Answers
All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is
[tex]S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}[/tex]
Multiply both sides by r :
[tex]rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n[/tex]
Subtract the latter sum from the first, which eliminates all but the first and last terms:
[tex]S_n-rS_n=a-ar^n[/tex]
Solve for [tex]S_n[/tex]:
[tex](1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}[/tex]
Then as gets arbitrarily large, the term [tex]r^n[/tex] will converge to 0, leaving us with
[tex]S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}[/tex]
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Related Questions
Kobi and I need to know which of the following is NOT a possible value for the number of pennies
Answers
Answer:
A. 85
Step-by-step explanation:
SInce nickels are worth 5 cents, the number of pennies must end with an 8 or a 3 in order for the total to end with a 3 ($9.83)
What is the result of adding these two equations?
Answers
Answer:
-5x - 8y = -5.
Step-by-step explanation:
4x + (-9x) -4y + (-4y) = -2 + (-3)
-5x - 8y = -5.
Answer:
-5x -8y = -5
Step-by-step explanation:
The question asks us to add the equations
4x - 4y = -2
+ -9x -4y = -3
------------------------
-5x -8y = -5
Which linear inequality is represented by the graph?
Answers
Answer:
y ≤ (1/2)x + 2
Step-by-step explanation:
Find the equation of the solid line. It is immediately evident that the y-intercept is (0, 2). The line also passes through (-4, 0). Starting at (-4, 0), x (the run) increases by 4 to 0 and y (the rise) increases from 0 to 2. Thus, the slope of this line is m = rise / run = 2/4, or m = 1/2.
Thus the equation of the line is y ≤ (1/2)x + 2.
Richie and his brother have a paper route. Together they can deliver all of the papers in 40 minutes, and Richie can do it alone in 90 minutes. Richie’s brother slept in one day, leaving Richie to deliver alone for 30 minutes. How long must the two of them work together to finish delivering the newspapers?
Answers
Answer
30 minutes
Step-by-step explanation:
Answer: approximately 26.66667 minutes
This converts to 26 minutes, 40 seconds
=================================================
Explanation:
Let's say there are 360 newspapers that need to be delivered.
The two brothers can get the job done in 40 minutes if they work together. Their rate is 360/40 = 9 newspapers per minute.
Richie can do the full job alone in 90 minutes. So his rate would be 360/90 = 4 newspapers per minute. In 30 minutes, he delivers 30*4 = 120 newspapers. This leaves 360 - 120 = 240 left over.
Divide this over the rate of 9 papers per minute to get 240/9 = 26.66667 approximately. It takes about 26.66667 minutes to finish up delivering the 240 remaining newspapers if the brothers work together.
The portion 0.66667 multiplies with 60 to get 0.66667*60 = 40.0002 which rounds to 40 (we have rounding error going on). This means
26.66667 minutes = 26 minutes, 40 seconds
A tiling company completes two jobs. The first job has $1200 in labor expenses for 40 hours worked, while the second job has $1560 in labor expenses for 52 hours worked. The relationship between the labor expenses and the hours worked is linear. Which equation can be used to calculate the y-intercept of the linear equation? 1200 = 40 (40) + b 1560 = 30 (40) + b 1560 = 30 (52) + b 1200 = 52 (30) + b
Answers
The slope (change in y/change in x) of the line is (1560 - 1200)/(52 - 40), which is equal to 30. We can plug this into the equation y = mx + b using either the point (40, 1200) or (52, 1560). The slope is represented by m and the y - intercept by b. Therefore, the two possible equations you could use are:
1200 = 30(40) + b
or 1560 = 30(52) + b
Using either equation, you'll get that b is equal to 0, which makes sense in the context of the problem, since it's reasonable to expect that the labor expenses would be 0 for 0 hours worked.
