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lidiya [134]
3 years ago
11

Kent worked in the houseware section of a department store. This year he set a record high for vacuum sales with567 vacuum sold.

The previous yearhigh was set last year, when 540 vacuums were sold. What is the percent of increase in sales from last year to this year?
Mathematics
1 answer:
Gemiola [76]3 years ago
5 0
First subtract the original high from the new high:
567 - 540 = 27 more vacuums sold.

Now divide the increase amount by the original high and multiply that by 100 to get the percentage:

27 / 540 = 0.05

0.05 * 100 = 5% Increase.
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Sum of two numbers is 24 and the difference is 15.What are the two numbers ?
Alexeev081 [22]
Let,
the bigger number  be "x"
the smaller number be "y"
Now, according to the question,
x + y = 24...........equation (1).............because the sum of numbers is 24
x - y = 15 .............equation (2)..................because their difference is 15

Taking equation (2),
x - y = 15
x = 15 + y ....................equation (3)

Now, Taking equation (1)
x + y = 24
(Substituting the value of "x" form equation (3) we get)
15 + y + y = 24
(Subtracting 15 on both sides, we get)
y + y = 24 - 15
2y = 9
y = 9 / 2
y = 4.5
Now, 
Taking equation (3)
x = 15 + y
(Substituting the value of y , we get)
x = 15 + 4.5
x = 19.5

So, the two numbers are 19.5 and 4.5

5 0
3 years ago
Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x
Serggg [28]

I assume C has counterclockwise orientation when viewed from above.

By Stokes' theorem,

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

so we first compute the curl:

\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k

\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k

Then parameterize S by

\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k

where the z-component is obtained from

1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v

with 0\le u\le\dfrac\pi2 and 0\le v\le\dfrac\pi2.

Take the normal vector to S to be

\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k

Then the line integral is equal in value to the surface integral,

\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}

6 0
3 years ago
Using the vertical line test. Is this a function?
marta [7]

Answer:

Can't get one(Read explanation)

Step-by-step explanation:

What you do to find out if its a function is see if any of the dots are in the same x value. If they are, its not a function. If they aren't it is a function.

7 0
3 years ago
Someone please help me!
Vlad1618 [11]

Answer:

A. x \leq -16  

B. b > 11

C. c \leq -13

D. x \geq -9

Step-by-step explanation:

<u>Given the following algebraic expression;</u>

A. \frac {3x}{4} \leq 12

We would simplify the equation by multiplying all through by 4;

4 * \frac {-3x}{4} \leq 12 * 4

-3x \leq 48

Divide both sides by -3;

x \leq -16

B. 5b - 28 > 27

Rearranging the equation, we have;

5b > 27 + 28

5b > 55

Divide both sides by 5

b > 11

C. 13c \leq -169

Divide both sides by 13

c \leq -13

D. 3x - 7 \geq 4x + 2

Collecting like terms, we have;

3x - 4x \geq 2 + 7

-x \geq 9

Divide both sides by -1

x \geq -9

8 0
3 years ago
I'll give more points here is what I need.
Serga [27]

Answer:

The answer to your question is x = 3; y = 3

Step-by-step explanation:

Data

angle = 45°

Opposite side = x

Adjacent side = y

hypotenuse = 3√2

To solve this problem, use trigonometric functions.

1) To find x, use the trigonometric function sine.

              sin Ф = Opposite side / hypotenuse

-Solve for Opposite side (x)

              Opposite side = hypotenuse x sin Ф

-Substitution

              Opposite side = 3√2 sin 45

-Simplification

               Opposite side = 3√2 (1 / √2)

               Opposite side = 3(1)

-Result  

               x = 3

2) To find y use the trigonometric function cosine

               cos Ф = Adjacent side / hypotenuse

-Solve for Adjacent side

                Adjacent side = hypotenuse x cos Ф

-Substitution

                Adjacent side = 3√2 x cos 45

-Simplification

                Adjacent side = 3√2 x (1/√2)

                Adjacent side = 3(1)

-Result

                y = 3

5 0
3 years ago
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