James paid off the loan on his motorboat in the year 2006. He originally borrowed $6500 to buy the boat, but with simple annual interest, he discovered that he paid a total of $8775 over the life of the loan. If James’s annual interest rate was 7%, in what year did his loan begin?

The box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

A box-and-whisker plot consists of the following values of a data set: min, max, lower quartile, median, and upper quartile.

Here, Given the data set,

30, 22, 22, 27, 28, 23, 24, 25, 26, 23

the five-number summary for the box-and-whisker plot would be:

Minimum: 22

Quartile Q1: 22.75

Median: 24.5

Quartile Q3: 27.25

Maximum: 30

Thus, the box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

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Answer:

[tex]slo pe \: = \frac{2}{7} [/tex]

Step-by-step explanation:

[tex]y1 = 3\\ x1 = - 8 \\ y2 = 7 \\ x2 = 6[/tex]

[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]sope = \frac{7 - 3}{6 - ( - 8)} [/tex]

[tex]slope = \frac{4}{6 + 8} [/tex]

[tex]slope = \frac{4}{14} [/tex]

[tex] = \frac{2}{7} [/tex]

Answer:

[tex]\textsf{slope}=\dfrac{2}{7}[/tex]

Step-by-step explanation:

[tex]\textsf{let}\:(x_1,y_1)=(-8,3)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(6,7)[/tex]

Using the slope formula:

[tex]\textsf{slope}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-3}{6-(-8)}=\dfrac{4}{14}=\dfrac{2}{7}[/tex]

Therefore, the slope between the two points (-8, 3) and (6, 7) is 2/7

Answer:

Step-by-step explanation:

A line perpendicular to the given line has a slope that is the negative inverse of the reference line.  

Rewrite the given equation in the format of y=mx+b, where mi is the slope and b is the y-intercept (the value of y when x = 0.

2x + 3y = 4

3y=-2x+4

y = -(2/3)X + (4/3)

The reference slope is -(2/3).  The negative inverse is (3/2), which will be the slope of a perpendicular line.  We can write the new line as:

y = (3/2)x + b

Any value of b will still result in a line that is perpendicular.  But we want a value of b that will shift the line so that it intersects the point (-3,-5).  Simply enter this point in the above equation and solve for b.

y = (3/2)x + b

-5 = (3/2)(-3) + b

-5 = -(9/2) + b

-5 = -4.5 + b

b = - 0.5

The equation of the line that is perpendicular to 2x + 3y = 4 and includes point (-3,-5) is

y = (3/2)x - 0.5

Answer:

(4,0)

Step-by-step explanation:

The point where the line cuts the x-axis is called the x-intercept.

x-intercept is when y = 0.

So given y = 0,

3x+4(0) = 12

3x =  12

x = 12/3

x = 4

therefore the point is (4,0)

The area of this hub cap is about  510.44625 cm².

The area of circle is pi times the square of the radius.

Area of circle =π r²

Circumference (C) = 2π r

80.07 = 2 (3.14) r

76.87/ (2x 3.14) =r

r = 12.75 cm

now, Area be

=π r²

= 3.14*12.5*12.75

=510.44625 cm²

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Answer: decrease the resources invested

Step-by-step explanation:

Answer:

[tex] {x}^{ - 2} = \frac{1}{ {x}^{2} } \: \: –> {7}^{ - 2} = \frac{1}{ {7}^{2} } = \frac{ 1}{49} \\ \\ {x}^{ - 1} = \frac{1}{ {x}^{1} } \: –> {7}^{ - 1} = \frac{1}{ {7}^{1} } = \frac{1}{7} \\ \\ {x}^{0} –> {7}^{0} = 1 \\ \\ {x}^{1} –> {7}^{1} = 7 \\ \\ {x}^{2} –> {7}^{2} = 49[/tex]

Answer:

13.) 314.2 in²

15.) 181.5 ft²

Step-by-step explanation:

The area of a circle is found using the equation:

A = πr²

In this equation, "π" represents the number pi (3.14....) and "r" represents the radius (half the diameter).

For 13.), you have been given the radius. Thus, you can substitute it into the equation and solve for "A".

A = πr²

A = π(10)²

A = π x (100)

A = 314.2 in²

For 15.), you have been given the diameter. To find the radius, you need to divide this value by 2. Once you find the radius, you can plug it into the equation and simplify like above.

diameter = 15.2 ft
radius = 7.6 ft

A = πr²

A = π(7.6)²

A = π x (57.76)

A = 181.5 ft²

The percentage of the original block cookie that is packaged and ready to be distributed to stores is: 12.6%.

To calculate the percentage of the original 100lb cookie that is packaged and ready to be distributed, we must perform the following operations:

We must calculate how much each package of 5 cookies weighs, for this we multiply the weight of each cookie (3 ounces) 0.18 pounds by the number of cookies in each package (5).

Next, we need to calculate how much the box containing 14 packages of cookies weighs by multiplying the weight of each package (0.9 lb) by the number of packages in each box (14).