Answer:
im pretty sure its C
Step-by-step explanation:
Hope this helped! :) Oh and I took the test on edge and got a good grade, but i didnt know if i got this right or wrong bc i couldnt look back at it
Identify an equation in point-slope form for the line perpendicular to
y=-2x+ 8 that passes through (-3,9).
O A. y - 9 = -2(x+3)
O B. y+3 - 3(x-9)
O C. y-9-(x + 2)
O D.y +9 = 2(x – 3)
Answers
The correct option is A. The equation in point-slope form for the line perpendicular to y = -2x + 8 and passing through (-3, 9) is: y - 9 = 1/2(x + 3).
To find the equation of a line perpendicular to y = -2x + 8 that passes through the point (-3, 9), we need to determine the slope of the perpendicular line.
The given equation is in slope-intercept form, y = mx + b, where m represents the slope. In this case, the slope of the given line is -2.
Since the perpendicular line has a slope that is the negative reciprocal of -2, we can determine its slope as 1/2.
Now that we have the slope (1/2) and a point (-3, 9) on the line, we can use the point-slope form of a line to write the equation:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Plugging in the values, we get:
y - 9 = 1/2(x - (-3))
Simplifying:
y - 9 = 1/2(x + 3)
Rearranging to match the given options:
y - 9 = 1/2(x) + 3/2
The equation in point-slope form for the line perpendicular to y = -2x + 8 and passing through (-3, 9) is:
y - 9 = 1/2(x + 3)
Therefore, the correct option is A.
Learn more about equation here
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Complete question is below
Identify an equation in point-slope form for the line perpendicular to
y=-2x+ 8 that passes through (-3,9).
A. y - 9 = 1/2(x+3)
B. y+3 = 3(x-9)
C. y - 9 = (x + 2)
D. y + 9 = 1/2(x – 3)
Rewrite the expression below using the Associative Property of Multiplication: (ab)c
Answers
Answer:
hope this helps
Step-by-step explanation:
(ab)c = (ac)b = (bc)a
Answer:
Here are a couple of examples (a+b)c or (c+b)a or (a+c)b
Step-by-step explanation:
To “associate” means to connect or join with something. According to the associative property of multiplication, the product of three or more numbers remains the same regardless of how the numbers are grouped. Here's an example of how the product does not change irrespective of how the factors are grouped.
A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12% vinegar. The chef wants to make 320 milliliters of a mixture that contains 23%vinegar. How much vinegar and how much Italian dressing should she use?
Answers
Answer:
Vinegar: 40 milliliters
Italian dressing: 280 milliliters
Step-by-step explanation:
I jus took the test :)
May someone please explain what a central tendency is I do not understand what it exactly means
Answers
median, the mode and the range.
Evaluate the following: −3 − (−2). (5 points) a. -5 B. -1 c. 1 d. -6
Answers
Answer:
B:-1
Step-by-step explanation:
-3-(-2)=-3+2=-1
Answer:
-1Step-by-step explanation:
[tex] - 3 - ( - 2)[/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] - 3 + 2[/tex]
Here, 3 > 2 , So, we have to enter the sign of 3 which is negative.
Calculate:
[tex] - 1[/tex]
Some rules:
[tex]( + ) \times ( + ) = ( + )[/tex]
[tex]( + ) \times ( - ) = ( - )[/tex]
[tex]( - ) \times ( - ) = ( + )[/tex]
[tex]( - ) \times ( + ) = ( - )[/tex]
Hope this helps..
FIRST GETS BRAINLLEST If you spin the spinner below 150 times, which of the following outcomes are reasonable? Select all that apply. A) Lands on blue 60 times B) Lands on red 120 times C) Lands on yellow 90 times D) Lands on yellow 44 times
Answers
Answer:
Step-by-step explanation:
Spinner pointing to red, blue or yellow is equally likely:
P(blue) = P(yellow) = P(red) = 1/3.
In a perfect world, the spinner would land on blue (1/3)(150) = 50 times; on red 50 times and on yellow 50 times.
