A. Write the first four terms of the sequence, given the nth term formula
1. an=2n+3
2. an=n2-1

B. Supply the missing term for each sequence
1. 57,__,37,__17
2. __,__,0,12,24,36
3. -4,8,__16,-20

C. Find the general rule or nth term for each sequence
1. 7, 12, 17, 22,...
2. 2, 6, 12, 20,...

D. Determine whether each sequence is arithmetic or not. Find the common difference for each arithmetic sequence

1. 4, 8, 12, 16,..
2. 13, 10, 7, 4,...
3. -10, -8, -6, -4,..
4. 1, 6, 8, 11, 12,..
5. 5,6,12,13

The volume of the triangular base prims is 21.6 inches cube.

A triangular base prism is a prism with a triangular base. Therefore, let's find the volume of the triangular prism.

volume of a triangular prism = base area × height

Therefore,

base area = 1 / 2 bh

where

Therefore, the triangular base has angles 45, 45 and 90 degrees. Using trigonometric ratios let's find the other legs.

tan 45 = opposite / adjacent

tan 45 = x / 6

x = 6 inches

Therefore,

base area = 1 / 2 × 6 × 6

base area = 36  /2

base area = 18 inches²

Hence,

volume of the triangular base prism = 18 × 1.2

volume of the triangular base prism = 21.6 inches³

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The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.

To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.

Algorithm/Abstract Strategy:

Start with the numerator, which is 3.

Identify the denominator, which is 5.

Interpret the fraction as a ratio or comparison between the numerator and denominator.

Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).

Perform the division: 3 ÷ 5.

Simplify the division to its simplest form, if necessary.

The result of the division, in this case, is the decimal representation of the fraction.

If required, convert the decimal representation to a percentage or any other desired form.

For example, if we perform the division 3 ÷ 5, the result is 0.6.

So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.

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Recall that a ⇒ b   ⇔   ¬a ∨ b. So we can write

q ⇒ (p ∧ r )   ⇔   ¬q ∨ (p ∧ r )

Then the negation of this would be, for instance,

¬(¬q ∨ (p ∧ r ))   ⇔   ¬(¬q) ∧ ¬(p ∧ r )

…   ⇔   q ∧ (¬p ∨ ¬r )

…   ⇔   (¬p ∧ q) ∨ (q ∧ ¬r )

…   ⇔   ¬(p ∨ ¬q) ∨ (q ∧ ¬r )

…   ⇔   (p ∨ ¬q) ⇒ (q ∧ ¬r )

It's impossible to tell what kind of statement your program is expecting, but since there are 5 slots available, my money would be on q ∧ (¬p ∨ ¬r ), so long as ¬p and ¬r are options.

Answer:

D 11%

$30

Step-by-step explanation:

1. A cyclist estimates that he will bike 80 miles this week. He actually bikes 90 miles. What is the percent error of the cyclists estimate rounded to the nearest percent?

A 8%

B 9%

C 10%

D 11%

Actual distance: 90 miles

Estimated distance: 80 miles

percent error = (estimate - real)/real × 100%

percent error = (80 - 90)/90 × 100%

percent error = -11%

His error is 11%. The negative sign just means his estimate is 11% less than the real distance.

Answer: 11%

2. Jack borrows $3,000 at a rate of 4% per year. How much total will he pay if it takes 3 months to repay the loan?

$10

$20

$30

$40

interest = Prt

where P = principal (the amount borrowed or deposited)

r = annual rate of interest

t = time

We have P = $3,000

r = 4% = 0.04

t = 3 months = (3 months)/(12 months) = 0.25 year

interest = $3,000 × 0.04 × 0.25

interest = $30

He pays a total interest of $30.

Answer:

Step-by-step explanation:

With a monthly repayment of $809.49, the total interest on the car loan will be $5,569.67.

We assume that there are monthly repayments and compounding interest on the car loan.

With periodic repayments and compounding interest, the total interest paid on the car loan will be as shown by the car loan calculator.

