Answer:53
Step-by-step explanation:
Each pencil cost $2.
Explanation: She had $24 before buying the pencils and after she had $10. 24-10=14 so the total she spent on pencils was $14. She bought 7 pencils so you divide 14 by 7 (14/7=2) which equals 2. So each pencil cost $2.
A) The constant of proportionality in this proportional relationship is 
B) The equation to represent this proportional relationship is y = 0.2x
<h3><u>Solution:</u></h3>
Given that,
The amount Naomi pays each month for international text messages is proportional to the number of international texts she sends that month
Therefore,
This is a direct variation proportion

Let "y" be the amount that Naomi pays each month
Let "x" be the number of international texts she sends that month
Therefore,

y = kx -------- eqn 1
Where, "k" is the constant of proportionality
Thus the constant of proportionality in this proportional relationship is:

<em><u>Last month, she paid $3.20 for 16 international texts</u></em>
Therefore,
y = 3.20
x = 16
Thus from eqn 1,

Substitute k = 0.2 in eqn 1
y = 0.2x
The equation would then be y = 0.2x
Answer:
The standard deviation for the income of super shoppers is 76.12.
Step-by-step explanation:
The formula to compute the standard deviation for the grouped data probability distribution is:
![\sigma=\sqrt{\sum [(x-\mu)^{2}\cdot P(x)]}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Csum%20%5B%28x-%5Cmu%29%5E%7B2%7D%5Ccdot%20P%28x%29%5D%7D)
Here,
<em>x</em> = midpoints

Consider the Excel table attached below.
The mean is:

Compute the standard deviation as follows:
![\sigma=\sqrt{\sum [(x-\mu)^{2}\cdot P(x)]}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B%5Csum%20%5B%28x-%5Cmu%29%5E%7B2%7D%5Ccdot%20P%28x%29%5D%7D)

Thus, the standard deviation for the income of super shoppers is 76.12.