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)

Given:

A storeowner made a list of number of greeting cards sold last month.

The store sold 167 thank-you cards, 285 birthday cards and 56 blank cards.

Required:

What is the probability that the next customer will buy a blank card expressed as a percent?

Explanation:

We will find total number of cards sold as:

167 + 285 + 56 = 508

Now we will find percentage of each type of card sold as:

Percentage of blank cards sold

Answer:

Hence, in percent probability of sold blank card is 11%.

rd

Answer:

x = 4

y = 13

Step-by-step explanation:

x + y = 17

y = 2x + 5

substitute for y:

x + (2x + 5) = 17

reduce:

3x + 5 = 17

subtract 5 from each side:

3x = 12

divide both sides by 3:

x = 4

y = 2(4) + 5

y = 13

Answer:

C

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k)are the coordinates of the centre and r is the radius

Given

2x² + 2y² - 4x + 16y = 128 ( divide through by 2 )

x² + y² - 2x + 8y = 64 ( collect x and y terms together )

x² - 2x + y² + 8y = 64

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 1)x + 1 + y² + 2(4)y + 16 = 64 + 1 + 16

(x - 1)² + (y + 4)² = 81 ← in standard form

with centre = (h, k ) = (1, - 4 ) → C

Let the number of questions on the test equal X which would be 100%

They answered 86 which equaled 98

Set up a ratio:

X/86 = 100/98

Cross multiply:

98X = 8600

Divide both sides by 98:

X = 87.75

Round to 87 questions

They will be able to spend $612.52 on their trip.

What is simple interest?

The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

Using the formula \(A = P(1 + r/n)^{(nt)\), where:

P = $500.00 (the principal)

r = 7% = 0.07 (the annual interest rate)

n = 1 (compounded annually)

t = 3 years

\(A = 500(1 + 0.07/1)^{(1*3)\)

\(A = 500(1.07)^3\)

A = 500(1.225043)

A = $612.52

Therefore, they will be able to spend $612.52 on their trip.

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Answer:

C

Step-by-step explanation:

An open circle is used to represent x > 4 as we do not want to include 4 in our solution set.

Treat the <, ≤, >, or ≥  as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.

Using the open instructions when we plot the inequality we see that x > 4 has an open circle at 4.

This indicates that we do not want to include 4 in our solution set.

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Answer:

product would be 6x^2-3x

Step-by-step explanation:

don't know the rest

For a translation and a rotation map of ΔHJK to ΔLMN is given by translating K to N and rotating about K until HK lies on the line containing LN. Option C is correct.

When a form travels around a fixed point or over the mirror line without altering, it is said to be translating.

When a form rotates around a fixed point, it is said to be rotating.

In conclusion, The translation and rotation of the map ΔHJK to ΔLMN Translate K to N and rotate about K until HK lies on the line containing LN.

Hence, Translate K to N and rotate about K until HK lies on the line containing LN is correct.

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Among any group of 20 people (where any two people are either friends or enemies), there are either four mutual friends or four mutual enemies.

Let's assume there is a group of 20 people. Choose a person, say person A. There are two Probablities: A has at least 10 friends, or A has at least 10 enemies. Without loss of generality, let's assume A has at least 10 friends.

Now consider the 10 friends of A. Either they are all friends with each other, or there are two among them who are enemies. In the first case, we have found a group of four mutual friends (A and the other three). In the second case, let's say B and C are enemies.

If B and C are both friends with A, then we have found a group of four mutual enemies (B, C, and the two friends of A who are enemies with each other).

If either B or C is not friends with A, then we have found a group of four people (A, B, C, and one of A's friends who is an enemy of B or C) who are either four mutual friends or four mutual enemies.

Hence, among any group of 20 people, there are either four mutual friends or four mutual enemies.

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The probability that of a sample of 75 guest orders, that 2 orders will be returned is approximately 0.150.

The average of 45 guests per day order food to their room.

Probability of a meal being returned is 3%.

Binomial distribution is given byP(x) = nCx * p^x * q^(n-x)

whereP(x) = Probability of x successesen = number of trialsp = probability of successq = probability of failure = 1 - p

The number of success x = 2, the number of trials n = 75, the probability of success p = 0.03, and the probability of failure q = 1-0.03 = 0.97

The probability that of a sample of 75 guest orders, that 2 orders will be returned is

P(2) = 75C2 * 0.03^2 * 0.97^73,825 * 0.0009 * 0.2786963P(2) = 0.298585535 ≈ 0.150

The probability that of a sample of 75 guest orders, that 2 orders will be returned is approximately 0.150.

