If three points are coplanar, they must be collinear. Since the answer is false, state a counterexample.

a. Total depreciation = $9700

b. Depreciation per kilometer = $0. 388 per kilometer

c. Vₙ = $35400 +  ₙt

d. Distance = 4723. 16 kilometers

e. Total distance =  29723. 16 kilometers.

i. The formula for total depreciation is given as;

Total depreciation = Cost of asset - Residual value

Cost of car = $ 35400

Residual value = $25700

Total depreciation = $35400 - $25700

Total depreciation = $9700

b. Depreciation per kilometer = Total depreciation/ distance travelled in kilometers

Depreciation per kilometer = $ [tex]\frac{9700}{25000}[/tex]

Depreciation per kilometer = $0. 388 per kilometer

c. Vₙ = V₀ + ₙt

t = time of depreciation

V₀ = $35400

Vₙ = $35400 +  ₙt

d. When the car costs $35400, it travelled 25000 kilometers

It costs $6688, it would travel 'x' kilometers

Cross multiply

$35400 × x = $ 6688 × 25000 kilometers

Make 'x' subject

x = [tex]\frac{6688 * 25000}{35400}[/tex]

x = [tex]\frac{167200000}{35400}[/tex]

x = [tex]4723. 16[/tex] kilometers

The car would travel 4723. 16 kilometers

e. To find the total distance

Total distance = 25000 + 4723. 16

Total distance =  29723. 16 kilometers.

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The value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36

The types of variation are;

y = (k × x²) / z³

where,

If y = 12, x = 4 and z = 2

y = (k × x²) / z³

12 = (k × 4²) / 2³

12 × 2³ = k × 4²

12 × 8 = k × 16

96 = 16k

k = 6

Find x when y = 1.728 and z = 5

y = (k × x²) / z³

1.728 = (6 × x) / 5³

1.728 × 5³ = 6x

1.728 × 125 = 6x

216 = 6x

x = 216/6

x = 36

Therefore, value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36

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Answer:

66666.66 seconds, or 1111.12 minutes

Step-by-step explanation:

Since you are earning 300 dollars per second, and you want to earn 20 million, or 20000000 dollars, you can divide 20 million by 300 to get the time it takes to reach your goal in terms of seconds:

[tex]\frac{20000000}{300}=66666.66[/tex] seconds

It will take you approximately 66667 seconds to reach your goal. If we divide by 60 to get this in terms of minutes, we get that it takes about 1111.12 minutes

Answer:

66.666.6 seconds

1,111.11 minutes

18.518518518499999 hours

Step-by-step explanation:

20,000,000÷300

=66,666.6666666

Change in minutes= 66,666.6666666÷60 =1,111.1111111

Change in hours= 1,111.11111111÷60=18.518518518499999

Answer: 24

Step-by-step explanation:

1. Number Them

Elf and Dwarf = 1

Hobbit = 2

Wizard = 3

Man = 4

* Elf and Dwarf are put together so that they are always sitting together

2. Multiply

1 x 2 x 3 x 4 = 24

Answer:

36

Step-by-step explanation:

To answer this question, we need to first understand the notation (f · x)(-2). This is a composite function, and another way to write this is f(g(-2)). This means that we have to find g(-2) and apply the function f to whatever this value is. Let's start by finding g(-2):

[tex]g(x)=x-2\\g(-2)=-2-2\\g(-2)=-4[/tex]

Now that we know g(-2) is -4, we can apply this to f:

[tex]f(x)=x^2-4x+4\\f(-4)=(-4)^2-4(-4)+4\\f(-4)=16-(-16)+4\\f(-4)=16+16+4\\f(-4)=36[/tex]

Therefore, our answer is 36

The expected money deposited in Clarie's account in next 12 months is listed below:

First, we must derive a formula that will generate the geometric sequence for the money remaining in Clarie's account:

[tex]c = c_{o}\cdot \left(1 + \frac{r}{100} \right)^{t}[/tex]     (1)

Where:

If we know that [tex]c_{o} = 300[/tex] and r = - 50, then the money left for each month is shown in the image attached below.

The image quality is poor to the point of being very hard to read. However, it coincides with the complete statement, which is presented in the question.

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Using it's formula, the present value of the amount is: $288.

The present value formula is:

[tex]PV = \frac{R}{(1 + r)^n}[/tex]

In which the parameters are:

Considering quarterly compounding, the parameters for this problem are as follows:

R = 450, r = 0.075/4 = 0.01875, n = 6 x 4 = 24.

