Answers
The [tex]n[/tex]-th term is
[tex]U_n = \dfrac14 n^2 (n+1)^2[/tex]
so the 39th term is
[tex]U_{39} = \dfrac14 39^2 40^2 = \boxed{608,400}[/tex]
Observe that
[tex]2^3 + 4^3 + 6^3 = 2^3 + 2^3\times2^3 + 2^3\times3^3 = 8\left(1^3+2^3+3^3)[/tex]
which suggests that
[tex]V_n = 8U_n = \boxed{2n^2(n+1)^2}[/tex]
Related Questions
two functions f and g are defined over the set r of real numbers as follows: f:x > x^2-2x-1 and g:x > x-1. find the value of x for which f(x)=g(x)-2
Answers
The value of x for which the function f(x)=g(x)-2 is x = 1 and 2
What is a function?
A function can be defined as an equation, expression, rule or law showing the relationship between two variables.
These variables are;
The dependent variableThe independent variableThe functions are given as;
f:x > x^2-2x-1 g:x > x-1For the function (x)=g(x)-2
Substitute the values, we get;
x² -2x - 1 = x - 1 - 2
collect like terms
x² - 2x - x = -3 + 1
add or subtract like terms
x² -3x + 2 = 0
x² - 2x - x + 2 = 0
(x² -2x) - (x + 2) = 0
x(x -2) - 1(x - 2) = 0
Then,
x = 1 and 2
Hence, the values are 1 and 2
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Solve the following radical equation.
6y2−22y+16⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+4=4y
Write your answer(s) beginning with the first answer box. If applicable, the second answer box may be left blank.
Answers
The solution to the radical equation is 2/5
How to determine the solutionFrom the question, we have the following radical equation
6y2−22y+16⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+4=4y
Complete the equation
So, we have the following representation
6√y² − 22y + √16 + 4 = 4y
Evaluate the radicals
The equation becomes
6y - 22y + 4 + 4 = 4y
So, we have
6y - 22y + 8 = 4y
Evaluate the like terms
So, we have the following
20y = 8
Divide both sides by 20
y = 2/5
Hence, the solution is 2/5
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Alexa took out a 12-year loan for $72,000 to pay for her home. If she paid
an extra $20,000 in interest, then what was her interest rate?
Answers
If the home loan compounds 12 times per year, her interest rate (APR) is 24.764%.
What is the annual percentage rate (APR)?The annual percentage rate (APR) is the yearly cost of borrowing.
The annual percentage rate (APR) is computed as the interest rate times the principal (balance).
The APR can be computed using an online finance calculator.
N (# of periods) = 12 years
PV (Present Value) = $72,000
PMT (Periodic Payment) = $0
FV (Future Value) = $-92000
Results:
I/Y = 24.764% if interest compound 12 times per year (APR)
I/Y = 27.778% if interest compounds once per year (APY)
I/period = 2.064% interest per period
Total Interest = $20,000.00
Thus, Alexa's interest rate (APR) for the 12-year loan of $72,000 for which she paid an extra $20,000 is 24.764%.
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The graph below shows f(x), which represents a parent function, and g(x), which represents a translation of that function.
On a coordinate plane, 2 exponential functions are shown. f (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1. It goes through (negative 3, 8) and crosses the y-axis at (0, 0.5). g (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1. It goes crosses the y-axis at (0, 14) and goes through (1, 5) and (2, 2).
Which statements about the functions are true? Check all that apply.
f(x) = (one-half) Superscript x
g(x) = (one-half) Superscript x + 4 – 2
The ranges of both functions are the same.
The domains of both functions are the same.
The translation from f(x) to g(x) is right 4 units and down 2 units.
Answers
The statements about the functions are true A. f(x) = 1/2ˣ
D. The domains of both functions are the same.E. The translation from f(x) to g(x) is right 4 units and down 2 units.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
We are given that On a coordinate plane, 2 exponential functions are shown. f (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1.
When evaluated in zero we have:
f(0) = 2(1/2)^0 = 2
So it crosses through the point (0, 2).
And when evaluated in x = 1, then
f(1) = 2(1/2)^1 = 1
Then it also passes through (1, 1). It goes crosses the y-axis at (0, 14) and goes through (1, 5) and (2, 2).
The answers are A, D, and E
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Answer:a,d,e
Step-by-step explanation:
i took the test
Please help I will give all stars!! I have a text on this tomorrow!!
