The summation notation for the geometric series will be expressed as [tex]\sum5(-2)^{n-1}\\[/tex]
Series and sequencesSeries are sum of sequences
Given the following alternating series as shown:
5 - 10 + 20 - 40 + 80
The series is geometrc series with the following parameters
First term "a" =5
ratio= -10/5 = 20/-10 = -2
Since the nth term of geometric sequence is expressed as:
Tn = ar^n-1
Tn =5(-2)^n-1
Hence the summation notation for the geometric series will be expressed as [tex]\sum5(-2)^{n-1}\\[/tex]
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Answer:
A
Step-by-step explanation:
help me find the surface area of this shape please
Step-by-step explanation:
Divide the solid into 2 cones.
SA of a cone
= πrl
l of cone 1
l² = r² + h²
l² = 9² + 12²
l² = 81 + 144
l² = 225
l = √225
l = 15cm
SA of cone 1
= πrl
= π × 9 × 15
= π × 135
= 135π
l of cone 2
l² = r² + h²
l² = 9² + 40²
l² = 81 + 1600
l² = 16081
l² = 126cm
SA of cone 2
= πrl
= π × 9 × 126
= π × 1134
= 1134π
SA of solid
= 135π + 1134π
= 1269π
ASAP PLEASEHELP ME WILL GIVE 50 POINTS AND MARK BRAINLIEST
A company has released the following possible designs for a new cereal box. The cost of production depends upon the cost of materials, which is determined by how much material is used. The amount of material used is equal to the surface area of the package plus some overlap. The amount of product contained in the package is the volume of the packaging.
Find the surface area and volume of the following possible cereal boxes. Determine the cost of making the cereal box assuming that cardboard costs $0.05 per square inch.
Change a speed of 630 kilometres per hour to a speed in metres per second. Show your working
Answer:
1750 m/s
Step-by-step explanation:
1km = 1000m
1 hour = 60 minutes = 3600 seconds
( 630 * 1000 )/ (60 * 60)
= 1750 m/s
someone please help find the perimeter
Answer:
26 metres
Step-by-step explanation:
(Assuming this is for the whole shape)
5 + 5 + 4 + 8 + 4
= 26 m
A philanthropist pledges to donate 18% of a
fund each year. If the fund initially has
$699,000.00, how much will the fund have
after 8 years?
Answer:
87.375
Step-by-step explanation:
i think it that because you haft to do divison
At lunch, kira eats either a burrito containing 490 milligrams of sodium or a peanut butter sandwich containing 700 milligrams of sodium. her doctor told her to reduce her sodium to no more than 4,000 milligrams per week. which inequality represents x, the number of microwave burritos, and y, the number of peanut butter sandwiches, she can eat each week? 490x 700y < 4000 490x 700y ≤ 4000 490x 700y > 4000 490x 700y ≥ 4000
The inequality represents x, and y, she can eat each week is,
490x+700y \leq 4000.
x be the number of microwave burritos
y be the number of peanut butter sandwiches
we know that
[tex]490x+700y \leq 4000[/tex].........inequality that represents the situation
What is the meaning of inequality?The mathematical expression in which the sides of an equation are not equal to each other.
we use a graphing tool
The solution is the shaded area
Please find the attached figure
Therefore,the answer is 490x+700y \leq 4000
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What is the area, in square feet, of the rectangle shown below?
Answer:
Step-by-step explanation:
A = l x w
l = length
w = width
Formula:
6 4/5 x 4 3/4
First, multiplying the integers:
6 x 4 = 24
Then you multiply the fractions(top x top and bottom times bottom):
4/5 x 3/4 = 12/20
Simplify:
12/20 = 3/5
Giving you 24 3/5
I hope this helps :)
Using ε − δ definition of a limit, show that limx→2
x+1
x =
3
2
The [tex]\lim_{x \to 2} x+1=2+1=3[/tex] using the ε − δ definition of a limit.
ε − δ definition of a limit?Epsilon-Delta defines a limit at a finite point that has a finite value.
