The nth term of the given sequence is 1/n².
What is arithmetic progression?An arithmetic progression (AP) is a sequence of numbers in which each term, starting from the second term, is obtained by adding a fixed constant value to the previous term. This constant value is called the common difference, and it remains the same throughout the sequence.
What is geometric progression?A geometric progression (GP) is a sequence of numbers in which each term, starting from the second term, is obtained by multiplying the previous term by a fixed constant value. This constant value is called the common ratio, and it remains the same throughout the sequence.
In the given question,
The given sequence is of the form:
1, 1/2², 1/3², 1/4², ...
So, the nth term can be written as:
1/n²
Therefore, the nth term of the given sequence is 1/n².
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Part B: create your own cube root function.
Come up with the equation of 2 different cube root functions. None of these can be the parent function y=^3 squared root of x. For each, find the domain, range, x- and y-intercepts, and describe any transformation for each. Also, give the coordinates of 3 points that you known are on the function (coordinates must be exact values).
Jen is studying how years of drought conditions have caused the water level of Richland Reservoir to drop. At the start of the study, the water in the reservoir was 65 meters deep. Jen observed that the depth of the water dropped by about 0.8 meters the first month of the study. She wants to know what the depth of the water will be if it continues dropping at the same rate. You can use a function to approximate the depth of the water in the reservoir x months after the start of the study. Write an equation for the function.
The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
What is a linear function?
A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.
We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:
D(x) = 65 - 0.8x
where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
Therefore, the equation for the function is D(x) = 65 - 0.8x.
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Hi please help me with this question
115° is the value of external angle.
Where is exterior angle?
Angles that are outside of a polygon but parallel to its inner angles are said to be its outside angles. The total of the two internal opposite angles is the measure of an outside angle. A triangle's one side is extended to form the triangle's exterior angle.
Exterior angles are those that exist between an extended side and the side that is immediately adjacent. A triangle's outer angles all have measurements that are equal to the sum of their two opposite sides. inner perspectives.
AD ║EG
∠BFC= 75°
∠EFB = 40°
∠FCD = ( 40+75)
= 115°
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which describes a quadrilateral
Answer: any shape with four sides
Step-by-step explanation:
Answer: 4 sides
Step-by-step explanation: The only qualification for a shape to be called a quadrilateral is that it has 4 sides
Hope this helps :)
7 x 10 the the power of -5
Answer:
0.00005
Step-by-step explanation:
you move 5 decimal places left starting from 7 and right it as a decimal.
Ans=0.00007
Which expression is equivalent to
Wi
203
156²
b(2/15b)
2a²c²
ਕੰਠ,
15b²
603
75a7b4
40a1329
? Assume a 0 and c + 0.
why do we even need to know this stuff I think it's b
plSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
2 wholes 3 tenths and 5 hundredths
Step-by-step explanation:
A sweater originally cost $42.75. Last week, Keisha bought it at 20% off.
What is the discount?
O A. $51.30
08 $42.95
c. $8.55
D. $42.55
Answer:
The discount is $8.55, which is option C.
Step-by-step explanation:
To find the discount, we need to calculate 20% of the original price:
Discount = 20% x $42.75
Discount = $8.55
Therefore, the discount is $8.55, which is option C.
You deposit $1,000.00 in an account earning 3.44% interest compounded monthly. How much will you have in the account in 8 years?
Answer: $1,282.31 in the account after 8 years.
Step-by-step explanation:
To calculate the future value of the investment, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $1,000.00 (the initial deposit)
r = 3.44% = 0.0344 (the annual interest rate)
n = 12 (the number of times the interest is compounded per year, since it is compounded monthly)
t = 8 (the number of years)
So, plugging in the values:
A = $1,000.00 * (1 + 0.0344/12)^(12*8)
A = $1,000.00 * (1 + 0.0028666666666667)^96
A = $1,000.00 * 1.2823139327534472
A = $1,282.31 (rounded to the nearest cent)
Therefore, you will have approximately $1,282.31 in the account after 8 years.
Solve by the substitution method. (If there is no solution, enter NO SOLUTION. Use the parameters x and y as necessary.)
2x − 4y = 40
−x + 2y = −20
(x, y) =
The solution to the system of equations 2x - 4y = 40 and -x + 2y = -20 is infinitely many solutions. The solution can be expressed as (x, y) = (2y + 20, y), where y can be any real number.
How many square millimeters are in 6 millimeters?
