The first five terms of the geometric sequence is 6, 18, 54, 162 and 486
Geometric progression is given by:
[tex]nth\ term=ar^{n-1}[/tex]
where a is the first term, r is the common ratio
Given that first term is 6, and common ratio is 3, Hence a = 6, r = 3
[tex]First\ term=6\\\\Second \ term=6(3)^{2-1}=18\\\\Third \ term=6(3)^{3-1}=54\\\\Fourth \ term=6(3)^{4-1}=162\\\\Fifth \ term=6(3)^{5-1}=486[/tex]
The first five terms of the geometric sequence is 6, 18, 54, 162 and 486
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A 15 kg ball is thrown into the air. It is going at 4m/s when thrown. How much potential energy will it have at the top?
Answer:
P.E = mgh = 120N
Step-by-step explanation:
v² = u² - 2as
At the top, the velocity is = 0
0² = 4² - 2 x 10 x s
4² = 20s
s = 16/20
s = 0.8metres.
It rose only 0.8metres.
Therefore P.E = 15 x 10 x 0.8
:. P.E = 15 * 8
:. P.E = 120N
What is the greatest exponent in the expression 8x-x^2+9-3x^4+5x?
Answer:
4
Step-by-step explanation:
trIangle ABC was reflated over y-axis. the coordinate of point A are(6,-4). what are the coordinate of A
Answer:
(-6,-4)
Step-by-step explanation:
Rule for reflection over the y axis (x,y) -----> (-x,y)
Explanation of rule : change the sign of the x value and keep the y value the same.
Applying rule to given coordinate
(6,-4) -----> change the sign of 6 to get -6 and keep -4 as it is -----> (-6,-4)
Refer to the attached image for more validation. Note that x=0 is the y axis
6x +16 >=51 kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Answer:
5.83333333
Step-by-step explanation:
6x + 16 = 51 (If that is what you actually intended to put)
6x + 16 - 16 = 51 -16
6x/6 = 35/6
x=5.83333333
Look at the graph below. What is the x-intercept?
Answer:
-3
Step-by-step explanation:
Whatever number the line passes on the x-intercept is the answer:)
Which value of x makes the following equation true?
4.8(x - 4) = -0.2x + 15.8
A. 6
B. 10
C. 7
D. 9
Answer:
C
Step-by-step explanation:
multiply through by 10
10{4.8(x-4)} = 10(-0.2x) + 10(15.8)
48(x-4) = -2x + 158
48x - 192 = -2x +158
48x + 2x = 158 + 192
50x = 350
divide through by 50
x=350/50
x=7
therefore, answer = C
A particle moves along the x-axis so that at time t ≥ 0 its position is given by x(t) = 2t3 - 21t2 + 72t - 53. At what time t is the particle at rest?
Step-by-step explanation:
The particle is at rest when the derivative of x(t), which is its velocity, is zero, i.e.,
[tex]\dfrac{d}{dt}[x(t)] = \dot{x}(t) = 0[/tex]
Since [tex]x(t) = 2t^3 - 21t^2 + 72t - 53,[/tex] its derivative is
[tex]\dot{x}(t) = 6t^2 - 42t + 72[/tex]
Equating this to zero, we get
[tex]6t^2 - 42t + 72 = 0 \Rightarrow t^2 - 7t + 12 = 0[/tex]
This is a familiar quadratic equation whose roots are
[tex]t = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]\;\;\;= \dfrac{7 \pm \sqrt{(7)^2 - 4(1)(12)}}{2}[/tex]
[tex]\;\;\;= \dfrac{7 \pm 1}{2}[/tex]
[tex]\;\;\;= 3\;\text{and}\;4[/tex]
This means that the particle will be at rest at t = 3 and t= 4.
Consider the equation of a circle If the line is its diameter. Then find the value of a.
Answer:
more info??? bc that doesn't make sense i guess
Solve for the value of X
Check the picture below.
A store sells laptops for $720 each. This price is 20 percent more than what it cost the store to buy each of them. Before the next model's release, store employees can purchase any remaining laptops at 23% off the store's cost. How much would it cost an employee to purchase one of these laptops at the sale? PLS HELP
It would cost an employee $443.52 to purchase one of these laptops at the sale.
The selling price of the laptops is $720 each. The cost price is 20 percent more than the cost price.
Cost price = Selling price - 20% of cost price
Cost price = 720 - 20% * 720 = $576
At the release, the laptops are at 23% off the store's cost. Hence:
Price of laptop at release = 576 - 23% of 576
Price of laptop at release = $443.52
It would cost an employee $443.52 to purchase one of these laptops at the sale.
