To find the sum of the finite geometric series 4 + 12 + 36 + 108 + ... + 972, we use the sum formula for geometric series. The common ratio is 3, and there are 6 terms in the series. The sum of the series is 1456.
Evaluating the Sum of a Finite Geometric Series:
To evaluate the sum of the finite geometric series 4 + 12 + 36 + 108 + ... + 972, you need to use the formula for the sum of a finite geometric series:
Sum = a ×([tex]r^{n}[/tex] - 1) / (r - 1)
where:
a is the first term of the seriesr is the common ration is the number of termsLet's identify these values:
First term, a = 4Common ratio, r = 12 / 4 = 3Number of terms, nTo find n, use the formula for the nth term of a geometric series: a * r^(n-1). Given the last term is 972, we solve:
4 × [tex]3^{n-1}[/tex]= 972
Divide both sides by 4:
[tex]3^{n-1}[/tex]= 243
Recognize that 243 = [tex]3^{5}[/tex], so:
n-1 = 5
n = 6
Now, apply the sum formula:
Sum = 4 × ([tex]3^{6}[/tex] - 1) / (3 - 1)
Simplify the expression:
Sum = 4 × (729 - 1) / 2
Sum = 4 × 728 / 2
Sum = 4 × 364
Sum = 1456
Therefore, the sum of the series 4 + 12 + 36 + 108 + ... + 972 is 1456.
what is the answer to x/3-9=-5
Answer:
12
Step-by-step explanation:
x/3-9=-5
x/3=-5+9
x/3=4
x=4*3
x=12
Simplify 5x * 1/x^-7 * x^-2
a) 5x
b) 5x^−6
c) 5
d) 5x^6
Answer: the one that has the correct notation form is correct
Step-by-step explanation: to the power is multilying
In a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If
1
4
of the drink is apple juice and
3
10
is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form
Answer:
orange : cranberry : apple : orange
9 : 5 : 6
Step-by-step explanation:
Given the following ratios (fraction):
[tex]\frac{apple}{total} =\frac{1}{4}[/tex]
[tex]\frac{orange}{total} =\frac{3}{10}[/tex]
in order to add/subtract fractions, we have to ensure that the denominators are the same, we can see that for the denominators listed above, the least common multiple for 4 and 10 = 20, hence we can re-write the above as :
[tex]\frac{apple}{total} =\frac{1}{4} =\frac{5}{20}[/tex]
[tex]\frac{orange}{total} =\frac{3}{10} =\frac{6}{20} [/tex]
Hence,
Fraction of cranberry juice of the total is,
1 - [tex]\frac{5}{20}[/tex] - [tex]\frac{6}{20}[/tex]
= [tex]\frac{20}{20}[/tex] - [tex]\frac{5}{20}[/tex] - [tex]\frac{6}{20}[/tex]
= [tex]\frac{9}{20}[/tex]
Because all the denominators are the same, we can assemble the ratios of each component by taking the ratios of the numerators
cranberry : apple : orange
= ratios of their numerators
= 9 : 5 : 6
Subtract —b+3 from —11b —4
Answer:
Step-by-step explanation:
STEP 1:
-11b-4-(-b+3)....bracket the equation that you are subtracting and add a mins sign infront of the bracket because you are asked to subtract -b+3 from -11b-4.
STEP 2:
-11b-4+b-3
the minus sign infront of the bracket changes the minus sign to a positive (+)sign because a minus(-) timesed by a minus is a positive(+). and a minus timesed by a positive(+) is a negative(-)
STEP 3:
-10b-7
add the b values together(11b-b) = 10b
add the numericals together -4+(-3)= -7
STEP 4:
final answer is -10b-7
What is 9 over 4 equal
Answer:
2.25
Step-by-step explanation:
Answer:
2.25
Step-by-step explanation:
4 goes into 9, two times which is why 2 is your whole number and 4 X 2 =8
The .25 is "4 x .25=1. And 8+1 equals 9.
A rhombus is ____ a quadrilateral.
