justin and Amy are trying to prove the Triangle Angle Sum Theorem. Justin draws a triangle on a piece of paper, tears off the corners, and arranges them to form a line. Amy constructs a line through one vertex that is parallel to the opposite side and uses the Alternate Interior Angles Theorem to show that the interior angles add up to 180°. Who proved the theorem? Explain. (1 point)
A Only Amy proved the theorem because she used postulates and theorems to construct a logical argument to show that the interior angles in a triangle add up to 180°.
B Only Justin proved the theorem because he demonstrated that the angles formed a line.
C Both Amy and Justin proved the theorem. Amy used postulates and theorems, while Justin used a demonstration.
D Neither Amy nor Justin proved the theorem.

The required altitude of the trapezoid ABCD is 2.5 cm.

The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. Take the average of the bases and multiply it by the height to determine the area of a trapezoid.

Here, we must utilise the area of a trapezoid formula, which is

where h is the height or altitude and b1 and b2 are the two bases.

\(Area =\frac{ (b_{1}+b_{2})h}{2}\)

Given are the values of Area = 7.5, b1 = 1, b2 = 5, and h is unknown.

Then,

7.5 = (1+5)h/2

7.5 = 3h

h = 2.5cm

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The questions created to answer the problem is Lanre borrowed a sum of ₹120 from bank at the rate of 12% per annum

And the exponential function is f(x) = 120 * (1.12)ˣ

We start by creating the required question that will be used in answering this problem

The question is stated as follows

Lanre borrowed a sum of ₹120 from bank at the rate of 12% per annum

From the question above, we have the following:

Inital amount, a = 1200

Rate of increase, r = 12%

Using the above as a guide, we have the following:

The exponential function of the situation is

f(x) = a * (1 + r)ˣ

So, we have the following representation

f(x) = 120 * (1 + 12%)ˣ

This gives

(a) f(x) = 120 * (1.12)ˣ

(b) The graph is attached

(c) The initial value is 120

(d) The rate of change is 12%

Hence, the function is f(x) = 120 * (1.12)ˣ

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Answer:

The answer should be x 4/-48

Step-by-step explanation:

I think this is the answer

Answer:

just checking something

Answer:

D

Step-by-step explanation:

The maximum profit of $400 is achieved by producing 20 tables and 20 chairs.

(a) Let x, y, and z be the number of bags of GRADE_A, GRADE_B, and GRADE_C produced, respectively.

The objective is to maximize the sales revenue, which is given by:

Revenue = 275x + 250y + 225z

The constraints are:

The sand used in the production of the bags of each mixture cannot exceed the capacity of the sand bin:

10x + 6y + 2z <= 2000

The pebbles used in the production of the bags of each mixture cannot exceed the capacity of the pebbles bin:

7x + 10y + 8z <= 3000

The rocks used in the production of the bags of each mixture cannot exceed the capacity of the rocks bin:

3x + 4y + 10z <= 4000

The number of bags produced must be non-negative:

x, y, z >= 0

The linear programming model for this problem is:

Maximize: 275x + 250y + 225z

Subject to:

10x + 6y + 2z <= 2000

7x + 10y + 8z <= 3000

3x + 4y + 10z <= 4000

x, y, z >= 0

(b) Let x and y be the number of tables and chairs produced, respectively.

The objective is to maximize the weekly profits, which is given by:

Profit = 12x + 8y

The constraints are:

The amount of oak used in the production of tables and chairs must not exceed the available oak:

5x + 2y <= 150

The amount of pine used in the production of tables and chairs must not exceed the available pine:

2x + 3y <= 100

The amount of labor hours used in the production of tables and chairs must not exceed the available labor hours:

4x + 2y <= 80

The number of tables and chairs produced must be non-negative:

x, y >= 0

The linear programming model for this problem is:

Maximize: 12x + 8y

Subject to:

5x + 2y <= 150

2x + 3y <= 100

4x + 2y <= 80

x, y >= 0

Solving this problem graphically, we plot the three constraints on a graph and find the feasible region. Then, we evaluate the objective function at the vertices of the feasible region to find the optimal solution.

The feasible region is shown in the graph below:

The vertices of the feasible region are A(0,0), B(0,33.33), C(20,20), D(25,10), and E(30,0).

Evaluating the objective function at each of the vertices, we have:

A: Profit = 12(0) + 8(0) = 0

B: Profit = 12(0) + 8(33.33) = 266.64

C: Profit = 12(20) + 8(20) = 400

D: Profit = 12(25) + 8(10) = 380

E: Profit = 12(30) + 8(0) = 360

Therefore, the maximum profit of $400 is achieved by producing 20 tables and 20 chairs.

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The linear regression model can be extended to accommodate certain forms of non-linear relationships between the response and predictor(s).  Polynomial regression is one specific method for incorporating non-linear associations within the linear regression framework.

It involves understanding the flexibility of the linear regression model and the techniques available to address non-linear relationships. While the linear regression model assumes a linear relationship between the response variable and predictors, it can still be useful in accommodating certain types of non-linear relationships.

By applying appropriate transformations to the predictor variables, such as taking their squares, logarithms, or other non-linear functions, we can introduce non-linear associations into the linear regression model. This allows the model to capture curvature or other non-linear patterns in the data.

Polynomial regression is a specific approach to incorporating non-linear relationships within the linear regression framework. It involves adding polynomial terms of the predictor variables to the model, such as squared or cubed terms. By including these polynomial terms, the model can account for non-linear relationships and capture more complex patterns.

It's important to note that while linear regression can be extended to accommodate some non-linear relationships, there may be cases where more advanced non-linear regression techniques or alternative models are necessary to adequately capture complex non-linear associations. Nonetheless, the inclusion of transformed predictor variables and the use of polynomial regression are valuable approaches to address non-linear relationships within the linear regression framework.

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Answer:

50.6

Step-by-step explanation:

The perimeter of the circle is 12.56 because we take 1/2 of 8 (the length of the short side of the rectangle) and multiply that by pie (or 3.14). Now that we know that the perimeter of the circle is 12.56 we add that to 8 (short side of the rectangle) and we add that to 15 twice (which is 30)

a) The average selling price in Bloomington is $301,596.27.

b) The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively.

c) There are 98 houses made primarily of brick and 102 not.

d) There is a positive moderate relationship between selling price and square footage of houses in Bloomington.

e) On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

The descriptive analysis in Bloomington has given the following insights: The average selling price in Bloomington is $301,596.27. The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively. There are 98 houses made primarily of brick and 102 not. There is a positive moderate relationship between selling price and square footage of houses in Bloomington. On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

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Answer:

the answer is 1.4N/kg

Answer:

see explanation

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = πd ( d is the diameter )

Here C = 32π , thus

πd = 32π ( divide both sides by π )

d = 32

Thus a coin with diameter 32 mm should fit through a slot of 35 mm

Answer:

30x - 18

Step-by-step explanation:

6(5x - 3)

30x - 18

6(5x) = 30x

6(-3) = -18

Combined:

30x - 18

Step-by-step explanation:

The graph that represents all values of x such that x > -3 and x < 2 is the graph of a vertical line segment located between -3 and 2 on the x-axis, but excluding these two points. This can be represented graphically as:

|

|

|

---------x---------

|

|

|

-3 2

Here, the open circles indicate that the points -3 and 2 are not included in the range of values for x.

Answer:

3 3/4 pound of bananas

hope this helps

The eccentricity of the conic section below is: A. closer to 0 than 1.

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, there are four (4) types of conic section and these include the following with their eccentricity:

In this context, we can reasonably infer and logically deduce that the eccentricity of the conic section is closer to zero (0) than one (1) because it represents a circle.

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The table shows the equivalent ratios 40:8 which can be simplified to 5:1. Equivalent ratios can be found by multiplying or dividing both the numerator and denominator by the same nonzero number. Ratios are useful in various real-life situations, such as cooking, map scaling, finance, and sports.

The table shows the equivalent ratios 40:8. The ratio 40:8 can be simplified by dividing both the numerator and the denominator by their greatest common factor (GCF) which is 8. Thus, the simplified ratio would be 5:1. This means that for every 5 units of the first quantity, there is 1 unit of the second quantity.In general, equivalent ratios are two ratios that express the same relationship between two quantities, but may have different values.

Equivalent ratios can be found by multiplying or dividing both the numerator and denominator by the same nonzero number.For example, if the given ratio is 2:3, then an equivalent ratio can be found by multiplying both the numerator and denominator by 2, resulting in 4:6. Similarly, another equivalent ratio can be found by dividing both the numerator and denominator by 3, resulting in 2/3.

There are various ways in which ratios can be used in practical situations. For instance, in cooking, ratios are used to determine the right proportions of ingredients to be used. In map scaling, ratios are used to scale down or up distances on the map. In finance, ratios are used to analyze financial statements and measure financial performance.

In sports, ratios can be used to compare athletes’ performances, such as goals scored in soccer, points scored in basketball, or runs scored in baseball.