Answers
5x - 3y = 7 is in slope intercept form is y = 5/3x - 7/3
How do you write slope intercept form?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
You can utilize two different versions of a line's general form to figure out its equation.
These are the formulas:
1) (y - y1) = m (x – x1), the Point-Slope Formula
2) The formula for slope-intercept, y = mx + b
The form you use depends on the information you are provided at the beginning, as the names suggest.
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Una deuda de $1500 se cancelará a un plazo de 6 trimestres con una tasa del 5% compuesto mensual. Determine:
a) El valor final que termina cancelando por la deuda contraída.
b) Calcule el tiempo (trimestres) que se demora el mismo préstamo inicial tomando como referencia una tasa del 12% anual compuesta.
Answers
a) Una deuda total de $ 4837.65 en un período de amortización debe ser pagada en seis trimestres.
b) Se requiere aproximadamente 42 trimestres para pagar la misma deuda.
¿Cómo determinar el valor final a pagar y el tiempo requerido de amortización?En este problema tenemos dos casos de préstamos bajo un modelo de interés compuesto, léase un caso acumulativo de intereses en el tiempo, en función de períodos definidos. La persona que recibe el préstamo se hace acreedora de una deuda, la cual debe ser amortizada en el tiempo. Ahora, bien, el modelo de interés compuesto se describe bajo la siguiente fórmula:
D' = D · (1 + r / 100)ˣ
Donde:
D - Deuda inicial, en unidades monetarias.D' - Deuda final, en unidades monetarias.r - Tasa de interés, en porcentaje.x - Número de períodos de amortización, en unidades de tiempo.a) Si sabemos que D = 1500, r = 5 y x = 24, entonces:
D' = 1500 · (1 + 5 / 100)²⁴
D' = 4837.65
La persona debe pagar una deuda total de $ 4837.65 en un período de amortización de seis trimestres (nótese que un año tiene cuatro trimestres).
b) Es preciso determinar el período equivalente para una tasa de interés compuesta anual de 12 %, esto es:
D' = D · (1 + r /100)ˣ
㏒ (D' / D) = x · ㏒ (1 + r / 100)
㏒ D' - ㏒ D = x · ㏒ (1 + r / 100)
x = (㏒ D' - ㏒ D) / [㏒ (1 + r / 100)]
x = (㏒ 4837.65 - ㏒ 1500) / [㏒ (1 + 12 / 100)]
x = 10.332 años (aprox. 42 trimestres)
El período de amortización es de aproximadamente 42 trimestres.
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Find two fractions with a sum of but with neither denominator equal to 3.
Answers
Answer:
2/6 +2/6= 4/6 and 4/6 reduced down is 2/3
Step-by-step explanation:
hope this helps
A password is to be made from a string of five characters chosen from the lowercase letters of the alphabet and the numbers 0 through 9.
(a) How many passwords are possible if there are no restrictions?
______ passwords
(b) How many passwords are possible if the characters must alternate between letters and numbers?
______ passwords
Answers
Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:
a) 60,466,176.
b) 5,961,600.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with n1, n2, ... ways to be done, each thing independent of the other, the number of ways they can be done is N=n1*n2*n3*....
Item a:
No restrictions, hence, for each of the five characters, there are 36 outcomes, hence n1=n5=36.
Then, the possible number of passwords is:
N=36^5=60,466,176
Item b:
The letters and the digits have to be alternated, hence:
Starting with a letter n1=n3=n5=36, n2=n4=10.
Starting with a digit n1=n3=n5=10, n2=n4=36.
Then, the possible number of passwords is:
N=36^3*10^2+10^3*36^2=5,961,600.
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93 divided by 585.9 steps to solve?
Answers
Which statement about irrational numbers is true?
A - irrational numbers can be found by squaring rational numbers
B - irrational numbers cannot be written as ratios of integers
C - The Pythagoreans loves irrational numbers
D - an irrational number can always be found by dividing two rational numbers
Answers
Answer:
B
Step-by-step explanation:
Irrational numbers are real numbers that cannot be written as a ratio of integers. They have decimal expansions that neither terminate nor become periodic.
Example: π , √2 , √3 are irrational numbers.
What is the slope of the line that contains the points negative 3, negative seven halves and (2, −4)?
Answers
Answer: -1/10
Step-by-step explanation:
Which function represents the graph of
Answers
The correct graph is the last one, positive at the left, and positive at the right, when x is positive.
What is function of graph?A relation from set A to set B is a function if every element of set Aonly one image in set B.It is a subset of A×B.The set of elements in Athat are plugged into the function is called the domain. The set of images of the elements in A, a subset of B is called the range of the function f.
