Answer:
1) Diverges. 2) Converges. 3) Converges. 4) Converges. 5) Diverges. 6) Diverges. 7) Converges. 8) Converges to 2.5. 9) Diverges
Step-by-step explanation:
In order to find the convergence or divergence of a geometric series, we have to focus on the absolute value of its radius
The theorem states that if [tex]|r|<1[/tex] then the series converges to [tex]\frac{a_{1} }{1-r }[/tex]
1) The radius is r = 4 which is greater than one so it Diverges.
2) The radius is [tex]r=\frac{-3}{4}[/tex] and [tex]|r|=\frac{3}{4}[/tex] which is less than 1 so it Converges.
3) The radius is 0.5 which is less than 1 so it Converges.
4) To figure out unknown radius, we divide the 2nd term from the first, in this case we have [tex]\frac{27}{81} =\frac{1}{3}[/tex] which is less than one so it Converges.
5) for this one, since the second term is bigger than the first, if we divide them, the answer would always be bigger than 1 so it Diverges.
The geometric series are given by the formula ∑[tex]C(r)^{n}[/tex] where c is a constant.
6) in this case our [tex]r = \frac{3}{2}[/tex] which is bigger than 1 so it Diverges.
7) [tex]r = \frac{-1}{4}[/tex] and [tex]|r|=\frac{1}{4}[/tex] which is less than one so it Converges.
to find the sum of a convergent geometric series, we use the formula [tex]\frac{a_{1} }{1-r}[/tex]
8) plug in given information
[tex]a_{1} = 3\\r = \frac{-1}{5}\\\\=\frac{3}{1-(-\frac{1}{5}) }\\= \frac{3}{1+\frac{1}{5} }\\= 2.5[/tex]
9) since [tex]r = -3[/tex] and [tex]|r|=3[/tex], r is greater than 1 and it Diverges.
Hopefully the work I did was right. Have a good one!
convert 5.82% to an equivalent decimal
5.82% = 0.0582 in decimal form.
The value of the equation is A = 0.0582
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 5.82 % be equation (1)
On simplifying the equation , we get
A = ( 5.82 ) / 100
On further simplification , we get
A = 0.0582
Therefore , the value of A is 0.0582
Hence , the equation is A = 0.0582
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Candice wanted to get into shape for the tennis match. Her coach said she needed to include running for at least 10 minutes a day. This week Candice ran every day for 12 minutes. What is the total distance Candice ran?
A. The missing information is the distance Candice can run per minute.
B. The missing information is there are 7 days in 1 week.
C. The missing information is the distance Candice can run in one day.
D. The missing information is the amount of time Candice has to get into shape before the match.
Answer:
The answer is C.
Step-by-step explanation:
They don't explain how to find the total distance Candice ran.
Answer:
C
Step-by-step explanation:
The owner of a pizza restaurant in France knows that the time customers spend in the restaurant on Saturday evening has mean 90 minutes and standard deviation 15 minutes. He has read that pleasant odors can influence customers, so he spreads a lavender odor throughout the restaurant. Presented are the times, in minutes, for customers on the next Saturday evening.
Answer:
hello your question is incomplete attached below is the missing part
Question : What is the value of the test statistic
answer : = 5.73
Step-by-step explanation:
Mean value = 90 minutes
std = 15 minutes
Calculate the test statistic
mean value of given data = ∑ x / n = 105.7
since the value of standard deviation is given we will assume a normal distribution
Hence we will apply z test statistics
z = mean value of given data - Mean value / 15 √30
= ( 105.7 - 90 ) / 15 √30
= 5.73
can someone help me? please!!!
Answer:
Down below
Step-by-step explanation:
i'm gonna break it down into two parts.
Half-circle
[tex]A=\frac{1}{2}(\pi r^2) \\16/2=8=r\\A=\frac{1}{2}(3.14*8^2)\\A= \frac{1}{2}( 200.96)\\A=100.48[/tex]
Square
[tex]A=bh\\A=16*16\\A=256[/tex]
now to get it all we add them
[tex]A=100.48+256\\A=365.48[/tex]
Make 6 prime number using 1,2,3,4,5,6,7,8,9
Answer:
13,67,29,17,19,23
Step-by-step explanation:
Answer:
1+2=3
2+3=5
4+3=7
9+2=11
9+4=13
3-1=2
After painting 3/8 of a fence he finds that he has painted 15 feet
Answer: I'm assuming you want to know how much surface area his fence is, so 40
Step-by-step explanation: First we can divide 15 by 3 to get 5, and then multiply 5 by 8. This gives us 40, which is our answer.
Hope this helps :)
Answer:
ok whats the question tho is it the total length of the fence if it is its 40 pretty sure
Step-by-step explanation:
3/8 of the fence lets say x, equals 15 feet
divide 15 by 3/8 to find x which is 40
An engineer stands 50 feet away from a building with a surveying device mounted on a tripod. if
the surveying device is 5 feet above the ground and the angle of elevation is 50°, find how tall is
the building.