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The median of X is 1;  P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and  the value of q such that P(X < q) = 0.95 is 1.9.

(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.

Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.

For 0 < x < 2, the CDF is:

F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x

Setting (1/2) * x = 0.5 and solving for x:

(1/2) * x = 0.5;  x = 1

Therefore, the median of X is 1.

(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.

For x > 2, the PDF is 0, so P(X > x) = 0.

Therefore, P(X > 2) = 0.

(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.

P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)

Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.

Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.

(d) The variance of X can be calculated using the formula:

Var(X) = E(X²) - [E(X)]²

To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:

E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3

To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:

E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Now we can calculate the variance:

Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33

Therefore, Var(X) is approximately 0.33.

(e) The expected value of X, E(X), is given by:

E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Therefore, E(X) is 1.

(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:

∫(0 to q) f(x) dx = 0.95

Since the PDF is constant at 1/2 for 0 < x < 2, we have:

(1/2) * (x) | (0 to q) = 0.95

(1/2) * q = 0.95

q = 0.95 * 2 = 1.9

Therefore, the value of q such that P(X < q) = 0.95 is 1.9.

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Answer:

A closed cone has 0 verticals.. but 1 vertice

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

Answer:

A i did this before

Step-by-step explanation:

The average temperature would be -2°Celsius

You just add up all the numbers, and the average of the numbers is the sum of all the numbers divided by the amount of numbers.

1+-6+14+-9+-15+8+-7=-14

-14/7=-2

Answer:75

Step-by-step explanation:

Yes, the given table is a valid discrete probability distribution.

The probability of each value of x (in this case, -5, -2.5, 0, 2.5 and 5) is between 0 and 1, which is a necessary requirement for a discrete probability distribution. Furthermore, the sum of all the probabilities is 1, which is another requirement for a discrete probability distribution.

In a discrete probability distribution, each outcome of a random variable must have a probability assigned to it, which must be greater than or equal to 0 and less than or equal to 1.

The probabilities must also sum to 1. In the given table, each value of x is assigned a probability, which satisfies the criteria. Additionally, the sum of all the probabilities is 1, which ensures that the probability distribution is valid.

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Answer:

12 for length, 6 for width

Step-by-step explanation:

Trust me its right

Answer:

12 for length 6 for width (:

Step-by-step explanation:

Answer:

16 flowers per bouquet

Step-by-step explanation:

if you try to solve this question using the given equations the answer will not make a lot of sense:

y = 24 - 1x

128 = 24 - 7x

-7x = 128 - 24 = 104

x = 104 / -7 = -14.86 flowers

the equation is not correct, it should be:

y = 240 - 1x

128 = 240 - 7x

7x = 240 - 128 = 112

x = 112 / 7 = 16 flowers per bouquet

Answer:

x^4 + x^3 + 13x + 5

Step-by-step explanation:

Answer:

D. <15/√346>

Have a nice day! :)

Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

Answer:

5

Step-by-step explanation:

Answer:

81mn

Step-by-step explanation:

3 to the power of 3 is 81

The quotient of the rational expressions shown above is given by, Answer: option (C) 7x²/6x-10

To simplify the expression 7x² / 3x-5 / 2x+6 / x+3

We need to perform the following steps:

Invert the divisor.

Change the division to multiplication.

Factor the numerator and denominator.

First, divide the first term in the numerator (7\(x^2\)) by the first term in the denominator (2x) to get 3.

Then multiply (2x + 6) by 3 to get 6x + 18 Subtract this from the numerator.

2x + 6 | 7\(x^2\) + 3x - 5

- (6x + 18)

_______

-3x - 23

Then subtract the following term from the numerator: -3x.

Dividing -3x by 2x gives -3/2.

Multiply (2x + 6) by -3/2. The result is -3x - 9.

Subtract this from the previous result.

3 - (3/2)x

_________

2x + 6 | - 14

The result of polynomial long division is -14.

Therefore, the quotient of the rational expression is (7\(x^2\) + 3x - 5) / (2x + 6) -14.

So the correct answer is option D: -14.

Cancel out any common factors.

Multiply the remaining terms to get the answer.

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Answer:

x-intercept: x = 8/3

y-intercept: y = 8

Step-by-step explanation:

x-intercept

\(y = 8 - 3x\)

\(0 = 8 - 3x\)

\(3x = 8\)

\(x = \frac{8}{3} \)

••••

y-intercept

\(y = 8 - 3x\)

\(y = 8 - 3 \times 0\)

\(y = 8\)