Answer:
3/12
Step-by-step explanation:
Hope it helps plz give brainliest! :D
Which geometric series converges?
Answer:
Option 2: 1 + 1/2 + 1/4 + 1/8+...
Step-by-step explanation:
When a geometric series converges, it has a common ratio that is in between -1 and 1. We can start by finding the common ratios of all the options and then see which one converges.
In the first option, each term is 3 times the term before it, meaning it has a ratio of 3. 3 does not fit in the range we defined, so this series does not converge.
In the second option, each term is half the term before it. This means the common ratio is 1/2. 1/2 is in the range, so this series converges.
In the third option, we can see that the common ratio is -4 since it is the number being brought to a power. -4 does not fit in the range we defined, so this series does not converge.
In the fourth option, we can see the common ratio is 2 since it is the number you multiply by tone more time to get the next term. 2 does not fit in the range we defined, so this series does not converge.
From this, we can see the second option(1 + 1/2 + 1/4 + 1/8+...) is the solution.
The geometric series [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] converges by the rule of convergence. Thus, the option [tex]2[/tex] from the given options is correct.
When a geometric series converges, it has a common ratio that is in between [tex]-1[/tex] and [tex]1[/tex].
The convergence of the geometric series depends on the common ratio [tex]r[/tex]. When [tex]r[/tex]>1, then the series diverges.When [tex]r[/tex]<1, then the series converges, and when [tex]r[/tex] = 1, then the series oscillates.
The common ratio [tex]r[/tex] of the series [tex]\dfrac{1}{81} +\dfrac{1}{27} +\dfrac{1}{9} +\dfrac{1}{3}[/tex] is greater than [tex]1.[/tex] So, the series diverges.
For the series, [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] , the common ratio [tex]r[/tex] is [tex]\dfrac{1}{2}[/tex], which is less than [tex]1[/tex] . So, the series converges.
For the series, [tex]\sum 7(-4)^n[/tex] , here the common ratio is [tex]-4[/tex] which does not lie in the range of convergence. Thus the given series is not convergent.
For the series,[tex]\sum \dfrac{1}{5}(2)^{n-1}[/tex] the common ratio is 2. So, the series is not convergent.
The geometric series is [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex].
Learn more about geometric series here:
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Can someone please help me with these 2 questions, pleaseeeee explain them too. :) Im also giving brainliest and this is worth 15 points.
The University of Arizona is monitoring the spread of a bacteria by placing 100 spores of the bacteria at the start of the project. The number, P, of the bacteria is expected to grow according to the differential equation dP over dt equals the product of 0.05 times P and the quantity 1 minus P over 2000, where P t is measured in days. When does the number of bacteria reach 1000?
Answer:
In 59 days, the number of bacteria reaches 1000.
Step-by-step explanation:
Given the data in the question;
by placing 100 spores of the bacteria at the start of the project,
p(0) = 100
dP over dt equals the product of 0.05 times P and the quantity 1 minus P over 2000
dp/dt = 0.05p( 1 - p/200 )
2000dp / p( 2000 - p ) = 0.05dt
[1 / p + 1 / 200-p ]dp = 0.05 dt
Now, we integrate
∫[1 / p + 1 / 200-p ]dp = ∫ 0.05 dt
ln p - ln [2000 - p ] = 0.05 + c'
ln[ p / 2000 - p ] = 0.05 + c'
p / 2000 - p = [tex]e^{0.05t + c'[/tex]
p / 2000 - p = k[tex]e^{0.05t[/tex]
Now, since p(0) = 100, we substitute
100 / (2000 - 100) = k[tex]e^{0.05(0)[/tex]
100 / 1900 = k × [tex]e^{0[/tex]
100 / 1900 = k × 1
k = 1 / 19
Therefore,
p / 2000 - p = k[tex]e^{0.05t[/tex]
p / 2000 - p = (1/19)[tex]e^{0.05t[/tex]
when p( t ) = 1000, then t will be;
1000 / (2000 - 1000) = (1/19)[tex]e^{0.05t[/tex]
1000 / 1000 = (1/19)[tex]e^{0.05t[/tex]
1 = (1/19 ) × [tex]e^{0.05t[/tex]
1/(1/19 ) = [tex]e^{0.05t[/tex]
(1 × 19)/1 = [tex]e^{0.05t[/tex]
[tex]e^{0.05t[/tex] = 19
0.05t = ln( 19 )
0.05t = 2.9444
t = 2.9444 / 0.05
t = 58.888 ≈ 59 days
Therefore, In 59 days, the number of bacteria reaches 1000.
