2. Create a sequence to fit the given criteria. Describe your
sequence using figures, words, or numbers. Provide the first
four terms of the sequence. Explain how you know that it is
a sequence.
a. Create a sequence that begins with a positive integer, is
decreasing by multiplication, and is finite.



Need help quick please

Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:

Yo, listen up, the parallelogram is where it's at,

A shape so brilliant, the angles are sat.

Parallel sides that never converge,

Internal angles that never diverge.

Each side an equal length,

A geometry prodigy's dream length.

The diagonals intersect, another line through the middle they meet,

Creating symmetry so neat.

A rectangle it could be,

But it's oblong, not square, can't you see?

With depth and width in perfect balance we see,

A two-dimensional form of complexity.

While the square is simple, the parallelogram is hip,

A mathematical masterpiece, skip, skip, skip!

four right angles keep the shape so tight,

Parallel lines dominate left and right.

Rotated or reflected without a care,

Its structural integrity beyond compare.

triangles form at each corner you'll note,

Acute or obtuse, depends on the protractor's groove.

A versatile shape with reason and purpose galore,

The parallelogram, simply, carries the floor.

From geometry to art, its angles they intrigue,

As a basis for patterns, its potential we can truly plug.

A forgotten form that deserves more acclaim,

Put the parallelogram on geometry's game!

This shape so underrated, rarely appreciated it seems,

But with logic and virtue, strong foundations it gleams.

The parallelogram, the parallelogram, Hooray!

This is why the parallelogram is the best shape, I say!

The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.

The given function is,

y = 1/2 x + 2.

Also, the domain of the function is {-4, -2, 0}.

Since, the domain of the functions defines the values of x,

And range defines the value of y in function.

The value of y at x = -4

y = 1/2(-4) + 2 = -2 + 2 = 0

At x = -2,

y = 1/2(-2) + 2 = -1 + 2 = 1

At x= 0,

y = 1/2 (0) + 2 = 2

The values of y are 0, 1 and 2.

Hence, the range of the function is {0, 1, 2}.

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The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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Answer:

3.) m < 7 = 155°, m < 8 = 25°

4.) m < 5 = 30°

   m < 6 = 30°

   m < 7  = 60°

   m < 8  = 60°

Step-by-step explanation:

3.) By definition, angles that do not share a common side are called nonadjacent angles. Two nonadjacent angles formed by two intersecting lines are called vertical angles.

m < 7 = 5x + 5

m < 8 = x - 5

m < 7 + m < 8 = 180°

Substitute the values of m < 7 and m < 8 into the equation:

5x + 5 + x - 5 = 180°

6x + 0 = 180°

6x  = 180°

Divide 6 on both sides of the equation to solve for x:

\(\frac{6x}{6} = \frac{180}{6}\)

x = 30°

Plug in x = 30° to find the value of m< 7 and m< 8:

m < 7 = 5x + 5 = 5(30) + 5 = 150 + 5 = 155°

m < 8 = x - 5 = 30 - 5 = 25°

4.) This problem is an example of angles on a straight line. By definition, the sum of angles on a straight line is equal to 180°.

Therefore, the measurements of the following angles add up to 180°:  

m < 5 = 5x

m < 6 = 4x + 6

m < 7 = 10x

m < 8 = 12x - 12

Substitute the values of each measurement onto the following equation:  

5x + 4x + 6 + 10x + 12x - 12 = 180°

Combine like terms:  

31x - 6 = 180°

Add 6 on both sides of the equation:

31x - 6 + 6 = 180° + 6

31x = 186

Solve for x:

\(\frac{31x}{31} = \frac{186}{31}\)

x = 6

Plug in x = 6° to find the values of m < 5,  m <  6,  m < 7, and  m < 8:

5(6) + 4(6) + 6 + 10(6) + 12(6) - 12 = 180°

180° = 180°

Therefore:

m < 5 = 5(6) = 30°

m < 6 = 4(6) + 6 = 30°

m < 7 = 10(6) = 60°

m < 8 = 12(6) - 12 = 60°

Answer:

22 1/2

Step-by-step explanation:

Answer:

A - 6

Step-by-step explanation:

The lines are parallel.