To find the limit, two variables, delta (δ) and epsilon (ε) are first created then the epsilon region is choosen so as to define a delta region.
[tex]\lim_{x \to 2} x+1=2+1=3[/tex]
The [tex]\lim_{x \to 2} x+1=2+1=3[/tex] using the ε − δ definition of a limit.
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PLEASE HELP VERY URGENT
Suppose you know the following facts about angle ABC and angle DEF: (1) both triangles have sides of length a and b (2) For angle ABC, a^2 + b^2 = c^2 (3) For angle DEF, angle F is a right triangle. Use the list of expressions below to find the value of c in angle ABC and the length of the hypotenuse of angle DEF.
The value of c in angle ABC is _______ and the length of the hypotenuse of angle DEF is ________.
A. square root of a^2 + b^2
B. a^2 + b^2
C. b^2 - a^2
D. square root of a^2 - b^2
E. a^2 - b^2
F. square root of b^2 - a^2
(if u have trouble reading the text look at the attached photo for the question)
Answer:
A. square root of a^2 + b^2 for both answers
Step-by-step explanation:
The first problem, we are given
a^2 + b^2 = c^2
What we do is solve for c.
sqrt(a^2 + b^2) = c
c = sqrt(a^2 + b^2)
For problem 2,
WE can apply the Pythagorean theorem because we have a right triangle.
The equations is
a^2 + b^2 = c^2 like the first problem
Solving gets us
sqrt(a^2 + b^2) = c
c = sqrt(a^2 + b^2)
Q1- Tommy pays $22.50 for 2.6 pounds of salmon. What is the price per pound of salmon?
Q2- The cost of 3 pounds of grapes is $6.57. What is the constant of proportionality that relates the cost in dollars, y, to the number of pounds of grapes, x?
Q3- 1/2 of a pizza cost $9.50. How much would it cost for one whole pizza?
Q4-The cost of 1/4 cup of ice cream is $3.00. How much would it cost for one whole cup?
A local weather enthusiast wants to see if the last five summers have been warmer than normal for eloy, arizona. from the national oceanic and atmospheric administration (noaa), he knows the 30-year average for july was 90° with a standard deviation of 2.1°. the last five summers recorded have an average of 93.5°. if he uses a = 5%, which of the following would be valid based on the data he has gathered? he can conclude that the summers have been warmer than the 30-year average. he can conclude that the summers will continue to be warmer for the next 10 years. he does not have enough information to make a decision. the average for the last five years fits with the 30-year average.
For the local weather of Eloy, Arizona, the average for the last five years fits with the 30-year average.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of a population
N = number of observations of population
X = mean
μ = population mean
The 30-year average for July was 90°. The standard deviation for this average is 2.1°. Thus, the temperature lies in the range around of 90° in July.
Therefore, the range of the temperature is,
t = 90 - 2.1 = 87.9
t = 90 + 2.1 = 92.1
The last five summers recorded have an average of 93. 5° and the value of a is 5%. Thus, the reduction is,
t = 92 - (92 x 2.5/100)
t = 89.70
This value of temperature lies in the range of 87.9-92.1 degrees Celsius. Hence, the two averages are probably the same.
Hence, for the local weather of Eloy, Arizona, the average for the last five years fits with the 30-year average. Option D is correct.
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Answer:
D, The average for the last five years fits with the 30-year average.
Step-by-step explanation:
edge
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
1) x=−y-2
2)x=−y+2
Step-by-step explanation:
Let's solve for x.
y=−x−2
Step 1: Flip the equation.
−x−2=y
Step 2: Add 2 to both sides.
−x−2+2=y+2
−x=y+2
Step 3: Divide both sides by -1.
x=−y−2
Let's solve for x.
3x+3y=6
Step 1: Add -3y to both sides.
