Answers
5[1-[tex](2/3)^{8}[/tex]/1-2/3] can be used to evaluate the series 8 E k=1 5 (2/3) k-1 through geometric series.
What do you mean by geometric series?A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios. In other words, the following term is obtained by multiplying each phrase in a geometric series by a constant.
Hence, a geometric series has the formula a, ar, ar2, where an is the first term and r are the sequence's common-ratio. Either a positive or negative integer can be used to describe the common ratio.
The given series is:
Now,we want to write an expression that can be used to evaluate this series.
Since this is a geometric series, we use the formula for the sum of the first k terms: Sk = a (1-[tex]r^{k}[/tex]/1-r)
From the given series the first term a= 5 is, and the common ratio is r =2/5 and k=8
We substitute the values to obtain:
S8= 5[1-[tex](2/3)^{8}[/tex]/1-2/3]
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Related Questions
dibuja una línea desde cada ecuación hasta la propiedad de igualdad que ilustra
Answers
Answer:
Lo siento, como modelo de lenguaje de IA, no tengo la capacidad de visualizar o dibujar gráficos. ¿Puedo ayudarte con algo más?
Brainliest for correct answer
Answers
Answer:
C 38.1 ft hope this helps
A few years ago, Sarah acquired a parcel of land valued at $14,300 . Today, that same parcel of land has a value of $15,444 . Find the percent increase in the property's value. Round your answer to the nearest hundredth, if necessary.
Answers
The percent increase in the vaIue οf the parceI οf Iand is 8%.
Tο find the percent increase in the vaIue οf the parceI οf Iand, we need tο determine the difference between the current vaIue and the οriginaI vaIue, and then express that difference as a percentage οf the οriginaI vaIue.
What is the fοrmuIa fοr percent increase?percent increase = (new vaIue - οId vaIue) / οId vaIue x 100%
PIugging in the vaIues given in the prοbIem, we get:
percent increase = ($15,444 - $14,300) / $14,300 x 100%
percent increase = $1,144 / $14,300 x 100%
percent increase = 0.08 x 100%
percent increase = 8%
Therefοre, the percent increase in the vaIue οf the parceI οf Iand is 8%.
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K-3/10 =1 The K-3/10 is a fraction
Answers
Answer:
K = 13
Step-by-step explanation:
We must solve for K
K - 3 / 10 = 1
Multiply both sides by 10
K - 3 = 10
K = 10 + 3
K = 13
he three data sets have the same mean and range, but is the variation the same? Prove your answer by computing the standard deviation. Assume the data were obtained from samples. (a) 4, 5, 11, 13, 13, 14 (b) 5, 7, 10, 10, 13, 15 (c) 3, 10, 11, 11, 12, 13
Answers
The standard deviations of the data are different.
Standard deviation:
The formula used to calculate the standard deviation of data is given by
Standard deviation = √[ ∑(x[tex]_{i}[/tex] - x)² /n ]x - mean of the data and n = number of observations
Here we have
(a) 4, 5, 11, 13, 13, 14
Mean of the data = [4 + 5 + 11 + 13 + 13 + 14 ]/6 = 60/6 = 10
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 96
=> √[ ∑(x[tex]_{i}[/tex] - x)²/n ] = √[ 96/ 6 ] = 4
(b) 5, 7, 10, 10, 13, 15
Since the mean of the data is equal for all
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 68
=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 68/ 6 ] = 3.36
(c) 3, 10, 11, 11, 12, 13
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 64
=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 64/ 6 ] = 3.26
Therefore,
The standard deviations of the data are different.
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What is 2^-2 equal to?
A. -4
B. -1/16
C. 1/4
D. 1/2
Answers
Answer:
best of my knowledge hope its right -4
Step-by-step explanation:
John is seven years younger than his sister Ann. The sum of their ages is 45. Find John's age. (you do not
need to write the equations)
Answers
Answer:
John is 19 and Ann 26
Step-by-step explanation:
to be for real i just counted
Ocean City bike rental shop charges a $17 fixed fee plus $6 an hour for renting a bike Jessica paid $65 to rent a bike how many hours did she pay to have to write checked out ?
