A carpenter wants to cut an 84 inches long board into two-pieces such that one piece is twice as long as the other piece. Set up an equation and find the length of each piece.

Answers

Answer 1
It’s not an equation but the shorter piece would be 28 inches and the longer piece would be 56 inches
Answer 2

Answer:

small piece = 28 inches

large piece = 56 inches

Step-by-step explanation:

The carpenter has one piece of wood 84 inches long. He wants to cut that piece of wood into two pieces. One piece will be 2 times as long as the other. Let's let x = the small piece of wood

2x + x = 84

In this equation, the longer piece is 2 times the shorter piece and the shorter piece is added, which equals 84 inches. Lets solve:

2x + x = 84

3x = 84

3x/3 = 84/3

x = 28

This means that the shorter piece is 28 inches. To find the longer piece, multiply 28 by 2 because the longer piece is twice the shorter piece. Therefore the longer piece is

28 × 2 = 56

Finally, we figured out that the short piece is 28 inches and the longer piece is 56 inches

We can double check this by doing 56 + 28 and making sure it equals 84


Related Questions

What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common? Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common. Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common. Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.

Answers

The statement about both functions that is true is:

Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

What is the domain and range for the function of y = f(x)?

The domain of a function is the set of values of input for which the function is valid.

The range is the dependent variable of a set of values for which the function is defined.

Given that:

f(x) = 4 - x

The slope (m) of the function = -1x-intercept = (4,0)y-intercept = (0,4)Domain =  [4,∞)

For function g(x) = -1 ×[tex]\mathbf{\sqrt{x-4}}[/tex]

The domain = x ≥ 4 and the solution set is [4,∞)The range g(x) = ≤ 0 and the solution set is [-∞, 0)The function g(x) does not have a y-intercept.

Therefore, from the given options, the statement about both functions that is true is:

Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

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Answer:

Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).

Step-by-step explanation:

I got it right on the test.

Where does billy bob johns

Answers

Answer:

in ur moms house

Step-by-step explanation:

Answer:

he doesn't

Step-by-step explanation:

&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = square numbers E = even numbers Complete the Venn diagram. E S D E & = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } S = square numbers E = even numbers Complete the Venn diagram . E S D E​

Answers

Answer:

E = [1,2,3,4,5,6,7,8,9,10,11,12]

S = [4,9]

E = [2,4,6,8,10,12]

The number that satisfies both conditions S and E is [4]

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

The numbers in the Venn diagram are given,

S          S∩E         E

1,9          4          2, 6, 8, 10, 12

What is a Venn diagram?

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

S = square numbers

This means,

1² = 1

2² = 4

3² = 9

S = {1, 4, 9}

E = even numbers

This means,

E = {2, 4, 6, 8, 10, 12}

Now,

S ∩ E = Numbers that are even and square.

S ∩ E = {4}

Thus,

The numbers in the Venn diagram are given,

S          S∩E         E

1,9          4          2, 6, 8, 10, 12

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Find the domain and range of the function graphed below. Write your answers in interval notation.

Answers

Answer:

Domain: [tex][-3, 1)[/tex]Range: [tex][-5, 4][/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The frequency table below represents the 30 best batting averages for a
semi-pro baseball league. Which ranges of batting averages were least
common among the players?
Batting Average Frequency
1
2
12
14
1
0.320-0.329
0.330 0.339
0.340 0.349
0.350-0.359
0.360-0.369
A. 0.340 0.349 and 0.350 - 0.359
B. 0.330
0.339 and 0.360 - 0.369
C. 0.320
0.329 and 0.330 -0.339
D. 0.320 0.329 and 0.360 -0.369

Answers

The ranges of batting averages were least common among the players is 0.320-0.329 and 0.360-0.369 , Option D is the correct answer.

What is meaning of Average ?

Average is the middle value of a set of data points , calculated by summing all the data points and then dividing by the number of points.

It is given that , 30 best batting averages for a semi-pro baseball league.

The ranges of batting averages were least common among the players

To find this , it has to be observed that which range has the lowest frequency

The range 0.320-0.329 and 0.360-0.369 has frequency of 1 which is the least among all

Hence Option D is the correct answer.

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The following data represent the number of people aged 25 to 64 years covered by health insurance​ (private or​ government) in 2018. Approximate the mean and standard deviation for age.
Age Lower Limit Upper Limit Number (millions)
25-34 25 34 26200000
35-44 35 44 33800000
45-54 45 54 33100000
55-64 55 64 29600000

Answers

Answer:

X=∑fX ∑f , where ¯X is the mean.

