On Friday, Ariel received a $450 paycheck. On
Saturday, she spent $30 on gasoline and $15 on lunch.
What percent of her paycheck did Ariel spend on
Saturday?

If the probability that an event will occur is changed as a result of the occurrence of a previous event, the events are said to be dependent events.

There, are two types of events- dependent and independent. Independent ones are those wherein the occurrence of one event has no effect on the probability of occurrence of another one. For example- you and your classmate passing a test are both independent events.

On the other hand, dependent events are those events that are affected by a change in any one of the events probability changing. For example- studying for a test and passing the test are both dependent events.

Thus, if the probability that an event will occur is changed as a result of the occurrence of a previous event, the events are said to be dependent events.

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Answer:

simplify(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

Step-by-step explanation:

derivative(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

limit(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

taylor_series_expansion(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

antiderivative(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

integral(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

equation_solver(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4))=0)

simplify(cube_root(27⋅x⋅exp(6)⋅y⋅exp(4)))

The difference in the widths, in meters, of the human hair and the piece of sand is [tex]1.4998*10^{-1}[/tex] m.

It is given in the question that:-

Width of a human hair = [tex]2*10^{-5}[/tex] m

Width of a piece of sand = [tex]1.5*10^{-1}[/tex]m

We have to find the difference in the widths, in meters, of the human hair and the piece of sand.

We know that,

Difference between the widths = Width of a piece of sand - Width of a human hair

Hence, we can write,

Difference between the widths =  [tex]2*10^{-5}[/tex] m - [tex]1.5*10^{-1}[/tex]m

We can write,

[tex]1.5*10^{-1}=15000*10^{-5}[/tex]

Hence,

Difference between the widths =

[tex]15000*10^{-5} - 2*10^{-5}= 14998*10^{-5} = 1.4998*10^{-1}[/tex] m

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Answer:

Simplifying

x = 9

Step-by-step explanation:

Simplifying

9x + -1 = 80

Reorder the terms:

-1 + 9x = 80

Solving

-1 + 9x = 80

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.

-1 + 1 + 9x = 80 + 1

Combine like terms: -1 + 1 = 0

0 + 9x = 80 + 1

9x = 80 + 1

Combine like terms: 80 + 1 = 81

9x = 81

Divide each side by '9'.

x = 9

The most appropriate choice for parabola will be given by-

Equation of  parabola that passes through the point (2, 2) and has a

vertex of (3, -1) is

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

What is parabola?

Parabola is a curve where every point on the curve is equidistant from a fixed point called the focus and a fixed line  called the directrix.

Equation of parabola is [tex]y = a(x - h)^2+k[/tex] where (h,k) is the vertex of the parabola

Here,

Equation of the parabola with vertex (3, -1) is

[tex]y = a(x - 3)^2-1[/tex]

The parabola passes through (2, 2)

[tex]2 = a(2-3)^2-1\\2 = a-1\\a=2+1\\a=3[/tex]

Equation of  parabola that passes through the point (2, 2) and has a

vertex of (3, -1) is

[tex]y = 3(x-3)^2 - 1\\[/tex]

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

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Answer:

24.8

Step-by-step explanation:

hope it help

have a nice day

Answer: Draw a picture of 2 1/2 cups of flour being added to 1 1/2 cups of sugar in a bowl.

Step-by-step explanation: wink wink

Answer:

3rd answer option (1.6, 1.4)

Step-by-step explanation:

the slope of the lines is different.

to see we transform the equations to the regular slope-intercept form

y = ax + b

with "a" being the slope and "b" being the y-intercept (the y value when x = 0).

1.5x + 0.2y = 2.68

0.2y = -1.5x + 2.68

y = -1.5x/0.2 + 2.68/0.2 = -7.5x + 13.4

1.6x + 0.3y = 2.98

0.3y = -1.6x + 2.98

y = -1.6x/0.3 + 2.98/0.3 = -5.33333...x + 9.93333...

-7.5 is not -5.3333...

so, the lines are not parallel nor overlap at all points.

therefore, they intersect at a point.

(1.6, 1.4) ?

the equations must remain true when using the coordinates :

1.5×1.6 + 0.2×1.4 = 2.68

1.6×1.6 + 0.3×1.4 = 2.98

2.4 + 0.28 = 2.68

2.68 = 2.68 correct

2.56 + 0.42 = 2.98

2.98 = 2.98 correct

yes, they intersect at (1.6, 1.4).

for (3.1, 0.5) already the x coordinate is way too large.

1.5×3.1 or 1.6×3.1 are already by themselves much larger than 2.68 or 2.98.

Answer:

Step-by-step explanation:

[tex](7\frac{7}{8} )(2\frac{1}{4} ) = \\\\\frac{567}{32} \\\\OR\\17\frac{23}{32}[/tex]

Answer:   -28 percent

Step-by-step explanation:

The equations of the line will be expressed as y = 4 and y = -2x + 11 respectively.

Slope of a line may be defined as the steepness of a curve on graph. Slope is denoted by 'm'. If we are given two points (x₁, y₁) and (x₂, y₂) then the slope of line can be given by m = (y₂ - y₁)/(x₂ - x₁). Now, we have a line y = 6 and this line is parallel to x-axis, so the slope of this line is zero. Since, we have to find the equation of line parallel to given line so the slope of the line parallel to line y = 6 will also be equal to zero. Now, equation of line from points (3, 4) and slope zero is given by

(y - 4) = 0×(x - 3)

=> y - 4 = 0

=> y = 4 which is the required equation.

Now, for the second part we have need to find the equation of line parallel to line y = -2x - 1 and from point (4, 3). The slope of new line is -2 which will be same as the given line as they both are parallel. Now, equation of line will be

(y - 3) = -2(x - 4)

(y - 3) = -2x + 8

y = -2x + 8 + 3

=> y = -2x + 11 which is the required equation.

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The equation of the function in the standard form is:

3x + y = 25.

Given, From the table we can get the dy/dx which is the slope (m) ,

Therefore,

dy/dx = (7 - 10 ) / ( 4 - 3 )

dy/dx = -3

f(x) = ax² + bx + c, where a, b, and c are all numbers and an is not equal to 0, is the definition of a quadratic function. A parabola is the shape of a quadratic function's graph. Despite the fact that a parabola's "width" or "steepness" and opening direction can change.

Now,

( y - y₁ ) = m ( x - x₁ )

Putting the value from the table,

( y - 10 )  = -3 ( x -5 )

⇒ y - 10 = -3x + 15

⇒ 3x + y = 25

Hence the equation of the line in standard form is 3x + y = 25.

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Answer:

Ray

Step-by-step explanation:

A ray has a starting point and then continues in one direction.

i  think so is correct

Step-by-step explanation:

there is no side marked y.

to get x :

the graphic shows us already the split of the overall object into sub-shapes :

2 right-angled triangles

1 rectangle

x is the sum of the width of the rectangle and the shorter leg of the larger, top right-angled triangle.

to get both we need to use Pythagoras :

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs of the triangle.

let's start with the shorter leg of the larger triangle.

the Hypotenuse is 18, and the longer leg is the same as the length of the "underlying" rectangle : 10.

so, we get

18² = 10² + leg1²

324 = 100 + leg1²

leg1² = 224

leg1 = sqrt(224) = 14.96662955...

now to the width of the rectangle.

it is the same as the longer leg of the smaller triangle on the right side.

its Hypotenuse is 5. its shorter leg is 2.

so, we get

5² = 2² + leg2²

25 = 4 + leg2²

leg2² = 21

leg2 = width rectangle = sqrt(21) = 4.582575695...

x = leg1 + leg2 = 14.96662955... + 4.582575695... =

= 19.54920524...

Now the given coordinates are,

(-4,10) and (2,-10)

Thus, we have,

x₁  = -4

y₁ = 10

x₂ = 2

y₂ = -10

Given ratio, m₁ : m₂ = 1 : 3

⇒ m₁ =  1; m₂ =  3

Let (x,y) be the coordinates of the point on the directed line segment from (-4,10) to (2,-10) that partitions the segment into a ratio of 1 to 3.

