Sterling has prepared the following two-column proof below. He is given that ∠OLN ≅ ∠LNO and he is trying to prove that OL ≅ ON. Triangle OLN, where angle OLN is congruent to angle LNO Step Statement Reason 1 ∠OLN ≅ ∠LNO Given 2 Draw OE as a perpendicular bisector to LN by Construction 3 m∠LEO = 90° Definition of a Perpendicular Bisector 4 m∠NEO = 90° Definition of a Perpendicular Bisector 5 LE ≅ EN Definition of a Perpendicular Bisector 6 ΔOLE ≅ ΔONE Hypotenuse-Leg (HL) Postulate 7 ∠LEO ≅ ∠NEO Transitive Property of Equality 8 OL ≅ ON CPCTC Sterling made two errors in the proof. Identify and correct the errors. Question 5 options:

Option B is the graph best represents the most reasonable distribution of the differences.

Any variable whose value is uncertain or any function that values each result of an experiment is referred to be a random variable. Discrete (having definite values) or continuous random variables are also possible (any value in a continuous range).

As a result, the random variables are so-called because it is impossible to determine their value with certainty; instead, we can only guess, and this estimate is known as the probability that a random variable will have a given value.

Here we assume the random variable X denotes the difference between the outcomes of rolling the two dice.

here the number of rolls is 500. As we know by central limit theorem every distribution approaches to normal distribution irrespective of the parent distribution. Since Normal is symmetric about the mean the most reasonable distribution is the second figure.

Option B is the correct answer.

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The complete question is as follows:

Answer: 128 square centimeters

Step-by-step explanation:

If the perimeter is 48 cm, then the sum of the lengths of any two adjacent sides must be 24 cm.

Since the length of one of these sides is given to be 8 cm, it follows the length of the corresponding adjacent side is 16 cm.

Thus, using the formula for the area of a rectangle, the area is 128 square centimeters.

The number of tiles Ricardo use for each mosaic is 81 and 1 tile left over.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, M Attend to Precision Ricardo has 325 tiles to make 4 mosaics.

Here, the number of tiles need for each mosaic is 325/4

4|325|81

  324

______

    1

Therefore, the number of tiles Ricardo use for each mosaic is 81 and 1 tile left over.

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To develop an equation to predict the surface area of a person as a function of their height and weight using numerical methods and MATLAB, you can follow these steps:

The required details for MATLAB in given paragraph

Begin by organizing the given data into two separate arrays: one for height (H) and one for weight (W). For example, you might create the following arrays:

H = [182 180 179 187 189 194 195 193 200];

W = [74 88 94 78 84 98 76 86 96];

A = [1.92 2.11 2.15 2.02 2.09 2.31 2.02 2.16 2.31];

Use the MATLAB function "polyfit" to fit a polynomial function to the data. You can specify the degree of the polynomial function based on the number of variables you want to include in the model. For example, to fit a second-degree polynomial function, you can use the following command:

p = polyfit(H,A,2);

This will fit a polynomial function of the form A = p(1) * H^2 + p(2) * H + p(3) to the data, where p(1), p(2), and p(3) are the coefficients of the polynomial.

Use the MATLAB function "polyval" to evaluate the fitted polynomial function at a specific value of H. For example, to estimate the surface area for a person with a height of 187 cm, you can use the following command:

A_estimated = polyval(p,187);

This will return the estimated surface area for a person with a height of 187 cm. You can use similar commands to estimate the surface area for different values of H

what do you mean by MATLAB?

MATLAB (short for "Matrix Laboratory") is a programming language and software environment for numerical computation, visualization, and programming. It is commonly used in scientific, engineering, and mathematical fields to analyze and visualize data, develop algorithms, and build mathematical models.

A function in MATLAB is a self-contained block of code that performs a specific task or computation. Functions are useful because they allow you to reuse code and make your programs more modular and easier to understand. In MATLAB, you can define your own functions or use built-in functions that are provided with the software.

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The phrase can be expressed as 3x-6, 3(x-2), x+2x-2-4, 4x-x+4-10 and x+x+x-2-2-2 and so on

It consists of several mathematical symbols organized in such a way that it can express mathematical concept.