Hence, the correct option is 150.

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Amrit's income is £27434.16.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let the Bethan's income be x

Amrit's income is 32% more than Bethan's income.

So, Amrit's income=x+32%

Amrit and Bethan's combined income is £54868.

According to given question we have

x+x+32%=£54868

2x+32/100=£54868

2x=54868-0.32

2x=54867.68

x=27433.84

Bethan's income=£ 27433.84

Amrit's income

=x+32%

=£ 27433.84+0.32

=£27434.16

Therefore,  Amrit's income is £27434.16.

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Answer:

6 is the y intercept and 1 is the slope, so it goes up 1 unit right 1 unit

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Use the distance formula:

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

Insert values:

\((-9,7)=(x_{1},y_{1})\\\\(0,-5)=(x_{2},y_{2})\\\\\sqrt{(0-(-9))^2+(-5-7)^2}\)

Two negatives make a positive. Simplify:

\(\sqrt{(0+9)^2+(-5-7)^2}\)

Simplify parentheses:

\(\sqrt{(9)^2+(-12)^2}\)

Simplify exponents:

\(\sqrt{81+144}\)

Simplify addition:

\(\sqrt{225}\)

Find the square root:

\(\sqrt{225} =15\)

The distance between the two points is 15.

:Done

The block matrix A I [^ 2 represents a matrix with A as the top left block and the 2x2 identity matrix I as the bottom right block. The dimensions of matrix C are p x p.

If we want to extract the bottom left block of this matrix, which we'll call C, we need to take the submatrix formed by the last two rows and the first q columns. Since the identity matrix has 2 rows, this means C will have dimensions 2 x q. In matrix notation, we can write:

C = [ A | 0 ] [ 0 | I ] = [ 0 | A ] [ I | 0 ]
          q columns           q columns          

where the vertical bar separates the two blocks in each matrix. So, the dimensions of C are 2 x q.

You are given a block matrix in the form:

[ A  C ]
[ I  B ]

Where A is a p x q matrix, and you are asked to find the dimensions of matrix C.

Since A is a p x q matrix, the number of rows in matrix C must be equal to the number of rows in A to ensure compatibility in the block matrix. Therefore, matrix C has p rows.

Now, let's consider the block matrix columns. The identity matrix I has the same number of rows and columns, which is p x p. Since A is p x q, we know that B must also be a p x p matrix for the block matrix to make sense.

The number of columns in matrix C must be equal to the number of columns in matrix B. Since matrix B is p x p, matrix C must have p columns.

Thus, the dimensions of matrix C are p x p.

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The slope of the perpendicular line is the inverse reciprocal of the line on which the line is perpendicular.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x can be used to express the change in the y coordinate with regard to the change in the x coordinate.

The slope of two parallel lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other. The relationship between the slope of perpendicular lines can be represented by the formula m1 if the slopes of the two perpendicular lines are m1, m2.

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As per the given equations, the greatest common factor of 52x²y⁵ and 135x³y² is x²y².

To find the greatest common factor (GCF) of 52x²y⁵ and 135x³y², we need to determine the highest power of each common factor that divides both terms.

Let's break down the given terms into their prime factors:

52x²y⁵ = 2² * 13 * x² * y⁵

135x³y² = 3³ * 5 * x³ * y²

Now, we look for the common factors and determine the highest power of each factor that divides both terms:

Common factors:

- x² (appears in both terms)

- y² (appears in both terms)

Highest power of x²:

- In 52x²y⁵, the power of x² is 2.

- In 135x³y², the power of x² is 2.

Highest power of y²:

- In 52x²y⁵, the power of y² is 2.

- In 135x³y², the power of y² is 2.

Therefore, the GCF of 52x²y⁵ and 135x³y² is x²y².

