A coordinate plane with 2 lines drawn. The first line is labeled f(x) and passes through the points (0, negative 2) and (1, 1). The second line is labeled g(x) and passes through the points (negative 4, 0) and (0, 2). The lines intersect at about (2.5, 3.2)
How does the slope of g(x) compare to the slope of f(x)?

The slope of g(x) is the opposite of the slope of f(x).
The slope of g(x) is less than the slope of f(x).
The slope of g(x) is greater than the slope of f(x).
The slope of g(x) is equal to the slope of f(x)

Answer:

mean = 24

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

the sum of the data set is

sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

there is a count of 7 in the data set , then

mean = [tex]\frac{168}{7}[/tex] = 24

The x^6y^7 term in the expansion will be 36x^2y^7.

The x^7y^2 term in the expansion will be 36x^7y^2.

In the given problem, we have the binomial expansion of (x - y)^n, which includes the term 126x^5y^4.

We will use the binomial coefficient formula to find the coefficients of the desired terms.

The general term of the binomial expansion is given by:

T(k) = C(n, k) * x^(n-k) * y^k

where C(n, k) is the binomial coefficient and can be calculated as:

C(n, k) = n! / (k!(n-k)!)

From the given term, 126x^5y^4, we have:

126 = C(n, 4)

x^5 = x^(n-4)

y^4 = y^4

Now we can find the value of n:

126 = n! / (4!(n-4)!)

Let's solve for n:

126 * 4! = n! / (n-4)!

504 = n! / (n-4)!

Now, we will find the coefficients of the terms x^6y^7 and x^7y^2.

The x^6y^7 term in the expansion will be:

T(k) = C(n, 7) * x^(n-7) * y^7

Since x^5 = x^(n-4), we have n - 4 = 5, so n = 9.

Substituting the value of n:

T(k) = C(9, 7) * x^2 * y^7

Using the binomial coefficient formula:

C(9, 7) = 9! / (7!2!) = 36

So, the x^6y^7 term in the expansion will be 36x^2y^7.

The x^7y^2 term in the expansion will be:

T(k) = C(n, 2) * x^(n-2) * y^2

We already found that n = 9, so substituting the value of n:

T(k) = C(9, 2) * x^7 * y^2

Using the binomial coefficient formula:

C(9, 2) = 9! / (2!7!) = 36

So, the x^7y^2 term in the expansion will be 36x^7y^2.

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The translation used to create the image A'B'C'D', from the pre-image, ABCD is; 7 units to the right

A translation transformation is one in which the location of the points on the pre-image is changes but the size, and orientation of the pre-image is preserved.

The coordinates of the vertices of the polygon ABCD are; (1, 5), (3, 1), (7, 1), (5, 5)

The coordinates of the vertices of the polygon A'B'C'D' are; (8, 5), (10, 1), (14, 1), (12, 5)

Whereby the vertices of the image and the preimage are;

A(1, 5), B(3, 1), C(7, 1), D(5, 5), and A'(8, 5), B'(10, 1), C'(14, 1), D'(12, 5), the difference in the x and y-values indicates;

A' - A = (8 - 1, 5 - 5) = (7, 0)

B' - B = (10 - 3, 1 - 1) = (7, 0)

C' - C = (14 - 7, 1 - 1) = (7, 0)

D' - D = (12 - 5, 5 - 5) = (7, 0)

Therefore, the transformation used to create the image A'B'C'D' from the pre-image, ABCD is a translation; 7 units to the right

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Answer:

They are collinear if they are on the same line

The height of the heater is approximately 6.6 feet.

According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.

We can use the Pythagorean theorem to find the height of the pyramid. Let's call the height "h". Then, the slant height is the hypotenuse of a right triangle with base and height both equal to 10 feet, so we have:

h² + 10² = 12²

Simplifying and solving for h, we get:

h² + 100 = 144

h² = 44

h ≈ 6.6 feet

Therefore, the height of the heater is approximately 6.6 feet.

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The vertex is (50, 630). The vertex is the peak and correspond with the coordinates of he maximum height of the arch.

The solutions is the base of the arch and this (20, 0) and (80, 0)

vertex form, y = -0.7(x - 50)² + 630

Quadratic equation factored form, y = -0.7 (x - 80) (x - 20)

The equations are the same when plotted on a graph and examined mathematically. physically it looks different.

the domain is (-∞, ∞)

The height of the monument 15 feet from the left side is 472.5 feet

since the zeroes of the quadratic equation is (20, 0) and (80, 0), hence we have that

y = a(x - 20)(x - 80) and the equation pass points (50, 630)

630 = a(50 - 20)(50 - 80)

630 = a * 30 * -30

630 = -900a

a = -0.7

Quadratic equation has a standard vertex form, y = a(x - h)² + k    

y = a(x - h)² + k

vertex (h, k) = (50, 630) and a = -0.7

plugging the values

y = -0.7(x - 50)² + 630

Quadratic equation has a standard factored form, y = a(x - h)² + k    

y = a(x - r2)(x - r1)

where r2 and r1 are the roots r1 = 20 r2 = 80 an a = -0.7

plugging the values

y = -0.7 (x - 80)(x - 20)

The height of the monument 15 feet from the left side is gotten from the graph

this is 15 feet from 20 hence x = 35 feet

from the graph it can traced to be 472.5 feet

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Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

Answer:

AB: y = 2x + 4

Step-by-step explanation:

Line AB is parallel to the line y = 2x + 3

When 2 lines are parallel they have the same coefficient of x.

=> AB: y = 2x + m (1)

Because line AB passes through the point (0, 4)

Replace x = 0; y = 4 into (1) => 2 × 0 + m = 4 => m = 4

So AB: y = 2x + 4

The line's equation in point-slope form is shown here. Point (2, 5) is the given point on the line, and slope 2 is the given slope of the line. The slope of this line is -1/2, which is the negative reciprocal of the slope.

A line's point slope form equation is [tex]y - y_1 = m(x - x_1)[/tex]. Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

We require a point on the line and the slope of the line in order to create a line equation in point-slope form. In point-slope form,

[tex]y - y1 = m(x - x1)[/tex]

As an illustration, suppose we want to formulate the equation of the line passing through the coordinates (2, 5) and having a slope of 2. The values can be entered into the point-slope form as follows:

y - 5 = 2(x - 2)Let's say the given line has the equation [tex]y - y1 = m(x - x1)[/tex], where (x1, y1) is a point on the line and m is the slope of the line.

we can use the given point (2, 5). Then we can plug in the values into the point-slope form:

[tex]y - 5 = (-1/2)(x - 2).[/tex]

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The height of the cylinderical can is approximately 1147.8 inches.

What is a cylinder?

A cylinder is a three-dimensional geometric object made up of two parallel and congruent circular bases that are joined by a curving lateral surface. The lateral surface has a uniform circular cross-section and is perpendicular to the bases. A cylinder's height is the perpendicular distance between its bases. Cans, tubes, and pipes are all instances of cylinders. The volume of a cylinder may be computed by multiplying its base area by its height, and the formula for the lateral surface area is 2πrh, where r is the radius of the base and h is the cylinder's height.

Now,

We can start by finding the radius of the can using the given diameter:

radius = diameter/2 = 5/2 = 2.5 inches

The surface area of the can is given by:

Surface area = 2πrh + 2πr²

where h is the height of the can, r is the radius, and π is the mathematical constant pi.

Substituting the given values, we get:

18064 = 2π(2.5)(h) + 2π(2.5)²

Simplifying and solving for h, we get:

18064 = 15.707h + 39.269

18064 - 39.269 = 15.707h

18024.731 = 15.707h

h = 18024.731/15.707

h ≈ 1147.8 inches

Therefore, the height of the can is approximately 1147.8 inches.

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Answer:

3.14 cm^2

Step-by-step explanation:

1. Find radius:

If diameter is 2, divide it by 2 to get radius = 1

2. Find formula:

A=πr^2

3. Plug in:

A = π(1)^2

4. Solve (multiply):

A = π(1)^2:

3.14159265359

Or

3.14 cm^2

Answer:

3.14 cm^2

Step-by-step explanation:

A=[tex]\pi[/tex]r^2

r=2

2/2=1

A=[tex]\pi[/tex](1)^2

=[tex]\pi[/tex]1

≈3.14x1

≈3.14cm^2

The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:

A   B   (A ⋁ B) ⋀ ~(A ⋀ B)

0   0                0

0    1                0

1     0               0

1     1                0

A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.

The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.

To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.

A   B   A ⋁ B   A ⋀ B   ~(A ⋀ B)   (A ⋁ B) ⋀ ~(A ⋀ B)

0   0      0            0             1                      0

0    1       1            0             1                      0

1    0       1            0             1                      0

1    1        1             1             0                     0

So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.

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Step-by-step explanation:

From a z-score table

   z-score = 1 corresponds to  .8413   or  84.13 percentile

     meaning 84 .13 % have a lesser score than you

Answer:

angle

Step-by-step explanation:

since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!

Answer: i know it is acute

None of the given options A, B, C, or D is correct as they all provide different answers.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

The question asks for the equivalent of 6 × 2. This means that we need to find a number that is equal to the result of multiplying 6 and 2 together.