If in real life the spinner lands on yellow 44 times (C) is most reasonable, as that is closest to the ideal 50 times.
A) Lands on blue 60 times - Reasonable outcome.
B) Lands on red 120 times - Not reasonable.
C) Lands on yellow 90 times - Not reasonable.
D) Lands on yellow 44 times - Reasonable.
If the spinner has three colors (red, yellow, and blue) with equal areas, and we spin it 150 times, the reasonable outcomes would be:
A) Lands on blue 60 times - Reasonable since there is an equal chance of landing on each color, and 60 is a fraction of 150 that falls within the expected range.
B) Lands on red 120 times - Not reasonable since the expected number of times for each color is 150 / 3 = 50, and 120 is significantly higher than this expected value.
C) Lands on yellow 90 times - Not reasonable since the expected number of times for each color is 150 / 3 = 50, and 90 is significantly higher than this expected value.
D) Lands on yellow 44 times - Reasonable since there is an equal chance of landing on each color, and 44 is a fraction of 150 that falls within the expected range.
Therefore, the reasonable outcomes would be A) Lands on blue 60 times and D) Lands on yellow 44 times.
To know more about outcome, refer here:
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Estimate the value of?
Answers
Answer:
D) 2.0
Step-by-step explanation:
We know that √2 = 1.414213562 ≈ 1.4, π ≈ 3.14, and √5 = 2.236067978 ≈ 2.2 . Next, I found out that √2π = 4.442882938 which rounds to 4.4. Then, I found out that 4.4 ÷ √5 equals to 1.96773982. So, if we round our answer to the nearest whole number, we will get 2.
Answer:
[tex]\boxed{Option \ D}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{2} \pi }{\sqrt{5} }[/tex]
Where [tex]\sqrt{2}[/tex] = 1.4 , π = 3.14 and [tex]\sqrt{5}[/tex] = 2.24
Plugging in the values
=> [tex]\frac{(1.4)(3.14)}{2.24}[/tex]
=> 4.396/2.24
=> 1.9
≈ 2.0
Estimate the solution to the system of equations.
Answers
Answer:
Find it in the explanation
Step-by-step explanation:
Equate the two solutions.
2x+3y=6 is exactly half of -4x+3y=12, so multiply 2x+3y=6 by 2.
Now we get
4x+6y=12 and
-4x+3y=12
Here what operation you use is your choice, but because I see a positive 4x and a negative 4x down below, I'm gonna use addition to cancel out the x.
Adding these two equations together, I get:
9y=24
y=24/9
in fraction form y= 2 and 2 thirds.
Plug that in any of the equations and solve for the value of x, which will be -1
Therefore, the coordinates are (-1, 2 and 2/3)
Answer:
The answer is x= -1/2 and y= 7/3 or 2whole 1/3.
hope it helps..
simplify the expression
[tex]10.8 + - 7.6 + 10.2h + 9.2[/tex]
Answers
12.4 + 10.2h
10.8 + -7.6 + 10.2h+9.2
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, -6), B(5, -6), C(5, -2) and D(2, -2). What is the perimeter of rectangle ABCD?
Answers
Answer:
Step-by-step explanation:
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \\\\[/tex]
A(2, -6), B(5, -6),
[tex]AB =\sqrt{(5-2)^{2}+(-6-[-6])^{2}}\\\\=\sqrt{(5-2)^{2}+(-6+6)^{2}}\\\\=\sqrt{3^{2}+0}\\\\=\sqrt{3^{2}}\\\\=3 units\\[/tex]
B(5,-6) ; C(5,-2)
[tex]BC = \sqrt{(5-5)^{2}+(-2-[-6])^{2}}\\\\ = \sqrt{0+(-2+6)^{2}}\\\\ = \sqrt{4^{2}}\\\\[/tex]
BC = 4 units
C(5, -2) ; D (2,-2)
[tex]CD = \sqrt{(2-5)^{2}+(-2-[-2])^{2}}\\\\ = \sqrt{(-3)^{2}+(-2+2)^{2}}\\\\ = \sqrt{(-3)^{2}}[/tex]
CD = 3 units
A(2,-6) ; D(2,-2)
[tex]AD = \sqrt{(2-2)^{2}+(-2+6)^{2}}\\\\ = \sqrt{0 +(4)^{2}}\\\\ = \sqrt{(4)^{2}}\\[/tex]
= 4 units
Perimeter = AB + BC + CD + AD
= 3 + 4 + 3 + 4
= 14 units
-2<3 multiple each side by -5 what is the resulting inequality
Answers
Answer:
[tex]\boxed{10>-15}[/tex]
Step-by-step explanation:
[tex]-2<3[/tex]
Multiply each side by -5.
