Answer:
1003
Step-by-step explanation:
The problem is a classic example of a telescoping series of products, a series in which each term is represented in a certain form such that the multiplication of most of the terms results in a massive cancelation of subsequent terms within the numerators and denominators of the series.
The simplest form of a telescoping product[tex]a_{k} \ = \ \displaystyle\frac{t_{k}}{t_{k+1}}[/tex], in which the products of n terms is
[tex]a_{1} \ \times \ a_{2} \ \times \ a_{3} \ \times \ \cdots \times \ a_{n-1} \ \times \ a_{n} \ = \ \displaystyle\frac{t_{1}}{t_{2}} \ \times \ \displaystyle\frac{t_{2}}{t_{3}} \ \times \ \displaystyle\frac{t_{3}}{t_{4}} \ \times \ \cdots \ \times \ \displaystyle\frac{t_{n-1}}{t_{n}} \ \times \ \displaystyle\frac{t_{n}}{t_{n+1}} \\ \\ \-\hspace{5.55cm} = \ \displaystyle\frac{t_{1}}{t_{n+1}}.[/tex].
In this particular case, [tex]t_{1} \ = \ 2[/tex] , [tex]t_{2} \ = \ 3[/tex], [tex]t_{3} \ = \ 4[/tex], ..... , in which each term follows a recursive formula of [tex]t_{n+1} \ = \ t_{n} \ + \ 1[/tex]. Therefore,
[tex]\displaystyle\frac{t_{2}}{t_{1}} \times \displaystyle\frac{t_{3}}{t_{2}} \times \displaystyle\frac{t_{4}}{t_{3}} \times \cdots \times \displaystyle\frac{t_{n}}{t_{n-1}} \times \displaystyle\frac{t_{n+1}}{t_{n}} \ = \ \displaystyle\frac{3}{2} \times \displaystyle\frac{4}{3} \times \displaystyle\frac{5}{4} \times \cdots \times \displaystyle\frac{2005}{2004} \times \displaystyle\frac{2006}{2005} \\ \\ \-\hspace{5.95cm} = \ \displaystyle\frac{2006}{2} \\ \\ \-\hspace{5.95cm} = 1003[/tex]
-6+ (-19) =
Evaluate
Dan takes an airplane to visit his parents. He pays the airline a total of $450. The cost of the ticket is $315. The airline also charges $15for every pound that the luggage goes over the 50 pound is Dan's luggage over the 50 pound limit?
Answer:
9
Step-by-step explanation:
Start with the total amount Dan paid and subtract the part of the payment that is for the ticket.
450-315=135
Assuming that all of that $135 was for luggage fees and each pound over the limit costs $15, then the question is, how many times did Dan pay $15 until he'd paid the full $135 luggage fee.
So divide $135 by $15.
135/15=9
So his luggage weighted 59 pounds, which is 9 pounds over the limit.
Write an equation of the line with a slope of -2 and y-intercept of 3
Answer:
y = -2x + 3
Step-by-step explanation:
the original formula is
y = mx + b
m is the slope
b is the inteception on the y axis
I need help I need help
Answer:
click on image
Step-by-step explanation:
click on the image
If I is parallel to m. Find x and y
Answer: make me brainlist
Step-by-step explanation: x=104
2 2/6 is equivalent to what?
When solving a quadratic in the form ax2 + bx + c = 0 we are really finding the x–intercepts. These x–intercepts are also called roots. What is another term for roots or x-intercepts? put it in a full sentence for me please
Answer:
solutions
Step-by-step explanation:
Another term for the roots or x-intercepts of the standard-form quadratic equation is "solutions." These are the values of x that make the equation true.
Solve the Inequality for x.
-5x + 20 < 5
A) x > 5
B) x < 3
C) x > 3
D) x < -5
Thanks!!! :D
Answer:
x>3
Step-by-step explanation:
-5x+20<5
-5x<5-20
-5x<-15
5x>15
x>15/5
x>3
Answer:
A) x > 3
Step-by-step explanation:
[tex]-5x + 20 < 5\\\rule{150}{0.5}\\-5x + 20 - 20 < 5 - 20 \\\\-5x < -15 \\\\\frac{-5x < -15}{-5}\\\\\boxed{x > 3}[/tex]
DASH
Hollywood Academy of Arts & Sciences
Select the correct answer. Press the Submit button.
