The series converges and its value is 8 - 1/b.
To evaluate the telescoping series ∑(infinity) 8^(1/n) - b^(1/(n + 1)), we need to use the property of telescoping series where most of the terms cancel out.
First, we can write the second term as b^(1/(n+1)) = (1/b)^(-1/(n+1)). Now, we can use the fact that a^(1/n) can be written as (a^(1/n) - a^(1/(n+1))) / (1 - 1/(n+1)) for any positive integer n. Using this property, we can rewrite the first term of the series as:
8^(1/n) = (8^(1/n) - 8^(1/(n+1))) / (1 - 1/(n+1))
Similarly, we can rewrite the second term of the series as:
(1/b)^(-1/(n+1)) = ((1/b)^(-1/(n+1)) - (1/b)^(-1/(n+2))) / (1 - 1/(n+2))
Now, we can combine the terms and get:
∑(infinity) 8^(1/n) - b^(1/(n + 1)) = (8^(1/1) - 8^(1/2)) / (1 - 1/2) + (8^(1/2) - 8^(1/3)) / (1 - 1/3) + (8^(1/3) - 8^(1/4)) / (1 - 1/4) + ... + ((1/b)^(-1/n)) / (1 - 1/(n+1))
As we can see, most of the terms cancel out, leaving us with:
∑(infinity) 8^(1/n) - b^(1/(n + 1)) = 8 - 1/b
So, the series converges and its value is 8 - 1/b.
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What's a venn diagram, how to draw it and the steps too!
What is a Venn Diagram?
Explain : A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science.
How to draw a Venn Diagram?
Explain : To create an intersecting Venn diagram, draw three circles that overlap in the middle. You'll be able to show which attributes are unique to each circle, which overlap between two, and which are common characteristics of all three groups. Two circles overlapping is a classic venn diagram
What is a venn Diagram mostly used for?
Explain : A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
Set notations: The concepts illustrated in Venn ...
Scaled Venn Diagram: Also called Area Propo...
Reuleaux Triangle: Shape formed from the int...
Intersection: The items that overlap in the sets. ...
Here's some question for Venn Diagrams!
A. What's the first step creating a Venn Diagram? https://www.math-only-math.com/practice-test-on-Venn-diagrams.html
B. What's the last step to create a Venn Diagram? https://www.purplemath.com/modules/venndiag4.htm
C. What does a Venn Diagram looks like?
( Try using those questions to partice more about Venn Diagrams! )
( Also, thank you for the points! )
A group of friends wants to go to the amusement park. They have no more
than $325 to spend on parking and admission. Parking is $11, and tickets cost
$39.25 per person, including tax.
Considering the definition of an inequality, the number of friends admitted must be less than or equal to 8, expressed as p ≤ 8
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
A group of friends have no more than $325 to spend on parking and admission. Parking is $11Tickets cost $39.25 per person, including tax.Being "p" the maximum number of people who can go to the amusement park, the inequality that expresses the previous relationship is
39.25 p + 11 ≤ 325
Solving:
39.25 p ≤ 325 -11
39.25 p ≤ 314
p ≤ 314÷ 39.25
p ≤ 8
Finally, the number of friends admitted must be less than or equal to 8, expressed as p ≤ 8
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The linear regression method seeks to predict values of a(n) variable based on values of a(n) variable.
The linear regression method seeks to predict values of a(n) dependent variable based on values of a(n) independent variable.
According to the statement
we have to explain the linear regression method and explain the way by which this method is used to predict the values.
So, For this purpose we know that the
Linear regression is the most basic and commonly used predictive analysis. Regression estimates are used to describe data and to explain the relationship.
And
Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.
from these definitions it is clear that the there is a presence of two types of variables which are dependent and independent variables.
So, The linear regression method seeks to predict values of a(n) dependent variable based on values of a(n) independent variable.
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The distance that you run around the track in gym class is considered ______ data.
A. discrete
B. neither continuous nor discrete
C. continuous
D. both continuous and discrete
The distance that you run around the track in gym class is considered continuous data.
