What is the 12th term of the arithmetic sequence where a1 = 5 and a6 = 20?

Answers

Answer 1

an=a1+d(n-1)
an=nth term
a1=first term
d=common differnce
n=which term

alrighty, a1=5

neat
an=5+d(n-1)
given a6=20
20=a6=5+d(6-1)
20=5+d(5)
20=5+5d
minus 5 both sides
15=5d
divide both sides by 5
3=d

so
an=5+3(n-1) is the formula for the nth term

12th term
a12=5+3(12-1)
a12=5+3(11)
a12=5+33
a12=38

the 12th term is 38

Related Questions

solve the equation by completing the square. round to the nearest hundredth if necessary. x^2-6x=20

Answers

x^2 - 6x = 20
x^2 - 6x + 9 = 20 + 9
(x - 3)^2 = 29
x - 3 = (+-) sqrt 29
x = 3 (+-) sqrt 29
x = 3 (+-) 5.39

x = 3 + 5.39 = 8.39 <=
x = 3 - 5.39 = - 2.39 <=

x^2-6x+(b/2)^2=20+(b/2)^2
x^2-6x+(6/2)^2=20+(6/2)^2
x^2-6x+(3)^2=20+(3)^2
x^2-6x+9=20+9
(x-3)^2=29
x-3=5.38 or -5.38
x=5.38+3 or -5.38+3
x=8.38 or -2.38

The teen club had a cupcake sale. they started with 126 cupcakes. they sold 2/3 of their cupcakes in the morning. how many were left for them to sell in the afternoon?

Answers

126 ÷ 3= 42
42×2= 84 (number of cupcakes sold)
126-84= 42 (number of cupcakes left)

What equation results from completing the square and then factoring? x2 + 6x = 13

Answers

Step 1: Subtract 13 from both sides.
x^2+6x−13=13−13x^2+6x−13=0
Step 2: Use quadratic formula with a=1, b=6, c=-13.
x=−b±√b2−4ac2ax=−(6)±√(6)2−4(1)(−13)2(1)
x=−6±√882
x=−3+√22 or x=−3−√22
Answer would be
x=−3+√22 or x=−3−√22

In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).

Answers

When you have a set of data points and you want to get a model out of it, you do data fitting. The first thing to do is plot the points using a scatter plot type of chart as shown in the picture. I used MS Excel as a tool for data fitting. On the left side of the picture, I used linear fitting. Then, it gives you the linear equation y=0.2907x + 2.2643. It has a correlation coefficient, R^2, of 0.9595. This measures how good your data fits the model equation. The closer it is to 1, the better. However, it is rare to get 1 because that is very ideal. A R^2 of 0.9595 is very satisfactory already. But if you want an even better model, the right side of the picture shows data fitting on a quadratic equation with an equation of y=0.0209x^2 +0.506x+2.0232 with R^2 of 0.9992.

Answer:

The closer this value is to 1 or -1, the better the fit. For linear, the correlation coefficient R2=.96. For quadratic, the R2=.99. For exponential, the R2=.91. This means quadratic is the best fit, very good actually since .99 is very close to 1.

Step-by-step explanation:

Find the product.

(n + 7)(n - 2)

n² - 5n - 14
n² + 5n - 14
n² - 5n + 14

Answers

The answer is n^2 + 5n - 14.

[tex](n+7)(n-2)\\\\n*n+(-2)*n+7*n+7*(-2)\\\\n^{2}-2n+7n-14\\\\n^{2}+5n-14[/tex]

(n+7)(n-2)
=n•n+(-2)•n+7•n+7•(-2)
=n²-2n+7n-14
=n²+5n-14. In conclusion, the product of (n+7) and (n-2) or (n+7)(n-2)=n²+5n-14. Hope it help!

Write the equation in exponential form.

