Determine weather the sequence 6,12,24,48 could be an an arithmetic sequence.

Determine Weather The Sequence 6,12,24,48 Could Be An An Arithmetic Sequence.

Answers

Answer 1

Answer:

The sequence cannot be arithmetic.

Explanation:

Given the sequence: 6,12,24,48

We want to determine if the sequence is arithmetic.

An arithmetic sequence is a sequence made in which the next term is obtained by the addition of a constant term called the common difference.

In the given sequence:

[tex]\begin{gathered} 12-6=6 \\ 24-12=12 \\ 48-24=24 \end{gathered}[/tex]

The difference between the terms is not constant.

Therefore, the sequence cannot be arithmetic.


Related Questions

FIRST TO ANSWER ALL GETS BRAINEST

Question 1(Multiple Choice Worth 2 points)


(Interior and Exterior Angles MC)


In triangle DEF, m∠D = (3x + 27)°, m∠E = (4x + 22)°, and m∠F = 68°. Determine the degree measure of the exterior angle to ∠D.


54°

58°

122°

126°

Question 2(Multiple Choice Worth 2 points)


(Interior and Exterior Angles MC)


In ΔJKL, m∠J = 78° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.


168°

102°

57°

12°

Question 3(Multiple Choice Worth 2 points)


(Interior and Exterior Angles MC)


Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 66)°, and the measure of ∠AWB is (5h − 18)°.


triangle UVW with side VW extended through point A and side UW extended through point B, with angle U labeled as 36 degrees


Determine the value of h.


h = 22.8

h = 23

h = 25.4

h = 48

Question 4(Multiple Choice Worth 2 points)


(Interior and Exterior Angles LC)


One interior angle of a triangle is 95.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?


42.25°

47.75°

84.5°

90°

Question 5(Multiple Choice Worth 2 points)


(Interior and Exterior Angles LC)


For ΔABC, m∠A = 28.7° and m∠B = 123.8°. Determine m∠C.


27.5°

62.5°

76.25°

152.5°

Question 6(Multiple Choice Worth 2 points)


(Interior and Exterior Angles MC)


For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.


m∠Y = 22°

m∠Y = 43°

m∠Y = 99°

m∠Y = 158°

Question 7(Multiple Choice Worth 2 points)


(Interior and Exterior Angles MC)


Triangle ABC is shown with exterior ∠z.


triangle ABC with angle A labeled 58 degrees, angle B labeled 44 degrees, and side AC extended with angle z labeled as exterior angle to angle C


Determine m∠z.


136°

102°

78°

58°

Answers

The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126° so option (D) is correct.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠D +  m∠E +  m∠F = 180°

(3x + 27) + (4x + 22) + 68 = 180

7x + 49 + 68 = 180

7x = 63

x = 9

So,  m∠D = (3(9) + 27)° = 54°.

The exterior angle of D = 180- 54 = 126°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".

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The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.Find the length of the third side c.

Answers

Statement Problem: The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.

Find the length of the third side c.

Solution:

Thus, the perimeter of a triangle with lengths a, b and c is;

[tex]P=a+b+c[/tex][tex]\begin{gathered} \text{Let a=7inches, b=5inches, P=19inches} \\ c=P-a-b \end{gathered}[/tex]

Thus, we have;

[tex]\begin{gathered} c=19-7-5 \\ c=7 \end{gathered}[/tex]

Thus, the length of the third side is 7inches

When solving an equation for x if you get 4=10, that means what?

Answers

Given: An equation where

[tex]4=10[/tex]

To Determine: the nature of the solution of the equation

Solution

Nature of solution: The example below relates to the nature of solution

[tex]\begin{gathered} Note:4=4(infinitely\text{ many solution\rparen} \\ a=4(one\text{ solution\rparen} \\ 4=10(no\text{ solution\rparen} \end{gathered}[/tex]

Hence, the equation has no solution

What will be the length of the railing from point A to point B? Show or explain how you got your answer.

Answers

To know the length of the railing from point A to point B you can use Pythagoras Theorem.

You draw a right triangle:

You use the given information to know the measure of the legs in the triangle:

You can see that the value of x is the height of 5 steps: 5(7.5 in).

Then:

[tex]x=5(7.5)=37.5in[/tex][tex]x=y=37.5in[/tex][tex]Z=2y=2(37.5in)=75in[/tex]

The B is equal to the lenght of 10 steps: 10(9.5in):

Then:

[tex]B=10(9.5in)=95in[/tex]

You have the next triangle:

You use the Pythagoras Theorem to find the h:

[tex]h=\sqrt[]{Z^2+B^2}[/tex][tex]h=\sqrt[]{75^2+95^2}[/tex][tex]h=\sqrt[]{14650}[/tex][tex]h=5\sqrt[]{586}\approx121.03in[/tex]The length of the railing from point A to point B is 121.03in

What is the slope of y-9=3(x+12)

Answers

Answer:

Step-by-step explanation:

A person tosses a coin 14 times. In how many ways can he get 10 heads?

Answers

1.4 because 14 divided by 10 is 1.4

!!!!!!!!!!!!!!!!!!!!!!!!!!!!helpppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The answer is:

D. 4x + 3

Answer:

4x + 3

Step-by-step explanation:

Three more means you're adding three to the number. So, you have + 3 right now. Four times the number of shells Talia collects is 4x with x representing Talia's shells. We don't know how many she has so it's represented by x. Now, put everything we have together. 4x + 3.

Hope this helps! :)

The graph of y=-2is is transformed to becomey=+5. Which of the folloA The graph is translated Sunits left and 2 units up.& The graph is translated 2 units left and Sunits ups.Oc.thegraph is mamiandumits left and sumits chosam.OD The graph is translated Sunits right and 2 units dow

Answers

Given the following function:

[tex]y=\sqrt{x-2}[/tex]

notice that the transformation:

[tex]y=\sqrt{x}+5[/tex]

can be written like this:

[tex]y=\sqrt{(x+2)-2}+5[/tex]

first, the +2 means that the graph moves 2 units left, and the +5 makes the graph move 5 units up.

A total of 240 people drove to a meeting. Of those peoplewho attended the meeting, 80% drove there. How manypeople attended the meeting?

Answers

The total number of people that drove to the meeting is 240

80% drove to the meeting

Let the total number of people who attended the meeting be x

Using the percentage and whole relationship

Part = percentage x whole

whole = x

part = 240

percentage = 80%

240 = 80/100 * x

240 = 0.8x

Divide both sides by 0.8

240/0.8 = 0.8x/0.8

x = 300

The total number of people that attended the meeting is 300

Laying down my n buffer is concerned after receiving her weekly paycheck she believes that her deductions for social security,Medicare,and federal income ta withholding (fit) may be incorrect Larsen is paid a salary of 4330 she is married filling jointly and prior to this payroll check has total earnings of 140,460 what are the correct deductions for social security Medicare and fit assume a rate of 6.3% on 142,809 for social security and 1.45% for Medicare

Answers

Correct deduction for social security Medicare and fit at 6.3% = 8,996.967

Correct deduction for Medicare at rate of 1.45% = 2,070.731

What is Medicare?

Medicare is defined as a type of health insurance that reduces the fees incurred by an individual following the reception of health services.

After deductions the total earning = 140,460

The correct deduction for social security, Medicare and fit at the rate of 6.3% of 142,809;

= 6.3/100 × 142,809

= 899696.7/100

= 8,996.967

The correct deduction for Medicare at the rate of 1.45%;

= 1.45/100 × 142,809

= 207,073.05/100

= 2,070.731.

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Which of the following could be the end behavior of f(x) = -x2 – 4?

