Mathematics College

## Answers

**Answer 1**

**Answer:**

AB = √3

**Step-by-step explanation:**

Since ABCD is a rectangle, all angles are 90°

∠CDA = 90°

⇒ ∠CDB + ∠BDA = 90

⇒ ∠BDA = 60

In ΔABD,

sin(∠BDA) = opposite/ hypotenuse = AB / BD

⇒ sin(60) = AB/2

⇒ AB = 2 sin(60)

⇒ AB = 2 (√3)/2

AB = √3

## Related Questions

please answer i am stuck

### Answers

**Answer:**

x intercept : -1

y intercept : 3

**Step-by-step explanation:**

We have 3x - y = -3 ---eq(1)

The x intercept is the value of x when y = 0 in eq(1),

⇒ 3x - 0 = -3

⇒ x = -3/3

⇒ x = -1

The y intercept is the value of y when x = 0 in eq(1),

⇒ 3(0) - y = -3

⇒ -y = -3

⇒ y = 3

A man goes 10m North and turns left and covers 6m. He again turns left and walks 5m. Which direction is he in from starting point?

### Answers

The man is in the **south direction** from the starting point.

Let's visualize the **movements **of the man step by step:

The man starts by going 10 meters north.

He then turns left (which means he is now facing west) and covers 6 meters in that direction.

Next, he turns left again (which means he is now facing south) and walks 5 meters.

To determine the **final direction** of the man from the starting point, we can consider the net effect of his movements.

Starting from the north, he moved 10 meters in that direction. Then, he turned left twice, which corresponds to a 180-degree turn, effectively changing his direction by** 180 degrees.**

Since he initially faced north and then made a 180-degree turn, he is now facing south. Therefore, the direction he is in from the **starting point** is "south."

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If 2x2 - 4x + 6 = 1 then A = 2, B = -4, and C = 6 in general form.

### Answers

In **general form**, the equation 2x^2 - 4x + 6 = 1 can be represented as A = 2, B = -4, and C = 5.

To determine the **values **of A, B, and C in the general form of the quadratic equation 2x^2 - 4x + 6 = 1, we can compare the given equation with the standard form of a **quadratic** equation, which is ax^2 + bx + c = 0.

In the given equation, we have:

2x^2 - 4x + 6 = 1

To put it in the general form, we need to move all the **terms **to the left side of the equation, so the right side is equal to 0:

2x^2 - 4x + 6 - 1 = 0

2x^2 - 4x + 5 = 0

Now we can identify the **coefficients **A, B, and C in the general form:

A = 2 (coefficient of x^2)

B = -4 (coefficient of x)

C = 5 (constant term)

The values of A, B, and C in the general form of the **equation **2x^2 - 4x + 6 = 1 are A = 2, B = -4, and C = 5.

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Solving for Side Lengths of Right Triangles

Quiz Active

1

2 3

O

4 5

с

Which relationship in the triangle must be true?

sin(B) = sin(A)

O sin(B) = cos(90 - B)

cos(B) = sin(180 - B)

O cos(B) = cos(A)

6

B

7 8

9

10

TIME REMAINING

12:30

### Answers

**Answer:**

6 is the sin

**Step-by-step explanation:**

Taking the period of daylight on a certain day to be from 5.30am to 7.00pm, calculate the periods of daylight and a darkness on that day. C.202°3°, 157°30' D. 195°, 165° A. 187°30M72°301 B. 135°, 225°

### Answers

The **periods **of daylight and darkness on that day are approximately:

Daylight: 202.5°

Darkness: 157.5°

Hence, the correct option is:

C. 202°3°, 157°30'

To calculate the periods of daylight and darkness on a certain day, we need to find the difference **between **the times of sunrise and sunset.

Sunrise time: 5.30 am

Sunset time: 7.00 pm

To find the period of daylight, we **subtract **the sunrise time from the sunset time:

Daylight = Sunset time - Sunrise time

First, let's convert the times to a 24-hour format for easier calculation:

Sunrise time: 5.30 am = 05:30

Sunset time: 7.00 pm = 19:00

Now, let's calculate the period of daylight:

Daylight = 19:00 - 05:30

To subtract the times, we need to **convert **them to minutes:

Daylight = (19 * 60 + 00) - (05 * 60 + 30)

Daylight = (1140 + 00) - (330)

Daylight = 1140 - 330

Daylight = 810 minutes

To convert the period of daylight back to degrees, we can use the fact that in 24 hours (1440 minutes), the Earth **completes **a full rotation of 360 degrees.

Daylight (in degrees) = (Daylight / 1440) * 360

Daylight (in degrees) = (810 / 1440) * 360

Daylight (in degrees) ≈ 202.5 degrees

To find the period of **darkness**, we subtract the period of daylight from a full circle of 360 degrees:

Darkness = 360 - Daylight

Darkness = 360 - 202.5

Darkness ≈ 157.5 degrees

Therefore, the periods of **daylight **and darkness on that day are approximately:

Daylight: 202.5°

Darkness: 157.5°

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Find the perimeter of a triangle with sides that are5 yards ,6 yards and 4 Yards

### Answers

Simply add up of the side lengths so, 4+5+6 =15

So perimeter is 15 yards

What is the distance from A to B?

10

108642

A(-8, -3)

-2

-6

-8

-10

B6, 6)

2 4 6 8 10

A 21 units

B. 15 units

C. 225 units

D. 3 units

### Answers

The **distance **from point A to point B is approximately 16.64 units. None of the given options (A, B, C, D) match this value exactly, so there seems to be an error in the options provided.

To find the distance from **point **A to point B, we can use the distance formula in Euclidean geometry. The distance formula **between **two points (x1, y1) and (x2, y2) is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, point A is (-8, -3) and point B is (6, 6). Plugging these values into the distance **formula**, we have:

distance = sqrt((6 - (-8))^2 + (6 - (-3))^2)

= sqrt((6 + 8)^2 + (6 + 3)^2)

= sqrt(14^2 + 9^2)

= sqrt(196 + 81)

= sqrt(277)

≈ 16.64

Thus, the distance between points A and B is roughly 16.64 units. Since none of the **available **options (A, B, C, or D) exactly match this value, there appears to be a problem with the options.

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Find the distance between the points A and B given below.

(That is, find the length of the segment connecting A and B.)

Round your answer to the nearest hundredth.

1 unit

A

B

### Answers

**Answer:**

I wish you good luck in finding your answer

Which of the following could be the ratio between the lengths of the two legs

of a 30-60-90 triangle?

Check all that apply.

A. √2:2

B. √√3:√√3

C. √5:3

D. 1 √3

□ E. 1: √2

O F. 2:3

SUBMIT

### Answers

**Answer: E**

**Step-by-step explanation:**

In this case the linear equations are given:

A company offers two data plans for cell phones. The plan A the linear function for the

charge is given by

y=10x

where x represents the total number of megabytes. The Plan B charge is calculated using

the linear function

y = 4x + 75.

How many megabytes would a customer need to use for Plan be to be a better deal?

1) more than 12.5 megabytes

2) less than 18.75 megabytes

3)

Plan b is always a better deal because the charge per megabyte is less than in

plan A

4) More than 10 megabytes.

5) More than 20 megabytes

### Answers

The customer would need to use more than 12.5 **megabytes **for Plan B to be a better deal. (Option 1) more than 12.5 megabytes).

To determine when Plan B would be a better deal than Plan A, we need to compare the **charges **for both plans based on the number of megabytes used.

Plan A is represented by the **linear function** y = 10x, where x represents the total number of megabytes used, and y represents the charge for the plan.

Plan B is represented by the linear function y = 4x + 75, where x represents the total number of megabytes used, and y represents the charge for the plan.

To find the point at which Plan B becomes a better deal, we need to find the x-value where the charge for Plan B is less than the charge for Plan A.

