PLEASE HELP ASAP GIVING 94 POINTS

The graph shows the prices of different numbers of bushels of corn at a store in the current year. The table shows the prices of different numbers of bushels of corn at the same store in the previous year.


A graph shows Number of Bushels on x-axis and Price of Corn in dollars on y-axis. The x-axis scale is shown from 0 to 14 at increments of 2, and the y-axis scale is shown from 0 to 112 at increments of 16. A straight line joins the ordered pairs 2, 16 and 4, 32 and 6, 48 and 8, 64 and 10, 80 and 12, 96.



Previous Year

Number of Bushels

Price of Corn (dollars)

2

12

4

24

6

36

8

48



Part A: Describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. (5 points)

Part B: How many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? Show your work. (5 points)

Using the slope - intercept relation, the equation of the line is y = 1.25x - 2508

The slope - intercept form of the equation can be obtained thus :

Slope, b = (y2 - y1) ÷ (x2 - x1)

Slope, b = (4.5 - 2.0) ÷ (2010 - 2008)

Slope = 2.5 / 2 = 1.25

Using any of the pair of points we can obtain the intercept thus :

2 = 1.25(2008) + c

2 = 2510 + c

2 - 2510 + c

c = - 2508.

Hence, the equation is y = 1.25x - 2508

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Answer:

Using the slope - intercept relation, the equation of the line is y = 1.25x - 2508

The slope - intercept form of the equation can be obtained thus :

General form ; y = bx + c

Slope, b = (y2 - y1) ÷ (x2 - x1)

Slope, b = (4.5 - 2.0) ÷ (2010 - 2008)

Slope = 2.5 / 2 = 1.25

Using any of the pair of points we can obtain the intercept thus :

2 = 1.25(2008) + c

2 = 2510 + c

2 - 2510 + c

c = - 2508.

Hence, the equation is y = 1.25x - 2508

Step-by-step explanation:

Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

Answer:

hello! :) have a good day!

W = 9

The coefficient of the last term in the binomial expansion is 1.

Given term is (x + 1)⁹.

The algebraic expansion of a binomial's powers is expressed by the binomial theorem or binomial expansion. The process of expanding and writing terms that are equal to the natural number exponent of the sum or difference of two terms is known as binomial expansion.

The binomial expansion formula for (a + b)ⁿ= ⁿC₀(aⁿb⁰)+ⁿC₁(aⁿ⁻¹b¹)+ⁿC₂(aⁿ⁻²b²)+ⁿC₃(aⁿ⁻³b³)+...............+ⁿCₙ(a⁰bⁿ)

Here, a = x, b = 1 and n = 9.

Substituting the values in the formula,

⁹C₀(x⁹{1}₀)+⁹C₁(x⁹⁻¹{1}¹)+⁹C₂(x⁹⁻²{1}²)+⁹C₃(x⁹⁻³{1}³)+......+⁹C₉(x⁰{1}⁹)

The last term is ⁹C₉(x⁰{1}⁹)

The coefficient of the last term = ⁹C₉ = 1.

Hence, the coefficient of the last term in the binomial expansion of (x+1)⁹ is 1.

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That have neither high-speed internet access nor a mobile computing device is 30%.

Venn diagrams are utilized in various fields including business, measurements, semantics, and so forth. Venn charts can be utilized to outwardly coordinate data to see the connection between sets of things, like shared characteristics and contrasts, and to portray the relations for visual correspondence.

In school, 60% of students have high-speed internet access, 30% have a mobile computing device, and 20% have both.

Venn diagram for the situation

Thus remaining 30% students hat have neither high-speed internet access nor a mobile computing device.

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Answer:

Step-by-step explanation:

x+x+9=65

2x=56

x=28

28,37

Answer:

one number= 28, other number= 37

Step-by-step explanation:

9+x+x=65

9+2x=65

2x=56

x=28

Answer:

statement 1 and 2 are true

Answer:

The cost of

A small bucket = x = $8

A Larger bucket = y = $13

Step-by-step explanation:

Let the cost of

A small bucket = x

A Larger bucket = y

Kim sold 3 small buckets and 14 large buckets of popcorn for a total of $206.

3x + 14y = 206... Equation 1

Melody sold 11 small buckets and 11 large buckets of popcorn for a total of $231.

11x + 11y = 231.... Equation 2

What is the cost for a small bucket and a large bucket of popcorn?

3x + 14y = 206... Equation 1

11x + 11y = 231 ....... Equation 2

We solve using Elimination method

Multiply Equation 1 by 11 and Equation 2 by 3 to Eliminate x

33x + 154y = 2266.... Equation 3

33x + 33y = 693....... Equation 4

We subtract Equation 4 from Equation 3

121y = 1573

y = 1573/121

y = $13

Solving for x

3x + 14y = 206... Equation 1

3x + 14 × 13 = 206

3x + 182 = 206

3x = 206 - 182

3x = 24

x = 24/3

x = $8

Hence, the cost of

A small bucket = x = $8

A Larger bucket = y = $13

Answer:

$15

Step-by-step explanation:

So first we see that alicia buys 3 books for $9 and that would be 27 because 3x9=27. Now we also see that she bought 2 magazines for $4 and that would be 8 because we are multiplying 4x2. Now we add 27 and 8 which would give us 35. She uses a $50 card to make the purchase. We subtract, 50-35 and we would get 15. So alicia has $15 left on the card.

