5+25+125+625+3125+15625 rewrite each series using sigma notation
Answers
2. You must find the ratio (r) between the adjacent members. Then, you have:
25/5=5
125/25=5
625/125=5
3125/625=5
15625/3125=5
3. Therefore, the ratio is:
r=5
4. Then, each term has te form 5^k. So, you have:
5^1=5
5^2=25
5^3=125
5^4=625
5^5=3125
5^6=15625
5. As you can see, "k" goes from 1 to 6.
6. The answer is shown in the image attached.
Final answer:
The series 5+25+125+625+3125+15625 can be rewritten in sigma notation as Σ 5*5^(n-1) from n=1 to 6, representing a geometric series with a common ratio of 5 and 6 terms.
Explanation:
To rewrite the series 5+25+125+625+3125+15625 using sigma notation, we first need to identify the pattern of the series. We notice that each term is 5 times the previous term, which is a characteristic of a geometric series. A geometric series can be expressed in sigma notation as Σ a*r^(n-1) from n=1 to N, where a is the first term, r is the common ratio between terms, and N is the number of terms.
In this series, a = 5, and r = 5. The series has 6 terms, so N = 6. Therefore, the series in sigma notation is Σ 5*5^(n-1) from n=1 to 6.
Related Questions
Find n (write in simplest radical form)
Answers
What does this mean? If you know the shortest side of a 30-60-90 triangle, you can find the longer leg by multiplying it by [tex] \sqrt{3} [/tex], and you can find the hypotenuse by multiplying the short leg by 2.
In the picture, note that the short leg of the triangle has a length of 9. Therefore, the long leg(or n) is simply 9[tex] \sqrt{3} [/tex]
what is the probability that a card picked at random from a 52-card deck of playing cards is a club or a jack?
Answers
[tex] |\Omega|=52\\
|A|=\underbrace{13}_{\text{clubs}}+\underbrace{4}_{\text{jacks}}-\underbrace{1}_{\text{jack of clubs}}=16\\\\
P(A)=\dfrac{16}{52}=\dfrac{4}{13}\approx31\% [/tex]
Answer:
A. 4/13
Step-by-step explanation:
4/13 in percent is 30%(30.7692308 percent)
For Plato Users
What number should be placed in the box to help complete the division calculation?
Answers
13*2 = 26
so the number in the box should be 260
helppppppppppppppppppppppppppppppppppp
Answers
The answer should be option B "d>0".
Reason:
First write the two equations:
5+d>5-d
Now to simplify it subtract 5 by 5:
5-5=0
Which equals:
d>5
(Since how the positive 5 came before the negative)
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Which explanation justifies how the area of a sector of a circle is derived?
Determine the percent of the sector of the circle divided by the degrees in a circle. Then find the number of triangles within a circle. Divide the two numbers and multiply by the area of the circle.
The sector of a circle is a fractional part of the circle. Determine the fraction of the circle that the sector represents. Multiply this fraction by the area of the entire circle.
The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle.
Find how many sector pieces fit in a circle. Divide this number by the total degrees in a circle. Then multiply the quotient by the diameter of the circle.
Answers
The angle of the sector is one fraction of 360°. Therefore the sector is a fraction of the entire circle. Multiply this fraction by the area of the entire circle and you get the area of the sector.
The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle justifies how the area of a sector of a circle is derived
The explanation that justifies how the area of a sector of a circle is derived is:
"The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle."
This method involves finding the fraction of the circle that the sector represents by dividing the central angle of the sector by 360 degrees. Then, multiply this fraction by the area of the whole circle to get the area of the sector.
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ2
Centered 7 meters above the ground, a Ferris wheel of radius 6 meters is rotating with angular speed 24 degrees per second.
a. Assuming that you begin at time t = 0 seconds at the lowest point on the wheel, find a formula that describes the distance h (in meters) from you to the ground after t seconds of riding.
b. At what times are you 10 meters above the ground? Please explain clearly how you got your solution.
Answers
a) The distance above the ground can be modeled using a cosine function.
.. h(t) = 7 -6cos(2πt/15)
b) h(t) = 10
.. 10 = 7 -6cos(2πt/15)
.. (10 -7)/-6 = cos(2πt/15)
.. 2πt/15 = π ±π/3 +2kπ
. t = 7.5*((1 ±1/3) +2k) . . . . . . . . seconds; k = any integer
You are 10 meters above the ground at t=5 seconds and every 15 seconds thereafter, as well as at t=10 seconds and every 15 seconds thereafter.