Here,
Given : Let's analyze our function, first we know that the parent cubic function:
We want to see which one of the given graphs is the graph of the function: f(x) = (1/2)*x^3
g(x) = x^3
Is positive for positive values of x and positive for positive values of x, then the graph is below the horizontal axis at the left, and above the horizontal axis at the right.
The graph below the horizontal Axis at left and above the horizontal axis at the right.
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The discount price of socks are $21. What is the regular price
Answers
Answer: To help you with this problem, I need to know the discount percentage.
Step-by-step explanation:
Which equation can pair with x – y = –2 to create a consistent and dependent system?
6x + 2y = 15
–3x + 3y = 6
–8x – 3y = 2
4x – 4y = 6
Answers
The required equation -3x + 3y = 6 can pair with x - y= -2 to create a consistent and dependent system.
The equation is given in the question, as follows:
x - y = - 2
First, we have to convert the standard form of the equation to slope-intercept form.
As per the question, we have
x - y = -2
Subtract x from both sides of the equation,
x - y - x = -2 - x
- y = -2 - x
Divide -1 by both sides of the equation,
y = x + 2
Comparing it with the slope-intercept form y = mx + b, we get
Slope m = 1, y intercept b = 2
Considering option (B),
-3x + 3y = 6
Add 3x on both sides of the equation,
-3x + 3x + 3y = 6 + 3x
3y = 3x + 6
Divide both sides by 3 of the equation,
y = x + 2
Comparing the slope-intercept form
m = 1 and y-intercept = 2
Hence, the correct answer would be an option (C).
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Please help me with this and quickly please!!!
Answers
0001255667
the middle ends up being 2 and 5
so 2+5= 7 7/2 is 3.5
The sum of three times a number and seven is greater than twice the number -4
Answers
Answer: x > -11
Step-by-step explanation:
3x + 7 > 2x - 4
First, we can simplify the right side of the equation by combining like terms:
3x + 7 > 2x - 4
then we can subtract 2x from both sides of the equation:
3x + 7 - 2x > -4
This gives us:
x+7 > -4
then we can add 4 to both sides of the equation:
x + 7 + 4 > 0
This gives us:
x + 11 > 0
then we can subtract 11 from both sides of the equation:
x + 11 - 11 > 0 - 11
This gives us:
x > -11
so the number is greater than -11.
Please as soon as possible,
I’ll give brainliest
Answers
1. The average rate of range for 3 to 4 days is -3.9.
2. Approximate rate of range for 3 days is 34.8.
How is the instantaneous rate of change estimated?Adding a very small increment, for example, can help us approximate the instantaneous rate of change at x = a.
The instantaneous rate of change is equal to the slope of the tangent line at a given location. The slope of secant lines can be used to calculate the slope at a point as each secant line's "run" gets closer to zero (the slope of the tangent line).
You can find the instantaneous rate of change of a function by computing the derivative at a specific point and then entering the point's x-value.
The speed at which that function changes right now.
IROC = f(a + 0.001) - f(a) / 0.001 f(a) = 0.1
1.
[tex]$$\begin{aligned}& \text { A.R.C }=\frac{\mathrm{A}(4)-\mathrm{A}(3)}{4-3} \\& \mathrm{~A}(4)=100(0.5)^{\frac{4}{15}} \\& \mathrm{~A}(4)=83.12378 \\& \mathrm{~A}(3)=100(0.5)^{\frac{3}{16}} \\& \mathbf{A}(3)=87.05505\end{aligned}$$A. R. C $=\frac{83.12378-87.05505}{1}$$$=-3.93127$$A. R. $\mathrm{C}=-3.9$[/tex]
2. it can be obtained by takibg derivative with respect 't';
[tex]$\mathrm{A}^{\prime}(\mathrm{t})=100\left(\frac{\mathrm{t}}{15}\right)(0.5)^{\left(\frac{t}{15}\right)-1}$\\rate of change in 3 days:$$\begin{aligned}& \mathrm{A}^{\prime}(3)=100\left(\frac{3}{15}\right)(0.5)^{\left(\frac{3}{15}\right)-1} \\& \mathrm{~A}^{\prime}(3)=34.82202\end{aligned}$$Approximate rate of change;$$\mathrm{A}^{\prime}(3) \approx 34.8$$[/tex]
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Which is the joint relative frequency for teachers who teach math and not English? Round the answer to the nearest percent.
