Answer:
I think Teresa needs 6 tablespoons of butter..
Step-by-step explanation:
Hope this right...but if it's not,im so sorry
Step-by-step answer:
Given:
A triangle
Perimeter = 60 cm
longest side = 4* shortest side (x)
Solution:
longest side = 4x
shortest side = x
third (intermediate side = 60 -x -4x = 60-5x
The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle. Hence
x + y > 4x
x + 60-5x > 4x
60 - 4x > 4x
8x < 60
x < 60/8 = 7.5, or
x < 7.5
Therefore to form a triangle, x (shortest side) must be less than 7.5 cm.
Examine the options: both 7 and 5 are both less than 7.5 cm.
40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.
Now also examine cases where 4x is NOT the longest side, in which case we need
4x>=y
or
4x >= 60-5x
9x >=60
x >= 6.67
so x=5 will not qualify, because 4x will no longer be the longest side.
The only valid option is x=7 cm
The side lengths for x=7 and x=5 are, respectively,
(7, 25, 28)
5, 20, 35 (in which case, the longest side is no longer 4x=20, so eliminated)
Answer:
The family of possible values for
are:

Step-by-step explanation:
By Linear Algebra, we can calculate the angle by definition of dot product:
(1)
Where:
- Angle between vectors, in sexagesimal degrees.
- Norms of vectors
and 
If
is acute, then the cosine function is bounded between 0 a 1 and if we know that
and
, then the possible values for
are:
Minimum (
)

Maximum (
)

With the help of a graphing tool we get the family of possible values for
are:

Answer:
5/36 or approximately 13.88...%
Step-by-step explanation:
First, we need to know the probability of rolling a 2 or 3. Because there are 6 sides, the probability is 2/6
Next, we have to find the probability of rolling an even number. With the numbers:
1, 2, 3, 4, 5, 6
1, 3, 5 are odd 2, 4, 6 are even
so, the probability of rolling an even number is 3/6
Finally, multiply the probabilities:
3/6*2/6=5/36
Answer:
5/36 or about 13.88%
38 quarts because four quart equals one gallon.