The given series is a geometric series and its sum is -22
The summation or sigma notation is used to express long summation into a single formula.
The series, given in a summation notation, is:
[tex]\sum\limits^6_{n=2} {(-2)^{n-1}}[/tex]
The formula inside the sum notation represent the nth term, a(n).
Let evaluate the terms for some n
a(2) = (-2)²⁻¹ = (-2)¹ = -2
a(3) = (-2)³⁻¹ = (-2)² = 4
a(4) = (-2)⁴⁻¹ = (-2)³ = -8
This form a new geometric series, with the first term, let say f(1) = -2 and common ratio = -2.
The number of terms in this new geometric series is 5.
Use the sum formula for a geometric series,
S(n) = a(1) . (rⁿ - 1)/(r - 1)
Substitute n = 5, a(1) = -2, and r = -2 into the formula:
S(5) = -2 . ((-2)⁵ - 1) / ((-2) - 1)
S(5) = -2 . (-33) / (-3) = -22
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Simplify each sum or difference. State any restrictions on the variables.
5y + 2 / x y² + 2 x-4 / 4xy
Simplification of each sum or difference of the given equation [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex] is equal to [tex]\frac{(xy+8y+4)}{2xy^{2} }[/tex] .Restriction on the variables is given by x≠0 , y≠0 .
As given in the question,
Given equation is [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex]
Simplify the given equation by taking the least common multiple,
[tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}\\\\\\= \frac{20y +8+2xy-4y}{4xy^{2}}\\ \\\\= \frac{2xy+16y+8}{4xy^{2}}\\ \\\\= \frac{xy+8y+4}{2xy^{2}}[/tex]
Restriction on the variables are x≠0 , y≠0.
Therefore, simplification of each sum or difference of the given equation [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex] is equal to [tex]\frac{(xy+8y+4)}{2xy^{2} }[/tex] .Restriction on the variables is given by x≠0 , y≠0 .
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HELP ME PLEASE I have no idea on how to do this!!!
Using it's concept, the average rate of change of the function in the intervals is given by:
a. 1.
b. -5/3.
c. -1.
d. 4.
e. -3.
f. 0.
What is the average rate of change of a function?
The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item a, we have that:
f(-3) = 0.f(-2) = 1.Hence the rate is:
r = (1 - 0)/(-2 - (-3)) = 1.
For item b, we have that:
f(-2) = 1.f(1) = -4.Hence the rate is:
r = (-4 - 1)/(1 - (-2)) = -5/3.
For item c, we have that:
f(0) = -3.f(1) = -4.Hence the rate is:
r = (-4 - (-3))/(1 - 0) = -1.
For item d, we have that:
f(1) = -4.f(2) = 0Hence the rate is:
r = (-0 - (-4))/(2 - 1) = 4.
For item e, we have that:
f(-1) = 0.f(0) = -3.Hence the rate is:
r = (-3 - 0)/(0 - (-1)) = -3.
For item f, we have that:
f(-1) = 0.f(2) = 0.Hence the rate is:
r = (0 - 0)/(2 - (-1)) = 0.
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6.13 round each number to the place of the underlined dight 1
Answer: 6.1
Step-by-step explanation:
If the digit after the underlined digit is 4 or less, then you round down. If the digit after the underlined digit is 5 or more, than you round up.
6.13 rounded to the nearest tenth is 6.1
Determine whether each set of numbers can be the measure of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.
a. 11,60,61
The following set of numbers, 11, 60, and 61, can be the measures of the sides of a right triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 11, b = 60, and c = 61
a + b > c 11 + 60 > 61 71 > 61 True
a + c > b 11 + 61 > 60 72 > 60 True
b + c > a 60 + 61 > 11 121 > 11 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
11^2 + 60^2 = 3721
2. Compare it to the square of the largest side.
61^2 = 3721
3721 = 3721
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle.
if they are smaller, then it is an obtuse triangle.
Hence, 11, 60, and 61 can be the measure of the sides of a right triangle.
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CCSS ARGUMENTS Write a two-column proof.
Given: BD bisects ∠B .
BD ⊥ AC
Prove: ∠A ≅ ∠C
∠A ≅ ∠C under the CPCT condition (coresponding parts of congurent triangles).
