Need help with geometric series'!
Please include a step by step explanation.
Answers
Answer:
[tex] - 13107[/tex]
Step-by-step explanation:
We would like to evaluate the following Geometric Series ,
[tex]\displaystyle\longrightarrow \sum _{n=1}^8 (-4)^{n-1 }[/tex]
In a geometric series, a common number is multiplied to the previous term in order to find the next term . And that common number is called common ratio (r) .
As we know that ,
[tex]\displaystyle\longrightarrow \sum_{x = 1}^n f(x) = f(1) + f(2) + \dots + f(n) [/tex]
So , we can write the series as ,
[tex]\displaystyle\longrightarrow (-4)^{1-1}+(-4)^{2-1}+\dots +(-4)^{8-1} [/tex]
Simplify,
[tex]\displaystyle\longrightarrow (-4)^0 + (-4)^1+(-4)^2+\dots +(-4)^7 [/tex]
We can find the common ratio by dividing and successive term by its preceding term , as ;
[tex]\displaystyle\longrightarrow r =\dfrac{-4}{1}=-4 [/tex]
Again , here ;
First term = a = [tex](-4)^0=1[/tex]Common ratio = [tex]-4[/tex]number of terms (n) = 8And we can find the sum of geometric series using the formula , ( this is used when the value of r is less than 1 , here it is -4 ) .
[tex]\displaystyle\longrightarrow \Bigg[ Sum = \dfrac{a(1-r^n)}{1-r}\Bigg] [/tex]
where the symbols have their usual meaning.On substituting the respective values, we have;
[tex]\displaystyle \longrightarrow\rm{ Sum }=\dfrac{ 1\{1-(-4)^8\}}{1-(-4)}\\ [/tex]
Simplify ,
[tex]\displaystyle\longrightarrow \rm{Sum} = \dfrac{1-65536}{1+4}\\[/tex]
[tex]\displaystyle\longrightarrow \rm{Sum} = \dfrac{-65535}{5} [/tex]
Simplify by dividing ,
[tex]\displaystyle\longrightarrow \underline{\underline{ \rm{Sum} = -13107}} [/tex]
And we are done !
Related Questions
How many 1 / 4 pound hamburgers can be made from 9 / 12 pound of meat?
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Answer: Hi
Step-by-step explanation:
A geometry test has 30 questions. 6 of the 30 questions are based on chapter 5. What is the ratio of questions from chapter 5 to the other questions on the test?
Answers
Answer:
total question = 30
question from ch 5 = 6
remaining questions = 30-6 = 24
ratio = 6 : 24 = 1 : 4 answer
Which equation has infinitely many solutions?
A) -6.8+3y+2.4=4.3-3y
B)1/3y+2.5-2/3y=1.2
C)5.1+2y+1.2=-2+2y+8.3
D)2/5y=2.3+3/2y
Answers
Answer:
c
Step-by-step explanation:
i dont really have an explanation but i got it right
Answer:
c
Step-by-step explanation:
What is the degree of the polynomial?
Answers
Answer:
5
Step-by-step explanation:
The highest order is x^5
if the square root of the natural number from 1 to 200 are calculated, the number of whole number will be
Answers
Answer:
first 15 no. only 1,2,3,4,5,6,7,8,9,10,11,12,13,14.
(X+1)²+(x+1)(5x-3) factoriser
Answers
Answer:
Step-by-step explanation:
(x +1)² + (x +1)(5x - 3) = (x +1)(x+1) + (x +1)(5x - 3)
(x +10 is the common term. SO, we can take out (x+1)
=(x +1) [ x + 1 + 5x - 3]
=(x + 1) (x + 5x + 1 - 3) {Combine like terms}
= (x +1)(6x -2)
Due to festive season, the price of air tickets increased by 15%. If the price of one ticket was $575 during the festive season, what was its price before the festive season?
answer fast
Answers
The price before the festive season is $488.75
Data;
percentage increase = 15%ticket price = $575The Price before the festive seasonTo calculate the price before the festive season, we simply need to subtract 15% from $575.
[tex]\frac{15}{100} = \frac{x}{575} \\x = 86.25[/tex]
The increase in the ticket is $86.25., Let's calculate the price before the festive season.
