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padilas [110]
3 years ago
9

In this activity, you will use equations to represent this proportional relationship: Olivia is making bead bracelets for her fr

iends. She can make 3 bracelets in 15 minutes.
Part A
Find the constant of proportionality in terms of minutes per bracelet.

Part B
What does the proportionality constant represent in this situation?

Part C
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part A. Be sure to assign a variable for each quantity.

Part D
Now find the constant of proportionality in terms of number of bracelets per minute.

Part E
What does the proportionality constant represent in this situation?

Part F
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part D. Be sure to assign a variable for each quantity.

Part G
How are the constants of proportionality you found in parts A and D related?

Part H
Are the two equations you developed in parts C and F equivalent? Explain.
​​
Mathematics
1 answer:
Valentin [98]3 years ago
3 0

Answer:

Step-by-step explanation:

A) The constant of proportionality in terms of minutes per bracelet is

15/3 = 5 minutes per bracelet

B) The constant of proportionality represents man hour rate

C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

t = kb

D) the constant of proportionality in terms of number of bracelets per minute is

3/15 = 1/5

E) The constant of proportionality represents production rate

F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

b = kt

G) The constants of proportionality are reciprocals

H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.

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In how many ways can you place 50 identical balls in six distinct urns such that each urn contains an odd number of balls
mezya [45]

Answer:

80730

Step-by-step explanation:

The answer is c(27,5)=27*26*25*24*23/5!. Here is why.

Let us solve a simpler problem. In how many ways 25 identical balls can be placed in six distinct urns such that no urn is empty?

25 balls in a row make 24 places for five dividers, so the answer is c(24,5).

2. Next problem. In how many ways 50 identical balls can be placed in six distinct urns such that no urn is empty and each urn contains even number of balls.

We group 50 balls in 25 pairs, so the answer is the same as in the previous problem which is

c(48/2,5)=c(24,5).

Let us denote the content of each urn as

u(1),u(2),…u(6). Note that each u(i) is even. Denote u(i) as u(i)=2k(i) where k is a natural number. We have

2k(1)+2k(2)+2k(3)+2k(4)+2k(5)+2k(6)=50.

3. Now let us proceed to the original problem where odd number of balls in each urn is required.

We have

2k(1)-1+2k(2)-1+2k(3)-1+2k(4)-1+2k(5)-1+2k(6)-1=50 or

2k(1)+2k(2)+2k(3)+2k(4)+2k(5)+2k(6)=56.

So the original problem reduces to previous problem where even number of balls in each urn is required but the total number of balls is 56 instead of 50.

Its answer is c(54/2,5)=c(27,5).

8 0
2 years ago
Sarah is making a pitcher of lemonade. She uses 3/4 cup of sugar and 1 2/3 cups of lemon juice. How many more cups of lemon juic
Aneli [31]

Answer:

11/12

Step-by-step explanation:

We compute

1 2/3 - 3/4 =

5/3 - 3/4 =

20/12 - 9/12 =

11/12 Cups

4 0
2 years ago
Which of the following coordinate planes shows the graph of the function y-3=-2(x+2)?
Ugo [173]

Answer:

-5=x

Step-by-step explanation:

3=-2 (x+2)

-2 (x+2) = -2x-4

3=-2x-4

-4 from 3 and -4

= -7=-2x

do the opposite "-2 to +2 "

=-5=x

8 0
3 years ago
Solve: 12.5 z – 6.4 = –8 z + 3(1.5 z – 0.5)
dolphi86 [110]

Answer:

Step-by-step explanation:

12.5z - 6.4 =-8z + 3(1.5z - 0.5)

12.5z - 6.4 = - 8z + 4.5z - 1.5

12.5z - 6.4 = - 3.5z - 1.5

Bringing like terms on one side

12.5z + 3.5z = - 1.5 + 6.4

16z = 4.9

z = 4.9/16

6 0
3 years ago
. In the U.S., from 2004−2015, the correlation coefficient for the relationship between the size of a cell phone data plan, x, a
bonufazy [111]

Answer: strong positive correlafion between data plan size 'x' and number of text messages sent 'y'

Step-by-step explanation:

'R' in statistics is used to denote correlation Coefficient. The correlation Coefficient is a value which ranges between -1 to +1. It tells us the level of relationship or correlation which exists between the relative movement of two variables, in this case the relationship between data plan size and the number of text messages sent in the US. R value of 0 depicts that no relationship exists between the two variables, R value closer the R value is to +1 and - 1 depicts the strength of positive and negative correlation of the two variables respectively.

A R value of +0.97 in the context above, depicts a strong positive correlation between data plan size and number of text messages sent in the US. That is large data size usually corresponds to large number of text messages and vice versa.

4 0
3 years ago
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