Two cupcakes require 2/3 of a cup of icing with one cup of icing. How many cupcakes would you be able to frost?

Answers

Answer 1

Answer: To determine how many cupcakes you can frost, you need to find the ratio of cupcakes to icing required. According to the given information:

- Two cupcakes require 2/3 of a cup of icing.
- This means that one cupcake requires (2/3) / 2 = 1/3 cup of icing.

Now, you can calculate how many cupcakes can be frosted with one cup of icing:

Number of cupcakes frosted = (1 cup of icing) / (1/3 cup of icing per cupcake)

Number of cupcakes frosted = (1 cup) / (1/3 cup) = 3 cupcakes

So, with one cup of icing, you would be able to frost 3 cupcakes.

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The volume Equals Four thirds pi r cubed of a spherical balloon changes with the radius. a. At what rate (cubed/in) does the volume change with respect to the radius when r equals 9 in question mark b. Using the rate from part a, by approximately how much does the volume increase when the radius changes from 9 to 9.5 in question mark

Answers

Answer:

Step-by-step explanation:

Given

Volume of spherical Balloon is given by

$V=(4)/(3)\pi r^3$

(a)Rate of change of balloon w.r.t to radius is given by

$\frac{\mathrm{d} V}{\mathrm{d} r}=3* (4)/(3)\pi r^2=4\pi r^2$

at $r=9\ in.$

$\frac{\mathrm{d} V}{\mathrm{d} r}=324\pi\ in.^2$

(b)Using the rate Volume change when radius increases from r=9 in. to r=9.5 in.

$\Delta V=4\pi (9)^2(9.5-9)=162\pi\ in.^3$

A jewelry designer is making a pendant. The pendant will be a circular dis (center O) with a circular hold cut out of it, as shown. The radius of the disc is 35 millimeters. Find the area of the pendant. Use 3.14 for π and round to the nearest tenth

Answers

Answer:

2884.8 millimeters squared

Step-by-step explanation:

Given:

The radius of the disc is 35 millimeters, so the area of it is:

π $r^(2)$ = 3.14* $35^(2)$ = 3846.5

Then, we find out the area of the circular hold cut out of the bigger one, its radius is a haft of the radius of the bigger circle = 35/2 = 17.5

π $r^(2)$ = 3.14* $17.5^(2)$ =961.6

=> the area of the pendant = 3846.5 - 961.6 =2884.8 millimeters squared

Solve the system of equations. 3x = -31 + 2y
5x + 6y = 23

a. x = -5, y = 8
b. x = - 29, y = - 28
c.no solution
d.infinite solutions

Answers

Answer:

a. x = -5, y = 8

Step-by-step explanation:

$\left\{\begin{array}{ccc}3x=-31+2y&\text{subtract}\ 2y\ \text{from both sides}\n5x+6y=23\end{array}\right\n\n\left\{\begin{array}{ccc}3x-2y=-31&\text{multiply both sides by 3}\n5x+6y=23\end{array}\right\n\n\underline{+\left\{\begin{array}{ccc}9x-6y=-93\n5x+6y=23\end{array}\right}\qquad\text{add both sides of the equations}\n.\qquad14x=-70\qquad\text{divide both sides by 14}\n.\qquad x=-5\n\n\text{Put it to the second equation:}\n\n5(-5)+6y=23\n-25+6y=23\qquad\text{add 25 to both sides}\n6y=48\qquad\text{divide both sides by 6}\ny=8$

I’m pretty sure i know how to do this but this test is 45% of my current grade so i’d like to make sure everything is right! thank you-3(b-3)=-3b+1

Answers

Answer:

-3(b-3) = -3b +9

Step-by-step explanation:

-3(b-3) = -3b +9

-3 x b = -3b

-3 x -3 = +9

I hope this is helpful

Camille uses a 20% off coupon when buying a sweater that costs $47.99. If she also pays 6% sales tax on the purchase, how much does she pay?

Answers

47.99-20%×47.99= $38.392 = a (price after being discounted)

Final price = a+ 6%×a = $40.69552

What is the inverse of the function f(x) = 2x – 10

Answers

f(x) is y given x
y=2x-10
inverse is switching x and y so
x=2y-10
solve for y
y=(x+10)/2

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