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Because Aaron, age 32, is a smoker, he must pay more for life insurance. Given that Company A charges 20% more for smokers, Company B charges 18% more for smokers, Company C charge 25% more for smokers and Company D charges 15% more for smokers, Aaron decides to buy his $250,000 policy from Company B. Which of the following statements is true? A 5-column table with 3 rows titled Annual Insurance Premiums (per 1,000 dollars of face value) 10 year term. Column 1 is labeled age with entries 30, 31, 32. Column 2 is labeled Company A with entries 1.30, 1.57, 1.86. Column 3 is labeled Company B with entries 1.29, 1.55, 1.86. Column 4 is labeled Company C with entries 1.40, 1.64, 2.07. Column 5 is labeled Company D with entries 1.49, 1.88, 2.25. a. Aaron is paying the smallest premium possible with Company B. b. Aaron is paying $93 more in premiums than he would with Company A. c. Aaron is paying $129 more in premiums than he would with Company C. d. Aaron could have chosen any company because the premiums are all the same. Please select the best answer from the choices provided A B C D
Answer:
answer B
Step-by-step explanation:
becuase b is bad for you
A doughnut shop sells 30 kinds of doughnuts. In how many ways can you get a bag of 12 doughnuts if you want at least 3 glazed doughnuts and at least 4 raspberry doughnuts
Answer:
86493225
Step-by-step explanation:
Hope it helps
If an angelfish is 6/5 inches, how many feet is it? I'm literally going to give you 100 points.
Answer:
0.1 foot
Step-by-step explanation:
1 inch = 0.083 foot
Formula: divide the length value by 12
So, multiply 0.083 to [tex]\frac{6}{5}[/tex]
[tex]\frac{6}{5} = 1.2[/tex]
1.2 × 0.83 = 0.996
approximatlry, 0.996 = 0.1
Therefore, [tex]\bold{\frac{6}{5}}[/tex] inches are equal to 0.1 foot.
A mother earned $8750 from royalties on her cookbook. She set aside 20% of this for a down payment on a new home. The balance will be used for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) that earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $420, how much money was invested at each rate?
Answer:
Step-by-step explanation:
The problem statement is not clear regarding which money is invested. We will assume it is the 80% of $8750 that is set aside for future education. That amount is
... 0.80 × $8750 = $7000
If x represents the amount invested at 7%, then the total interest earned is
... (7000 -x)×4% + (x)×7% = 420
... 280 +0.03x = 420
... x = 140/0.03 ≈ 4666.67
$4666.67 was invested at 7%.
$2333.33 was invested at 4%.
How do I do this? It's a modulus question.
help i need help look at question
Answer:
A
Step-by-step explanation:
because 12 is the smallest number/angle
If Alex is 14 years old, and Ben is 17 years old, in how many years will the sum of their ages be 169 years?
Answer:
69 years
Step-by-step explanation:
Sum of Alex's and Ben's current age
= 14 +17
= 31 years
For every year, Alex and Ben will each be one year older. Thus, 2 years would be added to the sum of their ages with each passing year.
Difference in the sum of their ages
= 169 -31
= 138 years
Number of sets of 2 years
= 138 ÷2
= 69
Thus, the sum of their ages will be 169 in 69 years.
An airplane can ascend at a rate of 50 1/2 meters in 2/3 of a second. How many meters can the airplane ascend in one second?
Answer:
78.75
Step-by-step explanation:
i need help plz help
Answer:
I believe its the nucleus
Step-by-step explanation:
Not entirely sure though, but its what I would pick
s.p. is 4000, profit is 25% than find c.p.please explain itt
[tex] \sf= \frac{100}{100 + 25} \times 4000 \\ = \frac{100}{125} \times 4000 \\ = \frac{4}{5} \times 4000 \\ = 4 \times 800 \\ = 3200[/tex]
[tex] \huge \sf \: Answer[/tex]
The cost price is 3200.
Hope you could get an idea from here
Doubt clarification- use comment section.
A bike path is 12.5 miles. Dominic is 70% of the way to the end. How far is Dominic on the path?
Pls help me
Answer:
p/12.5 = 70/100
Step-by-step explanation:
a percent is considered out of 100
since you know the total 12.5, that will fit as the whole
I been on this for days and no one can give me a right answer
Answer:
2x²=6x-5= x=3+i/2
-x²-10x=34= x = -(5+3i)
Step-by-step explanation: 2x²=6x-5 and -x²-10x=34 are the answers
Which answer shows the correct solution for 6x + 19x - 4 = 5(5x + 4)?