Answers
The required percentage of teachers who teach math but not English is 21%. Option B is correct.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Total teachers = 104
A number of teachers teach math but not English = 22
Percentage = 22 / 104 × 100%
Percentage = 21%
Thus, the required percentage of teachers who teach math but not English is 21%. Option B is correct.
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A clothing store is going out of business. To sell their remaining inventory, the managers drop the price of each item $5 at the end of each week until the item sells. Write the equation of this being shown.
Answers
The equation to represented the situation of drop the price of each item $5 at the end of each week until the item sells as used by the manager of the clothing store is
y = c - $5xHow to write the equation as used by the managerInformation given in the problem include
the managers drop the price of each item $5 at the end of each week
until the item sells
let c represent the cost of the item at the beginning
;et x represent the number of weeks
let y represent the cost at the end of each week
The equation is modeled as follows
the present cost c will drop by $5 each week
c - $5x
The cost after the drop that is at the end of the week
y = c - $5x
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10 + 5Y = X
40 + 10Y = X
Answers
Answer:
X = -50
Y = -30
Step-by-step explanation:
To find the value of Y and X, we can solve a system of equations. One way to do this is by substitution.
From the first equation:
10 + 5Y = X
We can substitute the value of X from the second equation:
10 + 5Y = 40 + 10Y
Then, we can subtract 10Y from both sides:
10 = 40 + Y
Finally, we can subtract 10 from both sides:
Y = -30
Now that we have the value of Y, we can substitute it back into either equation to find the value of X:
X = 10 + 5Y
X = 10 + 5(-30)
X = -50
So the solution is:
X = -50
Y = -30
Answer:
(x,y)=(-20,-6)
Step-by-step explanation:
Which equations are equivalent to Negative one-fourth (x) + three-fourths = 12 Select all that apply. (StartFraction negative 4 x over 1 EndFraction + three-fourths = 12 Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12 StartFraction negative x + 3 over 4 EndFraction = 12 One-fourth (x + 3) = 12 (StartFraction negative x over 4 EndFraction + three-fourths = 12
Answers
Negative 1 (StartFraction x over 4 EndFraction) + three-fourths 12 StartFraction negative x + 3 over 4 EndFraction = 12One-fourth (x + 3) = 12 is the equivalent equation.
What is equation?An equation is a mathematical statement that two expressions are equal. It consists of two expressions separated by an equal sign (=). Equations are used to describe relationships between unknown values, such as the relationship between the circumference and diameter of a circle. Equations can also be used to solve for unknown values, such as the area of a triangle.
These three equations are equivalent to Negative one-fourth (x) + three-fourths = 12. The first equation is the original equation, while the second and third equations are equivalent forms of the original equation. In the second equation, the negative one-fourth (x) has been moved to the other side of the equation, and in the third equation, the negative one-fourth (x) has been multiplied by one-fourth.
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The hypotenuse of a 45°-45°-90° triangle measures 24 inches. What is the length of the one leg of the triangle?
12 in.
12 StartRoot 2 EndRoot in.
24 in.
24 StartRoot 2 EndRoot in.
Answers
Answer:
Can you answer mine? I need help too
Step-by-step explanation:
Solve each expression using the order of operations.
64 ÷ 8 × 2 + 2 × 4 – 4 × 5
(3 + 9) × 2 ÷ 4
Answers
Answer:
64 ÷ 8 × 2 + 2 × 4 – 4 × 5= 4 (3 + 9) × 2 ÷ 4= 6
Please help!
Graph y = 5/3x - 9.
Answers
Answer:
I have graphed it and attached an image in the explanation.
Step-by-step explanation:
ignore text just answer ty <3
Answers
For which store location does 68% of the data lie between $19,371.18 and $22,295.48? A. location C B. location D C. location B D. location A
Answers
The store location for which % of the data lies between $19,371.18 and $22.295.48 is location C
What is standard deviation?You should be aware that Standard deviation explains the relation of data with mean.
For normal distributions, 68% of the data lies under one SD from the mean. Two standard deviations is within 95%, and three standard deviations would take up to 99%.
This implies that on taking (mean + SD) and (mean - SD), 68% of data would cover these two numbers.
Add and subtract SD from the mean to check which location will give $19,371.18 and $22.295.48.
