Match each series with the equivalent series written in sigma notation
Answers
Answer:
[tex]3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n[/tex]
[tex]4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n[/tex]
[tex]2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n[/tex]
[tex]3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
Match equivalent expressions
Solving (a):
[tex]3 + 12 + 48 + 192 + 768[/tex]
The expression can be written as:
[tex]3 \to 3*4^{0[/tex] --- 0
[tex]12 \to 3 * 4^{1[/tex] ---- 1
[tex]48 \to 3 * 4^{2[/tex] --- 2
[tex]192 \to 3 * 4^{3[/tex] ---- 3
[tex]768 \to 3 * 4^{4[/tex] ---- 4
For the nth term, the expression is:
[tex]Term = 3 * 4^{n[/tex] ---- n
So, the summation is:
[tex]3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n[/tex]
Solving (b):
[tex]4 + 32 + 256 + 2048 + 16384[/tex]
The expression can be written as:
[tex]4 \to 4 * 8^0[/tex] --- 0
[tex]32 \to 4 * 8^1[/tex] ---- 1
[tex]256 \to 4 * 8^2[/tex] --- 2
[tex]2048 \to 4 * 8^3[/tex] ---- 3
[tex]16384 \to 4 * 8^4[/tex] ---- 4
For the nth term, the expression is:
[tex]Term \to 4 * 8^n[/tex] ---- n
So, the summation is:
[tex]4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n[/tex]
Solving (c):
[tex]2 + 6 + 18 + 54 + 162[/tex]
The expression can be written as:
[tex]2 \to 2 * 3^0[/tex] --- 0
[tex]6 \to 2 * 3^1[/tex] ---- 1
[tex]18 \to 2 * 3^2[/tex] --- 2
[tex]54 \to 2 * 3^3[/tex] ---- 3
[tex]162 \to 2 * 3^4[/tex] ---- 4
For the nth term, the expression is:
[tex]Term \to 2 * 3^n[/tex] ---- n
So, the summation is:
[tex]2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n[/tex]
Solving (d):
[tex]3 + 15 + 75 + 375 + 1875[/tex]
The expression can be written as:
[tex]3 \to 3 * 5^0[/tex] --- 0
[tex]15 \to 3 * 5^1[/tex] ---- 1
[tex]75 \to 3 * 5^2[/tex] --- 2
[tex]375 \to 3 * 5^3[/tex] ---- 3
[tex]1875 \to 3 * 5^4[/tex] ---- 4
For the nth term, the expression is:
[tex]Term \to 3 * 5^n[/tex] ---- n
So, the summation is:
[tex]3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n[/tex]
Related Questions
70% in the SIMPLEST Form
Answers
Answer:
7/100
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 70 and 100 is 10
Divide both the numerator and denominator by the GCD
70 ÷ 10
100 ÷ 10
Reduced fraction:
7
10
Therefore, 70/100 simplified to lowest terms is 7/10.
which function is graphed below????
Answers
B. The sum of 3 and a number is -2, what is the number?
Answers
PLEASE HELP ME ASAP I NEED HELP
Answers
Answer:
4w = 25
w= 6.25
Step-by-step explanation:
We know that w + w + w + w is the same as 25 because the scale is balanced.
This is writted as 4w = 25
To solve for w, divide both sides by 4:
(4w)/4 = 25/4
w = 25/4
w = 6.25
pls answer me this :(
Answers
Answer:
GIVEN :-
[tex]x = -\frac{1}{2}[/tex][tex]y = \frac{2}{4} = \frac{1}{2}[/tex][tex]z= -\frac{2}{8} = -\frac{1}{4}[/tex]TO VERIFY :-
[tex]x + (y + z) = (x + y) + z[/tex]SOLUTION :-
L.H.S. =
[tex]x+ (y + z)[/tex]
[tex]=> -\frac{1}{2} + (\frac{1}{2} + \frac{-1}{4} )[/tex]
[tex]=> -\frac{1}{2} + (\frac{2 - 1}{4} )[/tex]
[tex]=> -\frac{1}{2} + \frac{1}{4}[/tex]
[tex]=> \frac{-2 + 1}{4}[/tex]
[tex]=> -\frac{1}{4}[/tex]
R.H.S. =
[tex](-\frac{1}{2} + \frac{1}{2} ) + \frac{-1}{4}[/tex]
[tex]=> 0 - \frac{1}{4}[/tex]
[tex]=> -\frac{1}{4}[/tex]
∴ L.H.S. = R.H.S. (Verified)
Each day for two weeks, Howard recorded values for the following two
variables.
2
• s, the number of students ahead of him in the lunch line when he got in
line
• m, the number of minutes elapsed between when he got in line and when
he sat down to eat
He then plotted his data on a scatter plot, with the horizontal axis representing
s and the vertical axis representing m, and drew a line of best fit. The equation
of the line was m = S + 1.
According to the equation of the line, if there are 52 students ahead of Howard
when he gets in the lunch line, how many minutes should he expect it to take
before he sits down to eat?
Answers
Given statement solution is :- If there are 52 students ahead of Howard when he gets in the lunch line, he should expect it to take approximately 53 minutes before he sits down to eat.
According to the equation of the line given as "m = S + 1," where m represents the number of minutes elapsed and s represents the number of students ahead of Howard in the lunch line, we can substitute the value of s as 52 to find the expected number of minutes.
m = S + 1
m = 52 + 1
m = 53
Therefore, if there are 52 students ahead of Howard when he gets in the lunch line, he should expect it to take approximately 53 minutes before he sits down to eat.
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Sue uses 1/3 cup of coconut oil in each pie that she makes for her mother's bakery. If Sue made 7 cakes, how much oil did Sue use in all? *
Answers
Ryan conducted a 6-day study observing the effects of an organic plant food on the growth of his sprouting bean plant. He tracked these two pieces of information:
the amount of plant food remaining in the container after each day’s feeding
the height of the plant over time
Ryan found that the amount of plant food remaining decreased an equal amount each day, and he used the entire 72 milliliters by the end of his study.Which statement is true about the relationship between the amount of plant food remaining and the number of days?
A:This relationship is a function because more than one amount of plant food remains each day.
B:This relationship is not a function because more than one amount of plant food remains each day.
C:This relationship is not a function because only one amount of plant food remains each day.
D:This relationship is a function because only one amount of plant food remains each day.
Answers
Answer:
B: This relationship is not a function because more than one amount of plant food remains each day
Step-by-step explanation:
It is given that Ryan did an experiment by observing the effects of plant food and the growth of the sprouting bean plant. He made a note of the height of the bean plant and the amount of food remaining in the container for the plant after feeding each day.
Thus he observed that the plant food in the container decreases by an equal amount everyday as the bean plant grew. Thus this states that it is not a function between the two as there are more than one plant food remaining each day for the plant.
A relationship is a function when one element belongs to one thing.
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all I need is the answer
thank you
Answers
hope this helps !!
Which number sentence is true?
8 – 4= 11 – 8
13 – 6 = 6-1
6 – 5 = 7 – 6
Done
Answers
Answer:
6-5 = 7-6
Step-by-step explanation:
Explanation:
8-4 = 11-8
4 ≠ 3
13-6 = 11-8
7 ≠ 5
6-5 = 7-6
1 = 1
Name the angle and the intercepted arc.
Answers
Answer:
Inscribed angle = <X
Intercepted arc = arc VW
Step-by-step explanation:
The inscribed angle in a circle is usually formed inside a circle when two segments intersect at a point in the circle. While intercepted arc is the section of the circumference of the circle encased by the two segments that forms the inscribed angle.
Thus,
Inscribed angle = <X
Intercepted arc = arc VW
Give the slope of the line which is perpendicular to
y = −3x −2
Answers
Answer:
1/3
Step-by-step explanation:
y = −3x −2
This is in the form y = mx+b where m is the slope
This line has a slope of -3
We want the slope of a line that is perpendicular
Lines that are perpendicular have slopes that are negative reciprocals
m = -(1/-3)
m = + 1/3
The slope of a line that is perpendicular is 1/3
Help!!
The results of a survey are represented in the two-way frequency table below. Complete the two-way frequency table.
Answers
Answer:
Female, E-Book=22
Male, Print=20
Total Female=44
Print total=42
The width of a box is x units.
The height of a box is 3 units.
The length of a box is (x + 10) units.
Which expression represents the volume of the box, in cubic units, when x > 0?
Answers
Answer:
3x² + 30x
Step-by-step explanation:
width of a box = x units.
height of a box = 3 units.
length of a box = (x + 10) units.
Volume of the box = length × width × height
= (x + 10) * x * 3
= (x + 10) * 3x
= 3x² + 30x
Volume of the box = 3x² + 30x
PLS HELP!!!
Using the Pythagorean theorem if necessary please round your answer to the nearest 10th
1. a=7 and b=10 find C the missing side length
2. b=12 and c=13 find A the missing side length
3. A=4 and b=10 find C the missing side length
Answers
Victor makes decorations for his birthday party. He needs 5/6 yard of ribbon for each decoration. How much ribbon does Victor need to make 7 decorations
Answers
Answer:
35/6
Step-by-step explanation:
first you have to multiply 7 by 5/6 and that will get you to the answer of 35/6
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What is the measure of arc wx in the diagram below?
