PLEASE HELP ME ASAP
Does the series converge or diverge? If it converges, what is the sum? Show your work
Answers
The series is a convergence series and the sum of the series is -8/3
The type of the seriesThe series is given as:
[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]
The above series has the following properties:
First term; a = -4Common ratio, r = -1/2Start by calculating the absolute value of the common ratio
Absolute value = |-1/2|
This gives
Absolute value = 1/2
The above value is less than 1.
It means that the series converges.
The sum of the seriesThis is calculated using:
[tex]S_{\infty} = \frac{a}{1 -r}[/tex]
So, we have:
[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]
Evaluate the sum
[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]
Evaluate the quotient
[tex]S_{\infty} = \frac{-8}{3}[/tex]
Hence, the sum of the series is -8/3
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Related Questions
4.
In the diagram of AABC below, DE || BC,
AD= 3, DB=2, and DE = 6.m
6
E
2
B
What is the length of BC?
1) 12
2) 10
3) 8
4) 4
C
Answers
hope this helps :))
Write your answer in simple solution (4x^3+2x+6)+(2x^3-x^2+2)
Answers
need help asap please!
Answers
Answer:
determinant: -15x = 3; y = 4; z = 1Step-by-step explanation:
The matrix of coefficients has one row corresponding to each equation. The constants in that row are the coefficients of the variables in the equation. Coefficients are listed in the same order on each row. A missing term is represented by a coefficient of 0.
coefficient matrix, determinantThe first attachment shows the coefficient matrix and its determinant.
__
solutionThe solution to the system of equations can be found by left-multiplying the constant vector by the inverse of the coefficient matrix.
[tex]\textbf{A$\cdot$X}=\textbf{B}\\\\\textbf{X}=\textbf{A}^{-1}\cdot\textbf{B}[/tex]
This multiplication is shown in the second attachment. It tells us ...
[tex]\textbf{X}=\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}3\\4\\1\end{array}\right][/tex]
Find the midpoint of A and B where A has coordinates (2, 3)
and B has coordinates (8, 9).
Answers
Step-by-step explanation:
Solution,Given,Coordinates of A and B are (2,3) and(8,9) respectively. Let A(2,3)= (x1,y1) and B(8,9)=(x2,y2)Midpoint of AB(m)=?Now,using midpoint formulam= {(x1+x2)/2 ,(y1+y2)/2}or m= {(2+8)/2,(3+9)/2}.°. m=(5,6)Answer:Mxy= [(Xa+Xb/2);(Ya+Yb/2)]
=(2+8/2);(3+9/2)
Midpoint= (5, 6)
Step-by-step explanation:
Suppose that y varies directly with x and inversely with z, and y = 4 when x = 8 and z = 14. find z when x = 36 and y = 6. first, what is the equation of variation? y =
Answers
The value of z if x = 36 and y = 6 is 42
Direct and inverse variationSuppose that y varies directly with x and inversely with z, hence the required expression will be:
y = kx/z
If y = 4 when x = 8 and z = 14 then;
4 = k(8)/14
8k = 56
k = 7
To find z when x = 36 and y = 6, we will have:
6 = 7(36)/z
1 = 7(6)/z
z = 42
Hence the value of z if x = 36 and y = 6 is 42
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Answer:
Keep it simple. Answer:
y=kx/z
k=7
z=42
Step-by-step explanation:
2/3 of a number is 48. What is 1/4 of the number ?
Answers
Answer:
your answer will be 18
Step-by-step explanation:
2/3 of 72 is 48, 1/4 of 72 is 18
i need some extra words here so hopefully this works
Given the following function: y=x^2+10x+25 Using your knowledge of discriminants, how many solutions does this function have?
Answers
Answer:
One solutionStep-by-step explanation:
Given function:y = x² + 10x + 25This is a quadratic function.
A quadratic equation has:Two solutions if discriminant is positive;One solution if discriminant is zero;No solution if discriminant is negativeFind the discriminant of the given function:D = b² - 4ac = 10² - 4*1*25 = 100 - 100 = 0This function has one solution since its discriminant is zero.
Answer:
one real solution
Step-by-step explanation:
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real solutions}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real solution}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real solutions}[/tex]
Given function:
[tex]y=x^2+10x+25[/tex]
Therefore:
[tex]a = 1[/tex][tex]b = 10[/tex][tex]c = 25[/tex]Substitute the given values into the discriminant:
[tex]\implies 10^2-4(1)(25)=0[/tex]
As the discriminant equals zero, there is one real solution.
1. Using the above
scatterplot, does there
seem to be a positive
correlation, a negative
or no
correlation,
correlation between
the number of
customers and sales?
Answers
Answer:
yes there is a correlation
Step-by-step explanation:
here's how I found this by looking up all key words.
Solve for h: h+4/-2=0.3 ([tex]h+\frac{4}{-2} =0.3[/tex])
Give Explanation please.
Answers
Answer: [tex]h=\frac{23}{10} =2.300[/tex]
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
[tex]h+\frac{4}{-2} -((\frac{3}{10} ))=0[/tex]
[tex]Simplify~ \frac{3}{10}[/tex]
[tex](h+\frac{4}{-2} )-\frac{3}{10} =0[/tex]
Subtracting a fraction from a whole
Rewrite the whole as a fraction using 10 as the denominator :
[tex]h-2=\frac{h-2}{1} =\frac{h-2x10}{10}[/tex]
Equivalent fraction: The fraction thus generated looks different but has the same value as the whole
Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to the lowest terms if possible:
[tex]\frac{(h-2)x10-(3)}{10} =\frac{10h-23}{10}[/tex]
[tex]\frac{10h-23}{10} =0[/tex]
When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, CalderonJ multiplys both sides of the equation by the denominator.
Here's how:
[tex]\frac{10h-23}{10} *10=0*10[/tex]
Now, on the left hand side, the 10 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
10h-23 = 0
Add 23 to both sides of the equation :
10h = 23
Divide both sides of the equation by 10:
h = 23/10 = 2.300
Final Answer: 2.3(decimal form) aka 23/10 (fraction)
what is the answer to 54785 plus 43543546546546
Answers
PRECISION In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was the average cost for 16 gallons of gasoline?
Answers
Answer:
46.272 or 46 34
125
Explains :
Let see :
Based on the given conditions, formulate: 16×14.46÷5
Calculate the product or quotient:231.36
5
Convert decimal to fraction:23136
100
5
Divide a fraction by multiplying its reciprocal:23136 × 1
100 5
Write as a single fraction:23136
100×5
Cross out the common factor:5784
25×5
Calculate the product or quotient:5784
5784 125
get the result: 46.272 or 46 34
125
Answer: 46.272 or 46 34
125
19. What are equivalent statements to a + 3 = 18 and 4 b = 32?
a = 18-3 and b = 32/4
a=18/3 and b = 32/4
a = 18/3 and b = 32-4
a = 18-3 and b = 32 - 4
Answers
Answer:
The choice second . a=18/3 and b = 32/4
Step-by-step explanation:
[tex]a + 3 = 18 \\ a = 18 - 3[/tex]
[tex]4b = 32 \\ \\ b = \frac{32}{4} [/tex]
Please help :)))))))))))))
Answers
Answer:
\frac{9}{20} (or 9/20, if this doesn't show up the right way in my answer.)
Step-by-step explanation:
Fist what we'll do here is divide 1000 by 450. 1000÷450=2\frac{2}{9} (2/9, if this doesn't show up the right way either).
Then, we'll apply the inverse formula. In case you've forgotten, the inverse of a number is what you have to multiply a number by to get 1. The inverse of 2/9 (too lazy to put it in that form anymore) is 0.45, or 9/20.
If that doesn't work, I might be interpreting this incorrectly.
Here.
Answer:
0.05, or 1/20
Step-by-step explanation:
So, we have the fraction. we can simplify it to 20/9, making the numerator 20. As previously stated, the inverse of a number is what you have to multiply a number by to get 1. So, 1÷20=0.05
Let me know which one works!
Warmest regards,
Sanjana
Professional 6th grader and quantum physics lover
An isosceles right triangle has an area of 8cm^2. What is the length of its hypotenuse?
Answers
Answer:
Given, an isosceles right triangle has area 8 cm². We have to find the length of its hypotenuse. We know that in an isosceles triangle two sides are of equal length. Therefore, the length of the hypotenuse is √32 cm.
X+17=38 which property is included in the justification for the steps used to solve the equation?
Answers
Looking at the problem statement, the question is asking for us to determine the justification for the steps that are used to help solve the equation. We are given the expression [tex]x + 17 = 38[/tex] to help achieve that goal.
Now that we know what we must do to finish this problem let us look how this equation can be solved. When the term solve the equation is used it refers to us solving for the unknown, in this case being the variable x. We can see that we have [tex]x + 17[/tex] on the left side and in order to solve the equation x must be alone so we would subtract 17 from both sides.
