Answer:
Sn = ∑ 4(-6)^n, from n = 0 to n = n
Step-by-step explanation:
* Lets study the geometric pattern
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
- The sum of n terms is Sn = [tex]\frac{a(1-r^{n})}{(1-r)}[/tex], where
a is the first term , r is the common ratio between each two
consecutive terms and n is the numbers of terms
- The summation notation is ∑ a r^n, from n = 0 to n = n
* Now lets solve the problem
∵ The terms if the sequence are:
4 , -24 , 144 , -864 , ........
∵ [tex]\frac{-24}{4}=-6[/tex]
∵ [tex]\frac{144}{-24}=-6[/tex]
∴ There is a constant ratio between each two consecutive terms
∴ The pattern is geometric
- The first term is a
∴ a = 4
- The constant ratio is r
∴ r = -6
∵ Sn = [tex]\frac{a(1-r^{n})}{(1-r)}[/tex]
∴ Sn = [tex]\frac{4(1-(-6)^{n})}{(1-(-6))}=\frac{4(1-(-6)^{n})}{(1+6)}=\frac{4}{7}[1-(-6)^{n}][/tex]
- By using summation notation
∵ Sn = ∑ a r^n , from n = 0 to n = n
∴ Sn = ∑ 4(-6)^n
Answer:
[tex] a_n = (4)(-6)^{n-1}, n =1,2,3,4,.... [/tex]
And we can verify:
[tex] n=1 , a_1 = 4 (-6)^{1-1}= 4[/tex]
[tex] n=2 , a_2 = 4 (-6)^{2-1}= -24[/tex]
[tex] n=3 , a_3 = 4 (-6)^{3-1}= 144[/tex]
[tex] n=4 , a_4 = 4 (-6)^{4-1}= -864[/tex]
And finally we can write the summation like this:
[tex] S_n = \sum_{i=1}^n 4 (-6)^{n-1} , n =1,2,3,... [/tex]
Step-by-step explanation:
For this case we have the following pattern of numbers :
4-24+144-864+...
And we want to express the sum in terms of a summation.
We can use the fact the the general term for the sum can be expressed as:
[tex] a_n = a_1 r^{n-1}[/tex]
And for this case we can identify the value of r dividing successive terms like this:
[tex] r = \frac{|24|}{|4|}= \frac{|144|}{|24|}=\frac{|864|}{|144|}= 6[/tex]
So for this case we know that the value of r =6 and the initial value 4 would represent [tex] a_1 = 4[/tex]
Since the sequence is alternating with + and - signs we can express the general term like this:
[tex] a_n = (4)(-6)^{n-1}, n =1,2,3,4,.... [/tex]
And we can verify:
[tex] n=1 , a_1 = 4 (-6)^{1-1}= 4[/tex]
[tex] n=2 , a_2 = 4 (-6)^{2-1}= -24[/tex]
[tex] n=3 , a_3 = 4 (-6)^{3-1}= 144[/tex]
[tex] n=4 , a_4 = 4 (-6)^{4-1}= -864[/tex]
And finally we can write the summation like this:
[tex] S_n = \sum_{i=1}^n 4 (-6)^{n-1} , n =1,2,3,... [/tex]
The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations.
What is the survey’s margin of error?
Answer:
±4
Step-by-step explanation:
The margin of error in a confidence interval is half the range:
(84 - 76) / 2 = 4
So the margin of error is ±4.
The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The margin of error of the survey will be ±4%.
What is the margin of error?The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.
The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations. Therefore, the margin of error can be written as,
Margin of Error = (84%-76%)/2 = 8%/2 = ±4%
Hence, the margin of error of the survey will be ±4%.
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Please help me out please
A = 1/2aP
P = number of sides x length of each side
P = 8 x 5.8
P = 46.4
A= 1/2 x 7 x 46.4
A = 162.4
disponemos de vino de dos calidades de diferentes precios de 0.35 y 0.80 si queremos obtener 200 de mezcla que resulte a 0.50 cuantos litros de cada clase tenemos que enpezar
To obtain a mixture of 200 liters with an average cost of 0.50, we need to start with approximately 133 liters of the wine with a price of 0.35 and approximately 67 liters of the wine with a price of 0.80.