No solution
Infinitely many
One solution
Answer:
No solution
Step-by-step explanation:
25x-4=5(5x+4)
Distributive Property= 25x-4=25x+20
Solve for x
-4=20
Not possible so no solution.
Answer:
A
Step-by-step explanation:
6x + 19x -4 = 5(5x+4)
6x + 19x -4 = 25x+20
6x + 19x- 25x = 20+4
Combine Like terms
0 = 20 +4
0 = 24
0 = 24 = No solution
HELP PLEASE I REALLY NEED IT
Answer:
18
Step-by-step explanation:
1/2 bh
1/2 (6)(6) multiply
1/2 (36) divide
18
Two researchers, Justin and Henry, work together to study what proportion of subjects have a certain genotype in the population. They each collect a simple random sample and they find that the sample proportion is 0.70. When they construct a confidence interval based on this sample proportion, Henry comes up with (0.632, 0.768) while Justin gets (0.652, 0.788). Indicate which interval has to be wrong and why.
Using confidence interval concepts, it is found that Justin is wrong, as his interval is not symmetric about the sample proportion of 0.7.
A confidence interval has two bounds, a lower bound and an upper bound. A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds. The margin of error is the difference between the two bounds, divided by 2.In this problem, the point estimate is of 0.7.
Henry's interval is symmetric, as [tex]0.768 - 0.7 = 0.7 - 0.632[/tex].Justin's is not, as [tex]0.788 - 0.7 \neq 0.7 - 0.652[/tex].Hence, Justin is wrong, as his interval is not symmetric about the sample proportion of 0.7.
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A survey of 600 nurses yielded the following information: 427 were health club members, 325 were smokers, and 245 of the health club members were smokers. How
many of the 600 surveyed nurses were health club members or were smokers?
The number of surveyed nurses that were health club members or were smokers is 316.
Let the total number of nurses be 600 nursesn(U) = 600Let H be health club members, n(H) = 427Let S be smokers, n(S) = 325If 245 of the health club members were smokers, then n(HnS) = 245 members.
The number of surveyed nurses that were health club members or were smokers = 600 - [(427 - 325) + (427-245)].
The number of surveyed nurses that were health club members or were smokers = 600 - (102+182) = 600 - 284.
The number of surveyed nurses that were health club members or were smokers is 316.
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Bill wanted to know how many times students at his middle school go to the beach each week during the summer. He surveyed every other middle school student at the mall last Saturday. After analyzing the data collected, Bill determined that the average student from his middle school goes to the beach about 2.4 times a week during the summer. What error did he make in the survey?
The survey was intended for Bill's middle school during the summer. The
survey was administered to students of other schools on a Saturday.
The type of error is the selection bias error.Reasons:
The type of error made is a non sampling error, given that the target of the
study is the number of times in a week students at his middle school
attend the beach during the summer.
The errors are; Selection bias error.
The given that the students survey are not from his middle school.The survey was carried out once on a Saturday, where the target was during the summer.The selection bias error is a type error that is due to the researcher
chooses what to study, such that the participant have common
characteristics rather than being random.
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What is g(x)?
10-
у
5
X
+
10
d
A
-5
-10
A. g(x) = -1x1
B. g(x) = -x
C. g(x) = -x2
D. g(x) = -2X
C
Step-by-step explanation:
This has a U like shape so it a parabola.
Parabola correlate with quadratic functions
[tex]y = {ax}^{2} + bx + c[/tex]
Since it Going down, the answer is C -x^2.
The function whose graph is given is g(x) = -x²
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that a graph, we need to find its function,
Since, the graph is a curve opened downwards, so it is a parabola, opened downwards,
The equation of the parabola is given by y = ax²+bx+c
Therefore, out of the given options we can say that the function is y = x²
Hence the function whose graph is given is g(x) = -x²
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Crater Lake in Oregon is shaped like a circle with a diameter of about 5.5 miles
a. How far is it around the perimeter of Crater Lake
b. What is the area of the surface of Crater Lake?
Give a step by step explanation please
Answer:
The perimeter of a circle is calculated with 2πr
The r stands for radius. The radius is half of the diameter.
So r=2.25
Plug it in 2π(2.25)
It was simplify to 4.5π
Which would simplify down to 14.14 miles rounding to the nearest hundredth.
80 is the product of Diego's height and 5.
Use the variable d to represent Diego's height.
Answer: The expression is 5d = 80. 80 ÷ 5 = 16. Therefore, the variable D is 16.