Answer:
1. The first three terms of the geometric sequence are 1, 5, 25
2. Sum of the 7th terms of the geometric sequence is 19531
Step-by-step explanation:
We'll begin by calculating the common ratio (r). This can be obtained as follow:
For Arthmetic sequence:
First term (a) = 1
3rd term (T₃) = a + 2d
3rd term (T₃) = 1 + 2d
13th term (T₁₃) = a + 12d
13th term (T₁₃) = 1 + 12d
For Geometric sequence:
First term (a) = 1
2nd term (T₂) = ar
2nd term (T₂) = 1 × r
2nd term (T₂) = r
3rd term (T₃) = ar²
3rd term (T₃) = 1 × r²
3rd term (T₃) = r²
From the question given above,
The first term of the arithmetic sequence is also the first term of the geometric sequence.
The 3rd term of the arithmetic sequence is the 2nd term of the geometric sequence i.e
3rd term (T₃) = 2nd term (T₂)
1 + 2d = r
The 13th term of arithmetic sequence is the 3rd term of the geometric sequence i.e
13th term (T₁₃) = 3rd term (T₃)
1 + 12d = r²
SUMMARY:
1 + 2d = r .... (1)
1 + 12d = r²..... (2)
Substitute value of r from equation 1 into equation 2
1 + 12d = (1 + 2d)²
1 + 12d = 1 + 2d + 2d + 4d²
1 + 12d = 1 + 4d + 4d²
Rearrange
1 – 1 + 4d – 12d + 4d² = 0
–8d + 4d² = 0
4d² – 8d = 0
4d(d – 2) = 0
d = 0 or 2
Since the common difference (d) can not be 0, thus, is 2
Substitute the value of d into equation 1
1 + 2d = r
d = 2
1 + 2(2) = r
1 + 4 = r
r = 5
Thus, the common ratio (r) is 5
1. Determination of the first three terms of the geometric sequence.
First term (a) = 1
Common ratio (r) = 5
2nd term (T₂) = ar
2nd term (T₂) = 1 × 5
2nd term (T₂) = 5
3rd term (T₃) = ar²
3rd term (T₃) = 1 × 5²
3rd term (T₃) = 1 × 25
3rd term (T₃) = 25
Thus, the first three terms of the geometric sequence are 1, 5, 25
2. Determination of the sum of 7th terms of the geometric sequence .
1, 5, 25
First term (a) = 1
Common ratio (r) = 5
Number of term (n) = 7
Sum of the 7th term (S₇) =?
Sₙ = a[rⁿ – 1]/r – 1
S₇ = 1[5⁷ – 1]/5 – 1
S₇ = [78125 – 1]/4
S₇ = 78124 / 4
S₇ = 19531
Thus, sum of the 7th terms of the geometric sequence is 19531
A box contains 1111 large marbles and 1111 small marbles. Each marble is either green or white. 66 of the large marbles are green, and 44 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.7727 = 77.27% probability that it is small or green
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
11 large + 11 small = 22 total marbles = 22 total outcomes
11 small marbles + 6 green large marbles = 17 desired outcomes.
What is the probability that it is small or green?
[tex]p = \frac{17}{22} = 0.7727[/tex]
0.7727 = 77.27% probability that it is small or green
A translation that maps the blue triangle onto the red triangle is :
Answer:
a translation of 5 units to the right followed of a translation of 2 units up.
Step-by-step explanation:
This seems to be a translation because if we measure the base of both triangles, we can see that the base of the blue triangle is 5 units long, and the base of the red triangle is also 5 units long.
To find the translation in this case, is easier to only analyze one point, so let's call A as the top vertex in the blue triangle and A' as the top vertex in the red triangle.
Here we only need to see the change between A and A'
So first, let's find the coordinates of both points.
The top vertex of the blue triangle is A (-3, 5)
The top vertex of the red triangle is A' (2, 7)
Now we need to find the difference between these points, this is the direct subtraction:
A' - A
(2, 7) - (-3, 5) = (2 - (-3), 7 - 5) = (5, 2)
So we get this, (5, 2)
This means that the translation is a motion of 5 units in the x-axis (because the number is positive, this means that the motion is in the positive x-axis)
And a translation of 2 units up.
Then the translation that maps the blue triangle into the red triangle is:
a translation of 5 units to the right followed of a translation of 2 units up.
Solve for y. y + 1 = 17 y = Submit
Answer:
y=16 bc 17 -16 =1 which if u do backward equals the same thing
and all together is
18y+1 and just leave it like that dont touch the numbers or anything bc you cant take a 1 and join it with a variable
you can only join numbers with numbers and variables with variables
What will be the total cost of treys on 2 truck when we the price of each trye is 35,00:00
Answer:
45$?
Step-by-step explanation:
(Please Help) ASAP!
POINT:30
Answer:
We have 4 triangles with base 3 and height 4 and a square with side length 3 so:
Triangles:
The area for a triangle is calculated by [tex]\frac{bh}{2}[/tex] where b is the base and h is the height so we have [tex]\frac{12}{2}\cdot 4[/tex] so we have a total area of 24.
[b]Square:[/b]
The area of a square is calculated by [tex]s^{2}[/tex] where s is the side length so we have the area is 9.
Now we put them together for the surface area so we get 24 + 9 = [tex]\boxed{33}[/tex]
Hope this helped!
(sorry for taking so long, TeX takes so long to type out(Math typesetting software))
Someone please help me!!!please give me the answer!!!
Answer:
A
Step-by-step explanation:
You can see that every hour the amount of medicine decreases by 1/2. At zero hours it is at 500 and at one hour it is at 250 and it keeps decreasing at the same rate making the answer A.
.A boat can travel 280 miles on 56
gallons of gasoline. How much
gasoline will it need to go 110 miles
Answer:
22 gallons
Step-by-step explanation:
280 miles / 56 gallons = 5 miles per gallon
110 miles/5 mpg = 22 gallons
HELP! THE ANSWER IS NOT C!
Answer:
The answer is B
Step-by-step explanation:
if correct plz mark brainliest and tell me if its wrong
An article summarized data from a survey of a random sample of a certain number of U.S. adults with investments of $10,000 or more. Based on the survey data, it was estimated that 38.5% of investors manage their investments by doing everything they possibly can online. But the authors of the article also noted that there was quite a difference between younger investors (ages 18 to 49) and older investors (ages 50 and older). For younger investors, 63% said they do everything they possibly can online, while the percentage for older investors was 28%.
A) Use the given information to estimate P(O), POLY), and P(OF) where 0 = event that a randomly selected Investor does everything possible online, Y = event that a randomly selected Investor is age 18 to 49, and F = event that a randomly selected investor is 50 years old or older.
B) Suppose that 40% of investors are between the ages of 18 and 49. Use the probabilities from part (a) and the estimate P(Y) = 0.40 to construct a hypothetical 1,000 table.
Y F Total
0
Not 0
Total 1,000
Use information in the table to calculate P(YO).
Which of the following sentences properly interprets this value in the context of this exercise?
A. The probability, given that a randomly selected investor is age 50 or older, that the investor does everything possible online is PLYO).
B. The probability, given that a randomly selected investor is age 18 to 49, that the investor does everything possible online is P(710).
C. The probability, given that a randomly selected investor does everything possible online, that the investor is age 50 or older is P(YO).
D. The probability, given that a randomly selected investor does everything possible online, that the investor is age 18 to 49 is Ayo).
E. The probability that the selected investor is age 18 to 49 is P(YO).
Answer:
Based On The Survey Data, It Was Estimated That 36% Of Investors Manage Their Investments By Doing Everything They Possibly Can Online. But The Authors Of The Article Also Noted That There Was A Quite A Difference Between . ... random sample of a certain number of U.S. adults with investments of $10,000 or more.
Step-by-step explanation:
Please make me brainiest
The height of the triangle is 3 meters longer than twice its base. Find the base and height if the area is 8 square meters. Round to the nearest hundreth.
9514 1404 393
Answer:
base: 2.18 mheight: 7.35 mStep-by-step explanation:
Let b represent the base of the triangle in meters. Then the height is ...
h = 3 +2b
and the area is ...
A = 1/2bh
8 = 1/2(b)(3 +2b)
16 = 3b +2b^2 . . . . . . . multiply by 2 and eliminate parentheses
2(b^2 +3/2b + (9/16)) = 16 + 9/8 . . . . . . complete the square
2(b +3/4)^2 = 17.125
(b +3/4)^2 = 8.5625 . . . . . divide by 2
b + 0.75 = √8.5625 ≈ 2.9262
b = -0.75 +2.9262 = 2.1762
h = 3 +2b = 7.3523
The base is about 2.18 meters and the height is about 7.35 meters.
Find the seventh term of the
geometric sequence, given the
first term and common ratio.
a_=1 and r=-2/3
[?]
Answer:
[tex]T_7 = \frac{64}{729}[/tex]
Step-by-step explanation:
Given
[tex]a =1[/tex]
[tex]r = \frac{2}{3}[/tex]
Required
Determine the 7th term
The nth term of a gp is:
[tex]T_n = a * r^{n-1[/tex]
So, we have:
[tex]T_7 = 1 * \frac{2}{3}^{7-1[/tex]
[tex]T_7 = 1 * \frac{2}{3}^{6[/tex]
[tex]T_7 = 1 * \frac{2^6}{3^6}[/tex]
[tex]T_7 = 1 * \frac{64}{729}[/tex]
[tex]T_7 = \frac{64}{729}[/tex]
For the function f(x) = 8x − 3
Find f(-3)
Answer:
-27
Step-by-step explanation:
8(-3)-3
-24-3
-27
hope this helps
Answer:
− 27
Step-by-step explanation:
Use the given functions to set up and simplify f ( − 3 ) .
Please Help......If you were to flip a coin 60 times, how many times would you expect the coin to land on heads?
Answer:
30
Step-by-step explanation:
Again there are TWO sides so it would be 50% chance of getting head, or 50% of getting tail. So it would probably be 30
Answer:
"50% of the time"
Step-by-step explanation:
Because the probability is limited to only 2 sides you have a 50% chance it will land on either heads, or tails.
Isaac Green Elimination (Level 1) Mar 17, 8:18:58 AM Find the solution of the system of equations. 8x + y = -13 8r 2y = 10
Answer:
y = 23
x = -4.5
Step-by-step explanation:
Given:
Equation
8x + y = -13 ......eq1
8x + 2y = 10........eq2
Find:
Solution
Computation:
Eq2 - Eq1
y = 23
From eq1
8x + y = -13
8x + 23 = -13
8x = -36
x = -4.5
One Positive number is five times another number the difference between the two numbers is 172 to find the numbers
Answer:
x= 43, y=215
Step-by-step explanation:
Let one number be x,
Let the other number be y.
x= 5y
x - y= 172
Putting value of x in equation 2.
5y - y = 172
4y = 172
y= 172/4
y= 43
Putting value of y in eq. 1
x= 5(43)
x=215.
Multiply the following binomials and simply your answer
(50pts!!!!!!) How would I solve this trig problem without using a calculator?
Answer:
B) 8Step-by-step explanation:
Givenx = 60°BC = 4To findAB = ?SolutionSince x = 60°, the other acute angle A is 30°
We have 30-60-90 right triangle
This triangle has side ratios:
1 : √3 : 2The ratios give us:
AB/BC = 2AB = 2*BC AB = 2*4 AB = 8Correct choice is B
Answer:
Step-by-step explanation:
B) 8
Step-by-step explanation:
Given
x = 60°
BC = 4
To find
AB = ?
Solution
Since x = 60°, the other acute angle A is 30°
We have 30-60-90 right triangle
This triangle has side ratios:
1 : √3 : 2
The ratios give us:
AB/BC = 2
AB = 2*BC
AB = 2*4
AB = 8
Correct choice is B
in order to save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother told him he can work no more than 15 hours in order to keep up with his homework. If Tom would like to make at least $75 to cover prom expenses, help him determine combinations of hours he can work between these two jobs.
a. Write and graph a system of inequalities.
b. Write two possible solutions:
I.
ii.
Answer:
6x + 7.50y ≥ 75
Step-by-step explanation:
Let x = # of hours he walks the dog
y = # of hours he washes cars
We also know that he cannot have any negative hours, so 2 lines that we need to graph will be y = 0, with everything above this line shaded in, and x = 0, with everything to the right of this line shaded in and these lines will be solid because you can have 0 hours.
Another equation will be x + y ≤ 15. We graph the line, which will be solid, y = -x + 15, and shade everything to the left of this line.
The last equation will be 6x + 7.50y ≥ 75. We graph this solid line, y ≥ (-6x + 75)/7.50 & shade everything to the right of this line. Any point inside the area shaded in by all 4 equations will be an answer. I'll leave this up to you.
Hope this helps!
Calculate the area of the given circle.
Answer:
d) 78.5 cm²Using the formula for Area of circle_
πr²
putting values_
π = 3.14
r² = (5)² = 25.
Therefore,
3.14 × 25
= 78.5
Find the missing exponent.
10
100,000
Submit
Answer:
10^4
what grade are you in
lol
I need help quick, I don't understand this question.
Right or Possible Right answers, I just need an answer.
2x+3=5` write this in statement form.`
Answer:
2 product of x & adding it from 3 is equals to 5 ..
The photo has everything
What is the reciprocal of 56/87?
Answer:
87/448
Step-by-step explanation:
Help please....................................................................
Answer:
Step-by-step explanation:
please count the multiplecation then you would look at the problem measure it into small bits
Jaylynn draws a hen on graph paper using the scale shown below. The hen has a height of 16 units in the drawing.
What is the height, in \text{cm}cmstart text, c, m, end text, of the actual hen?
Linda purchased a washing machine and dryer set for $1.299 a deferred payment plan. She needs to pay $80 per month for 6 months and the remaining balance in month 7. How much will Linda pay back in 6 months, and what will the amount of her final payment be?
Answer:
Linda will pay back $480 in 6 months. Her final payment will be $819.
Step-by-step explanation:
pls help w this question???
Answer:
1) 25
2) x=2, 1/3
Step-by-step explanation:
not sure exactly what number of real solutions means since im not in alg anymore but hope this helps. :)
A square room has a tiled floor with 225 square tiles. How many tiles are along an edge of the room?
Tiled floor with 225 square tiles means the area of the square room is 225.
Formula needed: A = (side)^2 or in short
A = s^2.
We need to find s.
225 = r^2
sqrt{225} = sqrt{r^2}
15 = r
There are 15 tiles are along an edge of the room.
Tyrone jogged 5 miles along the fitness trail. How many feet did he jog? How many inches did he jog?
Answer: Tyrone is body built so you can assume he takes very big steps so i'll say about 69 inches
Step-by-step explanation: The math is common sense
