Mathematics High School

## Answers

**Answer 1**

**Answer: 9**

**Step-by-step explanation: It's 9 because both can be divided by 9, as the largest time without going over. As you can see, 81 divided by 9 is 9, and 72 divided by 9 is 8. 8 and 9 are the closest they can be without going over 81 and 72, so it's 9. I hope this helps!**

**Answer 2**

The **GCF** of the **numbers** 81 and 72 is 3², which equals 9.

To find the greatest common factor (**GCF**) of 81 and 72, we can use several methods.

One common approach is to factorize both numbers and identify the **common factors.**

The prime factorization of 81 is 3⁴, and the prime factorization of 72 is 2³×3².

To find the **GCF**, we look for the highest power of common prime factors in both numbers.

The highest power of the common** prime factor** (3) is 3², since it appears as a factor in both numbers.

Therefore, the **GCF** of 81 and 72 is 3², which equals 9.

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## Related Questions

Is there a triangle whose sides have lengths 10.2 cm 5.8 cm and 4.5 cm a yes b no?

### Answers

Yes , **there can be a triangle** that can have the side lengths as 10.2cm , 5.8cm and 4.5cm .

it is only possible to **form a triangle **, when the sum of the any two sides of the triangle is greater than the third side of triangle .

the **side lengths** of the triangle are given as : 10.2cm , 5.8cm and 4.5cm ;

So , on **adding any two side lengths** and comparing it with third side ,

we get ;

⇒ 10.2 + 5.8 = 16 > 4.5 ; True

⇒ 5.8 + 4.5 = 10.3 > 10.2 ; True

⇒ 10.2 + 4.5 = 14.7 > 5.8 ; True .

All the three sides follow the condition ,

Therefore , the given side lengths form a triangle .

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To support a triangular kite, Hana

attaches thin strips of wood from each vertex

perpendicular to the opposite edge. She

then attaches the kite's string at the point

of concurrency. To calculate the point of

concurrency, she determines the coordinates

of each vertex on a coordinate plane. What

are the coordinates where the wood strips

cross? Round your answer to the nearest

hundredth.

### Answers

The slope of the** line parallel** to BC is 18/7 * (x + 0) is 18/7 y. the orthocenter is where concurrency occurs.

What is the slope of the line parallel to BC ?

Hana fastens tiny wood strips perpendicular to the opposing edge from each vertex. As a result, the orthocenter is where concurrency occurs.

Given: Hana fastens small wood strips** perpendicular **to the opposing edge from each vertex.

As a result, the orthocenter is where concurrency occurs.

Think of the ABC triangle with coordinates.

A(0, 0) B(0, 58), C(36, 44) (36, 44)

first determine the angles of the triangle's two sides.

Formula for slope: (y 2 - y 1)/(x 2 - x 1)

slope of the AB& A(0, 0) matrix side matrix, Slope of BC side B(0,58), B(0, 58) = (58 + 0)/(0 + 0) = 0 C(36,44) = (44 - 58)/(36 + 0) = - 14/36 = - 7/18

Use Equation of the altitude perpendicular to AB's point slope form after that.

The vertex in opposition to AB is point C.

A line perpendicular to AB has a slope of zero.

y-y 1 = m(x-x 1) y-44 = 0(x-36) y = 44

Altitude Equation Perpendicular to BC

The vertex opposite BC is Point A. A line perpendicular to BC has a **slope **of 18/7.

y + 0 = 18/7 * (x + 0)

y = 18/7 * x

Change the value of y in the equation above. y = 18/7 * x 44 = 18/7 * x

x = 17.11 The slope of the line parallel to BC is 18/7 * (x + 0) = 18/7 y.

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howard collected data from a random sample of 600 people in his town asking whether or not they attend church. based on the results, he reports that 48% of the people in his state attend church. why is this statistic misleading?

### Answers

This **statistic** is **misleading** because Howard surveys only his department and not **members** of all the **departments** that the company has.

When **studying** anything from a **population**, it is usual practice in statistics to **identify** a sample of that **group**.

However, the **sample** has to be **representative**.