In other words, we need to find the x-value that satisfies the inequality:

4x + 75 < 10x

To solve this **inequality**, we subtract 4x from both sides:

75 < 6x

Then, we divide both sides by 6:

12.5 < x

Therefore, the customer would need to use more than 12.5 megabytes for Plan B to be a better deal.

This means that option 1) "more than 12.5 megabytes" is the correct answer.

For any value of x greater than 12.5, the charge for Plan B will be less than the charge for Plan A, making it a better deal for the customer.

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Two sets that contain exactly the same elements are called ___ sets.

### Answers

Two **sets** that contain exactly the same elements are called "equal sets" or "identical sets."

In set theory, the concept of equality between sets is defined by the **axiom** of extensionality, which states that two sets are equal if and only if they have the same elements.

To illustrate this concept, let's consider two sets: Set A and Set B. If every element of Set A is also an element of Set B, and vice versa, then we say that Set A and Set B are equal sets. In other words, the sets have the exact same **elements**, regardless of their order or repetition.

For example, if Set A = {1, 2, 3} and Set B = {3, 2, 1}, we can observe that both sets contain the same elements, even though the order of the elements is different. Therefore, Set A is equal to Set B.

In summary, equal sets refer to two sets that possess exactly the same elements, without considering the order or repetition of the elements. The concept of equality is fundamental in set **theory** and forms the basis for various operations and theorems in mathematics.

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The table represents a logarithmic function f(x).

1 over 125 −3

1 over 25 −2

one fifth −1

1 0

5 1

25 2

125 3

Use the description and table to graph the function, and determine the domain and range of f(x). Represent the domain and range with inequality notation, interval notation, or set-builder notation. Explain your reasoning.

### Answers

The **graph** of the logarithmic function f(x) exhibits an increasing trend as x approaches positive infinity, while it approaches negative infinity as x approaches negative infinity. The domain is (0, +∞), and the range is (-∞, +∞).

To graph the given **logarithmic** **function** f(x), we can use the information provided in the table. The table gives us various values of x and their corresponding values of f(x). We can plot these points on a graph and connect them to visualize the function.

The table shows the following points: (1, 125), (-3, 1/25), (-2, 1/5), (-1, -1), (0, 5), (1, 125), (2, 2125), and (3, 3).

When we graph these points, we observe that the function starts at (-3, 1/25) and approaches positive infinity as x approaches positive infinity. Similarly, as x approaches negative infinity, the function approaches negative **infinity**.

From the graph, we can determine the domain and range of the function:

**Domain**: The domain of a logarithmic function is all real numbers greater than 0. In this case, since the function is defined for x = 1/5 and x = 3, the domain can be expressed as x ∈ (0, +∞).

Range: The range of a logarithmic function is all real numbers. In this case, the function takes values ranging from negative infinity to positive infinity. Therefore, the range can be expressed as f(x) ∈ (-∞, +∞).

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the value of tan80°×tan10°+sin70+sin 20

### Answers

The **value** of tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276

What is Trigonometry?

**Trigonometry **is the** branch of mathematics **concerned with specific functions of angles and their application to calculations. There are six **functions **of an angle commonly used in** trigonometry**. Their names and abbreviations are sine (**sin**), cosine (**cos**), tangent (**tan**), cotangent (**cot**), secant (**sec**), and cosecant (**csc**). These six **trigonometric functions **in relation to a right triangle are displayed in the figure.

Given:

tan(80°) × tan(10°) + sin(70°) + sin(20°)

Using **Trigonometric identity**

sin (A · B) = sin A cos B - cos A sin B

So, tan(80°) × tan(10°) + sin(70°) + sin(20°)

[tex]\rightarrow \tan (80 \times 10)=1[/tex]

[tex]\rightarrow\sin(70^\circ+20^\circ)=1.28171276[/tex]

[tex]\rightarrow 1.28171276+1=\bold{2.28171276}[/tex]

Hence, tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276

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Given that √x + √y=138 and x-y=1656, find x.

### Answers

The **value **of x is 5625 when √x + √y=138 and x-y=1656.

To solve for x using the given **equations**, we will use the method of substitution. Let's go through the steps:

Start with the equation √x + √y = 138.

We want to **express **y in terms of x, so solve for y in terms of x by isolating √y:

√y = 138 - √x

Square both sides of the equation to **eliminate **the square root:

(√y)² = (138 - √x)²

y = (138 - √x)²

Now, substitute the expression for y in the second equation x - y = 1656:

x - (138 - √x)² = 1656

Expand the squared term:

x - (138² - 2 * 138 * √x + (√x)²) = 1656

Simplify the equation further:

x - (19044 - 276 * √x + x) = 1656

Combine like terms and rearrange the equation:

-19044 + 276 * √x = 1656

Move the constant term to the other side:

276 * √x = 20700

Divide both sides of the equation by 276 to solve for √x:

√x = 20700 / 276

√x = 75

Square both sides to solve for x:

x = (√x)²

x = 75²

x = 5625

Therefore, the value of x is 5625.

By substituting this value of x back into the original equations, we can verify that √x + √y = 138 and x - y = 1656 hold true.

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How much is 700000 in Penny’s

### Answers

**Answer:**

$7000

**Step-by-step explanation:**

700,000 **dollars** is equal to 70,000,000 pennies.

To convert 700,000 to **pennies**.

We need to **multiply** the number by 100, since there are 100 pennies in a dollar.

1 dollar = 100 pennies.

So, 700,000 × 100

= 70,000,000

Therefore, 700,000 is equal to 70,000,000 **pennies**.

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Solve using inverse (matrix) method

5x - 4y + z = 12

x + 7y-z = -9

2x+3y + 3z = 8

### Answers

The solution to the system of equations using the** inverse matrix method **is x = -1, y = 2, z = 3.

To solve the system of equations using the inverse matrix method, we need to represent the system in matrix form.

The given system of equations can be written as:

| 5 -4 1 | | x | = | 12 |

| 1 7 -1 | [tex]\times[/tex]| y | = | -9 |

| 2 3 3 | | z | | 8 |

Let's denote the** coefficient matrix** on the left side as A, the variable matrix as X, and the constant matrix as B.

Then the equation can be written as AX = B.

Now, to solve for X, we need to find the inverse of matrix A.

If A is invertible, we can calculate X as [tex]X = A^{(-1)} \times B.[/tex]

To find the inverse of matrix A, we can use the formula:

[tex]A^{(-1)} = (1 / det(A)) \times adj(A)[/tex]

Where det(A) is the determinant of A and adj(A) is the adjugate of A.

Calculating the determinant of A:

[tex]det(A) = 5 \times (7 \times 3 - (-1) \times 3) - (-4) \times (1 \times 3 - (-1) \times 2) + 1 \times (1 \times (-1) - 7\times 2)[/tex]

= 15 + 10 + (-13)

= 12.

Next, we need to find the **adjugate **of A, which is obtained by taking the transpose of the cofactor matrix of A.

Cofactor matrix of A:

| (73-(-1)3) -(13-(-1)2) (1(-1)-72) |

| (-(53-(-1)2) (53-12) (5[tex]\times[/tex] (-1)-(-1)2) |

| ((5(-1)-72) (-(5(-1)-12) (57-(-1)[tex]\times[/tex](-1)) |

Transpose of the **cofactor matrix:**

| 20 -7 -19 |

| 13 13 -3 |

| -19 13 36 |

Finally, we can calculate the inverse of A:

A^(-1) = (1 / det(A)) [tex]\times[/tex] adj(A)

= (1 / 12) [tex]\times[/tex] | 20 -7 -19 |

| 13 13 -3 |

| -19 13 36 |

Multiplying[tex]A^{(-1)[/tex] with B, we can solve for X:

[tex]X = A^{(-1)}\times B[/tex]

= | 20 -7 -19 | | 12 |

| 13 13 -3 | [tex]\times[/tex] | -9 |

| -19 13 36 | | 8 |

Performing the** matrix multiplication, **we can find the values of x, y, and z.

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HELPPPPPP ME PLEASEEEEE!!

### Answers

**Answer:**

**Step-by-step explanation:**

The quadratic formula is y=ax^2+bx+c

If we move everything to the left side of the equation,

-6x^2=-9x+7 becomes

-6x^2+9x-7=0

a=-6, b=9, c=-7, so the third answer choice

A zoo has categorized its visitors into three categories: member, school, and general. The member category refers to visitors who pay an annual fee to support the zoo. Members

receive certain benefits such as discounts on merchandise and trips planned by the zoo. The school category includes faculty and students from day care and elementary and

secondary schools; these visitors generally receive a discounted rate. The general category includes all other visitors. The zoo has been concerned about a recent drop in

attendance. To help better understand attendance and membership, a zoo staff member has collected the following data.

Attendance

School

Visitor

Category 2011

General 154,213 159,204 163,933 169,606

Member 114,023 103,295

96,937 79,717

82,385 79,376

81,470

80,790

Total 350,621 341,875 342,340

330,113

(0) Construct a bar chart of total attendance over time. Comment on any trend in the data.

(b) Construct a side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis.

(c) Comment on what is happening to zoo attendance based on the charts from parts (a) and (b).

2012

2013

2014

### Answers

(a) Based on the total attendance data provided, a bar chart can be constructed to visualize the attendance trends over time. The horizontal axis represents the years (2011, 2012, 2013, 2014), and the vertical **axis **represents the total attendance. The bars will correspond to the attendance numbers for each year.

(b) A side-by-side bar chart can be created to compare the attendance by visitor category with the year as the variable on the horizontal axis. The visitor categories (school, general, member) will be represented by different colors or patterns, and the bars will show the attendance for each category in each year.

(c) By analyzing the charts from parts (a) and (b), we can observe the trends in zoo attendance.

(a) The bar **chart** of total attendance over time shows the following trend: In 2011, the attendance was 350,621. It decreased slightly in 2012 to 341,875, remained relatively stable in 2013 at 342,340, and then decreased again in 2014 to 330,113.

(b) The side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis provides a visual comparison of attendance for each category over the years.

The chart reveals that the general category consistently had the highest attendance throughout the years, followed by the school category. The member category consistently had the lowest attendance.

(c) Based on the charts from parts (a) and (b), it can be observed that there has been a general decline in zoo attendance over the years, with a notable decrease from 2011 to 2014.

The drop in **attendance** could indicate a potential issue that the zoo needs to address in order to attract more visitors.

Additionally, the consistently lower attendance in the member category suggests that the zoo may need to reconsider its membership benefits and strategies to retain and attract more members.

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If p1=(2,4,-3) and p=(3,-1,1) find parametric equation of

### Answers

The **parametric equation** of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

To find the parametric **equation **of the line passing through points P1(2, 4, -3) and P(3, -1, 1), we can use the vector equation of a line.

Let's denote the direction vector of the line as d = (a, b, c). Since the line passes through P1 and P, the **vector **between these two points can be used as the direction vector.

d = P - P1 = (3, -1, 1) - (2, 4, -3) = (1, -5, 4)

Now, we can express the parametric equation of the line as follows:

x = x0 + at

y = y0 + bt

z = z0 + ct

where (x0, y0, z0) is a point on the **line **and (a, b, c) is the direction vector.

Let's choose P1(2, 4, -3) as the **point **on the line. Substituting the values, we get:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

Therefore, the parametric equation of the line **passing **through P1(2, 4, -3) and P(3, -1, 1) is:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

where t is a parameter that varies along the line.

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Triangle ABC has the following coordinates: A=(5,-5), B=(3,-3), C=(5,-3) What are the coordinates of triangle A'B'C' if it is created by dilating triangle ABC with the origin (0,0) as the center of dilation and with a scale factor of 3?

### Answers

**Answer:**A' = (15, -15), B' = (9, -9), and C' = (15, -9)

**Step-by-step explanation:**

To dilate triangle ABC with a center of dilation at the origin (0,0) and a scale factor of 3, you need to multiply the coordinates of each vertex by the scale factor.

Let's calculate the coordinates of triangle A'B'C':

For point A:

x-coordinate of A' = scale factor * x-coordinate of A = 3 * 5 = 15

y-coordinate of A' = scale factor * y-coordinate of A = 3 * (-5) = -15

Therefore, A' = (15, -15)

For point B:

x-coordinate of B' = scale factor * x-coordinate of B = 3 * 3 = 9

y-coordinate of B' = scale factor * y-coordinate of B = 3 * (-3) = -9

Therefore, B' = (9, -9)

For point C:

x-coordinate of C' = scale factor * x-coordinate of C = 3 * 5 = 15

y-coordinate of C' = scale factor * y-coordinate of C = 3 * (-3) = -9

Therefore, C' = (15, -9)

Hence, the correct coordinates of triangle A'B'C' are A' = (15, -15), B' = (9, -9), and C' = (15, -9).

Un chavo mide 3 pulgadas + un 1/4 de pulgada y otro mide 9.045 cm que diferencia de tamaño hay entre ellos

### Answers

The difference in size between the two guys is approximately -0.3108 **inches**, which implies that the first guy is bigger than the second guy.

To calculate the difference in size between two people, one measuring in inches and the other measuring in centimeters, we must first convert all **measurements **to a common unit.

Guy measures 3 inches + 1/4 inch. We can convert 1/4 inch to a decimal fraction by dividing 1 by 4, which gives us 0.25 inches. So your measurement in inches would be 3 + 0.25 = 3.25 inches.

The other guy measures 9.045 cm. To convert **centimeters **to inches, we use the following **relationship**: 1 cm = 0.3937 inches. Multiplying the measurement in centimeters by 0.3937, we get the measurement in inches: 9.045 cm * 0.3937 = 3.5608 inches (approximately).

Now we can calculate the size difference between them. We subtract the measurement of the second chavo (3.5608 inches) from the measurement of the first chavo (3.25 inches):

3.25 inches - 3.5608 inches = -0.3108 inches.

The resulting difference is -0.3108 inches. This means that the second chavo is smaller in size than the first. Since the difference is **negative**, it indicates that the first chavo is bigger than the second.

In summary, the difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.

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Not sure whether to use integration by substitution or partial fractions?

### Answers

**Answer:**

**Step-by-step explanation:**

I think you have to use partial fractions. Substitution won't work because the numerator is not the derivative of the denominator. I hope I am correct on this.

I have attached just the partial fractions part of the question. I did not integrate.

An isosceles triangle has two angles both equal to x. The third angle is 45 degrees bigger than either of these. Find the value of x.

### Answers

**Let's use the fact that the sum of the angles of a triangle is always 180 degrees to solve this problem. Let the two equal angles be x, then the third angle is x + 45.Let's add all the angles together:x + x + x + 45 = 180Simplifying this equation, we get:3x + 45 = 180Now, we need to isolate the variable on one side of the equation. We can do this by subtracting 45 from both sides of the equation:3x = 135Finally, we can solve for x by dividing both sides of the equation by 3:x = 45Therefore, the value of x is 45 degrees.**

**Answer:**

**45°**

**Step-by-step explanation:**

**An isosceles triangle has two angles both equal to x. The third angle is 45 degrees bigger than either of these. Find the value of x.***Let's turn the question into an equation*

180 = x + x + x + 45

180 - 45 = 3x

135 = 3x

x = 135 : 3

**x = 45°**

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

check

180 = 45 + 45 + 45 + 45

**180 = 180**

same value the answer is good

find x using the trigonometric function

### Answers

The **value of x** in the diagram given in the question is 6

How do i determine the value of x?

