A boating company has the following notice at the gate:

"Children under the age of 13 are not allowed to operate a boat."

Part A: Write an inequality to show the age of children who are allowed to operate a boat. (5 points)

Part B: Describe in words how you can show the solution to this inequality on a number line. (5 points)

Answers

Answer 1
Part A: x≤13
Part B: Put a colored dot on the number 13 on the number line. Draw an arrow going left.
Answer 2

Answer:

Part A:

x > 13

Part B:

How to show this inequality on a number line is a closed circle on 13, going left of 13.

Step-by-step explanation:

Part A:

x represents the age of children who are allowed to operate the boat.

Our inequality is < because if you are of the age of 13 you are allowed to operate the boat,

the inequality x > 13 reads x (the age of children) is greater than or equal to 13

Part B:

How to describe inequalities on a number line;

Closed circle: less than or equal to - or - greater than or equal to ( < , > )

Open circle: less than - or - greater than ( < , > )

To the right of the number on the number line: greater than

To the left of the number on the number line: less than


Related Questions

please help solving the slope of this graph

Answers

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{60})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{30}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{30}-\stackrel{y1}{60}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -30 }{ 2 } \implies - 15[/tex]

The equation for a slope is Rise/Run or (y2- y1)/(x2 - x1)

1. We can use points (6,0) as x1, y1 AND point (4,30) as x2, y2.
2. Plug into equation
(30-0)/(4-6) = 30/-2 = -15

Therefore -15 would be the slope.

Andy said that 4/9 of his collection is action or comedy Cynthia said that Andy made an error explaine whether Andy is correct or incorrect and why
3/5 of the dvds are action and 1/4 of the dvds are comedy

Pls I need it done by midnight

Answers

From the information given, we can calculate that 7/10 of Andy's collection is either action or comedy. This means that Andy is incorrect, because he said that only 4/9 of his collection is action or comedy.

To see why Andy's estimate is too low, consider that 3/5 of the DVDs are action, which is greater than 4/9. Additionally, 1/4 of the DVDs are comedy, which is also greater than 4/9. Since some DVDs are both action and comedy, the total fraction of the collection that is either action or comedy is greater than 4/9.

Therefore, Cynthia is correct that Andy made an error in his estimate.

help me please first to answer will get brainiest

Answers

Answer:

Step-by-step explanation:

the study guide helps best

1/8 is correct answer

I WILL GIVE BRAINLIEST, BUT IT HAS TO HAVE AN EXPLINATION
Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. Explain what most likely happened in Sandy's experiment.

Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 500 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

Answers

Answer:

Step-by-step explanation:

To determine what most likely happened in Sandy's experiment, we need additional data on the outcomes of the virtual coin tosses in each experiment. Without this data, we cannot directly compare the experimental probability to the theoretical probability.

However, we can make some general observations based on the law of large numbers and the concept of convergence. The law of large numbers states that as the number of trials or experiments increases, the experimental results tend to converge towards the theoretical probabilities. This means that with a larger number of flips, the experimental probability is more likely to be closer to the theoretical probability.

Therefore, based on this principle, it is reasonable to assume that Sandy's experimental probability was likely closest to the theoretical probability in the experiment with 1,000 flips. As the number of flips increases, the chances of the experimental results aligning closely with the theoretical probability increase.

However, it is important to note that without the specific data on the outcomes of each experiment, we cannot definitively determine which experiment had the experimental probability closest to the theoretical probability.

Based on the given information, we can analyze Sandy's experiments with different numbers of coin flips and their relation to the theoretical probability.

1. Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips:
In this case, the experimental results of the 100 coin flips were the closest to what would be expected based on the theoretical probability. This suggests that the outcomes of the coin tosses were distributed in a manner that aligned closely with the expected probabilities of getting heads or tails.

2. Sandy's experimental probability was closest to the theoretical probability in the experiment with 500 flips:
Similarly, the experimental results of the 500 coin flips were closest to the expected outcomes based on the theoretical probability. This implies that the larger sample size provided more accurate results, reducing the impact of random fluctuations and yielding a distribution that better matched the theoretical expectations.

3. Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips:
Once again, the experimental results of the 1,000 coin flips were the closest to the expected probabilities based on the theoretical probability. With an even larger sample size, the impact of random variation would be further minimized, resulting in an outcome that more closely matched the theoretical expectations.

4. Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments:
This statement suggests that the experimental results perfectly matched the expected probabilities for all three experiments. However, it is highly unlikely for the experimental results to exactly match the theoretical probabilities due to the inherent randomness in flipping a coin. Therefore, it is less probable for this scenario to be true.

To summarize, the most likely scenario is that Sandy's experimental probability was closest to the theoretical probability in the experiment with the largest number of coin flips (1,000 flips). As the sample size increased, the experimental results became more accurate and aligned more closely with the expected probabilities.

ASAP!!

If 5×6=20+y,
what is the value of y?

Responses

5

6

10

30

Answers

Answer:10

Step-by-step explanation:

5x6=30

30-20=10

Y=10

Answer:

[tex] \sf \longrightarrow \: 5 \times 6 = 20 + y[/tex]

[tex] \sf \longrightarrow \: 20 + y = 5\times 6 [/tex]

[tex] \sf \longrightarrow \: 20 + y = 30[/tex]

[tex] \sf \longrightarrow \: y = 30 - 20[/tex]

[tex] \sf \longrightarrow \: y = 10[/tex]

Option [C] 10

I need help on a b and function 2
I dont get it

Answers

Answer:

For A: The first function has a greater ROC

For B: The first function has a negative slope

Step-by-step explanation:

Explication for A:

We already know that the R.O.C. (slope) is 2 for the first function, so all we need to do is substitute the values in the table into the following formula: y2-y1/x2-x1

after substituting: (-3-(-6))/(0-(-1))

simplify 3/1=3, since the ROC is 3, the second equation has a greater ROC than the first

Explanation for B:

The first function described is f(x)=20-3.5x

This is because the y intercept is the starting point, or how much money she has in the gift card. She spends 3.5 dollars per week, so we add a variable to represent the number of weeks, and its negative since she is spending, not earning. We also know that the slope is negative since y is decreasing as x is increasing, on the table.

The second function described is c(m)=5x+10

This is because the equation represents the total cost of renting a calculator, so both terms are positive.

To make a number pattern, Shana used the rule "Add 3," with a whole number as the starting number. Which statement must be true about Shana's list of numbers?

Answers

Answer:

you didnt put enough context in your question but if shana kept using three she would have mixed even and odds in her numbers if you could give more context to the question id be glad to help more

The statement that is true is that the pattern will consist of even and odd numbers no matter what whole number you begin with

ASAP!!

What is the solution to the equation 2x=6?

Responses

2

3

4

6

Answers

Answer:

Step-by-step explanation:

2x=6

x=3

2(3)=6

Answer:

3

Step-by-step explanation:

Please help! -Screenshot-

Answers

Answer:

|-1| < |-2|

Step-by-step explanation:

When the bars are on either side of the number, it takes the negative away. So |-1| < |-2| is the same as 1 < 2.

I really hope this helps!

A = 40 + .1(M-500) for M>500

B = 25 + .05M

20 minutes a day for 30 days = 600 minutes per month

A(600) = 40+.1(100) = $50

B(600) = 25 + .05(100) = $30

Plan B is less expensive

40+.1(M-500)= 25+.05M

40-25- .1(500) = .05-.1M

.05M = 35
M= 35/.05 = 700 minutes will have the same cost under plan A or B

40+.1(200) = $60 under plan A
25+.05(700) = $60 under plan B

Hailey goes to a restaurant and the subtotal on the bill was x dollars. A tax of 7% is applied to the bill. Hailey decides to leave a tip of 20% on the entire bill (including the tax). Write an expression in terms of x that represents the total amount that Hailey paid.

Answers

The total amount that Hailey paid can be represented by the following expression in terms of x:

Total amount = x + 0.07x + 0.20(x + 0.07x)

Simplifying the equation, we get:

Total amount = x + 0.07x + 0.20(1.07x)

Total amount = x + 0.07x + 0.214x

Total amount = 1.284x

Therefore, the expression in terms of x that represents the total amount that Hailey paid is 1.284x.

