Answer:
Step-by-step explanation:
Given two series A and B;
Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
Both series are geometric series since they have the same common ratio. Given the geometric series T₁, T₂, T₃, T₄..., the common ratio r is expressed as [tex]\frac{T_2}{T_1} =\frac{T_3}{T_2} =\frac{T_4}{T_3} = r[/tex].
a) For series A, Given T₁ = 10, T₂ = 4, T₃ = 8/5 and T₄ = 13/125
Its common ratio is expressed as [tex]\frac{4}{10} =\frac{8/5}{4} =\frac{13/125}{8/5} = 2/5[/tex]
Hence the common ratio of series A is 2/5
The sum to infinity of the geometric series will be expressed as [tex]s_\infty = \dfrac{a}{1-r}[/tex]
Note that the sum to infifnity is used since the series is tending to infinity.
a is the first term if the series = 10
r - 2/5
On substituting this values into the formula;
[tex]s_\infty = \dfrac{10}{1-2/5} \\\\s_\infty = \dfrac{10}{3/5} \\\\s_\infty = 10* 5/3\\s_\infty = 50/3[/tex]
Hence the sum of the series is 50/3
b) For the series B;
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...
The common ratio of the series is expressed as shown;
[tex]\frac{3/5}{1/5} =\frac{9/5}{3/5}= \frac{27/5}{9/5 } = r\\ r = (3/5 * 5/1) = 9/5*5/3 = 27/5*5/9 = 3[/tex]
Hence its common ratio is 3.
Sun of the series is expressed similarly as:
[tex]s_\infty = \frac{a}{1-r}\\ s_\infty = \frac{1/5}{1-3}\\\\s_\infty = \frac{1/5}{-2}\\\\[/tex]
[tex]s_\infty = 1/5 * -1/2\\s_\infty = -1/10[/tex]
Hence the sum of series B is -1/10
G = {(1, 1), (1, 2), (1, 3), (1, 4)} Is G a function and why? Yes, no two ordered pairs in this list has the same second element. Yes, there is more than one ordered pair in this list. No, there is a limited number of ordered pairs in this list. No, each ordered pair in this list has the same first element.
Answer:
No, each ordered pair in this list has the same first element.
Step-by-step explanation:
An input can only have 1 output, but multiple inputs can have the same output. How you can check this if you have a graph is if you can draw a straight line (top to bottom) anywhere on the graph and it intersects with the line once or not at all.
Answer:
No, each ordered pair in this list has the same first element.
Step-by-step explanation:
A function is a relation in which each possible input value leads to exactly one output value.Given: G = {(1, 1), (1, 2), (1, 3), (1, 4)}
It has same input (x=1) that leads to multiple outputs (y= 1,2,3,4). This relationship is not a function as per definition provided above.Correct answer choice is:
No, each ordered pair in this list has the same first element.What are all of the real roots of the following polynomial? f(x) = x^4 - x^3 - 13x^2 + x + 12
a) -1 and 1
b) -3, -1, 1, and 3
c) -3 and 3
d) -3, -1, 1, and 4
Answer:
1,-1,4,-3 so D
Step-by-step explanation:
0 = x^4 - x^3 -13x^2 + x + 12
x = 1,-1,4,-3
The final answer is -3,-1,1 and 4
What is the relation between roots and the biquadratic equation?The biquadratic equation is of the form ax⁴+bx³+cx²+dx+e and hence
The sum of roots is -b/a, the sum of the product of two roots is c/a, the sum of the product of three roots is -d/a, and the product of all four roots is e/a.
Solving the given problemThere is no specific method of solving a biquadratic equation, hence we use the trial and error method and also some form of the root.
So finding f(1) = 1-1-13+1+12 = 0 hence 1 is a root.
finding f(-1) = 1-(-1)-13-1+12 = 0 hence -1 is also a root.
So let other roots be p,q
Now we can use sum of roots formula which is p+q+1-1= 1, hence p+q=1
product of roots p*q*1*-1=12, pq= -12 substituting p = -12/q
-12/q+q = 1, multiplying q on both sides
q²-12=q, q²-q-12=0, q²-4q+3q-12 = 0, q(q-4q)+3(q-4)=0
(q-4)(q+3) = 0 hence the roots are 4,-3 also
Hence 1,-1,4, and -3 are the roots of the equation.
