The equation that represents the partial sum of the geometric series is 125, 25, 5, 1
Given the partial sum of a geometric sequence expressed as:
[tex]\sum\left { n=4 \atop {n=1}} \right. 125(\frac{1}{5} )^{n-1}[/tex]
If n = 1, the
a(1) = [tex]125(\frac{1}{5} )^{1-1}\\[/tex]
a(1) = [tex]125(\frac{1}{5} )^{0}\\[/tex]
a(1) = 125
If n = 2
a(2) = [tex]125(\frac{1}{5} )^{2-1}\\[/tex]
a(2) = [tex]125(\frac{1}{5} )^{1}\\[/tex]
a(2) = 25
If n = 3
a(3)= [tex]125(\frac{1}{5} )^{3-1}\\[/tex]
a(3) = [tex]125(\frac{1}{5} )^{2}\\[/tex]
a(3) = 5
If n = 4
a(4)= [tex]125(\frac{1}{5} )^{4-1}\\[/tex]
a(4) = [tex]125(\frac{1}{5} )^{3}\\[/tex]
a(4) = 1
Hence the equation that represents the partial sum of the geometric series is 125, 25, 5, 1
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Answer:
a
Step-by-step explanation:
Emma is making a recipe that needs 2 1/2 cups of sugar. Each
scoop contains 1/4 cup of sugar. How many scoops of sugar
does she need to add for the entire recipe?
The given partial fraction divided by the fraction of sugar in a scoop is
equal to multiplying the partial fraction by the reciprocal of the fraction.
The number of scoops of sugar needed is 10 scoops.Reasons:
The amount of sugar the recipe Emma is making needs = 2 1/2 cups
Amount of sugar in each scoop of sugar = 1/4 cups
Required:
The amount of scoops Emma needs to add for the entire recipe
Solution:
The amount of sugar needed = 2 1/2 cups
Amount of sugar per scoop = 1/4 cups/scoop
Therefore;
[tex]\displaystyle Number \ of \ scoops = \mathbf{\frac{Cups \ of \ sugar \ needed}{Cups \ of \ of \ sugar \ per \ scoop}}[/tex]Which gives;
[tex]\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}}[/tex][tex]\displaystyle 2 \frac{1}{2} = \frac{5}{2}[/tex]
[tex]\displaystyle \frac{ \frac{5}{2}}{\frac{1}{4} } = \mathbf{ \frac{5}{2} \times \frac{4}{1} = \frac{20}{2 }} = 10[/tex]
Therefore;
[tex]\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}} = 10 \, scoops[/tex]
The number of scoops she needs for the entire recipe is 10 scoops
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-0.7=-7/9z help me pleasseeee!
The cost of a season train ticket is reduced by $87.36 which corresponds to a 39% reduction. Find the original cost of the season ticket.
at what rate of simple interest will ₹4400 amount to ₹5610 in 5 years 6 months
Answer:
0.05 or 5%
Step-by-step explanation:
The formula for simple interest is as follows:
A = P(1+rt), with A representing the final amount, P representing the initial amount, r being the rate, and t being time. Plugging our values in, we have
5610 = 4400(1+5.5r). We know that 5 years and 6 months is 5.5 because 6 months = 0.5 years
5610 = 4400(1+5.5r)
expand
5610 = 4400 + 24200r
subtract 4400 from both sides to isolate the variable and its coefficient
1210 = 24200r
divide both sides by 24200 to isolate the variable
r = 0.05 or 5% as 0.05 * 100 = 5
Jenny is saving money to buy a bike that costs $164. She has $52 and will save an additional $8 each week. In how many weeks will she have enough money to buy the bike?
Answer:
14
Step-by-step explanation:
164 = 8x + 52
Subtract 52 from both sides
112 = 8x
Divide both sides by 8
14 = x
help me please brainlist if right
Step-by-step explanation:
1B.) Zero power rule
C.) 1
2B.) Product of powers rule
C.) y^(7+11) = y^18
3B.) Quotient of powers rule
C.) b^(18-5) =b^13
4B.) Power of a power rule
C.) 3^(2×2) =3^4= 81
5B.) None
C.) 729
can sommeone help solve equation
Step-by-step explanation:
3x + 10 < 3
3x + 7 < 0
3x < -7
x < -7/3 = -2.3333...
or
2x - 5 >= 5
2x >= 10
x >= 5
x < -7/3 or x >= 5
The table below shows a correct representation that 15 pounds (lb) of sugar cost $3:
A. True
B. False
Answer:
A True
Step-by-step explanation:
A 9-foot roll of waxed paper costs $4.32. What is the price per inch?
The price per foot is $0.91
Step-by-step explanation:
A 6-yard roll of butcher paper costs 16.38
1 yard = 3 foot
6 yards = 3 times 6 = 18 foot
the cost of 18 foot is $16.38
To find price per foot, we divide the cost of 6 yards by 18
16.38÷ 18 = 0.91
The price per foot is $0.91
A line has a slope of 0 and passes through the point (10, 2). What is its equation in slope intercept form?
Answer:
y = 10
Step-by-step explanation:
y = m x + C, where m is the slope and c is the intercept on the y axis. Plugging in the values of m and C, we get: y = 0 x + 10 = 0 + 10 = 10. Therefore, y = 10.
The equation of line that passes through the point P ( 10 , 2 ) and has a slope of 0 is y = 2
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the point be represented as P ( 10 , 2 )
And ,let the slope of the line be m = 0
Slope m = 0
Now , the equation of line is given by the formula y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 2 = 0 ( x - 10 )
On simplifying the equation , we get
y - 2 = 0
Adding 2 on both sides of the equation , we get
y = 2
Therefore , the value of A is y = 2
Hence , the equation of line is y = 2
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The parallelogram has the angle measures shown. Can you conclude that it is a rhombus, a
rectangle, or a square? Explain.
Answer:
Rhombus
Step-by-step explanation:
The angles add up to 144 degrees, so they can't be a rectangle or a square. Also, diagonals of rhombuses bisect the angles.
A line passes through the points (-4,1) and (-3,3). This line can be modeled by the equation y = mx + b.
Complete the table to determine the values of m and b.
Answer:
m= 2
b=9
Step-by-step explanation:
-4, 1 -3,3
put it into y2-x2 divided by y1-x1
y2= 3
x2= 1
y1= -3
x1=-4
3-1 divided by -4--3= 2/1 =2x
get one of the points either -4,1 or -3,3
If you use -4,1 -4=x 1=y
put it into y=mx+b and you get 1= -4(2)+b simplify
1=-8+b add 8 to other side b=9
Marissa bought 3 chocolate bars each week. How many chocolate bars will Marissa buy after 3 weeks?
please help meeeeeeeeeeee....
ty
Answer:
y = 1/26x - 2
Step-by-step explanation:
Subtract x both sides
-26y = 52 + (-x)
Divide by -26 both sides
y = -2 + 1/26x
y = 1/26x - 2
Where did this student make the mistake when solving this inequality?
2x + 4 > 5x - 5
-2x -2x
4 < 3x - 5
+5 +5
9 < 3x
/3 /3 (divide by 3)
3 < x
options:
When subtracting the same value from both sides you don't need to switch the inequality sign
There is no mistake, it was solved correctly
You don't subtract 2x from each side, you add 2x to each side
When dividing by 3 you should switch the inequality sign
Answer:
You don't subtract 2x from each side, you add 2x to each side
Which ordered pairs are solutions to the inequality 2y-x≤-6 ?
a. (0,-3) b. (5,10) c. (2, -2) d. (-5, 2)
Answer:
C
Step-by-step explanation:
Find the equation of the line shown.
у
10
9
8
7
6
5
4
3
2
N
O
Х
1 2 3 4 5 6 7 8 9 10
The equation of the line shown is y = 4 x
What is a straight line?A straight line is the shortest distance between two points. the equation of straight line is represented as [tex]y = mx + c[/tex]
m is the gradient
y2, y1, x2, x1 are gotten from the graph
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
[tex]m = \frac{8 - 4}{2 - 1}[/tex]
[tex]m = \frac{4}{1}[/tex]
m = 4
c is the intercept on x-axis
from the graph c = 0
substituting the values give:
y = 4 x
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DONT ASNWER IF YOU DON"T KNOW THE ANSWER
Are the two triangles similar? Why or why not?
Jane wrote all the natural numbers from 1 to 12. including 1 and 12.
how many numbers did Jane write?
Answer:
12 numbers
Step-by-step explanation:
1,2,3,4,5,6,7,8,9,10,11,12
Please help I’ll mark brainliest!!!
Answer:
B
Step-by-step explanation:
As x gets bigger or smaller, y approaches negative infinity
Please help what is the answer its a math question find the lcd!!!
Step-by-step explanation:
sorry I don't now but when I now I will tell you ok but mybe it 12×12×12
10)
4x-9
X + 18
Solve for x
Answer:
x = 9
Step-by-step explanation:
The alternate interior angles theorem tells us that these two quantities must be the same.
Therefore,
x + 18 = 4x - 9
x + 18 + 9 = 4x
x + 27 = 4x
27 = 4x - x
27 = 3x
x = 9
---
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Fifteen cards numbered 1-15 are placed in a hat. What is the probability that the card has a multiple of 3 on it, given that the card picked is an odd
number? Express your answer as a fraction in simplest form.
The probability that the card has a multiple of 3 and an odd number is 20%.