Use the image and information you have read to answer.
How is the object in this image similar to the AUV
developed by engineers at MIT?
A
They both cause damage to deep-sea coral reefs.
B
They both stay motionless at all times.
They both must remain on the bottom of the ocean.
D They both squirt jets of water to hold their position.
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O
Answer:
The answer is b
Step-by-step explanation:
Happy holidays ;)
help me solve thissss
Answer:
y = 35 degrees
Step-by-step explanation:
y + 55 = 90
(subtract 55 from both sides)
y = 35
The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width
Answer:
60 yards
Step-by-step explanation:
300 = 2(30 + w) + 2(w)
300 = 60 +2w + 2w
300 = 60 + 4w
240 = 4w
60 = w
The hypotenuse AB of the right triangle ABC is parallel to the axis of the abscess. Find the length of the hypotenuse if A (-1; 1) and C (3; -4)
Answer:
10.25
Step-by-step explanation:
The slope of AC is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -1)/(3 -(-1)) = -5/4
Then the slope of CB is the opposite reciprocal, 4/5. The equation of line CB in point-slope form is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -(-4) = 4/5(x -3) . . . . line CB
When y = 1 (to match the y-value of A), then ...
1 +4 = 4/5(x -3)
5(5/4) = (x -3) . . . . . multiply by 5/4
6.25 +3 = x = 9.25 . . . . add 3
Point B is (9.25, 1).
The length of the hypotenuse is ...
9.25 -(-1) = 10.25
Complete the equation of the line through (-10,3)(−10,3)left parenthesis, minus, 10, comma, 3, right parenthesis and (-8,-8)(−8,−8)left parenthesis, minus, 8, comma, minus, 8, right parenthesis.
Answer:
[tex] y = -\dfrac{11}{2}x - 52 [/tex]
Step-by-step explanation:
Line through points (-10, 3) and (-8, -8).
slope = (-8 - 3)/(-8 - (-10)) = -11/2
y = mx + b
y = (-11/2)x + b
-8 = (-11/2)(-8) + b
-8 = 44 + b
b = -52
y = (-11/2)x - 52
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line passing through (-10,3) and (−8, -8) is y=(-11/2)x-52.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The slope fo the line passing through (-10,3) and (−8, -8) is
Slope, m = (-8-3)/(-8+10) = -11/2
Now, equate a point in the equation,
3 = -10(-11/2) + C
3 = 55 + C
c = -52
Hence, the equation of the line passing through (-10,3) and (−8, -8) is y=(-11/2)x-52.
Learn more about Equation of Line:
https://brainly.com/question/21511618
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What is the answer to y=-2(-3/2)-9
Answer:
-6
Step-by-step explanation:
y = -2 x -3/2 - 9
3 - 9 = -6
Hey there!
y= -2 (-3/2) - 9
-2(-3/2) = [3]
y = 3 - 9
y = -6
Therefore, your answer is: y = -6
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
the number of Significant Figures in 13410000 *
Answer:
hhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
hhhhhhhhhhhh
Answer:
4
Step-by-step explanation:
13410000
Sig Figs4
13410000
Decimals0
Scientific Notation1.341 × 107
E-Notation1.341e+7
Words thirteen million four hundred ten thousand
URGENNTTT PLEASE ILL GIVE 50
Take Triangle ABC, A(2,-1), B(1,4) and C(-2,2). Do
the series of mappings to find A'B'C'.
First translate
it 3 units to the right and 2 units up, next reflect
about the x-axis, and finally rotate 180 degrees.