3x+3y+−3y=6+−3y
3x=−3y+6
Step 2: Divide both sides by 3.
x=−y+2
please help with this math question sceenshot below
Answer:
that would be the second option (-4,7)(-7,0)(-1,0)
Step-by-step explanation:
The answer is given away once you translate point S to the right 2 and down 3 making the point (-4,7) and there is only one answer with that point.
Koro - Sensei has 8 more students in his class than Ms.Fizzle. They have a total of 32 students together. Calculate the number of students in Koro - Sensei's class
Answer:
Koro-Sensei's class has 20 kids in it.
Step-by-step explanation:
This is simple.
Ex: 20-12 = 32
3. What is the surface area of this composite solid? Show your work.
5 ft
5 ft
3 ft
4 ft
10 ft
8 ft
By finding the area of the simpler parts, we will see that the total surface area of the figure is 348 ft^2
How we do get the surface area?
We can divide this in smaller parts. First, remember that for a triangle of base b and height h, the area is:
A = b*h/2
Then for each of the triangles in the image, the area is:
A = 8ft*3ft/2 = 12 ft^2
And we have two of these.
Then we have the base, a rectangle of 8ft by 10ft, with an area:
A' = 8ft*10ft = 80ft^2
Then we have the front and back sides, rectangles of 8ft by 4ft, with an area:
A'' = 8ft*4ft = 32 ft^2 (we have two of these).
Then the lateral sides, rectangles of 10ft by 4ft, with an area:
A''' = 10ft*4ft = 40ft^2 (we have two of these)
Finally, we have the top rectangles, of 5ft by 10ft, each with an area:
A'''' = 5ft*10ft = 50ft^2 (we have two of these).
Adding all the areas, we get:
Area = 2*(12 ft^2 + 32 ft^2 + 40ft^2 + 50ft^2) + 80ft^2 = 348 ft^2
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Andy is building a model train. A train in real life has a wheel diameter of 33 inches, a length of 20 feet, a width of 10 feet, and a height of 12 feet. If his model has a width of 8 inches, what does the height need to be?
A) 0.96 inches
B) 9.6 inches
C) 16 inches
D) 48 inches
Answer: B) 9.6 inches
Step-by-step explanation:
We will set up a proportion to solve. I will have the width of the model (in inches) as my numerator, and the height of the model (in inches) as the denominator.
-> To convert feet into inches, we multiply by 12.
[tex]\displaystyle \frac{120}{144} = \frac{8}{x}[/tex]
Cross multiply:
120 * x = 144 * 8
120x = 1,152
Divide both sides of the equation by 120:
x = 9.6
9.6 inches
The height should be B) 9.6 inches.
Wendell is building a doghouse using these pieces of wood:
The pieces of wood to build a doghouse with the highest point to the lowest point of 28 inches.
Each length with one mark (I) is 36 inches. Each length with two marks (II) is 18 inches. Each length with three marks (III) is 30 inches. Each end has a height (from the highest point to the lowest point) of 28 inches.
The doghouse will have the shape shown once it is built.
The shape of the doghouse.
Part A
If Wendell were to slice the doghouse in half with a slice parallel to the pentagonal bases, what shape would the slice be?
If Wendell were to slice the doghouse in half with a slice parallel to the pentagonal bases, the shape of the slice would be a pentagon.
What is a solid figure?A solid figure is a three dimensional shape having length, width and height. Examples of solid figures are cylinders, cone, pyramid and prism.
The shape represented by the doghouse would be a pentagonal prism. If Wendell were to slice the doghouse in half with a slice parallel to the pentagonal bases, the shape of the slice would be a pentagon.
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The speed of the jet Alyssa flew on from Boston to London was 480
mph. On her return flight, the speed of the jet was 600 mph with a tail
wind. What was Alyssa's average speed on the round trip? Round your
answer to one decimal place.
Please help ASAP!!!
Will mark brainiest!!!!!
Answer:
533.3 mph
Step-by-step explanation:
You want the average round-trip speed if the speed to London was 480 mph and the return trip to Boston was 600 mph.
SpeedThe average speed will be the total distance divided by the total time. The time is found by dividing the distance by the speed.