[tex]$575 - 86.25 = 488.75[/tex]
The price before the festive season is $488.75
Learn more on percentage here;
https://brainly.com/question/25545513
#SPJ1
Key Features of Graphs of Functions - Part 1
1. The following statement is false. Highlight the two words that should be
interchanged to make it a true statement.
In a function, every output value corresponds to exactly one input
value.
2 The following graph fails the vertical line test and is not a function.
у
X
leg
Part A Explain how the vertical line test shows that this relation is NOT a
function. Because it has 2 lines interseding
Bart B: Name two points on the graph that show that this relation is NOT a
function. The reason its not a function is because
Answers
Answer:
See below
Step-by-step explanation:
Q1.
In a function, every output value corresponds to exactly one inputvalue.
The words to be interchanged are underlined. The function as per definition has exactly one output for each input.
Q2.
Part A
Because it has 2 same input value for 2 different output valuesPart B
The two points are (4, -2) and (4, 2)Answer:
below
Step-by-step explanation:
Question 1:
In a function, every output value corresponds to exactly one input value.
The words that should be switched around are "output" and "input". This is because every input should have have only ONE output.
Question 2:
The following graph fails the vertical line test and is not a function. (YES)
Using the vertical line test to test whether the vertical line passes through the graphed function more then once. If it does, its not a function. If it doesn't, it is a function. Sadly, the vertical lines pass the point on two separate occasions which makes it not a function.
The vertical line shows gives the points (4, 2) and (4, -2).
Best of Luck!
Joanna and Kyle went to store. Joanna bought 2 erasers and 5 pens which altogether cost $17. Kyle
bought 4 erasers and 2 pens which he paid $10 for. Calculate the cost of one eraser and the cost of one
pen.
Answers
Answer: 2x + 3= 9
Step-by-step explanation: hope it's correct well your welcome
Answer:
Erasers are $1 and pens are $3
Step-by-step explanation:
2x+5y=17
4x+2y=10
y=5-2x
2x+5(5-2x)=17
2x+25-10x=17
8x=8
x=1
plug x in and get 3 for Y
I need help.. >w<
Which answer choice shows 36.95 written in expanded form?
O A) 3 + 6 + 9 + 5
OB) 30 + 6 + 0.9 + 0.5
OC) 30 + 6 + 0.9 + 0.05
OD) 30 + 6 + 0.9 + 0.005
Answers
Answer:
O C)30+6+0.6+0.05 hope this helps
Answer:
C) 30 + 6 + 0.9 + 0.05
Step-by-step explanation:
30. 0.9. 36
+6. +0.05. +00.95
---------. -------------. ---------------
36. 0.95. 36.95
----------. --------------. --------------
36+0.95=36.95
What is the slope of the equation y= 5/4 times -7/4
Answers
Answer:
5/4
Step-by-step explanation:
If the equation is
[tex] y = \dfrac{5}{4}x - \dfrac{7}{4} [/tex]
then the slope is the number multiplying x, so
slope = 5/4.
Answer:
5/4.
The x is a variable, not a multiplication sign.
The equation is
y=mx+b
the slope is the m.
Could you show how to Graph X>2?
Answers
Answer:
I hope this helps!
Which number is a solution of 5m < 6m + 6? a. -8 b. -7 c. -6 d. -5
Answers
5m < 6m + 6
5m - 6m < 6
- m < 6
x > - 6
- 5 is ok
check
5 * (-5) = - 25
6 * (-5) + 6 = - 24
and - 25 < - 24 is correct
Eight more than the quotient of a number and 6 equals 3.
Answers
Hey there!
First of all, the quotient of a number and 6 means you divide that number by 6.
Let the number be x.
Then, eight more means you add 8:
8+(6÷x)=3
That's the answer.
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
Steps:
Create an equation with the given information. (x/6) + 8 = 3
Solve for x by simplifying both sides of the equation, then isolating the variable.
x = -30
°F represents the
The temperature was 13° F. It dropped so that the temperature was o°F
change in temperature,
°F represents the change in temperature.
Write as a fraction
Answers
Step-by-step explanation:
it dropped to Celsius degree
Solve the equation and enter the value of x below.
