12. A colony of rabbits in the wild found that the colony doubles in population
every year. At first there were 10 rabbits. After how many years will there
be more than 160 rabbits?

The equation of resulting graph upon undergoing the transformations as described in the task content is; Choice B; y= |4 - x|-6.

It follows from the task content that the equation of the transformed graph be determined.

First, since the graph is reflected over the y-axis, the x-value becomes negative as; -x.

Hence, the resulting equation is;

y = |-x + 4|-8

y = |4 -x|-8

Also, when the graph is translated 2 units down; we have;

y -2 = |4 -x|-8

y = |4 -x|-8 +2

y = |4 -x| -6

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To solve the inequality, multiply both sides by (-5). The solution is b  ≤ 30 or (∞, 30]

Tips to solve linear inequalities:

Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis (  or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.

Example:  x ≥ 2 can be written as [2, ∞), while

                x > 0 is written as (2, ∞)

The given problem:

-b/5 ≥ -6

Notice that the variable, b, is already isolated on the left side. Multiply both sides by (-5) and flip the sign of the inequality ( since we multiply it by a negative number):

-b/5 . (-5) ≤ -6 . (-5)

b  ≤ 30

Using the interval notation, the solution is (∞, 30]

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Step-by-step explanation:

use distance formula for answer

The median and mode of the data set is

This is further explained below.

Generally, median = value of [tex]$\left(\frac{n+1}{2}\right)^{\text {th }}$[/tex] the position

- the value of [tex]$\left(\frac{20+1}{2}\right)^{\text {th }}$[/tex] the position

= value of the position

= value of [tex]$10^{\text {th }}$[/tex] position +0.5 (value of 10^th  position - value of 9th position)

Arranging the data below.

8,10,13,15,15,15,15,15,16,16,16$, $17,18,19,20,20,21,29,28,30

median =16+0.5(16-16)

median =16

mode = { value of maximum frequency }

mode =15

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The data set represents the number of students per faculty member for 20 public colleges 13 15 15 8 16 20 28 19 18 15 21 23 30 17 10 16 15 16 2[tex]$(10.5)^{\text {th }}$[/tex]0 15. Use five classes.

What is the median and mode of the data

Based on the calculations, the number of student tickets and adult tickets that were sold are 225 tickets and 425 tickets respectively.

Given the following data:

Total ticket receipts = 650 tickets.

The price for a student ticket = $11.50.

The price for an adult ticket = $13.00.

Total revenue = $8,112.50.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to determine the number of student tickets and adult tickets that were sold, we would translate the word problem into an algebraic expression as follows:

A + S = 650                              ......equation 1.

11.5S + 13A = 8,112.50              ......equation 2.

From eqn. 1, we have:

S = 650 - A                          ......equation 3.

Substituting eqn. 3 into eqn. 2, we have:

11.5(650 - A) + 13A = 8,112.50

7,475 - 11.5 A + 13A = 8,112.50

1.5A = 8,112.50 - 7,475

1.5A = 637.5

A = 637.5/1.5

A = 425 tickets.

For the student tickets, we have:

S = 650 - A

S = 650 - 425

S = 225 tickets.

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Answer:

Below in bold.

Step-by-step explanation:

The slope = rise / run

= 5/10

= 1/2.

General form of the straight line is

y = mx + c   where m = the slope and C is the y-intercept

Here m = 1/2. and c = 0

So, the answer is y = 1/2 x.

Answer: 3.08

Step-by-step explanation: hope this helps!!!!

Answer:

3.08 or 77/25

Step-by-step explanation:

I find answering this problem easiest if you use paper and Thats what I used

2 1/5/ 5/7 = 77/25= 3 2/25= 3.08

Spelled result in words is seventy-seven twenty-fifths (or three and two twenty-fifths).

The significant digits from the product of the values are 7

It is important to note the following;

Given the values;

Let's find the product

4.514 x 10^−3 × 3.09 x 10^7 × 2.80 x 10^3

39. 055128 × 10^-3 + 7 + 3

39. 055128  × 10^7

The significant digits are 7

Thus, the significant digits from the product of the values are 7

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Answer:437.019

Step-by-step explanation:

If you add together

4 hundreds-400

3 tens-30

7 ones-7

19 thousandths-0.019

It equals 437.019

The perimeter of the rectangle is 4 + 4w, where w is the width of the rectangle.

In this question,

a rectangle has a width w

Let l be the length of the rectangle.

A  length that is two more than its width.

⇒ l = 2 + w

We know that the perimeter of the rectangle is P = 2 × (length + width)

So, for the length l = 2 + w and width w, the perimeter of the rectangle would be,

P = 2 × (w + (2 + w))

We simplify above expression.

P = 2 × (2 + 2w)

P = 4 + 4w

Therefore, the perimeter of the rectangle is 4 + 4w, where w is the width of the rectangle.