Subtract 17 from both sides
[tex]x + 17 = 38[/tex][tex]x + (17 - 17) = (38 - 17)[/tex][tex]x = (38 - 17)[/tex][tex]x = 21[/tex]Therefore, we know that we must subtract the same number from both sides and this justification is known as the Subtraction Property of Equality. This basically states that an equal value needs to be subtracted from both sides and it will become a new equation but with the same result.
Answer:
Subtraction Property of Equality
Step-by-step explanation:
Given: x + 17 = 38
Algebraic Properties:
Addition: If a = b, then a + c = b + c
Subtraction: If a = b, then a - c = b - c
Multiplication: If a = b, then ac = bc
Division: If a = b, then a ÷ c = b ÷ c
To solve this equation, we know that we need to isolate the variable x. To do this, we need to subtract 17 from both sides to isolate x.
This is also known as the subtraction property of equality, which states that when the same thing is subtracted from both sides of an equation, the equation will still be balanced.
Subtract 17 from both sides:
x + 17 - 17 = 38 - 17
⟹ x = 21
Therefore, the subtraction property of equality is included in the steps used to solve this equation.
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what are the key features of the graph of a trigonometric function? How do you find them from a graph or an equation?
Answers
Answer:
The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.
They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).
Latoya created a factor tree and wrote the prime factorization of 90 shown below.
Answers
Answer:
it’s b
Step-by-step explanation:
the answer is 2x3x3x5, but it’s the same thing when you put an exponent of two on a 3.
Hope it helps
Sry if I’m wrong
Consider isosceles ΔXYZ.
What is the value of n?
What is the measure of leg XY? ft
What is the measure of leg XZ? ft
Answers
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of the legs XY and YZ is equal to 39 units.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°. An isosceles triangle has two sides out of three equal.
A.) The value of n can be found by equating XY and XZ together,
XY = XZ
9n + 12 = 15n - 6
12 + 6 = 15n - 9n
18 = 6n
n = 3
Hence, the value of n is 3.
The length of different legs of the triangle is,
B.) XY = 9n + 12 = 9(3) + 12 = 27 + 12 = 39
C.) YZ = 15n - 6 = 15(3) - 6 = 45 - 6 = 39
Hence, the length of the legs XY and YZ is equal to 39 units.
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Answer:
Step-by-step explanation:
3
39
39
Find the 14 term of the following geometric sequence.
10, 20, 40, 80,
Answers
Answer:
81920
Step-by-step explanation:
Finding the common ratio (r) :
20/102Finding the 14th term :
a₁₄ = ar¹⁴⁻¹a₁₄ = ar¹³a₁₄ = (10)(2)¹³a₁₄ = (10)(8192)a₁₄ = 81920Answer:
the 14th term in the sequence would be 81920.
Step-by-step explanation:
because you are multiplying by 2 each time to find the next multiply 80 by 2 giving you 160 again giving you 320 again giving you 640 than 1280 , 2560 ,5120 ,10240 ,20480 ,40960 ,finally the 14th number in the sequence multiplying 40960 by 2 would give you your answer of 81920.
I have a bag with 6 marbles numbered from 1 to 6. mathew has a bag with 12 marbles numbered from 1 to 12. matthew chooses one marble from his bag and i choose two from mine. in how many ways can we choose the marbles (where the order of my choices does matter) such that the sum of the numbers on my marbles equals the number on his?
Answers
Answer:
It would be 30.
Step-by-step explanation:
If we make a list of all the sums that we can get, we have:
1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6
These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.
That gets us to 15x2 which is 30.
The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
I have a bag with 6 marbles numbered from 1 to 6.
Mathew has a bag with 12 marbles numbered from 1 to 12.
1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6
These 15 sums can be chosen in two ways,
Since order matters, and we could do 2+1 instead of 1+2.
15 x 2 which is 30.
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help me I need the answer on paper help me now
Answers
Answer:
x = 144
Step-by-step explanation:
Angle sum of heptagon = 900
5x + 90 + 90 = 900
5x + 180 = 900
5x + 180 - 180= 900 - 180
5x = 720
Divide both sides by 5
x = 144
Ok help me I don’t understand stand this
Answers
Answer:
Step-by-step explanation:
Comment
It is not possible to figure out what choices are are given for the first blank. I will say that the probable choice has the word product in it.
The second blank is the actual number of choices. It is 3 page count times color or 3*4 = 12 different choices.
Answer
product
12
guys help just with part b for number 2!
