(8CQ) Determine whether the series -5+25-125+... is convergent or divergent.
Answers
Answer:
The answer is divergent ⇒ answer (b)
Step-by-step explanation:
* The series is -5 + 25 + -125 + ........
- It is a geometric series with:
- first term a = -5 and common ratio r = 25/-5 = -5
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = -5
∴ IrI = 5
∴ IrI > 1
∴ The series is divergent
Related Questions
Will give brainliest!!! Landry took out a cash advance of $ 240 on his credit card. If the bank charges him a $ 3.20 fee and his credit card company charges 3.4 percent of the advance, how much did the advance cost him?
Answers
Answer:
$ 11.36
Step-by-step explanation:
The advance cost him;
3.20 + 3.4% of 240
3.20 + (3.4/100)*240
3.20 + 8.16 = $ 11.36
If Logan's family can drive 23 1/8 miles on 1 gallon of gas,how far can they drive on 17 gallons
Answers
[tex]\bf \begin{array}{ccll} miles&\stackrel{gas}{gallons}\\ \cline{1-2}\\ 23\frac{1}{8}&1\\\\ x&17 \end{array}\implies \cfrac{23\frac{1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{23\cdot 8+1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{185}{8}}{x}=\cfrac{1}{17} \\\\\\ \cfrac{\frac{185}{8}}{\frac{x}{1}}=\cfrac{1}{17}\implies \cfrac{185}{8}\cdot \cfrac{1}{x}=\cfrac{1}{17}\implies \cfrac{185}{8x}=\cfrac{1}{17} \\\\\\ 3145=8x\implies \cfrac{3145}{8}=x\implies 393\frac{1}{8}=x[/tex]
If A=[tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex] and B=[tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex], find AB.
Answers
It's not C because
[tex](AB)_{1,1}=A_{1,c}B_{r,1}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}3\\-5\\-1\end{bmatrix}=-2[/tex]
where [tex](AB)_{1,1}[/tex] denotes the element of [tex]AB[/tex] in row 1, column 1, [tex]A_{1,c}[/tex] denotes the first row of [tex]A[/tex], and [tex]B_{r,1}[/tex] denotes the first column of [tex]B[/tex].
It's not A because
[tex](AB)_{1,2}=A_{1,c}B_{r,2}=\begin{bmatrix}-4&-3&5\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=16[/tex]
It's not D because
[tex](AB)_{2,2}=A_{2,c}B_{r,2}=\begin{bmatrix}-5&-4&-2\end{bmatrix}\begin{bmatrix}-4\\-5\\-3\end{bmatrix}=46[/tex]
So B must be the correct answer (and it is).
Examine the right triangle. What is the length of the hypotenuse, c?
Answers are in the pic
Answers
a^2+b^2=c^2 <----- the equation to find out sides for a right triangle
Every right triangle follows the pythagorean theorem: given the legs [tex]a[/tex] and [tex]b[/tex] and the hypothenuse [tex]c[/tex] we have
[tex]a^2+b^2=c^2 \implies c=\sqrt{a^2+b^2}[/tex]
In your case, a=3 and b=5, so we have
[tex]c=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}[/tex]
The figures below are similar. the area of the larger trapezoid is 121m^2. Find the area of the smaller trapezoid to the nearest square meter. Please help!
Answers
Answer:
54 square meters
Step-by-step explanation:
Similar figures have corresponding lengths as equal ratios.
Smaller trapezoid's base is given 12 and larger trapezoids base is given 18, so the scale factor is [tex]12k=18\\k=\frac{18}{12}\\k=1.5[/tex]
this means the lengths of larger is 1.5 times lengths of smaller.
In terms of area, the scale factor is squared. Hence the scale factor for area is [tex]k^2=(1.5)^2=2.25[/tex]
this means the area of larger is 2.25 times the area of smaller.
Now, Let area of smaller trapezoid be x so we can say: [tex]x(2.25)=121\\x=\frac{121}{2.25}\\x=53.78[/tex]
to nearest square meter, x = 54 meters squared
A yield sign measures 30 inches on all three sides. what is the area of the sign
Answers
Answer:
450
Step-by-step explanation:
To find an area of the triangle, you must first multiply the base and the height.
The following system has a solution: x=10, y=-3, z=14
Answers
In this problem, we have the following System of Three Equations in Three Variables, so our goal is to determine whether [tex]x=10, \ y=-3, \ z=14[/tex] is the solution to this system, that is, the ordered triple [tex]P(x,y,z)[/tex] where three planes intersect.