Answers
Answer:
8 hours
Step-by-step explanation:
To solve for the number of hours (h) Jessica paid, we can use this expression:
(65 - 17) ÷ 6 =?Why do we do this?We do this because in order to find the total number of hours spent renting the bike, we need to take the total amount of money spent and subtract the fixed fee from it. Then, we divide by 6 to get the total number of hours spent.
Solving what is in the parenthesis:
(65 - 17) ÷ 6 =?48 ÷ 6 =?8Therefore, Jessica spent 8 hours renting the bike.
Step by step
Your equation can be set up in slope intercept form y = mx + b
m is slope or rate of $6 /hour
b is y intercept or fixed cost of $17
y = $65 paid
x = the unknown hours of bike rental
65 = 6x + 17
Subtract 17 from both sides to isolate variable
65 - 17 = 6x + 17 - 17
Simplify
48 = 6x
Divide both sides by 6 to solve for x
48/6 = 6/6 x
Simplify
8 = x hours of bike rental
The cost of one burrito b, and one taco a is less than the cost of two burritos. Which
inequality represents this relationship?
b+a<2b
b+a
b+a> 2b
b + a ≤ 2b
Answers
Answer:
The inequality that represents this relationship is:
b + a < 2b
y= 4x^(3/2)+x^(1/2)
Find the differential of the function.
dy=
Answers
The differential of the function is dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
How to find the differential of the function.From the question, we have the following parameters that can be used in our computation:
y= 4x^(3/2)+x^(1/2)
Using the first principle of differentiation, we have
dy/dy = 3/2 * 4x^(3/2 - 1) + 1/2 * x^(1/2 - 2)
Evaluate the expressions
dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
Hence, the solution is dy/dy = 6x^(1/2) + 1/2x^(-1 1/2)
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Sally is going to Seattle for the summer. She has $9,999 and a plane ticket to Seattle from Destin,Fl costs $837. How much money does she have left over to spend?
Answers
Answer:
To find how much money Sally has left over to spend, we need to subtract the cost of the plane ticket from her starting amount of money:
$9,999 - $837 = $9,162
Therefore, Sally has $9,162 left over to spend after buying the plane ticket to Seattle.
Answer:
oh yes she has $9162 to spend ,
63, 00, 22,------? find out next number
Answers
The next number is 47, 1, and 27 in the sequence.
What is a number series?A number series is a sequence of numbers. To answer the questions regarding number series, we must first establish the rules that lead to the production of a number series.
The reverse of 63 is 36.
The sum of the digits of 63 is 6 + 3 = 9.
So, the following number is 36 + 9 = 45, followed by the next odd number, 47. Hence the following number is 47.
The reverse of 00 is 00.
The sum of the digits of 00 is 0 + 0 = 0.
So, the following number is 0 + 0= 0, followed by the next odd number, 0. Hence the following number is 0.
The reverse of 22 is 22.
The sum of the digits of 22 is 2 + 2 = 4.
So, the following number is 22 + 4 = 26, followed by the next odd number, 27. Hence the following number is 27.
Therefore, the next number is 47, 1, and 27 in the sequence.
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
Answer:
Step-by-step explanation:
its 1
What is the vertical asymptote and horizontal asymptote pic attached below
Answers
The required horizontal and vertical asymptote is x = 2, -2, and y = 1/4.
How to find Asymptotes?To find the vertical asymptotes of the given rational function, we need to look for values of x that make the denominator zero, since division by zero is undefined.
The denominator of the function is 4(x-2)(x+2), so the vertical asymptotes occur at x = 2 and x = -2. Therefore, the vertical asymptotes are:
x = 2, -2
To find the horizontal asymptote, we can use the fact that as x goes to positive or negative infinity, the function approaches the ratio of the leading coefficients of the numerator and denominator.
In this case, the leading term in the numerator is x² and the leading term in the denominator is 4x². Therefore, as x approaches positive or negative infinity, the function approaches:
y = (x² / 4x²) = 1/4
So, the horizontal asymptote is:
y = 1/4
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
[tex]f(x) = x^{2} -5x + 12[/tex]
The graph of the function is a parabola → true
____
The value of f(–10) = 82 → false[tex]f(-10) = (-10)^{2} -5(-10) + 12 = 100+50+12 = 162 \neq 82\\[/tex]
The graph of the function opens down → false The graph contains the point (20, –8) → false[tex]f(20) = (20)^{2} -5(20) + 12 = 400-100+12 = 312 \neq - 8\\[/tex]
The graph contains the point (0, 0) → false[tex]f(0) = 0^{2} -5(0) + 12 = 0 - 0 + 12 = 12 \neq 0\\[/tex]
Pls help asap rewarding Brainliest
Answers
Im not fully sure but it might be the 3rd one!
