Answer:
The following are the solution to the given points:
Step-by-step explanation:
Given value:
[tex]1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}[/tex]
Solve point 1 that is [tex]\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\[/tex]:
when,
[tex]k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\[/tex]
[tex]= \frac{1}{2} - \frac{1}{3}\\\\[/tex]
[tex]k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\[/tex]
[tex]= \frac{1}{3} - \frac{1}{4}\\\\[/tex]
[tex]k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\[/tex]
[tex]= \frac{1}{4} - \frac{1}{5}\\\\[/tex]
[tex]k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\[/tex]
Calculate the sum [tex](S=s_1+s_2+s_3+......+s_n)[/tex]
[tex]S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\[/tex]
[tex]=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\[/tex]
When [tex]s_n \ \ dt_{n \to 0}[/tex]
[tex]=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\[/tex]
[tex]\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}[/tex]
In point 2: [tex]\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}[/tex]
when,
[tex]k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\[/tex]
[tex]= \frac{1}{7 \times 8}\\\\= \frac{1}{56}[/tex]
[tex]k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\[/tex]
[tex]= \frac{1}{8 \times 9}\\\\= \frac{1}{72}[/tex]
[tex]k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\[/tex]
[tex]= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\[/tex]
[tex]k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\[/tex]
calculate the sum:[tex]S= s_1+s_2+s_3+s_n\\[/tex]
[tex]S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\[/tex]
when [tex]s_n \ \ dt_{n \to 0}[/tex]
[tex]S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066[/tex]
[tex]\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}[/tex]
similar triangle question
Answer:
60
Step-by-step explanation:
The triangles are similar so corresponding angles will be congruent. We also know this because both angles have two lines marking they are congruent.
Assume log bx = 0.49. Evaluate.
Logbx^2
Step-by-step explanation:
Use exponent property of logs.
logb(x²) = 2 logb(x) = 2(0.49) = 0.98
The value of logᵇ x² is 0.98 after using the logarithm properties the answer is 0.98.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
It is given that:
[tex]\rm log_b x=0.49[/tex]
The integer exponent:
In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is required to find the value of [tex]\rm log_b \ x^2[/tex]
As we know from the log property:
[tex]\rm log_a \ b^c = c \ log_a b[/tex]
[tex]\rm log_b \ x^2 = \rm 2log_b \ x[/tex]
[tex]\rm log_b \ x^2 = \rm 2(0.49)[/tex]
[tex]\rm log_b \ x^2 = 0.98[/tex]
Thus, the value of logᵇ x² is 0.98 after using the logarithm properties the answer is 0.98.
Learn more about the Logarithm here:
brainly.com/question/163125
#SPJ2
Simplify the expression: 5(2y + 2)
Answer:
10y+10
Step-by-step explanation:
5(2y+2)
5x2y=10
5x2=10
Answer:
10y+10 Is the answer.
just multiply 5 By whats in the bracket
Explain how to predict y-values using the equation of a regression line.A. Substitute a value of y into the equation of a regression line and solve for x.B. Use the graph of the regression line to determine the x-value that corresponds to the y-value for which you are solving.C. Substitute a value of x into the equation of a regression line and solve for y^.D. Substitute the correlation coefficient into the equation and solve for y^
Answer: C. Substitute a value of x into the equation of a regression line and solve for y
Step-by-step explanation: To predict y values using equation of the regression line, a given value of x is substituted into the equation as there are only two unknowns in the whole regression equation, which are the x value ( independent variable) and the y value (the dependent or predicted variable).
The regression equation is usually of the form:
y = mx + c (linear regression)
Where y = predicted or dependent variable
m = slope or gradient of the regression line
x = independent variable
c = intercept of the line (where it cross the y-axis)
What is the quotient of 1/6 divided by 2?
Answer:
1/12 or 0.083
Step-by-step explanation:
what is the simplified for the expression below?
Answer:
Option 1: [tex]-2x+3[/tex]
Step-by-step explanation:
[tex]-\frac{1}{5}\left(5x+20\right)-\frac{1}{4}\left(4x-28\right)[/tex]
Expand:
[tex]-\frac{5x+20}{5}-\frac{4x-28}{4}[/tex]
[tex]-\left(x+4\right)-\left(x-7\right)[/tex]
Remove brackets:
[tex]-x-4-x+7[/tex]
Group similar terms together:
[tex]-x-x-4+7[/tex]
[tex]-2x+3[/tex]
Mark is a coin collector at the first store he went to he bought 3 sets of 4 coins at the second store he bought 5 sets of 3 coins he then decided to sell 5 coins he totaled his number of coins and the gave his brother 8 coins how many coins does he have left?
Answer:
Step-by-step explanation:
14
Answer:
mark liked to collect at the first store he went to he brought 3 sets of 4 coins at second store he brought 5 sets of 3 coins he then decided to sell 5 coins he totaled his number of coins and gave his brother 8 coins how many coins does he have left
Your answer should be in the form p(x)+\dfrac{k}{x-1}p(x)+
x−1
k
p, left parenthesis, x, right parenthesis, plus, start fraction, k, divided by, x, minus, 1, end fraction where ppp is a polynomial and kkk is an integer.
\dfrac{x^2+2}{x-1}=
x−1
x
2
+2
Answer:
Step-by-step explanation:
the answer i got was -57
Functions can be rewritten is several forms.
The new form of the function is: [tex]\mathbf{f(x) = \frac{x^2}{x - 1} + \frac{2}{x-1}}[/tex]
The function is given as:
[tex]\mathbf{f(x) = \dfrac{x^2+2}{x-1}}[/tex]
Split
[tex]\mathbf{f(x) = \frac{x^2}{x - 1} + \frac{2}{x-1}}[/tex]
The form is given as:
[tex]\mathbf{f(x) = p(x) + \frac{k}{x - 1}}[/tex]
So, by comparison
[tex]\mathbf{p(x) = \frac{x^2}{x - 1}}[/tex]
[tex]\mathbf{k =2}[/tex]
Read more about functions at:
https://brainly.com/question/19580185
What is an equivalent expression with fewer terms than 3x-4-(5x+7)
An equivalent expression with fewer terms than 3x - 4 - (5x + 7) is - 2x - 11.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
3x - 4 - (5x + 7)
Expanding the brackets we get,
3x - 4 - (5x + 7) = 3x - 4 - 5x - 7
Taking alike terms together we get,
3x - 4 - (5x + 7) = 3x - 5x - 4 - 7
Solving we get,
3x - 4 - (5x + 7) = - 2x - 11
These are equivalent expression.
Thus, an equivalent expression with fewer terms than 3x - 4 - (5x + 7) is - 2x - 11.
To learn more about expressions :
brainly.com/question/11568837
#SPJ2
An airplane is carrying 90 passengers,which 5/6 of the capacity of the airplane.what the capacity of tge airplane?
Answer:
108
Step-by-step explanation:
the capacity of the airplane is 108 passengers.
To find the capacity of the airplane, we can set up an equation using the given information.
Let's denote the capacity of the airplane as "C".
We are given that 5/6 of the capacity (5/6C) is equal to 90 passengers.
So, we can write the equation as:
5/6C = 90
To solve for C, we can multiply both sides of the equation by the reciprocal of 5/6, which is 6/5:
C = (90) * (6/5)
C = 108
Therefore, the capacity of the airplane is 108 passengers.
Learn more about capacity here
https://brainly.com/question/29055851
#SPJ2
PLS HELP. A scientist studying bacteria begins with 20 cells. The bacteria population doubles every hour. Complete the table below to determine after how many hours there will be more than 500 bacteria cells. Time (hours) Number of bacteria cells 0 20 1 40 2 80 3 4 5 6 Write an exponential function to model this situation. Predict the bacteria population after 11 hours.
Answer: 3, 160 || 4, 320 || 5, 640 || 6, 1280
Step-by-step explanation:
The exponential function to model this situation is [tex]P(t) = 20\times 2^t[/tex]
What is an exponential function?An exponential function is a mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Given that, a scientist studying bacteria begins with 20 cells.
The bacteria population doubles every hour.
Let P(t) determines the population of the bacteria in 't' hours.
Hence, by the given information our function P(t) is modeled as:
[tex]P(t) = 20\times 2^t[/tex]
To find the population of the bacteria after 11 hours, put t = 11,
[tex]P(11) = 20\times 2^{11[/tex]
= 40,960
Hence the population of the bacteria after 11 hours will be 40,960.
Learn more about exponential function click;
https://brainly.com/question/29287497
#SPJ2
Manuel works at Cheesecake King. He earns $15 per hour as a busboy. The waiters he helps give him 25% of their tips. If Manuel worked 6 hours today, how much did he earn, without tips?
helppp meeeee pleaseeeee
Answer:
1.) 4
2.) -11
3.) -4
4. 19
Step-by-step explanation:
Solve for the indicated variable. 6y + 5x = 7 for x
Answer:
[tex]x = \frac{-6y+7}{5}[/tex]
Step-by-step explanation:
[tex]6y + 5x = 7[/tex]
Isolate x ;
[tex]5x = 7-6y\\\\5x =-6y+7[/tex]
Divide both sides of the equation by 5
[tex]\frac{5x}{5} = \frac{-6y+7}{5} \\\\x = \frac{-6y +7}{5}[/tex]
4(h+11)-15
The solution
Answer:
=4h+29
Step-by-step explanation:
I hope this helps you
Answer:
4h+29
Step-by-step explanation:
Distribute
4(h+11)-15
4xh=4h
4x11=44
Subtract the numbers
4h+44-15
44-15+29
4h+29
A fisher caught a large boat load of salmon. She decided to donate some of his fish to the local community, 1,672 people in all. To each person over the age of 50 she gave 16 fish and to each person under 50 she gave 96 fish. Only 3/4 of the over 50s collected their salmon and only 1/8 of the under 50s collected their fish. How many fish did the fisher distribute it total
Answer:
74 fishes
Step-by-step explanation:
Total number of people = 1672
Let us represent:
Number of people over the age of 50 = a
Number of people below the age of 50 = b
People over the age of 50 she gave = 16 fish
People below 50 she gave = 96 fish. Only 3/4 of the over 50s collected their salmon
= 3/4a collected fish = 0.75a
If a should collect = 96 fishes
0.75a =
Cross Multiply
=0.75a × 96 fishes/ a
= 72 fishes
Therefore, 3/4 of the over 50s collected 72 fishes.
1/8 of the under 50s collected their fish.
= 1/8b collected fish = 0.125b
If b people should collect = 16 fishes
0.125b people =
Cross Multiply
0.125b × 16 fishes/b
= 2 fishes.
Therefore, the total number of fishes shared
= 72 fishes + 2 fishes
= 74 fishes
Please solve......... thanks
Answer: 54 teaspoons of oregano
Step-by-step explanation: 1 can is 6 teaspoons so 9 cans would be 54 teaspoons because 9 x 6 = 54.
Hope this helps!
The prime factorization of ___ is 2⁴×5.
Answer:
the prime factorization of 80 is 2⁴×5
Step-by-step explanation:
Answer:
80 is the answer
Step-by-step explanation:
2^4=16
16*5=80
Hope I helped you! :-)
which of the following statements is true
ASAP
Answer:
A
Step-by-step explanation:
E is the center of the line (or segment) in this case
Those two dashes on segments AE and EC means they are congruent.
Point E is right in the middle of AC because AE and EC are congruent
Answer choice A is correct
In the figure below, triangle ABC is similar to triangle PQR, as shown below:. PLEASE HELP ME!!!!!!!!!!
Answer:
35 i think
Step-by-step explanation:
Please help me! I will mark brainliest! Thanks!
Answer: Group 12
Step-by-step explanation: The element is Mercury.
Given: f(x) = x+5 1 and g(x) = x - 2. x What are the restrictions of the domain of f(g(x))? 0 X -5 0 X-3 0 0 X2 KO There are no restrictions.
Answer:the answer is A
Step-by-step explanation:
A person buys a phone for $81 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $119.92 per month. Write an equation that can be used to determine the total cost, C(t), of this phone plan for t months. Then, find the cost for 23 months, assuming that the number of minutes the person uses does not exceed 2000 per month.
Answer:
2839.16
Step-by-step explanation:
119.92(m)+81=C(t)
119.92(23)+81=C(t)
2839.16=C(t)
The total cost will be equal to $2839.16. The expression to calculate the total cost is 119.92(m)+81=C(t).