Mathematical  phrase can be written in one or more different pattern to show the same expression.

As per question given, the phrase is expressed by

3x-6, where x is used to represent a number

the phrase can be written in 3(x-2)

other variable expressions of same phrase are x+2x-2-4

or 4x-x+4-10 or x+x+x-2-2-2

hence, a phrase can be written in one or more pattern to show same expression.

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Answer: 4 red and 12 blue

Step-by-step explanation: Answer to 9

We know that for every red rose, he plants 3 blue flowers. The rate is 1:3. If he grows 16, there will be 4 red roses and 12 blue ones. This is because the rate is 1:3 then there are 4 flowers in all. This is 1/4 of how much he wants to grow. So multiply each type of plant by 4. 1 times 4 is 4, so there are 4 red ones. 3 times 4 is 12, so there are 12 blue ones. Hope this helps!

Answer:

[tex]y=2/11[/tex]

Step-by-step explanation:

[tex]\lim{t \to \pm \infty} R(t)=\lim_{ t \to \pm \infty} \frac{30t+525}{165t+7000} =\frac{30}{165}=\frac{2}{11}[/tex]

BY using the inequality,

(67 + 65 + 64 + 88 + 2x)/5 ≥ 73,

we find the score she must make on final exam to pass the courses with an average of 73 or higher is x>=80.

An inequality is a mathematical statement that shows that one quantity is greater than or less than another quantity.

The average, or mean, of a set of numbers is a measure of the central tendency of the set.

This inequality states that the average of Shureka's scores on the four tests and the final exam must be greater than or equal to 73 in order for her to pass the course. Solving for x, we find that x ≥ 80.

The meaning of the answer to part (a) is that Shureka must make a score of 80 or higher on the final exam in order to pass the course with an average of 73 or higher. In other words, if Shureka makes a score of 80 or higher on the final exam, her average score on the five tests will be 73 or higher, which is the minimum required to pass the course. If she makes a score lower than 80 on the final exam, her average score will be less than 73, and she will not pass the course.

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There are solutions when k = -1 and when k = -3

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

|x + 3| - 2 = k

Removing the modulus sign

x + 3 - 2 = k -----(i) = x + 1 = k

-x - 3 - 2 = k -----(ii) -x - 5 = k

Putting k = -1

(i) x = -2 and (ii) x = -4

Putting k = -3

(i) x = -4 and (ii) x = -2

Since, x has solution on both the values of k

We can say that,

There are solutions when k = -1 and when k = -3

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a) The probability that both are girls is of: 21/150.

b) The probability that both are from the same school is of: 0.7333 = 73.33%.

How to obtain the probabilities?

The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

One girl from school A -> 7/15 probability.

One girl from school B -> 3/10 probability.

Hence the probability that both are girls is of:

p = 7/15 x 3/10 = 21/150.

The probability that the two boys are from the same school can be given by these two cases:

School A: 8/15 x 7/14.

School B: 7/10 x 6/9.

Then the probability is of:

p = 8/15 x 7/14 + 7/10 x 6/9 = 0.7333 = 73.33%.

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the answer is

a=p-3b-4c

To paint , 7 rooms in white or yellow, 128 possible outcomes are there.

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

There are seven rooms in the house and each can be painted either yellow or white.

And probability of total number of different outcomes

= total number of options

So, total number of different outcomes = 2⁷

 Total number of different outcomes = 128

Therefore the total number of outcomes are 128.

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The complete question is;

A house has seven rooms. Each room can be painted white or yellow. How many possible outcomes are there?

The total area of the shape will be;

⇒ 721 cm²

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Two congruent parallelograms are joined along their base to make the shape below.