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{(-2,8),(4,6),(10,4)} Which point, when added to the set, would form a relation that is not a function?
Answer:
Point : ( -2, 15 )
Step-by-step explanation:
A point that would make this relation not a function would be one that shares a common x - value with the other points. One common domain values for two range values would, when graphed, not follow the vertical test, hence making the relation not a function.
Let's say that the point is ( -2, 15 ). It has a common x - value with respect to the first point, ( -2, 8 ), and therefore would make this set not a function.
Answer:
Point : ( -2, 15 )
Step-by-step explanation:
Which set below is the domain of
{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)}?
(AD {-3, 0, 4, 5, -2} (CD, {2,-1,4}
(3) -3,4,5,-2) (D) {2,-1,0,4}
Answer:
Domain { -1,0,2,4}
Step-by-step explanation:
{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)}
The domain is the input values
Domain { 2,-1,0,-1,4}
We normally write them in order from smallest to largest and no repeating
Domain { -1,0,2,4}
Answer:
[tex]\large \boxed{\sf D. \ \{2,-1,0,4\}}[/tex]
Step-by-step explanation:
The domain are all possible values of x.
[tex]\{(2, -3),(-1,0), (0,4),(-1,5),(4, -2)\}[/tex]
The x values are 2, -1, 0, -1, and 4.
The domain of the set is {2,-1,0,4}.
According to Newton's Second Law of Motion, the sum of the forces that act on an object with a mass m
that moves in an acceleration a is equal to m . a
An object whose mass in 80 grams has an acceleration of 20 meters per seconds square.
What calculation will give us the sum of the forces that act on the object, in Newtons (which are
kg.m/s2)?
Choose 1 answer.
A 80 . 20
B 80 . 1000 . 20
C 80/1000 . 20
D 80/602. 20
Answer: 80/1000 • 20
Answer:
Screenshots attached! Hope it helps :)
Which graph shows Point P as (–5,6) and Point Q as (3,–4)?
Answer:
The third graph from the left.
Step-by-step explanation:
The points are located on the graph that was given below. Then the correct option is C.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The points are given below.
P(5, 6) and Q(3, -4)
Point P is located by moving 5 units towards the left and 6 units upwards.
Point Q is located by moving 3 units towards the right and 4 units downwards.
The points are located on the graph that was given below.
Then the correct option is C.
More about the coordinate geometry link is given below.
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Jenny is baking 56 cookie sandwiches for her friend’s birthday party. She plans to transport the cookie sandwiches in the same food storage container but is not sure if all 56 will fit inside of the container. Part A: Calculate the volume of one cookie sandwich to the nearest cubic unit. Use 3.14 for[tex]\pi[/tex] . Part B: Calculate the total capacity of the food storage container to the nearest cubic unit. Use 3.14 for[tex]\pi[/tex] . Part C: Given your calculations regarding the volumes in Parts A and B, do you anticipate that Jenny will be able to transport all of the cookie sandwiches in one food storage container? In two or more complete sentences, explain your reasoning.
Answer:
Part A: 5 inches³.
Part B: 302 inches³.
Part C: Yes. Explanation below.
Step-by-step explanation:
Part A: The cookie sandwiches appear to be flat cylinders. The volume for a cylinder is pi * r^2 * h.
In this case, the h = 1 inch and r = 1.25 inches.
pi * 1.25^2 * 1
= pi * 1.5625
= 3.14 * 1.5625
= 4.90625.
So, the volume of a single cookie sandwich is about 5 inches³.
Part B: As stated before, the volume of a cylinder is pi * r^2 * h.
In this case, the r = 4.5 inches, and the h = 4.75 inches.
pi * 4.5^2 * 4.75
= 3.14 * 20.25 * 4.75
= 63.585 * 4.75
= 302.02875.
So, the volume of the food storage container is about 302 inches³.
Part C: Given the calculations from Parts A and B, Jenny will be able to transport all the cookie sandwiches in the food storage container. This is because there are 56 cookie sandwiches, each with a volume of 5 cubic inches. That means that the cookie sandwiches will take up 5 * 56 = 280 cubic inches of space. There is about 302 cubic inches of space in the container, so there will still be 22 cubic inches of air inside the container after the cookies are inside.
Hope this helps!
Answer:
Part A: 5 inches^3
Part B: 302 inches^3
Part C: Yes, Jenny will be able to transport all the cookie sandwiches in the food container. This is because there are 56 cookie sandwiches and they each have a volume of 5 cubic inches. So, 56 times 5 equals 280 cubic inches of space. There are 302 cubic inches inside the container, so all the cookie sandwiches will fit inside.
Drag the sliders.
Shape A
Shape B
Which slider creates scale copies of the shape?
A-Slider for Shape A
B-Slider for Shape B
Answer:
the answer would be shape b
Answer:
B
Step-by-step explanation:
please help with this math question
Answer:
E H
F F
G E
I hope I helped.
The width of a rectangle is 14 feet less than 3 times the length. If the area is 24 fta,
find the width and length.
Width = 4 and Length = 6
Width = 2 and Length = 4
Width = 10 and Length = 12
Width = 6 and Length = 8
Answer:
Width: 4
Length: 6
Step-by-step explanation:
We can create a systems of equations for this problem, assuming W is width and L is length.
W = 3L-14
WL = 24
We can substitute W into the equation.
(3L-14)L = 24
3L²-14L = 24
3L² - 14L - 24 = 0
(3L+4)(L-6)=0
L = 6
Now we can find W by substituting L into the equation.
[tex]6\cdotw=24\\w = 4[/tex]
Hope this helped!
write 0.895 with 95 repeating on and on as a simplified fraction
PLZ HELP WILL GIVE BRANLIEST
Answer:
887/990
Step-by-step explanation:
0.8959595....
895.95 - 8.95 = 887
1000 - 10 = 990
Answer:
[tex]\huge\boxed{x = \frac{887}{990}}[/tex]
Step-by-step explanation:
The number given is 0.895..........
Let x = 0.895........
Then
10x = 8.95....... --------(1)
1000x = 985.95........ --------(2)
Subtracting (1) from (2)
1000x - 10x = 985.95..... - 8.95......
990 x = 887
Dividing both sides by 990
[tex]x = \frac{887}{990}[/tex] (In simplest form)
Which expression is equivalent to RootIndex 3 StartRoot x Superscript 5 Baseline y EndRoot?
Answer:
The answer is "[tex]x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]"
Step-by-step explanation:
Given value:
[tex]\to \bold{ \sqrt[3]{x^5y} }[/tex]
[tex]\to \sqrt[3]{x^5y} =(x^5y)^{\frac{1}{3}}[/tex]
formula:
[tex]\bold{(a.b)^n=a^nb^n}[/tex]
[tex]\to (x^5y)^{\frac{1}{3}}= x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]
The final value is: [tex]\boxed{\boxed{ x^{\frac{5}{3}} \cdot y^{\frac{1}{3}}}}[/tex]
Use the model below to find the area of the shaded region.
Answer:4/12
Step1- 3 times 4 is 12
Step2- count how many twelvths are shaded
Step3- 4 twelvths are shaded
Answer: 4/12
Answer:
C. 1/3 square yard
Step-by-step explanation:
Given:
The length of shaded area = 2/3 yardThe width of shaded area = 2/4 yardTo find:
The area of shaded regionSolution:
The shaded region is a rectangle. Area of a rectangle is the product of the length and width:
Area = 2/3 yard * 2/4 yard = 1/3 square yardAnswer choice: C. 1/3 square yard
Find mPRˆ(arc). A. 115 B. 95 C. 125 D. 100
Answer:
D. 100°
Step-by-step explanation:
Refer to picture attached
Lines QP and QR are tangent to radius of circle.
Triangles ΔQPO and ΔQRO are right triangles and line QO bisects angles of ∠PQR and ∠POR.
So as per sum of angles in right triangle, we have:
1/2∠PQR + 1/2∠POR = 90°1/2(81x-1)° + 1/2(100x)° = 90°(90.5x)°= 90.5°x= 1°Then:
mPR(arc)= (100x)°= 100*1°= 100°Correct answer choice is D. 100°
The center of a circle is at the origin on a coordinate grid. The vertex of a parabola that opens upward is at (0.9). If the
circle intersects the parabola at the parabola's vertex, which statement must be true?