[tex]-2 \times -5 <3 \times -5[/tex]
Switch signs when multiplying or dividing by a negative integer.
[tex]10>-15[/tex]
Answer:
10 > -15
Step-by-step explanation:
-2 < 3
We want to multiply each side by -5 and we want to see what happens:
-2 * -5 < 3 * -5
= 10 < -15
This is a wrong inequality as 10 is ahead of -15 on the number line.
HELP NOW A dartboard has 20 equally divided wedges, and you are awarded the number of points in the section your dart lands in. If you are equally likely to land in any wedge, what is the probability you will score more than 10 points?
Answers
Answer:
1/2 (or) 0.50 (or) 50%
Step-by-step explanation:
10 out of 20 wedges are worth more than 10.
10/20 = 1/2 (or) 0.50 (or) 50%
Answer:
0.75
Step-by-step explanation:
A class rolled number cubes. Their results are shown in the table. What is the experimental probability of rolling the number 4?
Answers
Answer:16.8 ur welcs
Step-by-step explanation:
Explanation: 4 x 8 is 32 but you cant go any higher so the probability is 8 out 35 i think
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
Answers
Answer:
15.62 = x
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
10 ^2 + 12^2 = x^2
100 +144 = x^2
244 = x^2
Take the square root of each side
sqrt(244) = sqrt(x^2)
15.62049935 = x
Rounding to the nearest hundredth
15.62 = x
Answer:
15.62
Step-by-step explanation:
We can use the Pythagorean Theorem.
10^2+12^2=c^2
100+144=c^2
244=c^2
15.62=c, or x=15.62
What is the y-intercept of line MN?
What is the equation of MN written in standard form?
Answers
Answer:
y-intercept of the line MN = 2
Standard form of the equation ⇒ x + y = 2
Step-by-step explanation:
Coordinates of the ends of a line MN → M(-3, 5) and N(2, 0)
Slope of a line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{5-0}{-3-2}[/tex]
= -1
Equation of the line MN passing through (-3, 5) and slope = -1,
y - 5 = (-1)(x + 3)
y - 5 = -x - 3
y = -x + 2
This equation is in the y-intercept form,
y = mx + b
where m = slope of the line
b = y-intercept
Therefore, y-intercept of the line MN = 2
Equation in the standard form,
x + y = 2
the first one is : -1
the second one is: y-5 = -1 ( x + 3)
the third one is: -x + 2
the first one to the right side is: 0,2
and the second one on the right side is: x+y=2
your welcome
The graph of the function f(x) = log5 (x) is stretched vertically by a factor of 2, shifted to the left by 8 units, and shifted up
by 3 units.
Find the equation of the function g(x) described above.
Answers
Answer:
We start with y = g(x) = f(x)
First, we have a vertical stretch by a factor of 2.
A vertical strech by a factor of A will be g(x) = A*f(x)
then in this case A = 2, so we have g(x) = 2*f(x)
Now we have it shifted left by 8 units.