How to determine the type of data?The variable is given as:
Distance
The distance travelled can take any value between 0 and the length of the track.
Take for instance;
The distance travelled can be 1km and it can also be 1.67 km
This means that the distance is continuous
Hence, the statement that completes the blank is (c) continuous
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Can someone help? ASAP
Question 4
[tex]\sin 30^{\circ}=\frac{y}{14\sqrt{3}}\\\\\frac{1}{2}=\frac{y}{14\sqrt{3}}\\\\\boxed{y=7\sqrt{3}}\\\\\\\\\cos 30^{\circ}=\frac{x}{14\sqrt{3}}\\\\\frac{\sqrt{3}}{2}=\frac{x}{14\sqrt{3}}\\\\\boxed{x=21}[/tex]
Question 5
[tex]\cos 45^{\circ}=\frac{x}{28}\\\\\frac{1}{\sqrt{2}}=\frac{x}{28}\\\\x=\frac{28}{\sqrt{2}}\\\\\boxed{x=14\sqrt{2}}\\\\\\\\\sin 45^{\circ}=\frac{y}{28}\\\\\frac{1}{\sqrt{2}}=\frac{y}{28}\\\\y=\frac{28}{\sqrt{2}}\\\\\boxed{y=14\sqrt{2}}[/tex]
When given an inverse variation, how do you find k?
can someone please help me?
answer choices:
A. sin (0)
B. cos (0)
C. sin (3/2)
D. cos (3/2)
E. sin ()
F. cos ()
Answer:
B, cos(0)=1
Step-by-step explanation:
cos(0)=1
Coordinate A is at point (1,0)
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
F(x)= 2(x-2)^2 + 2 is the correct equation of F(x)
A quadratic function is a polynomial function of the second degree. The general form of a quadratic function is this: f (x) = ax^2 + bx + c, where a, b, and c are real numbers and a≠ 0.
Graphs of quadratic functions
The term "parabola" refers to the graph of a quadratic function. A parabola essentially resembles the letter "U," yet it can be inverted or exactly this shape depending on the situation. The leading coefficient determines whether the graph of a quadratic function opens up or down; if it is more than zero, the parabola opens up; if it is less than zero, the parabola opens down.
It is given that graph of F(x), shown below, resembles the graph of G(x) = x^2, but it has been changed somewhat.
We need to find the equation of F(x)
In the figure, parabola opens up, the leading coefficient is greater than zero ,So option (d) is correct
Hence the equation of F(x) is 2(x-2)^2 + 2
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Draw a line segment of length 6.4 cm and divide it in to 4 equal parts.
Write the length of each part.
The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The line segment has a length of 6.4 cm. Hence:
Dividing into 4 equal parts = 6.4 / 4 = 1.6 cm
The length of each part of a the line segment is 1.6 cm if a line segment of length 6.4 cm and divided it in to 4 equal parts
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A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalent. The class has suggested four different methods.
PLEASE HURRY:Which describes the correct method?
Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent.
Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.
Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Answer:
Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
Step-by-step explanation:
x = 1
4x - (x + 5) = 4 - 6 = -2
8 - 3x - 3 = 8 - 3 - 3 = 2
Which table represents a linear function? Which quadratic function is represented by the graph?
The first table is a quadratic function while the second table is a linear function.
How to Interpret Function Tables?
1) For the first table, we have;
x y
0 5
1 0
2 -3
3 -4
4 -3
x = 2 and x = 4 have same value of y = -3 and as such it will be a Quadratic Function.
y = x² - 6x + 5
2) For the second table, we have;
x y
2 5
5 14
6 17
8 23
10 29
This table is a Linear function because slope is same and equal to 3 all through. Thus, the equation is y = 3x - 1
3) For the third table, we have;
x y
-3 8
-2 4
-1 2
0 1
1 0.5
This is an exponential function because equation can be modelled by;
y = 2⁻ˣ
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1
Select the correct answer.