Answer:
The circle has radius = 9 units, and its equation is:
[tex]x^2+y^2=81[/tex]
The parabola has equation of the form:
[tex]y=a\,x^2+9[/tex]
with [tex]a[/tex] being a positive number
Step-by-step explanation:
Given the characteristics of the two figures (circle and parabola) as described,
since the parabola intersects the circle at a single point (it vertex) then the radius of the circle centered at the origin must be 9. that makes the equation of the circle to have the following standard form;
[tex]x^2+y^2=9^2\\x^2+y^2=81[/tex]
Since there is no other info regarding the parabola, the most one can say about the equation of the parabola, is that in vertex form, the parabola's equation must be of the form:
[tex]y=a\,(x-x_{vertex})^2+y_{vertex}\\y=a\,(x-0)^2+9\\y=a\,x^2+9[/tex]
with [tex]a[/tex] being a positive number.
Use the graph to determine the vertex point of the quadratic function. Is the vertex a
maximum or a minimum?
Vertex (1,3),maximum
Vertex (3,1) minimum
Vertex (1,3),minimum
Vertex (3,1) maximum
Answer:
Vertex (3,1) minimum
Step-by-step explanation:
Hello, I attached a graph with two examples where you can see the Vertex and when this is a minimum vs maximum.
You can see in your graph that the vertex is the point (3,1) and this is a minimum.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
what is (7*7*7*7*7*7) * (7*7) in exponential form?
Answer:
7^8
Step-by-step explanation:
Answer:7^8
Step-by-step explanation:
0 3C = n
Use the data in the table to give an equation to represent the proportional relation
ship.
X Y
0.5 7
1. 14
1.5 21
2 28
y = 14x
y = 7x
7y = x
21y = x
Answer:
[tex]\huge \boxed{y=14x}}[/tex]
Step-by-step explanation:
x=0.5, y=7
x=1, y=14
x=1.5, y=21
x= 2, y=28
Let’s take the first equation.
y = 14x
y = 14(0.5) = 7
When x is 0.5, y is 7.
y = 14(1) = 14
When x is 1, y is 14.
y = 14(1.5) = 21
When x is 1.5, y is 21.
y = 14(2) = 28
When x is 2, y is 28.
Which expression can be used to convert 100 USD to Japanese yen?
wo competing gyms each offer childcare while parents work out. Gym A charges $9.00 per hour of childcare. Gym B charges $0.75 per 5 minutes of childcare. Which comparison of the childcare costs is accurate?
Math Question (10 Points):
Answer:
0
Step-by-step explanation:
Like terms are terms that have the same variable part.
The variable part of all three terms is u, so all terms are like terms.
5u + u - 6u =
= 5u + 1u 6u
= 6u - 6u
= 0
(NO TROLLS 3 TIMES THE CHARM) In △ABC, AB = BC = 20 and DE ≈ 9.28. Approximate BD.
Answer:
≈ 5.36
Step-by-step explanation:
If we have a triangle in which the angle measure of it being broken down are the same, that means that the legs in which the angle measures are the same will have the same length.
If we already know that DE ≈ 9.28, then we can subtract this from 20 and divide by two to get BD, which is equal to EC.
[tex]20-9.28=10.72\\10.72\div2=5.36[/tex]
However, I'm not 100% sure about this answer.
Hope this helped (and I hope I'm right)
Answer:
5.3589 or 5.36
Step-by-step explanation:
tan (15) = x / 20
x = 40 - 34.64
x = 5.36
plsss help meeeeeee!!!! Jakes club has 35 members. it's rules require that 60% of them must be present for any vote. at least how many members must be present to have a vote?
Answer:
21 members
Step-by-step explanation:
Jake's club
Total number of members = 35
percentage of members required to be present for any vote = 60%
= 60/100 × 35
= 0.6 × 35
= 21
NEED ANSWER FAST....FIRST ANSWER WILL BE BRAINLIST!!!!
For which data set would the mean absolute deviation be a good indicator of variation of the data?
Answer:
Bottom right.
Step-by-step explanation:
The bottom right stem-and-leaf plot is the best data set because the data is unimodal and centered, so the mean absolute deviation will be the smallest. To verify this algebraically, you can find the mean of the data set. Once you have done that, you can find the absolute value of the difference between each data value and the mean: |data value – mean|.
if
[tex] log_{x} \: a \: + log_{x} \: \frac{1}{a} = t[/tex]
what is the possible value of t?
