Answers
Answer:
1st option.
[tex]\sum_{k=1}^{6} \frac{1}{2k-1}[/tex]
Step-by-step explanation:
The given sequence is as follows:
[tex]1 + \dfrac{1}{3}+ \dfrac{1}{5}+ \dfrac{1}{7}+ \dfrac{1}{9}+ \dfrac{1}{11}[/tex]
Here, we can see that the denominator is in AP and the sequence is:
1, 3, 7, 9, 11
first term, a = 1
Common difference, d = 2
We know that nth term for an AP:
[tex]a_n = a+(n-1)d[/tex]
where a is the first term and
d is the common difference.
So, nth term for above AP:
[tex]a_n = 1+(n-1)\times 2\\\Rightarrow 2n-1[/tex]
Here, we have 'k' in place of 'n':
[tex]a_k = 2k-1[/tex]
And as per the given sequence in the question, the kth term is simply the reciprocal:
i.e. [tex]\dfrac{1}{2k-1}[/tex]
and sum is to be done up to k = 6 from k = 1.
Hence, the summation notation for the sequence
[tex]1 + \dfrac{1}{3}+ \dfrac{1}{5}+ \dfrac{1}{7}+ \dfrac{1}{9}+ \dfrac{1}{11}[/tex]
is:
[tex]\sum_{k=1}^{6} \frac{1}{2k-1}[/tex]
Related Questions
Juan uses 1/5 liter to water a small plant and uses 1/2 liter to water a large plant now he has 2/10 liters left in a pitcher how much did Juan have in the beginning
Answers
Answer:
9/10
Hope this helps :)
A jacket usually sells for $57.00. If the jacket is 40% off, and sales tax is 5%, what is the total price of the jacket, including tax?
Answers
Answer: $35.91
Step-by-step explanation:
Since the jacket is 40% off, we multiply the original price by 60% to get the price remaining. ($57 x 0.6 = $34.20)
Then, we multiply the new price by 105% (includes the 5% sales tax) to get the total price. ($34.20 x 1.05 = $35.91)
I need help with question 5 please
Answers
Answer:
4
Step-by-step explanation:
2, 4, 4, 5, 6, 8, 8, 9, 10, 12
Median: 7
Lower Quartile: 2, 4, 4, 5, 6
So, 4
Write a function with no horizontal shift for the sinusoid shown.
Answers
We have been given graph of a sinusoidal function. We are asked to write function formula for our given graph.
We know that [tex]\sin(0)=0[/tex] and [tex]\cos(0)=1[/tex]. We can see that our given function is starting at origin, so our graph is sine function.
We know that general form of sine is [tex]y=A\sin[B(x-c)]+D[/tex], where,
A = Amplitude,
Period: [tex]\frac{2\pi}{B}[/tex]
C = Horizontal shift,
D = Vertical shift.
We have been given that function has no horizontal shift, so the value of C is 0.
We can also see that midline of our function is x-axis, so there is no vertical shift as well that is [tex]D=0[/tex].
We can see that function goes up to 1 from midline and goes down to [tex]-1[/tex] from midline, so amplitude of function is 1 that is [tex]A=1[/tex].
We can see that period of our given function is [tex]4\pi[/tex] because it completes one cycle from [tex]-\pi[/tex] to [tex]3\pi[/tex]
[tex]4\pi=\frac{2\pi}{B}[/tex]
[tex]B=\frac{2\pi}{4\pi}=\frac{1}{2}[/tex]
[tex]y=\sin(\frac{1}{2}x)[/tex]
We can see that our function is reflected about x-axis, so our function will be [tex]y=-f(x)[/tex].
[tex]y=-\sin(\frac{1}{2}x)[/tex]
Therefore, our required function is [tex]y=-\sin(\frac{1}{2}x)[/tex].
3 × (6 × 7 – 2.5 × 4)
Answers
Answer: 96
Multiply
3×6×7=126
2.5×4=10
(3)(-10)
Subtract
126-30=96
Answer:
96.
Step-by-step explanation:
Using order of operations:- we deal with the parentheses first:
3 * (6 * 7 - 2.5 * 4) Multiplying before the subtract in the parentheses:
= 3 * (42 - 10) Now do the subtraction in the parentheses:
= 3 * 32
= 96.
Dale made $273 dollars for 13 hours of work. At the same rate how much would he make for 8 hours of work.
Answers
Answer:
$168
Step-by-step explanation:
273 dollars for 13 hours of work is a unit rate of 273/13=21 dollars per hour. Multiplying this by 8 hours of work, you get 168 dollars. Hope this helps!
Write the numeral 0.0284 × 10^4 in scientific notation. A. 28.4 × 101 B. 0.284 × 103 C. 2.84 × 102 D. 284
Answers
Answer:
2.84×10²
Step-by-step explanation:
0.0284×10⁴
Move the decimal point 4 places to the right.
284
Now write in scientific notation by moving the decimal point 2 places to the left, behind the 2.
