The convergence of the series ∑∧∞ 4.7.10…(3n+1) /1.2.3….n is π =3+. 1. 10. +. 4. 102. +. 1. 103. +. 5. 104. +. 9. 105. +. 2. 106
What is the convergence of a series?You should understand that any series that is not convergent is said to be divergent or to diverge
The reciprocals of the positive integers produce a divergent series
This can be written as π =3+. 1. 10. +. 4. 102. +. 1. 103. +. 5. 104. +. 9. 105. +. 2. 106 .... For x ∈ R, the (infinite) geometric series ∑n≥0 xn converges if |x| < 1 and ...
This is to say that the convergence series is the reciprocal of the series.
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I need help please
I don’t understand is algebra 1
it would take 12 weeks to save and buy the iphone.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Johny is saving money to buy an Iphone X which cost $1000.
He started saving money $300 he receieved for a birthday gift.
He saved allowance of $60 per week.
We need to find how long will it take for him to save and the Iphone X.
1000=300+60x
Subtract 300 from both sides
700=60x
Divide both sides by 60
700/60=x
11.66=x
Hence, it would take 12 weeks to save and buy the iphone.
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1.) How are the tangents of complementary angles related?
2.) How are the sine and cosine of complementary angles related?
3.) How are the two non-right angles in a right triangle related?
a.)They are equal.
b.)They are complementary.
c.)They are reciprocals.
(All these three questions have the same three answer choices.)
The relationship between the trigonometric ratios of the non-right angles in a triangle and the measures of the angles are;
1.) c.) They are reciprocals
2.) a.) They are equal
3. b.) They are complementary
What are non-right angles in a right triangle?The non-right angles in a right triangle are he two acute angles in the right triangle.
1) Complementary angles are angles that have a sum of 90°
Let A and B be two complementary angles, we get;
m∠A + m∠B = 90°
Let a and b represent the lengths of the opposite sides to the complementary angles ∠A and ∠B
Let side a represent the side opposite to the angle ∠A and let side b represent the side opposite to the angle ∠B, we get
tan(A) = a/b tan B = b/a
Therefore, tan(B) is the reciprocal of tan(A)
The correct option is c,) They are reciprocals
2) Let r represent the length of the hypotenuse of the right triangle, we get;
sin(A) = a/r
cos(A) = b/r
sin(B) = b/r
cos(B) = a/r
The values, sin(A) = cos(B), and sin(B) = cos(A), therefore;
The sine and cosine of complementary angles are equal, therefore, option a is correct3) The sum of angles in the right triangle is 180°, therefore;
m∠A + m∠B + 90° = 180°
m∠A + m∠B = 180° - 90° = 90°
m∠A + m∠B = 90°
The sum of the two non-right angles in a triangle is 90°, therefore, the two non-right angles re complementary.
The correct option is therefore; b.) They are complementary
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Which option is most similar in relation to the following word pair water:ocean
Water and ocean are two closely related words, as the ocean is the largest source of water on the planet.
Which option is most similar in relation to the following word pair water:ocean?Water is essential to life, and the ocean is the planet's largest reservoir of water.It covers over 70 percent of Earth's surface and contains 97 percent of the world's water. Water and ocean are linked in many ways.The ocean produces more than half of the oxygen in the atmosphere, and the ocean's currents and tides help regulate the climate.Water from the ocean evaporates into the atmosphere, eventually returning as rain, snow, and hail and replenishing the planet's fresh water supply.The ocean is home to a variety of organisms and species that rely on the water for their survival, as well as other resources such as food and shelter.Additionally, the ocean is an important source for human activities such as fishing, transportation, and recreation.In short, water and ocean are inextricably linked, and their relationship is essential to the health of the planet.To learn more about word pair water:ocean refer to:
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Suppose that Karen, Sue, and Peter all work 8 hours a day.
In an hour, Karen can make one widget or 4 thingamajigs.
In an hour, Sue can make one widget or one thingamajig.
In an hour, Peter can make 4 widgets or one thingamajig.
If they use the most efficient specialization to divide up their
time among themselves to together produce the same number
of widgets and thingamajigs, how many thingamajigs can they
make?