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a person buys a phone for $81 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $119.92 per month.
The expression will be formed as below:-
119.92(m)+81=C(t)
119.92(23)+81=C(t)
2839.16=C(t)
Therefore, the total cost will be equal to $2839.16.
To know more about an expression follow
https://brainly.com/question/25109150
#SPJ2
What is the volume, measured in cubic centimeters, of the box below? Do not
include units in your answer.
Answer:
20
Step-by-step explanation:
5 x 4 x 1
How do you do this question?
Answer:
∫ₑ°° 1 / (x (ln x)¹⁰) dx
∫₁°° x⁻³ dx
Step-by-step explanation:
A p-series 1 / xᵖ converges if p > 1.
∫ₑ°° 1 / (x (ln x)¹⁰) dx
If u = ln x, then du = 1/x dx.
When x = e, u = 1. When x = ∞, u = ∞.
= ∫₁°° 1 / (u¹⁰) du
p = 10, converges
∫₁₀°° x^(-⅔) dx
= ∫₁₀°° 1 / (x^⅔) dx
p = ⅔, diverges
∫₁°° 2 / x^0.5 dx
= 2 ∫₁°° 1 / x^0.5 dx
p = 0.5, diverges
∫₁°° x⁻³ dx
= ∫₁°° 1 / x³ dx
p = 3, converges
∫₂°° 1/(3x) dx
= ⅓ ∫₂°° 1/x dx
p = 1, diverges
Madam C.J. Walker is the first African American self-made millionaire. She made her fortune by inventing and selling specialized hair products, including an innovative Edge Control product that sold for $0.45 each. Which algebraic expressions describe the total amount of money spent by consumers for any number of Edge Control products sold, e?
Answer:
DCE
Step-by-step explanation:
you multiply
Algebraic expressions of the total amount of money spent by consumers for any number of Edge Control products is 0.45e.
What is expression?Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation : Divides left hand operand by right hand operand
For example 4/2 = 2
Given data as :
The selling specialized Edge Control product that sold for $0.45 each
The providing a more accurate expression is one that multiplies e by how much was spent on each one.:
⇒ (0.45)(e)
⇒ 0.45e
Hence, the algebraic expressions of the total amount of money spent by consumers for any number of Edge Control products is 0.45e.
Learn more about Expressions here:
brainly.com/question/13947055
#SPJ6
Need help ASAP!
A group of 40 students went on a field trip. Exactly 8 students wore blue shirts. What percent of the students on the field trip wore a blue shirt?
Answer:
i think its 5%
Step-by-step explanation:
because if you divide 40 by 8 you get 5
Answer:
5%
Step-by-step explanation:
divide 40 by 8 to get 5
In order for Brady to earn a B in his biology course, his test scores must average at least 80%. On the first 5 tests, he has an average of 77%. There is one test remaining in the course. What is the minimum score Brady needs to earn on the last test to receive a B in the class? Can you give a step by step explanation?
Hey there! I'm happy to help!
There were 5 tests needed to make an average of 77. These numbers have to add up to 385 (77×5) because that is what you divide by 5 to find the average which is 77.
Now, we want to find an average of 80 with 6 numbers. We multiply 80 and 6, showing us that the sum of these 6 numbers must be 480. Since 5 of these numbers are the same as with the 77 average, we know that one test score (the one Brady needs to get) is added to 385 to give us 480.
480-385=95
Therefore, Brady needs to earn a 95% on the last test to receive a B in the class.
What is the volume?
7ft
4ft
1ft
Alvin is going to take a flight from Seattle, Washington, to Atlanta, Georgia.
The flight leaves Seattle at 10:25 p.m. Seattle time and arrives in Atlanta at
6:10 a.m. Atlanta time. If Washington is in the Pacific time zone and Georgia
is in the eastern time zone, how long is the flight?
Use the following to help you answer the question.
12:00 p.m. eastern time = 11:00 a.m. central time = 10:00 a.m. mountain
time = 9:00 a.m. Pacific time.
Answer:
4 h 45 min
Step-by-step explanation:
Answer:4 h 45 min
Step-by-step explanation:
