A dealership is allowing residents to test drive the following vehicles: 2 sports cars, 3 vans, and 3 trucks. If you select a random car to test drive, what are the odds it is not a sports car? Write your answer in the form a:b as a fully reduced ratio.

The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.

[tex](a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]

(b) When x = 0.6 and q = 0.5 m/s, the speed of the wagon is approximately 0.243 m/s.

Reasons:

(a) The distance from the cart to the pulley, r is given by Pythagoras's

theorem as follows;

r = √((3 - 0.6)² + x²) = √(2.4² + x²)

The speed of the wagon = [tex]\mathbf{\dfrac{dx}{dt}}[/tex]

The speed of the rope, q = [tex]\mathbf{\dfrac{dr}{dt}}[/tex]

By chain rule, we have;

[tex]\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}[/tex]

[tex]\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}[/tex]

Therefore;

[tex]\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}[/tex]

[tex]\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}[/tex]

(b) The speed of the wagon when x = 0.6 if q = 0.5 m/s is given as follows;

[tex]\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243[/tex]

The speed of the wagon when x = 0.6 and q = 0.5 m/s, [tex]\dfrac{dx}{dt}[/tex] ≈ 0.243 m/s

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Question 2: -4/3

Question 3: -7/20

Answer:

The total change in water level over the past 2 years is [tex]\displaystyle -4 \frac{1}{6}[/tex].

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Fractions

Numbers

Step-by-step explanation:

Step 1: Define

Identify

Year 1 water change:  [tex]\displaystyle -2 \frac{1}{3}[/tex]

Year 2 water change:  [tex]\displaystyle -1 \frac{5}{6}[/tex]

Step 2: Find Total Water Change

Answer:

it is c. both i guess anyways thanks

i hope you passed and sorry for taking your points

Step-by-step explanation:

Answer:

I = $372.40

Step-by-step explanation:

Given the principal amount of $2,940, which is invested for 4 months at 3.8% interest rate:

Use the following simple interest formula to solve for the interest earned:

I = P × r × t

where:

I = interest earned

P = principal amount invested = $2,940

r = interest rate = 3.8% or 0.380

t = time = 4/12 months = ⅓ or 0.3333

Substitute to given values into the simple interest formula:

I = P × r × t

I = $2,940 × 0.380 × 0.3333

I = $372.40

Therefore, the simple interest earned in 4 months is $372.40.

Answer: The drill will reach -915 feet after 18 days.

Answer:

3m-8/7m+14

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + y = 18

y = 18 - x

xy = 72

x(18 - x) = 72

-x² + 18x = 72

0 = 72 - 18x + x²

x = (18 ± √(18² - 4(1)(72))) / (2(1))

x = (18 ± 6)/2

x = 12

x = 6

Answer:

38.5 in

Step-by-step explanation:

11.25 in + 11.25 in + 8 in + 8 in

= 38.5 in

Answer: 1.09

Step-by-step explanation:

First subtract the difference between the two:

200 - 50 = 150

Now divide that by 2:

150/2 = 75

Bills share is $75

Now add the $50 to 75 to get Ann's share:

75 + 50 = $125

Ann's share is $125

Bill's share is $75

Answer:

5/2

Step-by-step explanation:

Slope = Change in y/Change in x

Slope = 2 - 7/4 - 6

Slope = -5/-2

Slope = 5/2

-Chetan K

Step-by-step explanation:

we paint the walls and ceilings.

and we ignore any doors or windows (no information about them).

so, each room has then 5 rectangles : 4 walls and 1 ceiling.

when we say a room is 14 ft × 10 ft, this also means there are 2 sides of 14 ft and 2 sides of 10 ft.

and the area is 14×10 ft².

the area of the ceiling is the same as the area of the floor : 14×10 = 140 ft²

for the walls we have 2 rectangles of 14×8 = 112 ft², and 2 rectangles of 10×8 = 80 ft² (remember, the height of the room is 8 ft).

for the sister's room it is similar.

just a 12×10 = 120 ft² ceiling.

and 2 rectangles of 12×8 = 96 ft² and again 2 rectangles of 10×8 = 80 ft² as walls.

altogether we have then

140 + 112 + 112 + 80 + 80 + 120 + 96 + 96 + 80 + 80 ft²

that is in total

996 ft²

how many gallons of paint do we need for this ?

well, 1 gallon per 250 ft².

so, how often does 250 fit into 996 ?

