The series must converge to a finite value.
The proof is given below.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
The partial sums of the series satisfy the inequality s(n) ≥ 1000 for all n.
This means,
The sum of the series is bounded from below by 1000.
Now,
All terms of the series are positive, the sum of the series must either converge to a finite value or diverge to infinity.
For the sake of contradiction,
The series diverges to infinity.
Then for any M > 0, there exists an integer N such that,
a(N) + a{N+1} + a{N+2} + ... > M
This means,
The partial sums of the series start at index N.
i.e
s(N), s{N+1}, s(N+2), ... also diverge to infinity.
This contradicts the fact that they are all bounded from below by 1000.
Thus,
The series must converge to a finite value.
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Help I will mark brainliest!!!
Answer:
Step-by-step explanation:
I think it 5
Answer:
Step-by-step explanation:
The number that goes under the radical sign in 17.
The answer is [tex]\sqrt{17}[/tex]
use the distance formula to calculate the distance between to two points.
Distance (d) = √(3 - -1)² + (-1 - -2)²
= √(4)² + (1)²
= √17
please help me with this question thank you
The average rate of change of the function in the interval [5, 11] is -82.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂),
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
The table of values is shown in the image.
The average rate of change of the function in the interval [5, 11],
= the slope of the function in the interval [5, 11].
= (-623 + 131) / (11 - 5)
= -492/6
= -82
Therefore, -82 is the slope.
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which is the graph. ? help
Answer:2nd one
Step-by-step explanation: look carefully at the problem and you will see one thing that makes the only possible solution graph #2 I dont want to give you the answer just look carefully at the problem.
what is the solution of (x + 5)/(x + 3) < 1
Answer:
x < -3
Step-by-step explanation:
Inequality form: x < -3
Interval Notation: (-[tex]\infty}[/tex],-3)
Need help solving!!! ASAP!
Answer:
Step-by-step explanation:
ur mom
PLEASE HELP THANK YOU!
What is the answer to X
Answer: x = 7
Step-by-step explanation:
The right angle is equal to 90 degrees
Therefore (5x - 8) + (4x + 35) is equal to 90 degrees
5x - 8 + 4x + 35 = 90
5x + 4x + 35 - 8 = 90
9x + 27 = 90
- 27 -27 (subtract 27 from both sides)
9x = 90 - 27
9x/9 = 63/9 (divide both sides by 9)
x = 7
Check
5(7) - 8 + 4(7) + 35 = 90
35 - 8 + 28 + 35 = 90
Is 10.75 a negative sum?
Answer: No. It is positive
Step-by-step explanation:
I am assuming 10.75 is the sum and you are not missing another additive. A positive sum holds a value equal to or over zero while a negative sum is less than zero on the number line.
Solve the following quadratic-like equation
y 1/2 -3y 1/4+2=0
The value of y in [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex] is y = 1.189 for the quadratic-like equation.
What is a quadratic equation?Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
The equation [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex] is not a traditional quadratic equation, but it can be solved using numerical methods or by using a change of variables.
1) One possible method to solve the equation is to use the Newton-Raphson method, which is an iterative numerical method for finding the roots of a function. This method involves finding a first approximation for the root and then using that approximation to improve the estimate in each iteration until the root is found to a desired level of accuracy.
2) Another possible method is to change the variables to make the equation a traditional quadratic equation. For example, one could substitute [tex]y\frac{1}{4} = x[/tex] and then solve for x. This would result in the equation [tex]x^{2} - 3x + 2 = 0[/tex], which can be solved using the quadratic formula.
Let us substitute [tex]y\frac{1}{4} = x[/tex]
Then we have x² - 3x + 2 = 0
On solving
⇒ x² -2x - 1x + 2
⇒ x² -2x - 1x + 2
⇒ x(x - 2) -1(x + 2)
⇒ (x - 2)(x - 1)
Thus, x = 1 and x = 2
Solving for y
[tex]y^{\frac{1}{4}} = 2[/tex]
y = [tex]\sqrt[4]{2}[/tex]
y = 1.189
[tex]1.189^{1/2} = 1.09[/tex]
Thus, the value of y in [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex] is y = 1.189 for the quadratic-like equation.