Answers

Answer:

f(x) = -∞ as x → ±∞

Explanation:

The given function is

f(x) = -x² - 4

To know the end behavior, let's replace x by a greater number and by a smaller number, so

If x = 100

f(x) = -100² - 4

f(x) = -10000 - 4

f(x) = -10004

If x = -100

f(x) = -(-100)² - 4

f(x) = -10000 - 4

f(x) = -10004

So, we can see that no matter if x is negative or positive, the value of f(x) will be positive. Then, we can say that the end behavior is

f(x) = -∞ as x → ±∞

determine which of the following relations is a function.Xyxy-1010-32-55-1100025-5110-104O3-8-2124y-4-22346XOx01225y24267

Answers

The relation between the function is X cannot repeat itself.

We have given that,

functions table

We have to determine which relation is a function.

What is the function?

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

The relation between the function is

X cannot repeat itself

Therefore option C is correct.

Complete question: Determine which of the following relations is a function [see in attachment]

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Im kinda lost on how to solve these could you help me and teach me!

Answers

The angles ∠IDA, ∠YDA, and ∠RDI measures 121°, 59°, and 29.5°.

The angle ∠YDF is equal to 121°. The ∠IDA is vertically opposite angle. So, ∠ADI is equal to the ∠YDF. Hence, ∠IDA = 121°.

The angle ∠YDA and the angle ∠ADI form a linear pair. It means ∠YDA and ∠ADI are complimentary angles.

∠YDA + ∠ADI = 180°

∠YDA + 121° = 180°

∠YDA = 180° - 121°

∠YDA = 59°

The ∠FDI is vertically opposite angle to ∠YDA. So, ∠FDI is equal to the ∠YDA. Hence, ∠FDI = 59°. The ray DR bisects the ∠FDI. So, the angle ∠RDI is half of the angle ∠FDI.

∠RDI = (1/2)∠FDI

∠RDI = (1/2)59

∠RDI = 29.5°

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For each function graphed below, state whether it is one to one !!

Answers

[tex]\begin{gathered} G1\Rightarrow Yes \\ G2\Rightarrow No \\ G_3\Rightarrow Yes \\ G4\Rightarrow No \\ G5\Rightarrow No \\ G6\Rightarrow Yes \end{gathered}[/tex]

1 yard =3 feet1 meter= 100 cmNicholas walked 20 yards to get his mail. About how many meters did he walk?

Answers

Given:

1 yard = 3 feet

1 meter = 100 cm

Nicholas walked 20 yards to get his mail.

Here, we are required to convert 20 yards to meters.

Where,

1 yard = 0.9144 meter

20 yards = x meters

thus, we have:

[tex]20\text{ }\times0.9144\text{ = 18.29 meters}[/tex]

Therefore, Nicholas walked 18.29 meters to get to his mail.

ANSWER:

18.29 meters

Can someone help me

Which graph represents the solution set of the system of inequalities?


{y<−3x−2y≤x−2




Responses


A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1comma 1 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region below the dashed line and below the solid line is shaded.


Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1comma 1 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region below the dashed line and below the solid line is shaded.,


A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 1 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region above the dashed line and above the solid line is shaded.


Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 1 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region above the dashed line and above the solid line is shaded.,

Answers

The graph that represents the solution to the system of inequalities is given in the attachment below.

How to Determine the Graph to a System of Inequalities?

To find the correct graph that represents the solution to the system of inequalities, determine which inequality represents each of the line that is plotted on the graph.

The first inequality, y < -3x - 2, has a slope of -3, a y-intercept of -2, and an inequality sign "<" which means the shaded part will be below the a dotted or dashed boundary line.

The second inequality, y ≤ x − 2, has a slope of 1, a y-intercept of -2, and an inequality sign "≤" which means the shaded region is below a solid boundary line.

The graph that represents the above stated features is the graph of the system of inequalities shown below.

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some one please help me! quick!

Answers

m(4) = 110° due to the Transitive Property.

The Transitive Property states a that if a = b and b = c, then a = c.

m(3) + m(4) = 180 due to the definition of Supplementary Angles. All supplementary angles add up to 180°.

m(3) = 70° because 180 - 110 = 70.

Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.

Answers

The equation that represents the total cost is C = $400 + $125p .

What is the total cost?

The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.

Total cost = fixed cost + total variable cost

Total cost = fixed cost + (variable cost x total output)

C = $400 + ($125 x p)

C = $400 + $125p

Total cost when 0 phones are made =  $400 + $125(0) = $400

Total cost when 1 phone are made =  $400 + $125(1) = $525

Total cost when 2 phones are made =  $400 + $125(2) = $650

Total cost when 3 phones are made =  $400 + $125(3) = $775

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A physician borrowed $100,000 from credit union for 9 months at annual interest rate of 4%. What is the simple interest due on the loan?

Answers

Givens.

• The amount borrowed was $100,000.

,

• The time elapsed is 9 months.

,

• The annual interest rate of 4%.

The simple interest formula is

[tex]I=PRT[/tex]

Where P = 100,000, R = 0.04, and T = 9/12.

[tex]\begin{gathered} I=100,000\cdot0.04\cdot\frac{9}{12} \\ I=3,000 \end{gathered}[/tex]Therefore, the simple interest is $3,000.

the answer would be 3,000

If Mary fails her classes then she cannot graduate

Answers

True…I don’t know what the question is here???

HELP NEEDED ASAP PLS

Answers

The expression in the simplest form is -9x/10 + (5).

What is termed as the simplification?

Simplify simply means making something easier to understand. Simply or simplification in mathematics refers to reducing an expression / fraction / problem to a simpler form. It simplifies the problem by calculating and solving it.

We can —

Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This makes this same expression simple to understand and solve.

For the given equation;

= (-3x/5 - 7) - (-12 + 3x/10)

open the parenthesis;

= -3x/5 - 7 + 12 - 3x/10

Bring the variable part together.

= -3x/5 - 3x/10 - 7 + 12

Add variables and constant separately.

= -9x/10 + 5

Thus, the simplest form of the given expression is found as  -9x/10 + 5.

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if Robbie can do 35 Jumping Jacks in 60 seconds how many seconds would it take him to do 14 jumping jacks

Answers

Based on the number of jumping jacks that Robbie can do in 60 seconds, the number of seconds it will take to do 14 jumping jacks is 24 seconds

How to find the number of seconds?

To find the number of seconds that it takes Robbie to do 14 jumping jacks, find the number of seconds it takes to do a single jumping jack.

The number of seconds to do a single jumping jack is:

= 60 / 35

= 1.71 seconds

If 14 jumping jacks are to be done then the number of seconds would be:

= 1.71 x 14

= 24 seconds

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I need help with a table to plot the points

Answers

In order to plot a set of coordinates on a graph page, you would need to take account of every pair of x and y values provided. The line that goes horizontally is the x-axis (from left to right). All the negative values move from point zero (the origin).

The ordered pair, or the coordinates tells you where x and y intersect. For example, the first set of coordinates are (2, 9). That means, when x is 2, then y is 9.

Observe that x equals 2 on the right side of the horizontal axis. Next, you look for the spot where y equals 9.

Next step, you carefully trace the spot where x is 2, and trace it up a straight line and at the point where y equals 9 (at the upper part of the y axis), you put a tiny "X" to mark the spot where both values intersect.

Notice that while tracing from x, you move upwards, and while tracing from y, you move towards the right. That point defines the coordinates (2, 9) which is the first line on your table.

You follow a similar step for every one of the other coordinates, which are;

[tex]\begin{gathered} (2,9) \\ (4,3) \\ (6,-6) \\ (0,15) \\ (3,6) \\ (5,0) \\ (\frac{7}{3},8) \end{gathered}[/tex]

Please note that I've just attached the same graph, but this time I've labelled the points one by one.

This should help with reading the coordinates at every point.

Choose the best estimate for the quotient.

27.2/178.6

A) 5
B) 6
C) 50
D) 60

Answers

Answer:

B

Step-by-step :

The quotient is 6.5 so the estimate is closest to 6.

