Answer:
absolutely convergent
Step-by-step explanation:
given data
sin(n)/3^n
solution
we have given term [tex]\frac{sin(n)}{3^n}[/tex]
when n = 1
and we know that
value of sin(n) ≤ 1
so that we can say that
[tex]\frac{sin(n)}{3^n}[/tex] ≤ [tex]\frac{1}{3^n}[/tex] or [tex](\frac{1}{3})^n[/tex]
here [tex]\frac{1}{3^n}[/tex] is converges this is because common ratio in geometric series
here r is [tex]\frac{1}{3}[/tex] and here it satisfy that -1 < r < 1
so it is converges
and
[tex]\frac{sin(n)}{3^n}[/tex] is also similar
so it is converges
and here no [tex](-1)^n[/tex] term is
so we can say series is absolutely convergent
32. Identify all real and non-real zeros of the function f(x) = x^3 + 5x^2 + 3x + 15.
options:
A. x = 0, −5, 1.7i, −1.7i
B. x = 0,−5, 1.7i
C. x = −5, 1.7i, −1.7i
D. x = 0,−3, −5
Answer:
x = -5 or x = i sqrt(3) or x = -i sqrt(3)
Step-by-step explanation:
Solve for x:
x^3 + 5 x^2 + 3 x + 15 = 0
The left hand side factors into a product with two terms:
(x + 5) (x^2 + 3) = 0
Split into two equations:
x + 5 = 0 or x^2 + 3 = 0
Subtract 5 from both sides:
x = -5 or x^2 + 3 = 0
x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:
x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2
sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):
x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2
sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):
x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2
(2 i sqrt(3))/2 = i sqrt(3):
x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2
(2 (-i sqrt(3)))/2 = -i sqrt(3):
Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)
Answer:
C. x = −5, 1.7i, −1.7i
Step-by-step explanation:
Quick answer:
C. x = −5, 1.7i, −1.7i
explanation:
C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.
Complete answer:
All odd degree polynomials have at least one real root.
By the real roots theorem, we know that
if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).
Values of [tex]\pm[/tex]p/q are
On trial and error, using the factor theorem, we see that
f(-5) = 0, therefore -5 is a real root. By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i
The answer is {-5, +/- sqrt(5) i}, or again,
C. x = −5, 1.7i, −1.7i
Give this problem a try and try to solve this
Answer:
No solution
Step-by-step explanation:
Given equation is,
[tex]\frac{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}{1-x}+\frac{1-x^{-\frac{1}{2}}}{1+x^\frac{1}{2}}-\frac{(4+x)^\frac{1}{2}}{(1-x)^\frac{1}{2}}=0[/tex]
[tex]\frac{x^{\frac{1}{2}}+x^{-\frac{1}{2}}}{1-x}+\frac{1-x^{-\frac{1}{2}}}{1+x^\frac{1}{2}}=\frac{(4+x)^\frac{1}{2}}{(1-x)^\frac{1}{2}}[/tex]
[tex]\frac{(x+1)}{\sqrt{x}(1-x)}+\frac{(\sqrt{x}-1)}{\sqrt{x}(1+\sqrt{x})}=(\frac{4+x}{1-x})^{\frac{1}{2}}[/tex]
[tex]\frac{(\sqrt{x}+1)(x+1)+(\sqrt{x}-1)(1-x)}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^{\frac{1}{2}}[/tex]
[tex]\frac{x\sqrt{x}+x+\sqrt{x}+1+\sqrt{x}-1-x\sqrt{x}+x}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]
[tex]\frac{2x+2\sqrt{x}}{\sqrt{x}(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]
[tex]\frac{2(\sqrt{x}+1)}{(1-x)(1+\sqrt{x})}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex]
[tex]\frac{2}{1-x}=(\frac{4+x}{1-x})^\frac{1}{2}[/tex] if x ≠ ±1
[tex](\frac{2}{1-x})^2=\frac{4+x}{1-x}[/tex] [Squaring on both the sides of the equation]
[tex]\frac{4}{(1-x)}=(4+x)[/tex]
4 = (1 - x)(4 + x)
4 = 4 - 4x + x - x²
0 = -3x - x²
x² + 3x = 0
x(x + 3) = 0
x = 0, -3
But both the solutions x = 0 and x = -3 are extraneous solutions, given equation has no solution.
Answer:
Could you please help me Genius??????
This table shows a linear relationship.
The slope of the line is ?
