Answers
Answer:
C
Step-by-step explanation:
The formula is S=a1/1-r
The series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have a series shown in the picture.
The geometric sequence is shown in the options.
As we know, in the geometric sequence there is a first term and common difference
In the first sequence:
First term a = 2
Common difference = 2(0.1)/2
Common difference d = 0.1
The sum of the infinite series is:
S = a/(1 - r)
S = 2/(1 - 0.1)
S = 2.22
In the second sequence:
First term a = 15
Common difference = 15(0.3)/15
Common difference d = 0.3
The sum of the infinite series is:
S = a/(1 - r)
S = 15/(1 - 0.3)
S = 21.42
In the third sequence:
First term a = 4
Common difference = 4(0.2)/4
Common difference d = 0.2
The sum of the infinite series is:
S = a/(1 - r)
S = 4/(1 - 0.2)
S = 5
Thus, the series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.
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Related Questions
Given the following sets: A={ 2, 4, 6, 8, 10} B={ 3, 5, 7, 9} C={ 2, 3, 5, 7} N={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Match the following Unions and intersections to the correct set.
a) {2, 3, 5, 7, 9}
b){3, 5, 7, 9}
ｃ）{2, 3, 4, 5, 6, 7, 8, 10}
ｄ）{ }
ｅ）{2, 4, 6, 8, 10}
1.
What is A U C?
2.
What is A ∩ B?
3.
What is A ∩ N?
4.
What is B ∩ N?
5.
What is B U C?
Answers
2. d - only the numbers in both sets (there are none)
3. e - A is a proper subset of N, so their intersection is identical to A
4. b - B is a proper subset of N, so their intersection is identical to B
5. a - all the numbers in either of the sets
Due tomorrow help please
Answers
41 -39 = 2
43 -41 = 2
45 -43 = 2
These are all the same, so 2 is the common difference of the arithmetic sequence beginning with 39.
The Nth term is
[tex]a_{n}=a_{1}+(n-1)d\\a_{n}=39+2(n-1)\\a_{n}=37+2n[/tex]
The problem statement seems to ask for the 10th term and for a15. Here they are.
[tex]a_{10}=37+2\cdot 10=57\\a_{15}=37+2\cdot 15=67[/tex]
Betty makes pies. To make 6 pies, she uses 127 cups of flour. How many cups of flour are needed to make 1 pie?
Answers
Point X is the center of regular pentagon RSTUV. What is the measure of the angle of rotation that will map S onto U?
Answers
Final answer:
The measure of the angle of rotation that will map vertex S onto vertex U in a regular pentagon is 72 degrees.
Explanation:
The student is asking about an angle of rotation in a geometric context, specifically concerning mapping one vertex of a regular pentagon onto another through rotation about the center of the shape. In a regular pentagon, the angles between adjacent vertices are all equal, as it is a symmetrical shape. Since there are five vertices in a pentagon, you can divide the full rotation of 360 degrees by the number of vertices to find the angle of rotation that will map one vertex onto the next.
To map vertex S onto vertex U in a regular pentagon, you will need to rotate the pentagon by 360 degrees divided by 5 vertices, which is 72 degrees. Therefore, a rotation of 72 degrees around the center point X of the pentagon will map S onto U.
What is the 12th term of the sequence?
3, −9, 27, −81, 243, ...
Answers
The 12th term of the sequence 3, -9, 27, -81, 243, ... is 177,147.
Explanation:The given sequence is: 3, -9, 27, -81, 243, ...
To find the 12th term, we can observe that the sequence alternates between positive and negative, and each term is obtained by multiplying the previous term by -3. Starting with 3 as the first term, we can find the 12th term using the formula:
an = a1 * (-3)n-1
Substituting the values, we have:
a12 = 3 * (-3)12-1a12 = 3 * (-3)11a12 = 3 * (-32)5a12 = 3 * 95a12 = 3 * 59049a12 = 177,147Final answer:
The 12th term of the geometric sequence is -531441, found by using the formula for the nth term of a geometric series with a first term of 3 and a common ratio of -3.
Explanation:
The sequence given is geometric with each term being multiplied by -3 to obtain the next term. To find the 12th term of the sequence, we can use the formula for the nth term of a geometric sequence: Tn = a * rn-1, where a is the first term, r is the common ratio, and n is the term number.