We know that f(x - A) shift right the graph by A units (A positive), here A = 8.
then we have: g(x) = 2*f(x - 8)
Now we want shift up 3 units, if we have y = f(x) we can shift the graph up by A units as: y = g(x) + A (for A positive)
Then we have: g(x) = 2*f(x - 8) + 3
now, our function was f(x) = Log₅(x)
then g(x) = 2*log₅(x - 8) + 3.
Answer:
g(x)=2log5(x+4)−8
Step-by-step explanation:
please hurry!
The pie chart shows the number of students signing up for various athletic classes. Which bar diagram shows the percent of students signing up for Track and Field class?
Athletic Class Sign Up
1.) A bar diagram with 2 shaded squares and 8 unshaded squares.
2.) A bar diagram with 3 shaded squares and 7 unshaded squares.
3.) A bar diagram with 4 shaded squares and 6 unshaded squares.
4.) A bar diagram with 8 shaded squares and 10 unshaded squares.
Answers
Answer:
1) A bar diagram with 2 shaded squares and 8 unshaded squares.
Step-by-step explanation:
There are 100 students (40+15+20+25).
20 signed up for Track and Field.
20 out of 100 would equate to 20/100, or 2/10, or:
1) A bar diagram with 2 shaded squares and 8 unshaded squares.
Answer:
a
Step-by-step explanation:
the two squares are shaded and eight are not
20 POINTS. PLEASE HELP FAST. FIRST ANSWER GETS BRAINLIEST.
Answers
Answer:
bd=24
Step-by-step explanation:
I believe you would have to set up a proportion. 32/19.2=15.0/x. cross multiply 19.2 and 15 to get 288. then divide by 32 to get qd=9. then add qd and bq to get 24.
Write an equation in slope-intercept form for the line that satisfies the following condition.
slope 5 and passes through (2, 28)
Select one:
O a.y=5x - 28
O b.y = 2x - 2
O c. y= 28x + 18
O d. y = 5x + 18
Answers
Answer:
d. y= 5x+18
Step-by-step explanation:
y=mx+b is slope intercept form
Now we plug in the information given to us which is slope(m) is 5 and a point (x,y) which is (2,28).
So by substituting we get 28=5(2)+b
simplify to 28=10+b and when we subtract 10 from both sides to isolate 'b', we get that b = 18.
So now we use the values of slope(m) and the y-intercept(b) to write the equation:
y=5x+18
Hey there! I'm happy to help!
Slope-intercept form is a way to write the equation of a line, and it is very useful. It is y=mx+b. This equation shows how y is related to x on a line. The m represents the slope, which is the incline of the line. The b represents the y-intercept, or where the line hits the y-axis.
If you find any value for x and plug it into the equation, you will figure out what y-value it matches on the line. If you had the equation you could draw the line by plugging in x-values and plotting points and connecting the dots!
Anyways, we have a slope of 5. This means that so far our equation looks like y=5x+b. It does not tell us what the y-intercept is, so we need to figure it out!
If we have the values for m, x, and b, we can solve for y. Well, we don't have b, but we do have values for y, x, and m, so we should be able to solve for b!
We will plug in our point (2,28) and solve for b!
28=5(2)+b
28=10+b
b=18
Our y-intercept is 18.
So, we can write this equation in slope-intercept form for the line that follows the condition of slope 5 and passing through (2,28) below.
y=5x+18
Therefore, our answer is d. 5x+18.
Now you can find the equation of a line given the slope and a point! Have a wonderful day! :D
What is the area of the circle below? Use π = 3.14 to solve. Round your answer to the nearest hundredth. 160.36 feet² 184.96 feet² 190.56 feet² 200.96 feet²
Answers
Answer:
A =200.96 ft^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
The radius is 8
A = pi 8^2
A = 64 pi
Letting pi = 3.14
A = 64 ( 3.14)
A =200.96 ft^2
Answer:
[tex]\boxed{\mathrm{200.96 \: feet^2}}[/tex]
Step-by-step explanation:
Apply formula for the area of a circle.