The easier way to find the answer is to plug in the x, y and z values in the equations and figure out whether the equations satisfy the solutions. Then:
[tex]First \ Equation: \\ \\ 3(10)+7(-3)-14=-5 \\ \\ It \ satisfies \ the \ first \ equation \\ \\ \\ Second \ Equation: \\ \\ 9(10)-(-3)-4(14)=37 \neq 17 \\ \\ It \ doesn't \ satisfy \ the \ second \ equation[/tex]
STOP HERE! Since the x, y an z values doesn't satisfy the second equation, the [tex]x=10, \ y=-3, \ z=14[/tex] is not the solution to the system of equations.
Find the limit if it exists. Picture provided
Answers
Answer:
b. -1
Step-by-step explanation:
When evaluating a limit at a specific value like this, just plug in the number and evaluate.
(2)³ - 3(2)² + 3
8 - 12 + 3
-4 + 3
-1
Answer:
b. [tex]-1[/tex]
Step-by-step explanation:
The given limit is
[tex]\lim_{x \to 2} (x^3-3x^2+3)[/tex]
This is the limit of a polynomial function so we plug in the value of x directly to obtain;
[tex]\lim_{x \to 2} x^3-3x^2+3=(2)^3-3(2)^2+3[/tex]
Evaluate
[tex]\lim_{x \to 2} x^3-3x^2+3=8-12+3[/tex]
This simplifies to
[tex]\lim_{x \to 2} x^3-3x^2+3=-1[/tex]
The correct choice is B.
(1Q) Describe how to transform the graph of g(x) = lnx into the graph of f(x)= ln(x-4)+3?
Answers
Answer:
B
Step-by-step explanation:
The correct answer is to go 4 units right (the direction is opposite to the sign) and 3 units up. The up and down direction is the same number as after the function.
Red: Parent Function y = ln(x)
Blue: 4 units right. 3 units up.
Answer: B
Answer:
b
Step-by-step explanation:
This is the manipulated variable in an experiment or study whose presence or degree determines the change in the dependent variable. When graphed this is graphed usually on the horizontal axis.
Answers
Answer:
This is called the independent variable.
Step-by-step explanation:
We know this because it is independent of all outside factors. Additionally, the horizontal axis (also known as the x axis), is the axis known for the independent variable.
What are the solutions to the system of equations?
(_____ , 2) and ( _____ , _____ )
Answers
Answer:
(1, 2) and (-1, -2)
Step-by-step explanation:
Since y = 2x, the first blank tells you
2x = 2
x = 1
____
Since the variables are squared, a negative solution is as good as a positive solution, so x = -1 and y = -2 will also work.
What is the solution to the system of equations? Use the substitution method. Y=?3x+12x+5y=18
Answers
The answer is
[tex]y = - 3x + \frac{18}{5} [/tex]
A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 206 like rock, 161 like country, and 118 like jazz. Moreover, 30 like rock and country, 27 like rock and jazz, 22 like country and jazz, and 11 like all three types of music. What is the probability that a randomly selected student likes neither rock nor country? Note: A Venn diagram may be useful here.
Answers
Answer:
163/500 = 0.326
Step-by-step Explanation:
Drawing a Venn diagram for this, we will have 3 circles. One will represent rock, one will represent country, and one will represent jazz.
There are 11 students that like all 3 types of music. This means the number 11 goes in the intersection of all 3 circles.
There are a total of 30 students that like rock and country; taking out the 11 that like all 3, this leaves 30-11 = 19 students in the intersection of just rock and country.
There are a total of 27 students that like rock and jazz; taking out the 11 that like all 3, this leaves 27-11 = 16 students in the intersection of just rock and jazz.
There are a total of 22 students that like country and jazz; taking out the 11 that like all 3, this leaves 22-11 = 11 students in the intersection of just country and jazz.
There are 206 students that like rock; taking out the 11 that like all 3, the 19 that like rock and country, and the 16 that like rock and jazz, we have
206-(11+19+16) = 206-(46) = 160 in just rock.
There are 161 students that like country; taking out the 11 that like all 3, the 19 that like rock and country, and the 11 that like country and jazz, we have
161-(11+19+11) = 161-(41) = 120 in just country.
There are 118 students that like jazz; taking out the 11 that like all 3, the 16 that like rock and jazz, and the 11 that like country and jazz, we have
118-(11+16+11) = 118-38 = 80 in just jazz.
This leaves
500-(80+120+160+11+11+19+16) = 500-417 = 83 students that like none of the 3 types of music.
This means for the probability that a student likes neither rock nor country, they either like just jazz or none of the 3; this is (83+80)/500 = 163/500 = 0.326.