A) Never
B) Sometimes
C) Always
Answer:
C
Step-by-step explanation:
A rhombus always has 4 sides, making it a quadrilateral.
Feel free to ask further questions..
find an equation of the line such that the points (2/5,5) and (-2/5,4) are on the line.
The equation of the line is y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
The form of the linear equation is y = mx + b, where
m is the slope of the line, [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] b is the y-intercept, to find b substitute x and y in the equation by the coordinates of any point on the line∵ A line passes through points ( [tex]\frac{2}{5}[/tex] , 5) and ( [tex]-\frac{2}{5}[/tex] , 4)
∴ [tex]x_{1}[/tex] = [tex]\frac{2}{5}[/tex] and [tex]x_{2}[/tex] = [tex]-\frac{2}{5}[/tex]
∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 4
- Substitute them in the rule of the slope to find m
∵ [tex]m=\frac{4-5}{-\frac{2}{5}-\frac{2}{5} }[/tex]
∴ [tex]m=\frac{-1}{-\frac{4}{5}}=\frac{5}{4}[/tex]
- Substitute it in the form of the equation
∴ y = [tex]\frac{5}{4}[/tex] x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ Point ( [tex]\frac{2}{5}[/tex] , 5) lies on the line
∴ x = [tex]\frac{2}{5}[/tex] and y = 5
∴ 5 = [tex]\frac{5}{4}[/tex] ( [tex]\frac{2}{5}[/tex] ) + b
∴ 5 = [tex]\frac{1}{2}[/tex] + b
- Subtract [tex]\frac{1}{2}[/tex] from both sides
∴ [tex]\frac{9}{2}[/tex] = b
∴ y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation of the line is y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
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What is the value of a in the equation?
22 = a=11
Pls help
Answer:
242
Step-by-step explanation:
22=a/11
22*11= a
242 = a
a=242
Answer:
a=242
Step-by-step explanation:
Find the values of the variables xy, and z in the parallelogram. The diagram is not drawn to scale
Answer:
Therefore x = 33° , y = 40° and z = 109°.
Step-by-step explanation:
i) from properties of parallel lines a pair of alternate interior angles are equal
Therefore x = 33°
ii) from properties of parallelogram that a pair of opposite angles are equal, Therefore z = 109°.
iii) from the law of triangle that the sum of all angles in a triangle is 180° and also using the property of parallel lines that a pair of alternate interior angles is equal we can say that x° + y° + z° = 180° ⇒ 31° + y° + 109° = 180°, therefore y° = 180° - 140° = 40°.
Therefore x = 33° , y = 40° and z = 109°.
The values of x, y and z in the parallelogram is 52°, 38° and 90° respectively.
What is the value of x, y and z?The angles on the same side of the transversal of a parallelogram are supplementary, that is, 180°
So,
33° + 109° + y° = 180°
142 + y = 180
y = 180 - 142
y = 38°
x° + y° = 90°
x + 38 = 90
Subtract 38 from both sides
x = 90 - 38
x = 52°
x° + y° + z° = 180°
52 + 38 + z = 180
90 + z = 180
z = 180° - 90°
z = 90°
Hence,
x = 52°
y = 38°
z = 90°
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Let f(x) = 2x3 – 4x.
Find f(-2).
Answer:
Step-by-step explanation:
f(x) = 2x^3 - 4x.....find f(-2).....so sub in -2 for x
f(-2) = 2(-2^3) - 4(-2)
f(-2) = 2(-8) + 8
f(-2) = -16 + 8
f(-2) = -8 <==
We have [tex]f(x)=2x^3-4x[/tex], to find [tex]f(-2)[/tex] put -2 instead of x, [tex]f(-2)=2(-2)^3-4(-2)=-16+8=\boxed{-8}[/tex].
Hope this helps.
n-1-9n
simplify this please?
Answer:
-8n-1
Step-by-step explanation:
n-1-9n=n-9n-1=-8n-1
"$12 million per year. grow 10% compounded annually over the next 5 years. What will demand be in 5 years?"
