lesson 5: staying sharp
1. which value is the closest to 0.9·99?
a. 1,000
b. 81
c. 10,000
d. 10
answer with supporting work:
2. if (e,f)=(7,2) and (g,h)=(11,5), find the value of the following expression:
$\frac{h - f}{g - e}$
answer:
3. ravi glanced at the computer as he was downloading a file. what percent had downloaded?
36 kb of 40 kb downloaded...
__% downloaded
answer with supporting work:
4. fill in the blanks for the area model:
10 100 2
__ __ 12
16·12=(10+__)(__ + 2)
5. invent a five - value data set for which the mean is 6 and the mode is not 6.
6. choose an appropriate scale for each axis and plot the following points on the grid provided: (20,0) (-8,4) (12,-12) (0,-16).
one unit on the x - axis equals:
one unit on the y - axis equals:

Question

Accepted Answer

### 1.
# Explanation:
## Step1: Calculate $0.9\times99$
$$0.9\times99=(1 - 0.1)\times99=99-9.9 = 89.1$$
The closest value among the options is 81.
# Answer:
b. 81

### 2.
# Explanation:
## Step1: Identify the values
Given $(e,f)=(7,2)$ and $(g,h)=(11,5)$, so $e = 7$, $f=2$, $g = 11$, $h = 5$.
## Step2: Substitute into the expression
$\frac{h - f}{g - e}=\frac{5 - 2}{11 - 7}=\frac{3}{4}=0.75$
# Answer:
0.75

### 3.
# Explanation:
## Step1: Use the percentage - formula
The percentage formula is $\text{Percentage}=\frac{\text{Amount Downloaded}}{\text{Total Amount}}\times100$. Here, the amount downloaded is 36 KB and the total amount is 40 KB.
## Step2: Calculate the percentage
$\text{Percentage}=\frac{36}{40}\times100=\frac{3600}{40}=90$
# Answer:
90

### 4.
For the area - model:
We know that $16\times12=(10 + 6)(10+2)$
The blanks are filled as follows:
In the area - model, for the top - row: if the first box is 100 (which is $10\times10$), the first blank above 100 is 10 (since $10\times1 = 10$) and the blank to the right of 100 is 20 (since $10\times2=20$). The bottom - row: the blank below 100 is 60 (since $6\times10 = 60$) and the last blank is 12 (since $6\times2=12$).
# Answer:
The blanks are 10, 20, 60, 6, 10

### 5.
# Explanation:
## Step1: Recall the mean formula
The mean of a data - set $x_1,x_2,x_3,x_4,x_5$ is $\bar{x}=\frac{\sum_{i = 1}^{5}x_i}{5}$. We want $\bar{x}=6$, so $\sum_{i = 1}^{5}x_i=30$. And we want the mode to be different from 6.
## Step2: Invent the data - set
A possible data - set is $4,4,6,8,8$. Since $\frac{4 + 4+6+8+8}{5}=\frac{30}{5}=6$, and the mode is 4 and 8.
# Answer:
4, 4, 6, 8, 8

### 6.
For the $x$ - values: $- 8,0,12,20$, a good scale for the $x$ - axis could be 4.
For the $y$ - values: $-16,-12,0,4$, a good scale for the $y$ - axis could be 4.
# Answer:
One unit on the $x$ - axis equals: 4
One unit on the $y$ - axis equals: 4

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QUESTION IMAGE

Question

Explanation:

1.

Step1: Calculate \(0.9\times99\)

Step1: Identify the values

Step2: Substitute into the expression

Step1: Use the percentage - formula

Step2: Calculate the percentage

Answer:

2.