Since the section formula is given as,

So, x = (m₁x₁ + m₂x₂) / (m₁ + m₂)  

y =  (m₁y₁ + m₂y₂) / (m₁ + m₂)  

Put the values,

x = [1(-4) + 3*2)] / (1 + 3) = (-4+6) / 4 = 2/4

⇒ x = 1/2

Similarly y = [1(10) + 3*(-10)] / (1 + 3) = (10-30) / 4 = -20/4

⇒ y = -5

So, the required coordinates are (1/2, -5)

Thus, the coordinates of the point on the directed line segment that partitions the segment into a ratio of 1 to 3 is (1/2, -5).

Answer:(-3,-6)

Step-by-step explanation:

Answer: the answer for y=3x+7 is    x=y-7/3

the answer for y = -2x - 8   x=-8-y/2

Step-by-step explanation:

Answer:

50+((10n) =

so 50 is how much it cost to walk in the park and 10 is how much each ride (n) cost soif you know how many rides your ride you times that by 10 the add 10 to 50 and you get how much it will cost you for the day

1. We can use the sine law since we have two angles and one of the angles had the side opposite it.

2. We can use the sine law because we have two angles, we can find the third angle in the triangle. This means we have all three angles. We now have two angles and one of the angles has the side opposite it.

3. We have a right triangle. We could use the sine law because we have the right angle and the hypotense. We have two sides and one angle.

4. We have two sides and the included angle. We cannot use the sine law. We would have to use the law of cosines to solve this problem.

[tex]2 \sqrt[3]{5} [/tex]

2(3^√5

The hourly rate is $65 per hour. While the fees to set up the tent is $100 and to take down after t hours is 65t + 100.

As we can see, the relation between the total fees and the hours for renting in hours is related by the equation,

y = 65x + 100

We are assuming that the price is in dollar.

This is an equation of line in slope-intercept form.

In slope intercept form, the coefficient of x is the slope of the line, which is 65 here.

So, the rate at which the fees is changing with time is 65.

So, the hourly rate will be $65 per hours.

The fees when tent is set can be calculated by,

We should put x = 0, because it is the start,

So,

y = 100

So, the fee to set up is $100.

Let us say the tent is removed after t hours, so the fees will be,

y = 65t + 100.

Fees of taking down the tent is $(65t+100)

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Answer:

the multiplication of 2.2.20 and 9.5

Step-by-step explanation:

the total cost is $20.9

Answer:

w = 3

Step-by-step explanation:

-4w = -12

divide both sides by -4:

-4w/-4 = -12/-4

w = 3

Answer:

w=3

Step-by-step explanation:

1. divide -12 by -4

[tex]w = \frac{ - 12}{ - 4} [/tex]

[tex]w = 3[/tex]

On simplifying the proportion 18:54:12, we get answer as 3:9:2.

The following are crucial proportional characteristics:

If a: b = c: d, then a + c: b + d. Addendum

A - c: b - d if a: b = c: d. Subtrahendo

Dividendo states that if a: b = c: d, then a- b: b = c- d: d.

If a: b = c: d, then a Plus b: b Equals c+d: d. This is known as combining.

To put it another way, if a: b = c: d, then a: c = b: d.

On simplifying,

18:54:12

Firstly, dividing the all numbers by 3

= 6:18:4

Now dividing by 2

= 3:9:2

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Answer:

Kirsten owes $3240 more on the car.

Step-by-step explanation:

$3600 - $360 = $3240

Answer:

70 pages

Step-by-step explanation:

42=60% so 42/6=10% or 7, 7x4=40% or 28+42=70 pgs

The maximum area that the farmer can enclose for the rectangular garden is 488 sq ft and the dimensions of the rectangular garden are 24ft and 12 ft respectively.

It is given that a farmer decided to enclose a rectangular garden with one side using the barn of a tree and other 3 sides with 48 ft of fencing.

Let the length of the rectangle be y and the breadth of the rectangle be u.

