<h2>
Answer with explanation:</h2>
Let p be the proportion of the correct answers.
As per given , we have
, since the alternative hypothesis is right tailed , so the test is a one -tailed test.
If the student gets 52 answers correct out of 80.
i.e. the proportion of correct answers : 
Test statistic : 
P-value : 
[ by using p-value table for z (right-tailed)]
Since the p-value(0.0037) is less than the significance level (0.05), so we reject the null hypothesis.
Results : We have enough evidence to support the claim that a student knows more than half of the answers and is not just guessing.
Answer:
f⁻¹(x) = x+2 / 3
Step-by-step explanation:
Given function is:
f(x) = 3x-2
We have to find the inverse of the given function.
Put y = f(x) in given function, we have
y =3x-2
Adding 2 to both sides of the above equation we have
y+2 = 3x-2+2
y+2 = 3x
Dividing by 3 to both sides of the above equation, we have
y+2 / 3 = 3x / 3
y+2 / 3 = x
Put x = f⁻¹(y) in the above equation we have
y+2 / 3 = f⁻¹(y)
Swapping equation we have
f⁻¹(y) = y+2 / 3
Replace y with x we have
f⁻¹(x) = x+2 / 3 which is the answer.
Answer:
The given expression is a line equation with slope - 3 and y-intercept 9 .
Step-by-step explanation:
Given expression as
y - 2 = ( - 3) (x - 7)
Now, Rearranging the equation
i,e y - 2 = - 3 x + 7
Or, y = - 3 x + 7 + 2
Or, y = - 3 x + 9
Now, The equation is similar to the equation of any line
∵ <u>The standard equation of any line is written as</u>
y = m x + c
where m is the slope of line and c is the y-intercept
So, while comparing expression with line equation, we get
The equation of line as y = - 3 x + 9
Where - 3 is the slope of line and 9 is the y-intercept
So,The given expression is line equation
Hence, The given expression is a line equation with slope - 3 and y-intercept 9 . Answer
We know that
the area of a rectangle=length*width
let
length=x-3
width=x+8
area=42 ft²
so
42=(x-3)*(x+8)----------> x²+8x-3x-24=42--------> x²+5x-66=0
using a graph tool-------> to resolve the second order equation
see the attached figure
the solution is
x=6
hence
length=x-3------> 6-3-----> 3 ft
width=x+8 ------> 6+8----> 14 ft
the answer is<span>
the dimensions of the rectangle are 3 ft x 14 ft</span>