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show that the sum of two even or of two odd integers is even, whereas the sum of an odd and an even integer is odd.
The sum of two even integers or two odd integers is always even. However, the sum of an even and an odd integer is always odd.
The sum of two even integers or two odd integers is always even because an even integer is a multiple of two. Therefore, if two even integers are added together, the sum will also be a multiple of two (an even integer). Similarly, an odd integer is a multiple of two plus one, so when two odd integers are added together, the sum will be a multiple of two plus two (an even integer). On the other hand, the sum of an odd and an even integer is always odd because an even integer is a multiple of two and an odd integer is a multiple of two plus one. Therefore, when an even and an odd integer are added together, the sum will be a multiple of two plus one (an odd integer).
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Write an equation of the line parallel to Y=2/3x + 5/6 that passes through the point (-1,1)
Type an equation using slope-intercept from or using the given point in point-slope form
Felix is purchasing a brownstone townhouse for $2,800,000. To obtain the mortgage, Felix is required to make a 19% down payment. Felix obtains a 30-year mortgage with an interest rate of %6.5.
a) Determine the amount of the required down payment.
$_____?
b) Determine the amount of the mortgage.
$_____?
c) Determine the monthly payment for principal and interest.
$_____?(Round to the nearest cent.)
The amount of the required down payment is $532000.
The amount of the mortgage is $2710260/
The monthly payment for principal and interest is $7528.5
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
The amount of the required down payment would be 19% of $2800000 which is, = (19/100)×2800000.
= $532000.
Felix obtains a 30-year mortgage with an interest rate of %6.5 which is,
= [(2800000 - 532000)×6.5×30]/100.
= 2268×30×6.5.
= $442260 he has to pay in 30 years in addition to the principal of (2800000 - 532000) = 2268000.
P = $2710260
Now, 30 years has 30×12 = 360 months.
Therefore, His monthly downpayment would be,
= (2710260/360).
= $7528.5
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Learning aids, listed along the bottom of the window, are available for most problems on homework assignments and study plan practice but are not available on tests and quizzes. Identify the learning aid described in each part below.
One learning aid that provides an interactive walk-through for solving the particular problem you are working on is "view an example"
What does learning aid offer student?It is also known as teaching aids, which are an essential part of any classroom. Teaching aids can help students improve their reading comprehension skills, illustrate or reinforce a skill or concept, differentiate instruction, and relieve anxiety or boredom by presenting information in a new and exciting way.
Teaching aids also engage students' other senses because there are no restrictions on what aids can be used to supplement a lesson. As technology advances, so do teaching aids, which are now classified as audio aids, visual aids, mechanical teaching aids, audio-visual aids, and more.
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A 39 oz bottle of a new soda costs $3.31.
What is the unit rate, rounded to the nearest tenth of a cent?
Answer:
About $0.08 per an oz
Step-by-step explanation:
C. How much car can you afford to finance a new car if your proposed monthly payment is $240, for 60 months (5 years), with a credit score between 601-660?
Finance amount: __________________________________
Estimated percentage rate: ____________________
Amount of interest you will pay for the loan: _____________________________
Finance amount: The amount you can finance for a new car with a monthly payment of $240, for 60 months (5 years), depends on several factors, including the loan interest rate, the down payment, and the value of the car.
Estimated percentage rate: The interest rate for a new car loan with a credit score between 601-660 typically ranges from 5% to 10%.
Amount of interest you will pay for the loan: The amount of interest you will pay for the loan can be calculated by multiplying the loan amount by the interest rate and the number of months.
How to calculate the total interest?For example, if you finance $20,000 at a 7% interest rate for 60 months, the total interest paid over the life of the loan would be $3,140.
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Please help me with these three questions. Thank you!
The quadrilateral exists not a parallelogram.
How to estimate the distance QR?The formula to calculate the distance between two points is equal to
[tex]$$d=\sqrt{(y 2-y 1)^2+(x 2-x 1)^2}$$[/tex]
We have Q(-10,-2), R(1,-1)
substitute the values in the above equation, we get
[tex]& d=\sqrt{(-1+2)^2+(1+10)^2} \\[/tex]
simplifying the equation, we get
[tex]& d=\sqrt{(1)^2+(11)^2} \\[/tex]
d = √122 units
Find the distance TS
the formula to calculate the distance between two points is equal to [tex]$d=\sqrt{(y 2-y 1)^2+(x 2-x 1)^2}$[/tex]
we have
T(-11, -8), S(1, -7)
substitute the values in the above equation, we get
[tex]$d=\sqrt{(-7+8)^2+(1+11)^2}$[/tex]
simplifying the equation, we get
[tex]$d=\sqrt{(1)^2+(12)^2}$[/tex]
d = √145 units
We know that the opposite sides of QR and TS exist.
The opposing sides of a parallelogram are congruent, but in this case, QR TS.
√122 units ≠ √145 units
Therefore, the quadrilateral exists not a parallelogram.
The complete question is:
Determine whether the quadrilateral is a parallelogram using the indicated method Q(-10,-2), R(1,-1), S(1,-7), T(-11,-8) (Distance Formula)
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Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
Answer:
2A=B
Step-by-step explanation:
use ratio of axis to solve the scale. verify to second axis.
x axis: 4 A to 8 B
set Ratio A/4 = B/8 and solve
2A = B or A = (1/2)B
verify to sefond axis.
y axis: 3A to 6 B
A/3 = B/6
2A = B or A = (1/2)B
A sample of college students was asked how much they spent monthly on coffee. Approximate the standard deviation for the cost.
The standard deviation for the cost is given as follows:
$12.
How to obtain the standard deviation?The total number of students is given as follows:
7 + 20 + 20 + 14 + 10 = 71.
Considering the midpoint of each interval, and dividing their absolute frequencies by 71, the discrete distribution modeling the situation is given as follows:
P(X = 15) = 0.0986.P(X = 25) = 0.2817.P(X = 35) = 0.2817.P(X = 45) = 0.1972.P(X = 55) = 0.1408.The expected value is given by the sum of each outcome multiplied by it's probability, hence:
E(X) = 15 x 0.0986 + 25 x 0.2817 + 35 x 0.2817 + 45 x 0.1972 + 55 x 0.1408
E(X) = 35.
The sum of the differences squared between each observation and the mean, multiplied by their respective probabilities, is given as follows:
V(X) = (15-35)² x 0.0986 + (25-35)² x 0.2817 + (35-35)² x 0.2817 + (45-35)² x 0.1972 + (55-35)² x 0.1408
V(X) = 143.65.
The standard deviation is obtained taking the square root of V(X), hence:
S(X) = sqrt(143.65)
S(X) = $12. (rounding).
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b. The table shows the number of students at each school this
year. Use your expression to find the number of students the
school district can send to the state spelling bee this year.
Does your answer make sense? Explain.
The total angle made at the center of the pie chart is 360°
An angle is formed when two lines come together at a point. The distance between these two rays, known as the "opening," is measured as a "angle." This character represents it. Degrees and radians are frequently used to quantify an angle's circularity or rotation. Angles frequently appear in daily life.
In geometry, an angle is made when two rays are connected at their ends. These rays are known as the sides or arms of the angle. Continue reading to find out more about an angle's many parts.
Two rays form an angle when they come together at a point. The symbol represents a "angle," which is the phrase used to describe the "opening" between these two rays.
