Answers
Answer:
a) -7/9
b) 16 / (n² + 15n + 56)
c) 1
Step-by-step explanation:
When n = 1, there is only one term in the series, so a₁ = s₁.
a₁ = (1 − 8) / (1 + 8)
a₁ = -7/9
The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.
sₙ = sₙ₋₁ + aₙ
(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ
(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ
aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)
If you wish, you can simplify by finding the common denominator.
aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]
aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)
aₙ = 16 / (n² + 15n + 56)
The infinite sum is:
∑₁°° aₙ = lim(n→∞) sₙ
∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)
∑₁°° aₙ = 1
Related Questions
If X is at most 30 find x
Answers
Answer:
x[tex]\leq[/tex]30
Step-by-step explanation:
X can be many possiblities
So we can write it out with a smaller than sign and an equal sign
So now it means that x has to be smaller than 30 or equal to 30
a scientist performs an experiment in which he begins with 45.9 grams of reactants. assuming he does not lose any because of spilling of error, what should be the mass of his product at the end of the reaction?
Answers
Answer:
45.9 grams of product
Step-by-step explanation:
you should never end up with more products or less products than reactants
Calculate 3cm ,4cm, 10cm and 2cm
Answers
Answer:
19cm
Step-by-step explanation:
(chose one way)
1. way using commutativity
(3cm+4cm)+(10cm+2cm)=7cm+12cm=19cm
2. way just writing
3cm+4cm+10cm+2cm=19cm
Will mark brainliest
Answers
Answer: The third option
y = -6 + 2√6 ÷ 5 and y = -6 - 2√6 ÷ 5
Plz mark brainliest:)
Felipe has a flower bed
Answers
Answer:
man thats cool
Step-by-step explanation:
Using the Smith's BBQ Report, liquor sales for both weeks account for approximately what percentage of beverage sales for both weeks?
A 50%
B 40%
C 30%
D 20%
Answers
Answer:d
Step-by-step explanation:
Is the function even, odd, or neither?
Answers
Answer:
The function is neither even or odd
Step-by-step explanation:
g The average lifespan for a certain type of vehicle is 8 years and follows an exponential distribution. A lot contains 200 of these vehicles, brand new. What is the probability that 50 or more of them fail in the first 2 years
Answers
Answer:
The probability is [tex]P(A \ge 50 ) = 0.14321[/tex]
Step-by-step explanation:
The average life span is [tex]\pi = 8[/tex]
The sample size is n = 200
Generally we are told that average lifespan for a certain type of vehicle follows an exponential distribution
i.e
[tex]X \~ \ \ \ exp(8)[/tex]
Gnerally the probability distribution function for exponential distribution is
[tex]f(x) = \left \{ {{\lambda * e^{-\lambda * x }\ \ \ x\ge 0 } \atop {0 \ \ \ \ \ \ \ \ \ \ x < 0}} \right.[/tex]
Now [tex]\lambda[/tex] is the constant which is evaluated as
[tex]\lambda = \frac{1}{\pi}[/tex]
=> [tex]\lambda = \frac{1}{8}[/tex]
=> [tex]\lambda = 0.125[/tex]
Generally the that the vehicles will fail in less than 2 years is mathematically represented as
[tex]P(X \le 2 )= p= \int\limits^2_0 {\lambda e^{- \lambda * x} } \, dx[/tex]
[tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * x} } ]|\left 2 } \atop {0}} \right.[/tex]
[tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 2} } ] - [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 0} } ][/tex]
[tex]P(X \le 2 )= p= -0.77880 + 1[/tex]
[tex]P(X \le 2 )= p= 0.2212[/tex]
Generally the probability that the vehicle will fail in the first 2 years follows a binomial distribution with the mean evaluated as
[tex]\mu = n * p[/tex]
=> [tex]\mu = 200 * 0.2212[/tex]
=> [tex]\mu = 44.24[/tex]
The standard deviation is
[tex]\sigma = \sqrt{np(1 - p)}[/tex]
[tex]\sigma = \sqrt{200 * 0.2212 (1 - 0.2212)}[/tex]
[tex]\sigma = 5.86[/tex]
Using normal approximation of binomial distribution the probability that 50 or more of them fail in the first 2 years is mathematically represented as
[tex]P(A \ge 50 ) = 1 - P(A < 50 )[/tex]
Applying continuity correction
[tex]P(A \ge 50.5 ) = 1 - P(A < 50.5 )[/tex]
Here
[tex]P(A < 50.5 ) = P(\frac{A - \mu }{\sigma} < \frac{50 - 44.24}{5.87} )[/tex]
Generally
[tex]\frac{A - \mu }{\sigma} = Z (The \ standardized \ value \ of A )[/tex]
=> [tex]P(A < 50.5 ) = P( Z < 1.0664 )[/tex]
From the z-table the probability value of ( Z < 1.0664 ) is
[tex]P( Z < 1.0664 ) = 0.85679[/tex]
So
[tex]P(A \ge 50 ) = 1 - 0.85679[/tex]
=> [tex]P(A \ge 50 ) = 0.14321[/tex]
a maple tree shades an area of 7 1/2 m square. in the scale drawing, the maple tree shades an area of 12 1/2 cm square. in the scale drawing how many square centimeters represents 1 m squared
Answers
The number of centimeter squares in the scale drawing for each 1 m squared is 1.67.
What is Scale factor?The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.
Given that,
The area shaded by a maple tree is 7(¹/₂) m².
And, the area shaded in scale drawing is 12(¹/₂) cm².
The required number of square centimeters can be found by dividing the two areas as follows,
12(¹/₂) / 7(¹/₂)
= (25/2)/(15/2)
= 25 / 15
= 5 / 3
= 1.67
Hence, the number of centimeter squares in the scale area is 1.67.
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Suppose your cell phone plan charges a fixed rate of $10 per month plus 7 cents per minute. Create a table that shows the relationship between the total number of minutes you might use each month, m, and your total monthly cell phone bill, t.
Answers
One side of a triangle is half the longest side. The third side is 10 meters less than the longest side. The perimeter is 45 meters. Find all three sides.
m (smallest value)
m
m (largest value)
Answers
2x+x+2x-10 = 55
5x = 55
X=11
Smallest - 11 m
Largest - 22 m
3rd side - 12 m
Can someone help me find the coordinate??
Answers
Answer:
(2,4)Step-by-step explanation:
Midpoint =
[tex]( \frac{x_1+x_2}{2} \frac{y_1 + y_2}{2} )[/tex]
Endpoint :
[tex]x = \frac{x_1 + x_2}{2} \\ y = \frac{y_1 +y _2}{2} [/tex]
Have a nice day
para calcular el tanto por ciento de una cantidad tengo que
Answers
Answer:
Your answer is: Use the percentage formula: P% * X = Y
Step-by-step explanation:
Hope this helped : )
Su respuesta es: Utilice la fórmula de porcentaje: P% * X = Y
Espero que esto haya ayudado :)
-1 1/3 divided (-1.6)
Answers
Answer:
0.8333125
Step-by-step explanation:
Answer:
0.83
Step-by-step explanation:
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Which of the following is the value of the appropriate test statistic?A. z = -2.4736B. z = 2.4736C. tdf=−2.4736D. td f=2.4736
Answers
Answer:
A. z = -2.4736
Step-by-step explanation:
n1 = 25
n2 = 25
x1 = 5500
x2 = 5850
Sd1= 550
Sd2 = 445
Null hypothesis
μ1 - μ2 = 0
Alternate
μ1 - μ2 != 0
Pooled variance = ((25-1)*550²)+((25-1)*445²)/25+25-2
= 7260000+4752600/48
= 250262.5
Pooled sd = √250262.5
= 500.26243
Test statistic
Z =
5500-5850+10/500.26243*√1/25+1/25
= -2.47357 approximately
-2.4736
Which are removable discontinuities?
x = -2
x = -2 and x = 0
x = 0 and x = 4
x = -2, x = 0, and x = 4
Answers
Answer:
C
Step-by-step explanation:
Got it right on eng
Answer:C
Step-by-step explanation:
peter says, "If you subtract 11 from my number and multiply the difference by -2, the result is -26." What is Peter's number?
Answers
Answer:
24
Step-by-step explanation:
Reverse
-26/-2= 13
13+11=24
Check
24-11=13
13×-2= -26
I beleive the answer is 7.5 because -26 plus 11 = -15 then -15 divided by -2 = 7.5
this is probably wrong I didnt do it on paper
How many solutions does this equation have? 5 + 2(3 + 2x) = x + 3(x + 1) *
One Solution
Infinite Solutions
No Solutions
Answers
Answer:
no solutions
Step-by-step explanation:
Hi there!
Here is an answer:
[tex]5 + 2(3 + 2x) = x + 3(x + 1)\\11+4x=4x+3\\11=3,\;wrong[/tex]
Hope this helps)
Have a nice day!
what is the equation of the line for figures G and
H
Answers
Answer:
B = C + (C - A) = (51/50 + 51/50 - 2, 457/50 + 457/50 - 9) = (1/25, 232/25).