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The solution to the given system of linear equations is x = 2 and y = 8

From the question, we are to solve the given system of linear equations by elimination

The given system of equations is

3x + y = 14

4x - y = 0

Add the two equations

  3x + y = 14

+ 4x - y = 0

---------------------------

7x = 14

x = 14/7

x = 2

Substitute the value of x into the first equation

3x + y = 14

3(2) + y = 14

6 + y = 14

y = 14 - 6

y = 8

Hence, x = 2 and y = 8

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Answer:

2.222

Step-by-step explanation:

there is 1000 pieces of candy and 450 bags so 1000 ÷ 450 = 2.222

The value of EF is 26

A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord's endpoints.There is minor segment and major segment.

Since the two arcs are equal, i.e arc EF = arc CD, therefore,

chord EF = chord CD

9x-1 = 41 - 5x

collecting like terms

9x +5x = 41+1

14x = 42

divide both sides by 14

x = 42/14

x = 3

Therefore EF = 41-5x

= 41-5×3

= 41-15

= 26

therefore the value of EF is 26

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Answer:

is one third of that other number, one sixth of the original number.

Step-by-step explanation:

Answer:

angle A is 53

side AC is 0.2

bc= 0.25

Step-by-step explanation:

180-90-37= 53

AC= sin(37)= 3/x

BC=tan(37)=3/x

The value of "k" for which the determinant of the given matrix is zero is 2.5

The given problem asks to find the values of "k" for which the determinant of the given matrix is zero.

The given matrix can be represented as:

| 6 0 0 |
| 7 2 0 |
| 0 2 k+7 |

The determinant of the matrix is calculated as:

6 * (2(k+7)) - 0 - 0 - 7 * (2) * 0 + 0 - 0 = 12k - 30

To find the values of "k" for which the determinant is zero, we need to solve the equation:

12k - 30 = 0

Simplifying the equation, we get:

k = 2.5

Therefore, the value of "k" for which the determinant is zero is 2.5.

In general, the determinant of a matrix is a scalar value that represents some important properties of the matrix, such as invertibility and eigenvalues. If the determinant of a matrix is zero, it means that the matrix is singular and does not have an inverse. In the given problem, we have calculated the determinant of the matrix and found the values of "k" for which the determinant is zero. This helps us understand the properties of the matrix and the possible solutions to any equations involving the matrix.

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I apologize, I cannot visually perceive or manipulate colors or lines directly. However, if you provide me with the equations of the lines or any additional information about their slopes, I would be more than happy to help you match the slopes with the corresponding lines.

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To match the lines (l1, l2, l3) with their corresponding slopes, we need to assign letters representing the slopes to each set.

Without specific information about the lines l1, l2, and l3, it is not possible to determine the exact slopes or their corresponding letters. In order to match the lines with their slopes, we would need additional details such as the equations of the lines or the coordinates of points on the lines.

The slope of a line represents the rate at which the line changes vertically (y-axis) with respect to the horizontal (x-axis). It is typically denoted by the letter "m" in mathematical notation.

To accurately match the lines l1, l2, and l3 with their respective slopes, we require more information about the lines themselves. Once the equations or coordinates are provided, we can calculate the slopes using the formula for slope, which is the change in y divided by the change in x.

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Part 1: An increase in the price of fertilizer per pound will affect the supply curve for avocados.

The supply function for avocados is given by Q = 58 + 15p - 20pf, where p is the price of avocados and pf is the price of fertilizer. When the price of fertilizer rises by $1.60 per pound, it means that the value of pf in the supply function increases by $1.60. Consequently, the equation for the new supply curve becomes Q = 58 + 15p - 20(pf + 1.60). This adjustment reflects the decrease in supply resulting from the higher cost of production due to the increased fertilizer price.

Part 2: To determine how the supply of avocados changes in response to the price increase of $1.60 per pound of fertilizer, we need to evaluate the change in quantity supplied (ΔQ) at each price level. By substituting the new value of pf = original pf + $1.60 into the supply function, we can find the difference in quantity supplied.

For example, if the supply of avocados at a particular price was initially Q1, the new supply with the increased fertilizer price would be Q2. The change in supply can be calculated as ΔQ = Q2 - Q1, expressed in avocados per month. This value will indicate the magnitude and direction of the supply shift resulting from the change in fertilizer price.

The supply curve for avocados is influenced by the cost of production, including the price of inputs like fertilizer. When the price of fertilizer increases, it directly affects the production costs for avocado growers. The supply function reflects this relationship by incorporating the price of fertilizer (pf) as a factor.