Lastly, we need to calculate how much percentage the weight of each box is equal to the weight of the original 100 lb cookie that Latonya made. For that we divide 100 lbs. by 100 and multiply the result by the final weight of the box (12.6lbs).

Based on the above, each box contains 12.6% of the first 100-lb cookie Latonya made.

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Every term in pattern B is two times the corresponding term in pattern A

The correct option is (B).

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Given:

pattern A uses the rule add five pattern

pattern B uses the rule add 10

if we take example

5x2=10 and comparable to pattern A x2 to get the next number.

Hence, every term in pattern B is two times the corresponding term in pattern A.

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The correct option is (B).

The functions have complex roots from the image are

Functions (b) and (d). This is further explained below.

Generally, Function is simply defined as a connection between two or more variables that may be expressed mathematically.

In conclusion,  Functions with graphs that never touch or cross the x-axis are said to have complicated roots, not real ones.

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The data values that are outliers are 4 and 56.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier distorts the mean and median of the dataset.

In this data, 4 is smaller than the average of the data set and 56 is larger than the average numbers. They are the outliers.

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The graph state that the initial point is (6.9), and the terminal point is (2,1). The vertex of the parabola is  (3,0). Arrows along the parabola to indicate motion right to left.

Let take x = 4 - t    =t  =  4 - x       as equation  (1)

And y = (t - 1)^2       as equation (2)

Then input equation  (1)  into equation   (2)

y  = ( 4 - x - 1)^2

y = ( 3 - x)^2

y = ( x - 3)^2

So therefore, y = a ( x -3)^2  +  0

It can be written as y  = a(x - h)^2  + k      

Where, a = 1    

The vertex  known to be (h, k)  will be = (3,0).

The starting point is  if t = -2

Therefore, x  = (4 - -2)   = 6      

  y =  (-2 - 1)^2  = (-3)^2    = 9  

So x, y =  (6,9).

Note that if t  = 2

Then x = (4 - 2) =  2      

  y  =  (2 - 1)^2   = 1^2  

=  1    

Therefore, x, y =(2, 1).

Therefore, The graph of the parametric equations  state that the initial point is (6.9), and the terminal point is (2,1). The vertex of the parabola is  (3,0). Arrows along the parabola to indicate motion right to left.

See full question below

What does the graph of the parametric equations x(t)=4−t and y(t)=(t−1)^2, where t is on the interval [−2,2], look like?

The parametric equations graph as a portion of a parabola. The initial point is _____, and the terminal point is _____. The vertex of the parabola is ____. Arrows are drawn along the parabola to indicate motion ____.

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Answer:

πr²h= 1696

⇒r²=1696/3.14×15

⇒r²=36.009

⇒r=√36.009

∴r=6.0008=z

The value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = -x³

[tex]\rm g(x) = |\dfrac{1}{8}x-1|[/tex]

Plug x = 4 in the f(x)

f(4) = -4³ = -64

Plug the above value in the g(x)

[tex]\rm g(x) = |\dfrac{1}{8}(-64)-1|[/tex]

g(f(4)) = |-8-1| = |-9| = 9

Thus, the value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (B) is correct.

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If the  -8 is under the square root, then...

[tex]\displaystyle L = \lim_{x\to -3} \sqrt{x^2-8}\\\\L = \sqrt{(-3)^2-8}\\\\L = \sqrt{9-8}\\\\L = \sqrt{1}\\\\L = 1\\\\[/tex]

OR

If the -8 is not under the square root, then...

[tex]\displaystyle L = \lim_{x\to -3} \sqrt{x^2}-8\\\\L = \sqrt{(-3)^2}-8\\\\L = \sqrt{9}-8\\\\L = 3-8\\\\L = -5[/tex]

Either way, we replace x with -3 and simplify.

For more information, refer to the direct substitution rule for limits.

The limit of   [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex] is one.

A limit is the value that a function approaches as the input approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity.

The given limit is [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex]

Now replace x with -3 as limit value is -3

√(-3)²-8

Square root over minus three square minus eight

The three square is nine

√9-8

When eight is subtracted from nine we get one.

√1

The square root of one is always one

[tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex]=1

Hence, [tex]\lim_{x \to \-(-3)} \sqrt{x^{2} -8}[/tex] is one.

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Answer:

B

Step-by-step explanation:

an arithmetic squeegee is defined by

an = an-1 + d

that means that every term of the sequence is created by adding a constant d (the common difference) to the pervious term.

so, we get the common difference by caucuses the difference of 2 neighboring terms.

e.g.

a1 = 9

a2 = 22

a2 - a1 = 22 - 9 = 13

so, B. 13 is the right answer.

as a quick check if it is truly an arithmetic sequence, we can look, if all the other pairs have the same difference.

yes, they do. the difference is always 13.

Answer:

2400 words

Step-by-step explanation:

First choose the first letter. You have 5 choices of consonant for this.

Next choose the last letter. You have 4 remaining consonants for this.

Now you have 5 remaining letters which can be placed in any order.