For **example**: I want to estimate the **proportion** of New York state residents who are Buffalo Bills fans. So I ask, let's say, 1000 randomly selected Buffalo residents whether they are Buffalo Bills fans, and expand this to the entire **population** of New York State residents. This is not representative of all New York State residents, just Buffalo **residents**.

**Howard** wants to know the **proportion** of **employees** of a company who use the company's **healthcare**. He asks only his **department**. However, a company as multiple departments, which leads to the **statistics** found in Howard's **survey** being **misleading**.

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What is the relationship between doubling and halving?

### Answers

The **relationship **between Doubling and halving is that in halving we simply half one of the factors and in doubling we double the other.

The **Doubling and Halving** is a technique that is commonly used in Multiplication of two numbers .

Let us understand the Relationship between Doubling and Halving with help of an example ;

**Example **: To solve 25×16, it is not that simple to directly multiply these ,

By using the Doubling and Halving method ,

we could **double the number** 25 to make it 50 and

then **half the number** 16 to make it 8.

So , the equivalent expression becomes , [tex]50\times8[/tex] ,which is much easier to solve , that is 400 .

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The graph h shows the height, in meters, of a rocket t seconds after it was launched

### Answers

a) H0 = 15 m, is the** initial height**, the height of the rocket at time 0 s.

b) D = [0,5]

c) R = [0,35]

What is a domain?

The set of inputs that a **function **will accept is known as the domain of the function in mathematics. The range of values that we are permitted to enter into our function is known as the **domain **of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Here, we have

a) H0 is the initial height. It means the height of the rocket at time 0 s.

This value is 15 m.

b) The domain is all values of t between 0 and 5 seconds.

D = [0,5]

c) The range is all values of height from 0 to 35 meters.

R = [0,35]

Hence, a) H0 = 15 m, is the initial height, the height of the rocket at time 0 s.

b) D = [0,5]

c) R = [0,35]

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Complete question is: The graph H shows the height, in meters, of a rocket 1 seconds after it was launched.

a. Find H0). What does this value

represent?

b. Describe the domain of this function.

c. Describe the range of this function.

Answer:

Step-by-step explanation:

.

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function?

Part B: What does the y-intercept of the graph of the function f(d) represent?

### Answers

Given: f(d) = 11(1.01)d, which will display **equation** of the radius of the algae.

An easy equation is what?

Simple Equation: What Is It? two phrases along either side of a sign are connected by a **mathematical **equation. Usually, it only includes one **variable **and an equal sign. Example: 2x – 4 = 2.

Solution:

Part A: 11.79 = 11(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d= 11.79/11 (1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d(1.01)d= 1.071818 d = log 1.0718

When domain = 0 d = 0 f(0) = 11, the y-intercept is found (Part B) (1.01)

^{0}11(1.01)0\s= 11 x 1 = 11 f(d) = 11

Part C: Average rate of change, f/d = (f(7) - f(2)) / (7 - 2) = (11(1.01)711(1.01)211(1.01) 2) / 5 = 0.57 / 5 = 0.114

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Given: f(d) = 11(1.01)d, which will display equation of the **radius **of the algae.

An easy equation is what?

Simple Equation: What Is It? two phrases along either side of a sign are connected by a mathematical **equation**. Usually, it only includes one **variable **and an equal sign. Example: 2x – 4 = 2.

Solution:

Given:

f(d) = 11(1.01)d

To Find:

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function?

Part B: What does the **y-intercept** of the graph of the function f(d) represent?

Part A:

[tex]11.79 = 11(1.01)^{d}11(1.01)d\\(1.01)^{d}(1.01)d\\= 11.79/11(1.01)^{d}(1.01)\\= 1.071818\\d = log 1.071818 / log 1.01\\d = 6.97[/tex]

Part B:

y-intercept is obtained when domain = 0

[tex]d = 0 ⇒ f(0) = 11(1.01)^{0}11(1.01)0\\= 11 x 1 = 11\\f(d) = 11[/tex]

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if r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to ?

a. 3 (6)-1/2(6) +1

b. (6)/ 2(6)+1

c. 36-1/26+1

d. (6)-1/(6)+1

### Answers

If the expression [tex]r(x) = 3x - 1[/tex] and the expression [tex]s(x) = 2x + 1[/tex] , then the **expression equivalent to** [tex]\frac{r}{s} (6)[/tex] is (a) [tex]\frac{3(6)-1}{2(6) +1}[/tex] .