Answer:
2
Step-by-step explanation:
2,8 to 4,12 has a rise of 4 and a run of 2.
4/2 = 2
The slope is 2.
Remember rise/run!
Answer:
2
Step-by-step explanation:
We take take two points and use the slope formula
m = (y2-y1)/(x2-x1)
m = (12-8)/(4-2)
= 4/2
= 2
Using the insurance company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 14-year period. Round your answer to four decimal places.
Answer: 19.2222
Step-by-step explanation:
given data;
no of tornadoes = 2,1,0 because it’s fewer than 3.
period = 14 years
probability of a tornado in a calendar year = 0.12
solution:
probability of exactly 2 tornadoes
= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )
= 0.0144 * 0.2451 * 1092
= 3.8541
probability of exac one tornado
= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )
= 0.12 * 0.2157 * 182
= 12.7109
probability of exactly 0 tornado
= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )
= 1 * 0.1898 * 14
= 2.6572
probability if fewer than 3 tornadoes
= 3.8541 + 12.7109 +2.6572
= 19.2222
Benjamin’s and David’s ages add up to 36 years. The sum of twice their respective ages also add up to 72 years. Find their ages
Answer:
It can be any two numbers that sum up to 36.
eg:18+18,30+6,15+21
Step-by-step explanation:
Given:
Let Benjamin's age be x and David's age y.
x+y=36
2x+2y=72
Solution:
As twice of 36=72, any two numbers that add up to 36 ,will give a sum of 72 after multiplying them with 2.Therefore ,Benjamin's and David's age can be any set of numbers that sum up to 36.
PLEASE HELP QUICK!!!!!!! Find the length of a rectangle that has one side of length 8 and area 32
Answer:
4
Step-by-step explanation:
Length of one side=8
Area=32
Length of another side=x
8 into x = 32
X=32/8
=4
Which represents a measure of volume?
O 5 cm
O 5 square cm
05 cm
05 cm
Answer:
a) 5[tex]cm^{3}[/tex]
Step-by-step explanation:
Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.
When raising to 3, these dimensions are included and therefore 5[tex]cm^{3}[/tex] is a measure of volume.
Answer:
5cm^3
Step-by-step explanation:
Volume for a form will always be in cubic units.
Area of a shape will always be in squared units.
Length will not be in cubic or squared units.
Hence, the first option is a measure for volume.
The second option is equal to 5cm^2 which represents a measure for area, as does the fourth option.
The third option represents a measurement of length, for example the length of a line segment or the height of a figure.
the function y= -16t^2 + 248, models the hight y in feet of a stone t seconds after it dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground?
Answer:
[tex]t \: = 3.92 \: sec[/tex]
Step-by-step explanation:
When (t =0)
Height of cliff = 248 feet = 75.5m
Using Newton's equations of motion:
[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]
75.5 = 0 * t + 4.9 * t^2
Solving further :
[tex]t \: = 3.92 \: sec[/tex]
A researcher reports a 98% confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be [0.34, 0.38]. Therefore, there is a probability of 0.98 that the proportion of Drosophola with this mutation is between 0.34 and 0.38. True or False
Answer:
False
Step-by-step explanation:
The 98% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 98% confidence that the proportion of Drosophola with his mutation is between 0.34 and 0.38.
I need help badly best answer gets BRAINLIEST:)
Answer:
a = 55°, b = 65°, c = 65°, d = 60°, e = 120°, f = 60°
Step-by-step explanation:
Vertical angles are congruent. Since a and 55° are vertical angles, we know that a = 55°. Since b and 65° are vertical angles, we know that b = 65°. Alternate interior angles are congruent. Since b and c are alternate interior angles and b = 65°, we know that c = 65° as well. Since 60° and d are alternate interior angles, we know that d = 60°. Supplementary angles add up to 180°. Since d and e are supplementary and d = 60°, we know that e = 180 - 60 = 120°. Since vertical angles are congruent, we see that d and f are vertical angles and we know d = 60°, we also know that f = 60°.
