Sum of the given geometric sequence is -100.
What is geometric sequence?A geometric sequence is the special type of sequence in which the ratio of every two successive terms is constant.
Sum of each infinite geometric sequence
-50, -25, -12.5, ...
The infinite sum of geometric sequence is given by,
[tex]s_{\infty} =\frac{a}{1-r}[/tex]
Where a is the first term in the sequence and r is the common ratio.
[tex]s_{\infty} =\frac{-50}{1-(-0.5)}[/tex]
= -100.
Hence, sum of the given geometric sequence is -100.
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how many square feet of outdoor carpet will we need for this hole 12ft 7ft 2ft 3ft
Amount of square feet of outdoor carpet needed for the hole is 6 feet².
What is Area?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Given is a triangular region with a hole in the shape of a rectangle.
We need to find the area of the hole in order to find the amount of square feet of outdoor carpet needed for the hole.
Area of a rectangle = Length × Width
From the figure,
Length = 3 feet and Width = 2 feet
Area = 3 × 2 = 6 feet²
Hence 6 feet² of outdoor carpet is needed for the hole.
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Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 3, -15, 75, ...3,−15,75,....
The explicit formula for the geometric series is [tex]a_n = 3(5)^{n-1}[/tex].
What is geometric progression?A geometric series is one in which there is a constant separating the two succeeding numbers. In other words, to create a geometric progression, each succeeding term is multiplied by the constant term.
Given that the geometric sequence is,
3, 15, 75......
The common ratio of the series is calculated as the ratio of the second term to the first term,
r = 15 / 3
r = 5
The explicit formula can be written as:-
[tex]a_n = a_1(r)^{n-1}[/tex]
[tex]a_n = 3(5)^{n-1}[/tex]
Therefore, the formula is [tex]a_n = 3(5)^{n-1}[/tex].
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The function P(n) = 108 + 10 log(n) gives the
total sound power in decibels when n drill presses are operating in a factory. What is the total sound power, to the nearest decibel, when three drill presses are operating?
112.8 is the the total sound power, when three drill presses are operating
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.
We need to find the total sound power, to the nearest decibel, when three drill presses are operating
We have to consider n as 3
P(3) = 108 + 10 log(3)
=108+10×0.477
=108+4.77
=112.77
Hence, 112.8 is the the total sound power when three drill presses are operating
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PLEASE HELP!!! ITS DUE SOON!
The solutions to the system of linear equation (x, y) are 1 and 4/3 respectively
What is system of linear equationA system of linear equations is a collection of two or more linear equations with the same variables. The goal of solving a system of linear equations is to find the values of the variables that simultaneously satisfy all the equations in the system.
From the question given;
-x + 6y = 7 ...eq(i)
6x - 30y = -34 ...eq(ii)
From eq (i)
x = 6y - 7 ..eq (iii)
Put eq (iii) into eq (ii)
6(6y - 7) - 30y = -34
36y - 42 - 30y = -34
6y - 42 = -34
6y = -34 + 42
6y = 8
y = 4/3
Put y = 4/3 into eq (i)
-x + 6(4/3) = 7
-x + 24 / 3 = 7
x = 24/3 - 7
x = 1
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A triangle has a perimeter of 9x 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle? x 13 x − 1 8x − 7 17x − 1
The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.
Perimeter of the triangle is equal to
= 9x + 6
First side of the triangle = 5x
Second side of the triangle = 3x - 7
Let 'n' be the third side of the triangle
perimeter of the triangle = 9x + 6
⇒ 5x + 3x - 7 + n = 9x + 6
⇒ n + 8x - 7 = 9x + 6
⇒ n = 9x -8x + 6 + 7
⇒ n = x + 13
Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.
The above question is incomplete , the complete question is :
A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?
a. x + 13 b. x − 1 c. 8x − 7 d. 17x − 1
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a student committee has 6 membersâ€""4 undergraduate and 2 graduate students. a subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. what is the probability that there will be no graduate students on the subcommittee?
The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in
(4 choose 3) = 4 ways.
The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in
(6 choose 3) = 20 ways.
Therefore, the probability that there will be no graduate students on the subcommittee is:
Number of subcommittees with only undergraduate students / Total number of possible subcommittees
= 4 / 20
= 1/5
= 0.2
So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
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EFGHI~ WVUTS. Find EI and ST.
I
E 16
16
H
Submit
24
24
G
T
S
U
Write your answers as decimals or whole numbers.
EI =
ST=
18
W
18
The side lengths on the similar polygons are given as follows:
EI = 16.ST = 27.What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:
18/16 = 18/EI = ST/24.
Hence the length of EI is given as follows:
EI = 16.
The length of ST is obtained as follows:
18/16 = ST/24
16ST = 18 x 24
ST = 18 x 24/16
ST = 27.