Answer:
0.0093 square inches
Step-by-step explanation:
Pls help nonsence will be reported and banned offering 100 points!!! and brainiest
The inequality that determines the maximum number of speakers, x, Michael can buy is: B. $46.00 + $483.33 < $1,045.69
How to Solve Inequalities?To determine the maximum number of speakers, x, Michael can buy without spending more money than he has in his account, we need to use the following inequality:
Total amount spent on TV and speakers ≤ amount of money in the account
We know that Michael has $1,045.69 in his account, and he will spend $483.33 on a new television. Let x be the maximum number of speakers he can buy. Each speaker costs $46.00, so the total amount spent on the speakers will be $46.00x. Thus, we can write the inequality as:
$483.33 + $46.00x ≤ $1,045.69
Simplifying this inequality, we get:
$46.00x ≤ $1,045.69 - $483.33
$46.00x ≤ $562.36
x ≤ $562.36 ÷ $46.00
x ≤ 12.20 (rounded to two decimal places)
So the maximum number of speakers Michael can buy without spending more money than he has in his account is 12.20. However, since he cannot buy a fractional number of speakers, he can only buy a maximum of 12 speakers.
Therefore, the correct inequality that determines the maximum number of speakers, x, Michael can buy without spending more money than he has in his account is:
B. $46.00 + $483.33 < $1,045.69
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Justin purchased his dream car worth $18500 on a finance for 4 years. He was offered 6% interest rate. Assuming no other charges and no tax, we want to find his monthly installments.
Using simple interest his monthly installments are $1243.38
What is simple interest?The amount on Simple interest is given by A = P(1 + rt) where
P = principal, r = interest rate and t = timeNow, since Justin purchased his dream car worth $18500 on a finance for 4 years. He was offered 6% interest rate. Assuming no other charges and no tax, we want to find his monthly installments.
His installments are his principal. so, making P subject of the formula, we have that
P = A/(1 + rt)
Given that
A = $ 18500r = 6% = 0.06 and t = 4 yearsSubstituting the vales of the variables into the equation, we have
P = A/(1 + rt)
P = $ 18500/(1 + 0.06 × 4)
P = $ 18500/(1 + 0.24)
P = $ 18500/1.24
P = $ 14919.35 per year
To find his monthly installments, we divide P by 12.
So, P' = P/12
= $ 14919.35/12
= $1243.38
So, his monthly installments are $1243.38
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please help image attached x=?
Answer:
90
Step-by-step explanation:
it is a square
in a square all angles are equal to 90 degrees
b) Find the domain and range of g(x) 1÷(x-2) +5. what is the h value and k value for g(x)?
The domain = {x ∈ R : x ≠ 2} and the range = {g ∈ R : g ≠ 5} In light οf this, g(x) has a h value οf 2 and a k value οf 5.
What is an illustratiοn οf range?The difference between bοth the highest & lοwest values in statistics fοr a particular data cοllectiοn is called the range. Fοr instance, if the data set is 2, 5, 8, 10, 3, then the range is 10 - 2 = 8.
The definitiοn οf the functiοn g(x) is.
g(x) = 1/(x - 2) + 5
As the denοminatοr οf a fractiοn cannοt be zerο, the dοmain οf g(x) includes all real integers with the exceptiοn οf x = 2.
The range οf g(x) can be fοund by cοnsidering the behaviοr οf the functiοn as x apprοaches infinity οr negative infinity. As x apprοaches infinity οr negative infinity, the value οf g(x) apprοaches 5 (since the 1/(x - 2) term becοmes negligible cοmpared tο 5). Therefοre, the range οf g(x) is all real numbers except values very clοse tο 5.
It is pοssible tο rewrite the functiοn g(x) as fοllοws:
g(x) = (1/(x - 2)) + 5
This is in the fοrm:
g(x) = a/(x - h) + k
Where a = 1, h = 2, and k = 5.
Therefοre, the h value fοr g(x) is 2, and the k value fοr g(x) is 5.
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9.Weights of the NBA’s Top 50 Players Listed are the weights of the NBA’s top 50 players. Construct a grouped frequency distribution and a cumulative frequency distribution with 8 classes. Analyze the results in terms of peaks, extreme values, etc.
Frequency Distribution Table is down below.
Class Count Cumulative Frequency Table
160 - 180 3 3
181 - 201 5 8
202 - 222 14 22
223 - 243 14 36
244 - 264 10 46
265 - 285 2 48
286 - 306 1 49
307 - 327 1 50
Total 50 100
How to explain the distributionHere its peak is in between 202 to 243 frequency range. There are three extreme values that are 270, 295 and 325 pounds weight.
Median lies in the interval 223-243 and mean also lies in that interval. Maximum values lies in between 200 - 225 interval.
The distribution is left skewed.
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A cube has edges measuring 7 inches each find the volume
The volume of the cube of 7 inches when calculated is 343 cubic inches
Calculating the volume of the cubeA cube is a three-dimensional solid figure that has six faces, each of which is a square.
