How can yo order rational numbers from least to greatest

Initial salary =  $50,000 .

Rate of raise = 5% each year.

Therefore, each next year salary would be 105% that is 1.05 times.

5% of 50,000 = 0.05 × 50000 = 2500.

Therefore raise is $2500 each year.

According to geometric sequence first term 50000 and common ratio 1.05.

Applying geometric sequence formula

[tex]a_n = ar^{n-1}[/tex]

1) [tex]a_n = 50000(1.05)^{n-1}[/tex]

2) In order to find salary in 5 years we need to plug n=5, we get

[tex]a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4[/tex]

= 50000(1.21550625)

3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.

[tex]S_n = \frac{a(1-r^n}{1-r}[/tex]

Plugging n=10, a = 50000 and r= 1.05.

[tex]S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}[/tex]

[tex]S_10 = \frac{50000(0.050)^{10}}{0.05}[/tex]

= 628894.62678.

The answer is D, (3, -4)

[tex]14n+6p-8n=18p\ \ \ \ |\text{subtract 6p from both sides}\\\\14n-8n=12p\\\\6n=12p\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{n=2p}[/tex]

The correct solution for this equation is n = 2p.

I hope this helped! :)

B) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.

RPS is 90 degrees because of the vertical line theorem... opposite angles are always congruent.

Answer: RPS is 90 degrees

Step-by-step explanation:

[tex]y\geq2-2x\\\\\text{Let's the line}\ y=2-2x\\\\for\ x=0\to y=2-2(0)=2\to(0,\ 2)\\for\ x=1\to y=2-2(1)=0\to(1,\ 0)[/tex]

[tex]\text{draw a line and shade above the line}\\\\\text{Look at the picture}[/tex]

Answer:

Graph is attached below

Step-by-step explanation:

To graph the given inequality , replace the inequality sign by = sign

y≥2−2x

y=2−2x

Now make a table , assume some random number for x and find out y

x         y=2-2x

0          2

1           0

2          -2

Now graph all the points (0,2) (1,0) (2,-2)

Now we do shading. For shading use test point (0,0)

plug in 0 for x and 0 for y

[tex]y\geq 2-2x[/tex]

[tex]0\geq 2-2(0)[/tex]

[tex]0\geq 2[/tex] is false

So shade the region that does not contain (0,0)

The graph is attached below

The length of the longest bridge in the world is found by adding the length of the second longest bridge namely the Tianjin Grand Bridge, and the stated difference between the two bridges' lengths. After calculation, the length of the longest bridge in the world is found to be 540,700 feet.

To find the length of the longest bridge in the world, we should add the length of the Tianjin Grand Bridge (the second longest in the world) and the difference between the two bridges. In this case, the length of the Tianjin Grand Bridge is 373,000 feet and it's stated that this is 167,700 less than the length of the longest bridge.

So, we have to do the following calculation: 373,000 feet (length of the Tianjin Grand Bridge) + 167,700 feet (difference in length) = 540,700 feet.

So, the length of the longest bridge in the world is 540,700 feet.

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The number that is divisible by 3 and 9 is 40,653.

The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in maths.

We may face different situations every day where we use the division technique.

Given are numbers, we need to find which of them numbers are divisible by 3 and 9,

LCM of 3 and 9 is 9,

So numbers completely divisible by 9 will also be divisible by 3.

The only number from the option which is completely divisible by 9 is 40,653.

Hence, the number that is divisible by 3 and 9 is 40,653.

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Answer C, aka 3 is that line's slope.

Answer:

the slope of the line is 3

Step-by-step explanation:

Hello, I think I can help you with this

if you have two points of a line

[tex]P1=(x_{1},y_{1})\\ and\\P2=(x_{2},y_{2})[/tex]

you can find the slope using

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]

Step 1

Let

P1( 1, 3) and P2(3,9)

put the values into the equation

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{9-3}{3-1}\\m=\frac{6}{2}\\ m=3[/tex]

the slope of the line is 3

I hope it helps,Have a great day.

Hi!

Answer - Line R

Well refraction is the bending of something. I choose r because it may have refraction because of the 2 rectangles at the end of both sides.

Hope This Helps!

Answer:

[tex]y =\frac{1}{6} + 0.25x[/tex]

[tex]0 \leq x \leq23.33[/tex]

[tex]0 \leq y \leq 6[/tex]

Step-by-step explanation:

The machine always takes 10 minutes (or 1/6 hours) to warm up and performs each cycle in 15 minutes, or 0.25 hours.

The maximum amount of daily hours that the machine can work is 6 hours.

Therefore we can represent this situation by means of an equation of the form:

[tex]y =\frac{1}{6} + 0.25x[/tex]

Where

y = daily amount of hours the machine works.

x = number of daily cycles performed.

This equation is a linear function.  Because it has the form y = ax where a is a real number

The graph of this equation is shown in the attached image, where the gray shaded area represents the domain of the function.

The domain of the function is:

[tex]x\geq 0[/tex] (because you can not perform less than zero cycles a day)

[tex]x \leq23.33[/tex]. Because the machine can not exceed 6 hours per day, then it can not do more than 23.33 cycles.

So:

[tex]0 \leq x \leq23.33[/tex]

The range of the function is:

[tex]y \geq 0[/tex] (because you can not work less than 0 hours a day)

[tex]y \leq 6[/tex] (because the machine can not work more than 6 hours a day)

So

[tex]0 \leq y \leq 6[/tex]

That is 5 1/4 - 1 3/4

= 21/4 - 7/4

=14/4

= 3 1/2 inches

Yes, this table represents a function.

Function--

It is  a set of ordered pair of the type: (x,y) in which each input variable i.e. x is mapped to a single output i.e. y.

i.e. each of the value of x is mapped to a single y.

Here after looking the table we observe that each of the value of the independent variable i.e. Hours of training is mapped to a single value of the dependent variable i.e. monthly pay.

When a line is perpendicular to another line, the slope is the negative reciprocal of the other line's slope. So in this case, the slope would be 1, since the negative reciprocal of -1 is 1/1 which is 1.

To find the y-intercept, you have to substitute the point (8,2) into y = mx + b

2 = 1(8) + b

b = -6

The equation is y = x - 6

The equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6

The equation of the required line in slope-intercept form is expressed as:

y-y0 = m(x-x0) where:

Given the equation of the line as y = -x

Get the slope of the line

mx = -x

m = -1

Since the required line is perpendicular to this line, the required slope will be 1 (M = -(-1/1))

Get the required equation

Recall that;

y-y0 = m(x-x0)

y - 2 = 1(x-8)

y - 2 = x - 8

y = x - 8 + 2

y = x - 6

Hence the equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6.

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f(x) = 8000 - (8000)(0.11)x

     = 8000 - 880x

f(5) = 8000 - 880(5)

     = 8000 - 4400

     = 3600

Answer: $3,600

Answer:

$4467.25

Step-by-step explanation:

We have been given that a jet ski depreciates at 11% of its original value each year. The jet ski was $8,000 as it’s time of purchase.

We will exponential decay function to solve our given problem.

[tex]y=a\cdot(1-r)^x[/tex], where,

a = Initial value,

r = Decay rate in decimal form.

[tex]r=\frac{11}{100}=0.11[/tex]

[tex]y=\$8,000\cdot(1-0.11)^5[/tex]

[tex]y=\$8,000\cdot(0.89)^5[/tex]

[tex]y=\$8,000\cdot 0.5584059449[/tex]

[tex]y=\$4467.2475592[/tex]

[tex]y\approx \$4467.25[/tex]

Therefore, the value of ski jet after 5 years would be $4467.25.

Answer:

y= 126

Step-by-step explanation:

The given equation is: y= 3x-2x^2+5x^3

Substituting the value x=3 in the above equation,we get

   y= 3(3)-2(3)^2+5(3)^3

⇒y= 9-2(9)+5(27)

⇒y= 9-18+135

⇒y= 126

The answer is B. If you look at a graph of -tan (which is cot), the places the graph crosses -1 are at pi/4 plus kpi. If you add pi to pi/4, you get 5pi/4, and these two answers are in B only.

Im adding an answer so the other guy that gave an answer gets his points.

Answer:

(1)  Rotation of 90° counterclockwise about the origin (2) Translation 2 units right .

Step-by-step explanation:

We have been asked to determine a sequence of transformations that maps △ABC to △A′B′C'.

To map △ABC to △A′B′C′ first of all we have to rotate △ABC 90° counterclockwise (positive rotation) about the origin. After rotating △ABC 90° our new coordinates will be A(-3,-4), B(-3,-1) and C (-1,-2).

We can see that distance between A and origin is [tex]\sqrt{5}[/tex] and distance between A' and origin is also [tex]\sqrt{5}[/tex]. Distance between A and A' is [tex]\sqrt{10}[/tex], which forms a right triangle.