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sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to:
Sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to underestimate the true population variance and standard deviation.
The reason for this is that the sample variance and standard deviation are based on a sample of the population, not the entire population. The sample may not accurately represent the entire population, and thus the sample variance and standard deviation may not accurately reflect the true population variance and standard deviation. To correct for this bias, a correction factor is usually added to the sample variance calculation. For example, when estimating the population variance from a sample of size n, the sample variance is divided by (n-1) instead of n. This correction factor helps to provide a more accurate estimate of the population variance. Similarly, the sample standard deviation is calculated as the square root of the sample variance, and the correction factor is also applied to the sample standard deviation calculation. This corrected sample standard deviation is known as the unbiased sample standard deviation.
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Complete Question
sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to: What?
A bag contains an equal number of blue, green, pink, and red balls. If a ball is chosen at random 80 times, with replacement, predict the number of times the ball would be the color green. A.The color green would be chosen exactly 20 times. B. The color green would be chosen roughly 8 times, but probably not exactly 8 times. C.The color green would be of chosen roughly 20 times, but probably not exactly 20 times. D. The color green would be chosen roughly 10 times.
Answer: If a ball is chosen at random 80 times, with replacement, and there are an equal number of blue, green, pink, and red balls, then the probability of choosing a green ball each time is 1/4. Over many trials, the number of times a green ball is chosen would be roughly proportional to the probability of choosing a green ball, so we would expect the green ball to be chosen about 80 * (1/4) = 20 times.
However, since this is a random process, it is unlikely that the green ball will be chosen exactly 20 times. It is more likely that the actual number of green balls chosen will be slightly different, possibly higher or lower, than 20. So the answer is C: The color green would be chosen roughly 20 times, but probably not exactly 20 times.
Step-by-step explanation:
15a2+12b-9a2 Solve with step by step please
Answer:
(assuming the 2 was an exponent, if I am wrong don't use this answer) 6a^2 + 12b
Step-by-step explanation:
Add like terms
6a^2 + 12b
Given that BF =5, find FE.
According to the above, we can infer that the value of FE is: 10 cm
How to find the value of FE?To find the value of FE we must analyze the image of this triangle. Additionally, we must take into account the information we know, that is, the length of two sides (5 cm) and the height (4 cm), the area (20cm²).
So we must use the formula for the area of a triangle and isolate the values that we do know to find the value of the base.
A = b * h / 220cm² * 2 / 4 = 10cmAccording to the above, the value of segment FE is 10 cm.
Note: This question is incomplete. Here is the complete information:
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A bank account has an initial balance of $150. Over a one-week period the following occurred.
• $180 was spent on shoes.
• $300 of debt was added to the account as a cash advance.
• $250 of debt was repaid.
• $110 of debt was added because of a bank fee.
• $150 of debt was removed with a cash deposit.
What was the balance of the account at the end of the week?
To find the balance of the account at the end of the week, we need to calculate all the transactions:
Initial balance: $150
Shoes: -$180
Cash advance: +$300
Repaid debt: -$250
Bank fee: +$110
Cash deposit: -$150
So the final balance would be $150 - $180 + $300 - $250 + $110 - $150 = $-70.
This means the balance of the account at the end of the week would be -$70.
Which number is in the hundredths place 4982.6173
Answer:
1
Step-by-step explanation:
6 is tenths and after is 1 which is hundredths
Gordon currently brings in an annual salary of $92,338 and anticipates a raise of 5% every
year. What will his salary be in 3 years?
If necessary, round your answer to the nearest cent.
Answer:
Gordon will have $106892.8 in three years
Step-by-step explanation:
92338 (0.05 + 1)³=
92338(1.05)³=
92338 x 1.16 =
106892.8
Measure & T The optimal tilt for Keenan's solar panelis between 58° and 60° to the horizontal. Has Keenan placed his solar panel at an optimal angle?
Keenan has placed his solar panel at an optimal angle.
How determine if Keenan has placed his solar panel at an optimal angle?The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:
cos(C) = (a² + b² - c²) / 2ab
where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.
Check the attached image for labelling.
The angle we are trying to calculate is labelled C.
cos (C) = (20² + 18² - 19²) / (2*20*18)
cos (C) = 363/720
C = cos⁻¹(363/720)
C = 59.72°
Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.
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Complete Question
Check the attached image for complete question
HELP ASAP, WILL GIVE BRAINLIEST
Where is the above note played on the guitar?
Open second string
Open third string
Second string, first fret
Third string, second fret
Answer:
Second string, first fret.
Step-by-step explanation:
What is the formula used to calculate the surface area for a square pyramid?