Help please anyone. Thank You
Answer:
A) 144 yd²
Step-by-step explanation:
Base= 8x8=64
Side = 1/2*8*5=20
64+20+20+20+20=144 yd²
Answer:
168 sq yds
Step-by-step explanation:
5x8/2x2=40
8x8/2x2=64
8x8=64
40+64+64=168
Mario invested $5100 at 13%
to be compounded daily. What will be the value of Mario's investment in 2 years? Round your answer to the nearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
Answer:
Amount = $6614 and 19 cent
Step-by-step explanation:
Formula for compound interest is
A= p(1+r/n)^(nt)
Compounded daily
So n= 365*2= 730
T= 2
r= 0.13
P= 5100
A= p(1+r/n)^(nt)
A= 5100(1+0.13/730)^(730*2)
A= 5100(1+1.78082*10^-4)^(1460)
A= 5100(1.000178082)^1460
A= 5100(1.2969)
A= 6614.19
Amount = $6614 and 19 cent
Which ordered pair is a solution to the following linear system? y = x y = –x
Answer:
(2,2) (-1,-1)
Step-by-step explanation
i think this is there answer im sorry if im wrong
|3(x–2)|=12 pls help i need assistance
Answer:
x1 = -4
x2 = 6
Step-by-step explanation:
The 2 vertical lines are "absolute values" meaning whatever they contain has to be positive
For Example
|-3| = 3
So we can ignore if the answer we get is positive or negative because it will forced to be a positive
|3 x 4| = 12
|x - 2| = 4
x1 = 6
x2 = -2
36 minus 20 minus 32 times 1/4
Answer:
6
Step-by-step explanation:
36 - 20 - 32 x 1/4
=> 36 - 20 - 32/4
=> 36 - 20 - 8
=> 36 - 28
=> 6
Find the intersection point for the following liner function f(x)= 2x+3 g(x)=-4x-27
Answer:
( -5,-7)
Step-by-step explanation:
f(x)= 2x+3 g(x)=-4x-27
Set the two functions equal
2x+3 = -4x-27
Add 4x to each side
2x+3+4x = -4x-27+4x
6x+3 = -27
Subtract 3
6x+3 - 3 = -27-3
6x = -30
Divide each side by 6
6x/6 = -30/6
x =-5
Now we need to find the output
f(-5) = 2(-5) +3 = -10+3 = -7
Answer:
Step-by-step explanation:
big burgewr
a) which function has the graph with the greatest slope?
b) which functions have graphs with y intercepts greater than 3?
c)which function has the graph with a y intercept closest to 0
Answer:
a). Function (4)
b). Function (2)
c). Function (3)
Step-by-step explanation:
Characteristics of the functions given,
Function (1),
Form the given graph,
Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]-\frac{4}{1}[/tex]
= -4
Y- intercept of the given function = 2
Function (2),
From he given table,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{5-3}{0+1}[/tex]
= 2
y-intercept = 5 [Value of y for x = 0]
Function (3),
y = -x - 1
By comparing this equation with y = mx + b
Where 'm' = slope
and b = y-intercept
Slope = (-1)
y-intercept = (-1)
Function (4),
Slope = 5
y-intercept = (-4)
(a). Greatest slope of the function → Function (4)
(b). y-intercept greater than 3 → Function (2)
(c). Function with y-intercept closest to 0 → Function (3)
Look at parallelogram below d1 and d3 Are both 35 degrees what is the measurement of d2
Answer:
145 degrees
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary.
d2 = 180° -d1 = 180° -35°
d2 = 145°
A person tosses a fair coin until a tail appears for the first time. If the tail appearson thenth flip, the person winsndollars. LetXdenote the player’s winnings.ComputeE(X).
Answer: The answer in a is No while the answer in b is Yes
Step-by-step explanation:
Find the explanation in the attached file.
The multiplicative inverse of – 1 in the set {-1,1}is
Answer: The multiplicative inverse of – 1 in the set {-1,1} is -1.
Step-by-step explanation:
In algebra, the multiplicative inverse of a number(x) is a number (say y) such that
[tex]x\times y=1[/tex] [product of a number and its inverse =1]
if x= -1, then
[tex]-1\times y=1\Rightarrow\ y=-1[/tex]
That means , the multiplicative inverse of -1 is -1 itself.
Hence, the multiplicative inverse of – 1 in the set {-1,1} is -1.
Evaluate the expression for q = -2. 8q=
Answer:
-16
Step-by-step explanation:
8q
Let q = -2
8*-2
-16
Given the following diagram, find the required measures. Given: l | | m m 1 = 120° m 3 = 40° m 2 = 20 60 120
Step-by-step explanation:
your required answer is 60°.
Hello,
Here, in the figure;
angle 1= 120°
To find : m. of angle 2.
now,
angle 1 + angle 2= 180° { being linear pair}
or, 120° +angle 2 = 180°
or, angle 2= 180°-120°
Therefore, the measure of angle 2 is 60°.