Why is circle 1 similar to circle 2?
Circle 1: center (2, 3) and radius 4
Circle 2: center (2, 3) and radius 12
Answers
Circle 2 is a dilation of circle 1 with a scale factor of 3.
Answer: The answer is given below.
Step-by-step explanation: The given circles are:
Circle 1: centre (2, 3) and radius 4
Circle 2: centre (2, 3) and radius 12.
The equations of circle 1 and circle 2 are respectively given as :
[tex](x-2)^2+(y-3)^2=4^2,\\\\(x-2)^2+(y-3)^2=12^2.[/tex]
These two circles are drawn on the graph as shown in the attached figure.
We can easily see that the Circle 2 is a dilation of Circle 1 with a scale factor
[tex]S=\dfrac{12}{4}=3.[/tex]
Thus, the two circles are similar.
Sigma Notation: Need Help!!
Problem 1:
Evaluate the summation of 3 times negative 2 to the n minus 1 power, from n equals 1 to 5.
Choices:
A.-93
B.-33
C.33
D.93,
Answers
To answer this question, first solve the equation 3 x -2^(n-1) for n=1, n=2,
n=3, n=4, and n=5.
Where n=1
3 x -2^(1-1)
3 x -2^0
3 x 1
n1 = 3
Where n=2
3 x -2^(2-1)
3 x -2^1
3 x -2
n2 = -6
Where n=3
3 x -2^(3-1)
3 x -2^2
3 x 4
n3 = 12
Where n=4
3 x -2^(4-1)
3 x -2^3
3 x -8
n4 = -24
Where n=5
3 x -2^(5-1)
3 x -2^4
3 x 16
n5 = 48
The next step is to find the summation by adding n1 + n2 + n3 + n4 + n5.
3 + (-6) + (12) + (-24) + (48) =
3 - 6 + 12 - 24 + 48
= 33
The answer is C. 33
Final answer:
To solve the sigma notation problem, we individually calculate each term for n from 1 to 5 and sum them up, resulting in a total value of 33. Thus, the correct answer is C.33.
Explanation:
The problem involves evaluating a series using sigma notation. Specifically, we're looking at the summation of 3 × (-2)n-1, with n going from 1 to 5.
To find the solution, we need to calculate each term separately for each value of n, and then sum all of the calculated terms together.
For n=1: [tex]3 \times (-2)^{1-1[/tex] = 3 × 1 = 3For n=2: [tex]3 \times (-2)^{2-1[/tex] = 3 × (-2) = -6For n=3: [tex]3 \times (-2)^{3-1[/tex] = 3 × 4 = 12For n=4: [tex]3 \times(-2)^{4-1[/tex] = 3 × (-8) = -24For n=5: [tex]3 \times (-2)^{5-1[/tex] = 3 × 16 = 48Adding these values together: 3 - 6 + 12 - 24 + 48 = 33.
So the correct answer to the summation is 33, which corresponds to choice C.
What is the value of c such that x2 + 10x + c is a perfect square trinomial?
Answers
The value of c that makes x² + 10x + c a perfect square trinomial is c = 25.
What value of c makes the equation a perfect square trinomial?Given the equation in the question:
x² + 10x + c
A perfect square trinomial is of the form (ax² + bx + c), and it can be factored into (px + q)², where p and q are constants.
To find the value of c such that x² + 10x + c is a perfect square trinomial, we need to factor it as (px + q)².
Note that, the coefficient of x in the given trinomial is 10, so 2pq must equal 10.
Also, the coefficient of x² is 1, so p² must equal 1.
Hence, we have:
2pq = 10
p² = 1
From equation (2), we know that p could be either 1 or -1, after taking the square of both sides:
If p = 1, from equation (1) we have:
2pq = 10
2(1)q = 10
2q = 10
q = 10/2
q = 5
So, if p = 1 and q = 5, the perfect square trinomial is (x + 5)².
Let's expand to check:
(x + 5)² = x² + 10x + 25
Therefore, the value of c is 25.
Learn more about perfect square trinomials here: https://brainly.com/question/30594377
#SPJ3
Do two triangles with the same base and height have the same area
Answers
The area is half the product of base and height. If those dimensions are the same, the area is the same.
What is the area of a circle whose radius is 5 ft? 5π ft² 10π ft² 20π ft² 25π ft²
Answers
Answer:
The area of the circle is equal to [tex]25 \pi\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
In this problem we have
[tex]r=5\ ft[/tex]
substitute
[tex]A=\pi (5^{2})=25 \pi\ ft^{2}[/tex]
The area of a circle with a radius of 5 ft is equal to 25π ft² which is calculated using the formula A = πr². Below step-by-step calculation helps in understanding how to apply the formula correctly.
To find the area of a circle whose radius is 5 ft, we use the formula for the area of a circle: [tex]A = \pi r^2[/tex].
Step 1: Identify the radius (r) of the circle
[tex]r=5 \text{ ft}[/tex]Step 2: Plug the radius value into the formula
[tex]A &= \pi (5 \text{ ft})^2[/tex]Step 3: Square the radius
[tex](5 \text{ ft})^2 = 25 \text{ ft}^2[/tex]Step 4: Multiply this result by π (pi)
[tex]A = \pi \times 25 \text{ ft}^2[/tex]which gives [tex]A = 25 \pi \text{ ft}^2[/tex].
Therefore, the area of a circle with a radius of 5 ft is 25π ft².
find the fraction
53*53−32*32/61*61−44*44
Answers
2809 - 1024 / 3721 - 1936
Then subtract
1785 / 1785 = 1
The answer is 1. So the fraction is a whole number
Hope this helps
Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three?
Answers
The quotients are different because the order matters in division. When 3 is divided by 1/5 it becomes a multiplication problem with reciprocal of 1/5, yielding 15. However, when 1/5 is divided by 3, it becomes multiplication with reciprocal of 3 and yields 1/15.
Explanation:The reason that the quotient of three divided by one-fifth is different from the quotient of one-fifth divided by three is due to how division works in mathematics. To put it simply, the order of numbers in a division operation matters; it is not commutative like addition or multiplication.
When you divide 3 by 1/5, you're essentially asking, 'how many times does 1/5 fit into 3?'. Here, you're dealing with fractions and whole numbers. To perform the division, we multiply 3 by the reciprocal of 1/5, which is 5. The answer is 3 * 5 = 15.
But, when you divide 1/5 by 3, you're asking 'how many times does 3 fit into 1/5?'. Here, you need to multiply 1/5 by the reciprocal of 3, which is 1/3. The calculation is (1/5) * (1/3) = 1/15.
Learn more about Division Operations here:
https://brainly.com/question/12984208
#SPJ12
What is the sum of the first 7 terms of the series −4+8−16+32−... ?
Enter your answer in the box.
Answers
we have that
−4+8−16+32−.....
a1=-2*(-2)-----> -4
a2=-4*(-2)-----> +8
a3=+8*(-2)-----> -16
a4=-16*(-2)----> +32
a5=+32*(-2)----> -64
a6=-64*(-2)-----> +128
a7=+128*(-2)-----> -256
The sum of the first 7 terms of the series is
[a1+a2+a3+a4+a5+a6+a7]-----> [-4+8-16+32-64+128-256]-------> -172
the answer is -172
simplify the expression. write the answer using scientific notation 4(6.2x10^11)
Answers
= 2.48 × 10¹²
(scientific notation)
= 2.48e12
(scientific e notation)
= 2.48 × 10¹²
(engineering notation)
(trillion; prefix tera- (T))
= 2480000000000
(real number)
The correct answer is 2.48*10^12.
1. What is the simplest form of the radical expression? 4 fourth root of two x+ 6 fourth root of two x (1 point) 10fourth root of two x 10 fourth root of four x 20 fourth root of two x not possible to simplify,
Answers
4·⁴√(2x) + 6·⁴√(2x)
As you can see, the radicals are exactly the same: same index, same radicand.
Therefore you can treat it as if it was:
4 apples + 6 apples
which is 10 apples,
or in your case:
10·⁴√(2x)
Hence, the correct answer is option A.
1. The center of a circle is located at (5, −5) . The radius of the circle is 3.
What is the equation of the circle in general form?
x^2+y^2+10x−10y+47=0
x^2+y^2+10x−10y+41=0
x^2+y^2−10x+10y+47=0
x^2+y^2−10x+10y+41=0
2.The standard form of the equation of a circle is (x−5)2+(y−6)2=1.