Answer:
The building is 64.6 feet tall.
Step-by-step explanation:
To determine the height of the building, let the height from the top of the building to the top of the tripod be represented by x. So that;
Height of the building = x + 5
But,
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan [tex]50^{o}[/tex] = [tex]\frac{x}{50}[/tex]
x = 50 x Tan [tex]50^{o}[/tex]
= 50 x 1.1918
= 59.59
x = 59.59
Height of the building = x + 5
= 59.59 + 5
= 64.6 ft
The height of the building is 64.6 feet.
The amount of resistance, y, in a circuit varies inversely to the current, x, in the circuit. When 10 ohms of resistance are used in the circuit, 12 amperes of current are present. When 5 ohms of resistance are used in the same circuit, 24 amperes of current are present.
How many ohms of resistance are used in the circuit when 15 amperes of current are present? Round your answer to the nearest tenth, if necessary.
7.5 ohms
8 ohms
50 ohms
120 ohms
9514 1404 393
Answer:
(b) 8 ohms
Step-by-step explanation:
We are told that y varies inversely to x, so the relation can be modeled by ...
y = k/x
The value of k is ...
k = xy = (12)(10) = 120
Then for x=15, the resistance is ...
y = 120/15 = 8 . . . . ohms
Answer:
(b) 8 ohms
Step-by-step explanation:
We are told that y varies inversely to x, so the relation can be modeled by ...
y = k/x
The value of k is ...
k = xy = (12)(10) = 120
Then for x=15, the resistance is ...
y = 120/15 = 8 . . . . ohms
can you guys please help me this has to be turned in by 1 !!
Answer:
For 5. The answer is 55% of 60 is less than 60% of 65 because 55% of 60 is 33. And 60% of 65 is 39
For 6. 20% of 80 is equal to 80% of 20 because 20% of 80 is 16. And 80% of 20 is also 16
Y=-3x+5. Fill in the table using this function rule
X Y
1 8
2 11
3 14
4 17
5 20
6 23
7 26
8 29
9 32
10 35
11 38
12 41
13 44
14 47
15 50
16 53
17 56
18 59
19 62
20 65
What is 3^2/3 equal to
Answer:
3
Step-by-step explanation:
3^2=3×3=9
9/3=3
hope this helps
Answer:
The correct answer is 3.
Step-by-step explanation:
Hope this helped Mark BRAINLIEST!!!!
Help with number 2 please find the missing length
The average temperature for four days was 22°. What must the temperature be on the fifth day in order to make 23° the temperature for the five days?
Answer:
27°C
Step-by-step explanation:
Average temperature on 4 days
[tex] = \frac{total \: temperatures \: for \: 4 \: days}{4} [/tex]
Total temperatures for 4 days
= 4(22)
= 88
If the average temperature throughout 5 days is 23°,
total temperature for 5 days
= 5(23)
= 115
Temperature on the 5th day
= total temperatures for 5 days -total temperature for 4 days
= 115 -88
= 27°C
The roots of the equation 2x^2 + 4= 9x are imaginary?
The final statement is: The quadratic equations has real roots.
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: 2x²+4-9x=0
2x²-9x+4=0
2x²-8x-x+4=0
2x(x-4)-1(x-4)=0
(2x-1) (x-4) =0
Therefore the roots of the equation are 1/2 and 4 which are not imaginary.
Hence, The quadratic equations has real roots.
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Mark, Anthony, and Derek, are going on a road trip and will take turns driving the car. They need to decide who will drive first.
Which method assures that each of the three friends has a fair chance of being selected to drive first?
O A. "Using a random number generator, generate an integer. If the number is negative, Mark drives first. If the number is positive,
Anthony drives first. If the number is 0, Derek drives first.
OB.
Flip two fair coins. If both coins land on tails, Mark drives first. If both coins land on heads, Anthony drives first. If one coin
lands on tails and the other lands on heads, Derek drives first.
O C. Spin a spinner with four equal-sized sections labeled A, B, C, and D. If the spinner lands on A, Mark drives first. If the spinner
lands on B, Anthony drives first. If the spinner lands on C, Derek drives first. If the spinner lands on D, Mark drives first.
OD. Roll an ordinary die. If the die lands on 1 or 4, Mark drives first. If the die lands on 2 or 5, Anthony drives first. If the die lands
on 3 or 6, Derek drives first.
Answer: Option D
Step-by-step explanation:
I got it right on Edmentum/Plato
5g ∙ 7h in standard form
9514 1404 393
Answer:
35gh
Step-by-step explanation:
The standard form has one coefficient, and generally has the variables in lexicographical order.
35gh
A hexagonal prism has a base with an area of 15 square inches and the volume is 105 cubic inches.
.
Complete the sentence about the height of the prism.
The height of the prism is _____ inches,square inches,cubic inches
Answer:
I believe the answer would be 1575 cubic inches. Sorry if i'm wrong!
Answer:
The answer is 7 square in
Step-by-step explanation:
Do this formula
V=Bh
105=15h
h=7 square in
Please answer thank u ASAP.
Answer:
a?
Step-by-step explanation:
Witch is larger? 3/4 or 2/3
Please I need it now!,
Answer:
3/4
Step-by-step explanation:
3/4 2/3
find the lcm of the denominators
which is 12
and divide
What is the difference of 95,216 and 35,535? a59,681 b60,321 c60,781 D130,751
Answer:
the answer is A) 59, 681
Step-by-step explanation:
all you have to do is subtract
so 95,216 - 35,535= 59,681
hope i helped
-lvr
lang atino
Determine whether a triangle can be formed with the
5. 10 ft, 3 ft, 15 ft
The cost of 12 oranges and 7 apples is 5.36. Eight oranges and 5 apples cost 3.68. Find the cost of each
The "middle" term of the trinomial form of (3x + 5)(4x – 3)
is:
29x
- 3x
O 11x
0 2x
I want the answer the steps
Answer:
The "middle" term is 11x.
Step-by-step explanation:
(3x + 5)(4x - 3)
Solve this by using FOIL: first – outer – inner – last
F: 3x • 4x = 12x²
O: 3x • -3 = -9x
I: 5 • 4x = 20x
L: 5 • -3 = -15
Combine the terms.
12x² - 9x + 20x - 15
Combine like terms.
12x² + 11x - 15
The "middle" term is 11x.
Hope this helps!
PLEASE HELP I GOT IT WRONG EARLIER AND THE WRONG ANSWER WAS H PLS HELP!!
Answer:
H. 39.6
Step-by-step explanation:
i promise this is the right answer!
there is a mean, mode, range etc. calculator that can help you!
Find the common difference of the arithmetic sequence -2, -4, -6, ...
Answer:
-8
in this the arthmatic difference is table of 2
Answer:
the common d/f is that -2>-4>-6
15. The cost of an article including 15% for taxes is
$138.00. What is the cost of the article without
taxes?
Answer:
$120
Step-by-step explanation:
Set the cost of the article pre-tax as x.
x + 0.15x = 138
1.15x = 138
x = 138/1.15
x = $120
Answer: the cost of the article without taxes is $120.
The required cost of the article without taxes is $120.
How to calculate unit price of something?Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.
Thus, unit price of something is price of 1 thing.
Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.
We have been given the cost of an article including 15% for taxes is $138.00.
Lets Set the cost of the article pre-tax as x.
x + 0.15x = 138
1.15x = 138
x = 138/1.15
x = $120
Therefore, the cost of an article including 15% for taxes is $138.00. the cost of the article without taxes is $120.
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What is the inverse of y=2x^2-8
Answer:
f − 1 ( x ) = √ 2 ( x + 8 ) /2 , − √ 2 ( x + 8 ) /2
keep it under whole root
Step-by-step explanation:
Input the values into the formula below
to find the 8th term in the sequence.
1
-1, 4, -16,...
4)
Ist term • common ratioſdesired term - 1)
[?] •[ ][ - 1)
Answer:
The 8th term = -4,096
Step-by-step explanation:
Given:
¼, -1, 4, -16, . . .
Required:
8th term of the sequence
Solution:
1st term = ¼
Common ratio = -1/¼ = 4/-1 = -16/4 = -4
Desired term = 8
Plug in the values into the formula given:
[tex] \frac{1}{4} * -4^{(8 - 1)} [/tex]
[tex] \frac{1}{4} * -4^{7} [/tex]
[tex] \frac{1}{4} * -16,384 [/tex]
[tex] \frac{-16,384}{4} [/tex]
= -4,096
Find ECD
E
-D
C
31°
A
B
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the variance is 1.69 gallons and the mean is 15.9 gallons per day. If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water? Round your answer up to the next integer.
Answer:
A sample of 179 is needed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.85}{2} = 0.075[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.075 = 0.925[/tex], so Z = 1.44.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
A previous study found that for an average family the variance is 1.69 gallon?
This means that [tex]\sigma = \sqrt{1.69} = 1.3[/tex]
If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water?
A sample of n is needed, and n is found for M = 0.14. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.14 = 1.44\frac{1.3}{\sqrt{n}}[/tex]
[tex]0.14\sqrt{n} = 1.44*1.3[/tex]
[tex]\sqrt{n} = \frac{1.44*1.3}{0.14}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.44*1.3}{0.14})^2[/tex]
[tex]n = 178.8[/tex]
Rounding up
A sample of 179 is needed.