Write 0.641 as a fraction in simplest form

Answer:

The given Divisor = 405 and Dividend = 48849

The Quotient is 120 and the Remainder is 249

Hope it helps you

Number of hours Aviva's work for gross earnings of $662.30 for a week with regular rate of $10.80 per hour for 35 hour week and 1.5 of regular pay for overtime is 52.6hours.

Given,

Gross earning for week=$662.30

Regular rate per hour for 35hour week=$10.80

Overtime rate=1.5×(10.80)

For 'h' number of hours

(10.80×35)+(10.80×1.5) h=$662.30

⇒378 +16.20h=662.30

⇒h=284.30/16.20

⇒h≈17.6hours

Number of hours Aviva's work=35 +17.6

                                                  =52.6hours

Therefore, number of hours Aviva's work for gross earnings of $662.30 for a week with regular rate of pay $10.80 per hour for a 35 hour week and 1.5 of regular pay for overtime is 52.6hours.

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The percent of juniors whose score is at least 71 % is 69.15 %.

We are given that:

Test of the students are normally distributed.

Mean = μ = 71

Standard deviation = σ = 5

We need to find the percent of juniors whose score is at least 71 %.

Now, we know that:

z = ( x - μ) / σ

z = 100 - 71 / 5

z = 29 / 5

z = 5.8

So, percentage = 69.15 %

Therefore, we get that, the percent of juniors whose score is at least 71 % is 69.15 %.

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By decomposing the figure into simpler ones, we conclude that the area of the irregular figure is 108 square inches.

Here we have an irregular figure that can be decomposed into 3 simpler figures, these are:

Remember that the area of a rectangle is the product between the two dimensions, so the areas of these 3 rectangles are:

a = 6in*8in = 48in^2

a' = 10in*4in = 40in^2

a'' = 5in*4in = 20in^2

Adding these areas we get:

48in^2 + 40in^2 + 20in^2 = 108 in^2

The area of the irregular figure is 108 square inches.

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Answer:

the slope intercept form is 5y= -x+12

It costs less to hire Hank's Movers for times less than 7 hours.

The equation that can be used to represent the cost of hiring Acme movers is: $105 + $40t

The equation that can be used to represent the cost of hiring Hank's Movers : $55t

Where : t represent number of hours

The inequality sign that would be used is < less than or equal to

$55t < $105 + $40t

Combine similar terms

$55t - $40t  < $105

$15t < $105

t < 105 / 15

t < 7 hours

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The distance between the starting point(initial) and the ending point(last) is known as displacement is  9.46miles.

What is displacement?

In the first(1st) part of the race displacement of Erica is

d1 = 5.2 miles at 25(twenty-five) deg North of East

x(ax) and y-component of 1st(first) part of the race will be:

d1 = 5.2*cos 25(twenty five) deg i + 5.2*sin 25(twenty five) deg j

d1 = (4.71 i + 2.20 j) miles (this id d1)

In the second(2nd) part of the race

d2 = 6(six) miles towards north,

So

d2 = (6 j) miles (this is d2)

Now net(accurate) displacement of Erica will be, Using Vector addition(summation):

d = d1(4.71 i + 2.20 j) + d2(6j)

d = (4.71 i + 2.20 j) +(sum) (6 j)

d = 4.71 i +(sum) 8.20 j

So Magnitude of net(accurate) displacement will be:

|d| = [tex]\sqrt{4.71^2+8.20^2}[/tex]

|d| = 9.46 miles(nine.four-six) = distance between starting(initial) point and ending point

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Optionally you can replace 0.25 with the fraction 1/4

===================================================

Explanation:

The variable y varies directly with x, which means we have the template of y = kx for some constant k.

Plug in x = 8 and y = 2. Then solve for k

y = kx

2 = k*8

8k = 2

k = 2/8

k = 1/4

k = 0.25

Therefore, we go from y = kx to y = 0.25x

-------------

Check:

Plugging in x = 8 should get us to y = 2

y = 0.25x

y = 0.25*8

y = 2

The answer is confirmed.

Answer:

x∈(-3;0)∪(3;+∞).

Step-by-step explanation:

1) if to solve the inequality x³-9x>0, then

x(x-3)(x+3)>0, and solution is

x∈(-3;0)∪(3;+∝).