All the edges of a cube are of equal length. In this case, each edge of the cube measures 7 inches.
To find the volume of a cube, we need to multiply the length, width, and height of the cube together.
Since all edges of the cube are of equal length, we can simply cube the length of one of the edges to find the volume.
Therefore, the volume of this cube is calculated by multiplying the length of one edge by itself three times:
Volume = 7 x 7 x 7 = 343 cubic inches.
So, the volume is 343 cubic inches.
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Graph Set A: {(c,y):y>2x^2+5x-3
The scatter plot shows the resale value of the same make
and model car and the age of the car in years. Predict the
price you would pay if you purchase one of these cars that
is 9.5 years old.
rewrite the following without an exponet. 3^-4
Answer:i think -81
Step-by-step explanation:3x (-3) = -9. -9x(-3)=27. 27x(-3)= -81
Which function represents the reflection over the x-axis of f(x)=√x?
8
814
4
-4
do &
4
8
8
4
814
4
do £
O
1100
4 8
x
0
-1
-2
-4
y
0
-1
-1.41
-2
x
0
1
2
4
y
0
-1
-1.41
-2
Answer: 32 and 43
Step-by-step explanation:
Question is posted on the picture. Plssss help!!!
Step-by-step explanation:
that the answerrrrrrrrr
The reservoir dropped feet during a long dry spell and then rose feet following that. Which expression shows one way to calculate the total change in reservoir height over both years?
A.
B.
C.
D.
The tοtal change in reservοir height οver bοth years is a decrease οf 2 feet.
What is the tοtal difference in reservοir height between the twο years?The tοtal change in reservοir height οver bοth years can be calculated by finding the difference between the final height and the initial height.
Let's assume that the initial height οf the reservοir was H.
After the lοng dry spell, the reservοir drοpped 6 feet, which means its height became H - 6.
Fοllοwing that, the reservοir rοse 4 feet, which means its height became (H - 6) + 4 = H - 2.
Therefοre, the tοtal change in reservοir height οver bοth years can be calculated as:
Tοtal change = Final height - Initial height
= (H - 2) - H
= -2
Sο the answer is C) -0+. The tοtal change in reservοir height is a decrease οf 2 feet.
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D) what is the domain and range of the graphed function?
E) Isabel’s competition, who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0.
F) graph the function in part e
G) is your graph discrete or continuous? Explain.
The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.
What is a Continuous Function?A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.
We can express the total cost of an order as a function of the number of books sold, x, using the formula:
f(x) = 1.99x + 3
This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.
For example, if we sold 3 books, we can use the function to find the total cost:
f(3) = 1.99(3) + 3 = 9.97
This means that selling 3 books would cost $9.97 in total.
The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.
The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.
In contrast, a discrete function can only take on specific values, usually whole numbers or integers.
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Find an equation in standard form passing through the points (3,-6)(1,-2)(6,3)
An equation in standard form passing through the points (3, -6) and (1, -2) is 2x + y = -3.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (3, -6), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y +6 = \frac{(-2+6)}{(1 -3)}(x -3)[/tex]
y + 6 = -2(x - 3)
y = -2x + 3 - 6
y = -2x - 3
2x + y = -3
In this context, we can reasonably infer and logically deduce that an equation of the line that represents this table in standard form is 2x + y = -3.
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Mrs lee buys 10 pounds of vegetables to make traditional kimchi. If the cabbages alone weigh 7 pounds, what is the percentage of the weight of the cabbages
Answer:
the answer is 70%
Step-by-step explanation:
if all equals 100% and theres 10 pounds that means 7 pounds is eaqual to 70%
ASAP BELOW IS MY QUESTION
89⁴×10⁴
Answer:
627422410000
hope it helps
what is the answer of 10.9% of $8.85
Answer:
To find 10.9% of $8.85 we can convert the percentage into a decimal:
10.9% = 0.109
0.109x8.85 = $0.964
=$0.96 (Rounded to 2 decimal places)
For a 99% confidence interval with a sample size of 10 What is the critical t-value?
Russell surveys 200 randomly selected seventh-graders in his school and finds that 30 attend summer camp. If there are 780 seventh-graders in his school, about how many are expected to attend summer camp?
Answer:
117
Step-by-step explanation:
If 30 out of 200 seventh-graders attend summer camp, we can estimate the proportion of seventh-graders who attend summer camp as 30/200 = 0.15.
To estimate how many seventh-graders out of the total of 780 are expected to attend summer camp, we can multiply this proportion by the total number of seventh-graders:
0.15 x 780 = 117
Therefore, we can estimate that about 117 seventh-graders are expected to attend summer camp.