17 (algebra - substitution) *
interest is calculated using the formula ( i = \frac{prt}{100} )
find ( i ) when ( p = 3000 ), ( r = 6.5 ) and ( t = 2 )

18. algebra - expansion
expand ( 5x(2xy - 3y) )
(handwritten: ( 10x^2y - 15xy ))

19. algebra - factorization *
factor and simplify ( \frac{8x^2 - 6x}{12x - 9} )

20. algebra - equations *
solve for ( x ): ( 3(x - 1) = 2(x + 4) )

21. algebra - graphs & functions
complete the following table:
| equation | slope | ( x )-intercept | ( y )-intercept |
| --- | --- | --- | --- |
| ( y = -5x ) | | | |
| ( y = 5x ) | | | |

22. statistics
find the mean for the following distribution.
| score | 70 | 71 | 72 | 73 | 74 |
| --- | --- | --- | --- | --- | --- |
| frequency | 1 | 4 | 10 | 4 | 1 |

Question

17 (algebra - substitution) *
interest is calculated using the formula ( i = \frac{prt}{100} )
find ( i ) when ( p = 3000 ), ( r = 6.5 ) and ( t = 2 )

18. algebra - expansion
expand ( 5x(2xy - 3y) )
(handwritten: ( 10x^2y - 15xy ))

19. algebra - factorization *
factor and simplify ( \frac{8x^2 - 6x}{12x - 9} )

20. algebra - equations *
solve for ( x ): ( 3(x - 1) = 2(x + 4) )

21. algebra - graphs & functions
complete the following table:
| equation | slope | ( x )-intercept | ( y )-intercept |
| --- | --- | --- | --- |
| ( y = -5x ) |  |  |  |
| ( y = 5x ) |  |  |  |

22. statistics
find the mean for the following distribution.
| score | 70 | 71 | 72 | 73 | 74 |
| --- | --- | --- | --- | --- | --- |
| frequency | 1 | 4 | 10 | 4 | 1 |

Accepted Answer

### Question 17
# Explanation:
## Step1: Substitute the values into the formula
We have the formula for simple interest $ I = \frac{PRT}{100} $, and we are given $ P = 3000 $, $ R = 6.5 $, and $ T = 2 $. Substitute these values into the formula:
$ I=\frac{3000\times6.5\times2}{100} $
## Step2: Calculate the numerator first
First, calculate the product in the numerator: $ 3000\times6.5\times2 = 3000\times13 = 39000 $
## Step3: Divide by 100
Now, divide the result by 100: $ \frac{39000}{100}=390 $
# Answer:
$ 390 $

### Question 18
# Explanation:
## Step1: Use the distributive property (multiplication over subtraction)
The distributive property states that $ a(b - c)=ab - ac $. Here, $ a = 5x $, $ b = 2xy $, and $ c = 3y $. So, we multiply $ 5x $ with each term inside the parentheses:
$ 5x\times2xy-5x\times3y $
## Step2: Simplify each term
Simplify $ 5x\times2xy = 10x^{2}y $ and $ 5x\times3y = 15xy $. So the expanded form is:
$ 10x^{2}y - 15xy $
# Answer:
$ 10x^{2}y - 15xy $

### Question 19
# Explanation:
## Step1: Factor the numerator and the denominator
First, factor the numerator $ 8x^{2}-6x $. We can factor out a common factor of $ 2x $: $ 8x^{2}-6x = 2x(4x - 3) $
Next, factor the denominator $ 12x - 9 $. We can factor out a common factor of $ 3 $: $ 12x - 9 = 3(4x - 3) $
So the fraction becomes $ \frac{2x(4x - 3)}{3(4x - 3)} $
## Step2: Cancel out the common factor
We can cancel out the common factor $ (4x - 3) $ (assuming $ 4x - 3
eq0 $):
$ \frac{2x}{3} $
# Answer:
$ \frac{2x}{3} $

### Question 20
# Explanation:
## Step1: Expand both sides of the equation
First, expand $ 3(x - 1) $ using the distributive property: $ 3x - 3 $
Then, expand $ 2(x + 4) $ using the distributive property: $ 2x + 8 $
So the equation becomes $ 3x - 3 = 2x + 8 $
## Step2: Solve for $ x $
Subtract $ 2x $ from both sides: $ 3x - 2x - 3 = 2x - 2x + 8 $, which simplifies to $ x - 3 = 8 $
Then, add 3 to both sides: $ x - 3 + 3 = 8 + 3 $, so $ x = 11 $
# Answer:
$ x = 11 $

### Question 21
For the equation $ y=-5x $:
- **Slope**: In the slope - intercept form $ y = mx + b $ (where $ m $ is the slope and $ b $ is the $ y $-intercept), for $ y=-5x+0 $, the slope $ m=-5 $
- **$ x $-intercept**: To find the $ x $-intercept, set $ y = 0 $. So $ 0=-5x\Rightarrow x = 0 $
- **$ y $-intercept**: In the form $ y=-5x + 0 $, the $ y $-intercept $ b = 0 $

For the equation $ y = 5x $:
- **Slope**: In the slope - intercept form $ y=mx + b $, for $ y = 5x+0 $, the slope $ m = 5 $
- **$ x $-intercept**: Set $ y = 0 $, then $ 0 = 5x\Rightarrow x = 0 $
- **$ y $-intercept**: In the form $ y = 5x+0 $, the $ y $-intercept $ b = 0 $

| Equation | Slope | $ x $-intercept | $ y $-intercept |
| --- | --- | --- | --- |
| $ y=-5x $ | $ - 5 $ | $ 0 $ | $ 0 $ |
| $ y = 5x $ | $ 5 $ | $ 0 $ | $ 0 $ |

### Question 22
# Explanation:
## Step1: Recall the formula for the mean of a frequency distribution
The formula for the mean $ \bar{x}=\frac{\sum_{i = 1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}} $, where $ f_{i} $ is the frequency of the $ i $-th class and $ x_{i} $ is the mid - value (in this case, the score) of the $ i $-th class.
## Step2: Calculate $ \sum_{i = 1}^{n}f_{i}x_{i} $
- For $ x = 70 $ and $ f = 1 $: $ 70\times1=70 $
- For $ x = 71 $ and $ f = 4 $: $ 71\times4 = 284 $
- For $ x = 72 $ and $ f = 10 $: $ 72\times10=720 $
- For $ x = 73 $ and $ f = 4 $: $ 73\times4 = 292 $
- For $ x = 74 $ and $ f = 1 $: $ 74\times1=74 $

Now, sum these products: $ 70 + 284+720 + 292+74=70+(284 + 720)+(292 + 74)=70 + 1004+366=70+(1004 + 366)=70 + 1370 = 1440 $
## Step3: Calculate $ \sum_{i = 1}^{n}f_{i} $
Sum the frequencies: $ 1 + 4+10 + 4+1=20 $
## Step4: Calculate the mean
Now, divide the sum of the products by the sum of the frequencies: $ \bar{x}=\frac{1440}{20}=72 $
# Answer:
$ 72 $

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QUESTION IMAGE

Question

Explanation:

Question 17

Step1: Substitute the values into the formula

Step2: Calculate the numerator first

Step3: Divide by 100

Step1: Use the distributive property (multiplication over subtraction)

Step2: Simplify each term

Step1: Factor the numerator and the denominator

Step2: Cancel out the common factor

Answer:

Question 18