An item has a listed price of $65. If the sales tax rate is 5%, how much is the sales tax in dollars?

What is equation of a circle centered at (2, 4) with a radius of 2?

Bas_tet [7]

Answer:

(x-2)²+(y-4)²=4

Step-by-step explanation:

6 0

3 years ago

The following is a recipe for Gazpacho, a cold vegetable soup. Write how much of each item in the

denis23 [38]

9514 1404 393

Answer:

replace recipe quantities:

1/4 ⇒ 5/8; 1/2 ⇒ 1 1/4; 1 ⇒ 2 1/2; 1 1/2 ⇒ 3 3/4; 2 ⇒ 5

Step-by-step explanation:

The given recipe serves 4, so must be multiplied by 10/4 = 5/2 to make it make 10 servings.

The numbers in the recipe (ignoring units or ingredients) are ...

1/4, 1/2, 1, 1 1/2, 2

Each of these numbers needs to be multiplied by 5/2 to get the number for the larger recipe.

1/4 × 5/2 = 5/8

1/2 × 5/2 = 5/4 = 1 1/4

1 × 5/2 = 5/2 = 2 1/2

(1 1/2) × 5/2 = 3/2 × 5/2 = 15/4 = 3 3/4

2 × 5/2 = 5

Then, to make the larger recipe, rewrite it with the quantities replaced as follows:

old value ⇒ new value

1/4 ⇒ 5/8

1/2 ⇒ 1 1/4

1 ⇒ 2 1/2

1 1/2 ⇒ 3 3/4

2 ⇒ 5

__

For example, 1 1/2 lbs of fresh tomatoes ⇒ 3 3/4 lbs of fresh tomatoes

_____

<em>Additional comment</em>

If you actually want to create the recipe, you may find it convenient to use a spreadsheet to list quantities, units, and ingredient names. Then you can add a column for the quantities for a different number of servings, and let the spreadsheet figure the new amounts. (A spreadsheet will compute quantities in decimal, so you will need to be familiar with the conversions to fractions--or use metric quantities.)

8 0

3 years ago

How would I go about solving this problem???

schepotkina [342]

So.. if you take a peek at the picture below

the trunk is really just a half-cylinder on top of a square, with a depth of 2 meters

what's the volume? well, easy enough, take the volume of the cylinder, then half it
take the volume of the rectangular prism, and then add them both

$\bf \textit{volume of a cylinder}\\\\

\begin{array}{llll}
C=\pi r^2 h\\\\
\textit{half that}\\\\
\cfrac{\pi r^2 h}{2}
\end{array}\qquad 
\begin{cases}
r=radius\\
h=height\\
-------\\
r=\frac{1}{2}\\
h=2
\end{cases}\implies \cfrac{C}{2}=\cfrac{\pi \left( \frac{1}{2}\right)^2 2}{2}\\\\
-----------------------------\\\\
\textit{volume of a square}\\\\
V=lwh\qquad 
\begin{cases}
l=length\\
w=width\\
h=height
----------\\
l=1\\
w=1\\
h=2
\end{cases}\implies V=2$

now.. for the surface area... $\bf \textit{surface area of a cylinder}\\\\
\begin{array}{llll}
S=2\pi r(h+r)\\\\
\textit{half that}\\\\
\cfrac{2\pi r(h+r)}{2}
\end{array}\begin{cases}
r=radius\\
h=height\\
-------\\
r=\frac{1}{2}\\
h=2
\end{cases}$

now.. for the surface area of the prism... well

is really just 6 rectangles stacked up to each other at the edges

so... get the area of the lateral rectangles, and the one at the bottom, skip the rectangle atop, because is the one overlapping the cylinder, and is not outside, and thus is not surface area then

for the lateral ones, you have a front of 1x1, a back of 1x1 and a left of 1x2 and a right of 1x2, and then the one at the bottom, which is a 1x2

then add both surface areas, and that's the surface area of the trunk