Theorem: If two parallel lines are cut by a transversal, then same side interior angles are supplementary.

The angles measuring 16x + 4 and 80 are supplementary, so thjeir measures add to 180.

16x + 4 + 80 = 180

16x + 84 = 180

16x = 96

x = 6

The grams of cocoa does it contains is 36.57 grams

From the question, we have the following parameters that can be used in our computation:

Weight of the chocolate bar = 69

Proportion = 53%

This implies that

Grams of cocoa = weight of the chocolate bar * Proportion

Substitute the known values in the above equation, so, we have the following representation

Grams of cocoa = 53% * 69

Evaluate the products

Grams of cocoa = 36.57

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Answer:

Choice E and F

Step-by-step explanation:

acute = less than 90

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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Answer:

x=16

(x+4)=20

9x=144

Step-by-step explanation:

9x+x+4+x=180

11x+4=180

11x=180-4

11x=176

\(x = \frac{176}{11} \)

x=16

Answer:

5x and -7x

Step-by-step explanation:

they both end in the variable "x"

Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

The answer is C) (11,-10)

The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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Answer:

24sq.in

Step-by-step explanation:

Let, length be x and width be y.

x= 6y

2(x+y)=28

or, 2(6y+y)=28

or, 2×7y=28

or, 14y =28

y=2

x= 6×2=12

area= 12×2 = 24 sq.in

Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

Meaning of probability :

Probability is calculation of how likely some event will happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are going to happen.

The analysis of events governed by probability is called statistics.

According to the given information :

Red section = \(\frac{2}{5}\)

multiply numerator and denominator by \(2\) we get

Red section = \(\frac{4}{10}\)

 Blue section = \(\frac{1}{2}\)

 multiply numerator and denominator by \(5\) we get

 Blue section = \(\frac{5}{10}\)

 Green section = \(1\)- Red section - Blue section

 Green section =\(1-\frac{4}{10} -\frac{5}{10}\)

  Green section = \(\frac{1}{10}\)

Therefore Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

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Answer:

add, subtract, multiply and divide complex numbers much as we would expect. We add and subtract

complex numbers by adding their real and imaginary parts:-

(a + bi)+(c + di)=(a + c)+(b + d)i,

(a + bi) − (c + di)=(a − c)+(b − d)i.

We can multiply complex numbers by expanding the brackets in the usual fashion and using i

2 = −1,

(a + bi) (c + di) = ac + bci + adi + bdi2 = (ac − bd)+(ad + bc)i,

and to divide complex numbers we note firstly that (c + di) (c − di) = c2 + d2 is real. So

a + bi

c + di = a + bi

c + di ×

c − di

c − di =

µac + bd

c2 + d2

¶

+

µbc − ad

c2 + d2

¶

i.

The number c−di which we just used, as relating to c+di, has a spec

Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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Given:

Total number of candy in a bag is 15.

Number of orange flavored candy is 2

Number of cherry flavored candy is 6

Let A be the event of picking an orange or a cherry flavored candy from the bag.

Answer:

Step-by-step explanation:

To calculate the total balance on the next billing date, we need to consider the average daily balance and the unpaid balance from the previous month.

Given:

Average daily balance for November = $700

Unpaid balance at the end of November = $1,400

Annual percentage rate (APR) = 15.6%

Step 1: Calculate the interest charged for the month of November.

Interest = (Average daily balance * APR * Number of days in the month) / 365

Number of days in November = 30

Interest = (700 * 0.156 * 30) / 365 = $36.44 (rounded to the nearest cent)

Step 2: Add the interest to the unpaid balance to get the total balance on December 1.

Total balance = Unpaid balance + Interest

Total balance = $1,400 + $36.44 = $1,436.44

Therefore, the total balance on the next billing date, December 1, is $1,436.44 (rounded to the nearest cent).

The total balance on the next billing date December 1 is $1,509.20.

The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR).