Ill do anthing please help!!
Answer: 2π ft^2
Step-by-step explanation:
Area of a circle= π x the radius ^2
here your diameter is 4, and the radius is equivalent to half of the diameter so your radius equals 2.
A= π x 2^2
What is the volume of the cone?
Answer:
24π cm³
Step-by-step explanation:
Given the following data;
Radius, r = 3 cm
Height = 8 cm
To find the volume of a cone;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex]
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the equation, we have;
[tex] Volume = \frac{1}{3} * \pi * 3^{2}*8 [/tex]
[tex] Volume = \frac{1}{3} * \pi *9 *8 [/tex]
[tex] Volume = \pi * 3 *8 [/tex]
Volume of cone = 24π cm³
What is the measure of xº? Extra points !
Answer:
15 ° is correct answer
what is 1/8 times 2/7 in simplest form
Answer:
decimal form: 0.0357
fraction form: 375/10000
Step-by-step explanation:
The equation of a circle is (x-1)^2 +(y-2)^2=4. What is the center of the circle and what is the radius of the circle?
Answer:
Step-by-step explanation:
(x-1)²+(y-2)² =4 compare the given equation with the general one
(x-h)² +(y-k)² =r², where (h, k) are coordinates of the center and r is radius
so center is at ( 1, 2) and radius is 2
Find the median value. 1428, 961, 1258, 1324, 1185
How to find right triangle with Pythagorean theorem
Answer:
By using the formula of;
A² + B² = C²
Where A and B could be either of the 2 legs and C always have to be the hypotenuse of the right triangle. Hypotenuse is the longest leg of the triangle is the leg that's opposite to the right angle of the right triangle.
Hope this helps! I have attached a diagram for u to help you understand:
What's the first step in order to solve the exponential equation?
4-^5x = 21
Divide both sides by 21
O Convert the equation to a logarithm with a base of 21
O Divide both sides by 4
O Convert the equation to a logarithm with a base of 4
O The equation is already solved.
Answer:
I think it's A but I'm not sure
Find the measure of the arc or angle indicated. NO LINKS.
9514 1404 393
Answer:
10. A) 120°
11. D) 40°
12. D) 54°
13. A) 101°
Step-by-step explanation:
The applicable rules of angles and arcs are ...
the whole is the sum of the partsarcs of a circle total 360°an inscribed angle intercepts an arc of twice its measure__
10) Angles C and L intercept the same arc (DE) so will have the same measure.
15x = 16x -4
4 = x . . . . . . . . add 4-15x
arc DE = 2(15x) = 30(4) = 120 . . . degrees
__
11) Arc VW is twice the measure of angle X, so ...
9x +8 = 2(5x)
8 = x . . . . . . . . . subtract 9x
∠VXW = 5x = 5(8) = 40 . . . degrees
__
12) Arc EFG is twice the measure of angle W, so ...
70° +FG = 2(88°)
FG = 106° . . . . . . . . . subtract 70°
Arc FGW is twice the measure of angle E, so ...
106° +GW = 2(80°)
GW = 54° . . . . . . . . . . subtract 106°
__
13) Arc ST is twice the measure of angle R. The sum of arcs is 360°.