If the distance is d, the total time in hours is ...
d/480 +d/600 = (3/800)d . . . . . hours
Then the average speed is ...
2d/(3/800d) = 1600/3 ≈ 533.3 . . . . miles per hour
Alyssa's average speed on the round trip was 533.3 mph.
__
Additional comment
In the real world, eastbound speeds are usually faster than westbound speeds.
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Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1? f(x) = 3x2 5x 4 f(x) = 3x2 15x 12 f(x) = 3x2 – 5x 4 f(x) = 3x2 – 15x 12
A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is: [tex]3x^2-15x+12[/tex]
What is polynomial?An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
For this case we have that the following function complies with the given conditions:
[tex]f(x)=3x^2-15x+12[/tex]
To prove it, let's find the roots of the polynomial:
[tex]3x^2-15x+12=0[/tex]
By doing common factor 3 we have:
[tex]3(x^2-5x+4)=0[/tex]
Factoring the second degree polynomial we have:
[tex]3(x-1)(x-4)=0[/tex]
Then, the solutions are:
Solution 1:
[tex]x-1=0 \ or \ x=1[/tex]
Solution 2:
[tex]x-4=0\ \ or \ x=4[/tex]
Hence A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is:[tex]3x^2-15x+12[/tex]
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Answer:
f(x) = 3x² – 15x + 12
Step-by-step explanation:
I got it right on the unit test for edge
Suzie paid a total of \$324$324dollar sign, 324 for xxx tickets to a rock festival.
How much did each ticket cost?
Write your answer as an expression
Answer:
324 over x is the answer
Step-by-step explanation:
khan told me.
ik ur searching probs from khan hehe plol
The cost of each ticket as an expression is $324/x
Ratio and proportionRatios are written as fractions. For instance a/b can be written as a:b.
If Suzie paid a total of $324 for x ticket to rock a festivel, this is expressed as;
$324 = x ticket
The cost of each ticket is given as;
y = 1 ticket
324/y = x/1
y = 324/x
Hence the cost of each ticket as an expression is $324/x
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#SPJ6
y + 6 = 5(x – 4)
Write a formula fpr f(x) in terms of x.
Answer:
f(x) = 5x - 26
Step-by-step explanation:
y + 6 = 5(x - 4) ← distribute parenthesis by 5
y + 6 = 5x - 20 ( subtract 6 from both sides )
y = 5x - 26
Now y = f(x) , then
f(x) = 5x - 26
Answer:
f(x) = 5x - 26
Step-by-step explanation:
y + 6 = 5(x – 4)
Distribute
y +6 = 5x - 20
Solve for y
y +6-6 = 5x-20+-6
y = 5x - 26
Replace y with f(x)
f(x) = 5x - 26
Riley drank 8/10 quart of iced tea and her friend drank 0.3 quart. How much more of a quart of iced tea did Riley drink than her friend?
Answer:
1/2
Step-by-step explanation:
0.3 can be converted into 3/10. TO find out how much more of a quart of iced tea that Riley drank than her friend, we have to subtract the amount of iced tea that her friend drank from the amount that Riley drank.
8/10 - 3/10 = 5/10
Now, we have the opportunity to simplify the fraction. 5/10 is the same as 1/2. Therefore, Riley drank 5/10, or 1/2, more than her friend. I hope this helps! Have a lovely day!! :)
4+2 (x-1)=13
Find the value of for X
(Show working out)
Answer:
[tex]x = \frac{11}{2}[/tex]
Step-by-step explanation:
4+2 (x-1)=13
⇒ 2 (x - 1) = 13 - 4
⇒ 2 (x - 1) = 9
⇒ 2 x - 2 = 9
⇒ 2 x = 9 + 2
⇒ 2 x = 11
⇒ x = 11/2
Which function is represented by this graph?
O A. 1x) = |x+7|-3
O B. 1x) = |x-7| -3
O C. 1x) = |x+3|-7
O D. 1x) = |x-3|- 7
how do you do this???
