In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.
In case a, since the limit of the ratio of consecutive terms is 1, the series is convergent and its sum is equal to the limit of the sequence of partial sums of the series.In case b, since the limit of the nth root of the absolute value of the terms is 2/3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case c, since the limit of the ratio of consecutive terms is 0.8, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case d, since the limit of the ratio of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case e, since the limit of the ratio of consecutive terms is 3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case f, since the limit of the nth root of the absolute value of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit.Learn more about Convergent here:
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Can someone help with this !!!!
Answer:
[tex]f(g(4)) = f(4^2-3) = f(13) = 13 + 7 = 20[/tex]
[tex]g(f(5)) = g(5 + 7) = g(12) = 12^2-3 = 141[/tex]
[tex]f(f(1)) = f(1 + 7) = f(8) = 8 + 7 = 15[/tex]
Range of 63, 42, 28, 45, 36, 48, 32, 40, 57, 49
What is logically equivalent example?
Two statements are logically equivalent if they have the same truth value in all possible circumstances, meaning that they are either both true or both false in any given context.
For example, the statement "All dogs are mammals" is logically equivalent to the statement "All non-mammals are not dogs." Although the statements use different words and phrasing, they convey the same information and are both true.
Another example would be the statement "x>2" is logically equivalent to the statement "x>=3" because they both would have the same solutions.
Logical equivalence is important in logical reasoning, proof and in computer science where it is used to determine if two statements are logically equivalent which leads to simplify the boolean expressions.
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A person loans his friend $500. They agree to an annual interest rate of 5%.
Write an expression for computing the amount owed on the loan, in dollars, after 1 years If no payments are made.
If no payments are made then the then after 1 year the interest will go by 5% , therefore the amount to be paid will become , P + 25 = 525 $.
Principle + 5% of 500
Therefore, the equation becomes ,
Amount = P + 25
To calculate the interest ,
interest = principal × interest rate × term
= 500 x 5 x 1
= 2500.
A loan is defined as a thing or money which is borrowed, especially a sum of money that is expected to be paid back with an interest rate which is fixed by both the parties.
Loans are typically taken or granted by by corporations, financial institutions, and governments. They allow for growth in the overall money supply in an economy and open up competition by lending to new businesses.
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HELP PLEASE!!!!!!!!!
Answer:
x-coordinate
Step-by-step explanation:
To open a safe five numbers must be entered on a keypad. The keypad contains numbers 0-9. The numbers have to be entered in a certain order
to open the safe.
a. What are the TOTAL number of possible ways you can enter five numbers to open this safe (if there are NO restrictions on the numbers that
may be chosen)?
b. If no numbers repeat, then how many entries are possible?
c. What is the PROBABILITY that the safe's five numbers do not repeat? Write your answer as a percent rounded to the nearest tenth.
Answer:
30.2%
Step-by-step explanation:
a. For each slot there are 10 possible numbers (0-9). Since there are no restrictions, the number in each slot is independent of the other. We can calculate the total number of possibilities using the product rule.
N = 10 × 10 × 10 × 10 × 10 = 10⁵
b. For the first slot, there are 10 possibilities.
For the second slot, we cannot repeat the number that we used in the first slot, so there are 9 possibilities.
For the third slot, we cannot repeat any of the previous numbers, so there are 8 possibilities.
For the fourth slot, we cannot repeat any of the previous numbers, so there are 7 possibilities.
For the fifth slot, we cannot repeat any of the previous numbers, so there are 6 possibilities.
The total number of combinations without any repetitions are:
10 × 9 × 8 × 7 × 6 = 30,240
c. The probability that the safe's five numbers do not repeat is:
P = favorable outcomes / possible outcomes
P = 30,240 / 10⁵ = 30.2%
PLEASE HELP ASAP WILL MARK BRAINLEST!!!
Answer:
HELLLLLLLLLLLLLLLLLL NO
Step-by-step explanation:
A farmer sells 8. 5 kilograms of apples and pears at the farmer's market. 3/4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market? Express your answer in fraction and decimal form. Solve on paper. Then check your work on Zearn. The farmer sold kg or kg of pears
In fraction form, this is 6.375/8.5, or 3/4.In decimal form, this is 0.75.
What is fraction?Fraction is a mathematical expression which represents a part of a whole. It consists of a numerator and a denominator which are separated by a fraction bar. The numerator is the number of parts and the denominator is the total number of parts in the whole. Fractions can be used to represent parts of a whole number or parts of a physical object. Fractions can also be used to express ratios or rates.
