Answer:
1) y=⅚x -2⅓
2) y=8/3x -5
Step-by-step explanation:
<u>Point-slope form:</u>
y=mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient.
Gradient of given line= 
Thus, m=⅚
Susbt. m=⅚ into the equation,
y= ⅚x +c
Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.
When x=4, y=1,
1= ⅚(4) +c

Thus the equation of the line is
.
The gradients of perpendicular lines= -1.
Gradient of given line= -⅜
-⅜(gradient of line)= -1
gradient of line
= -1 ÷ (-⅜)
= -1 ×(-8/3)
= 

When x=3, y=3,

Thus the equation of the line is
.
Answer:
A sample of 997 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of
.
The margin of error is of:

A previous study indicates that the proportion of left-handed golfers is 8%.
This means that 
98% confidence level
So
, z is the value of Z that has a p-value of
, so
.
How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?
This is n for which M = 0.02. So






Rounding up:
A sample of 997 is needed.

- How do you simplify this?
- x²y+xy² / y²+2/5 × xy


Factor the expressions that are not already factored.
_____
<u>How </u><u>to</u><u> factorise</u><u> </u><u>:</u><u>-</u>
<u>NUMERATOR</u> 

Factor out xy.

<u>DENOMINATOR</u> 

Factor out 1/5.

_____
Continuing...

Cancel out y in both the numerator and denominator.

Expand the expression.

This can further simplified to as 

Answer:
2^6
Step-by-step explanation:
2 is being multiplied 6 times meaning it would be 2 to the 6th power.
Out of the four options,
A. 99 cm B. 105.98 cm C. 90 cm D. 104.5 cm,
option A is the correct answer.
Because 1 m = 100 cm and this is the nearest approximation. Thus, the<span>A student used A tape measures to estimate the length of a meterstick manufactured to he exactly 1 meter. </span>