Mathematics High School

## Answers

**Answer 1**

The graphical representation that is best and most appropriate for the data is **Box plot,** because the **median** can easily be determined from the large set of data. That is **option A.**

What is a box plot ?

The **box plot** is a type of graphical representation of data that gIves more than one detail about the data set such as;

minimum, first quartile, **median**, third quartile, and maximum.

Box plots allow you to compare multiple data sets better than others dues to the above listed features that it has.

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## Related Questions

What is the common differences for

3, 7, 11, 15, 19, 23

### Answers

**Step-by-step explanation:**

Each term goes UP by 4 from the one before it

common difference, ** d = 4 **

The diameter of a circle is 12.5 cm. What is the circumference of the circle? Question 1 options: 19.63 cm 35. 25 cm 39.25 cm 78.5 cm please tell me quick!!!!

### Answers

**Answer:**

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.

In this case, the diameter of the circle is given as 12.5 cm.

Substituting this value into the formula, we get:

C = π(12.5)

C = 39.25 cm

Therefore, the circumference of the circle is 39.25 cm.

Hence, the answer is** 39.25 cm.**

A counter in Adriana's kitchen is 1 meter wide and 3 meters long. Adriana wants to replace the counter with a granite countertop, which would cost $261.00 per square meter. How much would the granite countertop cost?

### Answers

** **The** granite** countertop would **cost** $783.00.

**Finding the cost of granite: **

To find the** cost **of granite find the amount of granite that can be used for the entire **kitchen**.

Since the kitchen floor is in a **rectangle** shape find the area of the kitchen floor using the** area **of a rectangle. Which will equal the amount of granite used for the kitchen.

Use the formula for the cost of the countertop, which is the **product **of the area, and the cost per **square meter**, to determine the total cost.

Here we have

A counter in Adriana's kitchen is 1 m wide and 3 m long.

Hence, the **area** of the countertop can be found by multiplying the length and the width:

Area of kitchen = **length **x width = 3 m x 1 m = 3 m²

The cost of the granite is given by $ 261.00 per square meter

The cost of the granite countertop will equal the** product **of the area and the cost per square meter:

Total Cost = 3 m² x $261.00/m² = $783.00

Therefore,

The** granite** countertop would **cost** $783.00.

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Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. What is the probability that Sky scored at least two goals? Express your answer as a common fraction.

### Answers

To solve this problem, we can use the binomial probability distribution. Let's define a** "success"** as scoring a goal and a **"failure"** as missing a goal.

Then, each attempt by Sky can be considered a **Bernoulli trial **with **probability of success** p = 1/2.

Let X be the number of goals that Sky scores in five attempts. Then, X follows a **binomial distribution** with parameters n = 5 and p = 1/2.

To find the probability that **Sky scores** at least two goals, we need to calculate the probability of the following events:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

We can use the **binomial probability formula** to calculate these probabilities:

P(X = k) = (n choose k) * [tex]p^k[/tex] *[tex](1-p)^(n-k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of **n distinct items.**

Using this formula, we get:

P(X = 2) = (5 choose 2) * [tex](1/2)^2[/tex] * [tex](1/2)^3[/tex] = 10/32

P(X = 3) = (5 choose 3) * [tex](1/2)^3[/tex] * [tex](1/2)^2[/tex] = 10/32

P(X = 4) = (5 choose 4) * [tex](1/2)^4[/tex] *[tex](1/2)^1[/tex] = 5/32

P(X = 5) = (5 choose 5) * [tex](1/2)^5[/tex] * [tex](1/2)^0[/tex] = 1/32

Therefore, the probability that Sky scores at least two goals is:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = (10 + 10 + 5 + 1)/32 = 26/32 = 13/16

So the probability that Sky scored at **least two goals is 13/16.**

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The total **probability** of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. So the probability that Sky scored at least two goals is 13/16.

To find the probability that Sky scored at least two goals, we can use complementary probability, which means finding the **probability** that she scored fewer than two goals (either 0 or 1 goal) and subtracting that from 1.1.

Probability of scoring 0 goals: Since there are 5 attempts and she is equally likely to make a goal or miss (1/2 chance for each), the probability of missing all 5 is (1/2)^5 = 1/32.2.

