Answer:
[tex]S_{\infty}=-\dfrac{625}{396}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given geometric series:
[tex]-\dfrac{125}{36}+\dfrac{25}{6}-5+6-...[/tex]
To find the common ratio, divide a term by the previous term:
[tex]\implies r=\dfrac{a_4}{a_3}=-\dfrac{6}{5}[/tex]
Substitute the found common ratio and given first term into the sum formula:
[tex]\implies S_{\infty}=\dfrac{-\frac{125}{36}}{1-\left(-\frac{6}{5}\right)}[/tex]
[tex]\implies S_{\infty}=\dfrac{-\frac{125}{36}}{1+\frac{6}{5}}[/tex]
[tex]\implies S_{\infty}=\dfrac{-\frac{125}{36}}{\frac{11}{5}}[/tex]
[tex]\implies S_{\infty}=-\dfrac{125}{36} \times\dfrac{5}{11}[/tex]
[tex]\implies S_{\infty}=-\dfrac{625}{396}[/tex]
Help please I will give brainlist
Find the least common multiple (LCM) for the pair of numbers 6 and 18
Answer:
the lcm is 6
Step-by-step explanation:
6 divided by 3 is 1
18 divided by 3 is 6
6 becomes 3 and 2
Answer:
18
Step-by-step explanation:
Since the question is asking for the least common multiple, you factor out the 6 in 18 and 6. This gives you 631 as the LCM because you have factored out 6 and this is the GCF because there are no more common factors between 3 and 1. Since 631 equals 18, 18 is the LCM
Find the slope of the line passing through the points (4,1) and (4,-5)
Answer:
Step-by-step explanation:
(4 , 1) ; x₁ = 4 and y₁ = 1
(4 , -5) ; x₂ = 4 and y₂ = -5
The slope of the the line is undefined as the line is parallel to y-axis
A company spent 32% of its annual budget
developing a new machine. What fraction of the
company's budget was spent developing a new
machine?
A. 1/32
B. 5/16
C. 8/25
D. 4/125
Answer:
C
Step-by-step explanation:
To find this answer you simply perform the division and see which one gives you 32
In this case 8/25=0.32 or 32%!
Find m∠ABC = 7x - 4 and m∠BDC = 9x - 1 and and m∠ABC = 107°, find x, m∠ABC and m∠BDC.
Answer:
m<BDC = 62 degrees
Step-by-step explanation:
Using the expression;
<ABC = <ABD + <DBC
107 = 7x-4 + 9x - 1
107 = 16x-5
16x = 107 + 5
16x = 112
x = 112/16
x = 7
Get m<DBC
m<BDC = 9x - 1
m<BDC = 9(7)-1
m<BDC = 63 - 1
m<BDC = 62 degrees
An aquarium is to be drained. The aquarium is shaped like a rectangular prism with length 40 in, width 22 in, and height 16 in. Suppose
water is pumped out of the aquarium at a rate of 704 in per minute. If the aquarium starts completely full, how many minutes does it take
to empty the aquarium?
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Answer:
20 minutes
Step-by-step explanation:
The volume is given by ...
V = LWH
V = (40 in)(22 in)(16 in) = 14,080 in³
If water is removed at the rate of 704 in³/minute, the time to remove it all is ...
t = quantity/rate = (14,080 in³)/(704 in³/min) = 20 min
It takes 20 minutes to empty the aquarium.
please help me I really need it
Answer:
Step-by-step explanation:
Because of the givens (a right angle a common Hypotenuse and a leg in each triangle) ΔSUT and ΔSUV are congruent. HL
That means that < SUT = < SUV so what you get out of that is
w + 10 = 3w Subtract w from both sides.
w - w + 10 = 3w - w
10 = 2w Divide both sides by 2
10/2 = 2w/2
w = 5
I don't know what A with a check mark below it is.
What value will make the equation true -21 - ? = 1and1/2
Answer:
the answer would be -21 - (-22 1/2)= 1 1/2
The value that will make the equation true would be -21 - (-22 1/2)= 1 1/2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that the equation as;
-21 - (-22 1/2)
Now the mixed fraction is 22 1/2 = 45/2
The difference of the equation is;
-21 - (-22 1/2)
-21 - (-45/2)
= 1 1/2
Learn more about equations here;
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Mr.James bought 19 crates of fruits.There were 64 fryits in each crate.If 320 were apples,414 were pears and the rest were mangoes,how many mangoes were there ?
Answer:
482 mangoes.
Step-by-step explanation:
multiply 64 x 19 which equals to 1216
subtract 320 from 1216 getting 896
Lastly, subtract 414 from 896 getting you answer of 482 mangoes.
Please tell me if you're still having trouble,I would be happy to help :) good luck!
x+12=31 solve for x i’m in a breakout room i have limited time to finish this
Answer: x=19
Step-by-step explanation:
x=31-12
x=19
solve for Angles 1 and 2 please
Answer:
angles 1 and 2 measure 118°
Step-by-step explanation:
A town has a population of 7000 and grows at 4% every year. What will be the population after 13 years, to the nearest whole number?
Answer:
The population would be 11,656 after 13 years.
Step-by-step explanation:
We can do the equation 7000(1+4/100)^13
Hope it helps :)
Saeed wants to have his birthday at an amusement park with a few of his friends but he can't spend no more then $80. The amusement park charge6a flat admission fee of $35 for a private party and 6.50 per person for food and drinks
Write an inequality that represents the total cost of seeds birthday for n people given his budget
Answer:
T=35X6.50
Step-by-step explanation:
Need HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
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Answer:
x = 6
Step-by-step explanation:
The similarity statement tells you ...
