Answer:
k=8.125
Step-by-step explanation:
just divide 13 by 1.6
(1) Compute the following sums:
(a) P150
i=1 2
(b) P50
n=1 n
(c) P60
n=10 n
(d) P25
n=1 3n2
(e) P55
i=1 (i + 2)
(f) P500
k=100 k
(g) P50
k=2 (k2 − 2k + 1)
(h) P20
m=10 m3
Solution: For the solutions to these, we will use the following results, which have been
established by Gauss’s formula, and the notation shown below for convenience:
S0(n) = Xn
i=1
1 = n S1(n) = Xn
i=1
i = n(n + 1)
2
S2(n) = Xn
i=1
i
2 = n(n + 1)(2n + 1)
6
S3(n) = Xn
i=1
i
3 =
n(n + 1)
2
2
(a) P150
i=1 2=2P150
i=1 1 = 2(150) = 300
(b) P50
n=1 n = (50)(50+1)
2 = 1275
(c) P60
n=10 n = P60
n=1 n − P9
n=1 n = (60)(61)
2 − (9)(10)
2 = 1785
(d) P25
n=1 3n2 = 3P25
n=1 = 3(25)(26)(51)
6 = 5525
(e) P55
i=1 (i + 2) = P55
i=1 i + P55
i=1 2 = (55)(56)
2 + 2(55) = 1650.
(f) P500
k=100 k = P500
k=1 k − P99
k=1 k = (500)(501)
2 − (99)(100)
2 = 120300
(g) P50
k=2 (k2 − 2k + 1) = P50
k=2 k2 − 2
P50
k=2 k + P50
k=2 1
= (P50
k=1 k2 − 1) − 2(P50
k=1 k − 1) + (P50
k=1 1 − 1)
= ( (50)(51)(101)
6 − 1) − 2( (50)(51)
2 − 1) + (1(55) − 1) = 40430
(h) P20
m=10 m3 = P20
m=1 m3 − P9
m=1 m3 = [ (20)(21)
2 ]
2 − [
(9)(10)
2 ]
2 = 46125
(2) A clock at London’s Heathrow airport chimes every half hour. At the beginning of the
n’th hour, the clock chimes n times. (For example, at 8:00 am the clock chimes 8 times,
at 2:00 pm the clock chimes fourteen times, and at midnight the clock chimes 24 times.)
The clock also chimes once at half-past every hour. Determine how many times in total
the clock chimes in one full day. Use sigma notation to write the form of the series before
finding its sum.
Solution: ¡¡ There is no solution for this problem. ¿¿
What is the largest multiple of 7?
Answer:
175
Step-by-step explanation:
In a video game, two characters follow paths represented by r = StartRoot 3 EndRoot + 2 cosine (theta) and r = 4 cos(θ), respectively. The characters travel at different speeds and could collide with each other. Which values of θ correspond to possible collision points? Check all that apply.
The point of collision is θ = π/6.
What are polar equations?A curve's polar equation is often stated with r as a function of θ and represented in polar coordinates.
The given equations are r = √3 + 2cosθ and r = 4cosθ.
The characters will collide at the intersection of these paths, the intersection of the two equations is given by:
√3 + 2cosθ = 4cosθ
4cosθ - 2cosθ = √3
2cosθ = √3
cosθ = √3/2
θ = cos⁻¹(√3/2)
θ = π/6
Hence, the point of collision is θ = π/6.
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Susan rides her bicycle 5 miles in 2/3 of an hour. At this rate, how many miles could she ride in 2 hours? Please help quick
Answer:
15 miles
Step-by-step explanation:
1 hour would be 7.5 miles an hour. So if you just add another one on then it'll be 15.
Sort these words with the correct definition.
Words: Theme, Convey, Poem, & Stanza.
Answer: convey- make an idea understandable; theme- subject or topic; poem- writing in speech and song, with stanzas; stanza- group of lines, verse
Step-by-step explanation:
what is the x- intercept of the line 5x- 2y=10?
Answer: x= -5/2 y=-5
Step-by-step explanation:
◘HURRY PLEASE◘
↓↓↓↓↓↓↓↓↓↓↓↓↓↓
Answer:
B, the parabola is narrower.
Step-by-step explanation:
Given the parent square function: x^2.
A vertical stretch by a scale factor of 3 is made to transform x^2 into 3x^2.
A stretch makes the function narrower, a compression makes the function wider.
Therefore the parabola is narrower.
do i use mean and standard deviation or median and interquartile range?
Answer: median and interquartile range
Step-by-step explanation:
I need help! Plz someone help me
Answer:
B
Step-by-step explanation:
24=12x+6y solve for y
Answer:
y = 4 - 2x
Step-by-step explanation:
Hope this helps! Have a great day!
