Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah’s annual gross income and annual net income.

Answer:

m∠B = 60°

b = 26 units

c = 30 units

Step-by-step explanation:

In a right triangle ACB,

By applying Sine rule,

[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{SinC}{c}[/tex]

m∠A = 30°, m∠C = 90°

m∠A + m∠B + m∠C = 180°

30° + m∠B + 90° = 180°

m∠B = 180° - 120°

m∠B = 60°

Therefore, [tex]\frac{\text{Sin30}}{15}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]

[tex]\frac{1}{30}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]

[tex]\frac{1}{30} =\frac{1}{c}=\frac{\frac{\sqrt{3}}{2}}{b}[/tex]

[tex]\frac{1}{30}=\frac{1}{c}=\frac{\sqrt{3}}{2b}[/tex]

[tex]\frac{1}{30} =\frac{1}{c}[/tex] ⇒ c = 30 units

[tex]\frac{1}{30}=\frac{\sqrt{3}}{2b}[/tex]

b = 15√3

b = 25.98

b ≈ 26 units

[tex]\dfrac{15 + 10i}{1 + 2i}=\\\\\dfrac{(15 + 10i)(1-2i)}{(1 + 2i)(1-2i)}=\\\\\dfrac{15-30i+10i+20}{1+4}=\\\\\dfrac{35-20i}{5}=\\\\7-4i[/tex]

Answer:

7-4i

Step-by-step explanation:

Multiplying the numerator and denominator by $1-2i$ gives

\begin{align*}

\frac{15+10i}{1+2i} &= \frac{15+10i}{1+2i}\cdot\frac{1-2i}{1-2i}\\

&= \frac{(15+10i)(1-2i)}{1^2 + 2^2} \\

&= \frac{5(3 + 2i)(1 - 2i)}{5} \\

&= (3 + 2i)(1 - 2i) \\

&= 3 + 2i - 6i - 4i^2 \\

&= 3 + 2i - 6i + 4 \\

&= \boxed{7 - 4i}.

Answer:

8.4 in

Step-by-step explanation:

Solution:-

- We consider the large right angle triangle namely, " XVW "

- We will recall all the trigonometric ratios that are applicable to all right angled triangles.

- While we are dealing with trigonometric ratios we have the following terms that needs to be correlated with the given specific problem:

            Hypotenuse ( H ): Side opposite to 90 degrees angle

            Base (B): The side adjacent to the available angle ( θ )

            Perpendicular (P): The side opposite to the available angle ( θ )

- We will go ahead and mark our respective sides as follows:

            Angle ( θ ) : 34°

            Hypotenuse ( H ) : XW = 15 in

            Base ( B ) : VW

            Perpendicular ( P ) : VX

- Now recall all the trigonometric ratios studied:

           sin ( θ ) = P / H = VX / XW

           cos ( θ ) = B / H = VW / XW

           tan ( θ ) = P / B = VX / VW

- Now choose the appropriate trigonometric ratio with two values given and one ( VX ) that needs to be determined as follows:

                             sin ( θ ) = P / H = VX / XW

                             sin ( 34° ) = VX / 15

                             VX = 15*sin ( 34° )

                             VX = 8.387 .. ( 8.4 ) in

Answer:

V > -15

Step-by-step explanation:

[tex]\frac{V}{3} +12>7\\\\\frac{V}{3}>-5\\\\V>-15[/tex]

Answer:

V > -15

Step-by-step explanation:

V/3 + 12 > 7

V/3 > -5

V > -15

Answer:

{-1, 3, 7, 11, 15}

Step-by-step explanation:

we just substitute the set of even numbers in the function f(x) given to get our corresponding set of odds numbers

for 0

2(0)-1=0-1=-1

for 2

2(2)-1=4-1=3

for 4

2(4)-1=8-1=7

for 6

2(6)-1=12-1=11

for 8

2(8)-1=16-1=15

Answer:

inverse = ( log(x+4) + log(4) ) / (2log(4)), or

c. y = ( log_4(x+4) + 1 ) / 2

Step-by-step explanation:

Find inverse of

y = 4^(-6x+5) / 4^(-8x+6)   - 4

Exchange x and y and solve for y.

