Find the sum of the first 80 terms of the sequence. Show all work for full credit. 1, -3, -7, -11, ...
Answer:
-12960
Step-by-step explanation:
The formula for the sum of terms =
Sn = n/2[2a + (n - 1) d]
n = number of terms = 80
The given sequence =
1, -3, -7, -11, ...
a = First term = 1
d = common difference
= Second term - First term
= -3 - 1
= -4
Therefore, the sum of the first 80 terms:
S80 = 80/2[2 × 1 + (80 - 1)]-4
= 40[2 + 79]-4
= 40 × 81 × -4
= -12960
The sum of the first 80 terms = -12960
Someone please help fast, I am really lost with the law of logarithms and need help with these questions in picture
We'll use the following log rules
Log rule 1: log(xy) = log(x)+log(y)Log rule 2: log(x/y) = log(x)-log(y)Log rule 3: log(x^y) = y*log(x)================================================
Part 1
Answer: 2a + 2c-------------
Work Shown:
Ln(100) = Ln(4*25)
Ln(100) = Ln(2*2*5*5)
Ln(100) = Ln(2)+Ln(2)+Ln(5)+Ln(5) ... using log rule 1
Ln(100) = a+a+c+c
Ln(100) = 2a + 2c
================================================
Part 2
Answer: 2a + b - c-------------
Work Shown:
Ln(2.4) = Ln(24/10)
Ln(2.4) = Ln[ (2*2*2*3)/(2*5) ]
Ln(2.4) = Ln[ (2*2*3)/5 ]
Ln(2.4) = Ln(2*2*3) - Ln(5) ... using log rule 2
Ln(2.4) = Ln(2)+Ln(2)+Ln(3) - Ln(5) .... using log rule 1
Ln(2.4) = a+a+b-c
Ln(2.4) = 2a+b-c
================================================
Part 3
Answer: -3a + b - 3c-------------
Work Shown:
Ln(0.003) = Ln(3/1000)
Ln(0.003) = Ln[ 3/( 10^3) ]
Ln(0.003) = Ln(3) - Ln(10^3) ... log rule 2
Ln(0.003) = Ln(3) - 3*Ln(10) ... log rule 3
Ln(0.003) = Ln(3) - 3*Ln(2*5)
Ln(0.003) = Ln(3) - 3*( Ln(2) + Ln(5) ) ... log rule 1
Ln(0.003) = b - 3*( a + c )
Ln(0.003) = b - 3a - 3c
Ln(0.003) = -3a + b - 3c
================================================
Part 4
Answer: 3a + 3b + 2c-------------
Work Shown:
All logs shown for this part are in base 2
log(5400) = log(54*100)
log(5400) = log(6*9*4*25)
log(5400) = log(2*3*3*3*2*2*5*5)
log(5400) = log(2^3*3^3*5^2)
log(5400) = log(2^3)+log(3^3)+log(5^2) ... log rule 1
log(5400) = 3*log(2)+3*log(3)+2*log(5) ... log rule 3
log(5400) = 3a + 3b + 2c
The planet Mars has a radius of 3400 km. What is the volume of Mars?
Write your answer in scientific notation to three decimal places.
Answer:
1.646×10¹¹ km³.
Step-by-step explanation:
From the question given, we obtained the following information:
Radius (r) = 3400 km
Volume (V) =.?
The shape of a planet is spherical in nature. Thus, we shall apply the formula for calculating the volume of a sphere to obtain the volume of Planet Mar as illustrated below:
Radius (r) = 3400 km
Pi (π) = 3.14
Volume (V) =.?
Volume of a sphere = 4/3 πr³
V = 4/3 × 3.14 × (3400)³
V = 4/3 × 3.14 × 3.9304×10¹⁰
V = 1.646×10¹¹ km³
From the calculations made above, the volume of Planet Mar is 1.646×10¹¹ km³
Donna arranges 32 tiles in equal rows, as shown below. Which expression
represents the number of tiles in each row?
32 x 4
32 + 4
32 : 4
32 - 4
The endpoints of (MP)are M(2,1) and P(12,6). If point K partitions (MP) in a ratio of MK:KP = 3:2, what are the coordinates of K?