7x + (-2) = -44
X =
Answers
7x - 2 = - 44
7x - 2 + 2 = - 44 + 2
7x = - 42
x = -42/7
x = -6
check
7 * (-6) + (-2) = - 42 - 2 = - 44
Answer:
7x+ (-2)=-44
x= -6
Step-by-step explanation:
you're welcome
D.g(x) = - 2
9
Which equation for g(x) represents the transformation of f(x) given that f(x) = x^2
g(x) = f(x) shifted up 2 units
i have more translation of quadratics questions i need some help on so if you’re willing let me know
Answers
Answer:
g(x) = x² + 2
Step-by-step explanation:
If we want to shift a function down, we subtract the number we are asked to move outside the function's argument:
⇒ To shift f(x) b units down → f(x) - b
Similarly, in function notation, if we want to shift a function up, we add the number we are asked to move outside the function's argument:
⇒ To shift f(x) b units up → f(x) + b
Given function f(x) = x²
Shift 2 units up ⇒ x² + 2
Therefore, g(x) = x² + 2
I’m order to make a profit on the milkshakes, you need to charge $0.04 per cubic inch of ice cream. Based on information, calculate the price that you should sell each milkshake for. Here are the totals of the ice cream 50.24, 127.56, 226.08
Answers
Answer:
Step-by-step explanation:
$ 50.24
Solve the inequality. 5+5(-7x+ 1) ≥ -130 write answer in the format variable inequality number
Answers
Answer:
x<_ 4
Step-by-step explanation:
first you distribute 5 to equal 5-35x+5 then you would carry the non variables to one side to be -35x>_-140 and the you would flip the sides because te variable is negative so it would be -35x<_ -140 the divid to get x<_4
Distribute -5
5+-35x+5>-130
Combine like terms
10+-35x>-130
Subtract 10 from both sides
-35x>-140
Divide by -35 on each side
(Flip the sign since you divide by a negative)
-35x/35 > -140/35
ANSWER x is less than or equal to 4
what does x equal in the equation [tex]\frac{3}{5}x- \frac{1}{4}x=7\\[/tex]
Answers
Answer:
[tex] x = 20 [/tex]
Step-by-step explanation:
[tex] \frac{3}{5}x - \frac{1}{4}x = 7 [/tex]
The LCD is 20, so multiply both sides of the equation by 20.
[tex] 20(\frac{3}{5}x - \frac{1}{4}x) = 20 \times 7 [/tex]
[tex] 4 \times 3x - 5 \times x = 140 [/tex]
[tex] 12x - 5x = 140 [/tex]
[tex] 7x = 140 [/tex]
[tex] x = 20 [/tex]
HELP PLEASEEEE THERES PICCTURESSS
Answers
Answer:
1 a,b,c,d
2 add 8 ,divide by 5 , switch sign
3 x<4, x<6, x>13, x>-4
Step-by-step explanation:
What is the value of [3(−2)−7]÷(1.5+0.5)?
Answers
Answer: -13/2
Step-by-step explanation: hope this helps plz mark as brainliest:)
IS THIS RIGHT PLZZ HELP ME !!
Answers
Answer:
The answer would be D.
Step-by-step explanation:
The answer would be D since 3 and -3 are opposite numbers (they are the same distance in units away from 0) and they add up to 0.
Hope this helps :)
Answer: The correct answer is D
Step-by-step explanation:
It’s D because -3 and 3 equal 0.
a circle with radius of 5cm sits inside a 11cm×11cm rectangle
Answers
Answer:
The area of the shaded region is
Step-by-step explanation:
A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected Each person's weight is recorded before starting the diet and one year after it is concluded. Based on the data shown at right (weight in pounds), Can we conclude that the diet has a long-term effect, that is, that dieters manage to not regain the weight they lose? Include appropriate statistical evidence to justify your answer.
BEFORE
158 185 176 172 164 234 258 200 228 246 198 221 236 255 231
AFTER
163 182 188 150 161 220 235 191 228 237 209 220 222 268 234
Answers
Using the t-distribution, as we have the standard deviation for the sample, it is found that it cannot be concluded that the diet has a long-term effect.