The expression is : X+.07x+ .2(x+ .07)

What is the area of the figure below

Answers

Answer:224

Step-by-step explanation:

Okay as you can see, the figure is divided into 3 shapes. 2 rectangles and a right trapezoid.

You can solve the area of the rectangle on the far right by doing 9x6 leaving you with 54.

For the other rectangles you can do 11x12 equaling 132. I got 11 because you know the top is 17 and as you see at the bottom that length you used for the first rectangle is 6, so you do 17-6. You get 12 from adding 9+3.  

For the right trapezoid the formula is A = ( a + b ) x h/2. So you can plug it in and say A=(12+7) x 4/2= 38.

You then add all the areas together (54+132+38= 224) leaving you with the answer of 224.

Which equation has the solution x = 3? Select each correct answer. Responses 9−3x=0 9 minus 3 x equals 0 9x−1=4 9 over x end fraction minus 1 equals 4 5x−7=1 5 x minus 7 equals 1 3x + 1 = 9 3, x, + 1 = 9 2x + 4 = 10 2, x, + 4 = 10 x3+5=6
PLEASEEE HELLP

Answers

Answer:

First two equations

Step-by-step explanation:

9-3x=0

9=3x

3=x

x=3

2x+4=10

2x=6

x=3

9x-1=4

9x=5

x=5/9

3x+1=9

3x=8

x=8/3

x^3+5=6

x^3=1

x=1

5x-7=1

5x=8

x=8/5

the answer is that x = 8/5

HELP ASAP!!

One student admission to an amusement park costs t dollars. Which expression represents the cost of admission for 4 students?


Responses

t

4t

t+4

t4

Answers

Answer:

See below

Step-by-step explanation:

1. The rule defining the function on the graph:

y = x -1, if x = (-3,-1)

y = -3x + 9, if x = [2, 4)

2. f(x) = |4x + 36|

y = 4x + 36, if x ≥ - 9

y = -4x - 36, if x < - 9

3. See attachment for the graph

4. Item 4 is not included in the question

Answer:

4t

Step-by-step explanation:

you times the amount of students by the cost of the admission

HELP PLS ASAP! A net of a rectangular prism is shown.
What is the surface area of the prism?

A. five hundred fifty and one-fourth cm2
B. four hundred twelve and three-fourths cm2
C. two hundred seventy-five and one-eighth cm2
D. one hundred thirty-seven and nine-sixteenths cm2

Answers

Answer:

the surface area of the rectangular prism is found as : S = 275 ¹/₈ cm².

Length l = 11 ³/₄ cm = 47/4 cm = 11.75 cm

width w = 5 ³/₄ cm = 23/4 cm = 5.75 cm

height h = 4 cm

surface area of the prism S = 2(lw + wh + hl)

S = 2(11.75*5.75 + 5.75*4 + 4*11.75)

S = 2*137.5625

S = 275.125

S = 275 ¹/₈ cm²

Answer:



,!
.
.

C:275 and 1/8

Look at the picture.

Answers

Answer:

12+15+50=77 inches²

Step-by-step explanation:

If each unit or cube is one inch, it will be (3x4x2)/2=12 inches² for the two triangles.

3x5=15 inches² for the rectangle.

And 5x5x2=50 inches² for the two bigger rectangles.

Odessa made this solid figure. I don’t really understand how I got this wrong but could anyone tell me the answer? thank you

Answers

Question:

What solid figure did Odessa make?

Answer:

Pyramid

It may look like the answer you put but it is 3d and is a pyramid

Hope this helps sorry I worded it weird

ASAP: Which equation best represents the line of best fit for the data in the scatterplot above?