Answer:
K(8, 4)
Step-by-step explanation:
Given:
M(2, 1), P(12, 6)
MK:KP = 3:2
Required:
Coordinates of K
SOLUTION:
Coordinates of K can be determined using the formula below:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
Where,
[tex] M(2, 1) = (x_1, y_1) [/tex]
[tex] P(12, 6) = (x_2, y_2) [/tex]
[tex] m = 3, n = 2 [/tex]
Plug in the necessary values to find the coordinates of K:
[tex] x = \frac{mx_2 + nx_1}{m + n} [/tex]
[tex] x = \frac{3(12) + 2(2)}{3 + 2} [/tex]
[tex] x = \frac{36 + 4}{5} [/tex]
[tex] x = \frac{40}{5} [/tex]
[tex] x = 8 [/tex]
[tex] y = \frac{my_2 + ny_1}{m + n} [/tex]
[tex] y = \frac{3(6) + 2(1)}{3 + 2} [/tex]
[tex] y = \frac{18 + 2}{5} [/tex]
[tex] y = \frac{20}{5} [/tex]
[tex] y = 4 [/tex]
The coordinates of K = (8, 4)
Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through (-8,0) and (0,8) Type the point-slope form of the equation of the line.
Answer:
Step-by-step explanation:
(8 - 0)/(0 + 8)= 8/8= 1
y - 0 = x + 8
y = x + 8
help me please this is due today!!!!!
could you help me answer this for a friend
Answer:
The correct option is option C(SAS) as there are 2 angles and 1 common side(BC) used to prove the triangles congruent..
Rachel works 5 days a week and works 7.5 hours on each of the days she works. How many hours does
Rachel work in 3 weeks
Answer: 112.5 hours
Step-by-step explanation:
What is the density of Basalt? Mass = 20g ; Volume = 6.47 cubic cm. Round
to TWO decimal places.
Answer:
3.09g/cm cubedStep-by-step explanation:
Density = mass/volume = 20/6.47
Is this statement true or false?
The period before we have written records is called prehistory
true
false
It's history
(2/3)^3(1/5•2/3)^-3(1/5)^4
PLS HELP
Answer:
1/5
Step-by-step explanation:
You have to do whats in the parentheses first then you start doing to exponets from left to right then you would multiply then you would get your answer 1/5.
44. Find the total area of the shaded rectangles.
9
х
х
2

Answer:
(x² + 18) units²
Step-by-step explanation:
Area of a rectangle = l*w
There are two shaded rectangles found inside the large rectangle. Let us represent the smaller shaded one as Rectangle 1, the bigger shaded rectangle as Rectangle 2.
Below are the dimensions and area if each of them:
Rectangle 1 (small shaded rectangle):
l = x
w = x
Area = x * x = x² units²
Rectangle 2 (bigger shaded rectangle):
l = 9
w = 2
Area = 9*2 = 18 units²
Total area of the shaded rectangles = x² + 18 = (x² + 18) units²
(3 + 5i) + (11 -7i) Write answer in standard form a +bi
Answer:
Step-by-step explanation:
3 + 11 + 5i - 7i
14 - 2i
Which expression is equivalent to 21 - (-5)?
O A. -21 + 5
O B. 21 + 5
O C. -21 - 5
O D. 21 - 5
HELP!!! Need Some Homework Help!
Answer:
( -4, 7 )
Step-by-step explanation:
The difference between (2,3) and (-1,5) is (-3,2)
Because (-3,2) is the length of half the line we need to add that figure to M to get point S
(-1,5) plus (-3,2) is (-4,7)
Need help with 2-5 plsssss
Answer:
5) m∠DEF = 18
Step-by-step explanation:
I cant answer the rest because they require a protractor
Use the given conditions to write an equation in point-slope form. Keep parenthesis in point-slope form. passing through (3,5) and (8,15).
Answer:
Step-by-step explanation:
(15 -5)/(8 - 3)= 10/5 = 2
y - 5 = 2(x - 3)
y - 5 = 2x - 6
y = 2x - 1
Find the distance of segment AB
A(-7,6) B(4,-2)
Answer:
13.6
Step-by-step explanation:
Suppose you work for a company that manufactures electronics. The development analysts estimate that 5% of their flagship product will fail within 2 years of the purchase date, with a replacement cost of $ 1200. A newly hired associate at the company proposes to charge $ 50 for a 2-year warranty. 1. Compute the expected value of this proposal. Let X be the amount profited or lost (by the company) on the warranties and P(X) is the probability. 2. Interpret the expected value in complete sentences.
The expected value of the proposal is -$10. This means that, on average, the company can expect to lose $10 per warranty sold.
Interpretation of the expected value:
The expected value of -$10 indicates that, on average, for every 2-year warranty sold, the company can expect to lose $10. This means that the proposal is not a profitable venture for the company. The replacement costs of the 5% of failed products are higher than the revenue generated by selling the warranties and cannot cover the potential losses.
To compute the expected value of the proposal, we need to calculate the amount profited or lost (X) by the company on the warranties and the probability (P(X)) of each outcome.
