Answers
[tex]\sum_{i=1}^{4}4(5)^{i-1} = (4(5)^{1-1}) + (4(5)^{2-1}) + (4(5)^{3-1}) + (4(5)^{4-1})[/tex]
[tex]=4+20+100+500 = 624 [/tex]
[tex]\sum_{i=1}^{5}3(4)^{i-1} = (3(4)^{1-1}) + (3(4)^{2-1}) + (3(4)^{3-1}) + (3(4)^{4-1}) + (3(4)^{5-1})[/tex]
[tex]=3+12+48+192+768=1023[/tex]
[tex]\sum_{i=1}^{2}5(6)^{i-1} = (5(6)^{1-1}) + (5(6)^{2-1})[/tex]
[tex]=5+30=35[/tex]
[tex]\sum_{i=1}^{4}5^{i-1} = (5^{1-1})+(5^{2-1})+(5^{3-1})+(5^{4-1}) [/tex]
[tex]=1 + 5+ 25+125 = 156[/tex]
So, our totals are: 624, 1023, 35, and 156. So clearly, 1023 > 624 > 156 > 35. W can write it as (your answer):
[tex]\sum_{i=1}^{2}5(6)^{i-1} <\sum_{i=1}^{4}5^{i-1} <\sum_{i=1}^{4}4(5)^{i-1} < \sum_{i=1}^{5}3(4)^{i-1} [/tex]
Hope this helps! If anything is confusing, you can always DM me.
∑ 4 * 5^(i-1) = 4 + 20 + 100 + 500 = 624
∑ 3 * 4^(i-1) = 3 + 12 + 48 + 192 + 768 = 1,023
∑ 5* 6^(i-1) = 5 + 30 = 35
∑ 5^(i-1) = 1 + 5 + 25 + 125 = 156
Answer:
∑ (i=1, 2) 5 * 6^(i-1) < ∑ (i=1, 4) 5^(i-1) < ∑ (i=1, 4) 4 * 5^(i-1) <
< ∑ (i=1, 5) 3 * 4^(i-1)
Related Questions
Is the number written in scientific notation? If not, explain.
a. 0.15 x 104
b. 7.06 x 10−8
c. 3.3 x 10012
Answers
The second example (7.06 x 10^-8) is correctly written in scientific notation, but the first (0.15 x 10^4) and third (3.3 x 100^12) examples are not. In scientific notation, the decimal part of the number should be between 1 and 10 and the exponent of 10 should be an integer.
Explanation:The topic is scientific notation. The number is expressed in scientific notation if it has the form a × 10^n, where 1 ≤ |a| < 10 and n is an integer.
Let's see if the given numbers are in scientific notation:
0.15 x 10^4 - No, this is not in scientific notation. The decimal part of the number, 0.15, is not between 1 and 10.7.06 x 10^−8 - Yes, this is correctly written in scientific notation. The decimal part of the number, 7.06, is between 1 and 10 and the power of 10 is an integer.3.3 x 100^12 - No, this is not in scientific notation. The power of 10 is supposed to be a straight integer, not another exponential number.Learn more about Scientific Notation here:https://brainly.com/question/16936662
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option b ( 7.06 x 10⁻⁸)
a. 0.15 x 104
No, this number is not written in proper scientific notation.
In scientific notation, the coefficient must be a number between 1 and 10.
So, 0.15 can be expressed as 1.5 by moving the decimal point one place to the right.
Hence, it should be written as 1.5 x 103.
b. 7.06 x 10-8
Yes, this number is written in proper scientific notation.
The coefficient, 7.06, is correctly between 1 and 10.
c. 3.3 x 10012
No, this number is not written correctly due to the format of the exponent.
The correct form should be 3.3 x 1012.
So, the corrected scientific notation is 3.3 x 1012.
Help please, explain each step or no points.
Answers
pop/500 = 5/7
pop = 500*5/7 ≈ 357
357 of the next 500 songs downloaded are expected to be pop songs.
Tropical forests are being lost at the rate of 5 million hectares per year. how many hectares per day is that? how many hectares per minute?
Answers
365 days in a year
1440 minutes in a day (24hrs)
A recipe cal for 2 1/2 cups of flour to make 2 dozen cookies.How many cups of flour would be required to bake 15 dozen cookies
Answers
2 1/2 * 7 1/2 = 18 3/4 cups of flour
2 1/2 = 2.5 as a decimal
2.5 ÷ 2 = 1.25
So, it takes 1.25 (1 1/4) cups of flour for each dozen of cookies.