Answers

Answer:

F : y = -x + 4

Step-by-step explanation:

The first observation about this scatterplot is that the best line of fit will be a line going diagonally from top left to bottom right(or bottom right to top left)

Such a line has negative slope

Equation will be of the form

y = mx + b where m is a negative number

We can eliminate H and I since both lines have a positive slope which means that the line will go in a diagonal bottom left to top right direction

Let's examine options F and G

F:  y = - x + 4
G: -9x + 3

Plug in some values for x from the graph and see which of the lines comes closest to the  y values  computed from the equations

At x = -5, the y value from the graph appears to be either 7 or 8

F: y = -x + 4 ==> -(-5) + 4 = 5 + 4 = 9; pretty close to graph's point value

G: -9x + 3 ==> -9(-5) + 3 = 45 + 3 = 48; this is greatly different from the graph value

At x = 0; the y value from graph is close to 4

From the equations we get
F: y = -x + 4 ==>  y = -(0) + 4 = 4; pretty darn close

G: y  -9x + 3 => y = -9 + 3 = -6; large difference

One more point
At x = 20, the point on the graph appears to be close to -19

From the equations we get

F: y = -x + 4 = -20 + 4 = -16; not too different

G: y = -9x + 3 = -9(20) + 3 = -180 + 3 = 177; way off

So the best line of fit would be

F : y = -x + 4

The equation that best represents the line of fit from the scatter plot is given as follows:

y = -x + 4.

How to define a linear function?

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.

From the scatter plot, we have that when x = 0, y = 4, hence the intercept b is given as follows:

b = 4.

When x = 20, y is approximately -16, hence the slope m is obtained as follows:

-16 = 20m + 4

20m = -20

m = -1.

Hence the function is:

y = -x + 4.

More can be learned about linear functions at https://brainly.com/question/15602982

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Lo graphs the relationship between temperature (in ° C) and elevation (in m) in 9 different cities on the coordinate plane below. What is the temperature in the city with an elevation of -9 m?

Answers

Answer:

7°C

Step-by-step explanation:

That is the point at top left.

x = -9; y = 7

Answer: 7°C

please answer correctly for 18 points, mathematics

Answers

Answer:

Step-by-step explanation:

Answer: Your answer is in the picture

Step-by-step explanation:

When using bar graphs x is right and y is up. An origin is the begining so 0,0 i hope that helped :).

Find the area of the figure below

Answers

The best answer is 69

WORTH 100 BRAINLY POINTS PLEASE HELP (7TH GRADE MATH)

Answers

Answer: A)-4, D)2, and F)5

Step-by-step explanation: inputs can’t repeat themselves or else it’s not a function.

Answer:

5, 2, and -4.

Step-by-step explanation:

A function cannot have x have the same number twice, but y can.

PLS HELP ME
ONLY PEOPLE WITH REAL AWNSERS!!

Answers

Answer:

7:20 p.m.

Step-by-step explanation:

First, we can find the distance that each friend will be from their house at the time when they meet each other.

To find this, we can multiply the ratio [tex]8 \text{ mi} : 7 \text{ mi}[/tex] by a constant such that the sum of both numbers in the ratio is 20, since the friends' houses are 20 miles apart. Solving for this constant:

[tex]\dfrac{20}{7 + 8} \\ \\ = \dfrac{20}{15} \\ \\ \boxed{=\dfrac{4}{3}}[/tex]

Multiplying the constant by both sides of the ratio:

[tex]\dfrac{4}{3}\left(8 \text{ mi}) : (7 \text{ mi}\right)\dfrac{4}{3}[/tex]

[tex]\boxed{= \dfrac{32}{3} \text{ mi} : \dfrac{28}{3} \text{ mi}\right)}[/tex]

So, we know that the first friend will have traveled 32/3 or 10 2⁄3 miles when they meet, and the second friend will have traveled 28/3 or 7 1⁄3 miles.

Now, to calculate what time they will meet, we can divide how far one of the friends has traveled by how fast they were traveling. This will give us the minutes it will take them to get to the meeting place. We can then add that amount of minutes to 6:00 p.m. to calculate when they will meet.

I will use the fast friend (traveling at 8 mph).

[tex]\dfrac{32}{3} \text{ mi} \cdot \dfrac{60 \text{ min}}{8 \text{ mi}}[/tex]

— Also note that I substituted 1 hour for 60 minutes in the mph ratio.