Answers

the answer is D. ( btw,the picture quality sucks,try cropping it)

My sister is 15 years older than i am. the sum of our ages is 41. find our ages

Answers

x = you, and y = ur sis

x + y = 41
y = x + 15

x + (x + 15) = 41
2x + 15 = 41
2x = 41 - 15
2x = 26
x = 26/2
x = 13 <== u r 13

y = x + 15
y = 13 + 15
y = 28 <== ur sis

How many square meters are in 350 square centimeters?

Answers

There are 3.5 square meters in 350 square centimeters. A way to help remember this is that the prefix "centi" means one hundred, and there are a hundred centimeters in one meter. Hope this helps:)

~Ash

Final answer:

To convert 350 square centimeters to square meters, divide by the conversion factor that 1 square meter equals 10,000 square centimeters, resulting in 0.035 square meters.

Explanation:

To convert 350 square centimeters to square meters, we should remember that 1 square meter is equal to 10,000 square centimeters because 1 meter is equal to 100 centimeters and for area, we need to square that conversion (100 cm × 100 cm).

We start with the given quantity of 350 square centimeters. Then, we use the conversion factor 1 square meter is 10,000 square centimeters to perform the calculation, which gives us:

350 cm² × (1 m² / 10,000 cm²) = 0.035 m².

Therefore, 350 square centimeters is equal to 0.035 square meters.

A bag contains 30 red tiles, 15 green tiles, and 5 yellow tiles. One tile is drawn and then replaced. Then a second tile is drawn. What is the probability that the first tile is yellow and the second tile is green?
A.
1%
B.
3%
C.
6%
D.
18%

Answers

Allright we know that the total number of tiles is 50 so we can assume that if you pick the first tile and its yellow ther is a (5/50) chance to pick it up and then REPLACED meaning that it is put back so you have still 50 tiles to choose from, if then you choose a green tile you have a (15/50) chance of picking it up

(5/50)*(15/50)=0.03 YOU HAVE A 3 PERCENT CHANCE!!!:D
^This is to calculate the probability of picking it in that order)^

Two numbers are in the ratio of 3 to 4. If nine is subtracted from each, they are in the ratio of 3 to 5. Find the numbers.

Answers

12:16= 3:4 when simplified
12-9=3
16-9=5
When subtracting 9 from each the new ratio is 3:5

Hope this helps!

Find the period of the function. y = 5 cos one divided by twox

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ % function transformations for trigonometric functions \begin{array}{rllll} % left side templates f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}} \\\\ f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\ f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}} \end{array} \\\\ -------------------\\\\[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ [/tex]

[tex]\bf \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\[/tex]

[tex]\bf \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]

so.. with that template in mind, let's see

[tex]\bf \begin{array}{llll} y=5cos&\left(\frac{1}{2}x\right)\\ &\ \uparrow \\ &\ B \end{array}\qquad period\qquad \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{1}{2}}\implies \cfrac{2\pi }{1}\cdot \cfrac{2}{1}\implies 4\pi [/tex]

Find the area of the triangle

Answers

The area of a triangle is equal to bh/2.
The base here is 8 and the height is 3.
8*3=24
24/2=12
The answer is B, 12 yd^2

Please Help!! Find the measure of angle 2. Image Attached

Answers

opposite angles = 180 degrees

180-111 = 69

angle 2 = 69 degrees

Webassign find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (6, 36), and the x-axis.

Answers

first find the tangent line

dy/dx=2x
at x=6, the slope is 2(6)=12
so
use point slope form
y-y1=m(x-x1)
point is (6,36)
so
y-36=12(x-6)
y-36=12x-72
y=12x-36

alright, so we know they intersect at x=6
and y=12x-36 is below y=x^2

so we do [tex] \int\limits^6_0 {x^2} \, dx - \int\limits^6_0 {12x-36} \, dx = \int\limits^6_0 {x^2-(12x-36)} \, dx = \int\limits^6_0 {x^2-12x+36} \, dx =[/tex]
[tex][\frac{x^3}{3}-6x^2+36x]\limits^6_0=(\frac{6^3}{3}-6(6)^2+36(6))-(0)=\frac{216}{3}-216+216=[/tex] [tex]72+0=72[/tex]

the area under the curve bounded by the lines and the x axis is 72 square units

To the nearest square unit, what is the area of the shaded region?