2) the graph is provided in the attachment (it is marked with red colour).

Answer:

$3,108.08 per month

Step-by-step explanation:

Calculator shows the answer as 3,108.0833 with the 33 repeating.  Rounding to the nearest cent (100ths place) gives $3,108.08

option (a) x = 9

Step-by-step explanation:

2/3x = 6

2x = 18

x = 18/2

x = 9.

Answer:

5.83

Step-by-step explanation:

You just divide the total amount by 3

Answer:

Each will pay $5.83

Step-by-step explanation:

Answer:

give me those points boy=o >:)

Step-by-step explanation:

While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function

f

(

x

)

=

b

x

by a constant

|

a

|

>

0

. For example, if we begin by graphing the parent function

f

(

x

)

=

2

x

, we can then graph the stretch, using

a

=

3

, to get

g

(

x

)

=

3

(

2

)

x

and the compression, using

a

=

1

3

, to get

h

(

x

)

=

1

3

(

2

)

x

.

Answer: Yes, it is.

Step-by-step explanation:

given: x is 0 and y is 3. Plug in the equation and solve

y=x+3

3=0+3

3=3

Yes, it is a solution

Answer:

number of males: 29

Number of females: 18

Step-by-step explanation:

X=number of females

X+11=number of males

X+X+11=47

2X+11=47

2X=47-11

2X=36

X=36/2

X=18

So number of females = 18

X+11=18+11=29

So number of males = 29

The equation in slope-intercept firm for this line is y = -4/3x - 13

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

Slope, m = -4/3

Point (x1, y1) = (-6, -5)

The linear equation is calculated as

y = m(x - x1) + y1

So, we have

y = -4/3(x + 6) - 5

Open the bracket

y = -4/3x - 8 - 5

Evaluate the difference

y = -4/3x - 13

Hence, the equation in slope-intercept firm for this line is y = -4/3x - 13

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Answer:

the slope of the table is -0.857

Answer:14

Step-by-step explanation:

Step-by-step explanation:

B is the midpoint of AC, in other words it is the halfway point.

So A to B should be equal to B to C

Our expression is:

2x + 9 = 37

Subtract 9

2x = 28

Divide by 2

x = 14

Answer:

750

Step-by-step explanation:

3/4 is 75%

Juan did 75% of the 1000 meters meaning he did 750

To get the answer u just do (3/4)*1000 and you get 750

Answer:

A Cartesian Plane is a plane in Geometry which is an flat surface of infinite size. It has two number lines that intersect at right angles at their zeros. One number line is horizontal, and the other number line is vertical. The point of intersection is the zero of each line. In the horizontal line, the numbers increase to the right. In the vertical line, the numbers increase up. The horizontal line is called the x axis. The vertical line is called the y axis. The center of the Cartesian Plane is the intersection of the two axes, the two number lines, and is called the origin. Points on the Cartesian Plane are described with two numbers in parentheses separated by a comma. The position of the point in the Cartesian Plane is given by the first number, called the x-coordinate, telling us the number of units to the right (positive) or left (negative) of the origin and by the second number, called the y-coordinate, telling us the number of units up (positive) or down (negative) from the origin.

Answer: 78

Step-by-step explanation:

first, you multiply 8 by 9 then you get 72, and then you can add the leftover cherries with 72 so 72 + 6 = 78

Answer:

Step-by-step explanation:

78

Answer:

500

Step-by-step explanation:

500*2=1000

1000/2=500

The expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width is 6x + 18.

Let the width of the rectangle be x units.

According to the given question.

The length of a rectangle is nine more than twice the width.

⇒ Length of the rectangle = 9 + 2x

As we know that, the perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width.

Therefore, the expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width

= 2[x + (9 + 2x)]

= 2[ x + 2x + 9]

= 2[ 3x + 9]

= 6x + 18

Hence, the expression for the perimeter of the rectangle whose  length of a rectangle is nine more than twice the width is 6x + 18.

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The value of x from the inequality is x < 3

An inequality is defined as a statement of an order relationship between two numbers or algebraic expressions.