TR/TP = XZ/XP
TR = x = TP(XZ/XP) = 12(18/36)
x = 6
Please answer the question in the picture because it would paste correctly thanksss
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
146 is equal to 12.08
12 3/4 is 12.75
12 5/8 is 12.63( I rounded it.Before it was 12.625)
Then you put it in order.
Find the 12th term of the arithmetic sequence whose common difference is d=-7 and whose first term is a = 10.
Answer:
87
Step-by-step explanation:
tn= a + (n-1)d
t12 = 10 + (12-1)7
=87
HELP NEEDED ASAP! Thanks :)
Answer:
3
Step-by-step explanation:
First we must find the total boxes of pens
15 + 9 = 24
Then we can divide the total cost by the total number of boxes of pens
$72 / 24 boxes = 3
pleaseeee helpppppp meeee
Solve using substitution y = -4x + 10 y = -x + 1.
will give brainleist if correct
Answer:
Hi! The answer to your question is (3,-2)
Step-by-step explanation:(
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
What is the answer to 1+1 ?
Answer:
2
Step-by-step explanation:
1+1=2
Thank you for coming to my TED Talk
Answer:
22
Step-by-step explanation:
Need the answer for x and y
Answer:
x = 2
BD = 41
Step-by-step explanation:
18x + 5 = 15x + 11
combine like terms:
3x = 6
x = 2
BD = 15(2) + 11 = 41
In ALMN, the measure of ZN=90°, NL = 6.8 feet, and LM = 9.4 feet. Find the
measure of ZL to the nearest tenth of a degree.
Answer:
Step-by-step explanation:
The answer is 43.7
Answer:
43.7
Step-by-step explanation:
7.
A company is able to sell 600 of its product in the first year of business.
products it is able to sll decreases by 20%. If this trend continues:
Each year however, the amount of
a) How many products will it be able to sell in year 5?
b) How many products will it have sold over the course of 5 years?
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Answer:
246 products in year 52017 products over 5 yearsStep-by-step explanation:
The n-th term of the geometric series is ...
an = a1(r^(n-1))
for first term a1 and common ratio r. The common ratio here is the growth factor: 1 -20% = 0.8. This means the 5th term (5th year sales) will be ...
a5 = 600(0.8^(5-1)) ≈ 246 . . . . . products sold in year 5
The sum is given by ...
sn = a1(1 -r^n)/(1 -r) = 600(1 -0.8^5)/(1-0.8) = 2017
The company will have sold about 2017 products over 5 years.
The possible values of x
are given by x+8≤6
The greatest possible value of 7x is
Answer:
if you help me with this ill help u with that problem
its very simple
https://brainly.com/question/22760971
Step-by-step explanation:
Ms. Smith allows her students to choose the mean, median, or mode of their set of test scores to be their final grade. Which measure of center should Erica use to get the highest average if her scores are 80, 90, 70, 60, 90?
Answer:
Mode
Step-by-step explanation:
because 90 is the grade that shows up the most!
I hope I helped :)
Measure of center that Erica should use is mode to get the highest average on her scores.
What is Mean, Median and Mode?For a set of data, mean is the average of all the elements in the data set.
Median is the element in the exact middle when numbers are arranged from smallest to largest or largest to smallest.
Mode is the element which is most repeated.
The given data set is,
80, 90, 70, 60, 90
Mean = (80 + 90 + 70 + 60 + 90) / 5 = 78
To find median, firstly arrange the numbers in order.
60, 70, 80, 90, 90
The middle element is the element in the third place, 80 which is the median.
90 is the only element which appears more than once. So mode is 90.
Mode gives the highest score.
Hence Erica should use mode as the measure of center to get the highest average.
Learn more about Measures of Central Tendency here :
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Can someone help me pls
Answer:
PΔJKL=66
Step-by-step explanation:
so we are given the line segments JK, KL, and LJ which are tangent to k(O), and also that JA=9, AL=10, and CK=14
JL=JA+AL (parts whole postulate)
JL=9+10=19 (substitution, algebra)
JA=JB=9 (tangent segments from the same point are congruent)
CK=KB=14 (tangent segments from the same point are congruent)
JK=JB+KB (parts whole postulate)
JK=9+14=23 (substitution, algebra)
LA=LC=10 (tangent segments from the same point are congruent)
LK=LC+CK (parts whole postulate)
LK=10+14=24 (substitution, algebra)
Perimeter of ΔJKL=LK+KL+LJ (perimeter formula for triangles)
Perimeter of ΔJKL=23+24+19=66 (substitution, algebra)
which of the following values are solutions to the ineuality x-7<5
Answer:
x>12
Step-by-step explanation:
Please Help!!! 15 Points!!! Will Mark Brainliest!!! Please show your work!!
A pick-up truck if fitted with new tires which have a diameter of 40 inches. How fast will the pick-up truck be moving when the wheels are rotating at 365 revolutions per minute? Express your answer in miles per hour rounded to the nearest whole number.
Answer:
14
Step-by-step explanation:
365*40=14600*60 minutes = 14 miles per hour
Find the area of each figure.
1536in (for rectangle). 288in (for triangle)
Area of rectangle: 48in* 32in = 1536 in
Area of triangle: 48in*12in÷1/2= 576/2=288in
Formula of area of triangle is b*h divided by 2
Formula of area of rectangle is length*width
Hope this helps!
If the probability of a chance event is 0.96, it is less likely to happen than which of the following probabilities of another chance event ?
1. 0.95
2. 0.75
3. 0.85
4. 1