To solve this problem, we will call "x" the quantity of liters of the wine with a price of 0.35, and "y" the quantity of liters of the wine with a price of 0.80 that we need to obtain the desired mixture.
We know that we want to obtain 200 liters of mixture, and the average cost of the mixture should be 0.50.
We can establish the following equations:
x + y = 200 (equation for the total quantity of mixture)
(0.35 * x + 0.80 * y) / 200 = 0.50 (equation for the average cost of the mixture)
Now solve this system of equations to find the values of "x" and "y".
From the first equation, we can solve for "x" in terms of "y" as follows:
x = 200 - y
Substitute this expression for "x" in the second equation
(0.35 * (200 - y) + 0.80 * y) / 200 = 0.50
Solving this equation, we can find the value of "y":
(0.35 * 200 - 0.35 * y + 0.80 * y) / 200 = 0.50
(70 - 0.35y + 0.80y) / 200 = 0.50
(0.45y + 70) / 200 = 0.50
0.45y + 70 = 0.50 * 200
0.45y + 70 = 100
0.45y = 100 - 70
0.45y = 30
y = 30 / 0.45
y = 66.67
Now that we have the value of "y," find the value of "x" by substituting it into the first equation:
x = 200 - y
x = 200 - 66.67
x = 133.33
However, we cannot have a fractional quantity of liters, so we must round these values to whole numbers.
Therefore, to obtain a mixture of 200 liters with an average cost of 0.50, we need to start with approximately 133 liters of the wine with a price of 0.35 and approximately 67 liters of the wine with a price of 0.80.
We have wine of two different qualities with prices of 0.35 and 0.80. If we want to obtain a mixture of 200 that results in 0.50, how many liters of each class do we need to start with?
A band has 36 members. They are arranged into 6 equal rows. How many band members are in each row? Can the same 36 members be placed into exactly 7 equal rows? Why or why not?
Answer:
6 people would be in each row // It isn't possible for there to be 7 equal rows
Step-by-step explanation:
36 members/6 rows= 6 people per row // 36 members/7 rows= 5.14..... people per row (just doesn't work!)
What is the length of the diagonal of square with perimeter 12 m? Express the answer as a simplified square root.
Answer: [tex]3\sqrt{2}\ m[/tex]
Step-by-step explanation:
The perimeter of a square is:
[tex]P=4s[/tex]
Where "s" is the lenght of a side of the square.
Then, if the perimeter of this square is 12 m, you can solve for "s" and find its value:
[tex]s=\frac{P}{4}\\\\s=\frac{12\ m}{4}\\\\s=3\ m[/tex]
You can calculate the length of the diagonal with this formual:
[tex]d=s\sqrt{2}[/tex]
Where "s" is the lenght of a side of the square.
Substituting the value of "s" into the formula [tex]d=s\sqrt{2}[/tex], you get that the lenght of the diagonal of this square is:
[tex]d=3\sqrt{2}\ m[/tex]
Please help me with this!!!!
Answer:
True
Step-by-step explanation:
A plane is a flat, infinite 2D surface, so when we say two things are coplanar, they can all fit on a single plane. In this case, all three lines a, b, c, and d lie on the same 2D surface, so we'd consider them coplanar. True.
Which of the following is unnecessary when multiplying these polynomials?
(2x∧3 + 2x∧2 - 3x)(9x∧2-4x+5)
A.
use the distributive property
B.
use the multiplication property of exponents
C.
combine like terms
D.
find the GCF
Answer:
Find the GCF
Step-by-step explanation:
When multiplying the following polynomials:
(2x^3 + 2x^2 - 3x)(9x^2-4x+5)
1. First we need to use the distributive property:
(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 2x^3 * 9x^2 - 2x^3 * 4x + 2x^3 * 5 + 2x^2 * 9x^2 - 2x^2 * 4x + 2x^2 * 5 - 3x * 9x^2 + 3x * 4x - 3x * 5.
2. Second, we need to use the multiplication property of exponents:
(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 - 8x^4 + 10x^3 + 18x^4 - 8x^3 + 10x^2 - 27x^3 + 12x^2 - 15x.