Hence the present value is:

[tex]PV = \frac{R}{(1 + r)^n}[/tex]

[tex]PV = \frac{450}{(1.01875)^{24}}[/tex]

PV = $288

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The coordinates of the polygon A'B'C'D' following a reflection across the x-axis and a translation 2 units up are;

The vertices of the polygon are;

A(1, 1), B(2, 3), C(3, 2), and D(2, 1)

Reflection over the x-axis gives;

(x, y) reflection across the x-axis → (x, -y)

Which gives;

A(1, 1) R x-axis → A''(1, -1)

B(2, 3) R x-axis → B''(2, -3)

C(3, 2) R x-axis → C''(3, -2)

D(2, 1) R x-axis → D''(2, -1)

Translation of the points ABCD 2 units up gives;

A''(1, -1) T(0, 2) → A'(1, -1 + 2) = A'(1, 1)

B''(2, -3) T(0, 2) → B'(2, -3 + 2) = B'(2, -1)

C''(3, -2) T(0, 2) → C'(3, -2 + 2) = C'(3, 0)

D''(2, -1) T(0, 2) → D'(2, -1 + 2) = D'(2, 1)

The coordinates of A'B'C'D' are therefore;

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They form supplementary angles when they are added together.

Reason for Being Called Supplementary Angles

It is given that the angle made by the wall in one room is 36° and the angle formed by the same wall in the other room is 144°.

This implies that,

∠1 = 36°

∠2 = 144°

∠1 and ∠2 are adjacent angles and,

∠1 + ∠2 = 36° + 144°

⇒ ∠1 + ∠2 = 180°

Hence, these two adjacent angles make a straight-line angle. Hence, they are supplementary angles.

What are supplementary angles?

Two angles that form a straight line angle, that is, angle equal to 180°, when they are added together are said to be a pair of supplementary angles.

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An angle will always be formed when two or more lines intersect. These can form a series of complementary or supplementary angles. Complementary angles add upt o a right angle, while supplementary angles are two or more angles formed that add up to [tex]180^{o}[/tex]. Thus two supplementary angles can be referred to as a linear pair.

Therefore the required statements and reasons for the question are stated below:

          STATEMENT                                 REASONS

1. Line l and line m intersect                  Given

2. <1 is supplementary to <2,                        

   <3 is supplementary to <4                 Linear pair theorem

3. m<2 + m<3 = [tex]180^{o}[/tex],      

   m<3 + m<4 = [tex]180^{o}[/tex]                               Definition of Supplementary angles

4. m<1 + m<2  = m<3 + m<4 = [tex]180^{o}[/tex]        Congruent Supplement Theorem

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Answer:

Step-by-step explanation:

  <3 is supplementary to <4                 Linear pair theorem

I took the plato test and got it right

The value of X that number of unit fails are 1/12.

According to the statement

we have a given that the there is a shipment of 60 highly sensitive accelerometer. And there is a testing of randomly 5 accelerometers.

And we have to find that the how much units that fails in the specifications.

So,

We find the value of X by use of Probability.

The probability that unit fails = number of units that chosen randomly / total units.

So, substitute the values in it then

The probability that unit fails = 5 / 60

The probability that unit fails = 1 / 12.

The probability that unit fails from 60 accelemoters  is 1 / 12.

So, The value of X that number of unit fails are 1/12.

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The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)

In this question we must find the equation of the line perpendicular to the segment BC and that goes through the point A(x, y) = (1, 3). First, the slope of the line segment BC is:

m = [1 - (- 3)]/[5 - (- 3)]

m = 4/8

m = 1/2

And the slope of the line is:

m' = - 1/(1/2) = - 2

The intercept of the line is found by using the explicit form of equation of the line, m' = - 2 and (x, y) = (1, 3):

3 = - 2 · 1 + b

b = 5

The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)

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Answer:

D

Step-by-step explanation:

We will use the order of operations to evaluate the expression.

From left to right , Multiplication/Division followed by Addition/Subtraction.

21 / 3 + 8 - 4

= 7 + 8 - 4

= 15 - 4

= 11

Therefore, the answer is D

Answer:

D) 11

Step-by-step explanation:

Division and multiplication always comes first in an equation. Since there is no multiplication in the expression, we can divde first.

21 / 3 = 7

Our new expression will be: 7 + 8 - 4

Now we can just add (7) , (8), and (-4) not caring about the order, since they are all addition or subtraction.

I'll do the addition first, but order does not matter.

7 + 8 = 15

15 - 4 = 11

So 11 is our final answer.

Looking at the answer choices, D has 11, so D is our answer for this question.

Answer:

Python will return:

True

Step-by-step explanation:

The math function ** is an exponent indicator.

The equation you made was:
[tex]2^2 =4[/tex]

When you run this in python, it will return as true.

It is run as a Boolean expression because you have already provided the answer to the expression with the "==" statement.

If you had provided an incorrect answer (setting it equal to any number other than 4), it would return False.

Answer:

2.78%

Step-by-step explanation:

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

We are told that the six-sided dice is fair. This means that each of the faces has the same probability of being rolled.