Step-by-step explanation:
A food truck sells tacos $1.25 a piece. The truck operator earned $360.00 last night.
How many tacos did the food truck sell last night?
28.8 tacos
288 tacos
300 tacos
2.88 tacos
Answers
Answer:
288
Step-by-step explanation:
Each taco is 1.25 dollars and you are trying to figure out how many tacos he sold to do this we make an equation.
Step 1
1.25 x = 360
x =is the amount of tacos sold.
Step 2
1.25 x = 360
/1.25 /1.25
to get x on its own we need to cancel out the 1.25 so we dived because it was multiplied to the x. we did the same on the other side to balance the equation.
Step 3
x = 288
we now need to identify what x is, we can see it is 288. If we trade x for what it means it is then this is your answer the amount of tacos sold=288
i hope this helps ;)
An accounting firm has 900 hours of on-the-clock staff time and 100 hours of reviewing time available to assign each week. The firm charges $300 for a tax return and $2000 for a small business audit. A small business audit requires 100 hours of staff time and 10 hours of review time. A tax return requires 12.5 hours of staff time and 2.5 hours of review time. In order to maximize their revenue for the week, how many small business audits and how many tax returns should the firm schedule? What is their maximum revenue for the week?
Constraints:
Objective Formula:
Answers
Answer:
The maximum revenue for the week is $19,000.
Step-by-step explanation:
Denote the variables as follows:
X = small business audit
Y = tax return
The maximizing function is:
Z = 2000·X + 300·Y
The maximizing function is subjected to the constraints:
100·X + 10·Y ≤ 900
10·X + 2·Y ≤ 100
0 ≤ X and 0 ≤ Y
The problem can be solved using the simples method as follows:
Let s and t be slack variables.
Initial:
x y s t b Basic
100 10 1 0 900 s (departing)
12.5 2.5 0 1 100 t
Z -2000 -300 0 0 0
(entering)
Step 1:
x y s t b Basic
1 1/10 1/100 0 9 x
0 1 -1/10 1 10 t (departing)
Z 0 -100 20 0 18000
(entering)
Step 2:
x y s t b Basic
1 0 1/50 -1/10 8 x
0 1 -1/10 1 10 y
Z 0 0 10 100 19000
(entering)
The optimal solution is:
X = 8
Y = 10
The maximum revenue for the week is $19,000.
3y + 7 - y = 5 + 2y + 2
Answers
final answer is all real numbers
The Valdez family bought a Blu-ray player on sale. The original price was $120. They received a 12% discount. How much did the Valdez family pay for the Blu-ray player after the discount?
Answers
Answer:
$105.60
Step-by-step explanation:
I think...
What is 0.4 as a decimal
Answers
Answer: 0.40 and 40%
Answer:
40%
Step-by-step explanation:
4(x - 2 + y) =4(x−2+y)=4, left parenthesis, x, minus, 2, plus, y, right parenthesis, equals
ill put in 50 brainly points
Answers
Answer:
x=4 and y=2
Step-by-step explanation:
The correct equation is,
⇒ y = - x + 3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 4 (x - 2 + y) = 4
Now, Simplify the expression as;
⇒ 4 (x - 2 + y) = 4
⇒ x - 2 + y = 4/4
⇒ x - 2 + y = 1
⇒ x + y = 1 + 2
⇒ x + y = 3
⇒ y = - x + 3
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Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 12 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Charles, Margaret, and Sean are chosen?
Answers
Using the combination formula, it is found that the probability that you, Charles, Margaret, and Sean are chosen is:
[tex]p = \frac{1}{495}[/tex].
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 4 people will be chosen from a set of 12, hence the number of ways to choose them is:
[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]
The desired combination is only one, hence the probability is:
[tex]p = \frac{1}{495}[/tex].
More can be learned about the combination formula at https://brainly.com/question/25821700
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Shelton mixed one 1/4 cups of purple cabbage into 3/8 cups of lettuce to make a big salad each day he eats 3/4 of a cup of salad which expression shows how many servings salad Shelton has?
Answers
Answer:[tex](1\frac{1}{4} + 2\frac{3}{8} ) / \frac{3}{4}[/tex]
Step-by-step explanation:
what is the area of 5in and 1 1/3
Answers
Country A is ten to the third power times greater than Country B. Country A has a population of 230,000,000. What is the population Of Country B. Help Pls
Answers
here is the equation I used: A=10^3+B
I need the right answers pls and tysmmm
Answers
Answer:
It's 21, you are correct!!
Step-by-step explanation: