Hence the correct option is:
A. as x→∞, y→−∞ as x→−∞, y→−∞.
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Please answer quickly!
19) The sum of the arithmetic series is - 397. (Correct choice: E)
33) The sum of the geometric series is 1700. (Correct choice: E)
How to determine the sum of a given series
19) Arithmetic series are sets of elements generated by a linear expression of the form:
aₙ = a₁ + (n - 1) · d (1)
Where:
aₙ - n-th term of the seriesa₁ - First term of the series n - Index of the n-th term of the series.d - Change between two consecutive elements of the series.If we know that a₁ = 27, n = 20 and d = - 5, then sum of the first 20 terms of the series is:
x = 27 + 22 + 17 + 12 + 7 + 2 + (- 3) + (- 8) + (- 13) + (- 18) + (- 23) + (- 28) + (- 33) + (- 38) + (- 43) + (- 48) + (- 53) + (- 58) + (- 63) + (- 68)
x = - 397
The sum of the arithmetic series is - 397. (Correct choice: E)
33) Geometric series are sets of elements generated by a exponential expression of the form:
aₙ = a₁ · rⁿ (2)
Where:
aₙ - n-th term of the seriesa₁ - First term of the seriesr - Ratio between two consecutive elements of the series.If we know that a₁ = 1458 and r = 1 / 3, then the sum of the first 6 terms of the geometric series is:
x = 1458 + 162 + 54 + 18 + 6 + 2
x = 1700
The sum of the geometric series is 1700. (Correct choice: E)
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