Given the inequality;

3x + 1 < 10

To determine the solution, we take the followings steps;

collect like terms

3x < 10 - 1

Find the difference between the terms

3x < 9

Make 'x' the subject of formula

x < 9/ 3

x < 3

Thus, the value of x from the inequality is x < 3

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(a) The leading coefficient is positive and the degree is odd, so:

(b) The leading coefficient is negative and the degree is even, so:

Answer:

I think its 12

Step-by-step explanation:

I think its 12 bc 4+4+4=12 Sorry if its wrong!  ):)

Solve the homogeneous equation

[tex]y'' + 3y' + 2y = 0[/tex]

Its characteristic equation is

[tex]r^2 + 3r + 2 = (r + 1) (r + 2) = 0[/tex]

with roots at [tex]r=-1[/tex] and [tex]r=-2[/tex], hence the characteristic solution is

[tex]y_c = C_1 e^{-x} + C_2 e^{-2x}[/tex]

For the nonhomogeneous equation, I'll use variation of parameters. We're looking for a solution of the form

[tex]y = u_1 y_1 + u_2 y_2[/tex]

to the equation

[tex]y'' + a(x) y'' + b(x) y = f(x)[/tex]

such that

[tex]\displaystyle u_1 = - \int \frac{y_2f(x)}{W(y_1,y_2)} \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{y_1 f(x)}{W(y_1,y_2)} \, dx[/tex]

The Wronskian [tex]W(y_1,y_2)[/tex] of the two fundamental solutions [tex]y_1=e^{-x}[/tex] and [tex]y_2=e^{-2x}[/tex] is

[tex]W(y_1,y_2) = \begin{vmatrix} y_1 & y_2 \\ {y_1}' & {y_2}' \end{vmatrix} = -e^{-3x}[/tex]

Then we have

[tex]\displaystyle u_1 = - \int \frac{e^{-2x} \cdot 4e^x \cos(3x)}{-e^{-3x}} \, dx = 4 \int e^{2x} \cos(3x) \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{e^{-x} \cdot 4e^x \cos(3x)}{-e^{-3x}} \, dx = -4 \int e^{3x} \cos(3x) \, dx[/tex]

Recall Euler's identity,

[tex]e^{(a+bi)t} = e^{at} (\cos(bt) + i \sin(bt))[/tex]

Then we have the general antiderivative

[tex]\displaystyle \int e^{(a+bi)t} \, dt = \frac1{a+bi} e^{(a+bi)t} + C = \frac{a-bi}{a^2+b^2} e^{(a+bi)t} + C[/tex]

Taking the real parts of both sides, we have

[tex]\displaystyle \mathrm{Re}\left\{\int e^{(a+bi)t} \, dt \right\} = \mathrm{Re}\left\{\frac{a-bi}{a^2+b^2} e^{(a+bi)t} + C\right\} \\\\ \int\,\mathrm{Re}\left\{e^{(a+bi)t}\right\} \, dt = \frac{e^{at}}{a^2+b^2} \mathrm{Re}\left\{(a-bi)(\cos(bt) + i \sin(bt))\right\} + C \\\\ \int e^{at} \cos(bt) \, dt = \frac{e^{at}}{a^2+b^2} (a\cos(bt)+b\sin(bt)) + C[/tex]

so that

[tex]\displaystyle u_1 = 4 \int e^{2x} \cos(3x) \, dx = \frac{4e^{2x}}{13} (2\cos(3x) + 3 \sin(3x))[/tex]

and

[tex]\displaystyle u_2 = -4 \int e^{3x} \cos(3x) \, dx = -\frac{2e^{3x}}3 (\cos(3x) + \sin(3x))[/tex]

We've found

[tex]y = u_1 y_1 + u_2 y_2[/tex]

[tex]\displaystyle y = \frac{4e^x}{13} (2\cos(3x) + 3 \sin(3x)) - \frac{2e^x}3 (\cos(3x) + \sin(3x))[/tex]

[tex]\displaystyle y = \frac2{39} e^x (5\sin(3x) - \cos(3x))[/tex]

Then the general solution to the differential equation is

[tex]\boxed{y(x) = C_1 e^{-x} + C_2 e^{-2x} + \frac2{39} e^x (5\sin(3x) - \cos(3x))}[/tex]