116"
Wo
45°
S
X
R
A. 116°
B. 45°
C. 710
D. 26°
someonee helpp plss
Answers
Answer:
to find the WX you have to use this formula
m>S=TR-WX/2
45=116-WX/2
90=116-WX
WX=116-90
WX=26
the answer is D 26
Answer:
D
Step-by-step explanation:
The secant- secant angle WSX is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] (116 - WX)° = 45° ( multiply both sides by 2 to clear the fraction )
116 - WX = 90° ( subtract 116° from both sides )
- WX = - 26° ( multiply both sides by - 1 )
WX = 26° → D
Steven earns extra money babysitting. He charges $31.00 for 4 hours and $46.50 for 6 hours. Enter an equation to represent the relationship. Let x represent the number of hours Steven babysit and y represent the amount he charges. The equation is y answer here
Answers
Answer:
y = 7.75x
Step-by-step explanation:
Steven earns extra money babysitting.
Step 1
Let us find the amount he earns per hour based on the charges given in the question.
a) He charges $31.00 for 4 hours
4 hours = $31
1 hour = x
Cross Multiply
4x = $31
x = $31/4
x = $7.75
b) And $46.50 for 6 hours.
6 hours = $46.50
1 hour = x
Cross Multiply
6x = $46.50
x = $46.50/6
x = $7.75
This means, Steven earns $7.75 per hour.
Step 2
Let
x represent the number of hours Steven babysit
y represent the amount he charges.
Therefore, an equation to represent the relationship is written as:
y = $7.75 × x
y = 7.75x
△ABC∼△DEF . Find DF.DF.
Answers
Answer:
do the answer is 24
in the picture there's the steps
Answer:
Step-by-step explanation:
since they are similar triangle use this ratio
AB/DE=AC/DF
4/12=8/3(x+1)
do cross multiplication
12*8=3*4(x+1)
96=12(x+1)
96=12x+12
96-12=12x
84/12=x
7=x
substitute the value of x
3(x+1)
3(7+1)
3*8
24
Find tan S and tan R. Write each answer as a fraction in simplest form
Answers
tan S:
opposite: 45
adjacent: 24
45/24 = 15/8
tan R
opposite: 24
adjacent: 45
24/45 = 8/15
We know the trigonometric ratios that tan = opposite/adjacent So, tan S is equal to 15/8 and tan R is equal to 8/15.
What are the trigonometric ratios?Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
We know that tan = opposite/adjacent
tan S
opposite: 45
adjacent: 24
So,
tan S = 45/24 = 15/8
tan R
opposite: 24
adjacent: 45
So,
tan R = 24/45 = 8/15
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A cable repair person has 7.9 meters of wire. Suppose each meter of the wire weighs 3.2 ounces. Find the weight of the wire.
Answers
Hope this helps:D
help me with this please (2)
Answers
Answer:
Step-by-step explanation:
surface are of triangular prism =(a+b+c)h+bh
=(5+5+4)11+4*6
=14*11+24
=154+24
=178 yd^2
PLS HELP ILL GIVE BRAINLIEST
Answers
Answer:
answer is 8
Step-by-step explanation:
take Lcm of 8 and 32
Answer:
8
Step-by-step explanation:
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Answers
Answer: Its the first one
Handy is making floor plan for a treehouse using a scale of 1 inch to 2 foot he wants to make the floor of the treehouse have a length of 8 foot how many inches should he show
Answers
Answer: [tex]4\ in.[/tex]
Step-by-step explanation:
Given
Handy uses a scale of 1 inch to 2 foot i.e. 1 inch of drawing represents 2 foot
For 8 foot length of tree house he draw x inch(say)
[tex]\therefore \ \dfrac{1\ \text{inch}}{2\ \text{foot}}=\dfrac{x}{8}\\\\\Rightarrow x=8\times \dfrac{1}{2}\\\Rightarrow x=4\ in.[/tex]
So, handy draw 4 inches.
Please help on how to solve this
Answers
Answer:
11,73 cm (round to the nearest hundredths) ; 112 degrees
Step-by-step explanation:
circumference = 2 x radius x π = 2 x 6 x π = 37,699112 cm
measure of the arc =
37,699112 : 360 = x : 112
x = (112 * 37,699112)/360 = 11,728613 cm
the measure of the angle is given = 112 degrees
Some red, white, and blue candies were placed in a bowl. Some contain nuts, and some do not. Suppose one of the candies were chosen randomly from all the candies in the bowl. According to the table below, if the candy is blue, what is the probability that it does not contain any nuts?
Answers
Answer:
c
sorry if I'm wrong.
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Answer: 40%
Step-by-step explanation:
I just did it
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Answers
someone please help!!! I’ll give you brainlist!
Answers
Answer: Point P
Step-by-step explanation:
Which type of function is shown in the table below?
х
f(x)
1
-4
2
-6
3
-8
ܠܛ
-10
5
-12
Not a function
O Linear
Submit Answer
Exponential
Quadratic
Answers
The table represents a linear equation, y = - 2x - 2.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
From, The given table the list of ordered pairs are,
(1, - 4), (2, -6), (3, - 8), (4, - 10), and (5, - 12).
By observing the ordered pairs and patterns we can form an equation,
y = - 2x - 2.
If we put the values of 'x' the equation will satisfy the values of 'y'.
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