For the given sequence, the first term a is 3 and the common ratio r is -3. The 12th term is found by placing these values into the formula:
T12 = 3 * (-3)12-1
T12 = 3 * (-3)11
T12 = 3 * (-177147)
T12 = -531441
Therefore, the 12th term of the sequence is -531441.
Divide. Give the quotient and remainder.
55 Divided by 8
Answers
therefore, quotient=6
remainder =7
In a class experiment, Sean finds that the probability that a student plays soccer is . If the school population is 300, how many students would we expect to play soccer, based on Sean's experiment?
Answers
well I just got out of a test and the answer was 144.
Find the first five terms of the sequence: an = 5an – 1 + 2; a1 = 3.
a) {3, 17, 87, 437, 2187}
b) {3, 15, 75, 375, 1875}
c) {3, 12, 17, 22, 27}
d) {3, 11, 27, 59, 123}
Answers
an=5an-1+2
where:
a1=3
then the other terms of the sequence will be:
a2=5a1+2
a2=5*3+2=17
a3=5a2+2
a3=5(17)+2
a3=87
a4=5a3+2
a4=5(87)+2
a4=437
a5=5a4+2
a5=(5*437+2)
a5=2187
hence the sequence will be:
3, 17, 87, 437, 2187
Answer: a) {3, 17, 87, 437, 2187}
2. Which of the following is equivalent to 5455 cm3?
(
0.5455 L
5.455 L
54.55 L
5455 L
Answers
How to find the sum of the squares of the lengths of the legs of a triangle of a=(-6,11) b=(2,8) c=(-1,0)?
Answers
To find the sum of the squares of the lengths of the legs of a triangle, use the distance formula to calculate the length of each leg and then square these lengths, summing the squares of the two legs that do not form the hypotenuse.
Explanation:To find the sum of the squares of the lengths of the legs of a triangle with vertices A=(-6,11), B=(2,8), and C=(-1,0), we first calculate the length of each leg using the distance formula, which is √((x2-x1)² + (y2-y1)²). For AB, AC, and BC we find distances:
AB = √((-6-2)² + (11-8)²)AC = √((-6+1)² + (11-0)²)BC = √((2+1)² + (8-0)²)Then, we square each leg's length:
AB² = ((-6-2)² + (11-8)²)AC² = ((-6+1)² + (11-0)²)BC² = ((2+1)² + (8-0)²)Finally, we sum up the squares of AB and AC because they represent the legs of the triangle:
Σ(leg squares) = AB² + AC²The sum of the squares of the lengths of the legs has now been found.
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Help on both 13 and 14. Show work please
Answers
14. ST = 2×(XY)
8z +3 = 2(3z +2)
2z = 1
z = 1/2
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years. Five years after Brian's initial investment, Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar)
Answers
Compound interest formula is [tex]A = P(1+r)^t[/tex]
Where P is the principal amount
r is the rate of interest
t is number of years
Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years
P = 10,000 , r= 4% = 0.04 , t =10
Plug in all the values
[tex]A = 10000(1+0.04)^{10}[/tex] = 14,802.44
Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.
P = 10,000 , r= 7% = 0.07 , t =5
Plug in all the values
[tex]A = 10000(1+0.07)^5[/tex] = 14,025.52
Brian balance after the interest period = $ 14,802.44
Chris balance after the interest period = $ 14,025.52
Balance in Brian's account is more than Chris account
Find the volume of the given prism. round to the nearest tenth if necessary.
a. 2,511.5 yd to the power of 3b) 1,255.7 yd to the power of 3c) 1,025.3 yd to the power of 3d) 1,450.0 yd to the power of 3
Answers
we know that
volume of the prism=area of the base*height
step 1
find the area of the base
the base is an equilateral triangle
calculate the area with the law of sines
Area=(1/2)*a²*sin C
where
a=10 yd
C=60° (three internal angles are equals)
Area=(1/2)*10²*sin 60°-----> 25√3 yd²
step 2
find the volume
volume of the prism=(25√3)*29-----> 1255.74 yd³ ------> 1255.7 yd³
the answer is the option
b) 1,255.7 yd to the power of 3
2) B $ 70.58
3) A 7 in
4) C 54 (pi)in^3
5) D 944 mm^3
~GENERAL OUT~
The day started at 48 degrees. by 3:00 p.m., the temperature has increased by 17 degrees. by nightfall, the temperature fell 17 degrees. what was the net change in temperature
Answers
Final answer:
The net change in temperature over the day is 0 degrees. After increasing by 17 degrees in the afternoon, the temperature fell by 17 degrees by nightfall, returning it to the starting temperature.