From the question given above, the following data were obtained:

Angle (θ) = 60Adjacent = 3**Hypotenuse = x =?**

The **value of x** can be obtained using cos ratio.

Cos θ = Adjacent / Hypotenuse

Cos 60 = 3 / x

Cross multiply

x × Cos 60 = 3

Divide both sides by Cos 60

x = 3 / Cos 60

= 3 / 0.5

= 6

Thus, the **value of x** is 6

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if 3+5 equals 8 then what does 5+3 equal?

### Answers

**Answer:**

8

**Step-by-step explanation:**

The meaningful domain of the linear model are all the possible values the x variable can take

on that make sense. The range is all the possible values for the linear model (the y values).

The top of the mountain is at 8920 feet and the base of the mountain is at 3300 feet

Identify

Domain

Range

### Answers

Domain: The **domain **is the range of valid heights for the mountain, which is from 3300 feet to 8920 feet.

Range: The range is the set of all possible heights of the linear model, which in this case is also from 3300 feet to 8920 feet.

Domain: The domain of the** linear model** in this context would represent the possible values for the x variable, which is associated with the height of the mountain.

In this case, the meaningful domain would be the range of valid heights that the mountain can have.

Since the top of the mountain is at 8920 feet and the base is at 3300 feet, the meaningful domain would be the **range **of heights between 3300 feet and 8920 feet.

Therefore, the domain in this scenario would be [3300, 8920].

Range: The range of the linear model in this context would represent the possible values for the y variable, which is associated with the height of the mountain.

The range would be the set of all **possible heights** that the linear model can produce.

In this case, since the top of the mountain is at 8920 feet and the base is at 3300 feet, the range would encompass all the valid heights within this range.

Therefore, the range in this scenario would be [3300, 8920].

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Akira has 3 cheeses to arrange on a cheese board. She would like to arrange them in a row. In how many different orders can she arrange them?

### Answers

**Answer:**

**Step-by-step explanation:**

Akira has 3 cheeses to arrange on a cheese board. She would like to arrange them in a row

The number of permutations of n distinct objects is given by n! (n factorial). In this case, Akira has 3 cheeses to arrange in a row. Therefore, the number of different orders she can arrange them is 3! = 6¹⁴.

So Akira can arrange the 3 cheeses in 6 different ways.

you are a trainer . .you have developed a 5 week training course for 20 trainees that will cost $140,000. what is the cost per trainee

### Answers

The **cost **per trainee for the 5-week training course is $7,000.

To find the cost per **trainee**, we divide the total cost of the training course by the number of trainees.

Total cost of the **training **course = $140,000

**Number **of trainees = 20

Cost per trainee = Total cost of the training course / Number of trainees

Cost per trainee = $140,000 / 20

Cost per trainee = $7,000

Therefore, the cost per trainee for the 5-week training **course **is $7,000.

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please help!!!!!!!!!!!!!!!!!!!!!!

### Answers

The **systematic sample **would be A. The city manager takes a list of the residents and selects every 6th resident until 54 residents are selected.

The **random sample **would be C. The botanist assigns each plant a different number. Using a random number table, he draws 80 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 80 plants is equally likely to be drawn using the random number table.

The **cluster sample **is C. The host forms groups of 13 passengers based on the passengers' ages. Then, he randomly chooses 6 groups and selects all of the passengers in these groups.

What are systematic, random and cluster samples ?

A systematic sample involves selecting items from a larger population at **uniform intervals**. A random sample involves selecting items such that every individual item has an equal chance of being chosen.

A cluster sample involves dividing the **population **into distinct groups (clusters), then selecting entire **clusters **for inclusion in the sample.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

### Answers

**Answer:**

B

**Step-by-step explanation:**

SAS Similarity theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Side 28 is congruent to side 11.2, whereas side 20 is congruent to side 8 and both angles are congruent. Therefore both triangles are similar.