Answer:
A = 15 units²
Step-by-step explanation:
Count the squares:
AB (height) = 6 units
CB (base) = 5 units
A = bh/2
A = (5)(6)/2
A = 30/2
A = 15 units²
I hope this helps!
Which expression represents the surface area of the pyramid?
Answer:
option d
Step-by-step explanation:
36+15+15+15+15
I hope it helped you
Barbara got a flat tire and does not have a spare. she needs her car for work, so she goes to a business that offers payday loans in order to get the money to buy a new tire. she borrows $75 and plans to pay it back when she gets paid in 8 days. barbara is charged a fee of $15 and the term on her loan is 8 days. approximately what is the annual percentage rate on her loan? a. 228% b. 487% c. 913% d. 973%
The annual percentage rate of the loan is approximately 913%. option c is correct.
What is the annual percentage?The yearly interest earned by an amount charged to borrowers or paid to investors is referred to as the annual percentage rate.
APR is a percentage that indicates the real annual cost of money for a loan or investment over the period of the loan.
The amount borrowed = $75
no of days =8 days
Fees charged = $15
The annual percentage is found as;
[tex]\rm r = \frac{final \ value}{initial \ value } -1 \\\ \rm r = \frac{f 90}{75 } -1 \\\\ r=0.20 \\\\[/tex]
If the rate of interest is 20% then the annually the rate is obtained as;
[tex]\rm r_{annual}= \frac{0.20}{8 \ days} \times \frac{365}{1 \ year} \\\\ \rm r_{annual}=913 /year[/tex]
Hence the annual percentage rate of the loan is approximately 913%. option c is correct.
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Answer:
C
Step-by-step explanation:
Barbara got a flat tire and does not have a spare. She needs her car for work, so she goes to a business that offers payday loans in order to get the money to buy a new tire. She borrows $75 and plans to pay it back when she gets paid in 8 days. Barbara is charged a fee of $15 and the term on her loan is 8 days. Approximately what is the annual percentage rate on her loan?
a.
228%
b.
487%
c.
913%
d.
973%
C
What is the surface area of the right cone below?
A. 3047 units-
B. 4967 units?
C. 1841 units-
D. 248 units
Answer:
184π units²
Step-by-step explanation:
see attached for reference
given sloped height = 15 units
base radius = 8 units
the height of the cone can be found by using the Pythagorean equation
(sloped height)² = height ² + (base radius)²
15² = h² + 8²
h² = 15²-8² = 161
h = √161
Base surface area = πr² = π 8² = 64π units²
Lateral Surface Area,
= πr √(r² + h²)
= π(8) √[ (8)² + (√161)² ]
= 8π√(64 + 161)
= 8π√225
= 8π (15)
= 120π
Surface area = base area + lateral surface area
= 64π + 120π
= 184π units²
Answer:
C. 184π units²Step-by-step explanation:
Surface Area of a cone : πrl + πr² = πr(l + r)
r = radiusl = slant heightSolving
SA = π x 8 (15 + 8)SA = π x 8 x 23SA = 184π units²What is the volume of the right triangular prism shown below?
V = Bh
b = 1/2bh
Answer:
165
Step-by-step explanation:
V=BH
B=[tex]\frac{1}{2\\}[/tex]BH
V=([tex]\frac{1}{2}[/tex] x 5 x 6) x 11
V= ([tex]\frac{30}{2}[/tex]) x 11
V= 15 x 11
V= 165 f[tex]t^{2}[/tex]
Quest
answe
Ms. Miller's English class kept track of how many books they read last school year.
Books read
13
41
24
97
67
103 75 120
27
53
39
108 49
111
84
44
20
Time
elapse
Which box plot represents the data?
00 12
HR MIN
Books read
SmartSc
out of 100
63
20
40
60
80
100
120
Books read
20
40
60
80
100
120
Answer:
cde
Step-by-step explanation:
thx everyone hahahhahaahha