Now,

We know that;

2 identical parallelogram whose area = 2 (Base x Height)

And, 2 identical right triangle = base x height

And, 1 rectangle = length x width

So, We get;

In parallelogram;

Base = 15 cm

Height = 11 cm

Hence, We get;

Area = 2 (15 x 11)

       = 330 cm²

And, Area of two identical right triangle;

Base = 11 cm

Height = 11 cm

Hence, Area = 11 × 11

                    = 121 cm²

Area of rectangle = 18 x 15 = 270 cm²

Thus, The total area of shape will be;

⇒ 330 + 121 + 270

⇒ 721 cm²

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Answer:

Part A is 100

Part B is 50

Part C is 25

all of it goes down by 15 so just keep subtracting

Step-by-step explanation:

I used common since and a sheet of paper

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =\frac{2\pi }{3} \end{cases}\implies A=\cfrac{~~ \frac{2\pi }{3 }\cdot 6^2 ~~}{2}\implies A=12\pi \implies A\approx 37.68[/tex]

Answer:

the football team sells 805,000 tickets each season

Step-by-step explanation:

average number of tickets sold per match=23,000

the average number of games played each session=35

the number of tickets sold on average each session = 23,000 x 35 which equals 805,000

so the average football club sells 805,000 tickets each season

Answer:

minimum value = 10

Step-by-step explanation:

the minimum value is at the left side of the whisker in the box plot, then

minimum value = 10

The area of the shaded region is given as follows:

0.879.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the percentile, the area in this problem is given by one subtracted by the p-value of z = -1.17, which is of 0.121.

Hence:

1 - 0.121 = 0.879.

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Only the transitive relation is true for the provided relation for (x, y) R if x y defined on the set of positive integers.

Assuming (x, y), R

To determine whether or not a relation is transitive, symmetric, antisymmetric, reflexive, or a partial order:

If (x, x)R for all x R x x for all x R, which is false.

b. Symmetric: For all (x, y) R, if "x" and "y" are related, then "y" is also related to "x."

In this case, x y y x for all (x, y) R, which is false.

c. Antisymmetric: If "x" and "y" are related, then "x" equals "y" for all (x, y) R.

In this case, x y and y x x = y are false.

not in opposition.

c. Transitive: If "x" and "y" are related, then

For all values of x, y, and z R, 'x' is connected to 'z'.

For any x, y, and z R, x y, y z x z.

True.

Therefore, only the transitive relation for the given relation for (x, y) R if x y defined on the set of positive integers is true.

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Answer:

36.96 calories

Answer:

there is no solution to the equation

Answer:

7 kg

Step-by-step explanation:

Newton's second law tells us that Force = Mass * Acceleration, also known as F = ma.

The downward acceleration due to gravity on Earth is usually taken to be 9.8 ms^-1.

Substitute the values into the equation:

68.6 = m * 9.8

Rearrange and simplify:

m = 68.6 / 9.8

m = 7 kg

Answer:  Based on the information you provided, it seems that the McQuires had a total of $793 in their account on Friday, and their wife wrote a check for $1,233.34 the next day. If this check cleared the bank, their account balance would be $793 - $1,233.34 = -$440.34.

Area under the given standard normal curve for the z-score between 0.97 to 1.26 is equal to 0.06219.

As given in the question,

Given values to find area under the standard normal curve = 0.97 to 1.26

From the table of area under the given standard normal curve

z - score of 0.97 is equal to 0.33398

z-score of 1.26 is equal to 0.39617

Area under given standard normal curve between z-scores 0.97 and 1.26

= P ( 0.97 < z < 1.26 )

= 0.39617 - 0.33398

= 0.06219

Therefore, the area under the given standard normal curve for the z-score between 0.97 to 1.26 is equal to 0.06219.

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(a) The printer will print 3.5 pages per minute.

(b) It will plant 0.13 acres of seed per pound.

What is a unit rate?

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.

(a) If a color printer prints 14 pages in 4 minutes.

   So it will print = 14/4

                           = 3.5 pages per minute

(b) If it takes 23 pounds of seed to completely plant a 3 - acre field

  So it can plant = 3/23

                           = 0.13 acres per pound.

Hence,

(a) The printer will print 3.5 pages per minute.

(b) It will plant 0.13 acres of seed per pound.

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Using the Leading Coefficient Test the end behavior of the given function f(x) = −x⁴ − 2x³ + 2x² − 5 is

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = −x⁴ − 2x³ + 2x² − 5

The end behavior is determined by the leading Coefficient =  −x⁴  and it is described as

x ⇒ ∞ f(x) ⇒ ∞

x ⇒ -∞ f(x) ⇒ -∞

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do 180-32=148 and then do 148÷2=74