To map △ABC to △A′B′C′ completely we will translate our △A′B′C' 2 units right. After translation our coordinates will be A'(-1,-4), B'(-1,-1) and C'(1,-2).

Therefore, a sequence of transformations that maps △ABC to △A′B′C′ is (1) rotation of 90° counterclockwise about the origin and (2) translation 2 units right.

Final answer:

The sequence of transformations is a rotation followed by a translation, which can map one triangle to another in the Euclidean plane.

Explanation:

A sequence of transformations that maps △ABC to △A′B′C′ can be described as a combination of basic transformations such as rotations, reflections, and translations. Based on the options given, the correct sequence to map △ABC to △A′B′C′ is a rotation followed by a translation. For example, if △ABC were rotated 90 degrees counterclockwise about the origin and then translated 2 units to the right, it could be mapped to a new position as △A′B′C′. It is important to note that the order of transformations can affect the outcome, and transformations are done in sequence.

The answer is 3 hours  40 minutes

1. 4x = 7(x - 3)       1.Given

4x = (7)(x) + (7)(-3)

2. 4x = 7x - 21       2.Distributive property

4x - 7x = 7x - 7x - 21

3. -3x = -21            3.Subtraction property of equality

-3x : (-3) = -21 : (-3)

4. x = 7                  4.Division property of equality

y = - [tex]\frac{2}{3}[/tex] x - 2

the equation of a line in ' slope - intercept form ' is

y = mx + c ( m is the slope and c the y- intercept ) calculate m using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0 , - 2 ) and (x₂ , y₂ ) = A( 6 , - 6 )

m = [tex]\frac{- 6+ 2}{6 - 0}[/tex] = [tex]\frac{-4}{6}[/tex] = - [tex]\frac{2}{3}[/tex]

y -intercept c = - 2 ( from graph )

y = - [tex]\frac{2}{3}[/tex] x - 2

x = - [tex]\frac{7}{4}[/tex] or x = 0

take out a common factor 2x

2x(4x + 7 ) = 0

equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

4x + 7 = 0 ⇒ x = - [tex]\frac{7}{4}[/tex]

To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. The derivative of sin(xy^2) with respect to x is cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx). Simplify the expression to find dy/dx.

To find dy/dx by implicit differentiation, we will differentiate both sides of the equation with respect to x.

We have the equation 5+4x=sin(xy^2). Taking the derivative of both sides, the left side will be 0 since it is a constant. On the right side, we use the chain rule.

The derivative of sin(xy^2) with respect to x can be written as cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx).

Simplifying further, dy/dx = (cos(xy^2) * (2xy^2 + x * 2y * dy/dx)) / (1 - x * 2y^2 * cos(xy^2)).

1. Qualitative

2. Quantitative

3. Quantitative, continuous data

4. Quantitative, discrete data

5. Quantitative, continuous data

I believe its asking you the formula to find the rows numbers moving forward

Examle row 5 will be 16, I believe that is B. 4n - 1

your answer is A

hope this helps :)

A = [tex]\frac{1}{2}[/tex]bh

[tex]\frac{1}{2}[/tex] × (bh) = A

[tex]\frac{bh}{2}[/tex] = A

bh = A × 2

bh = 2A

b = [tex]\frac{2A}{h}[/tex]

The answer is a: b= [tex]\frac{2A}{h}[/tex]

Given

Sue wants to buy a video that costs $24.95.

She has $3 in her pocket

a piggy bank full of quarters x

Find out the inequality can be used to represent the number of quarters sue needs to buy the game.

To proof

As given in the question

Sue wants to buy a video that costs = $24.95.

She has $3

The value of quaters in the piggy bank = x

1 $ = 4 quaters

First convert $24.95 in the quaters form

=  4 × 24.95

= 99.8 quaters

convert $3 in the quaters form

= 3 × 4

= 12 quaters

The equation become in the form

[tex]12 + x \geq 99.8[/tex]

x = 87.8 quaters

quarters sue needs to buy the game is  87.8 quaters.

Hence proved

x = 0

distribute parenthesis on both sides of the equation and simplify

3x - 7 - 4x = 10x - 8 + 1

- x - 7 = 10x - 7 ( subtract 10x from both sides )

- 11x - 7 = - 7 ( add 7 to both sides )

- 11x = 0 ( divide both sides by - 11 )

x = 0