1.25 × 15 = 18.75
ANSWER:
18.75 (18 3/4) cups of flour would be required to bake 15 dozen cookies.
Answer ASAP
Find the area
Answers
In this problem, you are asked to find the area of the trapezoid. The formula in finding the area of the trapezoid is:
A = [(a + b)/2] x h
Where a = base 1
b = base 2
h = height
Substituting the given measurements to the formula:
A = [(1.7 m + 6.7 m) / 2] x 5 m
A = (8.4 m / 2) x 5 m
A = 4.2 m x 5 m
A = 21 m^2
Therefore, the area of the trapezoid is 21 square meters.
Your sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks. you reach into the drawer in the dark and randomly pick out 2 pairs for your business trip. what is the probability your pick out in this order. 2 black pairs?
Answers
Black socks: 3
Probability to pick out black socks: 3/13
After one pick out (You picked out a pair of black socks):
Probability to pick out black socks: 2/12
Multiply them:
2/12 * 3/13 = 1/26 ≈ 0,038
The probability your pick out in this order 2 black pairs 1/26.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Mathematics to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory.
According to the question,
The sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks.
All socks together = 3+4+5 = 13
Black socks = 3
Probability to pick out black socks: 3/13
After one pick out (You picked out a pair of black socks),
Probability to pick out black socks: 2/12
Then, the probability = 2/12 × 3/13 = 1/26.
Hence the required probability = 2/12 × 3/13 = 1/26.
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what is 62% of 25 ?
im horrible at this plz help
Answers
Convert 62% into a decimal: 0.62. Then multiply them: 0.62 · 25, which equals 15.5 !
'of' means multiplication.
[tex]\sf 62\%\times 25[/tex]
Convert 62% to a decimal, divide it by 100(since percentages are parts of 100):
62/100 = 0.62
[tex]\sf 0.62\times 25[/tex]
Multiply:
[tex]\sf\boxed{\sf 15.5}[/tex]
HELP WITH THESE SERIES OF QUESTIONS!!
1. Factor the polynomial. 3x^3 − 27x^2 + 19
2. Factor the polynomial. 15z^3 + 25z^2
3. Factor the polynomial. 9x^7 + 33x^3
Answers
2. 5x^2 x (3x+5)
3. 3x^3 x (3x^4 +11)
Stacy fails 1/2 cup measuring cup seven times to have enough flour for cake recipe how much flour does the cake recipe call for
Answers
7 times of 1/2 cup = 7/2
7 times of 1/2 cup = 3 1/2 cups.
--------------------------------------------------
The recipe called for 3 1/2 cups of flour
--------------------------------------------------
solving the whole thing
Answers
x---------------> distance from people living to the city center
we Know that
Zone 1 covers people living within three miles of the city center
Zone 1 ------------> [x < 3 miles]
Zone 2 covers those between three and seven miles from the center
Zone 2 ------------> [ 3 <= x < = 7 miles]
Zone 3 covers those over seven miles from the center
Zone 3 ------------> [ x > 7 miles]
calculate the distance between two points to find the value of x
case A) point (0,0) point (3,4)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(4-0)² +(3-0)²]------> √[16+9]
x=√25-------------> x=5 miles
the answer Part A)
people living in (3,4)
x=5 miles -------------> covers Zone 2 [ 3 < =x <= 7 miles]
case B) point (0,0) point (6,5)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(5-0)² +(6-0)²]------> √[25+36]
x=√61-------------> x=7.81 miles
the answer Part B)
people living in (6,5)
x=7.81 miles -------------> covers Zone 3 [ x > 7 miles]
case C) point (0,0) point (1,2)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(2-0)² +(1-0)²]------> √[4+1]
x=√5-------------> x=2.23 miles
the answer Part C)
people living in (1,2)
x=2.23 miles -------------> covers Zone 1 [ x < 3 miles]
case D) point (0,0) point (0,3)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(3-0)² +(0-0)²]------> √[9]
x=√9-------------> x=3 miles
the answer Part D)
people living in (0,3)
x=3 miles -------------> covers Zone 2 [ 3 < =x <= 7 miles]
case E) point (0,0) point (1,6)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(6-0)² +(1-0)²]------> √[36+1]
x=√37-------------> x=6.08 miles
the answer Part E)
people living in (1,6)
x=6.08 miles -------------> covers Zone 2 [ 3 < = x <= 7 miles]
what is the inverse and then graph the function and its inverse f(×)=-5n-14
Answers
The inverse is x = -5y - 14 Now solve for y
x + 14 = - 5y
y = (x + 14)/-5 I have included a graph to show these two relationships.