1. exchange x, y

x = 4^(-6y+5) / 4^(-8y+6)   - 4

2. solve for y

x = 4^(-6y+5) / 4^(-8y+6)   - 4

transpose

x+4 = 4^(-6y+5) / 4^(-8y+6)

using the law of exponents

x+4 = 4^( (-6y+5) - (-8y+6) )

simplify

x+4 = 4^( 2y - 1 )

take log on both sides

log(x+4) = log(4^( 2y - 1 ))

apply power property of logarithm

log(x+4) = (2y-1) log(4)

Transpose

2y - 1  = log(x+4) / log(4)

transpose

2y = log(x+4) / log(4) + 1 = ( log(x+4) + log(4) ) / log(4)

y = ( log(x+4) + log(4) ) / (2log(4))

Note: if we take log to the base 4, then log_4(4) =1, which simplifies the answer to

y = ( log_4(x+4) + 1 ) / 2

which corresponds to the third answer.

Answer: 1,300 students went on the trip

Step-by-step explanation: So we know that 65% filled the seats so let's turn that into a fraction.  [tex]\frac{65}{100}[/tex] . Now we know that there are 2,000 seats in total so let's put that into a fraction. [tex]\frac{x}{2,000}[/tex]  The x represents the students that went on the trip.

               [tex]\frac{65}{100} = \frac{x}{2,000}[/tex]  we have to cross multiply

   65(2,000) = 100 (x)

    130,000   =  100 (x)          

    130,000   ÷  100                            

        1,300    =   x          So now we know that 1,300 went to the trip students

Answer:

The number of houses built in Town B is 56.

Step-by-step explanation:

We are given that in 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B.

Also, 70 houses were built in Town A during 210.

Let the number of houses built in Town B be 'x'.

So, according to the question;

Number of houses built in Town A = Number of houses built in Town B + 25% of the houses built in Town B

[tex]70 = x + (25\% \times x)[/tex]

[tex]70 = x(1+0.25)[/tex]

[tex]x=\frac{70}{1.25}[/tex]

x = 56

Hence, the number of houses built in Town B is 56.

Answer:

1.

a) exact form: -1 /14 or decimal form: -0.0714285

b) exact form: -23/120 or decimal form: -0.1916

2.

a) 89

b)98

c) 5.7

d) 4.8

3.

i) 2*2*2*2*2*2*3*3*3

ii) 3*3*3*5*5*5

iii) 2*2*2*2*2*2*2*2*2*2*2*2

iv) 2*2*2*2*2*2*5*5*5

9.

i) x = -9

ii) x + 1/7

I hope this helps get you started :)

Answer:

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

Step-by-step explanation:

You clear c, wich is the hypotenuse

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

Answer:

[tex]\boxed{Option \ C}[/tex]

Step-by-step explanation:

[tex]Sin \ Y = \frac{Opposite }{Hypotenuse } = \frac{XZ}{XY}[/tex]

[tex]Cos \ Y = \frac{Adjacent}{Hypotenuse} = \frac{YZ}{XY}[/tex]

[tex]Tan Y = \frac{opposite}{adjacent} = \frac{XZ}{ZY}[/tex]

Answer:

[tex]\boxed{\mathrm{C}}[/tex]

Step-by-step explanation:

sin [tex]\theta[/tex] = Opposite/Hypotenuse

sin (Y) = [tex]\frac{XZ}{XY}[/tex]

cos [tex]\theta[/tex] = Adjacent/Hypotenuse

cos (Y) = [tex]\frac{YZ}{XY}[/tex]

tan [tex]\theta[/tex] = Opposite/Adjacent

tan (Y) = [tex]\frac{XZ}{YZ}[/tex]

Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

Step-by-step explanation:

Notice that the cone and the pyramid have the same volume. This is important.

This follows the Cavalieri's principle that, for the case of 3 dimensions, as the present case, it states, roughly, that if we have two bodies like the cone and the pyramid, and if we have parallel planes crossing each section, and we always have the same area, these two bodies have the same volume.

In this case, both, cone and pyramid have the same volume, then (reciprocally):

B. The horizontal cross-sections of the prisms at the same height have the same area.

Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

Step-by-step explanation:

ap333x

Answer:

Hey there!

First, we want to find the radius of the circle, which equals the length of line segment AC.

Length of line segment AC, which we can find with the distance formula: [tex]\sqrt{25\\[/tex], which is equal to 5.

The equation for a circle, is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center of the circle, and r is the radius.

Although I don't know the center of the circle, I can tell you that it is either choice B or D, because the radius, 5, squared, is 25.

Hope this helps :) (And let me know if you edit the question)

Answer:  The equation of the circle is (x+1)²+(y+1)² = 25

Step-by-step explanation:  Use the Pythagorean Theorem to calculate the length of the radius from the coordinates given for the triangle location:  A(-1,-2), B(-1,1) and C(3,1)  The sides of the triangle are AB=3, BC=4, AC=5.

Use the equation for a circle: ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.

As the directions specify, the radius is AC, so it makes sense to use the coordinates of A (-1,-2) as the center.  h is -1, k is -2  The radius 5, squared becomes 25.

Substituting those values, we have (x -[-1])² + (y -[-2])² = 25 .

When substituted for h, the -(-1) becomes +1 and the -(-2) for k becomes +2.

We end up with the equation for the circle as specified:

(x+1)²+(y+1)² = 25

A graph of the circle is attached. I still need to learn how to define line segments; the radius is only the segment of the line between the center (-1,-2) and (1,3)

Answer: 0

Step-by-step explanation:

The given equation: [tex]6a^2+5a+4=3[/tex]

Subtract 3 from both the sides, we get

[tex]6a^2+5a+1=0[/tex]

Now , we can split 5a as 2a+3a and [tex]2a\times 3a = 6a^2[/tex]

So, [tex]6a^2+5a+1=0\Rightarrow\ 6a^2+2a+3a+1=0[/tex]

[tex]\Rightarrow\ 2a(3a+1)+(3a+1)=0\\\\\Rightarrow\ (3a+1)(2a+1)=0\\\\\Rightarrow\ (3a+1)=0\text{ or }(2a+1)=0\\\\\Rightarrow\ a=-\dfrac{1}{3}\text{ or }a=-\dfrac{1}{2}[/tex]

At [tex]a=-\dfrac{1}{3}[/tex]

[tex]2a+1=2(-\dfrac{1}{3})+1=-\dfrac{2}{3}+1=\dfrac{-2+3}{3}=\dfrac{1}3{}[/tex]

At [tex]a=-\dfrac{1}{2}[/tex]

[tex]2a+1=2(-\dfrac{1}{2})+1=-1+1=0[/tex]

Since, [tex]0< \dfrac{1}{3}[/tex]

Hence, the possible value of 2a+1 is 0.

Answer: It represents that 2 will be divided into 3 equal parts.

Step-by-step explanation:

The given fraction : [tex]\dfrac{2}{3}[/tex]

here, Numerator = 2

Denominator = 3

It represents that 2 will be divided into 3 equal parts.

Answer:450 cm

Step-by-step explanation:

Answer:

7 is the least.

Step-by-step explanation:

Their are 12 balls, and 6 of them are red. if you are to pick every single ball except the red ones, you cut the number of balls in half, and are left with 6 red balls, and 6 balls picked. Your next pick must be a red ball, making 7 picks.

Answer:

5inch

Step-by-step explanation:

15_10=5

because full length is 15 cm given on another side and length of some part of another side is. given.so we have to subtract it

Answer:

5 inches

Step-by-step explanation:

You can notice that the 15 in side is parallel to the 10 in side and the missing side

let x be the missing side

so x is 5 inches

Answer:No solution

Step-by-step explanation:An absolute value equation cannot equal a negative number

Answer:

False roots are x = -1 or x = 5/2 or x = 3/2

Step-by-step explanation:

Solve for x:

4 x^3 - 12 x^2 - x + 15 = 0

The left hand side factors into a product with three terms:

(x + 1) (2 x - 5) (2 x - 3) = 0

Split into three equations:

x + 1 = 0 or 2 x - 5 = 0 or 2 x - 3 = 0

Subtract 1 from both sides:

x = -1 or 2 x - 5 = 0 or 2 x - 3 = 0

Add 5 to both sides:

x = -1 or 2 x = 5 or 2 x - 3 = 0

Divide both sides by 2:

x = -1 or x = 5/2 or 2 x - 3 = 0

Add 3 to both sides:

x = -1 or x = 5/2 or 2 x = 3

Divide both sides by 2:

Answer:  x = -1 or x = 5/2 or x = 3/2

Answer:

False

Step-by-step explanation:

f(x) = 4x³ - 12x² - x + 15

Set output to 0.

Factor the function.

0 = (x + 1)(2x - 3)(2x - 5)

Set factors equal to 0.

x + 1 = 0

x = -1

2x - 3 = 0

2x = 3

x = 3/2

2x - 5 = 0

2x = 5

x = 5/2

4 is not a lower bound for the zeros of the function.