Nick and Linda are paid 52.25 for their work. Nick worked 1.5 hours, and Linda worked 4 hours. They split the money according to the amount of time each of them worked. How much is Nick's share of the money?
Answer:
5.00
Step-by-step explanation:
5.00
Write the equation of a line that passes through (0, -6) and (11, 1).
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)
help me please with geometry
Answer:
Step-by-step explaunfere:
The circumference of a circle is the distance around the outside of the circle. The diameter, and the circumference are the three defining aspects of every circle. Given the radius or diameter and pi you can calculate the circumference.
1- C ≈ 50.27 in
2- C ≈ 31.42 in
3- A ≈ 201.06
4- A ≈ 314.16
5- C = 14π = 43.982 ≈ 44 inches
π (Pi) times the Radius squared: A = π r2
or, when you know the Diameter: A = (π/4) × D2
or, when you know the Circumference: A = C2 / 4π
A phone company offers two monthly plans. Plan A costs $20 plus an additional $0.07 for each minute of calls. Plan B costs $16 plus an additional $0.11 for each minute of calls.
Question A) For what amount of calling do the two plans cost the same?
Question B)What is the cost when the two plans cost the same?
A nutrition label states that there are 36 grams of carbohydrates in each serving. This accounts for 12% of the daily value. How many grams of carbohydrates are recommended per day?
Answer:
300 grams of carbohydrates are recommended per day
Step-by-step explanation:
First, convert 12% daily value into decimal: 12/100=0.12
Since this is a word problem and we have 36 grams and 12% daily value, we should make an equation first.
We are looking for how many grams of carbs should be taken a day, so lets use x as the unknown. We need to find x!
0.12 x= 36 g
Now: divide 36 grams by 0.12
x= 36g/0.12= 300g
x= 300 grams of carbohydrates are recommended per day.
Someone answer my Algebra 2 question for 100 points! On my account
-3 1/6 divide (-1 4/9)
Answer:
2.19230769231
Step-by-step explanation:
turn that into a fraction use internet
What is the difference between: |x+3| = 10 & |x| + 3 = 10
Answer:
Step-by-step explanation:
|x+3| = 10 means the absolute value of x+3 equal 10, so the answer to that means x= -13 or x= 7 (i.e. |-13+3| = |-10| =10, |7+3| = |10| = 10)
|x| + 3 = 10 means the absolute value of just x, so the answer to that would be x= -7 or x= 7 (i.e. |-7|+3 = 7+3 = 10, |7|+3 = 7+3 = 10)
However, take everything I say with a grain of salt, because I struggle some with Absolute Value Equations as well.
I hope this helps give you an idea of what you're looking at, though :)
Find the slope of the line below. *
Answer:
I believe it would be -3,4.
Step-by-step explanation:
To find slope you use rise over run, where you count up first, then go to the side. If you count down on the left you count 3 boxes, but since its going down its negative. And to get the run you count over 4. Meaning it's -3,4
Which graph represents this equation?
y = 1/2x^2 + 2x - 6
Answer:
C
Step-by-step explanation:
y = 1/2x^2 + 2x - 6
When, x = 0, y = - 6
you don't need to find another variable. Because in number C u can find a graph that has y= -6 when x =0.
The graph of the given equation is the graph C
What is a graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given is an equation, y = x²/2+2x-6, we need to identify the graph for the same,
y = x²/2+2x-6
Put x = 0,
y = -6
Point = (0, -6)
Put x = 2,
y = 2+4-6
y = 0
Point = (2, 0)
Put x = -6
y = 18-12-6
y = 0
Point = (-6, 0)
If we see all these points are lying in graph C, which means the graph C is satisfying the condition of the given equation,
Hence, the graph of the given equation is the graph C
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What is 38,050,000 expressed in scientific notation?
A. 0.3805 x 108
B. 3.805 x 107
C. 0.38 x 10-8
D. 3.805 x 108
Answer:
B. 3.805 x 10^7
Step-by-step explanation:
Match each word to the appropriate example using the expression 5a + 9b − 4.
is a coefficient.
is a constant.
There are
terms in the expression.
Answer:
5 and 9 are coefficients , -4 is a constant, and there are 3 terms in this expression.
Step-by-step explanation:
desperate need of help please
Answer:
3/2
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 14, - 18) and (x₂, y₂ ) = (- 10, - 12) ← 2 ordered pairs from the table
m = [tex]\frac{-12+18}{-10+14}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]
Can someone please answer this question for me 3(7q−10)
Answer:
21q-30
Step-by-step explanation:
If u use the distributive property, 3*7 is 21, therefore it would be 21q, and 3*10 is 30, so, the final answer would be 21q-30.