[tex]= \dfrac{32}{3} \not\text{mi} \cdot \dfrac{60 \text{ min}}{8 \not\text{mi}}[/tex]

[tex]= \dfrac{32 \cdot 60}{3 \cdot 8} \text{ min}[/tex]

[tex]= \dfrac{32}{8} \cdot \dfrac{60}{3} \text{ min}[/tex]

[tex]= 4 \cdot 20 \text{ min}[/tex]

[tex]\boxed{= 80\text{ min}}[/tex]

Adding those minutes to 6:00, noting that 80 min = 1 hr 20 min:

[tex]\text{ } \ \, 6\!:\!00 \text{ p.m.}\\\underline{+ 1\!:\!20}\\\\\text{ }\, \boxed{7\!:\!20 \text{ p.m.}}[/tex]

So, the friends will meet at 7:20 p.m.

Answer:

7:20

I think

T-T

The table shows a list of numbers and the results after applying the rule "Double and then Add 2" describe a pattern in the table.
The numbers in the second column are all _____________This is because the sum of
________________and
________________ is always ______________

Answers

Answer:

Step-by-step explanation:

you need to do 5x2 =10-5=5 so

The number in the second column all end in 8 because the numbers in the first column area multiples of 5 When you double the numbers in the first column the results will all have a 0 in ones places.

A number is a numerical unit of measurement and labelling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers. More commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five. The number in the second column all end in 8 because the numbers in the first column area multiples of 5 When you double the numbers in the first column the results will all have a 0 in ones places.

To know more about number, here:

https://brainly.com/question/17429689

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PLEASE ANSWER ALL QUESTIONS!!! I'LL GIVE 30 PTS TO WHOEVER ANSWERS!! Find the area of each shape. (sorry if it's hard to read)

Answers

Answer:

Rectangle's is 28

Step-by-step explanation:

We multiply 9 * 4 to get rectangless shape and then we substract squares (2) shape 2*2*2

(9*4) - (2*2*2)= 28

(9*4)=36
(2*2*2)=4

36-4=28

Rewrite the expression c + 0.25c using fractions instead of decimal numbers.

Answers

Answer:

It would be c + 1/4c

I really hope this helps!!

treat the fraction like a decimal, think of how much more it would take for 0.25 to be a whole. 0.25,0.50,0.75, and 1.00. the fraction equivalents would be out of 4.
c + 1/4

Please also explain to me what favorable outcomes are

Answers

Answer:

Purple,Red and blue

Step-by-step explanation:

favorable outcomes are favorite colors

PEDMAS?

Example 1:

3+8(4-2)-7

Parentheses First = 3+8(2)-7
Exponents-none
Multiply/Divide 3+16-7
Add/Subtract 19-7 = 12

Example 2:

32-(9-5)+7x3-8÷2
Parentheses 32-(4)+7x3-8÷2
Exponents 6-4+7x3-8÷2
Multiply/Divide 6-4+21-4
Add/Subtract 2+17=19

Review

Directions: Compute the answers using PEMDAS.

1) 7 x 5 + 3=

2) 8 - (6 + 2)=

3) 10 - 6 + 5=

4) (21 3) x 2=

5) (12 6) + 6=

6) 3 + 10 5=

7) 8 + 4 - 2=

8) 7 + 5 - 5=

9) 16 8 - 1=

10) (20 - 17) - 3=

11) 8 + 2 - 7=

12) 18 (4 + 2)=

13) 8 - 6 + 7=

14) 5 - (18 6)=

15) 2 + 13 - 4=

16) (7 - 4) + 3=

17) 9 - 7 + 4=

18) 2 x 6 3=

19) 15 5 + 4=

20) 8 + 6 - 4=

Answers

Answer:

1. 38  

2. 0  

3. -1  

4. 14  

5. 8    

6. 5  

7. 10  

8. 7  

9. 1  

10. 0  

11. 3  

12. 2  

13. 5  

14. 3  

15. 11  

16. 6  

17. 2  

18. 4  

19. 7  

20. 10

Step-by-step explanation:

PEMDAS stands for Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction. It is a mnemonic device used to remember the order of operations when solving mathematical equations.