What are the zeros of this quadratic function?
fx)=(x-7)(x+8)
OA
x = 0 and x = 7
OB. x= 0 and x = -8
OC. x=-7 and x = 8
OD. x=7 and x = -8
Answer:
B
hope this helps :)
Answer:
D
Step-by-step explanation:
to find the zeros, equate f(x) to zero, that is
(x - 7)(x + 8) = 0
equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x + 8 = 0 ⇒ x = - 8
Which triangle is a translation of triangle P?
The ordered pair (10,63) is a solution to the inequality y
Please select the best answer from the choices provided
True
False
The ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. This illustrates that the statement is true.
What is an inequality?It should be noted that an inequality simply means a statement of an order relationship between two numbers and algebraic expressions.
From the information given, the equation illustrated is:
y < -0.2x² + 9x - 7.
63 < 0.2(10)² + (9 × 10) - 7
63 < 20 + 90 - 7.
63 < 103
In this case, the ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. This illustrates that the statement is true since sixty there is less than one hundred and three.
Therefore, this is true.
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Complete question:
The ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. Please select the best answer from the choices provided
True
False
How do we combine like terms with negative coefficients
5n+6+(-7n)
Answer:
- 2n + 6
Step-by-step explanation:
note that + (-) = -
5n + 6 + (- 7n)
= 5n + 6 - 7n ← collect like terms
= 5n - 7n + 6
= - 2n + 6
f(x) = x² + 5x-1 is shifted 3 units right. The result is g(x). What is g(x)?
O A. g(x) = (x+3)² + 5x-1
OB. g(x)=x2 + 5x+2
C. g(x) = (x+3)2 +5(x + 3) - 1
D. g(x) = (x-3)2 + 5(x-3) -1
Answer:
D
Step-by-step explanation:
When a function is being shifted to the left, all x values will be added by y units shifted. (The constant that comes with x is excluded, eg. 3x shifted by 2 units left, becomes 3(x+2) and not 3x+2.)
Likewise, when a function is being shifted to the right, all x values will be subtracted by y units shifted. (Constant rules applies as well.)
Given f(x) is shifted 3 units right,
the new function, g(x) becomes:
[tex] g(x) = {(x - 3)}^{2} + 5(x - 3) - 1[/tex]
Therefore the answer is D in this case.
Given f(x) =
8x+1
2x-9
what is the end behavior of the function?
ONA
LR
OAS X→∞, f(x) → 9; as x→ ∞, f(x) → 9.
-
OAS X→∞, f(x) →-9; as x, f(x) → -9.
OAS X →∞, f(x) → -4; as x → ∞, f(x) → -4.
As
OAS X-∞, f(x)→ 4; as x→ ∞, f(x)→ 4.
O
BASSENG
D
se
The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is [tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex].
The last option is correct.
What is the range of the function?The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.
The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.
From the information given:
[tex]\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}[/tex]
Inverse of [tex]\mathbf{\dfrac{8x +1}{2x -9 }}[/tex] becomes [tex]\mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}[/tex]
The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:
[tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex]
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Given that a does not equal b is it ever possible to have square root a + square root b = square root a+b? Someone please help.
Answer:Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.
If either a or b equals zero, then the sums would be the same.
Since the square root of 0 is 0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.
Step-by-step explanation:
The statement √a + √b = √(a + b) is not possible since a ≠ b
How to determine whether or not the statement is true?The operation involving surd is most likely an algebraic expression where in the case of surd the value in the square root are like the alphabets in algebraic expression.
Some surd operations are given as shown below:
√a + √a = 2√a√a × √a = a2√a + √a = (2 + 1)√a = 3√a3√a - 2√a = (3 - 2)√a = √a√a × √b = √(a × b) = √(ab)√a + √b = √a + √bNow, let us consider the question given:
a ≠ b√a + √b = √(a + b)Since a and b are not equal, it means
√a + √b ≠ √(a + b)
Thus, we can conclude that the statement √a + √b = √(a + b) is not possible
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f(x) = x^2 + 4x + 20 find the real roots. take your time if you want :)
Answer:
No real roots
[tex]x = -2 + 4i, x = -2 - 4i[/tex]
Step-by-step explanation:
Hello!
We can solve the quadratic by using the Quadratic Formula.
Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Quadratic Equation: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Given our Equation: [tex]f(x) = x^2 + 4x + 20[/tex]
a = 1b = 4c = 20Set the equation to 0 and solve using the formula.
Solve[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-4\pm\sqrt{4^2 - 4(1)(20)}}{2(1)}[/tex][tex]x = \frac{-4\pm\sqrt{16 - 80}}{2}[/tex][tex]x = \frac{-4\pm\sqrt{-64}}{2}[/tex][tex]x = \frac{-4\pm8i}{2}[/tex][tex]x = -2 + 4i, x = -2 - 4i[/tex]There are no real roots to the quadratic.
The red blood cell counts for a population of adult males can be approximated by a normal distribution with a mean of 5.3 million cells per microliter and a standard deviation of 0.3 million cells per microliter what is the minimum red blood cells count that can be in the top 28% of accounts
The minimum red blood cells count that can be in the top 28% of accounts is 5.61%.
Red blood cells, also called crimson cells, purple blood corpuscles, haematids, erythroid cells, or erythrocytes, are the maximum common type of blood cells and the vertebrate's primary approach of delivering oxygen to the body tissues thru blood drift thru the circulatory device.
A low RBC depends, also called anemia, can have an effect on the frame's capability to transport oxygen and vitamins around the cardiovascular machine. it may reason fatigue, dizziness, and heart palpitations. The maximum not unusual form of anemia is iron deficiency anemia. this can result from blood loss, malnutrition, or kidney problems.
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Can someone help me with this having trouble and show work please!!
Answer:
7a + b
Step-by-step explanation:
5a + 2a + 3b - 2b
= 7a + 3b - 2b
= 7a + b
What is the midpoint of the segment shown below? 10 A. (5, 1); (5, 4) B . (5, 1/2) -10 10 (5, - 3) C. (10, 1) D . (10, 1/2)
Based on the given parameters, the midpoint of the line segment is (5, 1/2)
How to determine the midpoint of the segment?The complete question is added as an attachment
From the figure, we have the following coordinates
(5, 4) and (5, -3)
The midpoint of the segment is then calculated using
(x, y) = 0.5 * (x1 + x2, y1 + y2)
Substitute the known values in the above equation
(x, y) = 0.5 * (5 + 5, 4 - 3)
Evaluate the sum and the difference
(x, y) = 0.5 * (10, 1)
Evaluate the product
(x, y) = (5, 1/2)
Hence, the midpoint of the line segment is (5, 1/2)
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What is the imagine point of (4,-2) after the transformation ry=-i ○ D1/2
The image point of (4,-2) after the transformations given is; (2,1).
What is the image point after the transformations?It follows from the task content that the point given is (4, -2) which first reflects over the y axis and hence, renders the new image to be; (4, 2) after which it undergoes a dilation of with dilation factor, 1/2 and hence, the image point is; (2,1).
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Find the value of z.
A. 100
B. 82
OC. 118
OD. 75
o'
105°
120°
68⁰
Answer:
B. 82
Step-by-step explanation:
I hope it helps you :)
The value of z in the given figure of circle with two lines dividing it into segments is 100.
We are given that the measures of angles ∠1 and ∠2 are 105° and 120°, respectively.
Step 1: Since the interior angles of a triangle add up to 180°, we know that the measure of ∠3 is 180° - 105° - 120° = 55°.
Step 2: Since ∠3 and ∠z are supplementary angles, we know that m∠3 + m∠z = 180°.
Step 3: Substituting the measures of ∠3 from step 1 into step 2, we get 55° + m∠z = 180°.
Step 4: Subtracting 55° from both sides of the equation in step 3, we get m∠z = 180° - 55° = 125°.
Step 5: Since m∠z = 125°, then z = 125°.
Therefore, the value of z is 100.
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The function has three factors. Two of these factors
are and Determine the values of a and b, and then determine the
other factor.
The values of a and b will be -2 and 22 while the other factor in the function is x - 3/2.
How to illustrate the function?The function is given as:
f(x) = ax³ - x² + bx - 24.