So perimeter of the fencing needed = y + 2u (as one side is barn)

∴ y + 2u = 48

⇒ y = 48 - 2u (equation 1)

Area = yu (equation 2)

Putting the value of variable y from equation 1 in equation 2 we have,

Area = (48-2u)u

∴ Area = 48u - 2[tex]u^{2}[/tex]

⇒ Area = -2[tex]u^{2}[/tex] + 48u

⇒ Area = -2([tex]u^{2}[/tex] - 24u)

⇒ Area = -2([tex]u^{2}[/tex] - 24u + 144) + 288   (using completing the square method)

⇒ Area = -2[tex](u-12)^{2}[/tex] + 288

So the maximum area is 288 sq units as for any value of u the area value will decrease as seen from the above equation.

So if Area = 288

Then yu = 288

⇒ u = 288/y equation 3

Putting this value in Perimeter equation 1 we have,

y = 48 - 2u

⇒ y = 48 - 2 x [tex]\frac{288}{y}[/tex]

⇒ [tex]y^{2} = 48y - 576[/tex]

⇒ [tex]y^{2} - 48y + 576 = 0[/tex]

⇒ [tex](y-24)^{2}[/tex] = 0

Solving we get y = 24 ft

Hence the value of u is calculated as follows:

⇒ u = 288 / y

⇒ u = 288/ 24 = 12 ft

The maximum area that the farmer can enclose is 488 sq ft and the dimensions of the rectangle are 24ft and 12 ft respectively.

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The air is filled inside the balloon at the rate of 1600π cm³/sec.

The rate during which air is blown into the balloon is identical to the rate that the volume of a balloon grows.

Volume of the spherical balloon;

V = (4/3)πr³

Given is dr/dt = 4 cm/sec.

To calculate the volume change with respect to time.

dV/dt when r = 10 cm.

Differentiate V = (4/3)πr³ with respect to t.

d(V)/dt = (d/dt)(4/3)πr³

dV/dt = (4/3)π. 3r² dr/dt

dV/dt = 4πr² dr/dt

Put the values.

dV/dt = 4π(10)² .(4)

dV/dt = 1600π cm³/sec

Thus, air is filled inside the balloon at the rate of 1600π cm³/sec.

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The correct answer is:  [D]:  " [tex]m = \frac{-5}{2}[/tex]  ".

______
Step-by-step explanation:
We are given:
" 5x  +  2y  =  -10 " ; Find the slope of the equation.
______
Rewrite this equation in slope-intercept format ;

that is:  " y =  mx  + b " ;

      in which:  
        y  remains as single value, as an 'output' ; or 'dependent  
variable', on the 'y-axis' (if graphed);
         isolated on the 'left-hand side' of the equation.
      m  is the coefficient of x in the equation; and represents the slope; for which we shall solve.
           {If there is no slope, then "m = 0" ; and "[0 * x = 0]." };
And the "slope-intercept format" is:  "y = b" }.
       b  represents the "y-intercept" ; i.e. when the line crosses the
"y-axis" when graphed;  that is, the "y-value" of the "coordinate" of the "y-intercept" ; [i.e. the value of "y" when "x = 0" ;  so;  " (0, b) ".

{ Note:  b  can equal "0" ; in those cases:  y = mx + 0 ; write as " y = mx "}.

{ If there is no slope, [i.e. "m = 0" ; and no "y-intercept" ;  [i.e. "b = 0"];
 Then:  write the equation accordingly—e.g. " y = [whatever number the graph represents]." }.

 Also, note that b can be a "negative number"; as well.
  In that case,  write an equation in "slope-intercept format" ; that is;  
   →" y = mx + b " ;   as:   " y = mx " .     
______
Given:  " 5x  +  2y  =  -10 " ;  
 Let's rewrite:    ↔  " 2y + 5x  =  -10 " ;  to get the "y-value" a bit closer to the 'left-hand side' of the equation.

