The formula for finding any term of the given sequence is [tex]a_{n}[/tex] = [tex]n^3[/tex].
According to the given question.
We have a sequence
-1,1,-1,1,-1,1....
As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.
The above of given sequence -1,1,-1,1,-1,1,..... is following a rule i.e. each term is the cube of its number of term.
Here,
The first term is -1, so the cube of -1 is -1.
The second term is 1, so the cube of 1 is 1.
So, the nth term of the given sequence is [tex]n^{3}[/tex].
Therefore, the formula for finding any term of the given sequence is given by
= [tex]n^3[/tex]
Where, n = Therefore, the formula for finding any term of the given sequence is given by
= [tex]n^3[/tex]
Where, n = -1,1,-1,1,-1,1, .......
So, for n = -1
The first term will be -1.
for n =1
The second term will be 1
for n= 1
The fourth term will be 1 and so on .
Hence, the formula for finding any term of the given sequence is [tex]n^3[/tex].
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Please help me find the answer to this question.
The lengths 12, 16, 10, 5, and 2 of the sides, AP, DQ, CS, PQ, and QR respectively, using the triangle proportionality theorem, gives the area of trapezoid BRSC as 40 square units.
What is the triangle proportionality theorem?The triangle proportionality theorem states that a line parallel to a side of a triangle and also intersects the other two sides, it divides the two sides proportionally.
Based on the theorem, where the other two sides are perpendicular, the parallel side divides the two sides equally.
The given parameters are;
The figure represented by ABCD = A parallelogram
The lengths of the sides of the figure are;
AP = 12
DQ = 16
CS = 10
PQ = 5
QR = 2
Required: The area of figure BRSC
Solution;
Given that ABCD is a parallelogram, we have;
AD = BC (definition of a parallelogram)
Using the triangle proportionality theorem, we have;
PQ = RS = 5 (segments bounded by equidistant parallel lines)
DQ - CS = AP - BR = 16 - 10 = 6 (Parallel vertical lines intersected by parallel lines at different heights)
AP - BR = 6
BR = 12 - 6 = 6
The area, A, of trapezoid BRSC is therefore;
A = RS × (BR + CS)/2
Which gives;
A = 5 × (6 + 10)/2 = 40
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What equation in the point slope form matches the graph line shown
A• y+6= 4/5 (x+3)
B•y-2=-3/4(x-6)
C•y-6=4/5(x-3)
B•y-5=-2/3(x+9)
to get the equation of any straight line, we simply need two points off of it, let's use the ones in the picture below.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-3)}}} \implies \cfrac{-2 +6}{2 +3} \implies \cfrac{ 4 }{ 5 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{\cfrac{4}{5}}(x-\stackrel{x_1}{(-3)}) \implies y +6= \cfrac{4}{5} (x +3)[/tex]
Write and solve the inequality that represents negative one fifth is greater than or equal to the product of negative two thirds and a number.
The solution of the given inequality is given as [tex]x\geq \frac{3}{10}[/tex]
What is an inequality?
Inequality is a declaration of an order connection between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
According to the question, the inequality may be written and solved as follows:
[tex]-\frac{1}{5}\geq -\frac{2}{3} x[/tex]
[tex]or, \frac{1}{5}\leq \frac{2}{3} x[/tex]
[tex]or,\frac{1}{5}* \frac{3}{2} \leq x[/tex]
[tex]or, x\geq \frac{3}{10}[/tex]
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Use the spinner to find following probability. The spinner is spun again if it stops on a line.
P (pointer landing on green)
The probability of the spinner's point landing on green is 22.23%.
What exactly is a pie chart?A pie is a kind of chart that displays data in the form of a circular graph.
We understand that the total value of the pie is always 100%. It is also understood that a circle does have a circumference of 360°. As an outcome, the total of all data points equals 360°. There appear to be mainly two pie chart formulas based on these:
To determine a percentage of a data set, we use the following format: 100 (Frequency ÷ Total Frequency) × 100To convert the information to degrees, we use the given equations: (Informed Data ÷ Total value of Data) × 360°When a circle is completely rotated, it forms a 360-degree angle in the center.
At the center of the circle, a complete rotation yields 360 degrees.
The total percentage of all colors is 100%.
Divide a value of green by 3.6 since 360 degrees / 100% = 3.6.
The total percentage of green displayed by the spinner's pointer is 80%.
P (probability of the cursor landing on green) = 80/3.6
Probability P (cursor landing on green) = 22.222... = 22.23 (approx.)