So the answer will be:

5⋅4⋅5!

20⋅120

2400

Answer:

≈0.71 or [tex]\frac{\sqrt{2}}{2}[/tex].

sin(45°) =  approximately 0.71. The value is also equal to [tex]\frac{\sqrt{2}}{2}[/tex].

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Answer:

See below ~

Step-by-step explanation:

Q1

⇒ Remember that sides opposing larger angles are greater in size

⇒ 75° > 54° > 51°

⇒ AC > BC > AB

Q2

⇒ The exterior angles lie outside the triangle

⇒ ∠1 + ∠2 = ∠6 (Exterior Angle Property)

⇒ ∠1 + ∠2 = ∠P (Exterior Angle Property)

⇒ ∠3 = ∠5 (Vertical Angles)

Answer:

1.1 x 10¹² mg of sodium

Step-by-step explanation:

(3.4 x 10³ mg)(3.27 x 10⁸) = 1.1 x 10¹² mg

Answer:

11,000

Step-by-step explanation:

10% of 10,000 is 1,000 so 5% is 500 and add 2 of 5% you get 1,000 and add it to the old price thus you get 11,000.

Answer:

13.2 units

Step-by-step explanation:

12 is to 7.2 as   (12+10) is to x

12/7.2   =  (12+10)/x

x = 22 * 7.2/12 = 13.2 units

Answer:

Step-by-step explanation:

16 - 4 = 12

16 + 4 = 20

then 20 ; 2 = 10

Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.

Answer:

Exact Area =

16pi - 32 square meters

Decimal Approx:

A = 18.3 sq m

Step-by-step explanation:

In degrees, it's 360° all the way around a circle. The 270° in the image is to show you that the small piece (the triangle and yellow segment) are in a 90° part of the circle. That is 1/4 of the circle, this helps with area two ways. We'll find 1/4 of the circle area and also, that makes the triangle base 8 and height 8. This helps us find triangle area. See image.

The polynomial function represented by the data is equal to D. f(x) = −x² + 10.

In order to determine the polynomial function represented by the data, we would substitute the value of x (-3) into the given set of functions as follows:

For option A, we have:

f(x) = 6x + 15

f(-3) = 6(-3) + 15

f(-5) = -18 + 15

f(-5) = -3 (False).

For option B, we have:

f(x) = -6x - 45

f(x) = -6(-3) - 45

f(x) = 18 - 45

f(x) = -27 (False).

For option C, we have:

f(x) = x² - 40

f(x) = -3² - 40

f(x) = 9 - 40

f(x) = -31 (False).

For option D, we have:

f(x) = −x² + 10

f(x) = −(-2)² + 10

f(x) = −9 + 10

f(x) = 1 (True).

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Complete Question:

A polynomial function is represented by the data in the table.

x = -5, -4, -3, -2, -1

f(x) = -15, -6, 1, 6, 9

Choose the function represented by the data.

A. f(x) = 6x + 15

B. f(x) = −6x − 45

C. f(x) = x² − 40

D. f(x) = −x² + 10

The area of the circle grows by a factor of 9, and the actual area is 360

The given parameters are:

Old area = 40

Scale factor = 3

When the circle is dilated, the new area becomes

New area = Old * (Scale factor)^2

Substitute 3 for scale factor

New area = Old * 3^2

Evaluate the exponent

New area = Old * 9

This means that the area of the circle grows by a factor of 9, and the actual area is:

New area = 40 * 9 = 360

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The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is,

⇒ - 12 + 20x ≥ - 6x + 9

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequality is,

⇒ - 4(3 - 5x) ≥ - 6x + 9

Now, We can simplify as;

⇒ - 4(3 - 5x) ≥ - 6x + 9

⇒ - 12 + 20x ≥ - 6x + 9

⇒ 20x + 6x ≥ 12 + 9

⇒ 26x ≥ 21

⇒ x ≥ 21/26

Thus, The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is,

⇒ - 12 + 20x ≥ - 6x + 9

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Answer:

You are to write a five paragraph literary essay based on one of the 4 prompts and what you have read and learned in this module. These are your options:

1. How do the events of "The White Umbrella" teach the narrator a lesson about shame and acceptance?

2. What role does creativity play in "The Bat-Poet"?

3. How does the character of Squeaky change over the course of "Raymond's Run"?

4. Discuss the influences of older family members on the protagonists and speakers in the stories and poems of this unit.

You are to write a five paragraph literary essay based on what you have read and learned in this module. Your final submission should meet the following requirements.

• Submit completed pre-writing and outline documents.

• Write an essay that contains an introduction with hook and thesis statement, supporting paragraphs with evidence and at least one quotation, and a conclusion that restates the thesis and reviews main points.

• Use transitions appropriate to the pattern of organization.

• Use vocabulary to create tone and voice.

• Cite primary source (quotation).

• Submit completed revision checklist.

• Vary sentence structure.

• Create sentences with parallel structures.

• Use technology in the writing process.

Step-by-step explanation: