The solutions are -
S3 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6)
S4 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7)
S5 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8)
The sum of the series is 1/3.
To find S3, we need to find the sum of the first 3 terms of the series:
S3 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6)
To find S4, we need to find the sum of the first 4 terms of the series:
S4 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7)
To find S5, we need to find the sum of the first 5 terms of the series:
S5 = (1/3) - (1/4) + (1/4) - (1/5) + (1/5) - (1/6) + (1/6) - (1/7) + (1/7) - (1/8)
To find the sum of the telescoping series, we can use the property of the telescoping series where the terms will cancel out. In this case, we can see that the first term of each group of two terms cancels out with the second term of the next group of two terms.
S = (1/3) - (1/8)
The series starts at n=2 and ends at infinity, so the sum of the series is the difference between 1/3 and the limit of 1/n as n approaches infinity, which is zero.
S= (1/3) -0 = 1/3
So the sum of the series is 1/3.
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The complete question is -
Calculate S3, S4, and S5 and then find the sum for the telescoping series: S=∑n=2∞(1/n+1)−(1/n+2). where Sk is the partial sum using the first k values of n.
(MATRIX EQUATIONS) Blake solves the system of equations by forming a matrix equation.
−x+4y=82x+3y=−5
He multiplies the left side of the coefficient matrix by the inverse matrix.
How does he proceed to the solution?
Drag the choices to correctly complete Blake's process.
For the given system of equations −x+4y = 8 & 2x+3y = −5
he proceed to the solution in following way,
Step 1: Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex] × [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]
Step 2: -1/11 [tex]\left[\begin{array}{ccc}3&-4&\\-2&-1&\\\end{array}\right][/tex]
Step 3: -1/11 [tex]\left[\begin{array}{ccc}-44\\11\\\end{array}\right][/tex]
Step 4: [tex]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]
What in the inverse matrix?Inverse matrix is a type of matrix which we get by taking the transpose of an adjoint matrix.
P⁻¹ = adj(P)/ |P|
|P| = Determinant of P
Property of inverse matrix,
P⁻¹×P = I
Given that,
system of equations
−x+4y = 8 & 2x+3y = −5
He multiplies the left side of the coefficient matrix by the inverse matrix
Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] = Inv. of [tex]\left[\begin{array}{ccc}-1&4&\\2&3&\\&\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]
By using property of inverse matrix
[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] = -1/11 [tex]\left[\begin{array}{ccc}3&-4&\\-2&-1&\\\end{array}\right][/tex]× [tex]\left[\begin{array}{ccc}8\\-5\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] = -1/11 [tex]\left[\begin{array}{ccc}-44\\11\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]
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Jane and Mary are Comic book fans, and each one has collected all n of the limited-edition Comic book figurines, with no repeats. Jane and Mary would each like to display some subset of their collection at the upcoming Comic book convention. However, Mary does not want to be outdone. He must include every figurine that Jane brings, and at least one additional figurine. How many ways can Mary and Jane choose figurines in such a way for the convention?
Mary and Jane have multiple ways to choose their subset of figurines for the comic book convention.
How to illustrate the number of ways?We know that Mary must include every figurine that Jane brings, so Mary must choose a subset of her collection that is at least x+1 figurines.
Since Mary must also choose at least one additional figurine, the total number of figurines that Mary can choose from is n-(x+1) + 1 = n-x
The total number of ways that Mary and Jane can choose their subsets is the product of the number of ways each can choose their subsets.
So, the number of ways is
(choose x out of n) * (choose x+1 out of n)
This is also known as binomial coefficient, which can be represented as nCx or (n x)
Hence the number of ways is
nCx * (n-(x))C(x+1)
Mary and Jane have multiple ways to choose.
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. Can a square also be classified as a rectangle? * Yes! Or No! you will get brainless helpppppp
Answer: yes
Step-by-step explanation: a square is always a rectangle but a rectangle is only a square when all sides are equal
Answer:
Absolutely!
Step-by-step explanation:
Since a square has 4 right angles, it can also be classified as a rectangle.
The formula for the volume, V, of a sphere with radius r is V=4/3 pi(r^3). If the radius of a baseball is 1 3/10 inches, what is the volume to the nearest cubic inch
The volume of the baseball to the nearest cubic inch is 9 cubic inches.
What is Sphere?A sphere is a three dimensional figure which consists of set of all the points which are at an equal distance from a point called the center of the sphere.
Volume is the space occupied by a three dimensional object.
Given that,
Radius of a baseball = 1 3/10 inches = (1 × 10 + 3) / 10 = 13/10 inches.
Also we know that,
Volume of a sphere = 4/3 π r³, where r is the radius.
Volume of the baseball = 4/3 π (13/10)³
= 4/3 π (1.3)³
= 4/3 π × 2.197
= 2.9293 π
= 2.9293 × 3.14
= 9.198 cubic inches.
≈ 9 inches³
Hence the volume of the baseball is 9 cubic inches.
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Find the additive inverse of 3−9x
Answer:
3(1-3x)
Step-by-step explanation:
factor out 3 from the expression
A helicopter, flying directly over a fishing boat at an altitude of 1200ft, spots an ocean liner at a 15 degrees angle of depression. How far from the boat is the liner.
Answer: The ocean liner is approximately 5.2 miles from the fishing boat.
Find the area of the trapezoid. HELP PLS
Answer:
27 cm^2
Step-by-step explanation:
The formula for finding area of trapezoid:
[tex] \frac{a + b}{2} \times h[/tex]
a and b are bases, h is height[tex] \frac{6 + 12}{2} \times 3 = 27[/tex]
The area is put in square cmSo the answer is 27 cm^2
What is the equation of the function shown in the graph? A y=−2x B y=12x C y=2x D y=−12x
Answer:I don’t onos
Step-by-step explanation:I don’t know
The conservation club has 32 members. There are 18 girls in the club.
What is the ratio of girls to boys in simplest form?
a.7/9
b.9/7
c.9/16
d.7/16
The requried ratio of boys in the club to girls is given as 7/9 or 7:9. Option A is correct.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
The conservation club has 32 members. There are 18 girls in the club.
Number of boys = 32 - 18 = 14
Ratio of boys to girls = number of boys / number of girls
= 14 / 18 = 7/9
Thus, the requried ratio of boys in the club to girls is given as 7/9 or 7:9. Option A is correct.
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Jenna’s Drama Club is selling tickets at school. Parent tickets cost $6 and student tickets cost $3. Polly hopes to make a minimum of $500 in tickets, selling a maximum of 120 tickets. Write a system of inequalities to represent this context.
Answer:
6p + 3s = 500
p + s = 120
Step-by-step explanation:
p represents the parents and s represents the students
the total amount of tickets should be p and s, hence why they equal 120
The total cost should be 500, and each parent ticket is $6 while each student ticket is $3 hence the 6p and 3s
10. Write the statements to correctly complete the algebraic proof.
If 2x-13-5, then x = 4.
Given: 2x 13 = -5
Prove: x 4
Proof:
1.
2.
3. 2x=8
4₁
Statements
X=4
2x 13+13= -5+13
W
(6 pts)
2x-13 = -5
Substitution Property
Reasons
1.
2. Addition Property
3.
4.
Division Property
Given
For solving the equation we are using
subtraction property and ,the division property.What is an Equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
The equation is 2x = 13 - 5
here by subtracting 5 from 13 we get 8
so 2x = 8
or x = 4 (proved)
for solving the equation we are using
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What is the ⌊4.5⌋ ? Question 1 options: 4.5, 4, 5, 3
Answer: 4.5
Step-by-step explanation: Those bars are absolute value. Hope it helps, please mark brainliest and give your thanks.
I need help with this question. I have attached a screenshot of this question.
Answer:
Not a lot of information given but if you are looking for the difference in price it is 31 CHF
It is 31 more CHF in Manchester than in Switzerland.
Step-by-step explanation:
1.55(145) = 224.75
224.75-193.75 = 31
Which is different? Responses Add −4.5 and 3.5 . Add negative 4 point 5 and 3 point 5. What is −4.5 increased by 3.5 ? What is negative 4 point 5 increased by 3 point 5? What is the distance between −4.5 and 3.5 ? What is the distance between negative 4 point 5 and 3 point 5? Find the sum of −4.5 and 3.5 . Find the sum of negative 4 point 5 and 3 point 5. Question 2 Find "both" answers. Answer for the "different" question: Answer for the "same" questions:
The expression that is different from "Add −4.5 and 3.5" will be "What is the distance between negative 4 point 5 and 3 point 5?"
How to illustrate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator
In this case, the expression that is different from "Add −4.5 and 3.5" will be "What is the distance between negative 4 point 5 and 3 point 5?" This is because finding the distance simply means:
= -4.5 - 3.5
= -8.0
This is different from the initial value.
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Find the value of X please answer 4, and 5! 25 points!!!!!!!!!!!!!