Hope it helps you.....
The average of 4 numbers is 15 , the sum of 3 numbers is 14 what is the fourth number
Answer:
46
Step-by-step explanation:
(14+x)/4 = 15
14 + x = 60
x = 46
Answer:
46
Step-by-step explanation:
Let a to d be number 1 to 4 respectively.
15 = (a + b + c + d) / 4
(a + b + c + d) = 60 ------> total sum of the 4 numbers
Since the sum of 3 numbers (assuming a to c) is 14,
Fourth number (d) = 60 - 14
= 46
That's how I would do it, hope this helps :)
Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.
The number of values of xx in the interval [0,5π][0,5π] satisfying the equation 3sin2x−7sinx+2=03sin2x-7sinx+2=0 is/are
Answer:
6
Step-by-step explanation:
Given, 3sin2x−7sinx+2=03sin2x-7sinx+2=0
⇒(3sinx−1)(sinx−2)=0⇒3sinx-1sinx-2=0
⇒sinx=13 or 2⇒sinx=13 or 2
⇒sinx=13 [∵sinx≠2]⇒sinx=13 [∵sinx≠2]
Let sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα
now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)
⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]
Hence, required number of solutions are 6
7. Over the past 50 years, the number of hurricanes that have been reported are as follows: 9 times there were 6 hurricanes, 13 times there were 8 hurricanes, 16 times there were 12 hurricanes, and in the remaining years there were 14 hurricanes. What is the mean number of hurricanes is a year
Answer:
Step-by-step explanation:
Let us first generate the frequency table from the information given:
Hurricane number(X) Frequency(f) f(X)
6 9 54
8 13 104
12 16 192
14 12 168
Total ∑(f) = 50 ∑f(x) =518
In order to determine the last frequency (the remaining years), we will add the other frequencies and subtract the answer from 50, which is the total frequency (50 years). This is done as follows:
Let the last frequency be f
9 + 3 + 16 + f = 50
38 + f = 50
f = 50 - 38 = 12
Now, calculating mean:
[tex]\bar {X} = \frac{\sum f(x)}{\sum(f)} \\\\\bar {X} = \frac{518}{50} \\\\\bar {X} = 10.36[/tex]
Therefore mean number of hurricanes = 10.4 (to one decimal place)
An empty swimming pool is to be filled to the top. The pool is shaped like a rectangular prism with length 10m, width 8m , and depth 4m. Suppose water is pumped into the pool at a rate of 16m cubed per hour. How many hours does it take to fill the empty pool?
Answer:
20 hours
Step-by-step explanation:
10*8*4=320 (volume of the pool)
320/16=20 hours
Answer:
20 hours
Step-by-step explanation:
10x8x4 = 320
320 / 16 = 20
it takes 20 hours to fill the empty pool
(01.01 MC) Monica earned $60 from a bonus plus $8.50 per hour (h) she worked this week. Which of the following expressions best represents Monica's income for the week? 8.50h + 60 8.50 + 60 8.50 + 60h 8.50 + h + 60
Answer:
Option (1)
Step-by-step explanation:
Monica earned a bonus = $60
Per hour earning in addition to bonus = $8.50
Let she worked for 'h' hours this week.
Then total earning from the hourly rate = $8.50h
Total earning for the week = Earning of 'h' hours + Bonus earned
= $(8.50h + 60)
Therefore, Option (1) will represent Monica's earnings for the week.
Answer:
8.50h + 60
Step-by-step explanation:
PLEASE ANSWER! Which expression is equal to the length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1?
A: sin 0/ cos 0
B: sin^2 0 + tan^2 0
C: sin 0 + cos 0
D: sin^2 0 + cos^2 0
Answer:
b
Step-by-step explanation:
b: sin^2 0 + tan^2 0 this is just a gut feelings its been awhile since i done this kind of think i hope i could help
The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ
What is Right triangle?A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.
What is Hypotenuse?A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.
Here,
The length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1 is 1 unit.
We know that,
[tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ=1
Hence, The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ
Learn more about Right triangle and Hypotenuse here
https://brainly.com/question/2869318
#SPJ2
In 2004, 50 out of every 100 drivers at the National Trucking Company passed their driver's license exam on their first try. In 2005, 62 of the drivers passed on their first attempt. What was the percent increase in the passing rate?
Answer:
I believe it's a 12 percent increase.
Step-by-step explanation:
50/100= 50%
62/100= 62%
62%-50%=12%