Total thingamajigs made by Karen, Sue and Peter = 48 and same as the number of widgets.
What is multiply?Multiply means enlarge or increase. Adding equal number of groups is termed as multiply. Multiply 4 by 4 means 4 is added to 4 in 4 times.
How many thingamajigs can they make?
given, Karen can make 1 widget in 1 hour.
In a 1-hour time period Sue can make 1 widget
Peter can make 4 widgets in 1 hour.
If they all work 8 hours in a day, then total number of widgets made by them will be
= 1 × 8 + 1×8 + 4×8 =48
They together can make 48 widgets in a day.
similarly, Karen can make 4 thingamajigs in 1 hour.
Sue can make 1 thingamajig in 1 hour.
Peter can make 1 thingamajig in 1 hour.
In total 8 hours period they together can make (4×8 + 1×8 +1×8)
48 thingamajigs.
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What multiplier would be used to increase a number by
15%?
O 0.15
O 1.15
O 1.5
The multiplier would be used to increase a number by 15% is, 1.15
What is multiplicative rate of change?The multiplicative rate of change is a number by which we get another number from the previous number, to get the value of this number , we have to divide the other number from the previous number.
Suppose
first number = X
second number = Y
second number is 15% more than first number
So, Y = X + 15% of X
Y = X + 0.15X
Y = 1.15 X
for multiplicative rate of change we have to apply divide operation,
⇒ P = Y/X
⇒ P = 1.15X/X
⇒ P = 1.15
Hence, the result is 1.15
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Identify the domain of f.
For which values a does lim x -> a f(x) not exist? Find all values a where lim x -> a f(x) exists, f is defined at a, but lim x -> a f(x) does not equal f(a).
The graph shows that the domain and range of the line segment were [-5, 1] & [-4, 7, correspondingly.
Describe domain.A function's domain is the set of values that it can accept. These figures represent a function like f's x-values (x). The domain of a function is the set of possible values on which it can operate. This set is the value which the return type after the x value has been entered. Y = f is a function where x is an independent variable and y is a dependent variable (x). If a value of x can be successfully utilized to produce a single value of y using a value of f, then that value is said to be within the domain of that function.
Here,
The domain denotes all conceivable possibilities for x, whereas the range denotes all possible values of y.
The graph shows that the domain and range of the line segment is [-5, 1] & [-4, 7, respectively.
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What is the value of X
Answer:
x = 17
Step-by-step explanation:
The sum of the interior angles of a triangle is 180
x + 17 + 4x - 34 + 6x + 10 = 180 Combine like terms
11x -7 = 180 Add 7 to both sides
11x - 7 + 7 = 180 + 7
11x = 187 Divide both sides by 11
[tex]\frac{11x}{11}[/tex] = [tex]\frac{187}{11}[/tex]
x = 17
Answer:
the answer is x=17 because the triangle is isosceles
What do I put as the response?
Step-by-step explanation:
the law of intersecting lines : the angles between both lines are the same on both sides of either line, just left-right mirrored.
that's why the angles are while going around the intersection point (starting with the known 37° angle) :
37° - supplementary angle - 37° - supplementary angle
and again from the start.
"supplementary" angles are pairs of angles that together are 180°. just like 2 neighboring angles at intersecting lines.
so, 37° = 7x - 5
example 4
116° is the supplementary angle of 4x.
that means
180 = 116 + 4x
64 = 4x
x = 64/4 = 16
Aa man was 26 years old when his son was born. Now,he is three times as old as his son. How old is the son now?
Answer:
His son is 13 years old now.
Step-by-step explanation:
Since the man was 26 years old when his son was born, his age is 26 more than his son's age, or mathematically speaking, x + 26 if the age of his son is x.
26 + x - dad's age
x - son's age
3 x son's age = dad's age
3x = 26 + x
2x = 26
x = 13
His son is 13 years old.
7. A manager has to choose three products out of five possibilities to take into production. How many different ways are there to choose three products out of five?
There are 10 different ways to choose three products out of five.
What are permutation and combination?
Permutation and combination are mathematical concepts used to study the arrangements and selections of items.
Permutation: An arrangement of items, where order matters.
Combination: A selection of items, where order does not matter.
In this case, the manager has to choose three products out of five possibilities, which is a combination problem. To find the number of different ways to choose three products out of five, we can use the formula: nCr = n! / (r! (n - r)!).
n = 5 (number of items)
r = 3 (number of items to be chosen)
nCr = 5! / (3! (5 - 3)!) = 5! / (3! 2!) = (5 x 4) / (2 x 1) = 10.
Hence, there are 10 different ways to choose three products out of five.
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Assume A varies directly as B^2. If B is multiplied by 3.55, how will it affect A. In other words: if we multiply B by 3.55, by how much would we have to multiply A, in order to preserve the same coefficient of proportion?
Write your answer as a decimal rounded to two decimal places.
Answer: 12.60
Step-by-step explanation: A = B^2. If B is multiplied by 3.55, then A = (3.55B)^2. That gives us A = 12.6025B. Round 12.6025 to hundredth and you get 12.60
The area of the figure below is 9ft.What is the height of the triangle if the base of the triangle is 4.5
[tex]area = \frac{1}{2} \times base \times height \\ 9 = \frac{1}{2} \times 4.5 \times h \\ 9 = 2.25h \\ \frac{9}{2.25} = \: \frac{2.25h}{9} \\ 4 = height[/tex]
pls help me this is urgent
A retailer received an invoice dated 7th June 2022 with trade discounts of 12% and 8% and cash discount terms of 7/10, 3/20, n/30. The net price after the trade discounts including transportation cost of RM200 was RM1,550.
a) Find the list price.
b) Find the last date to receive the cash discount.
c) Find the total payment if the payment was made on 12th June 2022.
d) Find the amount of discount obtained.
Customers who purchase items with discount of credit has 30 days to repay the balance. However, if clients pay for their products within 10 days,
How exactly is the trade credit calculated?A trade discount, often referred to as a functional reduction, can be applied as a fixed percentage or flat rate deduction from the a seller's initial catalogues list price, in which case the trading discount amount is calculated by multiplying the list price by the percentage difference. Calculating the trade discount requires knowledge of both the item's original list price and the trade discount percentage. The list price is multiplied with the trade discount % in decimal form to arrive at the trade discount.
Here,
they will receive a 2% discount. Customers need only pay $9,800
if they buy $10,000 from Group A underneath the terms 2/10 gross 30 and pay within ten days ($10,000 x 0.98 = $9,800).
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Please help me with this question.
i) The absolute change of the CPI from 2009 to 2014 is given as follows: 22,199.
ii) The absolute change of the Tuition from 2009 to 2014 is given as follows: $26.5.
iii) The relative change of the CPI from 2009 to 2014 is given as follows: 10.35%.
iv) The relative change of the Tuition from 2009 to 2014 is given as follows: 26.59%.
Tuition has increased more in this time period.
How to obtain the changes?The absolute change between two amounts is given by the absolute value of the difference of these two amounts.
Hence for the CPI from 2009 to 2014 is given as follows:
236736 - 214537 = 22,199
For the Tuition, it is given as follows:
126.15 - 99.65 = $26.5.
The relative change is given by the absolute change divided by the initial value and multiplied by 100%, hence:
CPI = 22199/214537 x 100% = 10.35%.Tuition: 26.5/99.65 x 100% = 26.59%.Due to the higher relative change, the Tuition increased more in this time period.
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According to the CDC, the fatality rate for measles is 0.2% in the United States. However, in developing countries it is approximately 25%. According to the World Health Organization about 75% of measles cases occurred in developing countries in 2019. How many deaths from measles are likely to have resulted? Round your answer to the nearest thousand.
The estimation number of death from measles occured in developing countries in 2019 is 1.9 million deaths.
To estimate the number of deaths from measles in developing countries, we can use the following calculation:
Deaths = (Total number of cases in developing countries) × (Fatality rate in developing countries)
According to the World Health Organization, 75% of measles cases occurred in developing countries in 2019. Assuming a total of 10 million cases worldwide, 7.5 million cases would have occurred in developing countries.
The fatality rate in developing countries is approximately 25%, so:
Deaths = (7.5 million cases) × (0.25) = 1.875 million deaths.