Explanation:
The student has asked about calculating the net change in temperature over the course of a day starting at 48 degrees. By 3:00 p.m., the temperature increased by 17 degrees, making it 65 degrees. But by nightfall, the temperature decreased by the same amount, falling back down to 48 degrees. The calculation of net change in this scenario is simple: subtract the starting temperature from the final temperature after all changes have occurred. In this case, the starting temperature was 48 degrees, it went up to 65 degrees, and then back to 48 degrees.
The net temperature change is therefore 48 degrees (final temperature) - 48 degrees (starting temperature), which equals 0 degrees. This means there was no net change in temperature over the course of the day. It is important to recognize that even though there was a temporary increase and subsequent decrease, the net effect cancels out, leaving the temperature the same as it started.
Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?
Answers
= (total distance)/(time of 1st journey + time of 2nd journey + time of 3rd journey)
Let d = the distance between Town A and Town B
So, total distance traveled = 3d
Time = distance/speed
time of 1st journey = d/x
time of 2nd journey = d/y
time of 3rd journey = d/z
Total time = d/x + d/y + dz
To simplify, rewrite with common denominator: dyz/xyz + dxz/xyz + dxy/xyz
So, total time = (dyz + dxz + dxy)/xyz
Average speed = (total distance)/(total time)
= 3d/[(dyz + dxz + dxy)/xyz]
= (3dxyz)/(dyz + dxz + dxy)
Divide top and bottom by d to get: (3xyz)/(yz + xz + xy)
Anna has leaned a ladder against the side of her house. The ladder forms a 72º angle with the ground and rests against the house at a spot that is 6 meters high. What length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?
Answers
Answer:
The best approximation of AB is 2 meters.Step-by-step explanation:
Notice that this situation models a right triangle, when the height, which is a leg of the triangle, is 6 meters.
Also, we know the angle between the ladder and the ground, which is 72°.
To find the distance from A to B, which from the bottom of the ladder to the bottom of the wall, we just need to use trigonometric reasons.
[tex]tan(72\°)=\frac{opposite \ leg}{adjacent \ leg}[/tex]
Why we use tangent? Because it relates both legs where we just need to find the adjacent one.
[tex]tan(72\°)=\frac{6}{AB}\\AB=\frac{6}{tan(72\°)} \\AB \approx \frac{6}{3} \\AB \approx 2 \ m[/tex]
Therefore, the best approximation of AB is 2 meters.
need help i havent done this since 2015 :// lolz
Answers
m∠R = m∠P = 180° -m∠Q
m∠Q = 107°
m∠P = 73°
25. If you draw any diagonal, it divides the figure into two congruent triangles (by the SSS postulate). Corresponding angles are congruent, so the diagonal is a transversal between parallel lines. Thus opposite sides are parallel and the figure is a parallelogram.
27. Opposite sides are equal, and the diagonals bisect each other. Your four equations are
2w+4 = 5w-6 . . . . w = 10/3
12 = 3x-3 . . . . . . . x = 5
6y = 4y+6 . . . . . . . y = 3
27 = (5/4)z +2 . . . z = 20
Answer:
2w+4 = 5w-6 . . . . w = 10/3
12 = 3x-3 . . . . . . . x = 5
6y = 4y+6 . . . . . . . y = 3
27 = (5/4)z +2 . . . z = 20
107 and 73
The cylinder below has a volume of 785 ft^3. and the cone has a volume of 314 ft^3.
(please see attached picture)
Which explains which figure has the greater height?
The cylinder has a greater height because the bases are the same, but the cylinder has a greater volume.
The cylinder has a greater height because the volume of the cylinder is greater than twice the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 4 times the volume of the cone.
Answers
Answer:
The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.