Red Line: y = -5x - 14
Blue Line: y = (x + 14)/-5
1000p for an answer please
Answers
A 3 lb bag of one brand of cat food costs $3.52. A 6 lb bag of another brand costs $6.80. Which brand is cheaper per pound?
Answers
We have then:
Mark 1:
3 lb costs $ 3.52
P = (3.52) / (3) = 1.17 $ / lb
Mark 2:
6 lb costs $ 6.80
P = (6.80) / (6) = 1.13 $ / lb
Answer:
Mark 2 is cheaper per pound:
1.13 $ / lb
Will give Metal! From 1948 to 1994, South Africa existed under a system of apartheid. Under this system, white South Africans- about 18% of the population- controlled all of the instruments of government: the Parliament, the Executive Branch, and the courts. Black and non-white South Africans had few legal rights and could not vote in elections. Voting was limited to white South African citizens. . This passage is describing what type of government? A) autocratic B) democratic C) dictatorship D) oligarchic,
Answers
How do I solve these trigonometric equations!!?
Find all solutions in the interval [0, 2π).
(sin x)(cos x) = 0
Find all solutions in the interval [0, 2π).
cos2x + 2 cos x + 1 = 0
Find all solutions to the equation.
cos2x + 2 cos x + 1 = 0
(I am not looking for easy answers to cheat, I just need help on how to solve them...Im a bit confused and my teacher is not avail),
Answers
What is the inverse of f(x) = 8x - 7
Answers
Work:
Y=8x-7 —> x=8y-7
Solve for y
x+7=8y
y=(x+7)/8
The inverse of the function f(x) = 8x - 7 can be found by switching the x and y, then solving for y. This gives the inverse function as f^-1(x) = (x + 7) / 8.
Explanation:The inverse of a function is calculated by switching the input and output variables. Given your question, we are to find the inverse of the function f(x) = 8x - 7. To do this, we first rename f(x) as y, giving us y = 8x - 7.
Next, we switch the positions of x and y, leading to x = 8y - 7. Then, to isolate y which represents the inverse function, we should solve the equation for y: x + 7 = 8y and y = (x + 7) / 8. So, the inverse of the function f(x) = 8x - 7 is f^-1(x) = (x + 7) / 8.
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A system of inequalities is graphed below. The variable x represents the number of cans someone is buying, and y represents the number of bottles. Conditions on the maximum amount of total weight and volume lead to two of the inequalities.
Which descriptions correspond to solutions of this system?
7 cans and 140 bottles
12 cans and 40 bottles
8 cans and 120 bottles
9 cans and 70 bottles
Answers
We will analyze each case to verify the answer
see the attached figure
Point A) 7 cans and 140 bottles------------> (x,y)=(7,140)----> is not solution
Point B) 12 cans and 40 bottles------------> (x,y)=(12,40)----> is not solution
Point C) 8 cans and 120 bottles------------> (x,y)=(8,120)----> is a solution
Point D) 9 cans and 70 bottles------------> (x,y)=(9,70)-------> is a solution
the answer is
the solutions are
8 cans and 120 bottles
9 cans and 70 bottles
the distance between between two distinct points on number line is always greater than zero?
true or flase,
Answers
Solve for x.
2x = 15 + x
Answers
The solution to the equation is x = 15.
We have,
To solve the equation 2x = 15 + x, we want to isolate the variable x on one side of the equation.
First, we can simplify the equation by subtracting x from both sides:
2x - x = 15 + x - x
This simplifies to:
x = 15
Thus,
The solution to the equation is x = 15.
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Which solid has six faces, four lateral faces, two bases, eight vertices, and 12 edges? square pyramid triangular prism rectangular prism triangular pyramid
Answers
*********************************************
Answer:
Rectangular Prism
Step-by-step explanation:
Select the ratios whose simplest form is 8/7
Answers
16:14
56:49
I hope this helps.
Answer:
48:42
16:14
56:49
Step-by-step explanation:
I hope I made your day
Glamour runs 2/3 mile each day she wants to know how many days she has to run before she has run a whole number of miles
Answers
2/3 × 1 = 2/3
2/3 × 2 = 4/3 (or 1 1/3)
2/3 × 3 = 2
You can also convert 2/3 to a decimal by dividing the numerator by the denominator and then multiply that to get a whole number.
ANSWER:
Glamour will have to run for 3 days to run a whole number of miles. The whole number is 2.
Michelle, Jennifer, and Betty volunteered to make cupcakes for a school fundraiser. They've been asked to make 100 cupcakes. Michelle can make 6 cupcakes in an hour. Jennifer can make 18 cupcakes in two hours. Betty can make 24 cupcakes in two hours. How long will it take to make 100 cupcakes if they work together?
A. 3 19/27 Houurs
B. 2 2/9 Hours
C. 4 1/6 Hours
D. 1 23/27 Hours
Answers
Final answer:
Michelle, Jennifer, and Betty have a combined rate of 27 cupcakes per hour. To make 100 cupcakes, it will take them 100 divided by 27, which equals 3 19/27 hours. The correct answer is A. 3 19/27 hours.
Explanation:
To determine how long it will take Michelle, Jennifer, and Betty to make 100 cupcakes together, we first need to find their individual rates of production.
Michelle makes 6 cupcakes per hour.
Jennifer makes 18 cupcakes in 2 hours, which is equivalent to 9 cupcakes per hour.
Betty makes 24 cupcakes in 2 hours, which is equivalent to 12 cupcakes per hour.
Adding these rates together gives us a combined rate of:
6 + 9 + 12 = 27 cupcakes per hour.
To find the time it takes to make 100 cupcakes, we divide the total number of cupcakes by the combined rate:
100 cupcakes ÷ 27 cupcakes/hour = 3 19/27 hours.
Therefore, the correct answer is A. 3 19/27 hours.
1. _____is when an asset increases in value.
~depreciation
~appreciation
~inflation
~purchasing power
2. when money loses some of its value over time, it is caused by_____
-inflation
-FICA
-purchasing power
-recalculating worth
ive tried i need help @bibby @phi someone :( @SolomonZelman,
Answers
1) Appreciation is when an asset increases in value.
2) When money loses some of its value over time, it is caused by inflation
The appreciating assets is any asset which value is increasing it is a an increased demand.
Therefore,
When value of assets increases in value?
Appreciation
1) Appreciation is when an asset increases in value.
Next,
The impact inflation has on the time value of money is that decrease the value of dollar over time.
Therefore,
2) When money loses some of its value over time, it is caused by inflation
Therefore,
1) Appreciation is when an asset increases in value.
2) When money loses some of its value over time, it is caused by inflation
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need help !!!Divide 5a^2 + 6a - 9 into 25a^4 + 19a^2 - a - 78.
Answers
Maybe i have not understood "into".
[tex] \dfrac{25a^4+19a^2-a-78}{5a^2+6a-9} =5a^2-6a+20+ \dfrac{-175a+102}{5a^2+6a-9} [/tex]
A credit card advertises an annual interest rate of 23%.
What is the equivalent monthly interest rate?
i=__^_t
Answers
the monthly rate is:
[1 + 23%]^(1/12) =1.23^(1/12) =1.0174 - 1 x 100 =1.74%
A scientist has 350 mg of a radioactive material. The material will cut in half every month. After how many months will there be .68mg left?
Answers
A total of 100 students play on the Sports Academy’s soccer, track, or basketball teams. No student plays on more than one team. 61 of the students are boys. There are 36 students on soccer teams, 19 are on the girls’ soccer team. There are 35 students on basketball teams, 18 are on the boys’ basketball team. How many boys are on the track team?
Answers
18+17 =35
61-35= 26
26 boys are on the track team.
There are 17 boys on the soccer team, 18 on the basketball team, and by subtracting the 35 boys playing these sports from the total of 61 boys, we find that there are 26 boys on the track team.
To find out how many boys are on the track team, we can start with the total number of boys, which is 61, and subtract the number of boys in the other two teams. We know that there are 36 students on the soccer teams, and 19 of them are girls, which means that 36 - 19 = 17 boys are on the soccer team. Next, there are 35 students on the basketball teams, and 18 of them are boys; thus we have 35 - 18 = 17 girls on the basketball team.
Now, let's add up the number of boys on the soccer and basketball teams to find out how many boys are left for the track team. The equation is 17 (soccer) + 18 (basketball) = 35 boys who are playing sports other than track. Finally, to get the number of boys on the track team, we subtract this sum from the total number of boys: 61 (total boys) - 35 (boys in other sports) = 26. This means that there are 26 boys on the track team.
Which expression represents the total surface area, in square meters, of the rectangular pyramid below?
Answers
h= hight of triangle
b= base
l= lenght
b= breath
Answer:
B
Step-by-step explanation:
:)
If mike drank more than half the juice inhis glass.what fraction of the juice could mike have drunk.