The answer is b that’s your answer 6

RANGE AND DOMAIN. GRAPSWhat is the Range of this Relation:{(3,0), (-2,6), (-1,4), (-2,0), (1,5)}

Answers

Given the relation:

[tex]\mleft\{\mleft(3,0\mright),(-2,6),(-1,4),(-2,0),(1,5)\mright\}[/tex]

The range of the relation can be thought of as the set of y-coordinates of a point (x, y). That is, as every second number of the ordered pairs. Additionally, the set should be ordered, and should not contain repeated values. This set is:

[tex]Range=\mleft\lbrace0,4,5,6\mright\rbrace[/tex]

Which of the following is a parent function?O A. f(x) = -3x° +1ОВ.B. f(x) = 2*O c.C. f(x)=23*O D. f(x)=3* - 5

Answers

ANSWER:

B.

[tex]f(x)=2^x[/tex]

STEP-BY-STEP EXPLANATION:

A parent function is the simplest formula in which no transformations have been made. Therefore, the function that would be the parent one of the answer options is:

[tex]f(x)=2^x[/tex]

Write the correct equation for the following statement.

You decide to rent a limo for prom. The rate is $250 plus $6 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
250+6m

If you travel 45 miles what will be your total bill at the end
of the evening?

Answers

Answer:

Easy;

Substitute m (miles) for 45.

250+6(45)

(6 dollars per mile, times 45 miles, plus the 250 flat rate)

250+270

520

So you would be charged 520 dollars total at the end of the evening.

Hope this helped!

Answer:

520

Step-by-step explanation:

so first you would multiply 6 by 45 which is 270 then add 250 which is 520

hope this helped, have a great day

Which equation is perpendicularl to 2x+3y=12A y=2/3X+5B y=-2/3X+5C y=3/2X+5D y= -3/2X+5

Answers

The equation of the line perpendicular to the given equation is;

[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]

Option C is the correct answer

Here, we want to select which of the equations in the option is perpendicular to the given equation

Firstly, we need to understand that for two equations to be perpendicular, then the product of their slopes must be equal to -1

Before we proceed to compare, we need to write the equation in the general form

The equation of the line written in the general form will be;

[tex]y\text{ = mx + b}[/tex]

where m represents the slope and the term b represents the y-intercept

Now, let us proceed to write the equation in the standard form;

We have this as;

[tex]\begin{gathered} 3y\text{ = -2x + 12} \\ \\ y\text{ = -}\frac{2}{3}x\text{ + 4} \end{gathered}[/tex]

Compared with the general form, we can see that the slope of this line is -2/3

Now let us get the slope of the line that would be perpendicular to it;

[tex]\begin{gathered} \frac{-2}{3}\times\text{ m = -1} \\ \\ m\text{ = }\frac{3}{2} \end{gathered}[/tex]

Now, the equation perpendicular to what was given will have a slope of 3/2

Fortunately, all the options in the question have been written in the general form

The one with a slope of 3/2 is option C

[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]

in one year, a town recorded a total of 79 days it did not rain, how many days did it rain

Answers

Answer:

286

Step-by-step explanation:

there are 365 in a year

365-79

286

hello thank you for viewing my question I seem to be stuck on this problem can you please help thank you

Answers

We have 9 boy kittens and 6 girl kittens, a total of 15 kittens.

9 cats will be selected and we have to calculate the probability that 5 boy kitttens and 4 girl kittens are chosen.

We could have modeled as a binomial experiment, but the probability of choosing a boy kitten is not constant after each selection. Then, we have to select an alternative method.

We can think of it of a combinatorial problem.

In this case, it is a combination problem, as the order of selection does not matter and each kitten is equivalent within its category.

Repetition is not allowed: a kitten selected can not be selected again.

We can start finding all the possible combinations for 9 kittens out of the total 15 kittens:

[tex]C(15,9)=\frac{15!}{9!(15-9)!}=\frac{15!}{9!6!}=5005[/tex]

The probability of selecting 5 boys and 4 girls will be the relation between the outcomes where there are 5 boys and 4 girls and the total number of outcomes we have just calculated.