What is the general form of the equation?
x^2+y^2−10x−12y−62=0
x^2+y^2+10x+12y+62=0
x^2+y^2−10x−12y+60=0
x^2+y^2+10x+12y+60=0
Answers
1) Answer D since (x-5)²+(y+5)²=9 ==>x²+y²-10x+10y+41=0
2) Answer C since (x-5)²+(y-6)²=1 ==>x²+y²-10x-12y+60=0
GIVING BRAINLIEST TO THE FIRST RIGHT ANSWER!!!!
The following is the correct way to show the product for 0.453 × 8.1:
True
False
Answers
Answer:
true
Step-by-step explanation:
Find the volume v of the described solid s. a right circular cone with height 7h and base radius 3r
Answers
r = 3 cm
h = 7 cm
s = 7.61577 cm
V = 65.9734 cm³
L = 71.777 cm²
B = 28.2743 cm²
A = 100.051 cm²
Agenda:
r = radius
h = height
s = slant height
V = volume
L = lateral surface area
B = base surface area
A = total surface area
π = pi = 3.14159
√ = square root
Formula: Volume of a cone: V = (1/3)πr²h
The volume of a right circular cone with height 7h and base radius 3r is ⅔ 9r² h.
Explanation:The volume of a right circular cone can be calculated using the formula V = ⅔ ² h, where r is the radius of the base and h is the height of the cone.
In this case, the height of the cone is 7h and the base radius is 3r.Plugging in the values, we have V = ⅔ (3r)² (7h) = ⅔ 9r² h.
Learn more about volume of right circular cone here:https://brainly.com/question/32160797
#SPJ11
An unlabeled hierarchical diagram of various astronomical bodies is shown below. The labels A, B, C and D can be used to represent the galaxy, Mars, universe, moon, and solar system.
Part 1: Which four astronomical bodies would you choose to represent the four labels in the diagram?
Part 2: Explain why the hierarchical level D is different from the rest.
Answers
The four astronomical bodies represents here are A represents Universe, B represents Galaxy, C represents Solar System, and D represents Mars.
The hierarchical level D is different from the rest is because Mars is a planet and unlike all other astronomical bodies it does not hold other astronomical bodies with in it.
What are astronomical bodies?"Astronomical bodies are objects in space like sun, moon, planets, and stars. They form a part of the vast universe we live in and are very far from Earth."
What is Universe?"The universe includes all space, time, and their objects that also includes planets, stars, galaxies, and other forms of matter and energy."
What is Galaxy?"Galaxy is a vast collection of dust, gas, billions of stars with their solar systems that are all held together by gravity."
What is Solar System?"Solar System is a gravitationally bound system of eight planets, their moons in orbit round the sun with small bodies like comets, meteoroids, and asteroids."
What is Mars?"Mars is the fourth planet from the sun and the second smallest planet in the Solar System."
To learn more about Mars and Solar System here
https://brainly.com/question/14742625
#SPJ2
1.Which explanation justifies how the area of a sector of a circle is derived?
Determine how many triangles can fit into a circle. Divide 360° by the number of triangles. Multiply the quotient by the area of the circle .
Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.
Determine the degree of the sector. Divide by 180° and then multiply it by the area of the triangle the sector is in.
Partition the circle into unit squares. Determine the area of the sector and multiply the area by the degree of the circle.
Answers
2) Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.
area of the circle is calculated by;
area = πr² , where r- radius of circle
the central angle of a circle is 360°. Area of the circle is calculated for central angle of 360°.
Sector is when 2 arms/ radii enclose a central angle between them.
area for 360° = πr²
area for 1 ° = area/ 360
area for central angle of sector = area * angle/ 360
the angle of sector is divided by 360 and taken as a fraction .this fraction of the total area of the circle is taken as the area of the sector.
To solve 5(2^x+4)=15, first divide each side by
Answers
Answer:5
Step-by-step explanation:
PLEASE CHECK THIS FOR ME
LET ME KNOW IF ITS CORRECT
Answers
Initial numbers of horse: W(0)=?
n=0→W(0) = 15 . b^0
W(0)= 15 . 1
W(0)= 15
Answer: Based on the model, the initial number of horses is 15.