Here are the answers to the review questions using PEMDAS:

1) 7 x 5 + 3= 38
2) 8 - (6 + 2)= 0
3) 10 - 6 + 5= 9
4) (21 / 3) x 2= 14
5) (12 / 6) + 6= 8
6) 3 + 10 x 5= 53
7) 8 + 4 - 2= 10
8) 7 + 5 - 5= 7
9) 16 / 8 - 1= 1
10) (20 - 17) - 3= 0
11) 8 + 2 - 7= 3
12) 18 x (4 + 2)= 108
13) 8 - 6 + 7= 9
14) 5 - (18 / 6)= 2
15) 2 + 13 - 4= 11
16) (7 - 4) + 3= 6
17) 9 - 7 + 4= 6
18) 2 x 6 / 3= 4
19) 15 / 5 + 4= 7
20) 8 + 6 - 4= 10

What is 0.¯45 expressed as a fraction in simplest form?

Answers

Let x = 0.¯45
Then 100x = 45.¯45
Subtracting the left equation from the right equation:
100x - x = 45.¯45 - 0.¯45
99x = 45
x = 45/99
The fraction 45/99 can be simplified by dividing both numerator and denominator by 9:
45/99 = 5/11
Therefore, 0.¯45 expressed as a fraction in simplest form is 5/11.
It is 5/11 hope u see this this will help u and Iiiii

What is 0.4¯5 expressed as a fraction in simplest form?

Answers

Answer:

If You are talking about 0.45 with the line over 5 ,that means the five is repeating and it nevers stops

Step-by-step explanation:

Answer all questions correctly, all questions answered will be assigned brainliest.

Answers

Answer: number 1:  A,C

number 2: C

number 3: C

Number 4: C, E, A

Step-by-step explanation:

I don’t think this is needed for such question

Answer:

1=A,B,E

2:C

3:C

4:B,C,E

5:B,C

6:B

7: I don't know this one

8:C

9:D

10:D

Step-by-step explanation:

Other Questions
Suppose a firm in a competitive industry has the following cost curves: ATC 3 4 5 6 7 Petit Refer to Figure 14-13. If the price is $3.50 in the short run, what will happen in the long run? A. Nothing. The price is consistent with zero economic profits, so there is no incentive for firms to enter or exit the industry B. Individual firms will earn positive economic profits in the short run, which will entice other firms to enter the industry, c. Individual firms will earn negative economic profits in the short run, which will cause some firms to exit the industry. D. Because the price is below the firm's average variable costs, the firms will shut down. On a test, the highest grade was 40.5 points higher then the lowest grade. The sum of the two grades was 138. Find the lowest grade. after patient h.m. had his hippocampi removed, he had retrograde amnesia that went back a few decades for some memories. what theory of consolidation does this evidence support? reduced-fat foods usually contain significantly fewer calories than their full-fat counterparts. T/F how does paragraph 2 relate to paragraph 1? what is the final volume in milliliters when 0.607 l of a 47.0 % (m/v) solution is diluted to 24.0 % (m/v)? calculate the van't hoff factor of na3po4 in a 0.40 m solution whose freezing point is 2.6c. the form of elder care that combines privacy and the independence of home life with some medical supervision is PLEASE HELP!!THANKS :) a function of the _______ is to cushion the impact with the pubic bone during sexual intercourse. the media in korea use hong bo as the name for government public relations sources. T/F diagram the hierarchy of structural levels in biology the most powerful state in west africa at the time of the arrival of islam was Makayla bought stock in a company two years ago that was worth x dollars. During the first year that she owned the stock, it increased by 12%. During the second year, the value of the stock decreased by 7%. Write an expression in terms of x that represent the value of the stock after the two years have passed. to change all margin settings, use the margins button on the ____ tab. which of the following is a primary responsibility of the opsec program officer at division level? sonata v, from john cages sonatas and interludes, is in ________ form. Which of the following techniques would be most appropriate for treating overeating or smoking? A) systematic desensitization. B) token economy. C) flooding What is the 'conflict thesis' in the history of science and religion? And why is this methodology historically problematic? Identify one relevant historical example that has been associated with it. a company reports the following data: interest expense $10,000 cost of goods sold $160,000 marketing expenses $70,000 administrative expenses $50,000 sales $400,000 stock dividends $5,000 income tax $20,000 depreciation expense $20,000 what are the firm's profit margins?