As a result, the probability which the pointer will land on the green is 22.23%.
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Find the value of x2 values that separate the middle 80 % from the rest of the distribution for 20 degrees of freedom.
The value of x² values that separate the middle 80 % from the rest of the distribution is
With alpha and degrees of freedom χ²= 12.443
And with alpha and degrees of freedom χ²= 28.412
Chi - Square Distribution:
The chi square distribution is the continuous distribution, where the degree of freedom is the sample size minus 1, and it is the parameter of the chi-square probability distribution.
Given,
Here we need to find the value of x² values that separate the middle 80 % from the rest of the distribution for 20 degrees of freedom.
Based on the given details,
Degrees of freedom = 20
Middle separate value = 80%
Which is equal to 0.8 in decimal point.
The significance level
=> ∝ = 1 - 0.8
=> ∝ = 0.2
But we need the area of the middle so we divide this significance level with 2
so that we get exactly the middle area .
Dividing
=> 0.2/2= 0.1
So we will have two values for chi square
One with
=> 0.8 + 0.1 = 0.9 alpha
and
one with
=> 0.1 alpha .
This is because the chi square is right tailed.
Now based on the chi square distribution table,
So with alpha 0.9 and 20 degrees of freedom χ²= 12.443
And with alpha 0.1 and 20 degrees of freedom χ²= 28.412
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What is the y - intercept of he line with the equation: y=2x+9
Answer:
Step-by-step explanation:
The y -intercept Is: b=9 or (0,9)
It's vote counting day for an election held in a country. The 3 TV stations updated the public about the number of votes cast starting at 7:00 in the morning. TV station A announces the vote counts every 2 hours, TV station B announces it every 3 hours, and TV station C announces it every 4 hours. At what time will the three TV stations announce the vote counts at the same time?
The 3 tv stations will announce the news again after 12 hours at 7 in the evening which is calculated by taking the LCM of the 3 intervals.
LCM or lowest common multiple of 2 or more numbers is defined as the minimum number which is lowest multiple of of the 2 or more numbers which is equal.
In mathematics and number theory. Since the result of dividing an integer by zero is not defined this definition only applies if both x and y are not equal to zero. However, given that 0 is the only common multiple of x and 0, some authors define LCM(x,0) as 0 for all x.
The intervals in which channels announce the news are 2 hours, 3 hours and 4 hours.
So we have to find the LCM of the numbers.
LCM(2,3,4)=12 as 12 is the smallest integer which is divided by all the other 3 numbers.
So the news channels will announce the news after 12 hours.
Since they announced at 7 in the morning so they would all announce the news again at 7 in the evening.
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Is 22/25 a terminating or repeating decimal
help...................................................
5 is the correct scale factor
This is because there are 5 little segments that go from C to the larger point in the top right corner. We need 5 pieces of segment CB to get segment CB' where B' is that top right corner point.
Put another way: If the distance from C to B is 1 unit, then the distance from C to B' is 5 units. This shows the distance has multiplied by 5, and that's the scale factor.
Points A and B have coordinates A(-4,2) and B(3,-6). Find the coordinates of point P, the weighted average of points A and B, in which point A has a weight of 4 and point B has a weight of 3.
A (-7/2, -5)
B (-1,-10/7)
C (-1/2, -2)
D (0,-20/7
The coordinates of the point P is P(x, y) = (- 1, - 10 / 7). (Correct choice: B)
How to determine the coordinates of a resulting point by weighted averages approach
In this problem we find the coordinates of two points on Cartesian plane, of which we must determine the location of a third point by using a formula based on a weight average-like formula:
P(x, y) = (4 / 7) · A(x, y) + (3 / 7) · B(x, y)
P(x, y) = (4 / 7) · (- 4, 2) + (3 / 7) · (3, - 6)
P(x, y) = (- 16 / 7, 8 / 7) + (9 / 7, - 18 / 7)
P(x, y) = (- 7 / 7, - 10 / 7)
P(x, y) = (- 1, - 10 / 7)
The coordinates of the point P is P(x, y) = (- 1, - 10 / 7).
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The hobbits Frodo, Sam, Pippin and Merry have breakfast at different times. Each one takes a quarter of the porridge in the pan, thinking that the other three have not yet eaten. What fraction of the porridge is left after all four hobbits had their breakfast?