Probability of scoring 1 goal: Sky could score in any of the 5 attempts, so we need to consider all possible ways of scoring one goal.

There are 5 ways (score in the 1st, 2nd, 3rd, 4th, or 5th attempt). The probability for each of these scenarios is (1/2)^5 = 1/32.

Therefore, the total probability of **scoring** 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

To express this as a common fraction, we can **simplify** it by **dividing** both the numerator and the denominator by their greatest common divisor (GCD), which is 2:26/32 = (26/2) / (32/2) = 13/16So the probability that Sky scored at least two goals is 13/16.

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I need help, I thought I understood it but this doesn't make any sense

### Answers

**Answer:**

**The corresponding sides:**

[tex]NO[/tex]**≅**[tex]ZW[/tex]

[tex]PM[/tex]**≅**[tex]XY[/tex]

[tex]MN[/tex]**≅**[tex]YZ[/tex]

[tex]OP[/tex]**≅**[tex]WX[/tex]

**The corresponding angles:**

[tex]< M[/tex]**≅**[tex]< Y[/tex]

[tex]< P[/tex]**≅**[tex]< X[/tex]

[tex]< O[/tex]**≅**[tex]< W[/tex]

[tex]< N[/tex]**≅**[tex]< Z[/tex]

Joanna rented a bike for Friday and Saturday. The cost of renting a bike on the weekdays is $7. She used a coupon and paid half the amount on Friday. The amount she paid on Saturday was $4 less than twice the regular cost of renting a bike on weekdays.

How much did she spend on renting the bike?

A.

$13.50

B.

$32.00

C.

$21.50

D.

$24.00

### Answers

The **amount** Joanna spent on renting the bike is $17.50 (option A).

What is amount?

The term "amount" can refer to a quantity or a numerical value of something. In essence, the term "amount" refers to a specific quantity or **number** of something.

According to given information:

The regular cost of renting a bike on Friday is $7, but Joanna only paid half that amount, which is $7/2 = $3.50.

Let's call the regular cost of renting a bike on Saturday "x". Then, according to the problem, Joanna paid $4 less than **twice** the regular cost of renting a bike on weekdays, which can be written as:

Cost on Saturday = 2($7) - $4 = $10

We know that Joanna paid $10 for renting the bike on Saturday, so we can solve for x in the **equation**:

Cost on Saturday = x - $4

$10 = x - $4

x = $14

So the regular cost of renting a bike on Saturday is $14.

Therefore, the total amount Joanna spent on renting the bike is:

$3.50 (for Friday) + $14 (for Saturday) = $17.50

Answer: The amount Joanna spent on renting the bike is $17.50 (option A).

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What is the measure of angle A in this triangle?

### Answers

**Answer:**

The Answer is 40°

**Step-by-step explanation:**

Base angles of an isosceles triangle are equal

x+30=70

x=70-30

x=40°

so,

<C=70°

<A+<B+<C=180°

let <A be X

X+70+70=180°

X+140=180°

X=180-140

X=40°

X=2x-10

40°=2x-10

2x=40+10

2x=50°

divide both sides by 2

x=25°

The measures of variation shows how data _ and includes what things

### Answers

The** measures **of **variation** show how data is spread out or dispersed and include range, variance, standard deviation, IQR, percentiles, and coefficient of variation.

The measures of variation show how data is** spread out** or **dispersed **from its average or **central tendency.** Measures of variation give information on the diversity, range, and distribution of the data. They include the following things-

**Range**: The difference between the largest and lowest values in the dataset.**Variance:** The normal of the squared differences from the mean.**Standard deviation**: The square root of the friction, which measures how important the data is spread out from the mean.**Interquartile Range( IQR):** The difference between the third quartile and the first quartile, which provides information on the range of the middle 50 of the data.**Percentiles**: Measures that indicate the position of a particular value relative to the rest of the data, similar to the standard, quartiles, and deciles.**Coefficient of Variation:** The rate of the standard divagation to the mean, which is a relative measure of variation that compares the spread of data to its average or central tendency.

By assaying the measures of variation, we can gain perceptivity into the nature and characteristics of the data and draw conclusions grounded on the degree of variation present.

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on september 23, 2013, president obama had an approval rating of 46% (according to a gallup poll). suppose a sample of 100 americans is taken that same week. what is the probability that the sample proportion has between a 42% and a 47% approval rating? (use 4 or more decimal places in your computations!)

