Although Alma did use a survey to ask her friends whether listening to music improves their test grades, she did not provide a sample nor could she experiment without using this variable. Thus, using the same reasoning, choices A, B, and C are excluded.
D) She did not use a random sample, and she tried to show cause and effect with an observational study.
Answer:
The side length of the triangle is 16
Step-by-step explanation:
The perimeter of the triangle is
P = 3t since the sides are all equal
The perimeter of the square is
P = 4s since the sides are all equal
We are given the perimeter of the square is 12
P = 4*12
P = 48
We are told the perimeters are equal
48 = 3t
Divide by 3
48/3 = 3t/3
16 =t
The side length of the triangle is 16
Answer: Divide the room into two figures (a rectangle and a trapezoid), then find the area of both figures and add them in order to calculate the area of the dining room.
Step-by-step explanation:
Divide the room into two figures: a rectangle and a trapezoid (as you can observe in the picture attached).
You need to find the area of the trapezoid and the area of the rectangle and then add them. This sum will be the area of the dining room.
First, you need to remember that:
1. The area of a rectangle can be calculated with this formula:

Where "l" is the lenght and "w" is the width of the rectangle.
2. The following formula is used to calculate the area of a trapezoid:

Where "B" and "b" are the bases of the trapezoid and "h" is the height of the trapezoid.
Therefore, the area of the dining room will be:
.
Answer:
Centre: 
Radius = 
Step-by-step explanation:
General formula for a circle:
, where
the radius of the circle and
is the centre of the circle.
To find the centre and radius of the circle we should re-write the given equation in the form of the general formula.
So, put the terms with the same variables together:

We can see that there is a common factor of
, so let's simplify by dividing by
:

Here we can get it into the general formula by completing the square.
We do this by turning a quadratic with form
into the form
, where d is half of the coefficient of
, e is
and c is the constant of the quadratic.
So let's re-write the equation of the circle:

Simplify: 
Now we can see that it's very similar to the general equation and all we have to do is bring the
over to the right side.

So, now we can find the radius and centre.


Answer:
Step-by-step explanation:
5 : 25
In simplest form
1 : 25
In fraction form
1/25
In decimal form
0.04
150 : 300
In simplest form
1 : 2
In fraction form
1/2
In decimal form
0.5