[tex]area=\pi r^2[/tex]
The radius is 8 ft.
[tex]A=\pi (8)^2[/tex]
[tex]A=64\pi[/tex]
Take [tex]\pi[/tex] as 3.14
[tex]A=64(3.14)[/tex]
[tex]A=200.96[/tex]
The time it takes to drive from Orangeville to the Vaughan Mills Mall is normally distributed with a mean of 52 minutes and standard deviation of 5 minutes. What intervals could you estimate, using the knowledge from this activity that do not include the mean as a max or min? For example, is an interval we could estimate? However, it includes the mean as the maximum of the interval. Another example is as an example of a probability interval that we know from this activity, but it includes the mean as the minimum.
Answers
Given:
Mean of 52 minutes and a standard deviation of 5 minutes.
Solution:
According to the empirical rule: For the normal distribution, all of the data will fall within three standard deviations of the mean.
1: 68% of the data will fall within the first standard deviation from the mean.
2: 95% of the data fall within two standard deviations.
3: 99.7% of the data fall within three standard deviations.
[tex]3SD =99.7\%=\mu\pm3\sigma\\[/tex]
Therefore, the 7 intervals and their probabilities are:
1. [tex]1SD=0.68=P(47<x<57)[/tex]
2. [tex]0.95=P(42<x<62)[/tex]
3. [tex]0.997=P(37<x<67)[/tex]
4.[tex]13.5\%=P(42<x<47)[/tex]
5.[tex]13.5\%=P(57<x<62)[/tex]
6. [tex]2.35\%=P(37<x<42)[/tex]
7.[tex]2.35\%=P(62<x<67)[/tex]
The temperature of a mixture is decreasing by 5∘C every hour. When it was first mixed, its temperature was recorded at −20∘C.
Which answer correctly represents the temperature of the mixture over time?
f(x)=−20x−5
That is incorrect.
f(x)=−5x−20
f(x)=−20x+5
f(x)=5x+20
f(x)=−15x
Answers
Answer:
f(x)=−5x−20
Step-by-step explanation:
It's decreasing 5 degrees every hour, which is represented by -5x
You also have to take away the 20 (-20) from where it started.
So, f(x)=−5x−20
Answer:
f(x) = -5x - 20
Step-by-step explanation:
f(x) = starting temperature + decreasing temperature * number of hours
= -20 + (-5) * x
= -20 - 5x
Please help i will make brainliest for correct answers! :)
Answers
Answer:
For 13, there are 25 possible words, and for 14, depending on what the meaning of leaves is in this, the answer is 590.
Answer:
The first one is 25 and the second is 1080.
Step-by-step explanation:
To find how many 5-letter words you can make out of the letters, H, Q, L, R, and S, find the answer to 5². 5² = 25, so we can make 25 5-letter words. To find the number of "leaves" on the tree, just multiply the number of choices for color, monitor size, hard-drive size, and battery type together. So, 5×9×12×2 = 1080, so there are 1080 "leaves" on the tree.
Hope this helps! Plz give me brainliest like you said, it will help me achieve my next rank.
A train travels 60km in y minutes.If this average speed is 400km per hour,find the value of y
Answers
Answer:
9
Step-by-step explanation:
Speed of the train is:
60 km / y minAnd average speed is:
400 km / h = replacing 1 h with 60 min400 km/ 60 min = 20 km /3 min = 60 km / 9 minComparing the two above, we see y= 9
Which of the following expressions are equivalent to 4 - (-5) +0?
Intro
Choose 3 answers:
A: 4- (-5)
B: 4+5
C: 4- (-5+0)
D: (4-5)+0
E: 4- (5-0)
Answers
Answer:
A, B, C
Step-by-step explanation:
4 - (-5) + 0
4 - (-5) = 4 + 5 (because a negative + negative = positive)
4 + 5 = 9
a, b and c all equal 9
hopefully this helped you!! :3
ExplainNation: