Answer:
[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]
Step-by-step explanation:
Given
[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]
Required
Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]
The above shows the sum of a geometric series and this will be calculated as shown below;
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]
Where
a = First term;
[tex]a = 3[/tex]
r = common ratio
[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]
[tex]r = 3[/tex]
Substitute 3 for r and 3 for a in the formula above;
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes
[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]
[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]
Hence;
[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]
Some lemon, lime, and cherry lollipops are placed in a bowl. Some have a
chocolate center, and some do not. Suppose one of the lollipops is chosen
randomly from all the lollipops in the bowl. According to the table below, if it
is known to be lemon, what is the probability that it HAS a chocolate center?
Answer:
45%
Step-by-step explanation:
There are 20 lollilops with lemon in total. 9 of them have a chocolate center. 9/20=0.45. To convert it into percentage you would multiply the number by 100. 0.45*100=45
The answer is 45%
"if it is known to be lemon" means we ignore any other flavor. I recommend covering up the other values, or you could highlight just the lemon column.
We have 9+11 = 20 lemon total. Of this 20 total, only 9 lemons have a chocolate center. So 9/20 = 0.45 = 45% of the lemon candies have a chocolate center.
a countrys population in 1995 was 206 million. In 1998 it was 210 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million
Answer:
254 million
Step-by-step explanation:
In a calculator it would to
210 x 1,0194^(10)
20x-4y=40
Find the slope of the linear equation
Answer:
the slope is 5
Step-by-step explanation:
Solve for y
20x -4y = 40
Subtract 20x from each side
20x-20x -4y = -20x +40
-4y = -20x+40
Divide each side by -4
-4y/-4 = -20x/-4 +40/-4
y = 5x -10
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
The slope is 5
Solve for y:
20x - 4y = 40
Subtract 20x to both sides
-4y = 40 - 20x
Divide -4 to everything
y = -10 + 5x
Therefore, the slope is 5
Best of Luck!
can somewon help me plx
Answer:
[tex]\boxed{392in^2}[/tex]
Step-by-step explanation:
Hey there!
Well to find SA we need to find the area of the rectangles.
So lets do the top rectangle,
6*6 = 36
Now lets do the the left rectangle,
10*6 = 60
Now lets do the far right one,
6*4 = 24
Now lets do the second highest rectangle,
4*6 = 24
Now lets do the rectangle facing the right side,
6*6 = 36
Now we can do the bottom rectangle,
6*10 = 60
Now lets do the 2 facing front and back,
6*10 = 60
4*4 = 16
60+16 = 76
76*2 = 152
Now we can add everything,
152 + 60 + 36 + 24 + 24 + 60 + 36
= 392 in^2
Hope this helps :)
Solve the system of equations 2x - y = 11 and x + 3y = -5
Answer:
x = 4, y = -3
Step-by-step explanation:
{2x - y = 11
{x + 3y = -5
You can use the substitution method by solving for x in the second equation:
x + 3y = -5
Subtract 3y from both sides:
x = -3y - 5
Now, substitute this value for x into the first equation:
2x - y = 11
2(-3y - 5) - y = 11
Distribute:
-6y - 10 - y = 11
Add 10 to both sides:
-6y - y = 21
Combine like terms:
-7y = 21
Divide both sides by -7:
y = -3
Next, substitute this value for x into the second equation:
x + 3y = -5
x + 3(-3) = -5
Multiply:
x - 9 = -5
Add 9 to both sides:
x = 4
Answer:
(7, 3)
Step-by-step explanation:
2x - y =11 2x-y =11
-2(x+3y)= (-5)-2 -2x-6y= 10
Then you will cross out the x, and add.
-7y =21 divide 7
y=-21/7 or y=3
Then you plug in the y where the y is and solve
2x-(3) = 11
2x = 14
x=7
What are the coordinates of the vertices of the polygon in the graph that are in Quadrant II? A) (4,–2) B) (4,3), (0,5), (0,1) C) (–5,2), (–3,2), (–3,4) D) (–1,0), (–5,2), (–3,2), (–3,4), (0,5), (0,1)
Answer:
C) (–5,2), (–3,2), (–3,4)
Step-by-step explanation:
A) (4,–2)
B) (4,3), (0,5), (0,1)
C) (–5,2), (–3,2), (–3,4)
D) (–1,0), (–5,2), (–3,2), (–3,4), (0,5), (0,1)
For quadrant two the points are always (-x,y) and x is always negative.
Image shows quadrant places.
How many of the positive integer factors of 15552 are perfect squares?
Please show work, will mark brainliest if correct
Answer: 9 integers factors
Step-by-step explanation:
Let's first find the factor of 15552
15552 / 2 = 7776
7776 / 2 = 3888
3888 / 2 = 1944
1944 / 2 = 972
972 / 2 = 486
486 / 2 = 243
273 / 3 = 81
81 / 3 = 27
27 / 3 = 9
9 / 3 = 3
3 / 3 = 1
Some of the factors of 15552 are:
2×2×2×2×2×2×3×3×3×3×3
4×4×4×9×9×3
4^2 × 9^2 × 4 × 3
The factor that are perfect square are:
4, 9, 16, 36, 64, 81, 144, 576, 1296
Therefore, 9 of the positive integer factors of 15552 are perfect squares.
What is the value of r in the equation?
-1.5(4-r)=-12
0 -6
-4
4
06
Answer:
r = -4Step-by-step explanation: I hope it helps :)
[tex]-1.5(4-r)=-12\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\\-1.5\left(4-r\right)\cdot \:10=-12\cdot \:10\\\\= -15\left(4-r\right)=-120\\\\\mathrm{Divide\:both\:sides\:by\:}-15\\\\\frac{-15\left(4-r\right)}{-15}=\frac{-120}{-15}\\\\4-r=8\\\\\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}\\\\4-r-4=8-4\\\\-r=4\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-r}{-1}=\frac{4}{-1}\\\\r=-4[/tex]
Answer:
r = -4
Step-by-step explanation:
-1.5(4-r)=-12
Divide each side by -1.5
-1.5/-1.5(4-r)=-12/-1.5
(4-r)=8
Subtract 4 from each side
4-r-4 = 8-4
-r = 4
Divide each side by -1
r = -4
Sally invested some money at 15 % interest. Sally also invested $172 more than 3 times that amount at
14%. How much is invested at each rate if Sally receives $1398.35 in interest after one year? (Round to
two decimal places if necessary.)
Answer:
Amount at 15%=$2,411
Amount at 14%=$7,405
Step-by-step explanation:
let
x= the amount at 15% rate.
y=amount at 14% rate
y= x times 3 plus $172
y= 3x + $172 (1)
x times 15% plus y times 14% equals a return of $1,398.35 after one year
0.15x + 0.14y= $1,398.35 (2)
Recall,
y= 3x + $172
Substitute (1) into (2)
0.15x + 0.14y= $1,398.35
0.15x + 0.14(3x+172)=1398.35
0.15x + 0.42x + 24.08=1398.35
Collect like terms
0.15x + 0.42x=1398.35 - 24.08
0.57x=1374.27
Divide both sides by 0.57
x=2,411
x=$2,411
Find y
y= 3x + $172
=3(2,411) + 172
=7,233+172
=7,405
y=$7,405
Amount at 15%=$2,411
Amount at 14%=$7,405
Check:
$2,411*0.15=$361.65
$7,405*0.14=$1036.70
Total=$361.65 + $1036.70
=$1,398.35
The area of a rectangular field is 6052 m².
If the width of the field is 68 m, what is its length?
Answer:
length = 89 mStep-by-step explanation:
Area of a rectangle = l × w
where
l is the length
w is the width
From the question
Area = 6052 m²
width = 68 m
To find the length substitute the values into the above formula
6052 = 68l
Divide both sides by 68
We have the final answer as
length = 89 mHope this helps you
PLZZ HELPP!! Water is poured from a 1.5 L water bottle into an empty glass until both the glass and the bottle are 3/4 full. What is the volume of the glass?
Answer:
0.5 L
Step-by-step explanation:
volume of bottle: 1.5 L
amount of water = 1.5 L
volume of glass: x
3/4 full is the same as 0.75 full
vol of water in bottle + vol of water in glass = total vol of water
0.75(bottle) + 0.75(glass) = 1.5
0.75(1.5) + 0.75x = 1.5
0.75x = 0.375
x = 0.5
help me plz can somewon help me i am bad at math mostly
Answer:
Definitely the bottom left
Step-by-step explanation:
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice,
where the rice-to-spice ratio is 15 : 1. He currently has 40 grams of the spice blend, and he can go buy
more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David
spends 4.50 dollars on rice.
How many servings can David make with the current amount of spice he has?
Answer:
8 servings of rice
Step-by-step explanation:
can somebody help me with this math problem
Answer:
D). 137
Step-by-step explanation:
1). 40 % of 50 = 20
50 + 20 = 70
2). 40 % 70 = 28
70 + 28 = 98
3). 40 % of 98 = 39.2, basically 39
98 + 39 = 137
137 is the right answer
Pls make my answer brainiest))))
What are the domain, range, and midline of the function f(x)=1/2cos(1/4x)-1?
Your function is: [tex]f(x)=\frac{1}{2}\cos \Big( \frac{1}{4x}\Big) -1[/tex]
Domain: $(-\infty, +\infty)-\{ 0 \}$ or $R-\{ 0 \}$
Range: $[-\frac{3}{2}, -\frac{1}{2}]$
Midline: $y=-1$
If two 6-sided dice are rolled, what is the
probability of rolling double 2s?
16.7%
There are 6 ways we can roll doubles out of a possible 36 rolls (6 x 6), for a probability of 6/36, or 1/6, on any roll of two fair dice. So you have a 16.7% probability of rolling doubles with 2 fair six-sided dice.
Answer:
The answer is 16.7%
Step-by-step explanation:
There are 6 ways we can roll doubles out of a possible 36 rolls (6 x 6), for a probability of 6/36, or 1/6, on any roll of two fair dice. So you have a 16.7% probability of rolling doubles with 2 fair six-sided dice. hope this helped
Find the interquartile range for a data set having the five-number summary: 3.5, 12, 19.1, 25.8, 31.8 A. 28.3 B. 13.8 C. 15.6 D. 12.7
Answer:
B. 13.8
Step-by-step explanation:
The five-number summary consists of five items which is usually displayed on a box plot, and can be represented in ascending order.
The five-number summary given: 3.5, 12, 19.1, 25.8, 31.8, represents the following in ascending order:
1. The minimum value = 3.5
2. First quartile (Q1) = 12
3. The median = 19.1
4. Third quartile (Q3) = 25.8
5. The maximum value = 31.8
The interquartile range = Q3 - Q1
Therefore, the interquartile range of the data = 25.8 - 12 = 13.8
Write an expression with exponents to find the total number of panes in 12 windows.
Answer:
Below
Step-by-step explanation:
Imagine our window has 4 panes (picture below)
Let T be the total number of panes:
There are 12 windows at total.
●T = 4×12
Notice that:
● 4 = 2×2
● 12 = 4×3 = 2×2×3
● T = 2×2×2×2×3 = 2^4×3
Which mean the same as 60%? Check all that apply
a.3/5
b. 0.06
c. 0.60
d. 6/10
e. 6/100
Factor this expression.
3x2 - 6x
Answer:
3x(x - 2)
Step-by-step explanation:
Both terms have a GCF (greatest common factor) of 3x so factoring that out, we get 3x(x - 2).
Answer:
3x ( x - 2 )
Step-by-step explanation:
First we hv to find wat is common in both of them.....
As we can see " 3x " is common in both of them
so....
If we take 3x from both the terms.... It will become....
3x square = 3x ( x )
-6x - 3x ( -2 )
Therefore the expression will become....
3 x square - 6x
= 3x ( x - 2 )
Hope this helps...
HAVE A GOOD DAY !!! ( no the biscuit ) (lol)
Pls mark my ans as brainliest If u mark my ans as brainliest u will get 3 extra pointsFind the m∠DCA A. 10 B. 29 C. 116 D. 40
Hence, the m∠DCA is 59.2
What is an angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs, and sometimes the arms of the angle.
How to solve?m∠DCB = (4x) + (6x-58) = 90
10x = 148
x = 14.8
m∠DCA = 4x
= 4(14.8)
= 59.2
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PLEASE HELP WILL GIVE BRAINLY!!!!!!!
Which are the roots of the quadratic function f(q) = q^2 - 125? Select two options.
A) q= 5/5
B) q= -5/5
C) q= 3/5
D) q= -3/5
E) q= 25/5
Answer:
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Since there is no constant value. This must be a special case.
So,
(q+5[tex]\sqrt{5}[/tex])(q-5[tex]\sqrt{5}[/tex])
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
help
7. Given the figure, find the desired measurements
Answer:
m∠F = 66°
m∠D = 57°
Step-by-step explanation:
It looks like you have ...
∠D = ∠E = (4x +1)°
∠F = (5x -4)°
The sum of the angles in the triangle is 180°, so we have ...
2(4x +1) +(5x -4) = 180
13x -2 = 180
x = 182/13 = 14
Then the angle measures are ...
∠D = ∠E = (4(14) +1)° = 57°
∠F = (5(14) -4)° = 66°
__
m∠F = 66°
m∠D = 57°
solve the equation
[tex] {5}^{n + 1} - {5}^{n} + {5}^{n - 1} = 105[/tex]
Answer:
n=2
Step-by-step explanation:
Hello, please consider the following.
