The first five terms of an arithmetic sequence are shown below: 20, 17, 14, 11, 8, . . . Let n represent the term number and f(n) the term in the sequence. The function represents the sequence.
ANSWER IS: f(n)= -3n +23
Step-by-step explanation:
everything can be found in the picture
Answer:
f(n) = -3n + 23
Step-by-step explanation:
Just got it right on EDG.
You are running in a 26-mile race.
You have run 17 miles so far.
What is the ratio of the miles you have left to the total number of miles in the race?
Answer:
17:26
Step-by-step explanation:
You can't simplify 17 therefore it would be 17:26 ratio.
I hope this helps! Please give me brainllest!
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Rewriting expressions. Image attached
9514 1404 393
Answer:
5z^(-5/3)
Step-by-step explanation:
The rules of exponents being used here are ...
\(\sqrt[n]{a}=a^{1/n}\\\\\dfrac{a^b}{a^c}=a^{b-c}\)
Using these rules on the given expression, we find ...
\(\dfrac{10\sqrt[3]{z}}{2z^2}=\dfrac{10}{2}z^{1/3-2}=\boxed{5z^{-5/3}}\)
What is the percent
increase from 70 to 77?
Percentage change = 10%
We can use the formula:
Percent change = \(\frac{New-Old}{Old}\) x 100
Percent change = \(\frac{77-70}{70}\)x100
Percent change = \(\frac{7}{70}\) x 100
Percent change = 0.1 x 100
Percent change = 10%
Answer: 53.9
Step-by-step explanation:
5^6/5^?=1/25
FIND MISSING EXPONENT
EXTRA POINTS
Answer:
8
Step-by-step explanation:
When the base are the same:
If you are multiplying, simply add the powers.
If you are dividing, simply subtract the powers.
In this case, you are dividing, so subtract:
\(\frac{5^{6} }{5^{8}} = 5^{6 - 8} = 5^{-2} = \frac{1}{25} \)
~
Find 3 ratios that are equivalent to the given ratio 3 over 6
Leah Deposited $7000 in an account that earns 2% interest compounded annually. How much interest will she have earned after 6 years?
Answer:
840
Step-by-step explanation:
7000×2×6 ÷ 100. since it is 2%
= 840
(TIMED PLEASE HELP!!) The area of the two triangles is given by the functions: Area of Triangle A: x2 + x Area of Triangle B: x2 – 3x Which function represents the sum of the areas of the two triangles? (a) 4x (b)–4x (c) x2 – 4x (d) 2x2 – 2x
Answer:
D
Step-by-step explanation:
Here, we are given the values of the areas of the two triangles and we want to find the sum of these areas
The sum can be found by adding the area of triangle A to the area of triangle B
That would be;
x^2 + x + x^2-3x = 2x^2 -2x
Answer:
d
Step-by-step explanation:
How do you write 5.000 as a percent?
Answer/Step-by-step explanation:
5.000 is already a percentage all you have to do is put a percentage sign after taking the decimals and zeros of the end. This is because 5.000 = 5 and 5/100 = 5%.
Data _____ involves creating new ways of modeling and understanding the unknown by using raw data
The complete statement is data analysis involves creating new ways of modeling and understanding the unknown by using raw data.
What is data analysis?Data analysis can be defined as the process of cleaning, changing, and processing raw data, to relevant information that helps in the decision making of a business.
The procedure of data analysis helps in reducing the risks involved in decision-making by providing useful insights and statistics,.
Analyzed data are often presented in charts, images, tables, and graphs.
Some types of data analysis are;
Diagnostic AnalysisPredictive AnalysisPrescriptive AnalysisStatistical AnalysisThus, the complete statement is data analysis involves creating new ways of modeling and understanding the unknown by using raw data.
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In order to start a small business, a student takes out a simple interest loan for \( \$ 5000.00 \) for 9 months at a rate of \( 8.25 \% \). a. How much interest must the student pay?
a. the principal (loan amount) is $5000, the rate is 8.25%, and the time is 9 months (expressed in years as 9/12). b. the student will have to pay $306.25 in interest, and the future value of the loan will be $5306.25.
a. The student must pay $306.25 in interest.
To calculate the amount of interest, we can use the formula for simple interest:
Interest = Principal × Rate × Time
In this case, the principal (loan amount) is $5000, the rate is 8.25%, and the time is 9 months (expressed in years as 9/12).
Plugging in these values into the formula, we can calculate the interest amount the student must pay.
b. The future value of the loan is $5306.25.
To find the future value, we add the interest amount to the principal amount.
The future value is calculated using the formula:
Future Value = Principal + Interest
By substituting the values of the principal ($5000) and the interest ($306.25), we can find the future value of the loan.
Therefore, the student will have to pay $306.25 in interest, and the future value of the loan will be $5306.25.
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In order to start a small business, a student takes out a simple interest loan for $ 5000 for 9 months at a rate of 8.25 %.
a. How much interest must the student pay?
b. Find the future value of the loan.
PLEASE HELP 10 MIN LEFT HELP ASAP 20 POINTS
Answer:
thats the answer D
Step-by-step explanation:
hope that helped
Answer:
the answer is b
Step-by-step explanation:
2
A line passes through the point (-9,5) and has a slope of
3
Write an equation in point-slope form for this line.
x 3
Answer:
y-5=3(x- (-9)
Step-by-step explanation:
Is x-3 a factor of 2x cubed minus 5x squared minus 5x plus 11? Explain WHY it is or is not a factor
Thus, x-3 is not a factor if 2x³ - 5x² - 5x + 11. To make it the factor subtract 5 from the dividend.
Explain about the factors of polynomial?A polynomial is factored when it is expressed as the product with two or more factors; this is somewhat the opposite of multiplying.
One of a single-variable polynomial's linear expressions is referred to as a factor. Many variables can affect a polynomial,
Given word problem.
2x cubed minus 5x squared minus 5x plus 11
This can be written as:
2x³ - 5x² - 5x + 11
So,
dividend : 2x³ - 5x² - 5x + 11
divisor = x-3 , x = 3
Put x = 3 in dividend , if it comes zero, it is the factor.
= 2x³ - 5x² - 5x + 11
= 2(3)³ - 5(3)² - 5(3) + 11
= 5 (remainder)
Thus, x-3 is not a factor if 2x³ - 5x² - 5x + 11. To make it the factor subtract 5 from the dividend.
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Here the points.
Good luck in the finals
Edit: 3 minutes later, no one wants it?!
Answer: good luck to you!
Step-by-step explanation:
Answer:
tysm for the points <33
Step-by-step explanation:
:)
A = a+b+c/3 Solve for b this is a literal equation problem please show steps
Answer:
\(b=3A-a-c\)
Step-by-step explanation:
\($A=\frac{a+b+c}{3} $\)
Multiply both sides by 3
\($3A=a+b+c $\)
Add \(-b-c\) both sides
\(3A-a-c=b\)
\(b=3A-a-c\)
Use differentials to approximate the change in the volume of a spherical balloon of radius 2 meters if the balloon deflates to a radius of 1. 8 meters.
The changes in the volume of the spherical balloon is approximately o.3351-meter cube.
the volume of the sphere =\(v=\frac{4}{3}\pi r^3\)
using the definition of differential to find the change we write
\(dv=\frac{4}{3}\pi (dr)^3\)
where, \(dr\)=\(r_{2}-r_{2}\)
\(dr\)=\(2-1.8\\\)
\(dr\) \(=0.2\)
\(dv=\frac{4}{3}\pi (0.2)^3\)
\(dv=0.3351\) approx.
where dr and dv represent the differential or change with respect to radius and volume in the above calculation. so first we apply differential on both sides of the formula of the sphere then we find its approximation by the next coming equation. so, the volume of the sphere is approximately 0.3351-meter cube here approximation represents that it is not the exact solution it is basically approximated solution.
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Answer:
3.2 π
Step-by-step explanation:
The volume V of a sphere with radius r is given by the formula V = (4/3) * π * r^3.
Taking the derivative with respect to r, we get dV/dr = 4 * π * r^2.
Let dr be the change in radius, which is 1.8 - 2 = -0.2.
The differential dV is given by dV ≈ (dV/dr) * dr = 4 * π * r^2 * dr.
Substituting r = 2 and dr = -0.2, we get dV ≈ 4 * π * 2^2 * (-0.2) = -3.2 * π.
So, using differentials, we estimate that the volume of the balloon decreases by approximately 3.2 * π cubic meters as it deflates from a radius of 2 meters to a radius of 1.8 meters.
The following cone has a slant height of 17
cm and a radius of 8
cm.
What is the volume of the cone?
Responses
480π
320π
544π
The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.
Manuel y Rosa, desean hacer un regalo a sus tíos por Fiestas patrias, para lo cual visitaron distintos centros comerciales donde venden artículos o herramientas de carpintería. En uno de ellos, observaron que una caja de herramientas les costaba 180 soles. Al no contar con ese monto, decidieron volver la primera semana de Julio, después de juntar sus ahorros. Pero se dieron cuenta que el precio se había incrementado en un 10% . Al faltarles dinero, decidieron volver la siguiente semana, en la que observan que el precio de la caja de herramientas se había incrementado en un 20% del precio que observaron en la primera semana de Julio. Ellos cuentan con 250 soles. Manuel dice: "el precio se ha incrementado en 35% del precio del precio inicial pero nos alcanza y nos sobra 7 soles" A lo que Rosa dice: " no se ha incrementado en un 35% pero sí nos sobrarían 5 soles?
Answer:
El incremento total con respecto al precio inicial es de 32% y Rosa tiene razón con respecto al porcentaje (no se incrementó 35%).
En cuanto al dinero que les sobra, ninguno de ellos está en lo correcto pues les sobran 12 soles.
Step-by-step explanation:
En un principio, la caja de herramientas costaba 180 soles.
Después de una semana el precio se incrementó 10%, el 10% de 180 soles es 18 por lo que la caja costaba 180 + 18 = 198 soles.
Ellos volvieron la siguiente semana y vieron que el precio se había incrementado un 20% con respecto a la semana anterior, el 20% de 198 es igual a 198 x 0.20 = 39.6 por lo que el precio ahora era de 198 + 39.6 = 237.6 soles.
Para saber el incremento total con respecto al precio inicial podemos hacer una proporción:
180 soles : 100
237.6 soles : x
Despejando x tenemos que:
\(x= \frac{237.6(100)}{180}=\frac{23760}{180}=132\)
Por lo tanto, el incremento total con respecto al precio inicial es de 32% y Rosa tiene razón con respecto al porcentaje (no se incrementó 35%)
Sin embargo, ellos cuentan con 250 soles y la caja cuesta 237.6 ≈238 soles, por lo tanto, les alcanza y les sobran 250 - 238 = 12 soles.
write the equation of the line that is parallel to Y=2/3 X -7 and passes through the point (-3,1)
Answer:
y=2/3x+3
Step-by-step explanation:
parallel means it stays the same so its still 2/3
now use the equation y=mx+b
plug in the slope which is 2/3
so we get y=2/3x+b
then plug in the 2 points
1= 2/3(−3)+b
1=-6/3+b
1=-2+b
add 2 to 1 and -2
3=b
so we get y=2/3x+3
what is 13/78 simplified
The solution is, 13/78 reduced to its simplest form is 1/6.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that, 13/78
now, we know that, 13*6 = 78
i.e. 13/ 13*6
=1/6
Hence, The solution is, 13/78 reduced to its simplest form is 1/6.
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Validation of the model and answering the question "what are my options" occur in the ___ phase of the IDC.
A. choice
B. design
C. intelligence
D. implantation
Validation of the model and answering the question "what are my options" occur in the design phase of the IDC (Intelligence, Design, and Choice) framework.
The IDC framework is a decision-making process that consists of three phases: Intelligence, Design, and Choice. Each phase corresponds to a specific set of activities and objectives.
In the intelligence phase, the focus is on gathering information, identifying the problem or decision to be made, and understanding the factors and variables involved. This phase involves data collection, analysis, and exploration to gain insights and knowledge about the problem domain.
In the design phase, the emphasis is on developing and evaluating potential options or solutions to address the problem or decision at hand. This phase involves creating models, prototypes, or simulations to represent the problem and exploring different alternatives.
Validation of the model is an important aspect of this phase to ensure that the proposed solutions align with the problem requirements and objectives.
The question "what are my options" is a fundamental question that arises during the design phase. It implies the exploration and generation of various possible choices or solutions that can be evaluated and compared.
Therefore, the design phase of the IDC framework encompasses the activities of validating the model and answering the question "what are my options." It involves refining and testing potential solutions to make informed decisions in the subsequent choice phase.
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Complete the square to re-write the quadratic function in vertex form:
Answer:
(x+2)^2 - 6
Step-by-step explanation:
Which equation represents this problem? The time it takes Tomás to bike to the community center is 2 minutes less than half the time it takes him to bike to the city park. It takes Tomas 18 minutes to bike to the community center. Let p = the time it takes Tomas to bike to the park
A:2p+1/2=18
B:1/2p+2=18
C:2p-1/2=18
D:1/2p-2=18
Answer:
Step-by-step explanation:
D
Consider the nonhomogeneous system 2x; – 6x2 + 3x3 = -4 -x} + x2 + x3 = 5 2.x, + 6x, -5x, = 8 Determine an inverse matrix by using adjoint's method. Find the unique solution of the linear system
The unique solution of the linear system is given by:
x1 = 43/5 + x/2 - x2/10 + x3/10
x2 = 11/5 + x/10 - x2/10 + x3/10
x3 = -2 - 2x/5 + x2/10 + x3/10
For finding the inverse matrix using the adjoint method, follow these steps:
Step 1: Write the given system of equations in matrix form:
[ 2 -6 3 | -4 ]
[-1 1 1 | 5 ]
[ 2 6 -5 | 8 ]
Step 2: Define matrix A as the coefficient matrix:
A = [ 2 -6 3 ]
[-1 1 1 ]
[ 2 6 -5 ]
Step 3: Define matrix B as the column vector of constants:
B = [ -4 ]
[ 5 ]
[ 8 ]
Step 4: Calculate the matrix of cofactors, C, and the matrix of minors, M:
C = [ C11 C12 C13 ]
[ C21 C22 C23 ]
[ C31 C32 C33 ]
M = [ M11 M12 M13 ]
[ M21 M22 M23 ]
[ M31 M32 M33 ]
Step 5: Calculate the determinant of A, denoted as |A|, using the formula:
|A| = 2C11 - 6C12 + 3C13
Step 6: Find the adjugated matrix, adj(A), by transposing the matrix of cofactors, C.
Step 7: Calculate the inverse matrix, A^(-1), using the formula:
A^(-1) = adj(A) / |A|
Step 8: Substitute the corresponding values for Cij and |A| to find A^(-1).
Step 9: Solve the system of equations by multiplying both sides of the matrix equation by A^(-1).
Therefore, the inverse matrix is found, and the unique solution of the linear system is obtained.
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Which of the following values of c are solutions of the inequality c-2<16? Select all that apply.
1. 2
2. 16
3. 17.5
4. 18
5. 20
An experienced ice skater spins on the ice, creating a perfect circle. Afterwards, she calculates that it must have a circumference of 25.12 feet. What is the circle's diameter?
Use 3.14 for Pi. If necessary, round your answer to the nearest hundredth.
The answer to two decimal places would be 7.98 feet, so we don't need to round further.
How to solve a circle?
To find the diameter of a circle given its circumference, we can use the formula:
Circumference = π × Diameter
where π is the mathematical constant pi (approximately 3.14).
In this problem, we are given that the circumference of the circle is 25.12 feet. So we can plug that value into the formula:
25.12 = 3.14 × Diameter
To solve for the diameter, we need to isolate the variable (Diameter) on one side of the equation. We can do this by dividing both sides of the equation by 3.14:
25.12 ÷ 3.14 = Diameter
This gives us:
Diameter = 7.98 feet
Therefore, the diameter of the circle is approximately 7.98 feet.
It's worth noting that since the problem statement only gives π to two decimal places, we should round our answer to the same level of precision. The answer to two decimal places would be 7.98 feet, so we don't need to round further.
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what is the answer to 97% of 345m
Answer:
334.65
Step-by-step explanation:
97% of 345 = 334.65
Im not anyone important, I just want to see if these questions are correct!
1. Simons savings account has approximately 100 dollars saved. Simon has a gift card that gives him 30% off on clothes, he buys a shirt that is worth . If Simon buys this shirt, how much with remain in his savings?
2. What is 430 as a percentage?
3. Factor the expression 16x - 24.
Answer:
Number 3 is 8(2x−3)8(2−3)
Step-by-step explanation:
At mattresses shop, 75% of the mattresses are memory foam and 20% are extra firm. Of the total mattresses at Mattress shop, 12% are extra firm memory foam mattresses. What percentage of the total mattresses are not extra firm non-memory foam mattresses?
E. 8
F. 17
G. 63
H. 80
Answer:
9
Step-by-step explanation:
the first few days have come a different person and I am sure how you can get to the claire family thing that you are
The percentage of the total mattresses that are not extra firm non-memory foam mattresses is 17%.
Let's break down the information step by step to find the percentage of the total mattresses that are not extra firm non-memory foam mattresses.
Let:
M = Total number of mattresses
MF = Memory foam mattresses
EF = Extra firm mattresses
MF&EF = Memory foam and extra firm mattresses (extra firm memory foam mattresses)
From the given information, we have:
1. 75% of the mattresses are memory foam: MF = 0.75 * M
2. 20% of the mattresses are extra firm: EF = 0.20 * M
3. 12% of the total mattresses are extra firm memory foam: MF&EF = 0.12 * M
Now, to find the percentage of mattresses that are not extra firm non-memory foam, we need to subtract the number of memory foam, extra firm, and extra firm memory foam mattresses from the total number of mattresses:
Not extra firm non-memory foam mattresses = M - (MF + EF - MF&EF)
Plugging in the values:
Not extra firm non-memory foam mattresses = M - (0.75 * M + 0.20 * M - 0.12 * M)
Not extra firm non-memory foam mattresses = M - (0.83 * M)
Now, the percentage of not extra firm non-memory foam mattresses is:
Percentage = (Not extra firm non-memory foam mattresses / M) * 100
Percentage = ((M - 0.83 * M) / M) * 100
Percentage = (0.17 * M / M) * 100
Percentage = 0.17 * 100
Percentage = 17%
So, the percentage of the total mattresses that are not extra firm non-memory foam mattresses is 17%.
The correct option is F. 17.
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