The formula used to calculate the surface area of a square pyramid is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
The square pyramid is the geometric shape that has a square base and 4 lateral face. The total number of faces will be five. The base shape is square and the side shape will be triangle. Number of edges in the square pyramid is eight
The surface area is the amount space covered by the surface of the object
Here the surface area of the square pyramid is
A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
Where A is the surface area of the square pyramid
a is the base edge
h is the height of the square pyramid
Therefore, the surface area is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]
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what is the difference between 95.827 and 58.39
Answer:
37.437
Step-by-step explanation:
Answer:
37.437
Hope it helps
Find the prime factorization of
the number 90.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[ ] × [ ] × [ ] × [ ]
Enter the number that belongs in the green box.
Answer:
2 × 3 × 3 × 5 = 2 × 3 × 3 × 5
Step-by-step explanation:
The prime factorization of 90 is 2 × 3 × 3 × 5, so the prime factors are 2, 3, 3, and 5. Ordering the factors from least to greatest, we have:
2 × 3 × 3 × 5 = 2 × 3 × 3 × 5.
An online furniture store sells chairs for $100 each and tables for $450 each. Every
day, the store can ship at most 16 pieces of furniture and must sell at least $3000
worth of chairs and tables. If 9 chairs were sold, determine the minimum number of
tables that the store must sell in order to meet the requirements.
The minimum number of tables the store must sell is 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Using t and c as variables, we get
100c + 400t ≥ 3000
c+t≤16
The online furniture store must sell at least $3000 worth of chairs and tables each day, and can ship at most 16 pieces of furniture.
If the store sells 9 chairs for a total of $900, it needs to sell at least 5 tables to reach a total revenue of $3000.
Since the total number of pieces of furniture sold is 14 (9 chairs + 5 tables), which is less than the maximum of 16, the store meets the daily shipping requirement.
Therefore, the minimum number of tables the store must sell is 5.
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A certain number is multiplied by 4 and the results equals 8 less than 8 times of the number. Find the number
The number is 2. To find the unknown number that satisfies the equation "4x = 8x - 8," we can simplify and solve for x, which gives us the answer x = 2.
Let's call the unknown number "x".
According to the problem statement, "A certain number is multiplied by 4 and the result equals 8 less than 8 times of the number" can be translated into the following equation:
4x = 8x - 8
Simplifying this equation, we can move 4x to the right side of the equation:
4x - 8x = -8
Simplifying further, we get:
-4x = -8
Dividing both sides by -4, we find:
x = 2
Therefore, the number is 2.
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-11x-11 ≥ −6+13x
X <
A sled is at rest at the top of a slope 2 m high. The sled has a mass of 45 kg. What is the sled’s potential energy? (Formula: PE = mgh)
Scatter plot 8 grades, help please!!!
Answer:
Step-by-step explanation:
go up to the 85 on the grade track that over until you meet the dot.
that dot says it would be 3 hours
what is 12x - 8 + 7x + 32
Answer: 19x+24
Step-by-step explanation: 12x−8+7x+3212−8+7+32 x12+24+7
Answer: 19x +24
Step-by-step explanation:
compatible numbers are used to estimate this sum. 181 204 which estimate is the most accurate? responses 350 350 375 375 425 425 450
The most accurate estimated sum of 181 and 204 is 380
The given numbers are 181 and 204
The compatible numbers are defined as the numbers that are easy to do the arithmetic operations. The arithmetic operations are addition, subtraction, division and multiplication etc.
To find the sum of the compatible numbers first we have to round the given numbers to the nearest tens or hundreds and do the the arithmetic operation
Round 181 to the nearest tens = 180
Round 204 to the nearest tens = 200
Then the sum of compatible numbers will be
180 + 200 = 380
Therefore, the most accurate estimation is 380
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NEED THIS ASAP
Find m/EFG.
m/EFG
Answer: 41 degrees
Step-by-step explanation:
121-39=82
82/2=41
the answer is 120 I need two possible number sentences using division pls
Answer:
240/2, 360/3
Step-by-step explanation:
240/2 and 360/3 both involve division and both of their answers are equal to 120, assuming these count as number sentences.
A group of friends will watch a movie that is 115 minutes long. They watch for 42 minutes before taking a break. Which inequality represents the number of minutes, m, they will watch after the break? please help mee
Answer:
Step-by-step explanation:
Let's say that after the break, the group of friends watches m minutes of the movie.
We know that they watched 42 minutes before the break, so the total time they have watched before and after the break is 42 + m minutes.
Since the movie is 115 minutes long, the inequality that represents the number of minutes they will watch after the break is:
42 + m < 115
So, the inequality that represents the number of minutes, m, they will watch after the break is:
m < 115 - 42 = 73
This means that m has to be less than 73 for the group of friends to finish watching the movie.
Which equation represents the relationship shown in the table?
Answer:
Diatance biked = rate • time