996 / 250 = 3.984 gallons.

since we get the paint most likely only in quantities of gallons, we need 4 gallons for the paint job.

Answer:

6 and a half 2 thirds are in 4 1/3

Step-by-step explanation:

2/3x=13/3

2x=13

x=6.5

Answer:

II and III only

Step-by-step explanation:

One variable quantity is said to vary jointly as a number of other variable quantities, when it varies directly as their product.

Answer:

The flower is 9 meters from the base of the tree.

Step-by-step explanation:

Use the Pythagorean theorem to solve. We are given the length of one leg and the length of the hypotenuse of a right triangle.

[tex]a^{2} +b^{2} =c^{2}[/tex]

where a and b are the legs, and c is the hypotenuse.

Plug in the given values and solve:

[tex]x^{2} +12^{2} =15^{2} \\x^{2} +144=255\\x^{2} =81\\x=9[/tex]

The flower is 9 meters from the base of the tree.

The percentage change in the number of burglaries over the two-year period is 35% .

The change in burglaries over the two-year period to have  a 40% increase is 6.7%.

Let's assume that the annual number of burglaries in 2011 is 1000. After the 50% increase in 2012, the number of burglaries would be: 1000(1.50) = 1500.

The number of burglaries after the 10% reduction in 2013 would be: 1500(.90) = 1350

The change in burglaries over the two-year period = (1350 / 100) - 1 = 35%

In order to determine how much burglaries would have to reduce in order to have a 40% change in burglaries, this formula would be used

(x - 1000) / 1000 = 0.40

x - 1000 = 400

x = 1400

The change in burglaries over the two-year period to have  a 40% increase = (1400 / 1500) - 1 = 6.7%

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[tex] \huge \bf \color{gold} \frac{3}{5} \div \frac{2}{6} = [/tex]

[tex] \tt \frac{3}{5} \times \frac{6}{2} = [/tex]

[tex] \tt \frac{18 \div 2}{10 \div 2} = [/tex]

[tex] \tt \frac{9}{5} = [/tex]

[tex] \boxed {\color{blue}{ 1 \frac{4}{5}}}[/tex]

THE RESULT IS 1 4/5

Answer:

The solution is 9/5 and 1/5

Step-by-step explanation:

3/5÷2/6

= 3/5×6/2

= 3/5×3

= 9/5

3/5÷6/2

= 3/5×2/6

= 3/5×1/3

= 1/5

Answer:

Enzo must have played 11 games.

Step-by-step explanation:

Since Enzo earns 5 tickets from every game and Beatriz wins 11 tickets from each game, we have to find the LCM (Least Common Multiple) since they earned the same amount of tickets when they stopped.

The LCM of 11 and 5 is 55.

To see how many games they both played we have to divide the amount of tickets they earn each time from the LCM (55).

Since Enzo earns 5 tickets from each game and both Enzo and Beatrice earned 55, Enzo must've played 11 games.

(If that makes sense lol)

A≈62.35

..................