Therefore, the probability of rolling one is:

[tex]\implies \sf P(x = 1)=\dfrac{1}{6}[/tex]

The probability of rolling six is:

[tex]\implies \sf P(x = 6)=\dfrac{1}{6}[/tex]

Therefore, the probability of rolling one and then six is:

[tex]\begin{aligned}\implies \sf P(x=1)\:and\:P(x=6) & = \sf \dfrac{1}{6} \times \dfrac{1}{6}\\& =\sf \dfrac{1}{36}\\& = \sf 0.0278\:(3\:s.f.)\\& = \sf 2.78\%\:(3\:s.f.)\end{aligned}[/tex]

Total elements in sample space=6

P(1)

P(6)

P(1 and 6)

As slope is undefined, then the slope of the line is parallel to the x axis.

In this problem we have a line that passes through two points, the slope is determined by definition of secant line:

m = [- 9 - (- 6)]/(8 - 8)

m = - 3/0

As slope is undefined, then the slope of the line is parallel to the x axis.

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The purpose of the graphic is to show the relationship between different educational qualifications and unemployment rate.

This is a situation in which employable individuals look for jobs and are unable to find one.

The key findings in this graphic is that the higher the level of education, the lesser the unemployment rate.

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Answer: 12x

Step-by-step explanation:

The question is asking what equation models the table above. You have to make an equation that when any of the times on the left column are plugged in, the value on the right column are outputted.

For 1, the equation should output 12. For 2, the equation should output 24. For 3, the equation should output 36, and so on.

Here, we see a pattern: for every value we input as the number of seconds, the height is 12 times more than that. Assuming x is the time and y is the height,

[tex]y=12x[/tex]

If we use any x on the left, it's corresponding height will be the y.

The area of the sector in radians is calculated as: B. 8π units squared.

The area of a sector where the central angle of the sector that is shaded in a circle is given in radians is calculated using the formula that is expressed as:

Area of sector = (1/2) × r²θ; where we have:

θ = the angle subtended at the center/central angle measure in radians

r = the radius of the circle

Given the following:

The shaded area is half of the circle. Its measure would be 180 degrees which when expressed in radians would be π.

Central angle measure in radians (θ) = π

Radius (r) = 4 units

Plug in the values into the area of sector formula

Area of sector = (1/2) × r²θ = (1/2) × (4²)(π)

Area of sector = (1/2) × (16)(π)

Area of sector = (1 × 16 × π)(2)

Area of sector = (16π)(2)

Area of sector = 8π units squared

In conclusion, the area of the shaded sector in the image given below is calculated as: B. 8π units squared.

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Answer:

3

Step-by-step explanation:

a = the other leg:

[tex]a^{2} =(2\sqrt{3} )^{2} -(\sqrt{3}) ^{2} =(4)(3)-3=12-3[/tex]

[tex]a^{2} =9[/tex]

[tex]a=\sqrt{9}[/tex]

[tex]a=3[/tex]

Hope this helps

The true statement is David's calculations are incorrect, he used the circumference and the height to find the volume.

Correct calculation:

C = 2πr

8.6 = 2 × 3.14 × r

8.6 = 6.28r

r = 8.6/6.28

r = 1.36942675159235 inches

convert 1.36942675159235 inches to cm

= 3.478343949044569 cm

Approximately,

r = 3.5 cm

Volume = πr²h

= 3.14 × 3.5² × 15.2

= 3.14 × 12.25 × 15.2

= 584.668 cm³

Approximately,

volume = 584.7 cm³

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Answer:

Step-by-step explanation:

jello :

3x=2(mod4)

multiply by ; 5

5×3x=5×2(mod4)

15x=10(mod4)

but : 15= -1 (mod4)   and 10= 2 (mod4)

-x=2 (mod4)

now multiply by ; -1 you have :  x= -2 (mod4)

-2=2(mod4)

conclusion : x=2 (mod4)  means : x=4k+2   k in Z

Answer: Options (2), (4), (5)

Step-by-step explanation:

When x = 1, y = 1. So, g(1)=1.

Using similar logic to test the other options, we see that the correct answers are options (2), (4), and (5).

The distance between the skate and point X is 16 feet

Given that the distance between point X and kite is 12 feet

and the distance between stake and kite is 20 feet

We need to find the distance between the stake and point X

Here,

Perpendicular = 12 feet

Hypotenuse = 20 feet

Base = ?

According to Pythagoras Theorem

(Hypotenuse)² =  (Perpendicular)²+(Base)²

(20)² = (12)² + (Base)²

∴ (Base)² = 400 - 144

∴ (Base)² = 256

∴ Base = 16 feet

Hence the distance between the Point X and the stake is 16 feet

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Making "a" the subject of the formula would give us: a = 8 - b - c/2

Given the formula, 8 = a+b+c/2, to make a the subject of the formula, we would isolate a in the equation.

8 = a+b+c/2

8 = (2a + 2b + c)/2

2(8) = 2a + 2b + c

16 = 2a + 2b + c

16 - 2b - c = 2a

Divide both sides by 2

16/2 - 2b/2 - c/2 = 2a/2

8 - b - c/2 = a

a = 8 - b - c/2

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