An elevator goes up 12 floors. I need help with this to I’m confused.
Answer:
Because, the situation is going up, the integer is +12 or 12.
Samuel invested $53,000 in an account paying an interest rate of 6.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 17 years?
Answer:
A≈165553.09
Step-by-step explanation:
To the nearest cent, there would be $174,529.50 in Samuel's account after 17 years of continuous compounding at an interest rate of 6.7%.
What is continuous compounding?The formula for calculating the amount of money in an account with continuous compounding is:
[tex]A = Pe^{(rt)}[/tex]
where:
A = the amount of money in the account after t years
P = the principal amount invested
r = the annual interest rate (as a decimal)
t = the time in years
e = Euler's number (approximately 2.71828)
Using this formula, we can calculate the amount of money in Samuel's account after 17 years as follows:
[tex]A = 53,000 \times e^{(0.067\times 17)[/tex]
A ≈ $174,529.50
Therefore, to the nearest cent, there would be $174,529.50 in Samuel's account after 17 years of continuous compounding at an interest rate of 6.7%.
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Given the formula for the arithmetic sequence, an = 6+ (n - 1)3, give the first 4 terms of the
sequence.
19
find the following:
[tex]a(n) = 6 + 3(n - 1)[/tex]
[tex]a(1) = 6 + 3(1 - 1)[/tex]
[tex]a(1) = 6 + 3 \times 0[/tex]
[tex]a(1) = 6 + 0[/tex]
[tex]a(1) = 6[/tex]
_________________________________
[tex]a(2) = 6 + 3(2 - 1)[/tex]
[tex]a(2) = 6 + 3 \times 1[/tex]
[tex]a(2) = 6 + 3 [/tex]
[tex]a(2) = 9[/tex]
_________________________________
[tex]a(3) = 6 + 3(3 - 1)[/tex]
[tex]a(3) = 6 + 3 \times 2[/tex]
[tex]a(3) = 6 + 6[/tex]
[tex]a(3) = 12[/tex]
_________________________________
[tex]a(4) = 6 + 3(4 - 1)[/tex]
[tex]a(4) = 6 + 3 \times 3[/tex]
[tex]a(4) = 6 + 9[/tex]
[tex]a(4) = 15[/tex]
a bag contains 5 red balls and some Blue Balls if the probability of drawing a blue ball is double that of red ball find the number of a blue balls in the back
Answer:
10
Step-by-step explanation:
Let the number of blue balls be x.
Number of red balls = 5
Total number of balls = x + 5
P (getting a red ball) = 5/x+5
P (getting a blue ball) = x/x+5
Given that
2(5/x+5) = x/x+5
10(x+5) = x^(2) +5x
x^(2)-5x-50=0
x(x-10)(x+5)
Now either x-10 = 0 or x+5= 0
But number of balls cannot be negative.
Hence, the number of blue balls is 10.
Find the value for f(-3) if f(x)=3x-5
Answer:
-14
Step-by-step explanation:
-3 replaces f which is x so its 3 time -3 which is -9 -5
Answer:
-14
Step-by-step explanation:
f(-3)= 3(-3) - 5
3 x -3 = -9
-9 - 5 = -14
-14 is your answer ;)
What is the slope of line p
The perimeter of a fence must be no larger than 500 feet in length. The longer side of the fence must be 10 feet more than twice the length of the shorter side. Write and solve and inequality to determine the maximum length of the shorter side of the fence.
Answer:
The shortest side of the fence can have a maximum length of 80 feet
Step-by-step explanation:
Inequalities
To solve the problem, we use the following variables:
x=length of the longer side
y=length of the sorter side
The perimeter of a rectangle is calculated as:
P = 2x + 2y
The perimeter of the fence must be no larger than 500 feet. This condition can be written as:
[tex]2x + 2y \le 500[/tex]
The second condition states the longer side of the fence must be 10 feet more than twice the length of the shorter side.
This can be expressed as:
x = 10 + 2y
Substituting into the inequality:
[tex]2(10 + 2y) + 2y \le 500[/tex]
This is the inequality needed to determine the maximum length of the shorter side of the fence.
Operating:
[tex]20 + 4y + 2y \le 500[/tex]
Simplifying:
[tex]20 + 6y \le 500[/tex]
Subtracting 20:
[tex]6y \le 500 - 20[/tex]
[tex]6y \le 480[/tex]
Solving:
[tex]y \le 480 / 6[/tex]
[tex]y \le 80[/tex]
The shortest side of the fence can have a maximum length of 80 feet