Step-by-step explanation:
Let us start with Frodo's breakfast. He starts eating a quarter of the porridge. Let us say the porridge is 100 spoons, to make dividing easier. After Frodo we have [tex]\frac{3}{4}[/tex] left of the original bowl; we are left with 75 spoons.
100 - [tex]\frac{1}{4}[/tex] = 100 - 25 = 75
Next, comes Sam's breakfast. He eats 75 - [tex]\frac{1}{4}[/tex] = 75 - 18.75 = 56.25 spoons left.
Next, we have Pippin's breakfast. He eats 56.25 - [tex]\frac{1}{4}[/tex] = 42.1875 spoons.
Lastly, we have Merry's breakfast. He eats 42.1875 - [tex]\frac{1}{4}[/tex] = 31.640625 spoons.
Now, we know we have 31.640625 spoons left. However, we need to know what fraction this is out of the original porridge bowl. So, we do:
31.640625 * 100 = 3164.0625 * 1 = 3164.0625
3164.0625% of the bowl remaining!
What a yummy breakfast!
Simplify. Assume a is greater than or equal to zero.
Answer:
3a² √2a
(o´▽`o)ﾉ xx
A coin is tossed and a die is rolled. What is the probability that the coin lands heads up and the number rolled is a 6 ?
The probability that the coin lands heads up and the number rolled is a 6 is 1/12.
Given that a die is rolled and a coin is tossed.
We have to find the probability that the coin lands heads up and the number rolled is a 6.
Probability of getting heads in tossing a coin = 1/2
Probability of getting 6 in rolling a die = 1/6
The event of tossing a coin and rolling die are independent.
Hence,
Probability that the coin lands heads up and the number rolled is a 6 =
Probability of getting heads in tossing a coin * Probability of getting 6 in rolling a die = (1/2)*(1/6) = 1/12.
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What is the answer okkkkkkkkkkk
Step-by-step explanation:
well,
23 < 12 + 0.04×x
11 < 0.04×x
11/0.04 < x
275 < x
x > 275 or x >= 276
so, for more than 275 monthly calls (that means 276 or higher) plan 1 is more economical.
at 275 calls is is plain even between both plans.
for fewer calls than 275 plan 2 is more economical.
On his quiz, Jim answered 1
10
of the questions incorrectly.
What percent is equal to?
10
Answer:
90%
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each linear graph to its slope
of the line given the following information. Write the
The slope is 5, and the line passes through the point (9, -9).
Answer:
y = 5x - 54
Step-by-step explanation:
that is the solution above
What is the critical value of the test statistic to test the mean child mortality rate for countries in africa is more than the mean child mortality rate for countries in south asia?
The critical value is [tex]5[/tex] for the statistical test to test the mean child mortality rate for countries in Africa and the mean child mortality rate for countries in South Asia.
The child mortality rate or under age as five mortality rate tells that the child is dying during birth timing or exactly at the age of five. Globally million kids are dying at the age of five due to diseases like pneumonia or diarrhea or malaria etc. It is a big concern as well as a matter of responsibility for the child's survival at the age of five.
Many places in the world suffer from these problems and countries with low income ranges have a burden of child mortality. This problem is unevenly distributed throughout the world. Child survival is a constrained resource nowadays. The maximum child death is in sub Saharan Africa due to severe acute malnutrition.
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grapn
given conditions.
The graph of f passes through (-9,8) and is perpendicular to the line whose equation is x = 4.
Answer:
y = 8
Step-by-step explanation:
x = 4 is the equation of a vertical line parallel to the y- axis.
A perpendicular line will be a horizontal line with equation
y = c ( where c is the value of the y- coordinates the line passes through )
the line passes through (- 9, 8 ) with y- coordinate 8 , then
y = 8 ← equation of perpendicular line
Is 3 + (-4) the same as -4 + 3? Explain
Answer:
Yes, 3 + (-4) is the same as -4 + 3.
Step-by-step explanation:
When doing addition problems such as this, the order of the numbers does not matter, even when negative numbers are included.
For example, 1 + 2 or 2 + 1 would equal 3.