How to find the card has a multiple of 3 on it, given that the card picked is an odd number?Given:
The number of cards: 15
Multiples of 3 and odd no are 3,9, and 15.
The number of cards Multiples of 3 and odd number = 3
Probability of getting a multiple of 3 cards = 3/15× 100
⇒ 20%
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.
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Which expression is equivalent to StartFraction RootIndex 7 StartRoot x squared EndRoot Over RootIndex 5 StartRoot y cubed EndRoot? Assume y not-equals 0. (x Superscript two-sevenths Baseline) (y Superscript negative three-fifths Baseline) (x Superscript two-sevenths Baseline) (y Superscript five-thirds Baseline) (x Superscript two-sevenths Baseline) (y Superscript three-fifths Baseline) (x Superscript seven-halves Baseline) (y Superscript negative five-thirds Baseline).
Answer:
[tex]\frac{5}{X^{2} } y^{2}[/tex]
Step-by-step explanation:
sorry the Y isn't under the 5 anyway hope this helped
Answer:
A is the answer.
Step-by-step explanation:
(X^7/2)(y^-3/5)
Acar moves at a constant speed of 50 miles per hour. How long
does it take the car to go 200 miles?
O 250 hours
150 hours
O 4 hours
O 10,000 hours
Answer:
4 hours · Speed = 50 mph · distance = time x speed · Time = 200 / 50 = 4 hours.
Step-by-step explanation:
7/24*5/14*16/25
PLS HELP!!!!!!!
7/24*5/14*16*25= 1/15
On a coordinate grid, point P is at (4, 3) and point R is at (−2, −5). Points Q and S are a reflection of both points across the x-axis. What are the coordinates of Q and S?
Q(−4, 3), S(2, −5)
Q(4, −3), S(−2, 5)
Q(−4, −3), S(2, 5)
Q(−4, 3), S(−2, 5)
Answer:
The answer would be B!
Step-by-step explanation:
Select all the polygons that have reflection symmetry.
A quadrilateral with two pairs of adjacent congruent sides, forming a kite.
A polygon is shaped like a composite figure made up of a rectangle with a small square on its top side and the same sized square on its right side.
A polygon shaped like a five-pointed star in which the left and right sides of the star are mirror images
A six-sided polygon that generally appears as a diagonally-oriented trapezoid attached to a shorter horizontally-oriented rectangle.
Assessment navigation
(added this for all^ my homies with k12 so its easier to find just ignore it)
Reflection Symmetry-
Line symmetry is also called as the reflection symmetry. If, at least one line that divides a figure into two halves such that one-half is the mirror image of the other half, exists, then the figure is said to be in reflection symmetry.
Analyzing all the 4 figures, it can be deduced that only 1st and 2nd figures have one symmetry line XX, as shown in the attachments.
3rd and 4th figures do not have any axisymmetric lines, so they are not in reflection symmetry.
How do I find x please I need help asap
Answer:
x=5
Step-by-step explanation:
Let's say the left side has points A, B, and C, with B in the middle, and the right side has points A, E, and D, with E in the middle
The Triangle Proportionality Theorem Converse states that if a line splits two sides of a triangle proportionally, the line is parallel to the remaining line.
Here, we can see that the sides are split into congruent lengths to each other, making their proportions 1:1. This proves the theorem converse, so 5x is parallel to 8x+10. Because the other two sides are connected to each other, with AB being a part of AC and AE being a part of AD, AB is parallel to AC and AE is parallel to AD. Given this, we can say that triangle ABE is similar to triangle ACD.
In a similar triangle, the lines corresponding to each other have the same ratio as other lines. This means that
AB/AC = AE/ED = BE/CD.
We are trying to find BE and CD to solve for x, and we can do this by finding the ratio between them
AC = AB + BC
BC = AB
AC = 2 * AB
AB / (2*AB) = BE / CD
1/2 = 5x/(8x+10)
multiply both sides by 2 to remove a denominator
1 = 10x / (8x+10)
multiply both sides by 8x+10 to remove the other denominator
8x+10 = 10x
subtract 8x from both sides to put the variable and its coefficients on one side
2x = 10
divide both sides by 2 to solve for x
x = 5
Alberta is going to take a 2-hour-26-minute flight from Chicago, Illinois, to
Denver, Colorado, that leaves at 11:49 a.m. Chicago time. If Illinois is in the
central time zone and Colorado is in the mountain time zone, what will be the
local time in Denver when the flight arrives?
Use the following to help you answer the question
12:00 p.m. eastern time = 11:00 a.m. central time = 10:00 a.m. mountain
time = 9:00 a.m. Pacific time.
A. 12:15 p.m.
B. 2:15 p.m.
C. 1:15 p.m.
D. 11:15 a.m.
SUBMIT
Answer: 1:15pm
Step-by-step explanation: