name AND define the two ways to classify polynomials

Answers

Answer 1

the 2 ways a polynomial can be classified is by its degree or by its number of terms.
Number of terms is each amount of individual term. A term is just a number and a variable (possibly to a power/degree). Terms are also separated using a function such as multiplication, addition, and subtraction.

The degree of a polynomial is just the greatest variable's power so if x^5 is the greatest power in that function, than that is the degree of the polynomial

Related Questions

Two friends mix blue paint and yellow paint to make batches of green paint, as shown in the tables. Jarrod Cups Blue Cups Yellow 3 2 Ian Cups Blue Cups Yellow 5 2 Which correctly compares their ratios of blue to yellow paint?

Answers

Jarrod:
Cups Blue Cups Yellow
3 2
Ian:
Cups Blue Cups Yellow
5 2
We have that their ratios are:
Jarrod: 3/2
Ian: 5/2
Comparing both ratios:
Jarrod uses 60% yellow paint and 40% blue paint.
Ian uses 71.4% yellow paint and 28.4% blue paint.
Answer:
Jarrod: 3/2
Ian: 5/2

What is the probability that a five-card poker hand contains the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts?

Answers

1/311875200.

There is exactly 1 way to have all 5 of these cards. For the first card, there are 52 total cards to be had; for the second, 51; for the third, 50; for the fourth, 49; and for the fifth, 48:

(1/52)(1/51)(1/50)(1/49)(1/48) = 1/311875200.

Final answer:

The probability of drawing the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts in that order from a 52-card deck is approximately 1 in 380,204,032.

Explanation:

The subject of the question is the probability of drawing specific cards from a 52-card deck. This problem involves choosing five specific cards: the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts.

To find the probability, we need to consider that the deck contains 52 distinct cards. Assuming that each card is equally likely to be drawn, the probability of drawing any specific card is 1 out of 52 (or 1/52). And because we want to draw these cards one after another, we multiply these probabilities together.

Thus, the probability of drawing these five specific cards from a 52-card deck in this order is (1/52) * (1/52) * (1/52) * (1/52) * (1/52), which is approximately 1 in 380,204,032. Please note that this probability is infinitesimally small because the event is highly specific. Also, the order of the cards matters in this calculation. If the order does not matter, the probability will be higher.

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6yd 9ft 4in times 2 equals

Answers

The easieast way to deal with this problem is to double evey single quantity. Hence, we have that this is equal to 12yd, 18feet and 8 inches. However, we now have to check; 3 feet are one yard hence we have that 18 feet are equal to 6 yards. Thus, 12yards and 18 feet are equal to 18yards. Also, 12 inches are one foot; we do not have enough inches there and the inch component stays the same. Hence, the answer is that the distance is now 18 yards and 8 inches.

What are the zeros of the polynomial function?

f(x)=x^2+9x+20

Enter your answers in the boxes.

Answers

First compute the discriminant delta:
9^2-4*1*20=1.
Using the quadratic formula, we get the solutions:
[tex] \frac{-9-1}{2} =-5\\ \frac{-9+1}{2}=-4 [/tex]
the solutions are then -4 and -5.

If ab = 8 and a^2+b^2=16, then what is the value of (a+b)^2

Answers

(a+b)^2= a^2+b^2 +2ab
= 16 + 2 (8)
= 16 + 16
= 32

The answer is 4*sqrt(8)
Attached is my work.

Prime numbers have less 1.than two factors.
2.more than two factors. 3.exactly two factors. 4.less than or equal to two factors.

Answers

3 is your answer

exactly 2 factors

Answer:

They just have 2 factors :/

Step-by-step explanation:

Bc yes

Study the function: F(x)=3/4x−7 and select the statement that is FALSE based on the lessons you have learned about the slope-intercept form of the equation of a line.

A: The slope of the function is .75 and would increase from left to right if you were to graph the function on a coordinate plane

B: The y-intercept is (0,-7)

C:The point (12,2) is a solution to the equation

D:The x-intercept is (10,0)

Answers

The Main answer is the function value at [tex]x=12[/tex] is [tex]2[/tex], not [tex]12[/tex], so the point [tex](12,2)[/tex] is not a solution to the equation. Therefore, statement C is false.

The statement that is FALSE based on the lessons about the slope-intercept form of the equation of a line is:

C: The point [tex](12,2)[/tex] is a solution to the equation

To check if a point is a solution to the equation, we substitute the coordinates of the point into the equation and see if it satisfies it. For the given function

[tex]F(x)= (3/4 )x-7:[/tex]

Substituting x=12 into the equation:

[tex]F(12)= 3/4 (12)-7\\F(12)=9-7\\F(12)=2[/tex]

The function value at [tex]x=12[/tex] is [tex]2[/tex], not [tex]12[/tex], so the point [tex](12,2)[/tex] is not a solution to the equation. Therefore, statement C is false.

COMPLETE QUESTION:

Study the function: [tex]F(x)=(3/4)x-7[/tex] and select the statement that is FALSE based on the lessons you have learned about the slope-intercept form of the equation of a line.

A: The slope of the function is .[tex]75[/tex] and would increase from left to right if you were to graph the function on a coordinate plane

B: The y-intercept is [tex](0,-7)[/tex]

C:The point [tex](12,2)[/tex] is a solution to the equation

D:The x-intercept is [tex](10,0)[/tex]

A real estate agent knows that he will receive a commission of $4,250 from the sale of a property when the deal is completed 37 days from now. Needing cash today, though, he signs a discount note at a credit union, using his expected commission as the maturity value. The discount rate is 9.55%. Find the effective rate (APR).

Answers

The effective rate can be conveniently calculated from
.. effective rate = r/(1-rt)
Assuming a 365 day year, this is
.. = 9.55%/(1 -0.0955*(37/365))
.. ≈ 9.64%

G let x be an exponentially distributed random variable with parameter λ = 1 / 2 . determine the probability distribution function of the random variable y = x 2 . what kind of distribution does y have?

Answers

[tex]X[/tex] has CDF

[tex]F_X(x)=\mathbb P(X\le x)=\begin{cases}1-e^{-\lambda x/2}&\text{for }x\ge0\\0&\text{otherwise}\end{cases}[/tex]

The CDF of [tex]Y[/tex] is then

[tex]F_Y(y)=\mathbb P(Y\le y)=\mathbb P(X^2\le y)=\mathbb P(X\le\sqrt y)=F_X(\sqrt y)[/tex]
[tex]\implies F_Y(y)=\begin{cases}1-e^{-\lambda\sqrt y/2}&\text{for }y\ge0\\0&\text{otherwise}\end{cases}[/tex]
[tex]\implies F_Y(y)=\begin{cases}1-e^{-(y/(4/\lambda^2))^{1/2}}&\text{for }y\ge0\\0&\text{otherwise}\end{cases}[/tex]

which is the CDF of a Weibull distribution with shape parameter [tex]\dfrac4{\lambda^2}[/tex] and scale parameter [tex]\dfrac12[/tex].

in 2010 , a city's population was 55,210 and it was declining at a rate of 1.09% each year. which is the best prediction for when the city's population will first be below 48,000?

Answers

Answer: 2023

Step-by-step explanation:

Since, the initial population of the city is 55,210,

And, it is declining at a rate of 1.09%.

Thus, the function that shows the population after x years since 2010 is,

[tex]f(x) = 55210(1-\frac{1.09}{100} )^x[/tex]

[tex]f(x) = 55210(1-0.0109)^x[/tex]

[tex]f(x) = 55210(0.9891)^x[/tex]

If the population of town is 48000 in x years.

⇒ [tex] 55210(0.9891)^x= 48000[/tex]

⇒ [tex] (0.9891)^x= 0.869407715993[/tex]

⇒ [tex]x = 12.769[/tex]

Therefore, after 12.769 years the population of town will be equals to 48,000

⇒ After 12.770 years the population will first be below 48,000.

⇒ After approx 13 years the population will first below 48,000.

⇒ Around 2023 the population will be first below 48,000.

Answer:2022

Step-by-step explanation:

Which rule describes a translation that is 8 units to the right and 2 units up?

(x, y) (x - 8, y + 2)

(x, y) (x - 8, y - 2)

(x, y) (x + 8, y - 2)

(x, y) (x + 8, y + 2)

Answers

(x-8, y+2).

When translating figures, a translation to the right subtracts from the x-coordinate (sort of the opposite of how we think of graphs that go to the right). Translations up would be adding to the y-coordinate.

What fraction of a gallon is 3 pints?

Answers

There are 8 pints in 1 gallon, so 3 pints is 3/8 of a gallon

There are 8 pints in a gallon, so 3 pints of that would be 3/8.

a customer deposits $2000 in a savings account that pays 5.2% interest compounded continuously. how much will be earned between the 3rd and 5th yeards?

Answers

The amount of money a customer will earn between 3rd year and fifth year will be given as follows:
FV=p(1+r/100)^n
where:
FV=future value
r=rate
n=time

The amount earned in the first 3 years will be:
FV=2000(1+5.2/100)^3=$2,328.50

The amount earned in 5 years will be:
FV=2000(1+5.2/100)^5=$2,576.97

The amount earned between 3rd and 5th
=2,576.96-2,328.50
=$248.46

What is the answer for # 24?

A B C or D

Answers

The volume of the space not filled by the sphere is the difference between the volume of a cube with edge length 6 inches and the volume of a sphere with radius 3 inches.

Cube

The volume of a cube of edge length s is

... V = s³

When the edge length is 6 in, the volume is

... V = (6 in)³ = 216 in³

Sphere

The volume of a sphere with radius r is

... V = (4/3)π·r³

When the radius is 3 in, the volume is

... V = (4/3)π·(3 in)³ = 36π in³

Space

Then the volume of the space between the cube and the sphere is

... Vcube - Vsphere = 216 in³ - 36π in³ ≈ 102.9 in³ . . . . corresponding to choice C

1.3 to the second power

Answers

1.3 to the 2nd power is 1.3^2
1.3^2 = 1.3 x 1.3 = 1.69

Suppose f(x) = 0.125x for 0 < x < 4. determine the mean and variance of x. round your answers to 3 decimal places.

Answers

Answers:

- mean: 2.667
- variance: 0.889

Explanation:

To get the mean and variance of x, we need to verify first whether...
- x is discrete or continuous random variable
- f is probability mass or probability density function

because if we cannot verify the 2 statements above, we can't compute the mean and the variance.

Since 0 < x < 4, x is a continuous random variable because x can be any positive number less than, which includes a non-integer.

Note that if the random variable is continuous and [tex]0 \leq f(x) \leq 1[/tex] for any values of x in the domain of f, then f is a probability density function (PDF).

Note that

[tex]0 \ \textless \ x \ \textless \ 4 \\ \Leftrightarrow 0.125(0) \ \textless \ 0.125x \ \textless \ 0.125(4) \\ \Leftrightarrow 0 \ \textless \ 0.125x \ \textless \ 0.5 \\ \Leftrightarrow 0 \ \textless \ f(x) \ \textless \ 0.5 \\ \Rightarrow 0 \ \textless \ f(x) \ \textless \ 1 (\text{Because }0 \ \textless \ f(x) \ \textless \ 0.5 \ \textless \ 1)[/tex]

Hence, for any x in the domain of f, 0 < f(x) < 1. Moreover, since x is a continuous random variable, thus f is a PDF.

First, we use the following notations for mean and variance:

E[x] = mean of x
Var[x] = variance of x

Since f is a probability density function, we can use the following formulas for the mean and the variance of x:

[tex]\boxed{\text{mean of }x = E[x] = \int_{-\infty}^{\infty}{xf(x)}dx}[/tex]

[tex]\boxed{\text{Variance of }x = \text{Var}[x] = E[x^2] - (E[x])^2}} [/tex]

To compute for the mean of x,

[tex]\text{mean of }x = E[x] \\ = \int_{-\infty}^{\infty}{xf(x)}dx} \\ = \int_{-\infty}^{\infty}{x(0.125x)}dx} \\ \boxed{\text{mean of }x = \int_{-\infty}^{\infty}{0.125x^2}dx}}[/tex]

The integral seems complicated because of the infinity sign. But because the domain of f is the set of positive numbers less than 4, that is,

[tex]\text{domain of }f = \left \{x : 0 \ \textless \ x \ \textless \ 4 \right \}[/tex]

the bounds of the integral for the mean can be changed from [tex]-\infty \ \textless \ x \ \textless \ \infty[/tex] to [tex]0 \ \textless \ x \ \textless \ 4[/tex] so that

[tex]\boxed{\text{mean of }x = \int_{-\infty}^{\infty}{0.125x^2}dx = \int_{0}^{4}{0.125x^2}dx}[/tex]

Hence, the mean is computed as

[tex]\text{mean of }x = \int_{0}^{4}{0.125x^2}dx \\ = \left[ \frac{0.125x^3}{3} \right]_{0}^{4} \\ \\ = \left[ \frac{0.125(4)^3}{3} \right] - \left[ \frac{0.125(0)^3}{3} \right] \\ \\ \boxed{\text{mean of }x = \frac{8}{3} \approx 2.667} [/tex]

Since the formula for variance is computed as

[tex]\text{Variance of }x = \text{Var}[x] = E[x^2] - (E[x])^2[/tex]

we must first compute for [tex]E[x^2][/tex] for which

[tex]E[x^2] = \int_{-\infty}^{\infty}{x^2 f(x)}dx \\ \\ = \int_{-\infty}^{\infty}{x^2(0.125x)}dx \\ \\ \boxed{E[x^2] = \int_{-\infty}^{\infty}{0.125x^3}dx}[/tex]

Similar to the computation of integral of the mean, we take note that

[tex]\text{domain of }f = \left \{x : 0 \ \textless \ x \ \textless \ 4 \right \}[/tex]

so that we can change the bounds of the integral, that is,

[tex]\boxed{E[x^2] = \int_{-\infty}^{\infty}{0.125x^3}dx = \int_{0}^{4}{0.125x^3}dx}[/tex]

Hence,

[tex]E[x^2] = \int_{0}^{4}{0.125x^3}dx \\ \\ = \int_{0}^{4}{0.125x^3}dx \\ \\= \left[ \frac{0.125x^4}{4} \right]_{0}^{4} \\ \\ = \left[ \frac{0.125(4)^4}{4} \right] - \left[ \frac{0.125(0)^4}{4} \right] \\ \\ \boxed{E[x^2] = 8}[/tex]

Because [tex]E[x] = \frac{8}{3} [/tex],

[tex]\text{Variance of }x \\ \\ = E[x^2] - (E[x])^2 \\ \\ = 8 - \left( \frac{8}{3} \right)^2 \\ \\ \boxed{\text{Variance of }x = \frac{8}{9} \approx 0.889}[/tex]

Final answer:

The mean of x is 1.35 and the variance of x is approximately 1.267.

Explanation:

To find the mean of x, we need to calculate the expected value. We can do this by multiplying each value of x by its corresponding probability and then summing up the results. In this case, using the given values and probabilities, we have 0(0.20) + 1(0.45) + 2(0.20) + 3(0.10) + 4(0.05) = 1.35. Therefore, the mean of x is 1.35.

To find the variance of x, we need to calculate the squared difference between each value of x and the mean, weighted by their respective probabilities. We then sum up these values. Using the formula for variance, we have (0-1.35)²(0.20) + (1-1.35)²(0.45) + (2-1.35)²(0.20) + (3-1.35)²(0.10) + (4-1.35)²(0.05). By simplifying this expression, we find that the variance of x is approximately 1.267.

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In which graph does y vary directly as x? It’s not C, I got it wrong.

Answers

Answer:

Step-by-step explanation:

A graph where y varies directly as x is a straight line that passes through the origin (0, 0). This is because when two variables vary directly, their ratio is constant, and in the case of y and x, this ratio is the slope of the line.

The equation for direct variation is y = kx, where k is the constant of variation. When we plot this equation on a graph with y on the vertical axis and x on the horizontal axis, we get a straight line that passes through the origin, with a slope of k.

For example, if we have a set of data points that vary directly, such as (1, 2), (2, 4), (3, 6), and so on, we can plot these points on a graph and draw a straight line that passes through the origin and all the points. This line represents the direct variation between y and x, and any other points that satisfy the equation y = kx will lie on this line.

In summary, a graph where y varies directly as x is a straight line that passes through the origin, with a constant slope representing the constant of variation.

what is the area of the white rectangle in square units

Answers

The length above is 13 units.
The length of the grey rectangle below is 4 units, so the length of the white rectangle below is 13 units - 4 units = 9 units.
The width of the white rectangle is 6 units.

A = LW = 9 units * 6 units = 54 units^2

Answer: 54

At noon, ship a is 50 km west of ship
b. ship a is sailing south at 10 km/h and ship b is sailing north at 20 km/h. how fast is the distance between the ships changing at 4:00 pm? (round your answer to one decimal place.) 23.05 incorrect: your answer is incorrect. km/h

Answers

Final answer:

At 4:00 pm, the distance between the ships is changing at a rate of 30 km/h.

Explanation:

To find how fast the distance between the two ships is changing, you can use the Pythagorean theorem, as the two ships are moving at right angles to each other (north and south). Let's denote the distance between the two ships as "D," the speed of ship A as "vA," and the speed of ship B as "vB."

At any given time, you have:

D² = (Distance ship A travels)² + (Distance ship B travels)²

Now, we can differentiate both sides of this equation with respect to time "t" to find how the distance "D" is changing:

2D * dD/dt = 2(vA * dA/dt) + 2(vB * dB/dt)

Here, dD/dt represents the rate of change of the distance between the ships, dA/dt is the speed of ship A (10 km/h), and dB/dt is the speed of ship B (20 km/h).

Plug in the values:

2 * (dD/dt) = 2 * (10 km/h) + 2 * (20 km/h)

Now, solve for dD/dt:

2 * (dD/dt) = 20 km/h + 40 km/h

2 * (dD/dt) = 60 km/h

Now, divide by 2:

dD/dt = 60 km/h / 2 = 30 km/h

So, at 4:00 pm, the distance between the two ships is changing at a rate of 30 km/h.

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For a science experiment,Juanita records the height of a plant every day in centimeters.What is the attribute measured in her experiment.

Answers

In Juanita's science experiment, the attribute measured is the plant's height, a key phenotypic trait in studying plant growth, which she records in centimeters, using consistent and precise units for scientific reliability.

The attribute measured in Juanita's science experiment is the height of a plant, which is a phenotypic trait important in plant biology. Juanita is collecting data related to plant growth by observing and recording the plant's height in centimeters daily. This meticulous tracking allows for analysis of plant growth patterns over time and the effect of various treatments, such as different fertilizers or amounts of water. The typical unit of measurement for the height of a plant is in centimeters or meters, which are part of the metric system used in scientific research.

During a laboratory experiment like the one Juanita is conducting, it is essential to measure such variables with precision and consistency. Measurements should be recorded using uniform units and methods to ensure reliability in the results, which may include the plant height, recorded in centimeters, at regular intervals. A graph representing this data might portray the number of days since the start of the experiment along the X-axis and the plant's height along the Y-axis, thereby allowing a visual assessment of the plant's growth over time.

A high school has 3636 players on the football team. the summary of the players' weights is given in the box plot. approximately, what is the percentage of players weighing greater than or equal to 194194 pounds?

Answers

To calculate the percentage of players weighing 194 pounds or more from a box plot, we need to know where 194 pounds falls in relation to the quartiles on the plot. Without the box plot details, we cannot perform the needed analysis.

The student's question appears to concern the analysis of a box plot depicted in their materials to find the percentage of players weighing 194 pounds or more on a football team. However, to accurately answer this question, we need the specific details from the box plot, including the median (Q2), first quartile (Q1), third quartile (Q3), and any outliers if provided. From the box plot, we would determine where the weight of 194 pounds falls in relation to the quartiles. If 194 pounds is at or above Q3, then you would expect a lower percentage of players above this weight; if it is below Q3, then the percentage could be higher.

The approach typically involves identifying the number of players within each quartile and calculating the corresponding percentages. Without the specific box plot data, we cannot perform these calculations. Should you provide the box plot details, we can review the quartiles and calculate the exact percentage of players weighing 194 pounds or more.

Six girls share 5 pints of milk equally.What fraction of a pint of milk does each girl get?

Answers

Each girl would get 1.2 Pints.
All you have to do is divide 6 by 5.

There are 20 goldfish in a pond. Their population is increasing by 20% each year. The same pond has 100 minnows. The minnow population is increasing by 10 minnows each year. Make a graph to find the year that the two species of fish will have the same population. In what year will the fish populations be approximately the same?

Answers

The graph is attached, showing the intersection point at 13.5 years and populations of 235.2 for each population.

We only consider the portion of the graph from x=0 on, since negative time is illogical. Tracing the graph we get the intersection point.

Answer:

13.5 years.

Step-by-step explanation:

We know that exponential growth function is in form [tex]y=a\cdot(1+r)^x[/tex], where, a is initial value and r is growth rate in decimal form.

Population of goldfish after x years would be [tex]y=20\cdot(1+0.20)^x[/tex].

We know that a linear function is in form [tex]y=mx+b[/tex], where, b is initial value and m is slope.

Population of minnow after x years would be [tex]y=100+10x[/tex].

Graphing both equations, we will get our required graph as shown in the attachment.

Since both graphs intersect at [tex]x=13.5[/tex], therefore, in the 13.5 years both populations will approximate the same.

Find the area of the triangle that divides the parallelogram in half

Answers

Could you please provide a picture so we can answer it better?

Hal wants to make a 2 ½ foot banner from a 5-foot length of cloth. If he has marked 2.0 on the cloth, what does he have to do to find 2 ½ feet?

Answers

He has to mark 0.5 more cloth.

He can divide the 2.5 piece into fifths, and then add one of those fifths onto the 2.0 piece, to get a 2 [tex] \frac{1}{2} [/tex] piece.
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Hope this helps!

The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was bought at a wholesale price of \$113.00$113.00dollar sign, 113, point, 00, and Jessica's Furniture Store marks up all furniture by 45\%45%45, percent.
At what price should the manager sell the couch?

Answers

Answer: $163.85

Explanation:

1) Data:

Purchase price: $ 113.00

mark up: 45%

2) Formula

selling price = purchase price + mark up

mark up = % * purchase price

3) Solution

mark up = 45% * $ 113.00 = 0.45 * $ 113.00 = $50.85

selling price = $ 113.00 + $ 50.85 = $ 163.85

Answer: $ 163.85

Answer:

163.85 bucks,bix,backs,boks :P

Step-by-step explanation:

In order to find the retail price, we must first find the amount of markup. Remember that a markup rate is a percentage of the wholesale price that a store adds to get a selling or retail price. With this knowledge, we can figure out the following equation:

markup rate× wholesale price = amount of markup

Since the markup rate is a percentage, we have to convert it into a decimal first. Percent means "out of one hundred," so 45% is equivalent to 45/100 which is also equal to 45 \ 100 so 45/100 = 0.45. 0.45 * 113 = 50.85.

Since the markup rate is a percentage of the wholesale price that is added to get the retail price, we can find the retail price with the following equation:

amount of markup + wholesale price = retail price. 50.85 + 113 = 163.85

what is -6x = -24
13 points

Answers

Divide the equation by the coefficient of x.
.. (-6x)/-6 = (-24)/-6
.. x = 4

_____
You asked "what is ..."
Answer: it is a "one-step" linear equation in x.

Follow the steps above and find c, the total of the payments, and the monthly payment. Choose the right answers. Jane Smart buys a new SUV. The price, including tax, is $22,500.00. She finances the vehicle over 60 months after making a $2,000 down payment. The true annual interest rate is 12%. What are Jane's monthly payments (principal plus interest)? To the nearest penny, c = $. Total of payments = amount financed + c = $. Total of payments ÷ number of payments = monthly payment = $.

Answers

Final answer:

To calculate Jane's monthly car loan payments, we must determine the amount financed, total of the payments, and monthly payment. After deducting the down payment from the price of the SUV, we find the amount financed. To calculate the total of the payments, we multiply the amount financed by the monthly interest rate. Finally, we divide the total of the payments by the number of months to find the monthly payment.

Explanation:

To find the monthly payments for Jane Smart's car loan, we need to calculate the amount financed, the total of the payments, and the monthly payment.

First, we calculate the amount financed by subtracting the down payment from the price of the SUV: $22,500 - $2,000 = $20,500.Next, we calculate the total of the payments, which is the amount financed plus the interest. To calculate the interest, we multiply the amount financed by the true annual interest rate and divide by 12 to get the monthly interest rate: ($20,500 * 0.12) / 12 = $205.Then, we add the amount financed to the total interest to get the total of the payments: $20,500 + $205 = $20,705.Finally, we calculate the monthly payment by dividing the total of the payments by the number of months: $20,705 / 60 = $345.08 (rounded to the nearest penny).

So, Jane's monthly payment for the SUV is $345.08.

A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

6 in3
24 in3
36 in3
48 in3

Answers

Volume of a cone = 1/3 r² π h
Volume of a cylinder = r² π h = 3 · V ( cone ) = 3 · 12 = 36 in³
Answer: C

Express the following sum in sigma notation:
1+4+7+10+13

Answers

The sum would be written as:
[tex]\Sigma_{n=1}^{5} (3n-2)[/tex]

It goes from n=1 to =5 because it is the first 5 terms of the sum.
The sequence has a first term, a₁, of 1. The common difference, d, is 3. The explicit formula would then be:
[tex]a_n=1+3(n-1)[/tex]

Using the distributive property to simplify, we would have:
[tex]a_n=1+3n-3 \\a_n=3n-2[/tex]

Final answer:

The given series is an arithmetic series with a common difference of 3. The sigma notation for this series is [tex]\[\sum_{n=1}^{5} (1 + 3 \cdot (n-1)).\][/tex]

Explanation:

The given series 1+4+7+10+13 is an arithmetic series, where the common difference between consecutive terms is 3. Sigma notation or summation notation is a way of expressing this long sum in a concise way. The rule for the nth term in your series is

[tex]$a_n = 1 + 3 \cdot (n-1)$, where $a_n$[/tex]

stands for the nth term. So, the sigma notation for this series would be

[tex]\[\sum_{n=1}^{5} (1 + 3 \cdot (n-1)).\][/tex]

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