The probability that a randomly selected student likes neither rock nor country is;
P(R' ∩ C') = 0.326
Let us denote them as follows;
Number that like rock music be R
Number that like Country music be C
Number that like Jazz music be J
Thus, as we are given we have;
R = 206
C = 161
J = 118
R ∩ C = 30 - 11 = 19
R ∩ J = 27 - 11 = 16
C ∩ J = 22 - 11 = 11
R ∩ C ∩ J = 11
Thus, number that liked only jazz music is;n(only jazz) = J - [(R ∩ J) + (C ∩ J) + (R ∩ C ∩ J)]
n(only jazz) = 118 - (16 + 11 + 11)
n(only J) = 80
Number of students that liked only Rock music;n(only Rock) = R - [(R ∩ C) + (R ∩ J) + (R ∩ C ∩ J)]
n(only Rock) = 206 - (19 + 16 + 11)
n(only R) = 160
Number of students that liked only country music;n(only country) = C - [(R ∩ C) + (C ∩ J) + (R ∩ C ∩ J)]
n(only country) = 161 - (19 + 11 + 11)
n(only C) = 120
Now, the number of students that like neither of the 3 music is;
A' ∩ B' ∩ C' = 500 - [(R ∩ C) + (R ∩ J) + (C ∩ J) + (R ∩ C ∩ J) + n(only J) + n(only R) + n(only C)]
⇒ 500 - (80 + 120 + 160 + 19 + 16 + 11 + 11)
⇒ A' ∩ B' ∩ C' = 83
Thus, number of students that likes neither rock nor country is;
n(A' ∩ B') = (A' ∩ B' ∩ C') + n(only C)
n(A' ∩ B') = 83 + 80
n(A' ∩ B') = 163
Thus, probability that a randomly selected student likes neither rock nor country = 163/500 = 0.326
Read more at; https://brainly.com/question/8945385
A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation, k?
A) xz/y
B) xy/z
C) z/xy
D) y/xz
Answers
[tex]A. \: \frac{xz}{y} [/tex]
EXPLANATION
If quantity x varies directly with y and inversely with z.
The we can write the mathematical statement,
[tex]x\propto \frac{y}{z} [/tex]
We introduce the constant of proportionality k, to obtain,
[tex]x = \frac{ky}{z} [/tex]
We now solve for k, by multiplying through by
[tex] \frac{z}{y} [/tex]
This implies that,
[tex] \frac{xz}{y} = k[/tex]
The correct choice is A.
Plot each set of points. Choose all that correctly define the quadrilateral in the coordinate plane. A(0, 0), B(0, 5), C(2, 5), D(2, 0) is a rectangle A(?2, 4), B(2, 4), C(4, 2), D(?2. 2) is an isosceles trapezoid A(0, 4), B(4, 1), C(0, ?5), D(?4, 1) is a square A(4, ?3), B(?2, ?3), C(?1, 1), D(5, 1) is a parallelogram
Answers
Answer:
quad
Step-by-step explanation:
Answer: the answers are a and d !!
Step-by-step explanation:
Identify the area of the rhombus. HELP PLEASE!!
Answers
Answer:
A = (x^2 - 2x - 8) m^2
Second option
Step-by-step explanation:
Area of rhombus = 1/2 d1 * d2
= 1/2(2x+4)(x-4)
= 1/2 (2x^2 -8x + 4x - 16)
= 1/2 (2x^2 - 4x - 16)
= x^2 - 2x - 8
A 2012 Gallup survey of a random sample of 1014 American adults indicates that American families spend on average $151 per week on food. The report further states that, with 95% confidence, this estimate has a margin of error of ±$7 . (a) This confidence interval is expressed in the form: “estimate ± margin of error.” What is the range of values (lower bound, upper bound) that corresponds to this confidence interval? (Enter your answers as a whole number.) lower bound: upper bound: (b) What is the parameter captured by this confidence interval? What does it mean to say that we have " 95% confidence" in this interval? The parameter captured by this interval is the population mean weekly spending on food ???? for all American adults. " 95% confidence" means that this interval was found using a procedure that produces correct results 95% of the time. The parameter captured by this interval is the populations weekly spending on food ???? for all American adults. " 95% confidence" means that this interval is correct 95% of the time. The parameter captured by this interval is the population mean weekly spending on food ???? for all American adults. " 95% confidence" means that this interval represents 95% of the population of American adults. The parameter captured by this interval is the populations weekly spending on food ???? for all American adults. " 95% confidence" means that this interval was found using a procedure that produces correct results 95% of the time.
Answers
Answer:135.9
Step-by-step explanation:you just have to multiply
Find the value of y. m angle 1 = 4y+22
Answers
I believe y = 41
Hope this helped!