[tex]{5}^{n + 1} - {5}^{n} + {5}^{n - 1} = 105\\\\5^{n-1}(5^2-5+1)=5^{n-1}(25-5+1)=21*5^{n-1}=105\\\\5^{n-1}=\dfrac{105}{21}=5=5^1\\\\\text{It means that}\\\\n-1=1 <=> n=2[/tex]
Let me know if you need more details.
Thank you
Triangle ABC is dilated to form new triangle DEF. If angle A is congruent to angle D, what other information will prove that the two triangles are similar by the AA similarity postulate?
Angle B is congruent to angle E.
Side AB is congruent to side DE.
Angle C is congruent to angle D.
Side BC is congruent to side EF.
Answer:
Step-by-step explanation:
option A , angle B is congruent to angle E { SINCE IT IS AA POSTULATE
Answer:
B=E (b)
Step-by-step explanation:
Solve x*2+5x+6=5x+10
Answer:
x = -2, 2.
Step-by-step explanation:
x*2 + 5x + 6 = 5x + 10
x^2 + 5x - 5x + 6 - 10 = 0
x^2 - 4 = 0
x^2 = 4
x = -2, 2 ( 2 solutions).
Help please all questions.
Answer:
A is A=25
B=10
B is 40
C is A=10
B=6.428
hope i helped you
sorry if it is incorrect
{(-2,8),(4,6),(10,4)} Which point, when added to the set, would form a relation that is not a function?
Answer:
Point : ( -2, 15 )
Step-by-step explanation:
A point that would make this relation not a function would be one that shares a common x - value with the other points. One common domain values for two range values would, when graphed, not follow the vertical test, hence making the relation not a function.
Let's say that the point is ( -2, 15 ). It has a common x - value with respect to the first point, ( -2, 8 ), and therefore would make this set not a function.
Answer:
Point : ( -2, 15 )
Step-by-step explanation:
What is the solution to the inequality 3t + 9 ≥ 15 ? please answer as soon as you can!!
Answer:
T≥2
Step-by-step explanation:
3t+9≥15
3T≥15-9
3T≥6
T≥2
Answer:
t ≥ 2
t ∈ [2 ; +oo)
Step-by-step explanation:
3t + 9 ≥ 15
3t ≥ 15 - 9
3t ≥ 6
t ≥ 6 : 3
t ≥ 2
t ∈ [2 ; +oo)
Machine A can fill 1 box of nails in 6 minutes. Machine B can fill 1 box of nails in 9 minutes. They started to work at the same time and they stopped also at the same time. In all they filled 100 boxes. How many were filled by machine A?
A-
1 box --- 6 minutes
y boxes --- 1 minute
y = 1/6
B-
1 box --- 9 minutes
t boxes --- 1 minute
t = 1/9
So...
r - used time
r(1/9 + 1/6)=100
r=(100.18)/5
r= 360 minutes
1/6 . 360 = 60 boxes
answer: 60 boxes
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
Let's use the concept of the rate of work to solve this problem. The rate of work is the amount of work done per unit of time.
Machine A's rate of work is 1 box of nails every 6 minutes.
Machine B's rate of work is 1 box of nails every 9 minutes.
Let's assume that machine A filled x boxes, and machine B filled y boxes. Since they worked for the same amount of time, the total number of boxes filled by both machines is 100.
So, the equation representing the total work is:
x (boxes filled by A) + y (boxes filled by B) = 100
Now, let's use their rates of work to form two more equations:
Rate of work of A = 1 box every 6 minutes
Rate of work of B = 1 box every 9 minutes
Since work = rate × time, we can write two equations:
x (boxes filled by A) = (1/6) * t (time in minutes)
y (boxes filled by B) = (1/9) * t (time in minutes)
Since they both worked for the same time, we can set the time for both machines as equal:
t = t
Now, we have a system of equations:
x + y = 100
x/6 = y/9
t = t
Let's solve the system of equations. We can start by substituting the value of y from the second equation into the first equation:
x + (x/6)*3 = 100
x + (x/2) = 100
Multiply both sides by 2 to eliminate the fraction:
2x + x = 200
3x = 200
x = 200/3
Now, let's find the value of y using the second equation:
y = (x/6)*3
y = (200/3)/6 * 3
y = 200/3
So, machine A filled 200/3 boxes of nails, which is approximately 66.67 boxes.
Machine B filled 200/3 boxes of nails, which is also approximately 66.67 boxes.
Since they cannot fill a fraction of a box, we can distribute the remaining 2/3 box between machine A and machine B, giving one extra box to each.
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
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