A recipe says to use 3.5 cups of flour to make 48 cookies. What is the constant of proportionality that relates the number of cookies made, y, to the number of cups of flour used, x. Round your answer to the nearest tenth.

Answers

Answer 1

Answer:

Answer: 0.07 cups/cookie

Step-by-step explanation:

The Constant of proportionality is the measure by which the number of cookies made, y increases to the number of cups of flour used, x.

If 3.5 cups of flour makes 48 cookies then how many cookies does 1 cup make;

= 3.5/48

= 0.07 cups/cookie

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If you bought something in Colorado for $80, you would be charged $2.32 in state sales tax. What is the state sales tax in Colorado?

Answers

The state sales tax in Colorado is 2.9%.

We know that because we divide 2.32/80. We have to find out what percent the tax is of the amount paid. The answer comes to 0.029. Multiply it by 100, and you get 2.9%

it will cause about the same as what was put in

Solve the equation. Show your work.

1/a =6/18

Answers

1 6
--- = ---
a 18

- simplify 6/18, which should be 1/3. therefore, a = 3.

Ex 3.7
12. find the area between the curve y=x³-2 and the y-axis between y= -1 and y=25

Answers

$y=x^3-2\nx^3=y+2\nx=\sqrt[3]{y+2}\n\n\int \limits_(-1)^(25)\sqrt[3]{y+2}\, dy=\n\int \limits_(-1)^(25)(y+2)^{\tfrac{1}{3}}\, dy=\n\left[\frac{(y+2)^{\tfrac{4}{3}}}{(4)/(3)} \right]_(-1)^(25)=\n$
$\left[(3)/(4)(y+2)^{\tfrac{4}{3}} \right]_(-1)^(25)=\n\left[(3)/(4)(y+2)\sqrt[3]{y+2} \right]_(-1)^(25)=\n(3)/(4)(25+2)\sqrt[3]{25+2}-\left((3)/(4)(-1+2)\sqrt[3]{-1+2}\right)=\n(3)/(4)\cdot27\sqrt[3]{27}-\left((3)/(4)\sqrt[3]{1}\right)=\n(3)/(4)\cdot27\cdot3-(3)/(4)=\n(3)/(4)(81-1)=\n(3)/(4)\cdot 80=\n3\cdot20=\n60$

Yeah, you'd have to use the inverse function to produce this result.

Let's get the inverse function first:

$y={ x }^( 3 )-2\n \n { x }^( 3 )=y+2\n \n x=\sqrt [ 3 ]{ y+2 }$

$\n \n \therefore \quad { f }^( -1 )\left( x \right) =\sqrt [ 3 ]{ x+2 }$

Now, we can solve the problem using:

$\int _( -1 )^( 25 ){ \sqrt [ 3 ]{ x+2 } } dx$

But to solve the problem more easily we make u=x+2, therefore du/dx=1, therefore du=dx.

When x=25, u=27.

When x=-1, u=1.

Now:

$\int _( 1 )^( 27 ){ { u }^{ \frac { 1 }{ 3 } } } du\n \n ={ \left[ \frac { 3 }{ 4 } { u }^{ \frac { 4 }{ 3 } } \right] }_( 1 )^( 27 )$

$\n \n =\frac { 3 }{ 4 } \cdot { 27 }^{ \frac { 4 }{ 3 } }-\frac { 3 }{ 4 } \cdot { 1 }^{ \frac { 4 }{ 3 } }\n \n =\frac { 3 }{ 4 } { \left( { 3 }^( 3 ) \right) }^{ \frac { 4 }{ 3 } }-\frac { 3 }{ 4 }$

$\n \n =\frac { 3 }{ 4 } \cdot { 3 }^( 4 )-\frac { 3 }{ 4 } \n \n =\frac { 3 }{ 4 } \left( { 3 }^( 4 )-1 \right)$

$\n \n =\frac { 3 }{ 4 } \cdot 80\n \n =60$

Answer: 60 units squared.

Answer of the question and method how to solve

Answers

1) 63/3 = 21

2) 16-9 = 7

3) 9+9*0= 9+(9*0)= 9+0= 9

4) 12*6= 72

I hope that's help and if you have questions please ask !

Some irrigation systems spray water in a circular pattern. You can adjust the nozzle so it sprays in certain directions. The nozzle in the diagram is set so it does not spray the house. If the spray has a radius of 12 ft, what is the approximate length of the arc that the spray creates?

Answers

L - length of the arc;
Length of the arc is 3/4 of a circumference.
C = 2 r π = 2 * 3.14 * 12 = 75.36 ft
L = 75.36 * 0.75 = 56.52 ft
Answer:
The approximate length of the arc is 56.52 ft.

Scientists use a form of shorthand call ____ to express very large or very small numbers?

Answers

Scientific notation. For example: 276 is the standard form of a number while 2.76 * 10^2 would be the same number in scientific notation.

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1+4=5 2+5=12 3+6=21 8+11=