Step-by-step explanation:
Just did the quiz
Wha is the greatest common factor of 1 and 27
Answers
A line passes through the points (-6,4) and (-2,2). Which is the equation of the line?
Answers
Answer:
The equation of the line is [tex]y=\frac{-1}{2}x+1[/tex]
Step-by-step explanation:
1. The equation of the line that passes through two points can be expresed as:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex] (Eq.1)
where [tex]x_{1}[/tex], [tex]x_{2}[/tex], [tex]y_{1}[/tex] and [tex]y_{2}[/tex] are the given points.
2. Name the points:
[tex]x_{1}[/tex]=-6
[tex]x_{2}[/tex]=-2
[tex]y_{1}[/tex]=4
[tex]y_{2}[/tex]=2
3. Replace the points in the Eq.1:
[tex]\frac{y-4}{x-(-6)}=\frac{2-4}{-2-(-6)}[/tex]
[tex]\frac{y-4}{x+6}=\frac{2-4}{-2+6}[/tex]
[tex]\frac{y-4}{x+6}=\frac{-2}{4}[/tex]
[tex]\frac{4(y-4)}{x+6}=-2[/tex]
[tex]4(y-4)=-2(x+6)[/tex]
[tex]4y-16=-2x-12[/tex]
[tex]4y=-2x-12+16[/tex]
[tex]4y=-2x+4[/tex]
[tex]y=\frac{-2x+4}{4}[/tex]
[tex]y=\frac{-2x}{4}+\frac{4}{4}[/tex]
[tex]y=\frac{-1}{2}x+1[/tex]
Compare the exponential and logarithmic models of population growth
Answers
exponential is how much something increases by the way, tell me if this helps
order them from least to greatest, with the least at the top.
6\pi -6
\pi 3
\sqrt{99}
Answers
/sqrt{99} : 9.94
6/pi - 6 : 12.85
/pi 3 : 31
Sorry if it was incorrect, I am bored haha
Arranging the numbers in ascending order is: √99 < 6π - 6 < π³
How to arrange the numbers in ascending order?Arranging numbers in ascending order simply means arranging them from smallest to the biggest.
Now, the given numbers are:
6π - 6
π³
√99
Let us simplify the numbers to get:
6π - 6 = 6(3.14) - 6 = 12.85
π³ = 3.14³= 31
√99 = 9.95
Thus, arranging in ascending order is:
√99 < 6π - 6 < π³
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A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
pair of intersecting lines
degenerate ellipse
degenerate hyperbola
line
point
degenerate parabola
Answers
pair of intersecting lines
degenerate hyperbola
Answer:
degenerate hyperbola
pair of intersecting lines
Step-by-step explanation:
ABC Bookstore sells new books, n, for $12, and used books, u, for $8. The store earned $112 revenue last month. The store sold 4 more used books than new books. Using the substitution method, how many new and old books did ABC bookstore sell?
A.n = 4; u = 8
B.n = 8; u = 4
C.n = 8; u = 12
D.n = 12; u = 8
Answers
Revenue from new books = 12n
Revenue from old books = 8u
Last month, the store earned $112 as revenue, so we can write:
12n + 8u = 112
The store sold 4 more used books than new books, so we can write:
u = n + 4
Using the value of u, in above equation, we get:
12n + 8(n+4) = 112
12n +8n + 32 = 112
20n= 80
⇒
n=4
Since,
u = n + 4
u = 4 + 4 = 8
Thus, the store sold 4 new books and 8 old books last month. So the correct option is A
What is the expected value of the game if 3 hits pay $6, 2 hits pays $4, 1 hit pays $2, and 0 hits pays costs $4?
Answers
[tex]P\left(3\:hits\right)=0.7\times 0.5\times 0.3=0.105[/tex]
The probability of getting 2 hits is
[tex]P\left(2\:hits\right)=\left(0.7\times 0.5\times 0.7\right)+\left(0.7\times 0.5\times 0.3\right)+\left(0.3\times 0.5\times 0.3\right)=0.395[/tex]
The probability of getting 1 hit is
[tex]P\left(1\:hit\right)=\left(0.7\times 0.5\times 0.7\right)+\left(0.3\times 0.5\times 0.7\right)+\left(0.3\times 0.5\times 0.3\right)=0.395[/tex]
The probability of getting 0 hit is
[tex]P\left(0\:hit\right)=0.3\times 0.5\times 0.7=0.105[/tex]
The expected value is solved by adding the products of the probability by the given pay. That is
[tex]E=0.105\left(6\right)+0.395\left(4\right)+0.395\left(2\right)+0.105\left(4\right)=3.42[/tex]
The expected value is $3.42.