Then, we can now calculate how many combinations of 9 kittens have 5 boys and 4 girls as a product of two combinations: the combinations for the boys C(9;5) and the combinations for the girls C(6;4).

We can calculate this as:

[tex]\begin{gathered} C(9,5)=\frac{9!}{5!4!}=126 \\ C(6,4)=\frac{6!}{4!2!}=15 \\ =>C(9,5)*C(6,4)=126*15=1890 \end{gathered}[/tex]

We can now calculate the probability as the ratio of combinations 1890/5005:

[tex]p=\frac{1890}{5005}\approx0.378[/tex]

Answer: the probability is 0.378.

Other Questions
If n = 100 and p= 1/5, what is the mean and standard deviation of this binomial distribution? If pH = -log [H+], find the pH of a substance that has a hydrogen concentration [H+] = 5.7 X 10-4.Round your answer to the nearest ten thousandth (4 decimals). An instantaneous dipole occurs when a molecule's moving electrons are briefly more concentrated in one place than another, causing the molecule to become temporarily polarized.TrueFalse purely competitive industry x has constant costs and its product is an inferior good. the industry is currently in long-run equilibrium. the economy now goes into a recession and average incomes decline. the result will be Why is Odysseus' success so remarkable? What does his defeat of the Cyclops tell you about heroes? Why do visit the zoo on cold days find the measure of Angel A? (Round your answer to the nearest whole number) Estimate by rounding to the nearest whole number.5.7 + 11.8 + 0.08--------------------------------------------------------------------------------------A: 19B: 17.9C: 18D: 26.0D: carpet baggers inc. is proposing to construct a new bagging plant in a country in europe. the two prime candidates are germany and switzerland. the forecasted cash flows from the proposed plants are as follows: 11. The Revolutionary War had many important turning points that were of great importance to the patriot cause. Why was the Battle of Bunker Hill important to the Patriot cause? Why was the Battle of Saratoga important to the patriot cause? Why was the Battle of Yorktown important to the patriot cause? 12. How did slaves use the Declaration of Independence to argue that they should be granted their freedom? What is -3 times 4?? Paving stones: 174 paving stones were examined for cracks, and 16 were found to be cracked. The same 174 stones were examined for discoloration, and 21were found to be discolored. A total of 3 stones were both cracked and discolored. One of the 174 stones is selected at random. Round all answers to fourdecimal places.Part 1 of 4(a) Find the probability that it is cracked.The probability that it is cracked is 0.0919SPart 2 of 4(b) Find the probability that it is discolored.The probability that it is discolored is 0.1207Part: 2/4Part 3 of 4(c) Find the probability that it is not cracked.The probability that it is not cracked is What is the length of the hypotenuse of a right triangle with legs of length 70 feet and 240 feet? 8. At the same concentration (100 mM which is 0.1 M), should themeasured absorbance at 500 nm for three red solutions (drink mix,cobalt (II) nitrate and cobalt (II) chloride) be similar.yes or no Model with MathematicsThe owner of a frozen yogurt stand considers different pricing options for a serving of yogurt plus toppings. For what number of toppings do the two options give the same price?A. Define the variables.B. Write a system of equations that models this situation.C. Graph the system. What is the intersection point?D. What is the solution of the problem?E. Is the solution reasonable for this situation? Explain. Write an equation point-slope form of the line that passes through the point (3,3) with slope 5/3 Free-body diagrams for four situations are shown below. For each situation, determine the net force acting upon the object. Your answer must include both the magnitude and the direction of the net force vector. You should have four (4) total responses to this question (labeled A, B, C, and D). Facts about Education What three factors contributed to the Persians' strong sense of identity? which event occurs in the long run? group of answer choices a restaurant hires another server. a new movie theater is built. an aircraft manufacturer adds another shift. a grocery store expands its hours of operation.