Which graph represents the solution to the inequality 0.5 is greater than or equal to the product of a number and −0.25?
A. number line with closed circle on 0.5 with arrow shaded right
B. number line with open circle on point on negative 0.5 with arrow shaded left
C. number line with closed circle on negative 2 with arrow shaded right
D. number line with open circle on 2 with arrow shaded left
Answers
Option C i.e. number line with closed circle on negative 2 with arrow shaded right represents the solution to the inequality.
What is inequality?
An inequality is a comparison relationship between two or more mathematical expressions.
We are given an inequality as 0.5 is greater than or equal to the product of a number and −0.25.
Let the number be x.
So, from the above information, we get the inequality as
0.5 ≥ -0.25x
Now, on solving the above inequality, we get the following
0.5 ≥ -0.25x
On multiplying by -1, we get
⇒-0.5 ≤ 0.25x
On dividing both sides by 0.25, we get
⇒-2 < x
Hence, Option C i.e. number line with closed circle on negative 2 with arrow shaded right represents the solution to the inequality.
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Jim was preparing for a marathon. He ran 5 3/8 miles on the first day, 7 1/3 miles the second, and 12 1/2 the third day. How far did he run altogether
Answers
Answer: Jim ran 25 1/4 miles altogether.
Step-by-step explanation: I saw him do it.
Need help ASAP
the value of each variable. If your answer is not
teger, express it in simplest radical form.
The length of a is
The length of b is
(Simplify your answer.)
Answers
Answer:
me too (help)
Step-by-step explanation:
f(t)= 5-2t is the answer -39.1%
Answers
Yeah, your right the answer would be -39.1%
if 9% of a number equals 10 find 27% of that number
Answers
Answer:
30
Step-by-step explanation:
You divide the number so 10 by 9 giving you the 1% of it and then you times that number by 27 to get 27%.
Answer:
30
Step-by-step explanation:
9%*3=27%
10*3=30
or more simply what you do to one you have to do to the other.
WILL GIVE BRAINLIEST
(Theoretical Probability MC)
Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.
List 1 List 2 List 3 List 4
O
0,0 0,0 0,0
G
O, GO, GO, G
B
O, B O, BO, B
G, O G, OG, O
G, B
G, B
G, B
G, G
G, G
G, G
B, B
B, BB, B
B, GB, GB, G
B, O B, O
G, O
O, B
G, B
Which list gives the sample space for pulling 2 marbles from the bag with replacement?
List 1
List 2
List 3
List 4
Answers
Here are the possible outcomes of randomly drawing two marbles from the bag:
O, G
O, B
G, O
G, B
B, O
B, G
There are six possible outcomes in total, each with an equal chance of occurring. Therefore, the theoretical probability of drawing an orange marble and a green marble from the bag is 1/6 or approximately 0.167.
. A survey was conducted to determine the types of occupations of the 1,200
residents of a town. The types of occupations are shown in the circle graph.
Occupations
Retail
25%
Education
15%
Industry
25%
Other
30%
Government
Based on the circle graph, how many more residents have an occupation in
industry than have an occupation in government?
A.360
B.300
C.240
D. 20
Answers
240 more residents have an occupation in industry than have an occupation in government. The solution has been obtained by using arithmetic operations.
It is believed that the four fundamental operations, often referred to as "arithmetic operations", can describe all real numbers. The four mathematical operations that produce the quotient, product, sum, and difference are divide, multiply, add, and subtract.
We are given a graph determining the types of occupations of the 1,200 residents of a town.
Percentage of residents having occupation in government is:
100% - 25% - 15% - 25% - 30% = 5%
Number of residents having occupation in industry is as follows:
25% of 1200 = 300
Similarly, number of residents having occupation in government is:
5% of 1200 = 60
Number of more residents that have occupation in industry than have an occupation in government is:
300 - 60 = 240
Hence, 240 more residents have an occupation in industry than have an occupation in government.