Answers
Answer:
22 8th graders
Step-by-step explanation:
if 25% of the 88 kids are 8th graders then do this.
88x.25=22
88x.75=66
there are 22 eighth graders
and 66 seventh graders.
Evaluate l-x-2yl for x = -2 and y = 3.
Answers
Step-by-step explanation:
|...| means absolute value of "...". that means always the "+" value of "...", even if it is negative.
in other words
|-x| = x
|x| = x
|-x - 2y| for x = -2 and y = 3
|- -2 - 2×3| = |2 - 6| = |-4| = 4
need help fast given lim x→c f(x) = "-4" and lim x→c g(f) =1/5 what is lim x→c [g(f)/f(x)]
Answers
Work Shown:
[tex]\displaystyle \lim_{x \to c}f(x) = -4\\\\\\\lim_{x \to c}g(x) = 1/5\\\\\\L = \lim_{x \to c}\frac{g(x)}{f(x)}\\\\\\L = \frac{\displaystyle \lim_{x \to c}(g(x))}{\displaystyle \lim_{x \to c}(f(x))}\\\\\\L = \frac{1/5}{-4}\\\\\\L = (1/5)*(-1/4)\\\\\\L = -1/20\\\\[/tex]
Put simply, we divide the two given values g(x) = 1/5 over f(x) = -4 to end up with -1/20
Please I need HELP!!!!!!
Answers
Answer:
I just need points I don't know your answer
Step-by-step explanation:
55 POINTS!!!!!! WILL GIVE BRAINLIEST!!!!!!! PLS HELP ASAP!!!!!
Danielle is trying to solve the equation [tex]8^x=\frac{1}{64}[/tex]. Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answers
Answer:
x=-2
Step-by-step explanation:
Given equation:
8^x= 1/64
Ensure both sides of the equation are in power format by changing 1/64
1/64 = 64^-1
8^x = 64^-1
2^3(x) = 2^6(-1)
The bases will cancel out each other
3(x) = 6(-1)
3x = -6
x = -6/3
x = -2
Check
8^x = 1/64
x = -2
8^-2
= 1/8²
= 1/8*8
= 1/64
(giving 100 points) What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places.
x y
4 3
6 4
8 9
11 12
13 17
A: y = 1.560x - 4.105
B: y = -4.105x + 1.560
C: y = 4.105x - 1.560
D: y = -1.560x + 4.105
please hurry
Answers
Answer:
Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]
where:
[tex]m[/tex] is the slope[tex]b[/tex] is the y-interceptTo determine the equation of the line of best fit from the given answer options, examine the relationship between the x and y values.
From inspection of the data, we can see that as x increases, y increases. Therefore, the slope of the equation will be positive.
(If the y-values decrease as the x-values increase, then the slope would be negative).
Therefore, we can immediately discount answer options B and D as they have negative slopes.
The x and y values are not very far away from each other. The options given for the slope are either 1.560 or 4.105. If the slope was 4.105, we would expect to see values of y that were further away from the x-values.
Therefore, the line of best fit is:
A: y = 1.560x - 4.105
To prove this, plot the 5 points on a graph and draw a line of best fit (see attached).
Choose 2 points on the line of best fit: (4, 2) and (11, 13)
Use the slope formula with these points to calculate the approximate slope:
[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}\approx\dfrac{13-2}{11-4}=\dfrac{11}{7}=1.57[/tex]
Thus proving that y = 1.560x - 4.105 is an appropriate option for the equation of the line of best fit.
please help me! will give the brainliest answer!
Answers
1, -1/3, 1/3, 1}
36. During rehearsal for the Founders' Day choir
program, the director, Mrs. Mazurek, tried 3 different
configurations, each using all the choir members at the
rehearsal. One configuration was to have only rows of
12, one was to have only rows of 15, and one was to
have only rows of 20. None of these configurations
worked because for each, the last row had 1 person
less than the other rows. What was the least of the
possible numbers of choir members at the rehearsal?
Answers
The LCM stands for the least common multiple. The least of the possible number of choir members at the rehearsal is 59.
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
Given the configurations of choir members at the rehearsal, which are,
One configuration was to have only rows of 12, One was to have only rows of 15, And one was to have only rows of 20.Now, it takes the LCM of 12, 15, and 20, then the LCM will be 60, But since None of these configurations worked because for each, the last row had 1 person less than the other rows. The number of members was 1 less than the LCM.
Hence, the least of the possible number of choir members at the rehearsal is 59.
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