To solve on paper, we can use the following equation:
Pears = 8.5 kg - (3/4 x 8.5 kg)
Pears = 8.5 kg - (6.375 kg)
Pears = 2.125 kg
Therefore, the farmer sold 2.125 kg of pears at the farmer's market in fraction form, and 0.75 in decimal form.
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Find the 6th term of the geometric sequence whose common ratio is 3/2 and whose first term is 4
6th terms of given geometric progression whose common ratio is 3/2 and first term is 4 is 243/8 using the farmula ar^(n-1).
What is a geometric sequence?
A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.
Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).
a = First term where
The common Ratio is r.
nth term = ar^(n-1)
6th terms ar^(6-1) = ar^5.
given is that r =3/2. a = 4.
6th term = 4 * (3/2)^5
= 4 * 3^5/2^5
=4*243/4*8
=243/8.
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a.) Macy’s is having a Black Friday sale where everything is 30% off.
How much will a dress that cost $180 be after the discount?
Answer: $126.00, the difference is 54.00
Step-by-step explanation:
126 ∛·÷÷∈∈πΔ≈∨∨⊃∪∡∠∉∉⇔βββ
DEF is a equilateral triangle solve for X
Answer:
x=12√3
Step-by-step explanation:
we can split the triangle into two right triangles
since we know that DEF is an equilateral triangle, that means that we will be dealing with a 30°-60°-90° special right triangle
since it is a 30°-60°-90° triangle,
x=12√3
1) Find the value of the expression.
6- y
for y = 2.6
Answer:
Answer:
1.3
Step-by-step explanation:
3.5 - y
y= 2.2
So substitute the Values and do 3.5 - 2.2 and you get 1.3 as answer
I hope This helped!
Answer:
1.3
Step-by-step explanation:
mrk me brainliest plzzzzzzzzz
NO LINKS, I WILL REPORT YOU
For what values of x and y must each figure be a parallelogram?
Need help please, and explanation.
Answer:
y = 30
x = 60
Step-by-step explanation:
4y and 2y are consecutive angles, which means they are equal to 180° when added together
that is the same with x and (5x - 180)
to solve, you set the equations to 180
solving:
4y + 2y = 180
6y = 180
y = 30
x + 5x - 180 = 180
6x = 360
x = 60
How do you find the missing side of an isosceles triangle?
Isosceles triangle has three sides, three angles, a base, a height, and an area in which two sides are equal to each other .
What is an isosceles triangle simple definition?
An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length. . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles
the sum of triangle is 180, sum of all the interior angles is equal to 180.
so if you know two angles then apply sum of triangles and find out the value of the third triangle.
isosceles triangle
An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.
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Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not.
n/q=b/a
please help
Answer:
[tex]a = \frac{bq}{n}[/tex]
Step-by-step explanation:
If we are trying to solve for "a", then we need it to be alone on one side of the equation.
[tex]\frac{n}{q} = \frac{b}{a}[/tex]
[tex]\frac{an}{q} = b[/tex]
[tex]a = \frac{bq}{n}[/tex]
the perimeter of a rectangle is 48 yards. The length is 14 yards.
Answer:
10 yards
Step-by-step explanation:
We know that to find the perimeter you have to multiply the length and width by 2 and add
We already know that the length is 14 yards
Multiply 14 by 2
14*2=28
Subtract 48 by 28 (the total of both the length and width multiplied by 2)
48-28=20
Divide 20 by 2
20/2=10
And your answer is 10 yards as the width
10+10+14+14=48 yards
Find the approximate area of the circle in the image. Use 3.14 for at
diameter = 9 in
O 20.25 square inches
O 63.585 square inches
O 254.34 square inches
O 81 square inches
Does anyone know how to solve this?
Answer:
domain[-5,-3)U(4,3)
range-(4,-4)
Step-by-step explanation
parentheses are used when the circle is open and brackets are used when the circle is filled in, domain is the x axis and range is the y axis
the H hotel charges $150 per night for a family suite. They also charge 11% sales tax. How much would be paid in tax for one night in the family suite?
Steve ran a 26-mile race at an average speed of 4 miles per hour. If Adam ran the same race at an average speed of 3 miles per hour, how many minutes longer did Adam take to complete the race than did Steve?
Answer:
Adam took 132 minutes longer than Steve.
Step-by-step explanation:
Let's find the time that takes Steve and Adam to complete the race. We will use the equation:
[tex] V = \frac{d}{t} [/tex]
Where:
d: is the distance = 26 miles
t: is the time =?