What accurately does the term "triangle congruency" mean?Two triangles are considered to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given: BD bisects ∠B and BD ⊥ AC.
To prove: ∠A ≅ ∠C
First, prove that △ABD≅△BDC.
∠DBA ≅ ∠DBC = Given: BD bisects ∠B∠BDA ≅ ∠BDC = (90°) Given: BD ⊥ ACSo, △ABD≅△BDC under AA condition.
Then, ∠A ≅ ∠C under CPCT condition.Therefore, ∠A ≅ ∠C under the CPCT condition (coresponding parts of congurent triangles).
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a. The number of Calories varies directly with the mass of cheese. If 50 grams of cheese contain 200 Calories, how many Calories are in 70 grams of cheese?
If 50 grams of cheese contain 200 Calories, 280 kcal are in 70 grams of cheese.
50g = 200 kcal
1g = 200 kcal / 50g
70g = (200 kcal / 50g) × 70g
= 280 kcal
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Complete the square. x²-24 x+__ .
144 I that’s to your problem
Have a great day!
find the average of -1/12 + 4/17 - 3/28
Answer:
16/1071
Step-by-step explanation:
The average is the given by summing all the numbers and deciding by how many numbers you have
So, the answer is given by:
(-1/12 + 4/17 - 3/28) / 3 which yields to 16/1071
3(x+8)=-6
Pleaseeee do the whole equation line and all
Answer:
x= - 10
Step-by-step explanation:
Divide both sides of the equation by 3, x+8= - 2. move the constant to the right side and change its sign, x= - 2 - 8. Calculate the difference and the solution will be x= - 10
Consider the inequality 38 ≤ bx + 8
What value of b will result in the solution x ≤ - 6?
For the value of (b = -5) the result of the solution is x ≤ - 6.
What is termed as the inequality?The term inequality refers to a mathematical equation wherein the sides are not equal. An inequality equates any two values and shows that one is less, greater, or equal to the value on either side of the equation.
Rule 1: When inequalities are connected, they can be crossed. As a result, if an is greater than b and b is greater than c, a will be greater than c as well.Rule 2: When you swap the values, the sign as well reverses.Rule 3: An inequality can be either > or, but not both at the same time.Rule 4: Reversing the sign by multiplying both sides of the inequality by the a negative sign.Consider the given expression;
38 ≤ bx + 8
Simplify the equation;
38 - 8 ≤ bx
30 ≤ bx
Multiply both side with negative sign; by the rule four, the sign of inequality will also change.
- 30 ≥ -bx
or -bx ≤ - 30
For converting the value to the expression x ≤ - 6; the value which should be divide the 30 is 5.
Thus,
-(-5)x ≤ - 30
Thus, the value of b is found as (b = -5).
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A bag of jelly beans contains 7 red, 11 yellow, and 13 green. Victoro picks two jelly beans from the bag without looking. What is the probability as a percent rounded to the nearest tenth that Victoro picks a green one and then a red one?
The probability, expressed as a percentage rounded to a nearest tenth, that Victoro chooses a green jelly then a red one is 0.1.
What is defined as the combinations in a probability?A combination is a preference of all or part of a group of objects, regardless of their order of selection.
You can choose the items in just about any order in combinations. Permutations and combinations are often confused.
Now, as per the given question;
The total number of red jelly beans in a bag is 7.
The total number of yellow jelly beans in a bag is 11.
The total number of green jelly beans in a bag is 13.
Thus, the total number of jelly beans in a bag is;
7 + 11 + 13 = 31.
First, Victoro picks the green one;
Thus, the probability of picking a green jelly out of total 13 green jellys is;
¹³C₁/ ³¹C₁ = 13/31
Now, as the second jelly picked by Victoro is red which is without replacement.
Thus, the probability for getting a red jelly out of total 30 left jellys is;
⁷C₁/ ³⁰C₁ = 7/30
Therefore, the total probability that Victoro picks a green one and then a red one is ;
= 13/31×7/30
= 91/930
= 0.097
= 0.10 (rounded to the nearest tenth)
Therefore, the probability of getting the red jelly after the green jelly is 0.10.
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please help with math homework
Using the Pythagorean Theorem, it is found that:
a) The hypotenuse is of 9.49 cm.
b) The new area of the triangle is of 30 cm².