For location A, we have
M-SD=23,124.70-1553.43=21,571.27
M SD = 23,124.70 + 1,553.43 = 24,678.4
For location B, we have
M - SD = 24,842.18 - 1,617.20 = 23,224.98
M + SD = 24, 842.18 + 1,617.20 = 26,459.38
For location C, we have
M - SD = 20,833.33 - 1,462.15 = 19,371.18
M + SD = 20,833.33 + 1,462.15 = 22,295.48
This implies the store location is C
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Correct question:
The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.
For which store location does 68% of the data lie between $19,371.18 and $22,295.48?
If the owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. The location that 68% of the data lie between $19,371.18 and $22,295.48 is: A. Location C.
How to find the location?Location A:
Mean -Standard Deviation
=23,124.70-1553.43
=21,571.27
Mean + Standard Deviation
= 23,124.70 + 1,553.43
= 24,678.4
Location B:
Mean -Standard Deviation = 24,842.18 - 1,617.20
Mean -Standard Deviation = 23,224.98
Mean + Standard Deviation
= 24, 842.18 + 1,617.20
= 26,459.38
Location C:
Mean - Standard Deviation
= 20,833.33 - 1,462.15
= 19,371.18
Mean + Standard Deviation
= 20,833.33 + 1,462.15
= 22,295.48
Therefore the correct option is C.
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The complete question is:
The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.
Location A Location B Location C Location D
Mean = 23,124.70
SD = 1,553.43 Mean = 24,842.18
SD = 1,617.20 Mean = 20,833.33
SD = 1,462.15 Mean = 21,432.82
SD = 1,512.10
For which store location does 68% of the data lie between $19,371.18 and $22,295.48?
what si the mad of the numbers: 240, 225, 227, 227, 228, 230, 230, 231, 238, 240
Answers
The MAD of the given set of numbers is 4.64.
What is MAD?The mean absolute deviation (MAD) is a variability metric that indicates the average distance between observations and their mean. MAD interprets the data in its original units. Larger values indicate that the data points are further apart from the mean. Lower values, on the other hand, represent data points clustering closer to it. The average absolute deviation is also known as the mean deviation.
The mean absolute deviation is defined in the same way as the standard deviation (SD). While they both measure variability, their calculations differ. Some proponents of MAD have suggested that it replace SD as the primary measure in recent years because it is a simpler concept that is more applicable in real life.
Lets find the mean of given data set:
240+ 225+ 227+ 227+ 228+ 230+ 230+ 231+ 238+ 240
= 2316
⇒ 2316/10 = 231.6
Find the distances of the mean
240 - 231.6 = 8.4
225 - 231.6 = 6.6
227 - 231.6 = 4.6
227 - 231.6 = 4.6
228 - 231.6 = 3.6
230 - 231.6 = 1.6
230 - 231.6 = 1.6
231 - 231.6 = 0.6
238 - 231.6 = 6.4
240 - 231.6 = 8.4
Add the distances
8.4+ 6.6+ 4.6 + 4.6 + 3.6 + 1.6 + 1.6 + 0.6 + 6.4 + 8.4 = 46.4
Divide the sum by the number of data points.
46.4/10 = 4.64
Thus, The Mad of the given set of numbers is 4.64.
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A bakery can make 44 cheesecakes for every 4 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses?
Answers
The table that represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery used will be:
Cream cheese Cheesecake
1. 11
2. 22
3. 33
How to illustrate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, the bakery can make 44 cheesecakes for every 4 blocks of cream cheese. This will be Illustrated as:
= 44 / 4
= 11 cheesecake per cheese.
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Find the domain and range for the function shown in the graph given below.
What is the domain?
what is the range?
(Type your answer in interval notation.)
Answers
Answer:
Step-by-step explanation:
y axis range is 35
Which of the following would be true regarding the following exponential expression?
3m 7/9
A - The exponent of 3 is 7/9.
B - If written in radical form, 9 would be the exponent
inside the radicand.
C - The rational exponent is 9/7.
Report an Error
question 4 of 5
D - If written in radical form, 7 would be the index.
E - If written in radical form, 9 would be the index.
Answers
Answer:
A - The exponent of 3 is 7/9.
Step-by-step explanation:
The expression 3^(7/9) can be read as "3 to the power of 7/9".
This means that the number 3 is being multiplied by itself 7/9 times.
For example
3^(2/3) can be written as cube root of 3, cube root of 3 is equal to 3^(1/3) .
When the exponent of an expression is a fraction, it can be written in radical form, with the denominator of the fraction as the index of the radical. However, it's not true in this case as the index is not 9 but 7.
So, the correct answer is A - The exponent of 3 is 7/9.