  Then: Let's subtract 5x from Each Side of the equation;
      2y + 5x − 5x  = -10 − 5x  ;

 to get:  " 2y =  -10 − 5x " ;

______
Method 1):
  We have: " 2y = -10 − 5x " ;

 Divide Each Side by 2 ; to isolate y on the 'left-hand side' of the equation, and to rewrite as an equation in the slope-intercept format :

  2y / 2 = (-10 − 5x)/2 ;

   →  [tex]y =\frac{-10-5x}{2}= \frac{-10}{2}-\frac{5x}{2}[/tex] ;
              →    [tex]\frac{-10}{2} =[/tex] -10 ÷ 2  = -5 ;

                   Rewrite the equation by replacing " [tex]\frac{-10}{2}[/tex] " ;  with:  -5 ;
              →  [tex]y = -5 - \frac{5x}{2}[/tex] ;

             Then, rewrite to get the equation in "slope-intercept format"

              →  [tex]y = -5 - \frac{5x}{2}[/tex] ;
                     [tex]= -5 + (-\frac{5x}{2})[/tex] ;  ↔ Rewrite:
                     [tex]= \frac{-5x}{2} + (-5)[/tex] ;   ↔ Rewrite again:
                     [tex]=\frac{-5x}{2} -5[/tex] ;

             →   [tex]y = \frac{-5x}{2} -5[/tex] .

Note:  " [tex]\frac{-5x}{2} = \frac{-5}{2} x[/tex] " ;

            →   [tex]y = \frac{-5}{2}x-5[/tex] ;

 This is the equation written in "slope-intercept format" ;

 that is:  " y = mx + b " ;

  in which:
 y is isolated as a single variable on the 'left-hand side' of the equation;

 m = [tex]\frac{-5}{2}[/tex] ; which is the slope; which is also the "coefficient" of x ;

 b = -5 ; which is the 'y-coordinate' of the "y-intercept" of the graph;
So, the slope; "m = -5/2" ; is the correct answer; which corresponds to:
Answer choice:  [D]: " m = [tex]\frac{-5}{2}[/tex]  " .
______

Method 2):

Given:  " 5x + 2y = -10" ; Find the slope of the line.

We want to rewrite the equation in the "slope-intercept format" ;

" y = mx + b " ; as explained above;

  to get the correct answer for m, the slope of the line.

" 5x + 2y = -10 " ↔ Rewrite as:
  2y + 5x =  -10 ;  since we want to isolate y as a single variable on the 'left-hand side' of the equation;  and by rearranging & rewriting this equation, the 2y is closer to the 'left' of the equation.

Now, subtract 5x from Each Side of the equation:
  2y + 5x − 5x = -10 − 5x ;
  to get:  2y = -10 − 5x ;

Now, Let's multiply the entire equation (i.e. "Each Side") by  -1 ;

to make the equation easier to handle;
    -1(2y) = -1 (-10 − 5x) ;
For the 'left-hand side' of the equation:
 -1*2y = -2y
For the 'right-hand side' of the equation:

Note the 'distributive property of multiplication'; as follows:
    a(b + c) = ab + ac ;
Likewise:  
-1(-10 − 5x) = (-1 *-10) + (-1 *-5x) ;

                 =  (10) + (5x) = 10 + 5x ;

Now, rewrite the entire equation:

-2y = 10 + 5x ;  ↔ Rewrite as;
   -2y = 5x + 10 ;  
Then, we divide Each Side of the equation by -2 ;
  to isolate y as a "single variable" on the 'left-hand side' of the equation;

   and to rewrite the equation in "slope-intercept format" ;

    -2y / -2 = (5x + 10) /-2 ;

    →  [tex]y=\frac{5x+10}{-2} =\frac{5x}{-2} +\frac{10}{-2} =\frac{5x}{-2}+(-5) =\frac{5x}{-2}-5[/tex] ;
    → [tex]y=\frac{5x}{-2} - 5[/tex] ;
which is written in "slope-intercept format" ; that is:
 " y = mx + b " ;

in which:  

y is isolated as a single variable on the 'left-hand side' of the equation;

m = [tex]\frac{5}{-2}[/tex] ; which does equal  " [tex]-\frac{5}{2}[/tex] " ;  which does equal " [tex]\frac{-5}{2}[/tex] " ;

which is the slope of the equation, as well as the 'coefficent of x' ;

b = -5 ; which is the 'y-coordinate' of the "y-intercept".
______
As such:  
The correct answer choice is:  [D]: " m = [tex]\frac{-5}{2}[/tex] " .
{Note: This is consistent with the answer choice from Method 1  above.}

______
Hope this answer and explanation is helpful.
Best of luck to you!
______

Answer:

8x-40=200

Step-by-step explanation: