we can always get the common ratio of a geometric sequence by simply dividing the current term by the previous term, in this case for the sake of simplicity let's divide 2/3 by 2, so
[tex]\cfrac{2}{3}\div 2\implies \cfrac{2}{3}\div \cfrac{2}{1}\implies \cfrac{2}{3}\cdot \cfrac{1}{2}\implies \cfrac{1}{3}\impliedby \textit{common ratio}[/tex]
so the sequence more or less looks like [tex]2~~,~~\cfrac{2}{3}~~,~~\cfrac{2}{9}~~,~~\cfrac{2}{81}~~,~~\cfrac{2}{243}[/tex]
so we'd want the sum of the first 5 terms
[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\\\ S_5=2\left( \cfrac{1~~ - ~~(\frac{1}{3})^5}{1~~ - ~~\frac{1}{3}} \right)\implies S_5=2\left( \cfrac{~~\frac{242}{243}~~}{\frac{2}{3}} \right)\implies S_5=\cfrac{242}{81}\implies S_5=2\frac{80}{81}[/tex]
On Thursday, Tyler's math teacher helped her write the expression t = -2(3 + h) to represent the temperature change for that day. Circle all of the expressions below that are equivalent to t = -2(3 + h).
a. t = 6 - 2h
b. t = 4h-6h - 6
c. t = -2h - 6
d. t = h(3.5 – 5.5) + (-6)
Answer:
-2 * 3 = -6
-2 * h = -2 h
C) is equivalent to this result
Write each expression without the absolute value symbol |3x+12|
Answer:
3x+12 if x>-4
0 if x=-4
-3x-12 if x<-4
1x4-9-5/9+100-0+0x67x0 brianlest first answer
The sum of a number $x$ and 4 equals 12.
An equation that represents this sentence is
.
Answer:
(3 x 1) x 4 = 12
Can somebody please help me? :(
Answer:
143 square meters
Step-by-step explanation:
The surface has a width of 11 meters and a length of 13 meters.
13 x 11 = 143.
Is this correct?
Find x.
A) 32
B) 8
C) 16
D) 24
Answer: D
Step-by-step explanation:
4x−4<8 AND 9x+5>23
Doing Khan Academy
HelP!!
Answer:
x<3 and x>2
Step-by-step explanation:
write the symbols this < and > to get the correct answer
Distrubutive property
1. 54+27=9 (_+_)
Answer:
9(6+3) = 54+27
Step-by-step explanation:
dunno how to explain but hope the answer helps
Hey there!
54 + 27 = 81
9(6 + 3)
= 9(6) + 9(3)
= 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9
= 18 + 18 + 18 + 18 + 9
= 36 + 36 + 9
= 72 + 9
= 81
Thus, the equation answwr is: 81
Therefore, the overall answer is:
9(6 + 3)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Please Help! Will Give Brainlest! Locks In an Hour! Please try again if brainly Deletes your Answer!
Answer:
The answer to your question would be -0.383
Step-by-step explanation:
I have no idea why it's deleting my answers, but that's the best choice.
et
Which is true regarding Armando's use of algebra tiles?
O He used the algebra tiles correctly.
He did not represent the two original factors correctly.
O The signs on some of the products are incorrect.
O Some of the products do not show the correct powers
of x.
Answer:
The Last One
Step-by-step explanation:
hope this helps :))
Unit 4: Congruent Triangles Homework 2: Angles of Triangles
The value of the third angle that can be found in the information given about the congruent triangles will be 45°.
How to solve the triangle?From the complete information, the angles that are given in the triangle are 76° and 59°.
It should be noted that the value of the total angles that are in a triangle is 180°. Therefore, the value of the last angle will be:
= 180° - (76° + 59°)
= 180° - 135°
= 45°
Learn more about triangles on:
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How many 3 digit numbers can be formed by 0; 2; 4; 5; 7 such that the digits are divisible by 5 and the repetition of any number is not allowed
Answer:
Three digit number to be divisible by 5 , the last digit should be 5 or 0
_ _ _5
Two remaining places can be filled in 4×3=12
_ _ _0
Two remaining places can be filled in 3×3=9 (0 cannot be filled in the first place, it will become 2 digit number).
Total =12+9=21
There are 6 orange marbles, 2 red marbles, 3 white marbles, and 4 green marbles in a bag. Once a marble is drawn, it IS replaced. Find the probability of selecting 2 orange marbles in a row P(orange, orange). Write your answer as a simplified fraction
The probability of selecting two orange marbles with replacement is 36/169.
Data;
Orange= 6Red = 2Green = 4Probability with replacementSince after each draw, the orange marble is replaced.
The total number of marbles in the bag is
6+3+4 = 13
And the number of orange marbles is 6.
For the first selection, the probability of selecting one orange is
[tex]P = \frac{6}{13}[/tex]
After drawn and replaced, the probability of selecting another marble is
[tex]P = \frac{6}{13}[/tex]
And the probability of selecting two orange marbles with replacement is
[tex]P = \frac{6}{13} * \frac{6}{13} = \frac{36}{169}[/tex]
The probability of selecting two orange marbles with replacement is 36/169.
Learn more on probability here;
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what do you call the statements that are assumed to be true and do not need proof?
Answer:
A postulate :)
Step-by-step explanation:
This is because a postulate is a statement that is assumed true without proof, while a theorem is a true statement that can be proven.
Hope this helps!
How long is 10% of a 24-hour day?
Answer:
2.4 hour is 10%
Step-by-step explanation:
Because 10% is equal to 0.1 24÷ 10% =2.4
If you were to buy a $1,000 computer in Tennessee, how much would it cost in
Williamson County? How much would you save if you bought it in Davidson County?
This refers to the tax paid to a governing body for the sales of certain goods and services.
In Williamson County, the sales tax rate is 9.75% = 9.75% × $1,000 = $1,097.5
In Davidson County , the sales tax rate is 9.25% = 9.25% × $1,000 = $1,092.5
The amount saved will therefore be $1,097.5 - $1,092.5 = $5.
Read more about Sales tax here https://brainly.com/question/9437038
can you please help me?
Answer:
$91.30
Step-by-step explanation:
Hours worked on Monday: 8.30 hours (4.15 in the morning and 4.15 in the afternoon)
8.30 hours x $11 per hour: $91.30
find the simple interest #70000 for 7 1/2 at 3% per annum
Answer:
I think 1575000 but not sure sorry if i'm wrong
I will give BRAINILEST
Answer:
The players club is playing with the players
Step-by-step explanation:
give me a good Answer to my Question
What is the scale factor of this dilation? a:1/2 b:2/3 c:3/4 d:3/2
The number of people at last Saturday's Norchester City game was 12 400. Season ticket holders made up 3/8 of the crowd. How many season ticket holders were there?
Answer:
4,650.
Step-by-step explanation: If the total number of people at the game is 12,400 and 3/8 of those people were Season ticket holders. You simply multiply 12,400 x (3/8).
I’m very confused I hate this
Answer:
12
Step-by-step explanation:
its as easy as this:
what is 4 times 3?
12
Answer: the answer is 12 .
Step-by-step explanation: multiply 4 shirts times 3 shorts will give you 12 . HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST
.THANKS .
Consider 4(2x + 3) = 2(4x + 6) after each
side of the equation is simplified.
Why does the equation have infinitely many
solutions?
Hope this helps you
Good luck
What is the formula of the curved surface of a cylinder?
Answer:
2πr × h = 2πrh
Step-by-step explanation:
that is the formula for a curved surface of a cylinder 2πr × h = 2πrh.
!Need answer quickly!
The preimage of the triangle (yellow) has the following coordinates:
A. (3,-4) (red dot)
B. (9,0) (yellow dot)
C. (7,-6) (blue dot)
Describe the translation from the preimage to the image and include how the x and y values of the ordered pairs changed. (Please put real answer or else I'll report you)
Answer:
(x-5;y+6)
Step-by-step explanation:
1) the difference between the coordinates before translation and after the translation is*: Δx=-5; Δy=+6, then
2) the rule of the translation is: (x-5;y+6).
* for example, the red dot. The difference for X is: -2-3=-5. The difference for Y is: 2--4=+6.
A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. What is the 90% confidence interval for the population mean? Use the table below to help you answer the question. Confidence Level 90% 95% 99% z*-score 1. 645 1. 96 2. 58 Remember, the margin of error, ME, can be determined using the formula M E = StartFraction z times s Over StartRoot n EndRoot EndFraction. 128. 75 to 147. 25 130. 98 to 145. 02 132. 10 to 143. 90 137. 38 to 138. 62.
The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
Suppose that we have:
Sample size n > 30Sample mean = [tex]\overline{x}[/tex]Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Then the confidence interval is obtained as
Case 1: Population standard deviation is known[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown.[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}[/tex]
For this case, we're given that:
Sample size n = 90 > 30Sample mean = [tex]\overline{x}[/tex] = 138Sample standard deviation = s = 34Level of significance = [tex]\alpha[/tex] = 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).At this level of significance, the critical value of Z is: [tex]Z_{0.1/2}[/tex] = ±1.645
Thus, we get:
[tex]CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90][/tex]
Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
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Which strategy would most help minimize the risk of being underinsured
The strategy that would most help minimize the risk of being underinsured is to take a higher deductible.
What is a deductible?It should be noted that a deductible simply means the amount that paid by an individual before the insurance holder will give the expenses.
In this case, the strategy that would most help minimize the risk of being underinsured is to take a higher deductible.
Learn more about deductible on:
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#SPJ1
Answer:
choosing max coverage
Step-by-step explanation:
Directions: Find each missing measure. 1.
Answer:
1. 19 Degrees
2. 63 Degrees
3. 37 Degrees
4. 119 Degrees
5. 69 Degrees
6. 71 Degrees
7.1 65 Degrees
7.2 48 Degrees
7.3 42 Degrees
Step-by-step explanation:
Angles in a triangle always add up to 180 degrees. (180-79-82=19 for the first one)
The little box in a triangle represent 90 degrees.
7.2 Vertical Angles are equal to each other
Hey, need to solve for x
2(x-3)=9x+8
Answer:
x = -2
Step-by-step explanation:
2x-6 = 9x+8
-7x = 14
x = -2
PLEASE RATE!! I hope this helps!!
Please help me!! I will mark you brainliest!
Answer:
Step-by-step explanation:
Right off the bat, you will know the lowest number is 52 and the highest number is 65, therefore there will act as the guides for your box and whisker plot. This eliminates answers B and C because they are not accurate to that.
Next, we find the median of the set of numbers by crossing out (writing it down, or imagining doing so) the numbers on either end consecutively to until you reach the center number, ours being 58. This eliminates answer A.
This leads us to belive answer D is the correct box and whisker plot.
Is (3, 1) a solution to this system of equations?
3x + 3y = 12
12x + y = 13
Yes or no
Answer: No
Step-by-step explanation:
(3,1) is not a solution because when plugging in x=3 and y=1 to the second equation, you get: 12(3) + 1 = 13 → 36 + 1 = 13 → 37 = 13, which is false.