7 organisms

Area of lawn that supplies oxygen for a particular multicellular organism = 625 sq ft

Total area of the lawn = 4,375 sq ft

Number of organisms = 4375/625

Number of organisms = 7

A total of 4,375 sq ft of lawn would provide the daily supplies of oxygen for 7 organisms

Answer:

A

Step-by-step explanation:

Given

y - 2x - 8 = 0 ( add 2x + 8 to both sides )

y = 2x + 8 → (1)

y² + 8x = 0 → (2)

Substitute y = 2x + 8 into (2)

(2x + 8)² + 8x = 0 ← expand left side using FOIL and simplify

4x² + 32x + 64 + 8x = 0

4x² + 40x + 64 = 0 ( divide through by 4 )

x² + 10x + 16 = 0 ← in standard form

(x + 8)(x + 2) = 0 ← in factored form

x + 8 = 0 ⇒ x = - 8

x + 2 = 0 ⇒ x = - 2

Substitute these values into (1) for corresponding values of y

x = - 8 : y = 2(- 8) + 8 = - 16 + 8 = - 8 ⇒ P (- 8, - 8)

x = - 2 : y = 2(- 2) + 8 = - 4 + 8 = 4 ⇒ Q (- 2, 4 )

Calculate the length of PQ using the distance formula

PQ = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = P (- 8, - 8) and (x₂, y₂ ) = Q (- 2, 4 )

PQ = \(\sqrt{(-2-(-8))^2+(4-(-8))^2}\)

      = \(\sqrt{(-2+8)^2+(4+8)^2}\)

       = \(\sqrt{6^2+12^2}\)

       = \(\sqrt{36+144}\)

       = \(\sqrt{180}\)

       = \(\sqrt{36(5)}\)

       = \(\sqrt{36}\) × \(\sqrt{5}\)

        = 6\(\sqrt{5}\) → A

Answer:

28 students did not fail.

Step-by-step explanation:

Since 7 is 1/5 of the class, then 4/5 of the class 28 because 7 * 4 = 28.

Brainliest would be greatly appreciated!!! Have a nice day!

Answer:

Simplifying

3u = 72

Solving

3u = 72

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Divide each side by '3'.

u = 24

Simplifying

u = 24

3u= 72

three will go to the other side so it will divide

and it well be

u= 24

Answer:

5,2

Step-by-step explanation:

The Surface area of Pyramid is equal to Option (B) \(72 m^2\) when base is square and their are 4 triangles.  

The surface area of a pyramid is the total area of all its faces. The formula to calculate the surface area of a pyramid depends on the shape of its base.

To find the surface area of this pyramid we should add area of all 4 triangles and 1 square base.

Area of Base = 4m * 4m

                      = \(16m^2\)

Area of Triangle = 1/2 *4* 7

                           = \(14m^2\)

Surface Area of Pyramid = Area of Base + 4 * (Area of Triangle)

                                         = \(16m^2 + 4(14m^2)\)

                                         = \(72 m^2\)

Therefore, Surface area of Pyramid is equal to  \(72 m^2\).

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Answer:

Step-by-step explanation:

(You will have to distribute first.)

-2(3x-5)=4(x+3)+8

-6x+10=4(x+3)+8

-6x+10=4(x+3)+8

-6x+10=4x+12+8

(Now you will have to add the numbers.)

6x+10=4x+12+8

-6x+10=4x+20

(Now you will have to subtract 10 from both sides of the equation.)

-6x+10=4x+20

-6+10-10=4x+20-10

(Now you will have to simplify.)

-6x=4x+10

(You will now subtract 4x from both sides of the equation.)

-6x=4x+10

-6x-4x=4x+10-4x

(You will now simplify again.)

-10x=10

(Now divide both sides of the equation by the same term.)

-10x=10

-----   ---- (Dividing -10)

-10  -10

(You will get x=-1 as the answer.)

Answer:

4.8, 3.14, -3.5, 1.4, 5.5, -5

Step-by-step explanation:

*Look at picture

Answer:

A or the first one

Answer:

  a) 489.77 ft from friend

  b) 470.80 ft from cliff

Step-by-step explanation:

Given a man on a 135 ft cliff sees his friend at an angle of depression of 16°, you want to know the distance of the man from his friend, and the distance of the friend from the cliff.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Tan = Opposite/Adjacent

The 135 ft height of the cliff is modeled as the side of a right triangle that is opposite the angle of elevation from the friend to the top of the cliff. (See attachment 2.) That angle is the same as the angle of depression from the top of the cliff to the friend.

The hypotenuse of the triangle is the distance between the man and his friend. The side of the triangle adjacent to the friend is the distance to the cliff.