The answer would be -21/4
Here’s how you solve it!
First move the variable to the left side which makes it change the sign to a negative
-4y➕1=22
Then you move the constant to the other side and change the sign
-4y=22-1
Now you subtract
22-1=21
-4y=21
Then divide both sides by -4
Then you are left with your answer
Y=-21/4
Hope this helps! :3
can someone PLEASE HELP ME ASAP!!!!!
Answers
Answer:
Last choice: 14 = (1/2)x(x - 12)
Step-by-step explanation:
base = x
height = x - 12
area = (1/2)bh
14 = (1/2)x(x - 12)
The answer is C. Thank Me Later ?
A company advertises that there are an average of 25 grams of potato chips in each bag of chips. A consumer group has collected a sample and wants to perform a test to see if the company is providing less than it advertises. H0: μ = 25 Ha: μ < 25 Which type of significance test should be used for this situation?
Answers
Answer:
one sample t-test will be appropriate in this case
Step-by-step explanation:
We are carrying out a hypothesis test of the mean with the population standard deviation being unknown. We shall estimate the population standard deviation with the sample equivalent, s in determining the value of the test-statistic.
Answer:
A left-tailed test
Step-by-step explanation:
What is the 101st term in the sequence 997, 989, 981, ...?
197
189
1805
1797
Answers
Answer: first option.
Step-by-step explanation:
Find the common difference d of the arithmetic sequence:
[tex]d=a_n-a_{(n-1)}\\d=989-997\\d=-8[/tex]
Then the formula for the 101st term is the shown below:
[tex]a_n=a_1+(n-1)d[/tex]
Where:
[tex]a_1=997\\d=-8\\n=101[/tex]
Substitute values into the formula. Therefore, you obtain:
[tex]a_n=997+(101-1)(-8)=197[/tex]
Answer:
[tex]a_{101}=197[/tex]
Step-by-step explanation:
The first term of the sequence is
[tex]a_1=997[/tex]
The given sequence is 997, 989, 981, ...
The common difference is
[tex]d=989-997=-8[/tex]
The nth ter of the sequence is
[tex]a_n=a_1+d(n-1)[/tex]
We plug in the first term and the common ratio to obtain;
[tex]a_n=997-8(n-1)[/tex]
[tex]a_n=997-8n+8[/tex]
[tex]a_n=1005-8n[/tex]
We substitute n=101 to get;
[tex]a_{101}=1005-8(101)[/tex]
[tex]a_{101}=197[/tex]
graph this Function 1: f(x) = −3x2 + 2
Answers
I guess that's f(x) = -3x^2+2
Well :
-3x^2+2=0
-3x^2=-2 / : (-3)
x^2= -2/-3
x^2= 2/3 / sqrt
x= +/ - sqrt(2)/sqrt(3)
We got the zero points.
x ~ +/- 0.81
f(0)= -3(0)^2 + 2
f(0)= 2
Mark three points:
(0.81;0)
(-0.81;0)
(0;2)
Connect with parabolic line and ya got a your graph
The area of rectangle bathroom floor is 53 5/8 feet. If the bathroom is 6 1/2 feet wide, what is the length
Answers
Answer:
The length is [tex]8\frac{1}{4}\ ft[/tex]
Step-by-step explanation:
we know that
The area of a rectangle is equal to
[tex]A=LW[/tex]
In this problem we have
[tex]A=53\frac{5}{8}\ ft^{2}[/tex]
[tex]W=6\frac{1}{2}\ ft[/tex]
convert to an improper fraction
[tex]A=53\frac{5}{8}=\frac{53*8+5}{8}=\frac{429}{8}\ ft^{2}[/tex]
[tex]W=6\frac{1}{2}=\frac{6*2+1}{2}=\frac{13}{2}\ ft[/tex]
substitute in the formula and solve for L
[tex]\frac{429}{8}=L\frac{13}{2}[/tex]
[tex]L=\frac{429*2}{8*13}=\frac{858}{104}\ ft[/tex]
Convert to mixed number
[tex]L=\frac{858}{104}=\frac{832}{104}+\frac{26}{104}=8\frac{1}{4}\ ft[/tex]
The length of the bathroom floor in this case is 8 1/4 feet.
The area of a rectangle is calculated by multiplying its length by its width. In this case, with the bathroom floor having an area of 53 5/8 square feet and a width of 6 1/2 feet, we can find the length as follows:
Area = Length x Width
53 5/8 = Length x 6 1/2
Length = 53 5/8 / 6 1/2
Length = 8 1/4 feet
Therefore, the length of the bathroom floor is 8 1/4 feet.