What are **Algebraic Expression** ?

The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For **Example **: [tex]3x+7[/tex] .

Here the two expressions are given as [tex]r(x) = 3x - 1[/tex] and [tex]s(x) = 2x + 1[/tex] ;

we have to find equivalent expression for [tex]\frac{r}{s} (6)[/tex] ;

By the **Division Property** of Algebraic Expression ;

it can be written as : [tex]\frac{r(6)}{s(6)}[/tex] ;

So , Substituting [tex]x=6[/tex] , in r(x) ,

we get ; [tex]r(6) = 3(6) - 1[/tex] , ......equation(1)

On Substituting [tex]x=6[/tex] , in s(x) ,

we get ; [tex]s(6) = 2(6)+1[/tex] , ....equation(2) ;

**Substituting the values** of r(6) and s(6) from equation(1) and equation(2) in [tex]\frac{r(6)}{s(6)}[/tex] ;

we get ;

⇒ [tex]\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}[/tex] ;

Therefore , the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is [tex]\frac{3(6)-1}{2(6) +1}[/tex] .

The given question is incomplete , the complete question is

If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?

(a) [tex]\frac{3(6)-1}{2(6) +1}[/tex]

(b) [tex]\frac{(6)}{2(6)+1}[/tex]

(c) [tex]\frac{36-1}{26+1}[/tex]

(d) [tex]\frac{(6)-1}{(6)+1}[/tex]

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What are 5 different types of units?

### Answers

Different types of **units** are CGS system units, FPS system units, MKS system units and **SI **units.

The (**CGS**)centimetre-gram-second system of units is how this is expressed. The metric system employs the centimetre to represent length or distance, the gram as the fundamental unit to represent mass or weight, and the second to represent time. Although there are other units of measurement in the system, they are all derived from just a few of these.

The (**FPS**)foot-pound-second system of units is what this is in its entire form. In this metric system, the foot serves as the default unit of length, and the pound serves as the default unit of mass and force. Finally, time is represented by the second.

This system's full name is (**MKS**)meter, kilogram, and second. The measuring of physical quantities is indicated by the usage of this metric system. Here, a meter is used to indicate length and a kilogram to indicate mass. Prior to their redefinition, it was renowned for establishing the foundation for the SI units.

International System of Units(**SI**) is the lengthier abbreviation for the units. It is the most recent and contemporary variety of metric system in use today. It is frequently utilized as the reference unit of measurement. It primarily includes the following seven units of measurement: second, metre, kilogram, ampere, Kelvin, Mole and candela.

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2. Divide $7200 into four parts proportional

to 1:2:3:4. How much is each part?

### Answers

Let's denote the first part as x. Then, the second part is 2x, the third part is 3x, and the fourth part is 4x. So, x + 2x + 3x + 4x = 10x = $7200. Solving for x, we get x = $720. Hence, the four parts are:

First part: $720

Second part: 2x = 2 * $720 = $1440

Third part: 3x = 3 * $720 = $2160

Fourth part: 4x = 4 * $720 = $2880

**Answer: **720, 1440, 2160, 2880

**Step-by-step: **

Create arbitrary variable a, such that 7200 = a + 2a + 3a + 4a.

Reduce to get 720 = a

and plug in a into the set {a, 2a, 3a, 4a} to get the answer

The length l of a pencil is 13cm to the nearest centimetre (cm) what number should go in the box to complete the error interval

### Answers

The correct expression for the given **error interval** is; 12.5 cm ≤ l ≤ 13.4

How to find the error interval?

**Error intervals** are defined as the **limits of accuracy** when a number has been rounded or truncated. These error intervals are the range of possible values that a number could have been before it was rounded or truncated.

Now, we can also say that Error interval is the range of values (between the upper and lower bounds) in which the precise value could possibly be.

Now, since the precise value is given as 13 cm after approximation to the nearest centimeter, then the **lower bound **will be 12.5 because it is the lowest number that can be approximated to 13. Meanwhile the **upper bound **will be 13.4 cm as it is the largest values that can be approximated to 13 cm. Thus, the **inequality **is;

12.5 cm ≤ l ≤ 13.4

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alberto sold half of his comic books. and then bought nineteen more. he now has 43. with how many did he start with

### Answers

**Answer:**

48

**Step-by-step explanation:**

First you should subtract 43 and 19

then you get a answer 24

Multiply it by 2

you get 48

**Answer:**

no. of books =48 books

**Step-by-step explanation:**

lets say that he started with

x

books so,

(X÷2)-19=43

X÷2=24

X=48

What is the equation of the line in slope-intercept form that passes through point (4, 5) and is parallel to the line y = −2x − 2?

### Answers

**Answer:**

y = -2x + 13

**Step-by-step explanation:**

In order to write an equation of the line in slope-intercept form, we first have to look at the equation:

y = mx + b

We know that *m* represents slope, and *b* represents the y-intecept, in other words, what y is equal to when x is equal to zero.

We already have y and x, (4,5), and the slope of the line, since the two lines are parellel, they share the same slope. So now, we have to pulg those values into the equation and solve for b:

(4,5)

y = 5

x = 4

m = -2

y = mx + b

(5) = (-2)(4) + b

5 = -8 + b

13 = b

So, equation of the line in slope-intercept form that passes through point (4, 5), is y = -2x + 13

Remeber that you can always graph to check your work!

I hope this helps! :)

A system of equations is shown below. y = 3x + 4 y = 7x – 2 What is the solution to the system?

### Answers

The **solution** to the **system** of **equations** is x = 3/2 and y = 11/2.

**What is the linear equation?**

The definition of a **linear** **equation **is an **algebraic** equation in which each term has an **exponent** of one and the** graphing **of the equation results in a **straight line**. An example of a **linear equation** is y=mx + b

We are given two equations:

y = 3x + 4

y = 7x – 2

We can set the two equations equal to each other and solve for x:

3x + 4 = 7x - 2

Subtracting 3x from both sides:

4 = 4x - 2

Adding 2 to both sides:

6 = 4x

Dividing both sides by 4:

x = 3/2

Now we can substitute this value of x back into either of the original equations to find the corresponding value of y. Using the first equation:

y = 3(3/2) + 4 = 9/2 + 4 = 11/2

Therefore, the **solution** to the **system** of **equations** is x = 3/2 and y = 11/2.

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the radius of a wheel rolling on the ground is 80 centimeters. if the wheel rotates through an angle of 60, how many centimeters does it move? express your answer in terms of pand then round to two decimal places.

### Answers

The** radius **of a wheel rolling on the ground is 80 **centimeters**. if the wheel **rotates** through an **angle** of 60. Therefore, It move to 84 cm.

**Circumference Of Circle:**

The **total length **of the **circle boundary. **The circumference of a circle is the **product** of the constant π and the** diameter** of the circle. A person walking across a **circular park **or a circular table needs this measure of circumference. The circumference is a length value and its units are the same as the length units. A **circle** is a round closed figure with all **endpoints equidistant **from a fixed point called the center.

The formula for the **circumference **of a circle is expressed using the **values** of the circle's radius 'r' and 'pi'. It is represented by the **equation **of circumference = 2πr. Using this perimeter formula, if you don't have a value for the** radius**, you can use the diameter to find it. To calculate the **circumference** is to use the formula circumference = π × diameter.

If you need to calculate the **radius **or **diameter**, consider the **circumference **of a circle and use the following formula:

** Radius = circumference/2π**

Now,

According to the Question:

If the **radius** is 80cm

and, the** circumference **is 2×π×80cm.

If the** wheel rotates** by 60° then a **fraction** 60/360 (= 1/6) of the **circumference **moves over the ground.

Therefore, the **distance** moved is

[tex]\frac{2*\pi*80 }{6}[/tex]

= 83.77580

≈ 84 cm.

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a cylindrical water tank with its circular base parallel to the ground is being filled at the rate of 4 cubic feet per minute. the radius of the tank is 2 feet. how fast is the level of the water in the tank rising when the tank is half full?

### Answers

**Answer:**

To solve this problem, we need to use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.

Step 1: We know that the radius of the tank is 2 feet and that it is being filled at a rate of 4 cubic feet per minute. We also know that the tank is half full, so we can assume that the height of the water in the tank is half the height of the tank itself.

Step 2: We can use the volume formula to find the volume of the tank when it is half full.

V = πr^2h

V = π(2^2)(h/2)

V = 4πh/2

Step 3: We can divide the rate of fill by the volume of the tank when it is half full to find the rate of change of the height of the water.

dh/dt = 4/(4π/2)

dh/dt = 2/π ft/min

Final Answer: The level of the water in the tank is rising at a rate of 2/π feet per minute when the tank is half full.

Evaluate the integral integral_1^squareroot 3 5 arctan(1/x)dx

### Answers

The final **integral** is [tex]=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}[/tex]

**Numerical** integrals are used to express concepts like volume, area, and displacement when infinitely small amounts of data are combined. Integral location is the integration process.

The signed area of the region in the plane that is circ*mscribed by the graph of a specific **function** between two points on the real line can be used to describe definitive integrals. Areas above the plane's horizontal axis are often positive, whereas those below it are typically negative.

[tex]\\\\\int _1^{\sqrt{3}}5\arctan \left(\frac{1}{x}\right)dx=\frac{5\left(2\sqrt{3}\ln \left(2\right)+2\pi -\sqrt{3}\pi \right)}{4\sqrt{3}}\quad \left(\mathrm{Decimal:\quad }\:2.34037\dots \right)\\\\=5\cdot \int _1^{\sqrt{3}}\arctan \left(\frac{1}{x}\right)dx\\\\=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}x_{123} \\\\=5\left[x\arctan \left(\frac{1}{x}\right)-\left(-\frac{1}{2}\ln \left|1+x^2\right|\right)\right]_1^{\sqrt{3}}[/tex]

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**Correct Question:**

[tex]\int _{\:1}^{\sqrt{3}}5\cdot \arctan \left(\frac{1}{x}\right)dx[/tex]

7. Describe the rule for each of the tables below:

a.

Row 1

Row 2

Rule:

5

7

7

11

15

37

19

35

29

55

### Answers

**Answer:**

**Step-by-step explanation:**

It is difficult to determine the rule for the table without further context or information. However, based on the pattern in the table, it appears that the rule for generating the second number in each row is to add 2 to the first number in that row. The rule for generating the third number in each row is to add 6 to the second number in that row. The fourth number is the sum of the first and the third number in that row.

PLSSS HELP IF YOU TURLY KNOW THISS

### Answers

**Answer:**

-15

**Step-by-step explanation:**

im thinking +[-15] and [-15] are the same thing

(Variance of a linear combination) Let X,Y be random variables and a,b,c be constants. Show that: var (aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y) (Hint: write the variance as a covariance and use bilinearity twice)

### Answers

To show that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X, Y), we can start by using the definition of **variance**, which is var(X) = E[(X - E[X])^2], and the definition of **covariance**, which is cov(X, Y) = E[(X - E[X])(Y - E[Y])].

Variance is a measure of the spread of a random variable's possible values. It is defined as the expected value of the squared **deviation** of a random variable from its mean. For a random variable X, the variance is denoted as Var(X) or σ^2(X) and is calculated as:

Var(X) = E[(X - E[X])^2]

Using these definitions, we can write:

var(aX + bY + c) = E[(aX + bY + c - E[aX + bY + c])^2]

Using the properties of **expectations** and **bilinearity**, we can simplify this to:

var(aX + bY + c) = E[(a(X - E[X]) + b(Y - E[Y]))^2]

Expanding the square and using bilinearity again, we get:

var(aX + bY + c) = a^2 E[(X - E[X])^2] + b^2 E[(Y - E[Y])^2] + 2ab E[(X - E[X])(Y - E[Y])]

Since the expectations of (X - E[X])^2 and (Y - E[Y])^2 are equal to var(X) and var(Y) respectively, we can substitute these values into the above equation to get:

var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)

Therefore, we have shown that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)

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find a cartesian equation for the curve and identify it. r = 7 cos(θ)

### Answers

The **cartesian equation **for the curve r = 7 cos(θ) is** [x -(7/2)]²+y² = 49/4**, which is the equation of a circle.

