Answer:
6
Step-by-step explanation:
subtract 5 from 107 is 102
102 divided by 17 is 6
Answer:
0.7557
Step-by-step explanation:
In this question use the Table of Standard Normal Probabilities for Negative z-scores and the Table of Standard Normal Probabilities for Positive z-scores
Where z=2.27 NORMDIST(2.27)=0.9884 (read from table for positive z-scores)
Where z=-0.73 NORMDIST(-0.73)=0.2327 (read from table for negative z-scores)
You know P(-0.73<z<2.27)= 0.9884-0.2327=0.7557
Since we know that dilation of a figure changes all sides of a figure by same factor.
Let us find out factor of dilation of our figure.
We will find side length QR of our quadrilateral QRST and its corresponding side QR' of quadrilateral Q'R'S'T'.
![\text{Length of QR}=5--1](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20QR%7D%3D5--1)
![\text{Length of QR}=5+1=6](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20QR%7D%3D5%2B1%3D6)
Let us find side length of Q'R'.
![\text{Length of Q'R'}=1--1](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20Q%27R%27%7D%3D1--1)
![\text{Length of Q'R'}=1+1=2](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20Q%27R%27%7D%3D1%2B1%3D2)
Let us compare both our side lengths to find factor of dilation,
![\frac{QR}{Q'R'}= \frac{6}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BQR%7D%7BQ%27R%27%7D%3D%20%5Cfrac%7B6%7D%7B2%7D)
![\frac{QR}{Q'R'}= 3](https://tex.z-dn.net/?f=%5Cfrac%7BQR%7D%7BQ%27R%27%7D%3D%203)
Upon cross multiplication we will get,
![QR=3\cdot Q'R'](https://tex.z-dn.net/?f=QR%3D3%5Ccdot%20Q%27R%27)
![Q'R'=\frac{1}{3} \cdot QR](https://tex.z-dn.net/?f=Q%27R%27%3D%5Cfrac%7B1%7D%7B3%7D%20%5Ccdot%20QR)
We can see that Q'R' is
of Q'R'. Therefore, our factor of dilation is
.
Answer: Nancy needs 26 minutes to driving to work.
Explanation:
Since we have given that
Time taken in eating breakfast = 10 minutes
Time taken in making her bed = 5 minutes
Let the total time taken by her in doing routine activities be x
Time taken in getting dressed is given by
![\frac{1}{3}x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx)
So, According to question,
![\frac{x}{3}+10+5=35\frac{1}{2}\\\\\frac{x}{3}+15=\frac{71}{2}\\\\\frac{x}{3}=\frac{71}{2}-15\\\\\frac{x}{3}=\frac{71-30}{2}=\frac{41}{2}\\\\x=\frac{123}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B3%7D%2B10%2B5%3D35%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5Cfrac%7Bx%7D%7B3%7D%2B15%3D%5Cfrac%7B71%7D%7B2%7D%5C%5C%5C%5C%5Cfrac%7Bx%7D%7B3%7D%3D%5Cfrac%7B71%7D%7B2%7D-15%5C%5C%5C%5C%5Cfrac%7Bx%7D%7B3%7D%3D%5Cfrac%7B71-30%7D%7B2%7D%3D%5Cfrac%7B41%7D%7B2%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B123%7D%7B2%7D)
Now, we need to find the time taken in driving to work which is given by
![\frac{123}{{2}-\frac{71}{2}=\frac{52}{2}=26\ minutes](https://tex.z-dn.net/?f=%5Cfrac%7B123%7D%7B%7B2%7D-%5Cfrac%7B71%7D%7B2%7D%3D%5Cfrac%7B52%7D%7B2%7D%3D26%5C%20minutes)
Hence, Nancy needs 26 minutes to driving to work.