Compounded continuously model are evaluated using exponential functions

There are 8.177 bacteria left after 40 days

The given parameters are:

[tex]\mathbf{a = 10}[/tex] --- the initial number of bacteria

[tex]\mathbf{r = 0.502\%}[/tex] --- the decay rate

[tex]\mathbf{n = 40}[/tex] --- the number of days

The amount of bacteria left each day is calculated using:

[tex]\mathbf{T_n = a \times (1 - r)^n}[/tex]

So, we have:

[tex]\mathbf{T_{40} = 10 \times (1 - 0.502\%)^{40}}[/tex]

Express percentage as decimal

[tex]\mathbf{T_{40} = 10 \times (1 - 0.00502)^{40}}[/tex]

Simplify the expression in bracket

[tex]\mathbf{T_{40} = 10 \times 0.99498^{40}}[/tex]

Evaluate

[tex]\mathbf{T_{40} = 8.1766}[/tex]

Approximate

[tex]\mathbf{T_{40} = 8.177}[/tex]

Hence, there are 8.177 bacteria left after 40 days

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Answer:

9/5

Step-by-step explanation:

Just divide the 9 by 1 so it'll be 9/5 hope it helps

[tex]2(x)+3-3=-6\\2(3)+3-3=-6\\6+3-3=-6\\6=-6\\[/tex]

[tex]x\neq 3[/tex]

As we can see, x cannot be equal to 3 as 6 cannot equal -6.

I hope I've helped! :)

The additive inverse of 5 modulo 8 is the number a such that

5 + a ≡ 0 (mod 8)

Then

a ≡ -5 ≡ -5 + 8 ≡ 3 (mod 8)

The multiplicative inverse is m such that

5m ≡ 1 (mod 8)

Use the Euclidean algorithm:

8 = 1•5 + 3

5 = 1•3 + 2

3 = 1•2 + 1

Then

1 = 3 - 1•2

1 = 3 - 1•(5 - 1•3) = 2•3 - 1•5

1 = 2•(8 - 1•5) - 1•5 = 2•8 - 3•5

and so

1 ≡ 2•8 - 3•5 ≡ (-3)•5 (mod 8)

which means the inverse of 5 is

-3 ≡ 8 - 3 ≡ 5 (mod 8)

Answer:

the info they gave us is to suppose that angle 6 is = 126°

step 1:

We know that angle 8 = angle 6 = 126°

Why? — when a circle (360°) is split by 2 lines that intersect, there will be 2 equal pairs of angles formed

step 2:

angle 2 = angle 8 = 126°

Why? — they’re alternate angles

step 3:

angle 4 = angle 2

Why? — when a circle (360°) is split by 2 lines that intersect, there will be 2 equal pairs of angles formed

step 4:

angle 1 = 180-126 (angle 4) = 54°

Why? — total angles in a straight line = 180°

Key Term:

Alternate angles:

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

well, let's say the original price is "x", which namely 100% of the price of the product, we also know that 285.60 is 34% of that.

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 285.60&34 \end{array}\implies \cfrac{x}{285.60}=\cfrac{100}{34}\implies \cfrac{x}{285.60}=\cfrac{50}{17} \\\\\\ 17x=14280\implies x = \cfrac{14280}{17}\implies x = 840[/tex]

[tex]Hiya![/tex]

Sokka is here to help!!

Here's the step:

[tex]x^2+1-3\frac{In(x)}{x}[/tex]

[tex]Mutiply[/tex] [tex]by:[/tex] [tex]3[/tex]

[tex]. \frac{In(x)}{x} :\frac{3In(x)}{x}[/tex]

[tex]= x^2+1-\frac{3In(x)}{x}[/tex]

ANSWER:

[tex]= x^2+1-\frac{3In(x)}{x} .[/tex]

Hopefully, this helps you!!

[tex]Sokka[/tex]

Answer:

C

Step-by-step explanation:

For example, if a is equal to 2.

[tex] \sqrt{2} {}^{2} = 2[/tex]

The answer is still the given number a.

The solution of the expression √a² is,

⇒ a

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ √a²

Where, 'a' is nonnegative real number.

Now, We can simplify as;

⇒ √a²

⇒ √ a × a

⇒ a

Thus,  The solution of the expression √a² is,

⇒ a

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