When we multiply 6 and 2, we get:

6 × 2 = 12

So, the equivalent of 6 × 2 is 12.

However, none of the answer options provided matches this answer.

Option A suggests that the equivalent of 6 × 2 is 2 × 1, which is equal to 2, not 12.

Option B suggests that the equivalent of 6 × 2 is 3 × 2, which is equal to 6, not 12.

Option C suggests that the equivalent of 6 × 2 is 9 × 3, which is equal to 27, not 12.

Option D suggests that the equivalent of 6 × 2 is 18 × 1/2, which is equal to 9, not 12.

Therefore, none of the options provided is correct.

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Answer: 4

Step-by-step explanation:

To find the unit rate, we can cross-multiply the fractions.

Multiplying the numerator of the first fraction by the denominator of the second fraction, we get 1/5.

Multiplying the numerator of the second fraction by the denominator of the first fraction, we get 1/20.

Now we have the equation 1/5 = 1/20.

To solve for the unknown, we can cross-multiply again, which gives us 20 * 1/5 = 4.

Therefore, the unit rate is 4.

Answer: The formula for the surface area of a sphere is given by 4πr^2, and since we have half of a sphere, the surface area of a dome (a half sphere) is 2πr^2.

Plugging in the radius r = 12 meters, we get:

Surface area = 2π(12)^2

Surface area = 2π(144)

Surface area ≈ 904.78

Rounding to the nearest whole number, we get the surface area of the dome as 905 meters squared. Therefore, the closest answer choice is 967 meters squared.

So the answer is: 967 meters squared.

Step-by-step explanation:

A. There are 9 sample spaces.

B.  The probability of choosing Chocolate, Fudge, and Rainbow is 1/9

What is meant by sample spaces?

In probability theory, a sample space is the set of all possible outcomes of a random experiment or process. It is used to define the space of events and calculate probabilities.

What is meant by probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. It is calculated by dividing the number of favourable outcomes by the total number of possible outcomes.

According to the given information

A. There are 9 possible combinations (3 ice cream flavors x 3 toppings x 1 sprinkle color), so there are 9 sample spaces.

B.  The probability of choosing Chocolate, Fudge, and Rainbow is 1/9, assuming all combinations are equally likely.

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By assuming that the farmer has goat and cows in the ratio 3:4, the  number of cows in the farm will be 32 cows.

To find out how many cows are in the farm, we need to know the total number of animals in the farm. Assuming the ratio of goats to cows is 3:4, we can write this as: [tex]3x : 4x[/tex]

Where 3x represents the number of goats, and 4x represents the number of cows. If we know that there are 24 goats, we can set up an equation to solve for x:

3x = 24

Dividing both sides by 3, we get:

x = 8

Now that we know the value of x, we can find the number of cows:

= 4x

= 4(8)

= 32

Therefore, there are 32 cows in the farm.

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There are 7 books in the stack.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find the number of books in the stack, we can divide the total mass of the stack by the mass of each book:

Number of books = Total mass of the stack / Mass of each book

In this case, the total mass of the stack is 21 kilograms, and the mass of each book is 3 kilograms.

Number of books = 21 kg / 3 kg/book

Simplifying the right side, we get:

Number of books = 7 books

Therefore,

There are 7 books in the stack.

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The approximated area of the shaded region is 92.54 square units

From the question, we have the following parameters that can be used in our computation:

The area of the shaded region in the figure is calculated as

Shaded region = Circle - Isosceles right triangle 1 - Isosceles right triangles 2

Using the given dimensions, we have

Shaded region = 3.14 * 6^2 - 1/2 * 5^2 - 1/2 * 4^2

Evaluate

Shaded region = 92.54

Hence, the shaded region is 92.54 square units

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Answer: C, 125

Step-by-step explanation: That is the slope of the line, which remains constant. The slope represents the distance over the time, and distance divided by time equals the speed. This means that the speed remains constant throughout.

Answer:

0

Step-by-step explanation:

0

The number of people who play only football is |A' ∩ B' ∩ C'| = 25. So, 25 people play only football.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of various methods and techniques to draw conclusions from data and make informed decisions.

The main goal of statistics is to provide a systematic approach to understanding and interpreting data, which can be used in a wide variety of fields, including business, social sciences, engineering, medicine, and many others. Statistics is used to study and analyze various types of data, including numerical, categorical, and ordinal data, as well as time series and spatial data.

Let A, B, and C be the sets of people who play football, baseball, and hockey, respectively. We know that:

|A| = 61, |B| = 65, |C| = 72

We also know that:

|A ∩ B ∩ C| = 22, |A ∪ B ∪ C| = 141, |A' ∩ B' ∩ C'| = 11

where A', B', and C' denote the complements of A, B, and C, respectively.

We can use the principle of inclusion-exclusion to find the number of people who play only two games. This principle states that:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Using the given values, we can substitute and simplify to get:

141 = 61 + 65 + 72 - |A ∩ B| - |A ∩ C| - |B ∩ C| + 22

|A ∩ B| + |A ∩ C| + |B ∩ C| = 75

We also know that an equal number of people play only two games, so let x be that number. Then:

|A ∩ B| = |A ∩ C| = |B ∩ C| = x

Substituting into the previous equation, we get:

3x = 75

x = 25

Therefore, 25 people play only two games. To find the number of people who play only football, we need to subtract the number of people who play baseball and hockey from the number of people who play only two games:

|A' ∩ B ∩ C| = x = 25

|A' ∩ B ∩ C'| = 11

|A' ∩ C ∩ B'| = x = 25

|A ∩ B' ∩ C'| = x = 25

|A' ∩ B| = 65 - (25 + 11) = 29

|A' ∩ C| = 72 - (25 + 11) = 36

|A' ∩ B' ∩ C| = 61 - (25 + 11) = 25

|A ∩ B' ∩ C| = 141 - (29 + 25 + 36 + 11) = 40

Therefore, the number of people who play only football is:

|A' ∩ B' ∩ C'| = 25

So, 25 people play only football.

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Answer:

a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]

where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).

In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.

Substituting these values into the formula, we get:

$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]

Simplifying and solving for P, we get:

P = $183,928.72

Therefore, you can afford a loan of approximately $183,928.72.

b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:

Total money paid = $1,000 x 360 = $360,000

Therefore, the total amount of money paid to the loan company will be $360,000.

c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:

Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28

Therefore, the amount of money paid in interest will be $176,071.28.

The equations that can be used to solve for y are y(y + 5) = 750,  y² – 5y = 750 and y(y – 5) + 750 = 0

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

The equations that can be used to solve for y, the length of the room are:

1. y(y + 5) = 750

2. y² – 5y = 750

3. y(y – 5) + 750 = 0

Option 1 and 2 are quadratic equations that can be solved by factoring, completing the square, or using the quadratic formula. Option 3 is also a quadratic equation but it requires rearranging to the standard form before applying the same methods. The last option, (y + 25)(y – 30) = 0, is not a quadratic equation but it can be easily solved using the zero product property.

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With given compound interest, it will take 27.25 years to pay off the loan.

What is Compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, the interest that is earned on both the principal amount and any previously accumulated interest. In other words, it is interest that is calculated not only on the original amount of money but also on any interest that has been earned previously. This can result in significant growth of an investment or loan balance over time, as the interest earned on the accumulated interest can compound exponentially. Compound interest can be calculated using a specific formula that takes into account the principal amount, the interest rate, and the compounding frequency.

Now,

First, we need to calculate the total amount of the loan. We round up the tuition and fees cost for 5 years to the nearest thousand dollars:

Total cost = $70,000

Rounded up to nearest thousand = $70,000

So, the amount of the loan is $70,000.

Next, we can use the formula N= (-log⁡(1-i*A/P))/(log⁡(1+i)) to calculate the number of monthly payments needed to pay off the loan.

N = (-log(1-0.0025*70000/250))/(log(1+0.0025))

N = (-log(1.75))/(log(1.0025))

N = 326.45

Rounding up to the nearest whole number, it will take 327 monthly payments to pay off the loan.

So, it will take 327/12 = 27.25 years to pay off the loan.

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Answer:

122.30 cm²

Step-by-step explanation:

Divide the polyhedron into shapes:

+) 2 triangles with the same area.

The area of the triangle is
(4.3×11)÷2 = 23.65 cm².
And with two triangles of the same area we take the sum of both areas
23.65 + 23.65 = 47.3 cm²

+) 3 rectangles with different areas.

(3×6) + (3×8) + (3×11) = 75 cm²

So the surface area is the sum of areas of the triangles and rectangles

47.3 + 75 = 122.3 = 122.30 cm²

The statements that are correct concerning the outcome of events between Jasmine and her classmates include the following:

Most students found a pine tree.

More students found a pine tree than a birch tree. That is option A and D respectively.

The quantity of students that found birch tree = 1/7 = 0.14

The quantity of students that found pine tree = 7/9 = 0.8

The quantity of students that found maple tree = 1/4 = 0.25

The quantity of students that found oak tree = 11/23 = 0.48

Therefore, the statement that are correct about the outcome of the event between Jasmine and her classmates is as follows:

Most students found a pine tree.

More students found a pine tree than a birch tree.

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Answer:

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