Answer:

a. 25%

b. 55%

c. 35%

Hope it helps you and pls mark as brainliest : )

Answer: x ≥  -5

Step-by-step explanation:

First, let's see how the function f(x) = IxI works:

if x ≥ 0, IxI = x

if x ≤ 0, IxI = -x

Notice that for 0, I0I = 0.

Ok, we want that:

|x+5| = x+5

Notice that this is equivalent to:

IxI = x

This means that  |x+5| = x+5 is only true when:

(x + 5) ≥ 0

from this we can find the possible values of x:

we can subtract 5 to both sides and get:

(x + 5) -5 ≥ 0 - 5

x ≥  -5

So the graph in the number line will be a black dot in x = -5, and all the right region shaded.

something like:

-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__ ...

Answer:

9th term geometric sequence (a9) = 1 / 256

Step-by-step explanation:

Given:

Geometric sequence 1,1/2,1/2²

First term (a) = 1

Common ratio (r) = A2 / A1 = (1/2) / 1 = 1/2

Number of term (n) = 9

Find:

9th term geometric sequence (a9)

Computation:

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

a9 = ar⁹⁻¹

a9 = (1)(1/2)⁸

a9 = (1/2)⁸

a9 = 1/256

9th term geometric sequence (a9) = 1 / 256

Answer:

-8 < x < -2

start number line at -10 and end it at 0

draw an open circle* over the dash indicating -8 and -2

connect the open circles

*open circle because it is less than and greater than, not less than or equal to and greater than or equal to

Answer:

-8<x<-2

Step-by-step explanation:

yw luv :D

Answer:

Below

Step-by-step explanation:

r us the radius of the base and h is the heigth of the cylinder.

The volume of a cylinder is given by the formula:

V = Pi*r^2*h

V/Pi*r^2 = h

We can write a function that relates h and r

Answer:

One of the cylinders is short and wide, while the other is tall and thin.

Step-by-step explanation:

sample answer given on edmentum

Answer:5c-3d

Step-by-step explanation: Collect the like terms such as 6c ,-c and 4d,-7d

Answer:

5c - 3d

Step-by-step explanation:

6c + 4d - c - 7d

Group like terms

6c - c + 4d - 7d

Add similar elements : 6c - c = 5c

5c + 4d - 7d

Add similar elements : 4d - 7d = - 3d

5c - 3d

I hope this helps

Work Shown:

sin(angle) = opposite/hypotenuse

sin(35) = 10/x

x*sin(35) = 10

x = 10/sin(35)

x = 17.434467956211 make sure your calculator is in degree mode

x = 17.4

Answer:

[tex]\boxed{17.4}[/tex]

Step-by-step explanation:

sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

sin (35) = [tex]\frac{10}{x}[/tex]

x = [tex]\frac{10}{sin(35)}[/tex]

x = 17.4344679562...

x ≈ 17.4

Answer:

27/2 units^3

Step-by-step explanation:

Formula for volume: l * w * h   or   a * h  because l * w = area.

27/5 ( which is area ) * 5/2 ( the height ) = 27/2

i hope this helps

The volume of the following rectangular prism is 27/2 units^3

We know that the rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism = Length X Width X Height

We are given the dimensions as Length = 5/2

Area = 27/5

Here a * h  because l * w = area.

Volume = Length X Width X Height

= area X Width

= 27/5 x 5/2

= 27/2

The volume is 27/2 units^3.

Learn more about a rectangular prism;

https://brainly.com/question/21308574

#SPJ2

Answer:

d

Step-by-step explanation:

Answer: E definition of midpoint

Step-by-step explanation:

Correct on Plato

Answer:

$14,580

Step-by-step explanation:

To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form

-In doing that, you get 2,000

-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000

-the value of the car after one year is now $18,000

Now, let's move to the second year.  This time find 10% of 18,000

-multiply 18,000 by 0.1 to get 1,800

-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200

-the value of the car after two years is now $16,200

Finally, let's look at the value of the car after three years.  Only this time, we will now find 10% of 16,200

-multiply 16,200 by 0.1 to get 1,620

-since value is being depreciated, or lessened, we will once again be subtracting.  Subtract 1,620 from 16,200 to get 14,580

Therefore, the value of the car after three years is now $14,580.