Answer:
(3-2)
Step-by-step explanation:
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Pythagorean theorem )
Answer:
5 sqrt(6) = x
Step-by-step explanation:
The pythagorean theorem states
a^2 + b^2 = c^2
Where a and b are the legs and c is the hypotenuse
7^2 + (sqrt(101))^2 = x^2
49+101 = x^2
150 = x^2
Take the square root of each side
sqrt(150) = sqrt(x^2)
sqrt(25*6) = x
5 sqrt(6) = x
Which type of correlation does this scatterplot show?
Answer:
i think the answer to this question is positive correlation
Step-by-step explanation:
this image below may help u
Creshawna has $52 in her bank account. She sells a few of her games and makes $134. She deposits that amount into her bank account. How much money does Creshawna have in her bank account after she deposits $134?
$180
$186
$190
$196
I'm pretty sure it's $186
Help help help math math
Answer:
Slope = 4
Step-by-step explanation:
Change in Y = 4
Change in X = 1
Slope = Δy/Δx = 4/1 = 4
Change 3/4 to a decimal! Please explain step by step to get marked as brainliest
Answer:
The answer is 0.75
Step-by-step explanation:
The line in a fraction that separates the numerator and denominator can be rewritten using the division symbol. So, to convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.
Another method without a calculator is:
Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.
Step 2: Multiply both top and bottom by that number.
Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)
Example:
Convert 3/4 to a Decimal:
Step 1: We can multiply 4 by 25 to become 100
Step 2: Multiply top and bottom by 25. It gives us 75/100.
Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);
Answer = 0.75
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
Cassie wants to purchase a pair of binoculars that is on sale for $155.75. The sales tax rate in his county is 7%.
Calculate the amount of sales tax Cassie will pay on the purchase. Round to the nearest cent if necessary.
sales tax: $
Listen to the complete question
Part B
Fill in the blank question.
How much will Cassie pay in all for the pair of binoculars after sales tax is included? Round to the nearest cent if necessary.
total cost: $
Answer:
$10.12
Step-by-step explanation:
Step one:
given data
we are told that the cost of binoculars is $155.75
and also the sales tax is 7%
Step two:
We want to first solve for the sales tax which is 7% of $155.75
=7/100* 155.75
=0.070*155.75
=10.12
Cassie will pay a tax of $10.12
Also Cassie will pay a total amount of
= 155.75+10.12
=$165.87
Algebra 1
What is the greatest possible error for a measurement of 4 inches?
inches
Três torneiras enchem uma piscina em 10 horas quantas horas levarão 10 torneiras para encher 2 piscinas
Answer:
Step-by-step explanation:
the price of an article is Marked 25% above the cost price .if it is solid the profit of Rs.500 after allowing 15% discount .what will be it's selling price
Answer:
Rs 8500
Step-by-step explanation:
For a cost price of c, the marked price is ...
marked = c +25%·c = 1.25c
After the 15% discount, the sale price will be ...
s = marked -15%·marked = 0.85·marked = (0.85)(1.25c) = 1.0625c
The profit will be the difference between the sale price s and the cost c:
p = s -c
500 = (1.0625c) -c = 0.0625c
Then the cost is ...
500/0.0625 = c = 8000
and the sale price is ...
s = c +p = 8000 +500 = 8500 . . . rupees
The selling price will be Rs 8500.
Four times a number, minus 4, is equal to three times the number, plus 6. Find the number
Answer:
42
Step-by-step explanation:
What is the sales tax on a jacket priced at $275 if the sales tax rate is 7%?
help me please please
Answer:
its 3 OR C
Step-by-step explanation:
Help help math math good luck
find the equation of a circle concentric with the circle x^2+y^2-2x-10y+1=0 passing through the point (2,-3)
Answer:
Step-by-step explanation:
x²+y²-2x-10y+1=0
compare with x²+y²+2gx+2fy+c=0
center is (-g,-f)
radius=√(g²+f²-c)
2g=-2
g=-1
2f=-10
f=-5
radius=(1,5)
c=1
let eq. of circle be x²+y²-2x-10y+c=0
∵ it passes through (2,-3)
2²+(-3)²-2(2)-10(-3)+c=0
4+9-4+30+c=0
c=-39
eq. of circle is is x²+y²-2x-10y-39=0