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Answer:

Box plot B

Step-by-step explanation:

Hope this helps

Answer: 38

Step-by-step explanation:

4*8 =32

32/2=16

16*3=48

48-10=38

The area and Perimeter of (ΔABC) are respectively; 17.5 square units and 24.16 units

The formula for the area of a triangle ABC with 3 coordinates is;

Area (ΔABC) = (¹/₂) |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

The coordinates are;

(x₁, y₁) = (-6, 6)

(x₂, y₂) = (2, 3)

(x₃, y₃) = (-3, -2)

Thus;

Area (ΔABC) = (¹/₂) |-6(3 − (-2)) + 2(-2 − 6) + -3(3 − 6)|

Area (ΔABC) = (¹/₂)|-30 - 16 + 9|

Area (ΔABC) = ¹/₂ * |-35|

We are taking absolute value and so;

Area (ΔABC) = ¹/₂ * 35

Area (ΔABC) = 17.5 square units

To get the perimeter, we will use distance formula between two coordinates and we have;

AB = 8.544

BC = 7.071

AC = 8.544

Thus;

Perimeter = 2(8.544) + 7.071

Perimeter = 24.16 units

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Olivia purchases gifts for her mom and grandma for Mother's Day. The  linear equations in first is a pair of sunglasses for $16.35 and the second is a bracelet. Her total spend $39.75.

Given that

o find

So, according to the question

We have

So, we can say that

Now, putting the all given values,

So, we get

                                             = $(39.75 - 16.35)

    The amount of bracelet = $ 23.4        

She spend $ 23.4 on bracelet for Mother’s Day.

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Answer:that is the slope intercept form

Step-by-step explanation: slope intercept form is y=mx+b

Answer: $0.39

Step-by-step explanation:

3.09/8=

0.38625=

0.38625=$0.39

The quotient of the given problem using laws of exponents is; 6 * 10⁰

We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.

This is;

(30 * 10⁻²⁴)/(5 * 10⁻²⁴)

Now, we can break this down into like terms to get;

(30/5) * (10⁻²⁴/10⁻²⁴)

= 6 * 1

Now, 1 can also be written as;

10⁰ = 1

Thus, the solution of the given problem is; 6 * 10⁰

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Answer:

0=18

Step-by-step explanation:

-3(3 - 4x) = 5(x - 1) + 7(x + 2)

-3( -4x + 3) = 5(x - 1) + 7(x + 2)

Answer:

1. i

2. -1

Step-by-step explanation:

The number of times the number 8.4493E13 isgreater than the number 7.994E-2 when displayed on a calculator is 1.05696E15.

8.4493E13 = 84,493,000,000,000

7.994E-2 = 0.07994

The number of times the number 8.4493E13 isgreater than the number 7.994E-2 can be obtained by dividing 8.4493E13 by 7.994E-2 as follows:

Number of times greater = 8.4493E13 / 7.994E-2 = 84,493,000,000,000 / 0.07994

Number of times greater = 1,056,955,216,412,310

When displayed on a calculator, we will have:

Number of times greater = 1.05696E15

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An ordinal scale provides more information than a nominal scale since values linked with an ordinal variable will be in natural order, whereas values connected with the nominal variable won't.

Ordinal variables as well as nominal variables are the two categories of variables listed here. This sort of variable cannot be submitted to the same forms of statistical tests as interval and ratio variables, hence it is crucial to be able to recognize them accurately. Both of these variables fall within the qualitative category. This contrasts with interval as well as rate variables, both of which are categorized as quantitative.

An illustration of an ordinal variable is a Likert scale with words for mood (such as joyful, neutral, or sad). An illustration of a nominal variable is the names of cities in the Canadian province of Alberta.

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Triangle ABC is reflected across the y-axis. The two congruent triangles are mirrored across the y-axis, thus they are reflected.

6: Give the translation rule, any coordinate point will shift 4 units to the left and rise up 8 units.

The translation rule describes how each coordinate point of the original triangle ABC moves to form the reflected triangle after the reflection across the y-axis.

To reflect a triangle across the y-axis, all you need to do is change the sign of the x-coordinate while keeping  the y-coordinate the same. Using this rule, every point on the original triangle ABC will move 4 units to the left and go up 8 units to create the reflected triangle A'B'C' after the reflection.

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Answer:

Step-by-step explanation:

x^2 cannot be negative so the minimum value of x^2 is at (0.0)

When x = -1 y = 1 and when x = 1 y = 1

- and so on for all values of x

SO, y = x^2 is symmetrical about the y axis.

and the axis of symmetry is the y axis or we can write it as the line x = 0.

Answer:

m<1 = 111 degrees, m<2 = 69 degrees

Step-by-step explanation:

The measure of angles 1 and 2 are supplementary, (two angles adding up to 180 degrees). Using this, set up the equation:

x + 88 + 3x = 180  

4x = 108

x=23 degrees

Next, substitute 23 into the given angles:

m<1 = (23 + 88) = 111 degrees

m<2 = 23 * 3 = 69 degrees

Thus, m<1 = 111 degrees, m<2 = 69 degrees. Hope this helps

8) The part shared by vector BC and vector CB is called the magnitude of the line segment.

9) (a) Another name for ∠C is ∠ACB.

(b) ∠ADF and ∠BDC are two angles with point D as the vertex.

(c) Another name for ∠1 is ∠FBD.

(d) Another name for ∠2 is ∠FDB.

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Answer:

rotate 180

Step-by-step explanation:

because you can try it urself

Answer: 60m

Step-by-step explanation: The formula is 1/2(bxh)

the base is 10m and the height is 12m.

1/2(10 x 12) =

1/2(120) = 60