Now, we have,
The product doesn't fail within 2 years, and the company earns $50 from the warranty.
The product fails within 2 years, and the company incurs a replacement cost of $1200 but keeps the $50 warranty fee.
The probability of the product not failing within 2 years is 1 - 0.05 = 0.95,
and the probability of the product failing within 2 years is 0.05.
Now, we have to find the expected value (E(X)):
[tex]E(X) = P(X_1) * X_1 + P(X_2) * X_2[/tex]
Where:
[tex]P(X_1)[/tex] = Probability of the product not failing within 2 years = 0.95
[tex]X_1[/tex] = Amount profited when the product doesn't fail within 2 years = $50
[tex]P(X_2)[/tex] = Probability of the product failing within 2 years = 0.05
[tex]X_2[/tex] = Amount lost when the product fails within 2 years = -$1150 (Replacement cost of $1200 - $50 warranty fee)
E(X) = 0.95 * $50 + 0.05 * (-$1150)
E(X) = $47.50 - $57.50
E(X) = -$10
The expected value of the proposal is -$10. This means that, on average, the company can expect to lose $10 per warranty sold.
Interpretation of the expected value:
The expected value of -$10 indicates that, on average, for every 2-year warranty sold, the company can expect to lose $10. This means that the proposal is not a profitable venture for the company. The replacement costs of the 5% of failed products are higher than the revenue generated by selling the warranties and cannot cover the potential losses. As a result, the company might want to reconsider the pricing of the warranty or look for other ways to reduce the potential costs associated with the product failures.
To learn more on probability click:
brainly.com/question/11234923
#SPJ3
Earth’s diameter is approximately 12,760,000 meters. What is that number in scientific notation?
Answer:
1.276 × 10-7 12.76 × 10-6 1.276 × 107 0.1276 × 108.
Step-by-step explanation:
How many at-bats did the player have?
Answer:
450
Step-by-step explanation:
17 full balls + (1/2+1/2)=1
18*25=450
Answer:
450 at - bats
Step-by-step explanation:
Home run = 50
Triples = 37.5
Doubles = 75
Singles = 125
walks = 62.5
Outs = 100
Total = 450
hopefully this helps you :)
Pls mark me brainlest ;)
6th grade math Please help
The water level in a pool drops 8 iches in a day so what is the average level drop in each hour
Answer:
0
Step-by-step explanation:
becuse 8 is in a day and the only thing could be 0 becuse in a hour you might not get much in an hour cuz an day is 24 hours but there might be a chance to be 1 but its mostly 0.
Noah is shopping for new socks. He sees many different options. One bag has 12 socks for $9.99, another bag has 20
socks for $14.99, and a third bag with 10 socks for $19.99. Which is the best deal for socks?
Answer:
the bag with 20 socks for $14.99
Answer:
Second bag having 20 socks for $ 14.99 is the best deal.
Step-by-step explanation:
To find the best deal, you have to find the unit rate
First bag:
Unit rate = 9.99 ÷ 12 = $ 0.8325
Second bag:
unit rate = 14.99 ÷ 20 = $ 0.7495
Third bag:
Unit rate = 19.99 ÷ 10 = $ 1.999
Second bag having 20 socks for $ 14.99 is the best deal.
Round $537.307 to the nearest cent
Answer:
$531.31
round to the nearest cent is round to 2 decimal places
Answer:
537.31 hope this helps you out
Which angles are right?
Check all that apply.
A. GFE
B. MLK
C. EFH
D. KLJ
Answer:
<MLK
<EFH
<KLJ
Step-by-step explanation:
Each Is At A Right Angle, I Just Answered This On My Quiz.
Simplify the ratio 24/36
Answer:
2:3
Step-by-step explanation:
24:36
24÷12=2
36÷12=3
Answer=2:3
Answer:
2 : 3
Step-by-step explanation:
24/36 ?
[tex] \frac{24}{36} \div \frac{12}{12} \\ = \frac{24 \div 12}{36 \div 12} \\ = \frac{2}{3} [/tex]
2/3 = 2 : 3
Pls help pls ASAP 1,2,3,4
Answer:
3
Step-by-step explanation:
Answer: the third on i think
Step-by-step explanation:
PLZ Help
This is due by 2:20
Answer:
The answer is 60 degrees.
Step-by-step explanation:
The three angles in any triangle add up to 180 degrees.
You know by the box at the bottom right that it's a right triangle and therefore that angle is 90 degrees. They also give you the 30 degree angle at the bottom left. So:
90 degrees + 30 degrees = 120 degrees.
180 degrees (total) - 120 degrees (first 2 angles) = 60 degrees (missing angle)
Hope this helps!