Number of students playing volley Ball = 48
Total number of students = 50 +48 +60 + 22 = 180
The measure of central angle representing the students playing volley Ball = 48 180 x 360° = 96°
:. The angle made by the volleyball playing student is 96°
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Given question is incomplete , the complete question is given below
The table shows the number of students of a school who play different games.
Game football volleyball cricket basketball
No. of 50 48 60 22
students
When the data shown in the table above is presented in a pie chart, what will be the measure of the central angle of the sector representing the students playing Volley Ball?
How much would you need to save each month in an account earning 4.7% interest (compounded monthly) to have saved $10,000 in two years?
To save $10,000 over two years, you would need to deposit $20,407 per month in an account earning 4.7% interest (compounded monthly).
what is interest ?Divide the capital by the cost of borrowing, the length of time, and certain other considerations to arrive at simple interest. Simple return = principal + interest + hours is the commercial formula. This method allows it easiest to calculate interest. The most basic technique to figure the interest is as a portion of the outstanding amount. He will only pay his share of the 100% interest, for example, if he borrowed $100 from a partner and agrees to repay the loan th with 5% interest. $100 (0.05) = $5. When you keep borrowing, you must pay interest, and when you give it out, you must lend money.
given
Future Value = Current Value x (Present Value + Interest Rate) (Years/frequency of payments per year)
FV = (-15,000 x [1+8%]^
[4/1])
PV is adverse because you are redistributing funds.
FV = $20,407
Calculator for Finances: Enter PV of -15,000 as
Make 4 N.
Set 8 as I/Y CPT FV and 0 as PMT
$20,407
To save $10,000 over two years, you would need to deposit $20,407 per month in an account earning 4.7% interest (compounded monthly).
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Can someone pls help me with the the questions that have the stars on them
Therefore , the solution of the given problem of quadratic equation comes out to be quadratic equation., cubic equation and leading coefficient is 1.
What is a quadratic equation ?For one-variable equations, the quadratic result x = ax2 + b + c=0 is used in regression modeling. The First Thesis basic Algebra asserts that there is just one solution because this equation has a second order. Both straightforward and complex solutions can be found. A "quadratic solution," as the name suggests, consists of four variables. This suggests that there might be a single squared word.
Here,
Given :
=> x² + 2x -5 its degree is 2
hence quadratic equation.
=> 4x³ -8 its degree is 3
hence cubic equation
=> 2x⁴ - 7x² -5x + 1 its degree is 4
hence its an degree 4 equation.
leading coefficient of:
=> x³ + 5x² + 28 -x
leading coeffcient is = 1
Therefore , the solution of the given problem of quadratic equation comes out to be quadratic equation., cubic equation and leading coefficient is 1.
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Find the average rate of change for f(x)= 6x+5 over the interval [4,7].
Answer:
6
Check if you have written the function equation properly. If you have, this is the answer
Step-by-step explanation:
Average rate of change is the first differential of the function
Given function is f(x) = 6x + 5
Rate of change = f'(x) = d/dx(6x) + d/dx(5)
= 6 + 0
= 6
The average rate of change(slope) is a constant throughout all values of the function and so also between[4, 7]
p(x) = C₁pxqn-x
When processing credit-card applications there is a 40% chance that an application will
have incomplete or insufficient information and require research. You have 5 applications
in your to-do pile and would like to leave early today.
(a) Fill in the values:
n
p=
(b) What is the probability of exactly three applications needing research? (enter a
number between 0 and 1, 4 decimal places)
Answer=
Answer=
q=
(c) What is the expected number of applications that will need research?
Answer=
(d) What is the probability of having AT LEAST the expected number of applications
needing research? (enter a number between 0 and 1, 4 decimal places)
The value regarding the probability shows that n is 5, p is 0.4 and q is 0.6.
How to calculate the valuesProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.
a)n=5
P=40%=0.4
q=1-p=1-0.4=0.6
b)p(x)= nc x p x q^n-x
p(x=3)=5C3×0.4^3×0.6^2
=0.2304
C) E(x)=np=5×0.4=2
Expected number of applications that will need research is 2
d)or(at least the expected number of applications)=p(x≥2)=1-p(x<2)
=1-{p(x=0)+p(x=1)
=1-{5C0×0.4^0×0.6^5 +5C1×0.4^1×0.6^4}
=1-0.3370
=0.6630
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HELP MEEEEEE LOOK AT THE LOW FPS PIC
Answer:
14,35,42,63,77
Step-by-step explanation:
Actually how to get the output you follow the rule;
n×7
the first will be;2×7=14
the second will be; 5×7=35
the third will be; 6×7=42
the forth will be; 9×7=63
the fifth will be; 11×7=77
The graph of a function f is shown below.
Find one value of x for which f(x) = 1 and find f(-1)
Step-by-step explanation:
remember, y = f(x)
so, the question is really for what x is y = 1 ?
and what is the y-value for x = -1 ?
a)
when we imagine a horizontal line through y = 1, at what points (x-value) does this line cross the function graph ?
as we can see, at x = -2 and x = 2.
pick one for your answer.
b)
now we imagine a vertical line through x = -1.
at what point (y-value) does this line cross the function graph ?
as we can see, at y = 4.
f(-1) = 4
6x−y=−14
2x−3y=6
Solve it in elimination method
Answer:
x = -3
y = -4
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}6x-y=-14\\2x-3y=6\end{cases}[/tex]
Multiply the second equation by -3:
[tex]\implies 2x(-3)-3y(-3)=6(-3)[/tex]
[tex]\implies -6x+9y=-18[/tex]
Add this to the first equation to eliminate the term in x:
[tex]\begin{array}{crcrcl}\vphantom{\dfrac12}& 6x & - & y & = & -14\\\vphantom{\dfrac12}+ & (-6x & + & 9y & = & -18)\\\cline{2-6}\vphantom{\dfrac12}&&&8y&=&-32\\\cline{2-6}\end{array}[/tex]
Solve the equation for y:
[tex]\implies 8y=-32[/tex]
[tex]\implies y=-4[/tex]
Substitute the found value of y into one of the original equations and solve for x:
[tex]\implies 2x-3(-4)=6[/tex]
[tex]\implies 2x+12=6[/tex]
[tex]\implies 2x=-6[/tex]
[tex]\implies x=-3[/tex]
Therefore, the solution to the given system of equations is (-3, -4).
Answer:
[tex]x = - 3[/tex][tex]y = - 4[/tex]Step-by-step explanation:
The given equations to us are ,
6x - y = -14 2x - 3y = 6In elimination method we eliminate any variable and then find the find the value of second unknown variable. Using that value we can find the value of 1st variable.
Multiply equation 1 by 3 ,
3(6x-y)=-14*3
18x - 3y = -42 ..... (3)
Now subtract equation 2 and 3 to eliminate y as,
2x - 3y - (18x -3y) = 6 -(-42)
2x -3y -18x +3y = 6+42
-16x = 48
x = 48/-16 = -48/16
x = -3
Substitute this value in equation 2 ,
2*(-3) -3y = 6
-6-3y =6
-3y =6+6
-3y = 12
y = -4
And we are done!
You take a random token from a bag that contains 8 red, 7 green, and 4 blue tokens. Let R be the set of red tokens, G = green tokens, and B = blue tokens. Write the odds as an unsimplified fraction. How many outcomes are in R, in other words n(R)? Enter an integer. How many outcomes are not in R, in other words n(R')? Enter an integer. What is the odds against R? Do not simplify your fraction. Enter the unsimplified fraction using /
Number of outcomes are in R,
⇒ n (R) = 8 / 19
And, Number of outcomes are not in R,
⇒ n (R') = 11 / 8
What is Combination?
A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
You take a random token from a bag that contains 8 red, 7 green, and 4 blue tokens.
Hence, Number of outcomes are in R,
⇒ ⁸ C ₁ / ¹⁹C₁
⇒ 8 / 19
⇒ n (R) = 8 / 19
And, Number of outcomes are not in R,
⇒ 1 - 8/19
⇒ 11 / 8
⇒ n (R') = 11 / 8
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WILL GIVE BRAINLIEST FOR BEST ANSWER!! HELP!
write a quantitative survey question(s)! i need a question that I can gather data on and I cant write a good enough question for statistics and geometry!
dont make it too simple please
The triangle is congruent by the Angle side Angle property.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.
The three parameters that are congruent are:-
BV ≅ BV ( common side)
∠1 ≅ ∠2 ( Bisector)
∠3 ≅ ∠4 ( Bisector)
Hence, the two triangles are congruent with each other.
The question on geometry is attached with the answer below.
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the lengths of the right sides of a right triangle were 12 cm and 16 cm The first side is increasing at a rate of 2 cm/sec and the second side is decreasing at a rate of 1 cm/sec so that the triangle keeps its shape Find the rate of change of the area of the triangle after two seconds have passed
The rate of change of the area of the triangle after two seconds have passed is 16 cm².
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Area of a right angled triangle = [tex]\frac{1}{2}[/tex] × base × height
Given that, the lengths of the right sides of a right triangle were 12 cm and 16 cm.
Initial area of the triangle = [tex]\frac{1}{2}[/tex] × 12 × 16
= 96 cm²
The first side is increasing at a rate of 2 cm/sec and the second side is decreasing at a rate of 1 cm/sec.
After 2 seconds, length of base = 12 + (2 × 2) = 16 cm
After 2 seconds, length of height = 16 - (2 × 1) = 14 cm
Area of the triangle after 2 seconds = [tex]\frac{1}{2}[/tex] × 16 × 14
= 112 cm²
Rate of change of area = 112 cm² - 96 cm² = 16 cm²
Hence the rate of change of area is 16 cm².
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14/5 + 33/10
Not sure how to answer this
Answer:
[tex]\frac{61}{10}[/tex]
Step-by-step explanation:
14/5=28/10
By changing the denominator so that they are equal, you can now add the two fractions together.
(28/10)+(33/10)=61/10
Hope this helped! :)
The consumption of feed and utilities for a plant that produces 60 metric tons per year (60 t/y) of Nylon 6 are given below. The plant fixed capital cost has been estimated to be $114MM. Estimate the cash cost of production. Raw materials 1. Caprolactam, 1.02 tons per ton product, price $1700 per metric ton Utilities 1. Fuel gas, 9 MMBtu/t product, cost $4.50/MMBtu 2. Cooling water, 32,000 galt product 3. Electrical power, 130 kWh/t product
Without the cost of the electrical power, the cash cost of production would be $104,040 + $2460 = $106,500 per year.
What is the addition?
Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.
The cost of raw materials can be calculated as follows:
Caprolactam: 1.02 tons per ton of product * 60 tons of product per year = 61.2 tons of caprolactam per year
Cost of caprolactam: 61.2 tons per year * $1700 per ton = $104,040 per year
The cost of utilities can be calculated as follows:
Fuel gas: 9 MMBtu per ton of product * 60 tons of product per year = 540 MMBtu per year
Cost of fuel gas: 540 MMBtu per year * $4.50 per MMBtu = $2460 per year
Cooling water: not a cost as it's a utility not charged
Electrical power: 130 kWh per ton of product * 60 tons of product per year = 7800 kWh per year
Cost of electrical power: Not specified, we need the cost per kWh to calculate it.
Hence, without the cost of the electrical power, the cash cost of production would be $104,040 + $2460 = $106,500 per year. If we had the cost of electrical power, we could add it to this amount to get the complete cash cost of production.
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