Answers

Since the diagram is a regular octagon, it can form 8 of the same triangles.
The area of one triangle= 1/2 x 15 x 18.11
=135.825
The area of the octagon = 135.825 x 8
= 1086.6
The area of shaded region will be the area of the octagon minus the square
The area of the shaded region = 1086.5-(15x15)
=861.6
Answer will be C as you need to round off to three significant figures

First we need to distribute it in parts of
2 trapezium
1 rectangle
These reading are for shaded region
Each side of octagone is 15 as it is regular
The height of octagone=18.11 x 2=36.22 this is one side of trapezium
and the other is 15 as it is regular
the height of trapezium=10.61 from the whole horizontal length is equal to vertical as it is regular octagone
then we need to subtract this horizontal length by 15 which is one of the side =36.22-15=21.22 then divide it by 2 so that can get height of each trapezium =10.61
so the area of each trapezium= 0.5 x (36.22+15) x 10.61=271.7
And of two are= 271.7 x 2 =543.4
The area of triangle = 15 x 21.22 ( this is not the area of rectangle shown it is the area of rectangle which is above it and part of shaded region.
=318.3
Area of shaded region = 543.44 + 318 3 =861.7=862 to nearest whole number
SO ANSWER IS C THAT IS 862 square units

Outside a home there is a keypad that will open the garage if the correct four digit code is entered.? How many codes are possible?

Answers

Assume that none of the digits on the keypad are repeated. This means that we have 10 digits: 0,1,2,3,4,5,6,7,8,9.

The number of ways to arrange 10 distinct digits is
10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800

Answer: 3,628,800
That is 3 million, 628 thousand, and 800.

Final answer:

There are 10,000 possible codes that can be entered into the keypad to open the garage.

Explanation:

The number of possible codes is determined by the number of choices for each digit of the code. In this case, there are 10 possible choices for each digit (0-9). Since there are 4 digits in the code, we can multiply the number of choices for each digit together to find the total number of possible codes: 10 x 10 x 10 x 10 = 10,000. Therefore, there are 10,000 possible codes that can be entered into the keypad to open the garage.

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What is the precise definition of an angle? question 1 options:?

Answers

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

andy states, " if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."

A.True
B.False

Answers

A. True, to bisect is to divide into equal or congruent halves. Because you can do so it means its going to be a parallelogram.

The statement "If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram." is True .

What is parallelogram?

"It is a quadrilateral whose opposite sides are parallel and equal in length."

What is diagonal?

"It is a straight line that connects the opposite corners of a polygon through its vertices."

According to the question

The statement states that

"if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."

Now ,

As per properties of parallelogram

In any quadrilateral the two diagonals bisect each other is a parallelogram .

Hence, The statement is True .

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5/14 divided by 3/4, what's the answer

Answers

Rule: (a/b)/(c/d)=(a/b)*(d/c)

(5/14)/(3/4)

(5/14)(4/3)

(5*4)/(14*3)

20/42

10/21

Answer: 10/21 or 0.47619...

This can be calculated by finding the reciprocal of 3/4, which is 4/3.

Next, you multiply 5/14 by 4/3. To multiply fractions, you multiply the two numerators and set it as the new numerator and multiply the two denominators and set it as the new denominator.

5 * 4 = 20
14 * 3 = 42

To simplify, you can divide each by 2 since it goes into both values.

20/2 = 10
42/2 = 21

Answer: 10/21

A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12 respectively. the probability that the sample mean is larger than 70 equals:

Answers

To solve this problem, we can use the z statistic to find for the probability. The formula for z score is:

z = (x – u) / s

Where,

u = the sample mean = 68

s = standard deviation of the samples = 12

x = sample value = 70

In this case, what is asked is the probability that the sample mean is larger than 70, therefore this corresponds to the right of z on the graph of normal distribution.

z = (70 – 68) / 12

z = 2 / 12

z = 0.17

Therefore finding for P at z ≥ 0.17 using the standard distribution tables:

P (z = 0.17) = 0.5675

But this is not the answer yet since this is the P to the left of z. Therefore the correct one is:

P (z ≥ 0.17) = 1 - 0.5675

P (z ≥ 0.17) = 0.4325 = 43.25%

The probability that the sample mean is larger than 70 is 43.25%

The probability that the sample mean is larger than 70 for a sample size of 40 from a population with a mean of 68 and standard deviation of 12 is approximately 14.69%.