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, the sides are given as follows:
3 cm and 9 cm.
Hence the hypotenuse is given by:
h² = 3² + 9²
h = sqrt(3² + 9²)
h = 9.49 cm.
The hypotenuse is of 9.49 cm.
What is the area of a right triangle?The area of a right triangle of sides a and b is given by half the multiplication of the sides, as follows:
A = 0.5ab.
For this problem, we have that:
The side of 3 cm is increased by 2 cm, hence a = 5 cm.The side of 9 cm is increased by 3 cm, hence b = 12 cm.Then:
A = 0.5 x 5 x 12 = 30 cm².
The new area of the triangle is of 30 cm².
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Consider a utility function that represents preferences over perfect complements: (1,2)=min{341,172}u(x1,x2)=min{34x1,17x2}.
According to the question, the utility function can be written as: [tex]U(x,y)=min(341,172)[/tex]
What is utility function and perfect complements?
A utility function is a standard rule which is assigned to all consumption bundles. And it is represented as two good models which are known as domain and codomain. It is also used to represent the individual items for the goods or services beyond their monetary value. Similarly, when two goods are consumed perfectly then they are called perfect complements.
Similarly, Perfect complement is: [tex]max(341,172)[/tex]
Therefore, the equations can be written for the points(1,2):
[tex]x_{1} +2x_{2} =172[/tex] and [tex]x_{1} +x_{2} = 341[/tex]
And the calculated equation is perfect complements:
[tex]x_{1} +2x_{2} =172[/tex] and [tex]x_{1} +x_{2} = 341[/tex]
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Preform the indicated operation 5/4 + 7/9
Answer:
5/4+5/9
45/36 +20/36
65/36
1 30/36
The temperature yesterday was 14 degrees Celsius. Today the
temperature dropped 14 degrees Celsius.
What is the current temperature?
Answer:
0
Step-by-step explanation:14 subtracted by 14 is 0
Please helppp due soon
Shelly picked out a pair of jeans to purchase that are marked $54.99. She has a coupon that gives her $10 off. She has a SPC card that gives her an additional 10% off the total cost before taxes. What will she pay for the jeans including 13% tax?
Answer:
assuming the coupon came b4 everything else : $ 45.75
Step-by-step explanation:
ten off of 54.99 is 44.99
10 % of 44.99 is 4.499
44.99 - 4.499 is 40.49
13% of 40.49 is 5.26
so 40.49 + 5.26 is 45.75
Samuel Sandoval sells furniture. He earns 4% commission on the first $2000 of sales. He earns 6%commission on all sales over $2000. Last week his furniture sales totaled $8230. How much did he earn make sure to show your work.
Answer:
Step-by-step explanation:
hi
Write the standard form of the equation of the circle that passes through the given point and whose center is at the origin.
(-6,0)
The equation of the circle that passes through the point (-6 , 0) and has a center located at the origin is x^2 + y^2 = 36.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , 0).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(-6 - 0)^2 + (0 - 0)^2
radius= √36
radius = 6
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = 6
(x - 0)^2 + (y - 0)^2 = 6^2
x^2 + y^2 = 36
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find L.C.M of 90 and 108
What’s 5 more than twice a number
Answer:
33 is the correct answer
Answer:
2x+5
Step-by-step explanation:
if the number is x
∴ 5 more than twice a number is
ll ll
V V
+5 *2
So, 2*x+5
Evaluate this exponential expression.
5•(3+6)²-62
Answer:
343Step-by-step explanation:
5×(3+6)²-62=
5×9²-62=
5×81-62=
405-62=
343
write each subtraction equation as an addition equation
a - 9 = 6
p - 20 = -30
z - (-12) = 15
x - (-7) = -10
Answer:
try it's your self i am sure you can do it.
Step-by-step explanation:
Let's go together
Consider the set t = {1, 2, 3, 4, 5, 6}. let r = {(a, b) | a divides b} be a relation on the set t. the tabular representation for the ordered pairs of the given relation r on the set t is:_________
The ordered pairs of the given relation r on the set t is ungrouped data.
What is ungrouped data?The data you initially collect from an experiment or study is known as ungrouped data. The data is unsorted, unclassified, or otherwise grouped; it is therefore considered to be raw. A list of numbers is an ungrouped piece of data.