Compound interest formula:
Amount = starting value x ( 1+ interest rate/compounds per year)^(compound per year x number of years)
Amount = 12,000,000 x (1+ 0.10/1)^(1x5)
Amount = 19,326,120.00
-4 (×+7)
What is the distributive property of this problem?
use the figure shown to determine which trigonometric ratio is incorrect?
a. sin 30°= 4/8
b. cos 60°=4/8
c. sin 60°= square root of 48 over 8
d. tan 30°= square root of 48 over 8
Answer:
Option d is incorrect.
Step-by-step explanation:
See the diagram attached.
a. [tex]\sin 30^{\circ} = \frac{AB}{AC} = \frac{4}{8}[/tex]. Hence, this is correct.
Here, sin Ф is given by perpendicular divided by the hypotenuse.
b. [tex]\cos 60^{\circ} = \frac{AB}{AC} = \frac{4}{8}[/tex]. Hence, this is also correct.
Here, cos Ф is given by base divided by the hypotenuse.
c. [tex]\sin 60^{\circ} = \frac{BC}{AC} = \frac{\sqrt{48}}{8}[/tex]. Hence, this is also correct.
d. [tex]\tan 30^{\circ} = \frac{AB}{BC} = \frac{4}{\sqrt{48}}[/tex]. Hence this is not correct.
Here, tan Ф is given by perpendicular divided by base.
Therefore, option d is incorrect. (Answer)
P+q=-2 p-q=8 Elimination using Add and Subtraction
Answer:
p+q = -2 ----- equation 1
p-q = 8 ------ equation 2
Adding both equations
p+q+p-q = -2+8
2p = 6
p = 6/2
p = 3
Subtracting equation 2 from equation 1
p+q - (p-q) = -2 - 8
p+q-p+q = -10
2q = -10
q = -10/2
q = -5
p= 3
q = -5
Step-by-step explanation:
Final answer:
The solution to the system of equations using the elimination method is p = 3 and q = -5.
Explanation:
The student is requesting assistance with solving a system of linear equations using the elimination method. The system given is:
p + q = -2
p - q = 8
We can eliminate the variable q by adding both equations together:
p + q + p - q = -2 + 8
2p = 6
p = 3
Now we can substitute p back into one of the original equations to find q:
3 + q = -2
q = -2 - 3
q = -5
The solution to the system is p=3 and q=-5.
A sequence can be generated by using an=4an−1 where a1=6 (a) 6, 20, 76, 300 (b)6, 24, 96, 384 (c)6, 10, 14, 18 (d) 6, 20, 100, 500
Answer:
Option (b) 6, 24, 96, 384
Explanation:
The complete question is:
A sequence can be generated by using [tex]a_n=4a_{(n-1)}[/tex] where [tex]a_1=6[/tex] and n is a whole number greater than 1. What are the first four terms in the sequence.
The given rule [tex]a_n=4a_{(n-1)}[/tex] is a recursive formula, which means that to find any term consecutive term, from the second one, you multiply the current term by 4.
Thus:
[tex]a_1=6\\ \\ a_2=4a_1=4\times 6=24\\\\ a_3=4a_2=4\times 24=96\\ \\ a_4=4a_3=4\times 96=384[/tex]
Answer:
The option (b) is correct as the sequence is generated as 6, 24, 94, 384,...
Step-by-step explanation:
Considering the sequence
[tex]a_{n} =4a_{n-1}[/tex]
As [tex]a_{1} =6[/tex]
So,
[tex]a_{n} =4a_{n-1}[/tex]
[tex]a_{2} =4a_{2-1}[/tex]
[tex]a_{2} =4a_{1}[/tex]
[tex]a_{2} =4.6[/tex]
[tex]a_{2} =24[/tex]
[tex]a_{3} =4a_{3-1}[/tex]
[tex]a_{3} =4a_{2}[/tex]
[tex]a_{3} =4.24[/tex]
[tex]a_{3} =96[/tex]
[tex]a_{4} =4a_{4-1}[/tex]
[tex]a_{4} =4a_{3}[/tex]
[tex]a_{4} =4a_{3}[/tex]
[tex]a_{4} =4.96[/tex]
[tex]a_{4} =384[/tex]
Therefore, the option (b) is correct as the sequence is generated as 6, 24, 94, 384,...