Answer:
4) 100
5) 120
Step-by-step explanation:
Finding unknown angle in polygon:4) Number of sides in the polygon = n = 6
Sum of all the angles of n-sided polygon = (n -2)* 180
= (6 - 2) *180
= 4 * 180
= 720
x + x + 9 + 90 + 120 +156 + 145 = 720
Combine like terms,
2x + 520 = 720
Subtract 520 from both sides,
2x = 720 - 520
2x = 200
Divide both sides by 2,
x = 200÷2
[tex]\sf \boxed{x = 100^\circ}[/tex]
5) Sum of all the angles of 5 sided polygon = ( 5 - 2)*180
= 3 * 180
= 540
x + x + x + x + 60 = 540
4x + 60 = 540
4x = 540 - 60
4x = 480
x = 480 ÷ 4
[tex]\sf \boxed{x = 120^\circ}[/tex]
Answer:
4.) You need 720 degrees sum for 6 sided polygon.
5.) You need 540 degrees for a 5 sided polygon.
Step-by-step explanation:
4.) -
120 + 156 + 145 + 90= 511
720 - 511 = 209.
209 - 9 = 200
200 / 2 = 100
X is equivalent to 100 Degrees
-
5.) -
Since X is the same for all sides we'll take 60 from 540 = 480
480 / 4 = 120
X = 120
symbol for sample standard deviation is
Answer:sThe symbol of the standard deviation of a random variable is "σ“, the symbol for a sample is "s". The standard deviation is always represented by the same unit of measurement as the variable in question. This makes its interpretation easier, compared to the variance.
Step-by-step explanation:
The model of a train is 5.5 in. The scale of that
model is 1: 40. What is the actual length of the
train ?
____feet.
The actual length of the train is calculated to be 18.33 feet
How to get the actual length of the trainScale factors are used to increase or decrease image. The situation of increment is usually called enlargement, and it is case for the problem.
solving for the factor, assuming the factor is k, using the ratio 1 : 40. the scale factor is 40 / 1 = 40
Solving for the actual length
actual length = scale facto * model length
actual length = k * 5.5 in
actual length = 40 * 5.5 in
actual length = 220 in
converting to feet
12 in = 1 foot
220 in = ?
cross multiplying
12 * ? = 220
? = 220 / 12
? = 18.33 feet
the actual length of the train is 18.33 feet
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IQ scores are normally distributed with mean mu equals 100 and standard deviation sigma equals 15. Calculate the standard deviation of the sampling distribution using a sample size of 25.
0.6
20.0
3.0
4.0
IQ scores are normally distributed with mean mu equals 100 and standard deviation sigma equals 15. the standard deviation of the sampling distribution is 3.
What is the standard deviation?Generally, The standard deviation of the sampling distribution, also known as the standard error, can be calculated using the formula:
standard error = (standard deviation of population) / (sqrt(sample size)).
In this case, the standard deviation of the population is 15, and the sample size is 25. So the standard error would be:
15 / sqrt(25) = 15 / 5 = 3
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13
Write as a mixed number.
3
Answer: 4 1/3
Step-by-step explanation:
(12 + 1) 3 = 12 3 + 1 3 = 4 + 1 3 = 4 1 3 13 3 = 4 1 3 Hence, 13/3 as a mixed number is 4 1/3
On Saturday, Carmen works no more than 8 hours at her job. Which inequality represents h, the number of hours Carmen works on Saturday?
The inequality h ≤ 8 represents the number of hours, Carmen works on the job.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
On Saturday, Carmen works no more than 8 hours at her job.
Let h be the number of hours, he works on the job.
According to the question,
h ≤ 8.
That means,
Carmen works less than or equals to 8 hours.
Therefore, the inequality is h ≤ 8.
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Diana scored 15 points in her basketball game last week.this week she scored 20% more than last week. how many points did she score this week
Step-by-step explanation:
last week = 15
this week 2o%
therefore =. last WK + this WK = 15×20÷100/1
= 300÷100/1=. 3
Diana scored 3point this week
please solve the file i will give brainliest
The expression of the weight carried by x hikers is x (3.4 + 4.6 + 2.2).
The weight carried by each hiker is 10.2 lb.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Three items are given.
The weight of each items are 3.4 lb, 4.6 lb, and 2.2 lb.
Now,
The total weight of all the items.
= 3.4 + 4.6 + 2.2
= 10.2 lb
The weight carried by x hikers.
= x (3.4 + 4.6 + 2.2)
= 10.2x lb
The weight carried by each hikers.
= 3.4 + 4.6 + 2.2
= 10.2 lb
Thus,
Weight carried by x hikers is 10.2x lb.
Weight carried by each hiker is 10.2 lb.
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Drag each symbol to the correct location on the equation. Not all symbols will be used.
Aidan collects leaves for an art project.
• He picks leaves from 8 different trees.
• He picks 12 leaves from each tree.
• He loses 7 leaves on his way home.
Complete the equation to find the number of leaves Aidan has now, n.
•1.
+
8
X
12
Reset
Next
7 = n
The equation to find the number of leaves which Aidan has now, n is given by 8 × 12 - 7 = n.
What is an equation?In Mathematics, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
Next, we would write the equation that gives n, the number of leaves Aidan would have after collecting leaves for an art project as follows:
The number of leaves that Aidan collected from 8 different trees is equal to 8 leaves. Additionally, Aidan picks 12 leaves from each tree to have a total of 96;
n = 8 × 12 = 96.
Lastly, Aidan lost 7 leaves on his way home. Therefore, we would subtract 7 leaves from the total number of leaves that Aidan collected from 8 different trees;
n = 96 - 7 = 89 leaves.
In conclusion, the complete equation is represented by 8 × 12 - 7 = n.
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Tabitha is working at a Honda dealership. She will receive 6% commission for each automobile she sells. If she sells 3 cars this week (for $23,000, $13,800, and $25, 760), how much will her commission be?
Answer:
Tabitha's commission would be 6% of the total sales from the three cars
Step-by-step explanation:
which is $(23,000 + 13,800 + 25,760) * 0.06 = $3,638.40
For questions 10-12, answer the questions about logic.
10. Write the inverse of
the statement below.
If you are over 18,
then you can vote.
11. Write the converse of
the statement below.
If this month is
February, then the
next month is March.
12. Write the
contrapositive of the
statement below.
If you have $400, then
you can afford a new
laptop computer.
If you cannot vote, then you are under 18. If the next month is not March, then this month is not February. If you cannot afford a new laptop computer, then you do not have $400.
What is Inverse, Converse and Contrapositive Statement?
Inverse Statement: The inverse statement, denoted pq, assumes the inverse of each of the original statements (if not p, then not q).
Converse Statement: The converse statement is notated as q→p (if q, then p).In the original "if-then" statement, the original statements trade places.
Contrapositive Statement: The conditional statement's inverse is "If not Q, then not P."
1) The inverse statement would be,
If you cannot vote, then you are under 18.
2) The converse statement would be,
If the next month is not March, then this month is not February.
3)The Contrapositive statement would be,
If you cannot afford a new laptop computer, then you do not have $400.
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I need the slope: (2, 1), (-1,-5), and (3,3)
Please and thank you
Answer: 1/2
Step-by-step explanation:
Slope = Δy/Δx = -3/-6 = 1/2
A package of Oreos has the unit price of $0.19 per ounce.a package of Nutter butters has a unit price of $0.21 per ounce which cookie is a better deal?
Answer:
Oreos is a better deal by lower unit price But i like Nutter Butters
Step-by-step explanation:
A package of Oreos is a better deal because it has a lower unit price per ounce. Oreos have a unit price of $0.19 per ounce, while Nutter Butters have a unit price of $0.21 per ounce.
(m² - +1/2)
n²_
m
1
+2)
(n + 1/1/12 ) " -
(m- // )
n-m
m-n
The proof of the given question is given in the solution as follows
What is a factorization example?A technique for factoring a number or a polynomial is called factorisation. The polynomials are divided into the sums of their component parts. As an illustration, x2 + 2x may be factored as x(x + 2), where x and x+2 are the factors that can be multiplied to obtain the original polynomial.
What are the 5 types of factorization?The six types of factoring are: greatest common factor, difference in two squares, grouping, sum or difference in two cubes, trinomials, and general trinomials.
In the given equation
we separate m2-1/n2 to (a+b)(a-b) form
and hence we get the answer as
(n+1/m)^m-n/(m-1/n)^m-n
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I need help plssss I need to pass this
Answer:
the growth factor of the initial amount is correct
It's not possible to build a triangle with side lengths of 3, 3, and 9.
O A. True
OB. False
SUBM
Explanation:
The shorter side lengths 3 and 3 add to 3+3 = 6, which is not larger than the remaining side 9. This is why a triangle is not possible.
For a triangle to be possible, we need the sum of any two sides to be larger than the third side. Refer to the triangle inequality theorem.
I recommend making slips of paper that are 3 inches, 3 inches, and 9 inches long (or replace "inches" with "centimeters"). Then try to make a triangle with those slips of paper. You should find such a task is impossible: as mentioned, the 3 inch sides come up short when trying to attach to the 9 inch side.
The statement "It's not possible to build a triangle with side lengths of 3, 3, and 9" is true.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
A triangle cannot be formed with side lengths of 3, 3, and 9.
To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
However, in this case, the sum of the lengths of any two sides is 3+3=6, which is less than the length of the third side, 9.
Therefore, it is not possible to form a triangle with side lengths of 3, 3, and 9.
Thus,
The statement "It's not possible to build a triangle with side lengths of 3, 3, and 9" is true.
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