Ungrouped data is a distribution type where each piece of information is presented in its rawest form. For instance, a batsman's five most recent scores are 45, 34, 2, 77, and 80.
Raw data is another name for ungrouped data.
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What is line parallel to -x?
Answer:
I think its -y
Step-by-step explanation:
Answer:
x is my answer
Step-by-step explanation:
i don't know sorry
Write each number as a percent.
1.72
Simplify each sum or difference. State any restrictions on the variables.
y / 2y + 4 - 3 / y + 2
The simplification of each or difference of the given expression [tex]\frac{y}{(2y+4)}-\frac{3}{y+2}[/tex] is equal to (y-6) /2(y+2). Restriction on the variables is given by y ≠ -2.
As given in the question,
Given expression [tex]\frac{y}{(2y+4)}-\frac{3}{y+2}[/tex]
Simplify the given expression by taking the least common multiple
[tex]\frac{y}{(2y+4)}-\frac{3}{y+2}\\\\\\= \frac{y}{2(y+2)}-\frac{3}{y+2}\\\\= \frac{y-6}{2(y+2)}[/tex]
Restriction on the variables is given by y ≠ -2.
Therefore, the simplification of each or difference of the given expression [tex]\frac{y}{(2y+4)}-\frac{3}{y+2}[/tex] is equal to (y-6) /2(y+2). Restriction on the variables is given by y ≠ -2.
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PLEASE ANSWER THIS!! ASAP! GIVE EXPLANATION OF HOW YOU GOT THE ANSWER (show your work!!) ASAP MATHE QUESTION
For this, we need to make ratios(unit per unit, in this case, red paint per white paint).
Sydney's Mix - [tex]\frac{7 red}{4 white}[/tex]
Maria's Mix - [tex]\frac{5 red}{3 white}[/tex]
Both of these fractions are improper, so you can make mixed fractions and then find their common denominators:
Sydney's Mix - 1[tex]\frac{3}{4}[/tex] = 1[tex]\frac{9}{12}[/tex]
Maria's Mix - 1[tex]\frac{2}{3}[/tex] = 1[tex]\frac{8}{12}[/tex]
Therefore, they do not have the same shade of pink because 1[tex]\frac{9}{12}[/tex] [tex]\neq[/tex] 1[tex]\frac{8}{12}[/tex] :)
What is the 25th term in the sequence 11, 20, 29, 38, 47…?
The 25th term in the sequence 11, 20, 29, 38, 47… is 227.
How to calculate the sequence?Based on the information illustrated, it should be noted that the 25th term in the sequence 11, 20, 29, 38, 47… will be calculated thus:
In this case, this is an arithmetic sequence. The formula to calculate the sequence will be:
= a + (n - 1)d
a = first term = 11
d = common difference = 9
The 25th term will be:
a + (n - 1)d
= 11 + (25 - 1)9
= 11 + (24 × 9)
= 11 + 216
= 227
The 25th term is 227.
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Which is the 7 th number in this pattern?
8,13,18,23,. . .
(F) 28
(G) 33
(H) 38
( I ) 43
Answer:
38
Step-by-step explanation:
well done .....I hope it's helpful
Find the sum of each finite arithmetic series. 5+6+7+ . . . . . . +11
The sum of the given arithmetic series 5+6+7+ . . . . . . +11 is 56.
Suppose we are given an arithmetic series:
a(1) + a(2) + a(3) + a(4) + .... + a(n)
Then, each term of the series follow the general formula:
a(n) = a(1) + (n-1) . d
Where:
a(n) = nth term
a(1) = first term
d = common difference = a(n) - a(n-1)
We are given:
5+6+7+ . . . . . . +11
Parameters we get from this series:
a(1) = 5
d = 6 - 5 = 1
a(n) = 11
We need to find n that results in a(n) = 11
Substitute a(n) = 11, a(1) = 5, and d = 1:
a(n) = a(1) + (n-1) . d
11 = 5 + (n-1) . 1
11 = n + 4
n = 7
The sum of the first n terms of an arithmetic series is:
S(n) = n/2 [ a(1) + a(n) ]
S(7) = 7/2 (5 + 11)
= 7 . 8 = 56
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