Keywords: sequence
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what is 40% of 75 i will give brainliest
Answer:
4/100
Step-by-step explanation:
bc google is smart
Suppose we want to choose 2 colors without replacement from the 3 colors
Question:
Suppose we want to choose 3 colors, without replacement, from the red, blue, green, and purple.
(a)How many ways can this be done, if the order of the choices is taken into consideration?
(b)How many ways can this be done, if the order of the choices is not taken into consideration?
Answer:
(a) 6 choices
(b) 3 Choices
Step-by-step explanation:
Given:
3 Colors
Order of choice : Red, Blue, Green
(a) Order of the choices taken into consideration :
When we are picking the first colour there are 3 color choice.
When we are picking second colour there are 2 choice and so on.
Therefore, total choices are = 3*2 = 6 choices
(b) Order of the choices not taken into consideration :
When to take this option we choose as [tex]3 \times 2[/tex] and the remove the duplicates
Therefore, choices are = [tex]\frac{(3 \times 2)}{(1 \times 2)}[/tex] =[tex]\frac{6}{2}[/tex] = 3 Choices
The concept of choosing colors without replacement has to do with probability, it means that once an item is selected, it is not put back in the set, thus changing the probability for the next selections.
Explanation:The question involves the concept of probability in Mathematics, particularly in choosing colors without replacement. This refers to the situation where you are picking something out of a set (like colors or marbles in a bag) and you don't put it back again. This changes the probability for future picks.
For instance, consider a bag containing three colors - red, green and blue. If you want to pick any two colors without replacement, we have three options for the first pick and then two for the second pick as one color is already taken out from the bag and not replaced. These options are (red, green), (red, blue), (green, red), (green, blue), (blue, red), and (blue, green).
The same concept applies when dealing with different scenarios like picking cards from a deck or marbles from a bag. Each subsequent pick after the first pick without replacement has one less option to choose from resulting in changes in probabilities with each step.
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6.50 is 25$ of what number?
Answer:
1.625
Step-by-step explanation:
25% or 6.50 is 1.625 so multiply 25 times 6.50 then divide it by 100
I WILL GIVE BRAINLEY TO THE MOST CORRECT AND FIRST ANSWER PLUS A LOT OF POINTSS!! PLEASE HELP ME ASAPPPP!
-2 + (-6y) + 5 y - 8y y=4
4x + 5 - 5x x=12
4x + 2y - x - 8 x =1 y =5
-3 + 9 -(-4y) + 5x x =1 y =-5
-8 - 4x + y - 6x x =-9 y =9
7x + 1 - y - 3x - (-9) x =7 y =-6
5x + (-y) + 8 -6x + 9y x =4 y =-2
7 - x + 4y - 6x -3y x =-1 y =8
-x - (-y) + (-x) - y + 5 x =-3 y =-6
a set of golf clubs is marked at 25% off. If the regukar price is $630, find the discount and sale price
Answer:
472.5
Step-by-step explanation:
This one is simple.
They way you figure this out is your times the amount of money for the original cost by the discout so the equation is 630 times .25 equals 157.5. You then take that disount price and minus it from the original price, which is 630 so the eqation 630 minus 157.5 equals 472.5.
Hope this helps and have a great day
Factor the following expression completely.
9y^4 - 4x^6
Answer:
(3y^2+2x^3)(3y^2-2x^3)
Step-by-step explanation:
Write 8.001 using words.
I need help!!
Answer:
eight and one thousandth.
Answer:
Eight and one thousandth
Step-by-step explanation:
Writing 8.001 in words is eight and one thousandth.
OR
Eight point zero zero one.
Note that the place value of the numbers are as follow:
8= units; 0 = tenth; 0 = hundredth and 1 = thousandth.
Immediately after the decimal point are tenth, hundredth and thousandth.
What does 7+7+7=3× explain too me how do I solve that problem
Answer:
What do u mean
Step-by-step explanation:
Is it
[tex]7 + 7 + 7 = 3x[/tex]
?
Answer:
Step-by-step explanation:
I've already answered this question.
The diameter of the sun is about 1.39 × 10^6 kilometers. The diameter of the Earth is about 1.27 × 10^4 kilometers. How many times larger in diameter is the sun than the Earth? Write your answer in scientific notation, and round the coefficient to the nearest hundredths place.
Answer:
1.09 x 10^2
Step-by-step explanation:
1.39 x 10^6 / 1.27 x 10^4 = 1.09448818898
1.09448818898 is rounded 1.09
10^6-4 = 10^2
So, 1.09 x 10^2
The sun is approximately 109.29 times larger in diameter than the Earth.
Explanation:To determine how many times larger in diameter the sun is compared to the Earth, we divide the diameter of the sun by the diameter of the Earth.
The diameter of the sun is 1.39 × 106 kilometers, while the diameter of the Earth is 1.27 × 104 kilometers.
Dividing the diameter of the sun by the diameter of the Earth, we get (1.39 × 106) / (1.27 × 104) = 109.29.
Therefore, the sun is approximately 109.29 times larger in diameter than the Earth.
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What is the answer to
4x +3 (2x - 1) - 4x
Find the median, first quartile, third quartile, and interquartile range of the data
32, 53, 72, 66, 47, 54, 49, 67, 71
Step-by-step explanation:
Given data is 32,47,49,53,54,66,67,71,72
Median = [tex](\frac{n+1}{2}) ^{th}[/tex] term
=[tex](\frac{9+1}{2} )^{th}[/tex] term
=[tex]5^{th}[/tex] term
=54
First quartile = [tex]\frac{1}{4} (n+1)^{th} term[/tex]
= [tex]\frac{47+49}{2}[/tex]
=48
Third quartile=[tex]\frac{3}{4} (n+1)^{th} term[/tex]
= [tex]\frac{67+ 71}{2}[/tex]
= 69
Interquartile range = (69- 48)
= 21
Answer:
27
Step-by-step explanation:
right on expo
A box was 3/4 full of marbles. The box fell on the floor. Thirty marbles fell out. This was 20% of the marbles in the box. How many marbles would a full box contain?
Answer:
200 marbles please rate brainliest
Step-by-step explanation:
PLEASE HELP ASAP!! THANK YOU SO MUCH!
The triangle given has base 60 and height 45
The scale says "1 unit:5 meters" which means that each unit on the grid is 5 meters. We can divide each dimension of the given triangle by 5 so we figure out how many units we'll need for each dimension of the new smaller triangle (that is similar to the original)
60/5 = 12
45/5 = 9
The smaller triangle must have a base of 12 and a height of 9
See the diagram below.
The area of this new triangle is (base*height)/2 = (12*9)/2 = 108/2 = 54 square units.
-3x+2y=-3
4x-y=-1 what is the answer
Answer:
X= -9/10
y= -2 3/5
Step-by-step explanation:
Multiply equation one by 4 and equation two by 3 to eliminate X
it becomes
-12x + 8y =-12
12x - 3y = -1
add equation one and two,
you'll be left with 5y= -13
divide both sides by 5
y = -13/5 improper fraction
= -2 3/5
Now substitut y = -2 3/5 into any of the original equations to get x.
using equation two, we have
4x -(-2 3/5) = -1
4x + 2 3/5 = -1
4x = -1 - 2 3/5
the LCM of 5 is 5 , so
4x = -5-13/5
4x = -18/5
crossmultiply
4x x 5 = -18
20x = -18
divide both sides by 20
we have x = -18/20, when you cancel further , you have x = -9/10