V: is the speed
For Steve we have the following time:
[tex] t_{s} = \frac{d}{V_{s}} = \frac{26 mi}{4 mi/h} = 6.5 h*\frac{60 min}{1 h} = 390 min [/tex]
And the time of Adam is:
[tex] t_{a} = \frac{d}{V_{a}} = \frac{26 mi}{3 mi/h} = 8.7 h*\frac{60 min}{1 h} = 522 min [/tex]
So, the difference between the time of Adam and Steve is:
[tex] \Delta t = t_{a} - t_{s} = 522 min - 390 min = 132 min [/tex]
Hence, Adam took 132 minutes longer than Steve.
I hope it helps you!
Ayuda la tengo que entregar hoy
Answer:
Step-by-step explanation:
1.6
2.30
3.?
4.60
5.84
6.330
lines are and s are parallel. what is m1
Answer:
30 degrees
Step-by-step explanation:
A restaurant serves a bowl of candies to their customers. The bowl of candies Gabriel receives has 10 chocolate candies, eight coffee candies, and 12 caramel candies. After Gabriel chooses a candy, he eats it. Find the probability of getting candies with P (chocolate or coffee)
Answer:
3/10
Step-by-step explanation:
Let the total number of candies =
10 chocolate candies + 8 coffee candies + 12 caramel candies = 30 candies
Probability of picking a chocolate candy = P(chocolate) = 10/30
Probability of picking a coffee candy = P(chocolate) = 8/30
Hence, the probability of getting candies with P (chocolate or coffee)
= P(chocolate) + P(coffee)
= 10/30 + 8/30
= 18/30
= 3/10
Therefore, the probability of getting candies with P (chocolate or coffee) is 3/10
Which of these are statistical questions that you could ask to gather data on the types of transportation to school?
Select all that apply.
A.
Does Thomas ride the bus to school?
B.
How do students in sixth grade get to school?
C.
How many miles do you travel to and from school each day?
D.
What is the height of a school bus?
E.
Do any students own bicycles?
Answer:
A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.
The closest ones are - B and E
SOMEBODY PLEASE HELP ME AND GIVE THE ANSWERS TO THIS!
Answer:
1.v divided by n 2. im not sure how much money you have 3.true
Step-by-step explanation:
PLEASE HELP (sorry for uploading alot I just want to good grade on this) NO LINKS PLEASE. RIGHT ANSWER GETS BRAINLIST
Answer:
C. Function 1: Difference of 1
Step-by-step explanation:
Function 1
m = ∆y / ∆x = 6/2 = 3
Function 2
Slope intercept form
m = 2
-------------------------
Function 1 is greater
Difference
3 - 2 = 1
this is confusing for me please someone help T-T
Answer:
x = 39
y = 129
Step-by-step explanation:
to find x you do
x +51 = 90
subtract 51 from both sides
x = 39
to find y
we already know part of y is a right angle (90 degrees)
so we need to find the tiny other part
this tiny other part is equal to x
so
90 +39 = 129
Why is 3 a polynomial?
A variable has a degree of zero and no exponent. Each constant polynomial has a degree of zero.
A polynomial is what?A polynomial only uses addition, subtraction, multiplication, and non-negative integer exponentiation of the variables as its operations. In mathematics, the term "indeterminate" is frequently used to describe variables. A polynomial is an equation that combines variables, constants, and exponents while using addition, subtraction, multiplication, and division of numbers (No division operation by a variable).
A variable has no exponent, the degree is 0. The degree of each constant polynomial is zero .
Since 3 can be expressed as [tex]3 X 0[/tex] and is a constant polynomial, it has a degree of [tex]0[/tex].
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A train travels 315 km in the same time that a car travels 265 km. If the train travels on average 20 km/h faster than the car, find the average speed of the car and the time taken to travel 265 km.
Answer: 106 km/h,2.5 hr
Step-by-step explanation:
Given
The train travels 315 km in the same time car travels 265 km
The average speed of the train is 20 kmph faster than car
Suppose, speed of the car is v and it travels 265 km in t hours
[tex]\therefore \dfrac{315}{v+20}=\dfrac{265}{v}\\\\\Rightarrow 315v=265\left (v+20\right)\\\\\Rightarrow 315v=265v+5300\\\Rightarrow 50v=5300\\\Rightarrow v=106\ km/h[/tex]
Time taken to travel is
[tex]\Rightarrow t=\dfrac{265}{106}}\\\\\Rightarrow t=2.5\ h[/tex]
How do you tell if something is a difference of squares?
A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.
what is perfect square ?Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.
If a binomial is found to be a difference of squares, it is factored into two binomials. the first being the first term's square root less the second term's square root.
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