Car loan = $43,000

Down payment = $0

Fixed Annual Percentage Rate (APR) = 4.9%

Loan term = 5 years

Car Loan Calculator with monthly Repayment:

Payment = $809.49/month

Interest Paid =$5,569.67

Total Paid = $48,569.67

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Problem 1

--------------------

Explanation:

a1 = 1.7 = amount of concrete for the first step

a4 = x = amount of concrete for the fourth step

Sn = sum of the first n terms of an arithmetic sequence

Sn = (n/2)*(a1 + an)

S4 = (4/2)*(a1 + a4)

S4 = 2(1.7+x)

S4 = 2x+3.4

S4 = 17

2x+3.4 = 17

2x = 17-3.4

2x = 13.6

x = (13.6)/2

x = 6.8

We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d

an = nth term of an arithmetic sequence

an = a1 + d(n-1)

a4 = a1 + d(4-1)

a4 = a1 + 3d

6.8 = 1.7 + 3d

6.8-1.7 = 3d

5.1 = 3d

(5.1)/3 = d

1.7 = d

d = 1.7

Coincidentally, the common difference is the same as the first term. This won't always happen.

Now we can compute the 12th term

an = a1 + d(n-1)

a12 = 1.7 + 1.7(12-1)

a12 = 20.4

which is then used to find the sum of the first 12 terms

Sn = (n/2)*(a1 + an)

S12 = (12/2)*(a1 + a12)

S12 = 6(1.7 + 20.4)

S12 = 132.6

=============================================================

Problem 2

--------------------

Explanation:

The center is (h,k) = (0,10) which is where the nozzle is located.

The distance from (0,10) to (0,25) is 15 units, so r = 15.

Also, the distance from (0,10) to (0,-5) is also 15 units.

Plug those values into the equation below.

\((x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-10)^2 = 15^2\\\\x^2 + (y-10)^2 = 225\\\\\)

That equation represents the boundary of the circle, which is where the water can reach.

=============================================================

Problem 3

--------------------

Explanation:

Or note that,

a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 =  4.39587

which must mean,

This is based off the idea that \(a_n = a(r)^{n-1}\)

So,

a6 = a1*(0.81)^5

a6 = 6.7*(0.81)^5

a6 = 2.33614554867

a6 = 2.336

Answer: It will be A that is the best answers

The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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Answer:

(2+n)-3

That's how you write if that is what you want.

Answer:

1/52

Step-by-step explanation:

The probability is the ratio of the favorable event to the total number of events. Then the probability of drawing 5 is 0.0769.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

As shown above, a classic deck of cards is made up of 52 cards, 26 are black, and 26 are red.

Each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red).

Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King).

Then the probability of drawing a 5 of one suit will be given as

Total event = 52

Favorable event = 4 {5 club, 5 spade, 5 heart, and 5 red}

Then we have

\(\rm P=\dfrac{4}{52}\\\\P=\dfrac{1}{13}\\\\P=0.0769\)

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Answer:

16%

Step-by-step explanation:

20/125 = 0.16

0.16 x 100 = 16% (multiply by 100 to get a percentage)

The answer is on the picture

We are given the following data set:

We are asked to find the mean value, to do that we need to add them all together and divide the result by the number of digits we have, in this case we have 4 numbers, therefore the mean value is the following

The student's mean quiz score is 14.75

.

Thanks and have a great day!

Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1. Therefore, the displacement of P from the origin when t = 2 is -8/3 meters.

A function is a mathematical concept that describes a relationship between two sets of values, called the domain and the range. It is a rule or a set of rules that assigns a unique output value for every input value in the domain. In other words, it is a process that takes one or more inputs and produces a corresponding output. Functions are commonly represented using equations, graphs, or tables. They are used in various branches of mathematics, science, engineering, and technology to model real-world phenomena, make predictions, and solve problems.

Here,

(a) To find the acceleration, we need to take the derivative of the velocity function with respect to time:

a = dv/dt

= d/dt (t³ - 4t² + 5t + 1)

= 3t² - 8t + 5

(b) To find the values of t for which the magnitude of the acceleration is instantaneously zero, we need to solve the equation:

|a| = |3t² - 8t + 5|

= 0

This occurs when 3t² - 8t + 5 = 0, which factors as (3t - 5)(t - 1) = 0. Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1.

(c) To find the displacement of P from the origin when t = 2, we need to integrate the velocity function from t = 0 to t = 2:

s = ∫(v dt)

= ∫(t³ - 4t² + 5t + 1 dt)

= (1/4)t⁴ - (4/3)t³ + (5/2)t² + t + C

We know that s(0) = 3, so we can solve for C:

3 = (1/4)(0)⁴ - (4/3)(0)³ + (5/2)(0)² + 0 + C

C = 3

Therefore, the displacement of P from the origin when t = 2 is:

s(2) = (1/4)(2)⁴ - (4/3)(2)³ + (5/2)(2)² + 2 + 3

= -8/3 meters

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Answer: \(g(-2)=2a\)

Step-by-step explanation:

\((f \cdot g)(-2)=f(-2)g(-2)\\\\\therefore a \cdot g(-2)=2a^2 \implies g(-2)=2a\)

The function g(-2) from the given functions is 2a.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(-2)=a and (f·g)(-2)=2a².