Bob started mowing his lawn at 9:55. It took 70 minutes. At what time did bob finish mowing?
Answers
60 minutes = 1 hour
55 + 5 = 60 70 - 5 = 65 10:00
10:00 + 60 min = 11:00 65 - 60 = 5
11:00 + 5 min = 11:05
Bob finished mowing at 11:05
PLEASE HELP
In the same circle, chord AB determines a 115° arc and chord AC determines a 43° arc. Find m∠BAC.
(2 answers)
Answers
Answer:
101 or 36 degrees
Step-by-step explanation:
If you add up the measures of the arcs it is 158. That means BC is 202 degrees. Divide it by 2 to find the angle. For the second answer, remember the question did not specify if the arcs were major or minor so you can flip them around.
Answer:
m∠BAC is 101° or 36°.
Step-by-step explanation:
Given,
[tex]m(\widehat{AB})=115^{\circ}[/tex]
[tex]m(\widehat{AC})=43^{\circ}[/tex]
To find : The measurement of angle BAC,
Let O be the center of the circle.
Since, here we have to cases ( shown in diagram ),
In Case 1 :
[tex]m\angle BOC = 360^{\circ}-[m(\widehat{AB})+m(\widehat{AC})][/tex]
[tex]=360^{\circ}-(115^{\circ}+43^{\circ})[/tex]
[tex]=360^{\circ}-158^{\circ}[/tex]
[tex]=202^{\circ}[/tex]
By the central angle theorem,
[tex]m\angle BAC = \frac{m\angle BOC}{2}[/tex]
[tex]=\frac{202^{\circ}}{2}=101^{\circ}[/tex]
In Case 2 :
[tex]m\angle BOC = m(\widehat{AB})-m(\widehat{AC})[/tex]
[tex]=115^{\circ}-43^{\circ}[/tex]
[tex]=72^{\circ}[/tex]
Again by the central angle theorem,
[tex]m\angle BAC = \frac{m\angle BOC}{2}[/tex]
[tex]=\frac{72^{\circ}}{2}=36^{\circ}[/tex]
Given a triangle with angles of 23, 90, 67, what type of triangle is it: acute, equiangular, obtuse, or right?
Answers
Answer:
It is a right triangle because if it contains a 90 degree angle (a right angle), it's a right triangle.
Step-by-step explanation:
It would be a right angled triangle because all triangles with a 90 degree angle are right angle triangles : 90 degrees is a right angle
There are red and blue balls in a bag. The number of blue balls is 27 and the red balls are 4/ 7 of all balls. What is the total number of balls in the bag?
Answers
➷ We know this:
3/7 = 27
You need to find the value of 1/7
To do this, divide by 3
27/3 = 9
1/7 = 9
Multiply this by 7 to get the total number of balls:
9 x 7 = 63
There are 63 balls.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
a car insurance company paid 1758.90 to repair a car that has been rear ended. this was 75% towards the total cost of the repair. what was the total cost
Answers
Answer:
Step-by-step explanation:
$2345.20
The total cost price of the car is $2,345.2.
Given that, a car insurance company paid 1758.90 to repair a car that has been rear-ended. This was 75% of the total cost of the repair.
We need to find what was the total cost price of the car.
What is the cost price?The amount paid to purchase an article or the price at which an article is made is known as its cost price. The cost price is abbreviated as C.P. Selling Price: The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.
Let the total cost price be x.
Now, 75% of x=1758.90
⇒0.75×x=1758.90
⇒x=$2,345.2
Therefore, the total cost price of the car is $2,345.2.
To learn more about the cost price visit:
https://brainly.com/question/11027396.
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The string is 120 feet long and stretched taut. The kite string makes an angle of 70° with the ground. How high above the ground is the kite flying. Show Your Work
Answers
Answer:
112.76 feet
Step-by-step explanation:
This is a right triangle trig problem. We have the length of the string which serves as the hypotenuse of the triangle, and we also have the reference angle (the angle the string makes with the ground) and we are looking for the height of the height, which is also the height of the triangle, which is also the side opposite the reference angle. So it's our job now to figure out which trig ratio relates the side opposite the reference angle to the hypotenuse. That's the sin ratio (opposite/hypotenuse). Set it up like this:
[tex]sin(70)=\frac{x}{120}[/tex]
Multiply both sides by 120 and then do the math in degree mode on your calculator. That gives you that x = 112.7631145
Don't know how many decimal places you need, but there you go!
Which graph represents the solution of the system of inequalities?
Answers
You need to rewrite the first equation to solve for y to get y >1+3x
Then graphing the two equations, the bottom right becomes the correct answer.