2) If b=1.35, the annual percent growth rate of the number of horses: r=?
b=1+r
1+r=1.35
Solving for r:
1+r-1=1.35-1
r=0.35
r=0.35*100%
r=35%
Answer: If b=1.35, the annual percent growth rate of the number of horses would be 35 %.
find the equation of the straight line passing throughthe point (3,5) which is perpendicular to the line y=3x+2
please explain
Answers
5=(3)(-1/3)+b Plug in x and y
5=-1+b
6=b
Y=-1/3x+6
2.. When two lines are parallel to each other their gradient is the same I.e m¹ =m²...
This question will make use of the first rule...
The second straight line was given to be y =3x+2.. Generally a straight line has the formula y=mx+c(where m=gradient, c=intercept)
So in y=3x+2(the gradient here is 3)
Now from the first rule the product of this line and the line of coordinates (3,5) is - 1..
:- m1*m2=-1
3×m2=-1
m2 = - 1/3....this is the gradient of the line with coordinate (3,5)
Gradient = (y-y₁)/(x-x₁)
-1/3 = (y-5)/(x-3)
Cross multiply you'll have
-1(x-3)=3(y-5)
-x+3=3y-15
3y+x-15-3=0
3y+x-18=0........... Checked....
Or 3y+x=18......
Hope this helped....?
Graph the ordered pairs for y=4x+2 using x={-2,1,2}
Answers
The graph of the ordered pairs is a straight line graph with x,y values (-2, -6), (1, 6), and (2,10).
What are ordered pairs.
In geometry, Ordered pairs are the values of x and y on the coordinate plane. They are called ordered pairs because they are usually arrange in (x,y) axis.
For a linear equation, the graph is a straight line graph. From the information given:
y = 4x + 2
The slope of the line (m) = 4The y-intercept (b) = 2The points x-axis {-2, 1, 2} are marked on the graph and the corresponding y-values are {-6, 6, 10} respectively.
The supply and demand curves reflect data for a specific brand of sunglasses. Which circumstance best explains the shift of the demand curve from D to D1?
a. An ad campaign highlights the sustainable resources used to make the sunglasses.
b. Consumer reports indicate that the sunglasses break easily.
c. Fuel costs increase, making it more costly to produce the sunglasses.
d. Tax incentives encourage the producer to hire more workers.
Answers
Since there is a decrease in quantity and supply the answer would be Consumer reports indicate that the sunglasses break easily.
Answer "A" is definitely wrong
You are paid $8.50/hr at your part-time job. Your deductions are FICA (7.65%), federal tax withholding (9.15%), and state tax withholding (7.5%). Your travel expenses are $6.00 per day worked. You work 16 hours over a 4-day period of time. What is your net income after travel expenses?,
Answers
The junior class has 50 students. Twenty-five students take only french, 15 take only Latin, and 10 take both. If a student is chosen at random from the class, what is the probability that the student takes latin?
A.)1
B.)1/2
C.)
1/4
Answers
Therefore:
15+10 =25 total students taking Latin
25students / 50 total students = 1/2
The answer is 1/2.
Answer: B ) [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given: The number of students in junior class n(S)= 50
The number of students take only Latin n(L-F)= 15
The number of students take only French n(F-L)=25
The number of students take both = n(F∩L)=10
The number of students take Latin n(L)=n(L-F)+n(F∩L)=15+10=25
Therefore, the probability that the student takes Latin is given by :-
[tex]\text{Probability(Latin)}=\frac{\text{number of students take latin}}{\text{Total students}}\\\\=\frac{25}{50}=\frac{1}{2}[/tex]
Mark's father travels 463 miles every month for his job. How many miles does he travel in 8 months?
Answers
That would be 3,704 miles.
solve for x: 7/8-1/x=3/4
x = 1
x = 2
x = 4
x = 8
Answers
9514 1404 393
Answer:
x = 8
Step-by-step explanation:
[tex]\dfrac{7}{8}-\dfrac{1}{x}=\dfrac{3}{4}\\\\7x-8=6x\qquad\text{multiply by $8x$ to clear fractions}\\\\\boxed{x=8}\qquad\text{add $8-6x$}[/tex]
__
If you don't mind dealing with fractions, you can add 1/x -3/4 to get ...
7/8 -3/4 = 1/x
1/8 = 1/x . . . . . . . simplify
x = 8 . . . . . . . . . . take reciprocals; equivalently, multiply by 8x.