Deaths = 1.875 million deaths ≈ 1.9 million deaths
So, 1.9 million deaths from measles are likely to have resulted in developing countries in 2019.
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Someone pls help this is important
An integer which can be used to represent a diver's elevation if the diver is 40 feet below sea level is -40.
What is an integer?In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).
On the other hand (conversely), a negative integer simply refers to a whole number that is less than zero (0), but do not include decimals or fractions.
In this context, we can reasonably infer and logically deduce that an integer which can be used for representing a diver's elevation when he or she is 40 feet below sea level would be the negative integer -40.
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Jakub is building a shed. He wants the concrete base to be bigger than the shed.
What is the perimeter of the base?
The outer perimeter of the rectangular base will be 34 meters.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
The outer dimension of the base will be given as,
L = 8 + 1 + 1
L = 10 m
W = 5 + 1 + 1
W = 7 m
The outer perimeter of the rectangular base will be given as,
P = 2(7 + 10)
P = 2 x 17
P = 34 m
The outer perimeter of the rectangular base will be 34 meters.
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4 more than the quotient of 24 and a number m
(x - 12)(x + 5)/(x - 3)³≤0
The range of values of x for the given expression (x - 12)(x + 5)/(x - 3)³≤0 is ,
( -∞ , -15] and [3, 12]
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given expression,
(x - 12)(x + 5)/(x - 3)³ ≤0
by using wavy curve method it can be state that,
function hold negative value,
1. when x is less than -15
⇒ x ≤15
2. when x is in between
⇒ 3≤ x ≤12
Hence, range of x is ( -∞ , -15] and [3, 12]
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22 people fit comfortably in a 15 feet by 10 feet area. Use this value to estimate the size of a crowd that
is 10 feet deep on ONE side of the street along a 1 mile section of a parade route.
Answer:
Step-by-step explanation:
First, we need to convert the area of 15 feet by 10 feet to square feet. That is 15*10 = 150 sq ft.
We know that 22 people fit comfortably in a 150 sq ft area, so we can estimate the number of people that can fit in a given area by dividing the area by the number of square feet per person.
So if we have an area of 10 feet deep on one side of the street along a 1-mile section of a parade route, we can estimate the number of people that can fit in that area by using the following equation:
(Area of crowd) / (Square feet per person) = Number of people
We know that 1 mile = 5280 feet, so the area of the crowd is 10*5280 = 52,800 sq ft.
Now we can estimate the number of people that can fit in that area by dividing the area by the number of square feet per person:
52,800 sq ft / 150 sq ft/person = 352 people
So, we can estimate that around 352 people can fit comfortably in a crowd that is 10 feet deep on one side of the street along a 1-mile section of a parade route.
to graduate you must take at least 12 core credits and 6 electives credits and you can take no mre than a total of 26 credits write a system of inequalities that defines how many of each of you can take
The system of inequalities that defines how many of each you can take is: C≥12,E≥6,C+E≤26. Option A
How to define the inequalityThe questions says that you must take at least 12 core credits
let core courses be = C
This tells us that C has to be greater than or equal to 12
C ≥ 12
Then it says that you must take at least 6 electives as well. This would be represented in the same way.
E = elective
E ≥ 6
Lastly, it says that you can take no more than a total of 26 credits
Hence your credit has to be 26 in number or less.
This would be written as C + E ≤ 26
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Complete question
To graduate you must take at least 12 core credits and 6 electives credits and you can take no more than a total of 26 credits. Write a system of inequalities that defines how many of each you can take.
C≥12,E≥6,C+E≤26
C+E≥18,C+E≤26
C+E≥18,C+E<26
C≤12,E≤6,C+E≤26
Find the different by subtracting the second polynomial from the first.
4a-3b+2c and -6a+4b-2c-2
Answer: -2a+b-2
Step-by-step explanation:
Pls help Darnell is an election officer. On election day, he travels to the polling place, which is 4.4 miles away from his home. On a map of Harrison County, these two places are 8 inches apart. What is the scale of the map? Write your answer in simplest form using whole numbers.
Answer:
The scale of the map is 1 : 34848---------------------------------
Real distance is 4.4 miles and on the map it is 8 inches.