2.84×10²
A used car dealer prices her cars so that she makes a minimum profit of 15% on each car sold. If she acquired a car for $4,500, which inequality can be used to determine the acceptable selling prices, p, of that car? 1.15 p less-than-or-equal-to 4,500 1.15 p greater-than-or-equal-to 4,500 p less-than-or-equal-to 1.15 (4,500) p greater-than-or-equal-to 1.15 (4,500)
Answers
Answer:
[tex]p\geq 1.15(4,500)[/tex]
Step-by-step explanation:
If she makes a minimum profit, we need to use the symbol [tex]\geq[/tex], which indicates minimum quality.
Let's call [tex]p[/tex] profit, so the inequality which represent this problem would be
[tex]p\geq 1.15(4,500)[/tex]
The price of the car is multiplied by 1.15, because she must add her profit comission which is 0.15 or 15%.
Therefore, the right answer is the last choice.
Answer:
D
Step-by-step explanation:
i did the same thing
Yesterday, two friends went into a bank to open savings accounts. Megan started by putting $80 in her account, and she will deposit an additional $15 each week. Noah made no initial deposit, but he will add $25 more each week. In a few weeks, the friends will have the same account balance.
Answers
Answer:
8 weeks
Step-by-step explanation:
We are to find the number of weeks that they will have the same account balance.
Let the number of weeks be x.
Megan started by putting $80 in her account, and she will deposit an additional $15 each week. This means after x weeks, she will have:
80 + 15x
Noah made no initial deposit, but he will add $25 more each week. After x weeks, he will have:
25x
To find the number of weeks for their amounts to be the same, we equate their amounts to one another:
80 + 15x = 25x
Collexting like terms and solving for x:
80 = 25x - 15x
80 = 10x
=> x = 80 / 10 = 8 weeks
After 8 weeks, the money in their accounts will be the same.
geometry please help!!
Answers
what is (1−2g+4h)x5
Answers
Answer:
-10g+20h+5 is the answer when you do distribution.
Five students picked berries in Australia. They worked for 3 days. If they picked for 8 hours each day and together made a total of $960, how much was each person making per hour?
Answers
Answer:
8$ an hour
Step-by-step explanation:
first you do 8×3 then 960÷24 then 40÷5 so in the end you get 8 dollars an hour
Which of the following is a binomial with degree 4?
A. 4x4 − 5x3 + 2x2 − x + 1
B. 3x4 + 1
C. 4x − 3
D. A binomial cannot have degree 4.
Answers
Answer:
the answer is A
Step-by-step explanation:
hope it's help
Solve similar triangles can someone please answer
Answers
Answer:
Step-by-step explanation:
[tex]\frac{XY}{PQ}=\frac{YZ}{QR}\\\\\frac{19.5}{6.5}=\frac{10.5}{k}\\\\[/tex]
Cross multiply,
19.5*k = 10.5 * 6.5
[tex]k =\frac{10.5*6.5}{19.5}\\\\k=3.5[/tex]
The table shows Peter's net worth statement. Assets are shown as positive numbers, and liabilities are shown as negative numbers. The value of Peter's house is not given. Peter's net worth is $101,800. Based on the information in the table, what is the current value of Peter's house?
Answers
Answer:
Value of House = $98000
Step-by-step explanation:
The sum of all of the assets and liabilities + value of the house = $101,800
Value of House + $900 - $3400 + $16900 - $16300 + $4500 + $1200 = $101,800
=> Value of House + $3800 = $101,800
=> Value of House = $101,800 - $3800
=> Value of House = $98000
The current value of Peter's house will be $98000.
A table is given which shows Peter's net worth and assets are shown as positive numbers, and liabilities are shown as negative numbers.
We have to find out the current value of Peter's house if , Peter's net worth is $101,800.
What will be the resulting value ; 35 - 10 - 5 + 10 = ?
The resulting value will be 30.
As per the question ;
The sum of all of the assets and liabilities plus value of the house is equal to $101,800.
Assume value of house = x
⇒ x + $900 - $3400 + $16900 - $16300 + $4500 + $1200 = $101,800
⇒ x + $3800 = $101,800
⇒ x = $101,800 - $3800
⇒ x = $98000
Thus , the current value of Peter's house will be $98000.
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What is slope? Provide two examples of realistic situations where slope manifests itself. In each example make sure to state what units the slope is expressed in.
Answers
Answer:
1. A slope is a surface of which one end or side is at a higher level than another; a rising or falling surface.
"he slithered helplessly down the slope"
Some real life examples of slope include: in building roads one must figure out how steep the road will be. skiers/snowboarders need to consider the slopes of hills in order to judge the dangers, speeds, etc. when constructing wheelchair ramps, slope is a major consideration.
The value of V-16 is not-4 because
O A. 1624
B. (-16) 2-4
C. 42 16
O D. (-4)2 = -16
Answers
Answer:
b plz mrk brainly
Step-by-step explanation:
In the diagram below of circle O, OB and OC are radii, and chords AB, BC,
and AC are drawn.
B
С
Which statement must always be true?
1) ZBAC & ZBOC
2) MZBAC -
3) ABAC and ABOC are isosceles.
4) The area of ABAC is twice the area
of ABOC.
m_BOC
Answers
Answer:
It would be number 2. measure of angle BAC is equal to half the measure of angle BOC.
Step-by-step explanation:
This is because of inscribed angles.
In the diagram below of circle O, OB and OC are radii, and chords AB, BC, and AC are drawn. The correct statement is B. m < BAC = 1/2 m < BOC.
How to explain the circle?From the information given, (a + b) + (a + c) + (b + c) = 180°
2a + 2b + 2c = 180°
2a + 2b = 180° - 2c
2(a + b) = 180° - 2c
Therefore, m < BAC = 1/2 m < BOC.
In conclusion, the correct option is B.
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Find the obsolete value
l-9l 2. l64l 3. l-22l
Answers
Answer:
see below
Step-by-step explanation:
The absolute value means take the non negative value
l-9l = 9
l64l =64
l-22l=22
Answer:
1. 9 2. 64 3. 22
Step-by-step explanation:
The obsolute value is how far away the number is from zero
For example:
I-94I is 94
but
-I94I is -94
if the negative is outside the equation then its a negative
an object is translated by (x + 4, y - 2). If one point in the image has the coordinates (5 , -3), what would be the coordinates of it’s pre-image?
Answers
Answer: (9,-5)
Step-by-step explanation:
(5+4,-3-2)= (9,-5)
What are the answers
Answers
Answer:
Insert question here--->
Step-by-step explanation:
Find the solution to x^2+2=27
Answers
Answer:
x = 5
Step-by-step explanation:
x^2 +2 = 27
x^2 = 27 - 2
x^2 = 25
x = [tex]\sqrt{25\\\\}[/tex]
x = 5
Answer: x equals 5
Step-by-step explanation:
27 minus 2 is 25, the square root of 25 is five.
What would be the mass of 234 ml of water??
Answers
Answer:
0.233298 kg is the mass of 234 ml of water
Step-by-step explanation:
Mathematically,
mass = density * volume
henry, to get the mass of that volume, we shall need to multiply it by the density of water.
The density of water is 997 kg/m3
To achieve consistency in units, we shall convert 234 ml to m3
Mathematically 1ml = 1 * 10^-6 m^3
Thus, 234 ml = 234 * 10^-6 m^3
Therefore the mass of water will be = 234 * 10^-6 * 997 = 0.233298 kg
f(x) = 2(x − 5), find f(8).
Answers
Answer:
6
Step-by-step explanation:
f(8)=2(8-5)
f(8)=2(3)
f(8)=6
have a great day
Please help! Correct answer only!
I've been on this question for more than an hour...
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking a 3 and then picking a 3?
Simplify your answer and write it as a fraction or whole number.
Answers
Answer:
You have three card : 3, 4, 5 and 6.
You first pick one card randomly, the probability of picking a 3 is:
P = 1/4
You then pick a second card without putting the first card back, the probability of picking a 3 is:
P = 1/3
=> The probability of picking a 3 and then picking a 3:
P = (1/4) x (1/3) = 1/12
Hope this helps!
:)
26 is what percent of 130?
Please answer quickly no jokes.
Answers
First, divide.
26 / 130 = 0.2
Second, multiply.
0.2 * 100% = 20%
Therefore, 26 is 20% of 130
Best of Luck!
Which of the following is equal to ? 1 divided by 5^-2
Answers
Answer:
5^2 or 25.
Step-by- step explanation:
1 / 5^-2
= 1 / 1/25
= 25.
Answer:
[tex]25[/tex]
Step-by-step explanation:
[tex]1 \div {5}^{ - 2} \\ 1 \div \frac{1}{ {5}^{2} } \\ 1 \div \frac{1}{25} \\ 1 \times \frac{25}{1} \\ = 25[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Express 0.82 as a percent
Answers
Answer:
82%
Step-by-step explanation:
For what value of b, would the equation 34(12x−9)+b4=5−3(2−3x) have infinitely many solutions? Enter the numerical value only
Answers
Answer:
23/16
Step-by-step explanation:
i looked it up on a website and got this question right on my test
The given expression is a linear function and has a unique solution.
Given,
For what value of b, would the equation 3/4(12x−9)+b/4=5−3(2−3x) have infinitely many solutions?
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
Here,
3/4(12x−9)+b/4=5−3(2−3x)
12x - 27 / 4 + b / 4 = 5 - 6 + 9x
12x - 9x = -1 + 27/4 - b / 4
3x = 23 - b / 4
Here the expression is a linear function of x, so the expression has a unique solution not infinitely many solutions.
Thus, the given expression is a linear function and has a unique solution.
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A company is designing a new cylindrical water bottle. The volume of the bottle will be 230 cm cubed 3. The height of the water bottle is 7.3 cm. What is the radius of the water bottle? Use 3.14 for π.
Answers
Answer:
Step-by-step explanation:
I don't say you have to mark my ans as brainliest but if it has really helped you plz don't forget to thank me...