### Answers

If a sample of 100 **Americans **is taken that same week, then the **probability **that "sample-proportion" has between a 42% and a 47% approval rating is 0.7693 or 76.93%.

To calculate the probability that the **sample-proportion** falls between 42% and 47% for a sample of 100 Americans, we use the standard normal distribution.

The Sample size (n) is = 100,

The Sample proportion (p) = 46% or 0.46,

The "**Standard-deviation**" (σ) = √(p×(1-p)/n) = √(0.46×(1-0.46)/100) ≈ 0.0497,

We now calculate the "z-scores" corresponding to the lower and upper bounds of the desired range,

We know that, the value of "z" is (x - μ)/σ,

where x = desired proportion, μ = **mean **proportion, and σ = standard deviation,

So, The probability that the sample proportion has between a 42% and a 47% "**approval-rating**", is written as :

⇒ P(0.42 < x < 0.47) = P[(0.42 - 0.46)/0.0497 < z < (0.47 - 0.46)/0.0497],

⇒ P(0.42 < x < 0.47) = P[-0.807 < z < 2.015],

⇒ P(0.42 < x < 0.47) = 0.9783 - 0.209,

⇒ P(0.42 < x < 0.47) = 0.7693,

Therefore, the required probability is 0.7693 or 76.93%.

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4.834 * 10 ^ 9 as an ordinary number

### Answers

Answer:

4834000000

That is your answer.

What is the value of g(x)=x^2+4x

### Answers

The value of g(x) = x^2 + 4x depends on the value of x.

If, for example, x = 2, then:

g(2) = 2^2 + 4(2) = 4 + 8 = 12

If x = -3, then:

g(-3) = (-3)^2 + 4(-3) = 9 - 12 = -3

In general, we can evaluate g(x) for any value of x by substituting that value into the expression x^2 + 4x.

.

The method of completing the square can be used to transform the equation x² - 6x + 8 = 0 into the form (x-p)² = q

### Answers

**Answer:**

p = 3, q = 1

**Step-by-step explanation:**

well, let's think about what (x - p)² actually is.

let's do the multiplication (what a square is) :

(x - p)(x - p) = x² - px - px + p² = x² - 2px + p²

now, we compare the theoretical equation to the actual equation :

x² - 6x + 8 = 0

x² - 2px + p² = q

x² = x² check

-6x = -2px

-6 = -2p

p = -6/-2 = 3

that gives us

x² - 6x + 9 = q

compare this to

x² - 6x + 8 = 0

we subtract the second equation from the first

x² - 6x + 9 = q

- x² - 6x + 8 = 0

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

0 0 1 = q

there you have it.

Point A = (5,4). If you rotated A 90 degrees about the point (2,-1), what would be the coordinates of A'?

### Answers

Point A = (5,4). If you **rotated **A 90 degrees about the point (2,-1), the coordinates of A' is (-1,2).

Describe Rotation?

Rotation is the process of rotating an object or a point around a fixed point or axis. In mathematics, rotation refers to a **transformation **that preserves the size and shape of an object while changing its orientation. It is a basic geometric transformation that is used in various fields, including mathematics, physics, engineering, and computer graphics.

In a two-dimensional space, a rotation is typically described by an angle of rotation and a fixed point, which is known as the center of rotation. The angle of rotation represents the amount by which the object is rotated, while the center of rotation is the point around which the object is rotated. In a three-dimensional space, a rotation is described by an axis of rotation and an angle of rotation.

To rotate point A 90 degrees counterclockwise about the point (2,-1), we can use the following formula:

A' = (x', y') = (a + (x - a) cosθ - (y - b) sinθ, b + (x - a) sinθ + (y - b) cosθ)

where (a,b) is the center of rotation and θ is the **angle **of rotation (90 degrees in this case).

Substituting the given values, we get:

a = 2, b = -1, x = 5, y = 4, θ = 90 degrees

x' = 2 + (5 - 2) cos(90) - (4 + 1) sin(90) = 2 - 3 = -1

y' = -1 + (5 - 2) sin(90) + (4 + 1) cos(90) = -1 + 3 = 2

Therefore, the **coordinates **of A' are (-1, 2).