The scale is:
8 in : 4.4 miles = Divide both sides by 81 in : 0.55 milesor
1 in : 0.55 * 63360 in = Convert 1 mile = 63360 inches1 : 34848The probability that a randomly chosen sales prospect
Answer:
Step-by-step explanation:
will make a purchase is dependent on a variety of factors. These include the product or service being offered, the price point, the customer's needs and wants, the customer's current financial situation, and the salesperson's ability to effectively communicate the value of the product or service. Many businesses will use analytics and data to track customer purchasing habits and trends, as well as the effectiveness of their marketing and sales strategies. This allows them to better determine the probability of a sale. Additionally, a salesperson's past performance, customer relationships, and other factors all influence the probability of a sale. Ultimately, the probability of any given sale is unique to each customer and situation.
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The value of x in degrees will be 6° and 11° using properties of parallel lines.
What Qualities Characterize Parallel Lines?They are typically equal-distance, parallel straight lines. The lines here are parallel. They never come together no matter how far you extend them in any one way.
Pairs of equal-sized angles that are both obtuse or acute and are generated on the same side of the transversal are known as corresponding angles. Each pair of comparable angles on the same side of the crossing transversal is equal to the other.
The alternative angle theorem states that alternate interior angles or alternate exterior angles that come from cutting two parallel lines are congruent.
In the above figure,
8x + 7 = 55
8x = 55 - 7
x = 6
Measure of the angle will be 8 × 6 + 7 = 49
In 11)
10x + 10 = 9x + 21 (by using first corresponding angles and then alternate angles)
⇒x = 11
The value of x in degrees will be = 11° using properties of parallel lines.
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There is 25 pounds of dog food in a bag. There are approximately 2.2 kilograms in 1 pound. PLEASE HELP ME !! THANK YOU SMM!!
Which statement is true?
A. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/22.
B. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
C. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25
Answer:
C
Step-by-step explanation:
kilograms x pounds of dog food = ?
2.2 x 25 = 55
process of elimination;;;
A- correct answer, wrong setup
B- wrong answer, correct setup
C- correct answer, correct setup. makes the most sense
D- wrong answer, wrong setup
Find the perimeter of triangle ABC. Round your answer to two decimal places.
2
4
6
8
10
-2
-4
-6
-8
-10
2
4
6
8
10
-2
-4
-6
-8
-10
A
B
C
The perimeter of Triangle ABC, given the triangle in drawn in the graph, would be 40 .54 units .
How to find the perimeter ?To find the perimeter of the triangle , you first need to find the lengths of the sides of the triangle .
The lengths would be the distance between the points A , B , and C .
The vertices are : A ( - 1 , - 8) , B ( -4 , 6 ) and C ( 4 , 9 ) .
The distance between the points can be found by the formula:
= √(( x₂ – x₁ )² + ( y₂ – y₁) ²)
The distance between AB is 14.3 units
The distance between BC is 8. 54 units.
The distance between AC is 17.7 units.
The perimeter is:
= 14.3 + 8. 54 + 17. 7
= 40 .54 units
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What is 7, 10, 13, 16, as a linear function
Answer:
This is a sequence of numbers that can be expressed as a linear function. The linear function would be of the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, m = 3 and b = 7, so the linear equation for this sequence is y = 3x + 7.
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Plot -7/5 and it's opposite on a number line
Answer: find zero on the number line then put a dot on -7/5 (-1 2/5) then do the same on positive 7/5 (1 2/5
Step-by-step explanation:
find zero on the number line then put a dot on -7/5 (-1 2/5) then do the same on positive 7/5 (1 2/5 . I think that is correct sorry if it isnt.
Step-by-step explanation:
HELP PLSS URGENTTT
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An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
What is a polynomial?When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).
The sum of terms with the notation kxn, where k is any number and n is a positive integer, is referred to as a polynomial.
Using a binomial and a trinomial as a product, one can factor the sum or difference of two cubes. It follows that x3+y3=(x+y)(x2+xy+y2) and x3+y3=(xy)(x2+xy+y2).
If an expression can be thought of as the difference of two perfect squares, then a3 - b3 = (a - b)(a2 + ab + b2). To prevent issues, use parentheses. The trinomial phrase should be free of inner parenthesis.
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