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The circle graph was missing in the question which has been attached below.
Need help on solving this math problem!!
Answers
Answer:Hello!-47 s the answer :)
Step-by-step explanation:
Tonya says that her favorite number is 44. Pena says that Tonya's number is 9 more than her favorite number.
Write an equation to represent the relationship between Tonya’s and Pena’s favorite
numbers.
Answers
Answer:
Let's assume Pena's favorite number as "p".
According to the problem, Tonya's number is 9 more than Pena's favorite number, so Tonya's favorite number would be p + 9.
But Tonya says her favorite number is 44, so we can write:
p + 9 = 44
This equation represents the relationship between Pena's and Tonya's favorite numbers.
please help me with trigonometry
Answers
The length of the guy wire to the nearest foot would be = 10 ft.
How to calculate the length of the guy wire?The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.
The distance from the stake to the pole (opposite) =a = 5 ft
The distance from the pole to the tower (adjacent) =b= 9ft
The length of the guy wire= c = X
Using the Pythagorean formula:
c² = a² + b²
c² = 5² + 9²
c² = 25+81
c² = 106
C = √106
C= 10 ft ( to the nearest foot)
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Complete question:
A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.
Determine whether the study is an experiment or an observational study, and then identify a major problem with the study.
In a survey, 1465 Internet users chose to respond to this question posted on a newspaper's electronic edition: "Is news online as satisfying as print and TV news?" 52% of the respondents said "yes."
Question content area bottom
Part 1
This is an
▼
experiment
observational study
because the researchers
▼
do not attempt to modify
apply a treatment to
the individuals.
Part 2
What is a major problem with the study?
A.
This is a convenience sample with voluntary response, which has a high chance of leading to bias.
B.
There is no blinding or replication, which has a high chance of leading to bias.
C.
The sample is not very large.
D.
The results apply only to Internet users
Answers
The study is classified as an observational study, and the problem is given as follows:
A.
This is a convenience sample with voluntary response, which has a high chance of leading to bias.
What are experiments and observational studies?Experiments are studies in which there are two groups, with different features, and then the effect of a feature is studied.
For an observational study, there are no changes, just a question is asked, as is the case for this problem.
Convenience samples lead to bias as many people that share characteristics can answer.
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The number of trout in a stocked lake is given by the
equation T = 1800 (1.15)n where n is the number of months since the start of the trout season.
a. How many trout will there be in 2.5 months?
b. How many trout were there 2 months before the season opened?
Answers
a. To find the number of trout in 2.5 months, we can substitute n = 2.5 into the given equation:
T = 1800 (1.15)^n
T = 1800 (1.15)^2.5
T ≈ 2708.67
Therefore, there will be approximately 2,709 trout in the lake after 2.5 months.
b. To find the number of trout 2 months before the season opened, we need to use a negative value of n that represents the time before the start of the trout season. If we assume that the start of the season is month 0, then 2 months before the start of the season would be month -2. Thus, we can substitute n = -2 into the given equation:
T = 1800 (1.15)^n
T = 1800 (1.15)^(-2)
T ≈ 980.92
Therefore, there were approximately 981 trout in the lake 2 months before the start of the trout season.
Need help with number 90
Answers
Answer:
a = 16.5
b = 8.8
Step-by-step explanation:
Write an equation for the line shown in the graph (ik the picture is blurry but help me if you know)
Answers
By answering the above question, we may state that As a result, the coordinates graph's line has the equation y = (4/5)x + 11/5.
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
In order to determine the line's equation, we must first determine the slope (m) of the line using the following formula:
m = (y2 - y1) / (x2 - x1) (x2 - x1)
where the coordinates of the two sites the line travels through are (x1, y1) and (x2, y2), respectively.
In place of the values we hold:
m = (7 - 3) / (6 - 1) (6 - 1)
m = 4 / 5
Now that we have the slope, we can solve the equation of a line using the point-slope form, which is:
y - y1 = m(x - x1) (x - x1)
where one of the locations the line travels through is (x1, y1).
y - 3 = (4/5)(x - 1) (x - 1)
y = (4/5)x - 4/5 + 3 y = (4/5)x + 11/5 is equal to y - 3 = (4/5)x - 4/5.
As a result, the graph's line has the equation y = (4/5)x + 11/5.
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