To determine this probability, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means will be approximately normal if the sample size is large enough (n ≥ 30 is a common benchmark).

The standard error of the mean is calculated using the formula:

SE = σ / √n

Where σ is the population standard deviation and n is the sample size.

In this case:
σ = 12
n = 40

Therefore,

SE = 12 / √40 ≈ 1.8974

The z-score is calculated using the formula:

z = (M - μ) / SE

Where M is the sample mean,
μ is the population mean,
SE is the standard error.

Given,
μ = 68
M = 70

Therefore,

z = (70 - 68) / 1.8974 ≈ 1.054

Using the z-table, we find the probability that a z-score is less than 1.054 is approximately 0.8531.

However, we need the probability that the sample mean is greater than 70, so we subtract this from 1,

1 - 0.8531 ≈ 0.1469

Thus, the probability that the sample mean is larger than 70 is approximately 0.1469, or 14.69%.

HELP QUICK!!!
An ellipse has foci F1(9, 0) and F2(11, 6), and the point (1, 6) is on the ellipse. Identify the constant sum for the ellipse.
a 20
b 10
c 0
d 100

Answers

The first step is to find the distance from the given point to each of the two foci as follows:
Distance D1:
(D1)^2 = (9-1)^2 + (0-6)^2 = 100
D1 = 10
Distance D2:
(D2)^2 = (11-1)^2 + (6-6)^2 = 100
D2 = 10

The constant sum is the summation of the two distances as follows:
constant sum = D1 + D2 = 10 + 10 = 20

The correct choice is:
a) 20

Answer: 20

Step-by-step explanation:

A and b are complementary angles find a and b a=3/4x-13 b=3x-17

Answers

3/4x-13+3x-17=90

3 3/4x-30=90

3 3/4x = 120

x=32

A=11
B=79

linear function graph express in slope intercept form

Answers

The slope intercept form is y=(1/4)x-4

An electronic device that previously sold for $21 has been reduced to 17.43. the price reduction, rounded to the nearest whole percent is

Answers

percent decrease = (new number - original number) / original number...* 100
= (21 - 17.43) / 21....* 100
= 3.57 / 21....* 100
= 0.17 * 100
= 17%.....the price reduction was 17%

The price reduction, rounded to the nearest whole percent is [tex]17[/tex]%.

What is whole number?

The whole numbers are the part of the number system which includes all the positive integers from 0 to infinity. These numbers exist in the number line.

What is Percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

According to question, an electronic device that previously sold for $[tex]21[/tex] has been reduced to [tex]17.43[/tex]

We have to find the price reduction, rounded to the nearest whole percent .

So percentage reduction

[tex]=\frac{21-17.43}{21}[/tex]×[tex]100[/tex]%

[tex]=0.17[/tex]×[tex]100[/tex]%

[tex]=17[/tex]%

Hence, price reduction, rounded to the nearest whole percent is [tex]17[/tex]%.

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1. Evaluate 6.314 - 9.77.

3.456
-3.464
-3.456
-16.084

2. Evaluate -5.118 - (-4.1).

-9.218
-1.018
1.018
9.218

3. Find the value of x + y for x = 75.9 and y = 2.65.

10.24
102.4
78.55
79.55

4. Find the value of -x + y for x = 75.9 and y = 2.65.

-78.55
78.55
73.25
-73.25

Answers

Evaluate 6.314 - 9.77.

3.456
-3.464
-3.456 ☆
-16.084

2. Evaluate -5.118 - (-4.1).

-9.218
-1.018 ☆
1.018
9.218

3. Find the value of x + y for x = 75.9 and y = 2.65.

10.24
102.4
78.55 ☆
79.55

4. Find the value of -x + y for x = 75.9 and y = 2.65.

-78.55
78.55
73.25
-73.25☆

Answer:

1. -3.456

2. -1.018

3. 78.55

4. -73.25

Step-by-step explanation:

In Algebra, the following notations have to be considered.

Algebra is a branch of mathematics that deals with the computation of numbers irrespective of the signs involved.

- × - = +

+ × - = -

- × + = -

+ × + = +

Therefore,

1. 6.314 - 9.77 = -3.456

2. -5.118 - (-4.1) = -5.118 + 4.1 = -1.018

3. x + y for x = 75.9 and y = 2.65.

This requires substitution

75.9 + 2.65 = 78.55

4. -x + y for x = 75.9 and y = 2.65

= -75.9 + 2.65

= -73.25

If BC=5.3, CD=8.8, and AD= 14.3, find AB to the nearest tenth.

Answers

The picture above shows us that triangle ABC and triangle ACD are similar triangles by showing us that then have congruent angles. This tells us that each side of the triangle is bigger/smaller than the other triangle by the same factor. To find this out, we use two corresponding sides of the two triangles. In this case, two corresponding lengths that are given to us are BC and CD. If we divide CD by BC, this tell us that triangle ACD is approximately 5/3 bigger than triangle ABC. Using this, we can figure out the length of AB. We simply take 14.3 and divide it by 5/3. We divide because we are trying to mind the magnitude of the length of the smaller triangle. If we were looking for the length of the larger triangle, we would have multiplied. After dividing 14.2 by 5/3, we find that the length of AB is about 8.6.

Step-by-step explanation:

8.6 is the answer to the equation

At a sandwich shop they offer 3 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. Each type of sandwich has a combination of exactly 3 ingredients: 1 bread, 1 meat, and 1 cheese. How many types of sandwiches are possible?

Answers

Final answer:

The sandwich shop could yield a total of 45 types of sandwiches based on the three categories provided; namely, bread, meat, and cheese. According to the counting principle in mathematics, you multiply the amount of options available from each category to get the total combinations possible.

Explanation:

In the scenario described, to determine the possible number of sandwiches, we need to analyze the provided combinations. We have 3 types of bread, 5 kinds of meat, and 3 kinds of cheese. Each sandwich exactly contains one item from each category.

To find out all possible sandwich combinations, we multiply the number of choices in each category. This is known as the counting principle.

So, the formula would be:
Number of sandwich combinations = Types of Bread * Types of Meat * Types of Cheese

Plugging the given numbers into this formula, we get:
Number of sandwich combinations = 3 * 5 * 3 = 45

So, there are 45 possible sandwich combinations available in this sandwich shop.

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The rate of inflation is 3% . The cost of an item in future years can be found by iterating the function c(x) = 1.03x. Find the cost of a $1500 refrigerator in three years if the rate of inflation remains consistent .

********PLEASE HELP********

Answers

This is the concept of business mathematics, given an inflation rate of 3%, that has modeled the price of items using the function c(x)=1.03x, the cost of the refrigerator in 3 years will be as follows;
cost after 1 year:
c(1)=1.03*1500
=1545
cost after 2 years
c(2)=1.03*1545
=1591.35
the cost after 3 years will be:
c(3)=1.03*1591.35
=$1,639.09

midpoint of 4 – 3i and –2 + 7i please help!!!!!

Answers

hello :
let : z = 4-3ii z' = -2+7i
the distance between the points 4-3i and -2+7i is : |z - z' |
|z - z' | = |4-3i+2-7i| = |6-10i | =√(6²+(-10)²) =√136

PLEASE HELP ^^^^^^^^^^^^

Answers

Let's work this problem out:

Step one:4(-2) = -8, right?

Step two: 3(-7) = -21, right?

Step 3: So, -8 + (21) = 13,right?

Your answer would be: 13 (option B.)

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