Using the above relations, we have ...

  sin(16°) = (cliff height)/(distance to friend)

  tan(16°) = (cliff height)/(distance to cliff)

Solving for the variables of interest gives ...

  distance to friend = (cliff height)/sin(16°) = (135 ft)/sin(16°) ≈ 489.77 ft

  distance to cliff = (cliff height)/tan(16°) = (135 ft)/tan(16°) ≈ 470.80 ft

The ma is 489.77 ft from his friend; the friend is 470.80 ft from the cliff.

__

Additional comment

The distances are given to more decimal places than necessary so you can round the answer as may be required.

<95141404393>

Answer:

20

Step-by-step explanation:

67 ÷3.35=20

hop this helps

The probability that the sum of two fair, six-sided dice is between 3 and 11 (inclusive) is approximately 0.7222 or 72.22%. The total number of favorable outcomes is 31 + 15 = 46.

To find the probability that the sum of two fair, six-sided dice is between 3 and 11 (inclusive), we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

The possible outcomes for rolling two dice can be represented by a sample space of 36 equally likely outcomes, as each die has 6 possible outcomes (1, 2, 3, 4, 5, 6).

We can calculate the favorable outcomes by considering the combinations of two numbers that sum to a value between 3 and 11.

To simplify the calculation, we can break down the favorable outcomes into two cases:

1. The sum is between 3 and 7 (inclusive): In this case, we have the following favorable outcomes:

  - (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

  - (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

  - (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

  - (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

  - (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

  - (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)

  The total number of favorable outcomes in this case is 31.

2. The sum is between 8 and 11 (inclusive): In this case, we have the following favorable outcomes:

  - (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)

  - (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3)

  - (6, 4), (6, 5), (6, 6)

  The total number of favorable outcomes in this case is 15.

Therefore, the total number of favorable outcomes is 31 + 15 = 46.

Since there are 36 possible outcomes in the sample space, the probability of the sum of two dice being between 3 and 11 (inclusive) is given by:

P(sum between 3 and 11) = favorable outcomes / total outcomes = 46 / 36 = 23 / 18 ≈ 0.7222.

Hence, the probability that the sum of the two numbers showing is between 3 and 11 (inclusive) is approximately 0.7222, or 72.22%.

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We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer:

That shape orientation changes.

a) The inequality that models this situation is given as follows: 24x ≤ 250.

b) The solution to the inequality is given as follows: x ≤ 10.41.

c) The number of baseballs that can be purchased is of at most 10.

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

As the cost of each baseball is of $24, the constant is given as follows:

k = 24.

The equation giving the total cost of purchasing x baseballs is given as follows:

y = 24x.

The budget to spend is of $250, hence the inequality is given as follows:

24x ≤ 250.

The solution is given as follows:

x ≤ 250/24

x ≤  10.41.

As the number of baseballs is a countable amount, at most 10 baseballs can be purchased, rounding down the amount.

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Answer: 250

Step-by-step explanation:

Given

12% of the Pizzas had extra cheese

If those pizzas were 30 in number

Suppose, x be the total Pizzas

So, 12% of x is 30

\(\Rightarrow x\times \dfrac{12}{100}=30\\\\\Rightarrow x=250\)

Thus, 250 Pizzas were maid last week

Overall, equations provide a mathematical representation and understanding of relationships, while tables present data points in a structured format.

When comparing an equation and a table, you can examine their characteristics, purpose, and the information they provide. Here are some points to consider when making comparisons:

Representation:

An equation represents a mathematical relationship between variables using symbols and mathematical operations. A table presents data or values in a structured format, typically organized into rows and columns.

Communication of Information:

Equations provide a concise and general representation of a relationship, allowing for predictions, calculations, and modeling. Tables present specific data points or values, providing a visual representation of how variables are related or how they change.

Variables:

Equations involve variables, which can be manipulated to explore different scenarios and analyze the relationship between quantities. Tables display specific values or data points for variables, showing how they vary or are related based on the given information.

Visualization:

Equations can express relationships symbolically and provide a mathematical understanding, but they may not offer a visual representation of data. Tables provide a visual representation of data points, allowing for a quick overview and easy comparison of values.

Flexibility:

Equations offer flexibility in terms of adjusting variables and parameters to explore different scenarios and make predictions. Tables can be easily modified or expanded by adding or removing data points to reflect new observations or additional information.

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The tennis ball will hit the ground \(5\) seconds after being dropped from an initial height of  \(400\)feet.

To determine when the tennis ball hits the ground, we need to find the value of t when h becomes 0, since at that time the height of the ball is zero, which means it has hit the ground.

So, we can set  \(h = 0\) and solve for t:

\(0 = -16t^2 + 400\)

Adding 16t^2 to both sides:

\(16t^2 = 400\)

Dividing both sides by 16:

\(t^2 = 25\)

Taking the square root of both sides:

\(t = \pm5\)

Since we cannot have a negative time, we can disregard the negative solution.

Therefore, the tennis ball will hit the ground  \(5\) seconds after being dropped from an initial height of  \(400\) feet.

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