3. We need to combine like terms:
(2x^3 + 2x^2 - 3x)(9x^2-4x+5) = 18x^5 +10x^4 -25x^3 + 22x^2 - 15x.
We don't need to find the GCF.
Please please help me out
Answer:
x = 2[tex]\sqrt{34}[/tex]
Step-by-step explanation:
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
x² = 6² + 10² = 36 + 100 = 136
Take the square root of both sides
x = [tex]\sqrt{136}[/tex] = [tex]\sqrt{4(34)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{34}[/tex] = 2[tex]\sqrt{34}[/tex]
Please help me out please!!!!!!!! :)
Answer:
12.3
Step-by-step explanation:
cos(35) = y/15
y = 15 * cos(35) = 12.3
Answer:
y = 12.3 cm
Step-by-step explanation:
Since the triangle is right with hypotenuse 15, use the cosine ratio to solve for y, that is
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{15}[/tex]
Multiply both sides by 15
15 × cos35° = y, hence
y ≈ 12.3
Which of the following is equivalent to 2 ln e^ln 5x = 2 ln 15?
Answer:
x = 3
Step-by-step explanation:
Given in the question an equation,
[tex]2lne^{ln5x}=2ln15[/tex]
Step 1
[tex]e^{lnx}=x[/tex]
so,
[tex]2ln(5x)=2ln15[/tex]
Step 2
cancel 2 on both sides of the equation
[tex]ln{5x}=ln15[/tex]
Step 3
[tex]ln{5x}-ln15=0[/tex]
[tex]ln\frac{5x}{15}=0[/tex]
Step 4
[tex]ln\frac{x}{3}=0[/tex]
Step 5
[tex]e^{ln\frac{x}{3}}=e^{0}[/tex]
Step 6
x/3 = 1
x = 3(1)
x = 3
the center of the inscribed circle of a triangle has been established. Which point on one of the sides of a triangle should be chosen to set the width of the compass
a. intersection of the side and the median to that side
b.intersection of the side and the angle bisector of the opposite angle
c. intersection of the side and the perpendicular passing through the center
d. intersection of the side and the altituide dropped from the opposite vertex
Answer:
c. intersection of the side and the perpendicular passing through the center
Step-by-step explanation:
The radius of the incircle is the distance from the center of that circle (known) to the nearest point on any side. That point is at the intersection of a perpendicular line through the center of the incircle.
What is the overlap of Data Set 1 and Data Set 2?
A. High
B. Moderate
C. Low
D. None
I'd say it's high: both datasets are made of 8 elements, and 6 of those 8 are in common: the only element belonging to dataset 1 but not dataset 2 is 5, and the only element belonging to dataset 2 but not dataset 1 is 10.
The overlap between Data Set 1 and Data Set 2 will be high. Then the correct option is A.
How do determine the overlap of the data set?The number of the data will be 8.
If the number of data overlaps is less than 4, then low.
If the number of data overlaps is equal to 4, then moderate.
If the number of data overlaps is greater than 4, then high.
The number of data that overlap is 6.
The overlap between Data Set 1 and Data Set 2 will be high.
Then the correct option is A.
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A guide climbs a mountain at the rate of 30 minutes for every 50 feet. How many hours will it take the guide to climb 750 feet
Answer: 7.5 hours
Step-by-step explanation:
750/50=15 to see how many times he climbed 15 feet
15 times 30=450 (total minutes)
450/60=7.5 hours
Answer:7.5
Step-by-step explanation:
450/60
What is the volume of a cone with a radius of 5 inches and a height of 8 inches?
[tex]V=209.44[/tex] | Formula for the volume of a cone: [tex]V=\pi r^2\frac{h}{3}[/tex]
The ratio of cups of orange juice concentrate to cups of water in punch is 1:3 if James made 32 cups of punch how many cups of orange juice did he need
Answer:
We have 8 cups of orange juice
Step-by-step explanation:
orange juice: water: total
1 : 3 : 4
Multiply everything by x
1x 3x 4x
We have 32 cups total
4x = 32
Divide each sice by 4
4x/4 = 32/4
x = 8
We have 8 cups of orange juice
3*8 = 24
We have 24 cups of water
The ratio of orange juice to water in the punch is 1:3, which means that for every single cup of orange juice, there are 3 cups of water. To find out how many cups of orange juice were used to make 32 cups of punch, we find out what 1 part out of the total 4 parts is, which is 32 ÷ 4 = 8. Therefore, James used 8 cups of orange juice for the punch.
Explanation:The subject of the question is Mathematics and it pertains to the concept of ratios in particular. The ratio of orange juice concentrate to water is given as 1:3. This means that for every 1 cup of orange juice, James uses 3 cups of water. So, the total parts in the punch are 1 (for orange juice) + 3 (for water) = 4 parts.
However, James made 32 cups of punch. Hence, to find out how many cups of orange juice he used, we need to find out what 1 part out of the total 4 parts is. To do this, you divide the total punch made (32 cups) by the number of total parts (4).
Therefore, 32 cups divided by 4 equals 8 cups. Hence, James used 8 cups of orange juice to make the punch.
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Which graph represents the parabolic equation
(x − 2)2 = 12(y − 3)?
ANSWER
Option B
EXPLANATION
The equation given to us is;
[tex] {(x - 2)}^{2} = 12(y - 3)[/tex]
Comparing this to the general parabolic equation:
[tex] {(x - h)}^{2} = 4p(y - k)[/tex]
We have h=2 and k=3.
The vertex of this parabola is (h,k) which is (2,3).
This parabola also opens upwards because the value of p is positive.
The correct graph is B.
Which of the following are the x-intercepts on the graph of the function shown below?
[tex]f(x)=(x+2)(x-7)[/tex]
A, 7
B. -2
C. 2
D. -7
Answer:
Option A, 7 and Option B, -2
(7,0) and (-2,0)
Step-by-step explanation:
Given in the question a function f(x) = (x+2)(x-7)
Step 1
Expand the function (x+2)(x-7)
x(x-7)+2(x-7)
x² - 7x + 2x - 14
x² - 5x - 14
Step 2
To find the x-intercepts we will substitute y with 0
y = x² - 5x - 14
0 = x² - 5x - 14
(x-7)(x+2) = 0
x = 7
x = -2
Answer:
The x-intercepts would be 7 and -2.
Step-by-step explanation:
help please thank you.
first answer choice is yes or no.
other answer choices are: 3 4 5 6
Hello there! Here are your answers:
Does Kerri's dot plot match the data in the tally table? No.
Look at any of the hours on the chart vs dot plot. Let's take 4 for example. In the tally table, there are 6 class mates. In the plot, there are 3. So no, it is not the same.
The answers for the other problems are in this order (since it's the number of circles on the dot plot at the given hour):
5 - classmates spent 3 hours at the park
3 - classmates spent 4 hours at the park
6- classmates spent 5 hours at the park
4 - classmates spent 6 hours at the park
I hope this was helpful and let me know if you need more help! :) Have a great day! :)
Answer:
the other guy is right
Step-by-step explanation:
-~- boiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii laggy
Someone please help??
Answer:
the correct answer would be c, g(x)=2^x+2
Step-by-step explanation:
We can eliminate the first and the last option because the line is going upwards, not downwards(it would if it was negative or had the negative sign in front). We can cross out the second option because if it was 2^x+3, then it would be crossing (0,4) on the y-axis. Therefore the correct option is C, since it crosses right at (0,3).
hope this helps :)
Re-write this question to make it a statistical question:
How old am I?
it means that you must write "How old am I" into a statistical question
A statistical question is a question asked with the goal of collecting data. You could rewrite the question so that it says something like, “How old were you when..” That way the responses will vary and you would be able to graph and compare them.
The statistical question of the given statement is How old were you then.
The following tells about the statistical question:A statistical question is one that can be answered by collecting data and for which there will be variability in that data.For example, there will likely be variability in the data collected to answer the question, "How much do the animals at Fancy Farm weigh?" but not to answer, "What color hat is Sara wearing?"A statistical question is a question that can be answered by gathering data and a question for which we expect to have variation in the data we collect.Hence, the statistical question of the given statement is How old were you then.
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What is the surface of a sphere with a radius of 13 units?