Mean = 115/4 = 28.75

Standard deviation = [tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]     n = the number of items = 4

Standard deviation = √28.37/4 = √7.0925 = 2.66317

Step-by-step explanation:

Mean is the number which is obtained by adding the values of all the items of a series and dividing the total by the number of items.

Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values

So, Class intervals are given here.

We have to find the middle point of the class interval.

So,

Class interval= 25- 34

Middle point= [tex]\frac{34-25}{2}[/tex]= [tex]\frac{9}{2}= 4.5[/tex]

Let's add 4.5 to the lower interval,

=> 25 + 4.5= 29.5

This is the median point and do the same for the other intervals too

i.e 39.5,49.5 and then 59.5 then multiply the number with the middle point.

So midpoint times the number. So, we get

29.5 * 21.7 = 640.15 & so on we get 129,...

Then add these numbers together. So that becomes 5375.75. And what about the total number here, that is

=>21.7 + 32.8 + 36.8 + 21.7= 118.5

So here,

Mean value, that should be equal to the sum of mean times the number divided by the total number here,

Mean= [tex]\frac{5375.75}{118.5}[/tex] = 45.36

So, this is the mean value.

Standard deviation:

Standard deviation =  [tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]

[tex]\sigma[/tex] = population standard deviation

N = the size of the population

[tex]x_{i}[/tex] = each value from the population

[tex]\mu[/tex] = the population mean

So here is what we have to do,

We have to subtract the mean value from the middle point that is,

=>45.36- 21.5 and squared plus 45.36 -39.5 Squared. And plus this is 45.36 -49.5 Squared plus 45.36 -59.5 squared. And then, this is 45.

Let me just inside the apprentices Inside the practices, this is 45 .36 29.5 and take the square of this one And then add another one Which is 45.36 39.5 and then take the square this one too. And plus inside parentheses, this is 45.36 minus Which is 490.5 And then squared. That is 45.36 And -59 0.5 so And then take the square, there's 12 if you just add all of them, so we will get five 47.1184.

So the standard deviation is the square of 547, divided by The total frequency here.

Standard deviation = √28.37/4 = √7.0925 = 2.66317

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The length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°. What is the approximate length of the radius of the circle?

Answers

The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

Length of the arc of a circle:

s = 7.34 units

The measure of central angle:

θ = 81 degrees =  1.413 radians

s = rθ

r is the radius of the circle

7.34 = r(1.413)

r = 5.19 ≈ 5.2 units

Thus, the radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

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Answer:

The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

Step-by-step explanation:

Problem 5. Utility Bills The monthly utility bills in a city are normally distributed and
represented by the variable X, with a mean of $100 and a standard deviation of $12. Find the
probability that a randomly selected utility bill is
(a) less than $70,
(b) between $90 and $120,
(c) more than $140.
(2 points)
(2 points)
(2 points)
Hint: Convert the normal distribution X to Standard normal using Z formula Z =
and then look the Z-values from the table and then find the probability.
X-μ
6

Answers

The probabilities in the question are

0.00620.74990.000429

How to solve for the probabilities

a. For  x < 70

we have

z< 70 - 100/12

= z < -30/12

= -2.5

Such that p (x<70) = 0.0062

Hence the probability that is is less than $70 = 0.0062

b.  between $90 and $120,

90 - 100/12. 120 - 100/12

= -0.8333 <z< 1.67

p(90<x<120) = 0.95224 - 0.20234

= 0.7499

0.7499 is the probability of  between $90 and $120.

c. more than $140

140-100/12

= P(Z>3.3333)

= 0.000429

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6. Five years ago, Ross was N times as old as
Amanda was. If Amanda is now 19 years old,
how old is Ross now in terms of N?

Answers

Answer:

14N+5

Step-by-step explanation:

Five years ago; Rose Nx

Amanda x

Now; Rose Nx+5

Amanda x+5=19

x=19-5=14years

Rose(NOW) =14N+5

A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.

A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half.

Each bag of soil covers 20 square yards. How many bags should the farmer purchase?

Answers

The farmer should purchase 2 bags of soil for his farm.

What is Area of rectangle?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.

The shape of the farm, according to the picture is a parallelogram.  the total area can be calculated as follows:

Area = b X h

where

b = base

h = height

base = 6.5 + 2.5 = 9.0 yards

height = 6 yards

Area = 6 × 9 = 54 square yards.

40 square yards requires 1 bag of soil .

54 square yards will require ?

cross multiply

Bags required = 54 / 40 = 1.35 bag

Thus, the farmer will require 2 bags of soil for his farm.  

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an airplane that is flying at an altitude of 30 000 ft is beginning to descend at a rate of 1000 feet per minute. a helicopter is beginning its trip, starting at an altitude of zero feet. the helicopter ascends more slowly than the airplane, going up at a rate of 500 feet per minute. after how many minutes will the airplane and the helicopter be at the same altitude

Answers

Based on the altitudes of both the airplane and the helicopter, the number of minutes until they are at the same altitude is 20 minutes.

When will the airplane and helicopter be at the same altitude?

Assuming the minute both will be on the same altitude is x, the altitude that the airplane would be at that point is:

= 30,000 - 1,000x

The helicopter's altitude would be:

= 0 + 500x

Putting them together gives:

30,000 - 1,000x = 500x

30,000 = 1,500x

x = 30,000 / 1,500

= 20 minutes

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Suppose the measures of the interior angles of a convex quadrilateral are four consecutive odd numbers. Find the measure of the third angle.

Answers

Might be 90 degrees not 100% sure tho

Answer:

91 degrees

Step-by-step explanation:

Sum of angles in a quadrilateral: 360 degrees

87, 89, 91, 93 are four consecutive odd numbers that add up to 360

third angle is 91 degrees

Which of the numbers below are whole numbers?
A. 0
B. 0.388
C. 2454
D. 602.49
E. 996
F. 719557

Answers

Answer:

a whole number is a number with no decmils other than .0000 and is not a fraction where the top and bottom are equal

whole: a,c,e&f

not:b&d

The answers are A, C, E & F.

Whole numbers are numbers that don’t have any decimal points aside from .0000 & are not a fraction in some sort of way.

Which absolute value function defines this graph?

Answers

The vertex of the graph is at (-2, 3).

This means the equation is of the form [tex]f(x)=a|x+2|+3[/tex].

Substituting in the coordinates of one of the other points on the graph that is not the vertex, such as (-1, -1),

[tex]-1=a|-1+2|+3\\\\-1=a+3\\\\a=-4[/tex]

So, the equation is [tex]\boxed{f(x)=-4|x+2|+3}[/tex]

In the past month, Ryan has had five pizzas delivered. He kept a record of how long it took to get the
pizzas: 35 minutes, 25 minutes, 15 minutes, 40 minutes, and 50 minutes.
If the sixth time he orders pizza, it takes 95 minutes, how will this affect his data?
a.) It will have little to no effect on both the mean and the median.
b.) It will have little to no effect on the mean, but it will make the median a less useful measure
of center.
c.) It will make both the mean and the median less useful measures of center.
d.) It will have little to no effect on the median, but it will make the mean a less useful measure
of center.

Answers

It will have little to no effect on the median, but it will make the mean a less useful measure of center.

How to determine the effect?

The initial data elements are given as:

35, 25, 15, 40, 50

When a new data element is added, we have:

35, 25, 15, 40, 50, 95

See that 95 is far from the other data elements.

This means that 95 is an outlier of the data elements

Outliers have effects on the mean and it renders the mean useless.

However, it has little to no effect on the median

Hence, the true statement is (d)

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Answer:

Step-by-step explanation:

it will have little to no effect on the median but will make the mean a less useful measure of center.

Big Oil, Inc. has a preferred stock outstanding that pays an $7 annual dividend. If
investors' required rate of return is 10 percent, what is the market value of the shares?
If the required return declines to 6 percent, what is the change in the price of the stock?

Answers

The change in the price of the stock is $46.67.

How to calculate the change in price?

From the information given, the current price will be:

= Annual dividend / Required rate

= 7/0.1

= $70

The market value of the shares will be:

= 7/6%

= 7/0.06

= $116.67

Therefore, the change in the price of the stock will be:

= $116.67 - $70

= $46.67

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The graph below have the same shape. What is the equation of the red graph

Answers

Answer:

G(x)=x³-1

because it intersect at the negative side of y

Answer:

g(x) = x³ - 1

(option C)

Step-by-step explanation:

We know that the shape of the graph has not changed, as stated in the question, meaning that the change has not happened as a direct change to x (like 2x³ instead of x³).

The entire graph has been moved down and not left/right, which would have happened inside the parenthesis (like g(x) = (x³ - 3)).

Because it has been shifted down (as evident by the y-intercept), and we know that the shape has not changed, we know that the original function was shifted down 1 --which can be expressed by the equation g(x) = x³-1

Find y please help !!!

Answers

Answer:

20°

Step-by-step explanation:

take the sum of 3y + 10 and y and equal it to 90° that creates an equation making it easier for you to continue

Answer:

Y = 20°

let's assume the opposite angle of Y to be X

angle Y = angle X ( vertically opposite angles)

3y + 10 + X + 90° = 180° ( forming linear pair)

3y + X + 100 = 180°

X + 3y = 80° ----(1)

Y + 3y = 80°

4y = 80°

y = 20°

three-quarters of a pile of bricks were used for a certain project. when two thirds of the reminder had been used, 50 bricks were left. how many bricks were there in the original pile?​

Answers

Answer:

200 Bricks

Step-by-step explanation:

1/3 of the bricks were not used(which was 50 bricks), meaning that 3/3 is 150 bricks of the pile. Since 150 is 3/4 of the original pile, that means that there was 200 bricks at the beginning.

Alex's recipe calls for 1/3 cup of chocolate chips for every 2 cups of flour. If he increases the
amount of flour to 3 cups, how many cups of chocolate chips will he need?

Answers

Answer:

1 cup

Step-by-step explanation:

1/3 cup of chocolate chips : 2 cup of flours

So 1/3:2 = x:3

Because we want to find x, the number of how many cups of chocolate chips he needs.
you can cross multiply where you get 1/3·3=2x
which is 1=2x and x=1

Emma bought 1305 bags of carrot for 16910 dollars. Find the unit rate in terms of bags per dollar.

Answers

Answer: $12.96

Given:

1305 bags of carrots purchased

Total cost = $16,910

Step-by-step explanation:

To find the unit cost, divide 16910 by 1305 to find the cost of one bag of carrots:

[tex]\frac{16910}{1305} = 12.96[/tex]  (rounded to nearest hundredth)

8 cm
6 cm
2 cm
Find the surface area of the rectangular prism.
Surface Area = [?]cm²

Answers

Answer:

152cm²

Step-by-step explanation:

math and stuff and things


A giant tortoise can travel 0.11 miles in 1 hour. At this rate, how long would it take the tortoise to travel 3 miles?

Answers

Answer:

about 27.27 hours.

Step-by-step explanation:

If it can travel 0.11 miles in 1 hour, we need to divide 3 miles by 0.11 miles to get the number of hours it would take to travel 3 miles. 3/0.11 is 27.27 repeating.

Hope this helps!

Answer:

27.27 hours

Step-by-step explanation:

You need to set up a proportion. I did distance over time.

[tex]\frac{.11 mi }{1 hr} = \frac{3 mi}{x hr}[/tex]

Cross multiply

.11x = 3

Divide by .11

x = 27.27

Evaluate: y(x+x)+3, where x=1 and y=3 A. 3 B. 10 C. 9 D. 5

Answers

Answer:

C. 9

Step-by-step explanation:

y(x+x) +3

{x= 1 , y= 3}

Putting values..

3 (1+1) +3

= 3 (2) +3

= 6 + 3

= 9

So, the option C. 9 is the correct answer.

find the perimeter: (use 3.14 for pi):

Answers

Answer:

10.676 mm

Step-by-step explanation:

The perimeter of a circle (circumference) formula is 2*(3.14)*r. Therefore since r is 1.7,  2*3.14*1.7 = 10.676 mm.

Hope this helps!!! Please mark me as brainliest!!!

Answer is 10.(A). Jus use your calculator

Toyota manufactures most of the vehicles it sells in the United Kingdom in Japan. The base platform for the Toyota Tundra truck line is ¥1,650,000. The spot rate of the Japanese yen against the British pound has recently moved from ¥197/£ to ¥190/£. How does this change the price of the Tundra to Toyota's British subsidiary in British pounds? Explain.

Answers

When the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.

Prices = 1,650,000

Exchange rates = ¥197/£

Change in exchange rate = ¥190/£

So, here Original price of the Toyota tundra is

                                   = 1,650,000 ÷ 197

                                    = 8375.63

New import price is = 1,650,000 ÷ 190

                              = 8,684.21

Percentage change in the price of the imported trucks should be

= ( New price - Old price) / old price *100                                                                                                                             = (8,684.21 - 8375.63) ÷ 8375.63                                                                                                                   = 3.68%

Hence , when the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.

(This is the percentage change in the Japanese yen as the price of the truck remains unchanged).

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A cake recipe requires 4 and one-half cups of flour to make 1 cake. How many cakes can be made by a baker who has 16 cups of flour?

