Respuesta :
See below for the solution to the questions
The survey question
Survey questions that are unbiased must be open-ended and must not assume or limit the respondent to options.
The given question is limited to wonderful lasagna and chicken, and it does not consider respondents that prefer other meals
Hence, the survey question is biased.
Simplified form of expression
The expression is given as:
√27 - √48
Expand
√(9 * 3) - √(16 * 3)
Take the square roots of 9 and 16
3√3 - 4√3
Evaluate the difference
-√3
Hence, the simplified form of the expression √27 - √48 is -√3
Slope of perpendicular line
The points are given as: (7,12) and (4,15)
The slope (m) is calculated as:
m = (y2 - y1)/(x2 - x1)
This gives
m = (15 - 12)/(4 - 7)
Evaluate
m = -1
The slope of a line perpendicular to the points is:
Slope = -1/m
This gives
Slope = -1/-1
Evaluate
Slope = 1
Hence, the slope of a line perpendicular to the points is -1
Rewriting an expression
The expression is given as:
[tex]\frac{9m^{-6}n^2p^{-1}}{12mn^{-5}p}[/tex]
Apply the product and the quotient laws of indices
[tex]\frac{9n^{2+5}}{12m^{1 + 6}p^{1+1}}[/tex]
Evaluate the exponents
[tex]\frac{9n^7}{12m^7p^2}[/tex]
Divide 9 and 12 by 3
[tex]\frac{3n^7}{4m^7p^2}[/tex]
Hence, the expression with positive exponent is [tex]\frac{3n^7}{4m^7p^2}[/tex]
The price at highest profit
We have:
P = -25d² + 500d
Differentiate and set to 0
0 = -50d + 500
Add 50d to both sides
50d = 500
Divide by 50
d = 10
Hence, the price at the highest profit is $10
Simplified form of expression
We have:
(5x² + 11x - 9) - (2x² - 3x + 5)
Open the brackets
5x² + 11x - 9 - 2x² + 3x - 5
Collect the like terms
5x² - 2x² + 11x + 3x - 9 - 5
Evaluate the like terms
3x² + 14x - 14
Hence, the simplified expression is 3x² + 14x - 14
The equation of line
The point is given as: (-4,-6)
The slope (m) is given as: -3
The equation is calculated as:
y = m(x - x1) + y1
This gives
y = -3(x + 4) - 6
Expand
y = -3x - 12 - 6
Evaluate
y = -3x - 18
Hence, the equation of the line is y = -3x - 18
Number of ways to load a song
The given parameters are:
Songs, n = 60
Selected songs, r = 5
The number of ways to load the 5 songs is:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives
[tex]^{60}C_5 = \frac{60!}{(60 - 5)!5!}[/tex]
Evaluate the difference
[tex]^{60}C_5 = \frac{60!}{55!5!}[/tex]
Expand
[tex]^{60}C_5 = \frac{60 * 59 * 58 * 57 * 56 * 55!}{55!5!}[/tex]
Divide
[tex]^{60}C_5 = \frac{60 * 59 * 58 * 57 * 56}{5!}[/tex]
Divide
[tex]^{60}C_5 = 5461512[/tex]
Hence, there are 5461512 ways to load the songs.
The solution to the equation
The equation is given as:
x² - 4x + 3 = 0
Expand
x² - 3x - x + 3 = 0
Factorize
x(x - 3) - 1(x - 3) = 0
Factor out x - 3
(x - 1)(x -3) = 0
Solve for x
x = 1 or x = 3
Hence, the solutions to the equation are x = 1 and x = 3
The y-intercept
We have:
y = 3x² + 2x - 13
Set x = 0
y = 3(0)² + 2(0) -13
Evaluate
y = -13
Hence, the y-intercept of y = 3x² + 2x - 13 is -13
The solution to system of equations
We have:
2x + y = -7
-3x - 2y = 10
Multiply the first equation by 2
4x + 2y = -14
Add this to the second equation
-3x + 4x - 2y + 2y = 10 - 14
Evaluate the like terms
-x = -4
Solve for x
x = 4
Substitute x = 4 in 2x + y = -7
2(4) + y = -7
Expand
8 + y = -7
Solve for y
y = -15
Hence, the solution to the equations is x = 4 and y = -15
Read more about system of equations at:
https://brainly.com/question/14323743
Read more about linear equations at:
https://brainly.com/question/1884491
Read more about combination at:
https://brainly.com/question/11732255
Read more about statistical questions at:
https://brainly.com/question/12150562
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