Since (x - 2) and (x - 4) are the factors, they will give functions of 8a + 2b = 28 and -16a - b = 10.
This will be solved by elimination method and the values of a and b will be -2 and 22.
Therefore, f(x) = -2x³ - x² + 22x - 24
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Which equation represents a population of 250 animals that decreases at an annual rate of 12% ?
Answer:
f(t)=250(1-0.12)^t
or
f(t)=250(0.88)^t
Step-by-step explanation:
Use the formula f(t)=P(1+b)^t
Plug in the information.
f(t)=250(1-0.12)^t
or
f(t)=250(0.88)^t
The only thing I did in the second equation is I subtract 0.12 from 1.
Hope this helps!
(‼️‼️I WILL MARK BRAINLIEST PLEASE HELP‼️‼️)Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 5
(-3,-1)
A
(-1,-4) C
B(2,-2)
A' ([?], [ ])
B' ([ ], [ ])
C' ([ ], [ ])
Answer:
A' (-15, -5)
B' (10, -10)
C' (-5, -20)
Answer:
A ' (-15, -5)
B ' (10, -10)
C ' (-5, -20)
Step-by-step explanation:
The scale factor is [tex]K=5[/tex]. This tells us to multiply each coordinate, of each point, by the scale factor (5) to get the dilated points.
Point A is at [tex](-3,-1)[/tex] and moves to [tex]A ' (-15, -5)[/tex] after multiplying the x and y coordinates by 5. The same applies to points B and C as well.
Point B moves from [tex](2,-2)[/tex] to [tex]B' (10,-10)[/tex] because [tex]2*5=10[/tex] and [tex]-2*5=-10[/tex]. This also means that Point C moves from [tex](-1,-4)[/tex] to [tex]C' (-5,-20)[/tex] because [tex]-1*5=-5[/tex] and [tex]-4*5=-20[/tex].
The dilation rule can be written as [tex](x, y)[/tex] → [tex](5x, 5y)[/tex]
As a result of the dilation, triangle A'B'C' has sides that are 5 times longer compared to the corresponding sides of triangle ABC.
What is the range of the function f(x) = 6x – 2 over the interval of 3 < x ≤ 8
The range of f(x) = 6x – 2 is [16,46]
According to the statement
we have given the function f(x) = 6x – 2 and the given interval is 3 < x ≤ 8
we know that to find the range of function we have to fill the values in it and then find the range of this function.
So, range is basically a difference between the lowest and the highest value.
Here the given function is f(x) = 6x – 2
when f(3) then
f(3) = 18-2
f(3) = 16.
and when f(8) then
f(8) = 48-2
f(8) = 46.
after put the values we seen that the range of this function is 16,46.
So, The range of f(x) = 6x – 2 is [16,46]
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Answer is :
16 and 46Step-by-step explanation:
Given function
[tex]\sf f(x) = 6x - 2 [/tex]
We need to the find the range of the function over the interval of 3 < x ≤ 8
When, x is 3
Put x = 3 in the given function,
[tex]\sf f(3) = 6(3) +2 [/tex]
[tex]\sf f(3) = 18 - 2 [/tex]
[tex]\sf f(3) = 16 [/tex]
when, x is 8
Put x in the given function,
[tex]\sf f(8) = 6(8) -2 [/tex]
[tex]\sf f(8) = 48 - 2 [/tex]
[tex]\sf f(8) = 46 [/tex]
Hence range of the function f(x) = 6x – 2 is 16 and 46.
The width of a rectangle is represented by 4x, and its length is represented by (3x+2). Write a polynomial for the perimeter of the rectangle.
Answer:
2(7x + 2)
Step-by-step explanation:
Perimeter of a Rectangle = 2 x Length + 2 x Width.
Given Length = 4x, Width = 3x + 2,
Perimeter of Rectangle = 2(4x) + 2(3x + 2)
= 8x + 6x + 4
= 14x + 4 (Degree one polynomial)
= 2(7x + 2)
Instructions: Find m
Check the picture below.
we could also look at it from the inscribed angle theorem, bearing in mind that the intercepted arc is 180°.