Given r =7 cosθ

**Multiplying **throughout by ‘r’,

r² =7r cos θ --- (1)

**Consider x² + y² = r²** and put x = r cos θ --- (2)

x² + y² = 7x

Using completing the **square method:**

x² - 7x + (7/2)² + y² = (7/2)²

[x - (7/2)]² + y² = 49/4

(x - 7/2)² + (y - 0)² = (7/2)²

This is the equation of the circle with a **center **(7/2, 0) and **radius **of 7/2.

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write an expression to represent the sum of three consecutive odd integers in which n is the least number.

### Answers

An **expression **to represent the sum of three consecutive odd integers is **3n + 3**

The term expression in math is known as a sentence with a minimum of two numbers or **variables **and at least one math operation.

Here we have given that an expression to represent the sum of three consecutive odd **integers **in which n is the least number.

As here we have given that since the smallest integer is n,

And then it can be written as n+1 and n + 2 are the **consecutive **integers after that.

And then finally here we have to know that if you **add **them all up, then it becomes (n) + (n+1)+(n + 2) or simply 3n+3.

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Below is a multiple correlation table. Based on the correlation values, which predictor would lead to the least prediction error in predicting happiness using simple regression

### Answers

From the correlation table , based on the correlation values , then **the predictor** that would lead to least prediction error in predicting happiness using simple regression is **stats class** .

What is **Predictor Variable** ?

The predictor variable is used to predict the future outcome based on some given circ*mstances. The Other names by which predictor variable is known as "criterion variable" and "explanatory variable" .

the best predictor from the given **correlation table **is the highest value in the table ; irrespective of the sign .

We have to predict happiness using the **simple regression** ;

So to find the predictor , we select the row in the **happiness **row ,

we can see that the biggest value for the happiness row is 0.41 , which is the stats class .

Therefore , The predictor that lead to least **prediction error** is Stats Class .

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write and solve the differential equation that models the verbal statement. the rate of change of n is proportional to n. (use k for the proportionality constant.) dn dt

### Answers

Therefore , the solution of the given problem of **differential equations **comes out to be y = cos x + c.

What is differential equation?

Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an **arithmetic** progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same. Arithmetic progression can be of two types: There are a finite number of terms in a finite **geometric** progression. The series' early, late, tolerance, and number of terms can be determined.

Here,

Given :dy/dx = x+1

dy = (x+1)dx

=>y = 1/2x² + x +c

dy/dx = -sinx

dy = -sinx dx

=> y = cos x + c

Therefore , the solution of the given problem of differential equations comes out to be y = cos x + c.

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what are the composite factors of 12 ?

### Answers

**Answer:**

The prime factors of 12 are 2 x 2 x 3.

So the composite factors of 12 are:

1, 2, 3, 4, 6 and 12.

Holly's garden is divided into 5 equal sections. She will fence the garden into 3 areas by grouping some equal sections together. What part of the garden would each fenced area be? please help I forgot how to do it for my lil brother just answer E

### Answers

There are two ways to **fence** the garden in 3 areas with some **equal** sections.

2/5, 2/5, 1/5 and 3/5, 1/5, 1/5.

**Fraction** definition

A fraction depicts a **segment** or component of the **whole**. It represents the equal parts that make up the whole. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that are taken.

Given The garden is **divided** into 5 equal pieces, each of which is 1/5 of the total garden size.

By arranging some equal parts together, she will fence the garden into three sections. There are two ways to do this.

(1/5 +1/5) = 2/5

(1/5 +1/5) = 2/5

1/5

these are the 3 areas 2/5, 2/5, 1/5.

and

(1/5 +1/5 + 1/5) = 3/5

1/5, 1/5

these are 3 areas = 3/5, 1/5, 1/5.