Answer:
t= 0
Step-by-step explanation:
Using the rules of logarithms
log x + log y = log(xy)
[tex]log_{b}[/tex] 1 = 0
Given
[tex]log_{x}[/tex] a + [tex]log_{x}[/tex] [tex]\frac{1}{a}[/tex] = t ,then
[tex]log_{x}[/tex] (a × [tex]\frac{1}{a}[/tex] ) = t
[tex]log_{x}[/tex] 1 = t , thus
t = 0
Find the value of a. A. 52 B. 26 C. 104 D. 93.5
Answer:
Option (A)
Step-by-step explanation:
To find the value of 'a' we will use the tangent-chord theorem,
"Angle formed by the chord and a tangent to the circle measure the half of the intercepted minor arc"
Angle 'a' is formed between the chord and the tangent.
Measure of the intercepted arc = (2 × 52)°
Therefore, measure of the angle 'a' = [tex]\frac{104}{2}[/tex]
a = 52°
Therefore, Option (A) will be the correct option.
Find the m∠RLU. A. 20 B. 42 C. 84 D. 10
Answer:
b is the correct answer. p is 10
The value of m∠RLU = 10.
How to estimate the value of m∠RLU?Given: (5p - 8) and (2p + 22)
Simplifying both of the equation, then we get
5p - 8 = 2p + 22
Add 8 to both sides of the equation, then we get
5p - 8 + 8 = 2p + 22 + 8
simplify
5p = 2p + 30
substract 2p from both sides of the equation
5p - 2p = 2p + 30 - 2p
3p = 30
p = 30/3
p = 10.
m∠RLU = 10
Therefore, the correct answer is option D. 10.
To learn more about angles and triangle
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Find the measure of FG. A. 9 B. 10 C. 11 D. 8
Answer:
x =11
Step-by-step explanation:
(whole secant) x (external part) = (whole secant) x (external part)
( 15+x-2) * (x-2) = (19+x-3) * (x-3)
Combine like terms
(13+x) *(x-2) = (16+x) *(x-3)
Distribute
11x+x^2-26=13x+x^2-48
Subtract x^2 from each side
11x -26 = 13x -48
Subtract 11x from each side
-26 = 2x-48
Add 48 to each side
22 = 2x
Divide by 2
11 =x
what are the four different ways to solve a quadratic equation? When would you prefer to use each method?
Answer:
4
Step-by-step explanation:
factoring , using square roots , completing the square and the quadratic formular
Answer:
See below.
Step-by-step explanation:
The four main ways to solve a quadratic equation are:
1) Factoring, 2) Completing the Square, 3) Graphing, and 4) Quadratic Formula.
Each method has it's own pros and cons.
1) Factoring. You should factor when the given equation is easily factor-able or already factored. For instance:
[tex]0=x^2-4x-12\\0=(x+7)(x-1)[/tex]
These problems are easily factored so factoring is preferred here. However, factoring will not always work.
2) Completing the Square. You complete the square if you are able to complete the perfect square trinomial with only integers. For instance:
[tex]x^2-2x-7=0\\(x^2-2x+1)-7-1=0\\(x-2)^2-8=0[/tex]
However, you wound't use completing the square if:
[tex]x^2-3x+2=0\\(x^2-3x+9/4)+2-9/4=0[/tex]
The perfect square trinomial includes fractions so you would use alternative methods here (and factoring works here!).
Despite the complexity of completing the square, if done correctly, it works every time. However, sometimes, it can be time-consuming.
3) Graphing. Graphing (if on paper) is time-consuming. You would only use graphing when you only need an approximation. Unless directed to, you probably won't need to use graphing.
However, if you have a graphing calculator, graphing the equation can allow you to check your answer. So, graphing won't get you precise answer, but it will allow you to check your answer is necessary.
4) Quadratic Formula. Use the quadratic formula if the equation isn't factor-able and completing the square is too tedious. For instance:
[tex]4.1x^2-3x-7=0\\[/tex]
This doesn't seem factor-able and completing the square will take a while. Graphing won't get the exact answer, so the quadratic formula is the only avenue left.
The quadratic method, like completing the square, will always work.
Only con is that you need to memorize the formula.
plls 20 poinsts will mark brainlest
Answer:
My answer is in the attached image.
Randomly pick 5 points from a sphere. Show that you can always find a closed semi-sphere (half a sphere and boundary) that contains 4 points.