RS +ST +TR = 360°
119° +2(70°) +TR = 360°
TR = 101° . . . . . . . . subtract 259°
komplike türkçe karşılığı
Answer:
football is better
Step-by-step explanation:
football is better
Cevap: Yapılması zor olan
ẞaşarılar dilerim
i will give Brainiest if you are right
Answer:
d) $7.82
Step-by-step explanation:
just multiply the 2 numbers
Find the area of the credit card:
2 1/4 inch, 3 1/3 inch.
Answer:
4
Step-by-step explanation:
Find the measure of the angle indicated
Answer:
50?
Step-by-step explanation:
im not sure please think about it, but I think it might be 50
middle school math (05.02)The area of the parallelogram below is square meters. 6 m 8 m 2 m Numerical Answers Expected! (Picture included)
Distributive property
2(x + 1)
Answer:
Multiply using the distributive property which will give you the answer 2x + 2.
Step-by-step explanation:
Answer:
2x + 1
Step-by-step explanation:
2 * (x + 1) |
\/
2x + 1
Write (4b^4)^2 without exponents.
Answer:
(4*b*b*b*b)*(4*b*b*b*b)
John's age increased by 11 is 5 less than 5 times his age. How old is he?
If x represents John's age, which of the following equations could be used to solve this problem?
O x + 11 - 5 = 5x
O x + 11 = 5x -5
O x + 11 = 5 - 5x
How much principal must be deposited to have a balance of $2,229,
compounded semiannually at 3% for 3 years?
Answer:
2038.51
Step-by-step explanation:
Compound interest formula:
[tex]FV=PV(1+\frac{i}{n})^{n*t}\\2229=PV(1+\frac{.03}{2})^{2*3}\\2229=PV(1.093443264)\\2037.514547=PV[/tex]
Find the distance between the points (-15, 3) and (-9, 8).
Answer:
61 units
Step-by-step explanation:
Pls help I need a good grade
Answer:
5. 12, 6. 14, 7. 36, 8. 17, 9. 8, 10. 24
Step-by-step explanation:
Evaluate f(3m-4) given
What is the slope of the following table?
x y
-2 3
0 2
2 1
4 0
Answer:
-1/2
Step-by-step explanation:
At a customer service call center for a large company, the number of calls received per
hour is normally distributed with a mean of 130 calls and a standard deviation of 10
calls. What is the probability that during a given hour of the day there will be less
than 129 calls, to the nearest thousandth?
Statistics Calculator
.460Answer:
Step-by-step explanation:
14) 4.5a = 9.0
15) 4.8b = 36
Problem Solving Strategy: Write an Equation
Write an equation for each problem using the variable -n. Then solve and check the equation.
16) Allan has 84 baseball cards. This is 19 fewer cards than Mike. How many baseball cards does Mike have?
17) Jamie can ride her bike 3 times as fast as Michelle can jog. If Jamie rides her bike at a rate of 12 miles per hour, how fast can Michelle jog?
Problem Solving Strategy: Mental Math
Study each equation, then solve.
18) 5 + r = 6 - r
19) z - 16 = - 16
20) 7n - 7 = 0
Answer:
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
Are the polynomial functions even or odd ?
If you mirror the graph along the x axis and it lies on itself ( mirror image) it is even, if not it is odd.
If you mirror the top graph the high/ low points would be opposite so the top graph is odd
The bottoms graph can be mirrored so the bottom graph is even.
HELP
What is the equation of the trend line in the scatter plot ?
Answer:
y=-x+8
Step-by-step explanation:
Slope = (y₂-y₁)/(x₂-x₁) = (1-8)/(7-0) = -7/7 = -1
Y-intercept = (0,8)
Therefore, the equation of the trend line is y=-x+8
(05.05 HC) Figure ABCD has vertices A(-4, 1), B(2, 1). C(2, -5), and D(-4, -3). What is the area of figure ABCD?
A:24
B:30
C:36
D:45
Answer:
The answer is A
Step-by-step explanation:
I got it right on the test.