3 + (-4) = -1
-4 + 3 = -1
Hope this helped you! Let me know if you need more clarification. :)
Triangle ABC has vertices A(–1, 0), B(4, 0), and C(2, 6). If ΔABC is translated using the function rule (x, y) → (x – 6, y – 5) and then rotated 180° clockwise, what would be the coordinates of the vertices of ΔA’’B’’C’’?
a. A’’(–5, 7), B’’(–5, 2), C’’(1, 4)
b. A’’(7, 5), B’’(2, 5), C’’(4, –1)
c. A’’(7, 5), B’’(2, 5), C’’(4, 1)
d. A’’(–7, –5), B’’(–2, –5), C’’(–4, 1)
Answer:
b. A''(7, 5), B''(2, 5), C''(4, –1)
Step-by-step explanation:
Given vertices of ΔABC:
A = (-1, 0)B = (4, 0)C = (2, 6)Translation mapping rule:
(x, y) → (x – 6, y – 5)
Therefore:
A' = (-1 - 6, 0 - 5) = (-7, -5)B' = (4 - 6, 0 - 5) = (-2, -5)C' = (2 - 6, 6 - 5) = (-4, 1)Rotation of 180° clockwise rule:
(x, y) → (-x, -y)
Therefore:
A'' = (-7, -5) = (7, 5)B'' = (-2, -5) = (2, 5)C'' = (-4, 1) = (4, -1)Learn more about transformations here:
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Classify the function
-10
-5
10
5
-5
-10
5
10
the function is (5)(-10)
find two consecutives positive integers such that the square of the smaller integer, added to 3 times the larger integer is 24
Answer:
4 and 5
Step-by-step explanation:
Give Brainliest if I helped!
Use the Hypotenuse Theorem
Answer:
Image result for Use the Hypotenuse Theorem
The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.
Step-by-step explanation:
if there are 72 residents on 12 floors in a hotel, then there are 18 residents on _____ floors of the hotel
A 20
B 18
C 9
D 3
Answer: D. 3
Step-by-step explanation:
Let's make a proportion:
72 residents - 12 floors
18 residents - х floors
Hence,
[tex]\displaystyle\\x=\frac{18*12}{72} \\\\x=\frac{18*4*3}{18*4} \\\\x=3\ floors[/tex]
Bill has a paper route. It takes him 50 minutes
to deliver newspapers to his 40 customers. How
long will it take Bill to complete his route if he
adds 20 more customers in his neighborhood?
Answer:
75 min or 1 hour 15 min
Step-by-step explanation:
20 is 50% of 40 so add 50% of 50 min to the total. Half of 50 is 25 so you add 25 min
Answer:
if bill takes
40 customers =50 minutes
20 customers= 50÷2 =25 minutes
so 50 minutes + 25 minutes= 75 minutes in total.
What is the distance between points J and K?
Please, show your work.
Answer:
the answer would be 12 units.
Step-by-step explanation:
now you may count the number line and find that you find 6 units, BUT you need to check the values. You can simply do an equation 4 - - 8 = 12 or you can do 6 *2 which is 12.
Ferrera is 3/4 as old as June, and Tomasso is 1. 1/2 times as old as Ferrera. How many times as old as June is Tomasso? Write
your answer as a fraction.
June is 9 / 8 times as old as Tomasso in the question.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Ferrera is 3/4 as old as June, and Tomasso is 1. 1/2 times as old as Ferrera.
The number of the times will be calculated as below:-
F = ( 3 / 4) J
T = 1 ( 1 / 2 ) F
T = ( 3 / 2 )F
Put the value of F in the second equation.
T = ( 3 / 2) ( 3 / 4 )J
T = ( 9 / 8)J
Therefore, June is 9 / 8 times as old as Tomasso in the question.
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Two spherical pieces of cookie dough have radii of 3 centimeters and 5 centimeters, respectively. The pieces are combined to form one large spherical piece of dough. What is the approximate radius of the new sphere of dough? Round to the nearest tenth.
The radius of the new sphere of dough is 5.3368
In the given statement is :
Two spherical pieces of cookie dough have radii of 3 centimeters and 5 centimeters, respectively. The pieces are combined to form one large spherical piece of dough.
To find the approximate radius of the new sphere of dough
V 1 = 4/2 · 3³ π = 108/3 π
V 2 = 4/3 · 5³ π = 500/3 π
The new sphere: V = V 1 + V 2 = 608/3 π
4/3 r³ π = 608/3 π / : π/3
4 r³ = 608
r³ = 608 : 4 = 152
r = ∛152
r = 5.3368 cm
Hence, The radius of the new sphere of dough is 5.3368
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I need this answered for me please
Answer:
[tex]\frac{w}{2}[/tex] + 9 = 7
Step-by-step explanation:
Answer:
[tex] \frac{w}{7 } + 9 = 7[/tex]