Sphere = 4PiRsquared
Radius = 13
13 x 13 = 169
169 x 4= 676 Pi
5e surface is 676Pi
Answer:
The correct answer is option B. 676π units²
Step-by-step explanation:
Formula:-
The surface area of a sphere = 4πr²
Where r is the radius of sphere
To find the surface area of given sphere
Here r = 13 units
Surface area = 4πr²
= 4 * π * 13²
= 4 * π * 169 = 676π units²
Therefore the correct answer is option A. 676 units²
Meg has 21 feet of ribbon that she wants to divide into of a foot pieces. How many of a foot pieces are there in 21 feet?
Answer:21
Step-by-step explanation:
if there are 21 feet of ribbon and we need it in foot long pieces there are 21
Answer:
35
Step-by-step explanation:
Please help me out with this
Answer:
Step-by-step explanation:
Formula
a^2 + b^2 = c^2
Givens
a = x
b = 20.2
c = 14.7 + x
Solution
x^2 + 20.2^2 = (14.7 + x)^2 Expand the brackets
x^2 + 408.04 = 14.7^2 + 29.4x + x^2 Cancel the x^2
408.04 = 216.9 + 29.4x Subtract 216.9 from both sides.
191.98 = 29.4x Divide by 29.4
6.52993 = x Answer.
6.5 to the nearest tenth.
Answer:
x = 6.5 cm
Step-by-step explanation:
The tangent to the circle forms a right angle with the radius x
Using Pythagoras' identity on the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides
The hypotenuse is (x + 14.7) ← opposite the right angle, hence
(x + 14.7)² = x² + 20.2² ← expand parenthesis on left side
x² + 29.4x + 216.09 = x² + 408.04 ( subtract x² from both sides )
29.4x + 216.09 = 408.04 ( subtract 216.09 from both sides )
29.4x = 191.95 ( divide both sides by 29.4 )
x ≈ 6.5 cm
What is the value of B?
Answer: 120
Step-by-step explanation:
Please help with this question!! I am out of points now!! I need this!
Answer:
C
Step-by-step explanation:
Draw in <QOS. That's the central angle. It is also 60 degrees.
<R which has Q and S as its end points, = 1/2 the central angle (always) so <R = 30 degrees.
C
Is it possible to have exactly 100 coins consisting only of pennies, dimes, and quarters so that the 100 coins are worth exactly $5
Answer:
yes
Step-by-step explanation:
Membership to a national running club is shown in the table which answer describes the average rate of change from year 3 to year 5?
Membership increased by an average of 6,600 people per year from year 3 to year 5
Membership decreased by an average of 6,600 people per year from year 3 to year 5
Membership decreased by an average of 13,200 people per year from year 3 to year 5
Membership increased by an average of 13,200 people per year from year 3 to year 5
Answer:
"Membership decreased by an average of 6,600 people per year from year 3 to year 5"
Step-by-step explanation:
To get average rate of change from year 3 to year 5, we need to divide the change from year 3 to 5 by 2 (because from year 3 to 5 is 2 years).
THe change is:
83.6 - 96.8 = -13.2
We divide by 2 to get per year average rate of change:
-13.2 / 2 = -6.6
In thousands, that is 6600 decrease.
2nd answer choice is right.
The equation for the circle is:
x2+y2+16x−24y+159=0 .
What is the center of the circle?
the center is : (-8 , 12)
Kory calculated several numbers in his calculator. The result displayed 1.3E-2 on the calculator screen. Which equivalent number(s) does this represent? 13 × 102 130 0.013 1.3 × 10-2 -0.013
Answer:
1.3×10⁻² = 0.013
Step-by-step explanation:
The "E" stands for "×10^", so 1.3E-2 means 1.3×10^-2.
Of course 10^-2 = 1/10^2 = 1/100 = 0.01, so
1.3E-2 = 1.3×10^-2 = 1.3×0.01 = 0.013
_____
This notation was used by early computers to print results where the character set was limited and superscripts could not be printed.
Interquartile range for 16,23,25,27,29,33,35,40,43
Answer:
the interquartile range is 13.5
minimum 16
maximum 43
medium 29
lower Q1 24
upper Q3 37.5 or 38
Range 27