Answers

Answer:

3 cakes

Step-by-step explanation:

just flow by the formula then ignore the remainder and take the whole number which is 3 then that becomes your answer good day.

what steps do you need to do to evaluate the following expression? Select two options. –5(–2) Drag 5 sets of –2 tiles to the window. Drag zero pairs to the window. Remove the 5 groups of –2 tiles. Remove 5 negative tiles from the window.

Answers

To solve the expression given , Drag zero pairs to the window and then Remove the 5 groups of –2 tiles , Option b and c is the right answer

What is an Integer Tile method ?

It is a teaching method in which materialistic representation is done for concepts like addition and subtraction .

It is used for kids who find it difficult to understand adding a negative integer etc.

For the expression given

-5 (-2)

Drag zero pairs to the window and then Remove the 5 groups of –2 tiles.

Therefore Option B and C is the right answer.

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Kira plans to buy a used van that costs $14,000. The dealer requires a 20% down payment. The rest of the cost is
financed with a 4-year, fixed-rate amortized auto loan at 3.5% annual interest with monthly payments.
22
Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent
if necessary. If necessary, refer to the list of financial formulas.
(a) Find the required down payment.
S

$ 0
(b) Find the amount of the auto loan.
Aa
(c) Find the monthly payment.

Answers

A: 2800

B: 11200

C: 250.39 per month

Im stuck on this to could you guys explain how you do this

Answers

The required equation of a line is y = -3x- 1

Equation of a line

The equation of a line in slope-intercept form is expressed as:

y = mx + b

where

m is the slope

b is the y-intercept

Using the coordinate point (0, -1) and (-1, 2)

Slope = 2-(-1)/-1-0

Slope = 3/-1

Slope =-3

Since the line crosses the y-axis at (0, -1), hence the value of b is -1

Determine the equation

y = mx + b

y = -3x + (-1)

y = -3x- 1

Hence the required equation of a line is y = -3x- 1

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Which of the following steps is important to critical thinking?a. implementing solutionsb. utilizing factsc. holding firm to conclusionsd.answering questions Plssss help will give brainliest!!! Any model is based on making assumptions because How do I answer these? Pregntale a Jorge si hace ejercicio en un gimnasio.Pregntale a Franklin si trabaja por la noche. Use the graph of the function provided to find the indicated values. Which of the following is an unsafe lab behavior?a. Wearing loose comfortable clothing so you can concentrate on the lab.b. Tying back long hair so it stays in place.c. Wearing close toe shoes.d. Reading all instructions before beginning. What are the zeros of the quadratic function f(x)=6x^2+12x-7 Hello,I need help with this exercise.A ball is launched upward at a speed of 20 meters per second (m/s) from a 60-meter tall platform. The equation for the balls height (h in meters) at time t seconds after launch is h = -4.9t2 + 20t + 60. How long before the ball hits the ground? What is the maximum height of the ball? What controversial prosthetics may confer an athletic advantage over able-bodied runners?A. Wooden prosthetics B. Running bladesC. Myoelectric prosthetics D. Harnessed prosthetics What is wrong with the sentence . After giving birth to six puppies, I anxiously watched over my sleeping dog. Do your best and answer every question.w1 whats is this1 pointkSaucepanSkillet/Fry panDry Measuring CupLiquid Measuring Cup beginning inventory plus net purchases is: How was Rockefeller able to build his monopoly across the oil industry?He bought up oil refineries, cut costs, and reinvested his profits in other refineries.He confined his business to Ohio so he could buy all the refineries there.He found newer and cheaper ways to refine oil, increasing his profits.He began to sell kerosene as well as oil, expanding his market. simplify the ratio 42:63 For hes the super realist who must perforce perceive taut truth before the taking of each stance or stepin his supposed advance toward that still higher perchwhere Beauty stands and waits with gravity to start her death-defying leapConstantly Risking Absurdity (#15),Lawrence FerlinghettiHow does the poet create layers of meaning by using the word "gravity? Check all that apply.Gravity can refer to a serious situation.Gravity reminds the reader that there is a risk of falling when climbing in high places.Gravity is a symbol for beauty.Gravity is personified with human characteristics.Gravity sounds like the word grave, which relates to the death-defying leap. If students sit 3 per bench, we are short 3 benches. If they sit 5 per bench,2 benches are left empty, and one bench only has 4 students. How manybenches are there? A movement that keeps the distal end of the body segment fixed in one location describes what type of kinetic chain moveme The left ventricle pushes blood into what vessel(s)? which of the following types of patients cannot be treated with smm? What are the solutions to the following system of equations?2x y = 6 y = x2 9 (3, 0) and (1, 8) (3, 0) and (4, 2) (3, 0) and (1, 8) (3, 0) and (4, 2)