Answer:
b = 7√3
Step-by-step explanation:
This 30°- 60°- 90° triangle has the proportions:
side opposite of the 30° angle = x
side opposite of the 60° angle = x√3
side opposite of the 90° angle = 2x
____________________________
Given the side opposite of the 30° angle which is 7 units long, this can be thought of as x. Knowing the proportions of the other sides, we can find b knowing that this is the side opposite of the 60° angle which is x√3.
Since x = 7, x√3 = 7√3, and therefore
b = 7√3.
Answer:
<h2>Her prediction will be somewhat likely to be close to the actual value.</h2>
Step-by-step explanation:
A correlation coefficient of 0.55 implies a weak positive correlation, because it's close to 0.50. Remember that strong correlations are 1 or -1, positive or negative, and the middle of the interval represents no correlation.
Having said that, 0.55 indicates some correlation, but weak. Therefore, the right answer is C.
Answer:
a. 113.1 cm^3.
b. 339.29 cm^3.
c. 18 cm.
d. 508.94 cm^3.
e. 169.65 cm^3.
Step-by-step explanation:
a. (4/3) * pi * (3^3) = (4/3) * pi * 27 = 36 * pi = 113.0973355, which is about 113.1
.
b. 113.0973355 * 3 = 339.2920066, which is about 339.29 cm^3.
c. Since the radius of a tennis ball is 3 cm, the diameter is 6 cm. There are three tennis balls, and the diameters added up become the height of the cylinder. 6 + 6 + 6 = 18 cm.
d. pi * (3^2) * 18 = pi * 9 * 18 = pi * 162 = 508.9380099, which is about 508.94 cm^3.
e. 508.9380099 - 339.2920066 = 169.6460033, which is about 169.65 cm^3.
Hope this helps!!
Answer:
or 
Step-by-step explanation:
This is factorable.
The leading coefficient is 1.
Since this is a quadratic all we have to do is find two numbers that multiply to be c and add up to be b to factor the expression that is to the left of the equal sign.
By the way a quadratic expression looks like
.
So we want to find two numbers that multiply to be -6 and add up to be -1.
Those numbers are -3 and 2 since (-3)(2)=-6 and -3+2=-1.
So the factored form is:
.
Since we have a product is zero then at least one of the factors need to be zero in order for the equation to hold.
So this means we have the following two equations to solve:
or 
First equation we will add 3 on both sides.
Second equation we will subtract 2 on both sides.
or 