Here, (f·g)(-2)=2a²

f(-2)·g(-2)=2a²

a·g(-2)=2a²

g(-2)=2a²/a

g(-2)=2a

Therefore, the function g(-2) is 2a.

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Answer:

21 I think, might be wrong.

Answer:

Mean Absolute Deviation: 4

Step-by-step explanation:

A mean absolute deviation is measured how much the values in the data set are likely to differ from the mean.

Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

The quantity of candy that Eric ate would be = 14/15

The quantity of Candy Kim had = 2⅓ pounds.

The quantity of Kims candy that Eric ate = 2/5

That is 2/5 of 2⅓.

The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15

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Answer:

\(y(x)=c_1e^{-x}+c_2xe^{-x}+c_3x^2e^{-x}\)

Step-by-step explanation:

We can determine the characteristic equation all we have to do is:

let y' = m, hence y" = m², y'" = m³

Therefore, the higher-order differential equation becomes:

m³ + 3m² + 3m + 1 = 0

(m + 1)(m² + 2m + 1) = 0

(m + 1)(m + 1)(m + 1) = 0

(m + 1)³ = 0

m = -1, -1, -1

Therefore the general solution is given as:

\(y(x)=c_1e^{-x}+c_2xe^{-x}+c_3x^2e^{-x}\)

\(c_1,c_2,c_3\ are\ constants.\)

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'

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Answer:

its gonna be 212 fam

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

The variable of study is

X: number of complaints per industry (Categorized: Bank, Cable, Car, Cell, Collection

Considering this is a categorical variable, and the hypothesis is that all categories have the same probability, you have to apply a Chi-Square  Goodness to Fit test.

Observed frequencies per category

1) Bank: 26

2) Cable: 44

3) Car: 42

4) Cell: 60

5) Collection: 28

Total= 200

Statistical hypotheses:

H₀: P₁=P₂=P₃=P₄=P₅=1/5

H₁: At least one of the proposed proportions is different.

α: 0.01

\(X^2= sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}\)

For this test the formula for the expected frequencies is:

\(E_i= n * P_i\)

So the expected values for each category is:

\(E_1= n * P_1= 200*1/5= 40\)

\(E_2= n * P_2= 200*1/5= 40\)

\(E_3= n * P_3= 200*1/5= 40\)

\(E_4= n * P_4= 200*1/5= 40\)

\(E_5= n * P_5= 200*1/5= 40\)

\(X^2_{H_0}= \frac{(26-40)^2}{40} +\frac{(44-40)^2}{40} +\frac{(42-40)^2}{40} +\frac{(60-40)^2}{40} +\frac{(28-40)^2}{40} = 11.5\)

This test is one tailed and so is its p-value, under a Chi-square with 4 degrees of freedom p-value:  0.021484.

The p-value is less than the significance level so the decision is to reject the null hypothesis.

c. The industry with most complaints is the cellular phone providers

I hope this helps!

Answer:

75 degrees

Step-by-step explanation:

The shape is a trapezoid. When finding angle measurements in trapezoids:

Angle A + Angle C = 180 degrees

Angle B + Angle D = 180 degrees

Because you need to find the angle of B, we will use Angle B + Angle D = 180 degrees to solve this. Angle D is 105 degrees, so 105 + Angle B = 180. 180-105 equals 75, so angle B is 75 degrees.

Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

Answer:

-5/6

Step-by-step explanation:

By the application of Analytical geometry the rate of change of y with respect to x is -5/6.

what is Analytical geometry?

Analytical geometry is a branch of mathematics that studies geometric shapes and figures using analytical methods. It is a branch of mathematics that uses algebraic techniques to describe geometric shapes and figures. It involves the use of analytical equations and formulas to study geometric concepts. Analytical geometry is used to study the properties of points, lines, angles, circles, and other geometric shapes. It can also be used to solve problems involving angles, distances, and areas of figures. In addition, analytical geometry can be used to find the intersection of two lines, calculate the area of a circle, and calculate the volume of a cylinder. Analytical geometry is a powerful tool used in many scientific and engineering fields.

The rate of change of y with respect to x for this line is -5/6
Therefore -5/6 is rate of change in this graph.

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