What is the best first step in solving the equation 4 + squrt(6x) = 5?
Answers
what is the height of the beach sign?
and what is the height of the beach umbrella?
I'm not sure if both images were attached, oops. but please help! I'll mark as brainliest! thank you!
Answers
[tex] tan 45 = \frac{8}{x} [/tex]
[tex](tan 45)(x) = 8 [/tex]
[tex]x = \frac{8}{tan 45} [/tex]
[tex]x = \frac{8}{1} [/tex]
[tex]x = 8[/tex]
The height of the umbrella is 8.
Hope this helps :)
A student takes a 15 question
a. True
b. False quiz and guesses at every answer. what is the probability that the student gets exactly 10 questions right, given that the student got the first question right?
Answers
Tan α = - 4/3 lies in quad 2, and cos β = 2/3 lies in quad 1 find
a. cos(α + β)
b. sin( α+β)
c. t...
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[tex]\cos^2x+\sin^2x=1[/tex]
[tex]\tan^2x+1=\sec^2x=\dfrac1{\cos^2x}[/tex]
[tex]\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta[/tex]
[tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta[/tex]
Not sure what part (c) is asking for, but I assume it's [tex]\tan(\alpha+\beta)[/tex], in which case
[tex]\tan(\alpha+\beta)=\dfrac{\sin(\alpha+\beta)}{\cos(\alpha+\beta)}[/tex]
If [tex]\tan\alpha=-\dfrac43[/tex], then
[tex]\dfrac1{\cos^2\alpha}=1+\left(-\dfrac43\right)^2=\dfrac{25}9[/tex]
[tex]\implies\cos\alpha=\pm\dfrac35[/tex]
We know that [tex]\alpha[/tex] lies in quadrant 2, i.e. [tex]\dfrac\pi2<\alpha<\pi[/tex], so we expect [tex]\cos\alpha<0[/tex]. So we take the negative root. We also find that
[tex]\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}\iff-\dfrac43=\dfrac{\sin\alpha}{-\frac35}\implies\sin\alpha=\dfrac45[/tex]
If [tex]\cos\beta=\dfrac23[/tex], then
[tex]\sin^2\beta=1-\left(\dfrac23\right)^2=\dfrac59\implies\sin\beta=\pm\dfrac{\sqrt5}3[/tex]
Since [tex]\beta[/tex] lies in quadrant 1, i.e. [tex]0<\beta<\dfrac\pi2[/tex], we know that [tex]\sin\beta>0[/tex], so we take the positive root.
Now,
[tex]\cos(\alpha+\beta)=-\dfrac35\cdot\dfrac23-\dfrac45\cdot\dfrac{\sqrt5}3=-\dfrac52-\dfrac4{3\sqrt5}[/tex]
[tex]\sin(\alpha+\beta)=\dfrac45\cdot\dfrac23+\left(-\dfrac35\right)\cdot\dfrac{\sqrt5}3=\dfrac8{15}-\dfrac1{\sqrt5}[/tex]
Then it follows that
[tex]\tan(\alpha+\beta)=\dfrac{\frac8{15}-\frac1{\sqrt5}}{-\frac52-\frac4{3\sqrt5}}=\dfrac{54-25\sqrt5}{22}[/tex]
What are the inputs of the function below?
Please help
Answers
Explanation:
The function declaration is f(x) where x represents the input. The input in the table given is the row labeled with x. Hence the inputs are -8 2 4 6 as shown in the table. So the correct option is Option (C) -8 2 4 6.
-i
Answer:
Input of the function are -8,2,4,6
Step-by-step explanation:
Input of a function are the domain .
Domain is the values of x. So inputs are the value of x in the table
Input of the table is x and output is f(x)
Input are the values that gives the output f(x)
From the table the x values are -8,2,4 and 6
Input of the function are -8,2,4,6