Given,

Then, the percentage rate for November = \(\sf\frac{15.6}{100}\) × 700

\(\sf = \$109.20\)

Balance on 1st December = unpaid balance at the end of November + percentage rate

\(\sf = $1400 +$109.20\)

\(\sf =\$1509.20\)

Therefore, the total balance on the next billing date December 1 is $1,509.20.

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Answer: Answer is D

Step-by-step explanation: Took the quiz in EDJENUITY

d fgrthrthrhtrhtrhtrhrhrthrh

A sample of 24 pieces of work is considered for the checking the quality of the work,

a) Upper control limit of 99.73% confidence interval is 4

Lower control limit of 99.73% confidence interval is Zero.

The process is in control because all the values of the blemishes per unit are lie within the control limits .

The Control limits consist of two limits lower control limit and upper control limit within which the value of the statistical observations of a product are expected to lie. If the values lie outside these limits, then the process is called out of statistical control. We have,

Kate Drew has been hand-painting wooden Christmas ornaments for several years.

Sample size = 24 pieces

confidence level = 99.73% = 0.9973

The number of blemishes per unit is given as:

1,1,2,3,1,0,2,0,0,1,3,1,0,1,2,0,0,2,1,2,3,2,1,1.

The control limits are to be computed for the number of defects per piece . Let us consider the number of defects per piece be denoted by c. In that case, the control limits for c chart are used. The upper control limit (UCL) and lower control limit (LCL) for c chart is given by,

UCL = c-bar + 3 s.d

LCL = c-bar - 3 s.d

where c-bar = 1/n(€c) average number of defects

So, c-bar is computed as,

c-bar = (1+1+2+3+1+0+2+0+0+1+3+1+0+ 1+2+0 +0+2 + 1+2 +3+ 2+1+1) /24 = 30/24 = 1.25

put the data in Excel sheet and calculate required limits using Excel Commands.

Excel Command for Average, c-bar

=Average( Range of numbers who's average you want to calculate )

In my excel sheet, = Average ( H2 : H25)

= 1.25

Excel Command for Standard deviations,

=STDEV( numbers who's standard deviations you want to calculate)

here, =STD(H2:H25) , output= 0.98907

UCL = 1.25 + 3( 0.98907)

= 4.217

LCL = 1.25 - 3( 0.98907)

= - 1.717

but defective item can never be negative so, Lower control limit is Zero.

Hence, for the given data, the upper control limit for the number of defects is 4 and the lower control limit is 0.

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Answer:

1. d thousandths

2. c ten thousandths

3. a tenths

4. d 6

5. a tenths

6. b five and four hundredths

Step-by-step explanation:

Answer:

∠ABD≈31.974°

Step-by-step explanation:

Since BD is a diameter, ΔABD is a right triangle with BD as its hypotenuse.

Using BD=d, solve for ∠ABD using sin⁻¹(4.5/d)

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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Notice that if we find the total number of students, we can find the number of those that decided not to take French by subtracting the ones that took French from the total number of students.

We have the next relations:

In other words:

Then, there are 800 students in total

The number of students that did not choose to take French their junior year is:

184 is the answer.

The graph that shows the line y = - 3 x + 1 would be B. Graph B.

To find the graph, you need to find the x and y values from the given equation of line y=-3x+1.

Then look at the graph that has these points.

For x = -2:

y = -3(-2) + 1

y = 6 + 1

y = 7

For x = -1:

y = -3(-1) + 1

y = 3 + 1

y = 4

For x = 0:

y = -3(0) + 1

y = 0 + 1

y = 1

For x = 1:

y = -3(1) + 1

y = -3 + 1

y = -2

For x = 2:

y = -3(2) + 1

y = -6 + 1

y = -5

For x = 3:

y = -3(3) + 1

y = -9 + 1

y = -8

So, the y values for x = -3 to x = 3 are:

x = -3: y = 10

x = -2: y = 7

x = -1: y = 4

x = 0: y = 1

x = 1: y = -2

x = 2: y = -5

x = 3: y = -8

The graph that has these points is therefore Graph B.

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