Hence there are only **two ways** to fence the garden into three areas by grouping some **equal** sections.

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The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and show that it is a parallelogram.

A(-2, 3), B(-5, 7), C(3, 6), D(6, 2)

### Answers

The quadrilateral is **parallelogram, **When the vertices of quadrilateral ABCD are given.

A parallelogram is a** two-dimensional** shape that has a pair of two parallel and congruent sides. It is the **simplest **type of quadrilateral that has **opposite** sides equal and parallel.

The opposite angles of a parallelogram are also **equal **and the sum of two consecutive angles is always **supplementary.** It has two **unequal **diagonals.

A point always represents the location of a **particular **place or position in a standard cartesian system, and the **coordinates **of the point represent the distances from the **respective **coordinate axis.

For example, consider a point P(x,y), in which the coordinates x and y are the perpendicular distances from the x-axis and the y-axis respectively.

The formula to find out the distance between two points is generally known as the **Distance formula **which can be expressed as:

**d=√(x₂−x₁)²+(y₂−y₁)²**

Given:

The vertices of the quadrilateral

A B C D: A(-2,3),B(-5,7),C(3,6), D(6,2).

The measure of the sides of the quadrilateral

d=√(x₂−x₁)²+(y₂−y₁)²

AB=√(-5-(-2))²+(7-3)²

Ab=√(-3)²+4²

AB=√25

**AB=5units.**

BC=√(3+5)²+(6-7)²

BC=√(8)²+1²

**BC=√65 units.**

CD=√(6-3)²+(2-6)²

CD=√3²+4²

CD=√25

**CD=5 units.**

AD=√(6-(-2))²+(2-3)²

AD=√(-8)²+1²

**AD=√65 units**.

The **diagonals**:

BC=√(3+5)²+(6-7)²

BC=√(8)²+1²

BC=√65 units.

AC=√(3+2)²+(6-3)²

AC=√(5)²+3²

AC=√25+9

**AC=√34 units**

Here, **AB=CD **and** BC=AD** and** AC≠BC**

Thus, the given quadrilateral is parallelogram.

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Solve each equation.

2y^2+11y+10=0

### Answers

The **solution** of the given **quadratic equation** are,

[tex]y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex].

**What is quadratic equation?**

Any **equation** in algebra that can be written in **standard form** as where x stands for an unknown value, where **a**, **b**, and **c** stand for known numbers, and where **a ≠ 0** is true is known as a **quadratic equation**.

Consider, the given equation:

2y^2 + 11y + 10 = 0

Compare this equation with [tex]ay^2 + by + c = 0[/tex]

⇒ a = 2, b = 11, c = 10

Consider, the quadratic formula

[tex]y = \frac{-b+-\sqrt{xb^2-4ac} }{2a}[/tex]

Plug the values of a, b, c in the quadratic formula.

⇒

[tex]y = \frac{-11+-\sqrt{11^2-4(2)(10)} }{2(2)} \\y = \frac{-11+-\sqrt{121-80} }{4}\\ y = \frac{-11+-\sqrt{41} }{4} \\y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex]

Hence, the **solution** of the given **quadratic equation** are,

[tex]y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}[/tex].

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System of Inequalities Problem Solving Task

Wait!! I Need my Weights!

Eric runs a dive boat named the Lois Ann. He has been struggling to fill his boat and he doesn't understand why. Eric provides weights for the scuba divers that go out on the boat. He has a maximum of 220 pounds of weight available for the divers to use and estimates that the average adult needs 20 pounds of weight and the average child needs 10 pounds of weight. Eric also likes to provide his divers with tanks to use. For each trip each adults requires 2 tanks and each child requires only 1 tank. The Lois Ann can accommodate at most 30 tanks and can hold a maximum of 20 scuba divers on any trip.

1) Write inequalities to represent all of the constraints in Eric's problem. Use x for the number of adults and y for the number of children.

Please help!!! I WILL GIVE BRAINLIEST

### Answers

The **inequalities** to represent all of the constraints in **Eric's problems** using x for the number of adults and y for the number of children are as follows:

x + y <= 20 (maximum number of scuba divers)2x + y <= 30 (maximum number of tanks)20x + 10y <= 220 (maximum weight for scuba divers)x, y >= 0 (non-negative number of adults and children)

What is an inequality?

An **inequality** is a **statement** that compares two expressions using one of the following symbols: **<, >, <=, >=, or ≠**. The expressions being compared can be numbers, variables, or a combination of both.

The **result** of an inequality is either **true** or **false**. For example, the inequality 2x + 3y < 6 represents a set of ordered pairs (x,y) that satisfy the inequality. It describes all the points on a coordinate plane that fall under the solution set of the inequality.

From the inequalities above,

x + y <= 20 (maximum number of scuba divers) means that since the Lois Ann can only accommodate 20 scuba drivers, whether adults or children, their addition could be less than but not above 20

2x + y <= 30 (maximum number of tanks) means the capacity of Lois Ann is 30 tanks and the number of children is 10, and adult is 20, it implies that either all adults and all children or some adults participated twice (2x) plus children, it is their figure can be less than or equals to 30

20x + 10y <= 220 (maximum **weight** for scuba divers) implies that their entire weight whether adult or children cannot be more than 220

x, y >= 0 (**non-negative** number of adults and children) implies that no onee is undetermined of his placement as to whether such is adult or children.

Therefore, the correct answer is as given above

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During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed in a horizontal circle as shown. Knowing that the speed of the hammer is 2.5 m/s and θ = 60°, determine (a) the tension in wire BC, (b) the radius of the circle, rho.

### Answers

(a) The value of the** tension** in wire BC will be = 80.4 N

(b) The value of the **speed** of the hammer’s head will be = 2.30 m/s

Mass of the head of the hammer = 7.1 Kg.

The **speed** at which it is revolving = v

value of ρ=0.93 m

The value of the angle θ=60°

**Tension** is described as the** force** transferred through a rope, string, or wire when pushed by opposing forces. The tension force is directed along the **length** of the wire and draws **energy** evenly on the bodies at the ends.

(a) Now, we will first calculate the value of the tension in wire BC,

First, we will note

[tex]$$a_A=a_n=\frac{v_A^2}{\rho}$$[/tex]

(a)

[tex]$+\Sigma F_y=0: T_{B C} \sin 60^{\circ}-W_A=0$[/tex]

or we can write it as:

[tex]$$\begin{aligned}T_{B C} & =\frac{7.1 \mathrm{~kg} \times 9.81 \mathrm{~m} / \mathrm{s}^2}{\sin 60^{\circ}} \\\end{aligned}$$[/tex]

=> =80.426 N

=>= 80.4 N (approx)

(b) Now calculate the **speed** of the hammer’s head.

[tex]$\quad+\Sigma F_x=m_A a_A: T_{B C} \cos 60^{\circ}=m_A \frac{v_A^2}{\rho}$[/tex]

or

[tex]$$v_A^2=\frac{(80.426 \mathrm{~N}) \cos 60^{\circ} \times 0.93 \mathrm{~m}}{7.1 \mathrm{~kg}}$$[/tex] = 2.30 m/s

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Note: The correct question may be like this:

During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at a constant speed v in a horizontal circle as shown. If ρ=0.93m and ,θ=60° determine (a) the tension in wire BC, (b) the speed of the hammer’s head.

The needed diagram is attached below

12 in ,10 in 8 in what type of triangle is

### Answers

The **type **of **triangle **that is given by the dimensions, is a Scalene triangle.

What are types of triangles ?

A **scalene triangle** has sides that are all measured differently. In such a triangle, no side will be the same length as any other side. Every interior angle in a scalene triangle is also unique.

The lengths of two of the three sides in an** isosceles triangle** are equal. The angles that are opposite the equal sides are therefore equal. An isosceles triangle, in other words, has two equal sides and two equal angles.

Each side of an **equilateral **triangle has an equal length. Each internal angle in this scenario will be 60 degrees in length. An equilateral triangle is often referred to as an equiangular triangle since its angles are equal.

The dimensions here are not the same which means that all the sides are not equal and so this is a **scalene triangle.**

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