As the price of fertilizer per pound rises, the term -20pf in the supply equation causes a decrease in the quantity supplied at each price level. This implies a leftward shift of the supply curve, indicating a reduction in the overall supply of avocados in the market. The magnitude of the shift can be determined by calculating the change in quantity supplied (ΔQ) using the new value of the fertilizer price. The supply curve is dynamic and changes in input prices can lead to significant shifts in the quantity of avocados supplied.

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Problem:

The point at which a graph hits the x-axis is known as :

Solution:

The zero of the function. This point is characterized by the coordinate

(x, y) = (0, y). Notice that at this point, the coordinate x is always zero.

The given problem requires us to find the volume of the solid generated by rotating a region bounded by the given curves around the x-axis.  The region is bounded by the given curves\(, y = -x² + 12x - 32 and y = 0.\)The shaded region is bounded by the curves \(`y = -x² + 12x - 32` and `y = 0`\).

The graph of the shaded region is shown below: The limits of integration of the area A (region) are from x = 4 to x = 8 since these are the values where the curve \(`y = -x² + 12x - 32`\)crosses the x-axis.

We'll use the method of disks to compute the volume of the solid generated by rotating the region about the x-axis.Let's consider a disk of radius `r` and thickness `dx` as shown below:

This disk has a volume given by\(`dV = πr²dx`.\)By considering a vertical slice of the shaded region of thickness `dx`, we obtain the radius `r` of the disk as `r = y` and the thickness `dx` as `dx`.

Thus, the volume of the solid generated by rotating the region about the x-axis is given by:\(V = `∫_4^8πy^2 dx`\)Since \(`y = -x² + 12x - 32`\), we have:\(V = `∫_4^8π(-x² + 12x - 32)² dx`\)On simplifying, we get:\(V = `(64/5)π(10√10 - 57)`\)Therefore, the volume of the solid generated by rotating the region about the x-axis is \(`(64/5)π(10√10 - 57)`\).

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\( \sf \: 1. \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 - 5}{ - 2 - 3} \bigg]\bigg[ \frac{14 - 21}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{ - 1}{ - 5} \bigg]\bigg[ \frac{ - 7}{ - 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{1}{ 5} \times \frac{ 7}{ 6} \\ \)

\( \sf \longrightarrow \: \frac{7}{30} \\ \)

C) 7/30 ✅

________________________________

\( \sf \: 2. \bigg[ \frac{7+ ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 + ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 - 6}{ - 4 - 9} \bigg]\bigg[ \frac{20 - 45}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 4 - 9} \bigg]\bigg[ \frac{ - 25}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 13} \bigg]\bigg[ \frac{ -25}{ 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{ - 25}{ - 78} \\ \)

\( \sf \longrightarrow \: \frac{ 25}{ 78} \\ \)

A] 25 / 78 ✅

________________________________

\( \sf \: 3. \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4 - 5}{ - 2 - 4} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{-18}{ 4} \bigg] \\ \)

\( \sf \longrightarrow \frac{18}{ - 24} \\ \)

\( \sf \longrightarrow -\frac{6}{ 8} \\ \)

\( \sf \longrightarrow -\frac{3}{ 4} \\ \)

C] -3/4 ✅

________________________________

\( \sf \: 4. \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7- 3}{ - 6 - 2} \bigg]\bigg[ \frac{18 - 6}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 6 - 2} \bigg]\bigg[ \frac{12}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 8} \bigg]\bigg[ \frac{12}{ -1} \bigg] \\ \)

\( \sf \longrightarrow \frac{48}{ 8} \\ \)

\( \sf \longrightarrow \frac{6}{ 1} \\ \)

\( \sf \longrightarrow 6 \\ \)

D] 6 ✅

________________________________

\( \sf \: 5. \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8 - 2}{ - 5- 6} \bigg]\bigg[ \frac{40 - 48}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 5- 6} \bigg]\bigg[ \frac{-8}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 11} \bigg]\bigg[ \frac{-8}{ 1} \bigg] \\ \)

\( \sf \longrightarrow \frac{-48}{ - 11} \\ \)

\( \sf \longrightarrow \frac{48}{ 11} \\ \)

B] 48/11 ✅

________________________________

Answer:

D.

Step-by-step explanation:

This is because the square root of 135 is 11.6189, which is between 11 and 12.