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DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!! 20 POINTS

Students in a high school mathematics class decided that their term project would be a study of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as “strict”. They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students.

1. Describe the parameter of interest and a statistic the students could use to estimate the parameter.

2. Is the best design for this study a sample survey, an experiment, or an observational study? Explain your reasoning.

3. The students quickly realized that, as there is no definition of “strict”, they could not simply ask a student, “Are your parents or guardians strict?” Write three questions that could provide objective data related to strictness.

4. Describe an appropriate method for obtaining a sample of 100 students, based on your answer in question 1.

### Answers

The **parameter** of interest in this scenario is the **proportion **of students in the school who think of their parents or guardians as "strict".

What is the statistical parameter?

Focussing on the strict guardians is a population parameter, but since it is impractical to survey all 1000 students in the school, the students plan to obtain data from a sample of students.

To estimate this **population **proportion, the students could use the sample proportion as a **statistic**. They can randomly select a sample of students from the school and ask them if they consider their parents or guardians as "strict". The proportion of students in the sample who say "yes" can be used as an estimate of the proportion of all students in the school who consider their parents or guardians as "strict". The sample proportion is a statistic that provides an estimate of the population parameter of interest.

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An angle measures 37.6° more than the measure of its complementary angle. What is the measure of each angle?

### Answers

Therefore , the solution of the given problem of **angles** comes out to be the complementary angle measures 26.2 degrees.

What does an angle mean?

The largest and smallest walls of a **skew** are determined by the intersection of the lines connecting its ends. Two pathways might meet at a crossroads. Another result of two entities interacting is an angle. If anything, they resemble dihedral **shapes**. Two line beams can be arranged in a variety of ways between their ends to form a two-dimensional curve.

Here,

Let's write x degrees for the initial angle's measure.

The first angle is measured to be 37.6 degrees greater than its complimentary angle based on the information provided.

Because complementary angles sum to 90 degrees, we may construct the equation shown below:

=> x = (90 - x) + 37.6

If we simplify, we get:

=> x = 90 - x + 37.6

=> x + x = 90 + 37.6

=> 2x = 127.6

When you divide both sides by 2, you get:

=> x = 127.6 / 2

=> x ≈ 63.8

Therefore, the initial angle is roughly 63.8 degrees in size.

By deducting the first angle's measurement from 90 degrees, we may determine the complementary angle's measurement:

=> 90 - x = 90 - 63.8 = 26.2

Consequently, the complementary angle measures 26.2 degrees.

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Select the correct answer. Solve the following equation for x. x2 - 36 = 0 A. x = 1; x = -36 B. x = -1; x = 36 C. x = -6; x = 6 D. x = -18; x = 18

### Answers

**Answer:The solution is x= +6, -6.**

**Step-by-step explanation:**

**What is Quadratic equation?**

**A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.**

**The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written.**

**Roots of a Quadratic Equation**

**The roots of a quadratic equation are the two values of x, which are obtained by solving the quadratic equation. These roots of the quadratic equation are also called the zeros of the equation.**

**Given:**

**x² - 36 =0**

**x² = 36**

**x= √36**

**x= ±6**

**hence, the solution is x= +6, -6.**

Garlan makes a commission based upon the value of all he sells at his new job. For example in 30 minutes of his first workday, he earned $15 in commission for selling $150 worth of shoes.

### Answers

If Garlan earned $15 in commission for selling $150 worth of shoes, then his commission rate is 10% (15/150 = 0.1 or 10%). This means that for every dollar worth of shoes he sells, he earns 10 cents in commission.

To find out how much he earned in commission for a different amount of sales, you can multiply the total value of the sales by his commission rate. For example, if he sells $300 worth of shoes, his commission would be:

Commission = Total value of sales x Commission rate

Commission = $300 x 0.1

Commission = $30

So Garlan would earn $30 in commission for selling $300 worth of shoes.

Can someone help me fast with this please!?!?!

If s(d) represents the number of songs downloaded in a year d, what is the interpretation of s(2020) = 5,220,000.

A. 5,220,000 songs were downloaded in the year 2020.

B. There is not enough information to interpret the information.

C. In the year 2020 $5,220,000 was earned from downloaded songs.

D. 2,020 songs were downloaded at a cost of $5,220,000.

### Answers

the correct answer is A.

5,220,000 songs were **downloaded **in the year 2020.

If s(d) represents the number of songs downloaded in a year d, what is the interpretation of s(2020) = 5,220,000?

The interpretation of s(2020) = 5,220,000 is "5,220,000 songs were downloaded in the year 2020".

Therefore, the correct answer is A. 5,220,000 **songs **were downloaded in the year 2020.

**Interpretation **refers to the process of explaining or giving meaning to information, data, or phenomena. It involves analyzing and making sense of information to draw **conclusions **or make decisions based on the findings.

Interpretation can involve subjective judgment and may depend on the perspective, assumptions, or biases of the interpreter.

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I am giving all my points if you answer this asap! You can make any polynomial you want just use one from column A and one from B. PLEASE HELP!!!!!

You are going to design an advertisem*nt for a new polynomial identity that you are going to invent. Your goal for this activity is to demonstrate the proof of your polynomial identity through an algebraic proof and a numerical proof in an engaging way! Make it so the whole world wants to purchase your polynomial identity and can't imagine living without it!

You may do this by making a flier, a newspaper or magazine advertisem*nt, making an infomercial video or audio recording, or designing a visual presentation for investors through a flowchart or PowerPoint.

You must:

Label and display your new polynomial identity

Prove that it is true through an algebraic proof, identifying each step

Demonstrate that your polynomial identity works on numerical relationships

Warning! No identities used in the lesson may be submitted. Create your own using the columns below. See what happens when different binomials or trinomials are combined. Square one factor from column A and add it to one factor from column B to develop your own identity.

Column A

(x − y)

(x + y)

(y + x)

(y − x)

Column B

(x^2 + 2xy + y^2)

(x^2 − 2xy + y^2)

(ax + b)

(cy + d)

### Answers

The **polynomial identity **created from the **columns **is (x - y)(x^2 + 2xy + y^2) + (x + y)(x^2 - 2xy + y^2) = 2x^3 - 2xy^2

Creating a polynomial identity

Introducing the new **polynomial identity**:

(x - y)(x^2 + 2xy + y^2) + (x + y)(x^2 - 2xy + y^2) = 2x^3 - 2xy^2

Algebraic proof:

Expanding the **left side **of the equation:

(x^3 - xy^2 + 2x^2y + xy^2 + y^3) + (x^3 + xy^2 - 2x^2y + xy^2 + y^3)

= 2x^3 + 2y^3

Simplifying the left side of the **equation**:

2x^3 - 2xy^2 = 2x^3 - 2xy^2

Therefore, the **polynomial identity **is true.

Numerical proof:

Let x = 2 and y = 3.

(x - y)(x^2 + 2xy + y^2) + (x + y)(x^2 - 2xy + y^2) = 2x^3 - 2xy^2

(2 -3y)(2^2 + 2(2)(3) + (3)^2) + (2 + 3)(2^2 - 2(2)(3) + 3^2) = 2(2)^3 - 2(2)(3)^2

-20 = -20

Therefore, the **numerical proof **also shows that the polynomial identity is true.

Advert

Invest in our new **polynomial identity **today! With this identity, you can simplify complex **polynomial** expressions and solve equations in a much easier and quicker way.

Say goodbye to tedious **algebraic manipulations **and hello to the future of **polynomial **algebra!

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which of the following descriptive measures may be calculated when data has been grouped into class intervals in a frequency distribution? a. the mean for grouped data. b. all of these measures can be computed. c. the variance for grouped data. d. the standard deviation for grouped data.

### Answers

The **mean **for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution. (Option A)

When data has been grouped into class **intervals**, it is not possible to calculate the exact mean of the data. Instead, we use the midpoint of each class interval as a representative value for that interval. Then, we calculate the weighted average of these midpoints to find the mean for grouped data.

Options C and D, the **variance **and standard deviation, respectively, cannot be directly computed from grouped data. However, we can estimate them using the assumed normal distribution of the data within each class interval and the mean for grouped data.

Therefore, the correct answer is option A: the mean for grouped data can be calculated when data has been grouped into **class intervals** in a frequency distribution.

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Find the circumference of each circle with a diameter of 20.2 in. Use 3.14 for the value of Pi. Round your answer to the nearest tenth. IM IN 7TH

### Answers

**Answer:**

3.14×10.1×10.1

3.14×102.01

320.311

=320.300

for the following data on non-conforming tennis balls weight, what is the centerline? index n np p 1 180 24 0.133 2 180 28 0.156 3 180 21 0.117 4 180 26 0.144

### Answers

The** centerline** for the control chart will be 0.135.

The centerline of a** control chart** is the **horizontal** line that represents the process mean, which is calculated as the **average** of the sample means.

In this case, we can calculate the sample **means** by multiplying the sample size n by the sample** proportion **p for each sample and then **summing** these values across all samples. We can then divide this sum by the total sample size (4*180) to get the overall sample mean.

The calculations are shown below:

Sample 1 mean = n1 * p1 = 180 * 0.133 = 23.94

Sample 2 mean = n2 * p2 = 180 * 0.156 = 28.08

Sample 3 mean = n3 * p3 = 180 * 0.117 = 21.06

Sample 4 mean = n4 * p4 = 180 * 0.144 = 25.92

Overall sample mean = (23.94 + 28.08 + 21.06 + 25.92) / (4*180) = 0.135

Therefore, the centerline for the control chart would be 0.135.

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a researcher wants to determine if extra homework problems help 8th grade students learn algebra. an 8th grade class is divided into pairs and one student from each pair has extra homework problems and the other in the pair does not. after 2 weeks, the entire class takes an algebra test and the results of the two groups are compared. to be a valid matched pair test, what should the researcher consider in creating the two groups?

### Answers

The **researcher **should consider the following steps when creating the two groups: Random assignment, Pairing students with similar abilities, Controlling for potential confounding variables,

Collecting data and analyzing results.

Random assignment:

To minimize any **potential **bias, the researcher should randomly assign one student from each pair to receive extra homework problems while the other does not.

Pairing students with similar abilities:

In order to make a valid comparison, the researcher should pair students with similar algebra skills or previous performance in the subject.

This way, any observed differences in the test results are more likely to be due to the extra homework rather than differences in ability.

Controlling for potential confounding variables:

The researcher should control for any other factors that could **influence **students' algebra test results, such as attendance, study habits, and teacher quality.

After the two-week period, the researcher should collect the test scores of both groups and compare their performance.

This can be done using **statistical **methods, such as a paired t-test, to determine if there is a significant difference between the groups.

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the following declaration statement is constructed incorrectly. correct the statement.int[] hours = 8, 12, 16;

### Answers

The corrected **statement **should look like this:

```java

int[] hours = {8, 12, 16};

```

It looks like you are trying to create an **integer **array in Java called "hours" and initialize it with the values 8, 12, and 16. The given statement has incorrect syntax.

Declare the integer array using "int[]" followed by the variable name "hours".

This tells the Java compiler that you want to create an array of integers called "hours".

Use the assignment operator "=" to assign values to the array.

Enclose the values you want to assign to the array within curly braces "{" and "}" and separate each value with a comma.

The corrected statement should look like this:

```java

int[] hours = {8, 12, 16};

```

Now, the "hours" integer array is **initialized **correctly with the given values.

The syntax for declaring and initializing an integer array in Java is:

```java

data Type[] array

Name = {value1, value2, value3, ...};

```

In this case, "data Type" is "int", "array

Name" is "hours", and the values are 8, 12, and 16.

Remember to keep your code clean and concise to avoid **syntax **errors and make it easier for others to understand.

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What is -7(7-2p)=-22+5p

### Answers

To solve the equation -7(7-2p)=-22+5p, you can start by distributing the -7 on the left-hand side of the equation:

-7(7-2p) = -49 + 14p

Substituting this expression into the original equation gives:

-49 + 14p = -22 + 5p

Next, you can simplify by moving all the terms with p to one side of the equation, and the constant terms to the other side. Adding 49 to both sides gives:

14p = 27 + 5p

Subtracting 5p from both sides gives:

9p = 27

Finally, you can solve for p by dividing both sides by 9:

p = 3

Therefore, the solution to the equation -7(7-2p)=-22+5p is p = 3.

**Step-by-step explanation:**

-49+14p=-22+5p

-49+22=5p-14p

-27=-9p

p=3

Discuss the similarities and the differences between the Empirical Rule and Chebychev's Theorem What is a similarity between the Empirical Rule and Chebychev's Theorem? 0 A. O B. ° C. Both apply only to symmetric and bell-shaped distributions. Both do not require the data to have a sample standard deviation. Both calculate the variance and standard deviation of a sample. D. Both estimate proportions of the data contained within k standard deviations of the mean What is a difference between the Empirical Rule and Chebychev's Theorem? A. The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions O B. Chebychev's Theorem estimates proportions of data contained within infinite standard deviations and the Empirical Rule has a limit of 5 standard deviations ° C. The Empirical Rule assumes a small data set (less than 50 values) where Chebychev's Theorem has no limit on data size. O D. Chebychev's Theorem applies only to distributions which are approximately symmetric or bell-shaped and the Empirical Theorem has no restrictions

### Answers

A. The correct option for similarity is option D - Both estimate proportions of the data contained within k **standard deviations** of the mean.

Both the Empirical Rule and Chebyshev's Theorem are used to estimate the **proportion **of data contained within a certain number of standard deviations from the mean.

Therefore, option 'D' is the correct answer: Both estimate proportions of the data contained within k standard deviations of the **mean**.

B. The correct option for difference is option A - The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and **Chebychev's **Theorem makes no assumptions.

The Empirical Rule assumes that the distribution is approximately symmetric and bell-shaped, while Chebyshev's Theorem makes no assumptions about the shape of the distribution.

Another difference is that the **Empirical Rule** is only applicable for normal distributions, while Chebyshev's Theorem can be applied to any distribution.

Therefore, option 'A' is the correct answer: The Empirical Rule assumes the distribution is approximately **symmetric **and bell-shaped and Chebychev's Theorem makes no assumptions.

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Find the length of each segment.

13. YW and WZ

### Answers

The **length** of each **segment** is:

YW = 5 units

WZ = 8 units

How to find the length of each segment?

The** length** of each **segment **can be found by using "bisector of an angle in a triangle theorem".

The** theorem** states that "the bisector of an angle in a **triangle** theorem divides the opposite sides in the ratio of the sides containing the angle".

Applying the theorem on the given triangle, we can say:

XY/XZ = YW/WZ

8/12.8 = (t/2)/(t-2)

8(t-2) = 12.8(t/2)

8t - 16 = 6.4t

8t - 6.4t = 16

1.6t = 16

t = 10

YW = t/2

YW = 10/2

YW = 5 units

WZ = t - 2

WZ = 10 - 2

WZ = 8 units

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Solve for X then find the measure of all the angles. The question is in the picture.

### Answers

The **value **of x is 10, and the measure of the two **angles **with x is 50°

How to find the value of x?

We can see that the two angles in the image are** vertical angles**, so their measure is the same, then we can write:

5x = 7x - 20

Solving the** linear equation** we get.

20 = 7x - 5x

20 = 2x

20/2 = x

10 = x

That is the value of x.

The measures of the two angles are:

5x = 5*10 =50 degrees.

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in a binomial experiment, the . a. probability of success does not change from trial to trial b. probability of success does change from trial to trial c. probability of success could change from trial to trial, depending on the situation under consideration d. probability of success is always the same as the probability of failure

### Answers

In a **binomial experiment**, the option (a) probability of success does not change from trial to trial

In a binomial experiment, each trial is** independent **of the previous trials, and the probability of success remains constant throughout the experiment. Therefore, option (a) is correct.

Option (b) is incorrect because the** probability** of success does not change from trial to trial.

Option (c) is partially correct because the probability of **success** could change from trial to trial in certain situations, but this would not be considered a binomial experiment.

Option (d) is incorrect because the probability of success and **failure** must add up to 1 in a binomial experiment, but they are not necessarily equal to each other.

Therefore, the correct option is (a) probability of success does not change from trial to trial

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Find the value of x and y

### Answers

**Answer: x = 40 degrees and y = 80 degrees**

**Step-by-step explanation: Using the fact that the sum of the interior angles of a triangle is 180 degrees, we can find that x = 40 degrees in the triangle on the left. For the polygon on the right, we can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees to find that y = 80 degrees. **

**Therefore, x = 40 degrees and y = 80 degrees.**