What are the hypotheses tested?At the null hypotheses, it is tested if there is no difference in the weights, that is:
[tex]H_0: \mu_A - \mu_B = 0[/tex]
At the alternative hypotheses, it is tested if the weights decrease, that is:
[tex]H_1: \mu_A - \mu_B < 0[/tex]
What is the mean and the standard deviation of the distribution of the difference?Using a calculator, for each sample, we have that:
[tex]\mu_B = 210.8, s_B = 33.85, sE_B = \frac{33.85}{\sqrt{15}} = 8.74[/tex]
[tex]\mu_A = 207.2, s_A = 33.47, sE_A = \frac{33.47}{\sqrt{15}} = 8.64[/tex]
Hence, for the distribution of differences, we have that:
[tex]\overline{x} = \mu_A - \mu_B = 207.2 - 210.8 = -3.6[/tex]
[tex]s = \sqrt{sE_B^2 + sE_A^2} = \sqrt{8.74^2 + 8.64^2} = 12.3[/tex]
What is the test statistic?It is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Then:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{-3.6 - 0}{12.3}[/tex]
[tex]t = -0.29[/tex]
What is the decision?Considering a left-tailed test, as we are testing if the mean is less than a value, with a standard significance level of 0.05 and 15 + 15 - 2 = 28 df, the critical value is of [tex]t^{\ast} = -1.7[/tex].
Since the test statistic is greater than the critical value for the left tailed test, it cannot be concluded that the diet has a long-term effect, as the null hypothesis is not rejected.
To learn more about the t-distribution, you can check https://brainly.com/question/13873630
Is 2 greater than 2.5?
Answers
Answer:
2.5 means “two and five tenths”, or 2+5/10 . Adding two positive numbers together will make a number that’s larger than either of those two numbers, so 2.5 is greater than 2.
Step-by-step explanation:
2.5 is greater than 2.
Hopefully this helps you!
-Keira
ASAP NO LINKS SOLVE 2 QUESTIONS PLEASE
71. If March of a certain year has 5 Sundays, on what days of the week could St. Patrick's
Day fall? (St. Patrick's Day is March 17")
73. how many positive integers less than 1000 have the sum of the digits equal to four?
Answers
71 = When Is St. Patrick’s Day?
St. Patrick’s Day is officially observed on March 17 each year, though celebrations may not be limited to this date. The significance of March 17 is that it’s said to be the date of St. Patrick’s death in the late 5th century (circa A.D. 493).
St. Patrick’s Day Dates
Year St. Patrick’s Day
2021 Wednesday, March 17
2022 Thursday, March 17
2023 Friday, March 17
2024 Sunday*, March 17
73 = 28
Write an equation in Slope-Intercept Form of the line that is perpendicular to the graph of the given equation
and passes through the given point.
y= 4x + 8
(4,2)
Answers
Answer:
-1/4x
Step-by-step explanation:
At book fair, the ratio of adults to children is 7 : 3
The ratio of girls to boys at the book fair is 4 : 1
What percentage of the people at the book fair are boys?
Answers
The percentage of the boys at the book fair is 6%
What is a percentage?Percentages are used in mathematics as a decimal ratio expressed in a fraction of 100. It is represented with a symbol known as %.
At a book fair, the ratio of adults to children are:
7 : 3
The total number of people at the book fair = 7 + 3 = 10
The percentage of adults are:
[tex]\mathbf{=\dfrac{7}{10}\times 100\%}[/tex]
= 70% are adults
The percentage of children are:
[tex]\mathbf{=\dfrac{3}{10}\times 100\%}[/tex]
= 30% are children
However, if from the children, 4 are girls and 1 is a boy.
The total number of children at the fair = 4 + 1 = 5
The percentage of girls are:
[tex]\mathbf{=\dfrac{4}{5} \times 30\%}[/tex]
= 24%
The percentage of boys at the book fair is:
[tex]\mathbf{=\dfrac{1}{5} \times 30\%}[/tex]
= 6%
Learn more about percentages here:
https://brainly.com/question/24304697
Plzz answer I will give you brainliest and 17 points
Answers
divide 140.50 by 10
that equals 14.05
now you know what 1 click costs
multiply that by 8000
that equals 112,400
that is your answer