The given quadratic expression; 5b² -6b -2 is prime because the discriminant is not a perfect square.
<h3>
What is the discriminant of the expression?</h3>
According to the task content; it is required to identify if the expression is prime.
On this note, it follows that the discriminant of the expression can be evaluated as follows;
= 36 -(4× 5 × -2)
= 76.
Hence, the expression is prime since 76 is not a perfect square.
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Answer:
The two numbers are -164 and -287
They could also be 164 and 287
Step-by-step explanation:
The ratio of 2 numbers 4/7
x/y = 4/7
Using cross products
7x =4y
Their difference is 123
x-y = 123
x = 123+y
Substituting in
7(123+y) =4y
Distribute
861 +7y = 4y
Subtract 7y from each side
861 +7y-7y = 4y-7y
861 = -3y
Divide each side by -3
861/-3 = -3y/-3
-287 = y
Now we need to find x
x = 123+y
x = 123+ -287
x = -164
The numbers could also be 164 and 287
The difference is 287-164 = 123
And the ratio is 164/287 = 4/7
The probability of E and F expressed as P(E and F) equals;0.12
<h3>How to solve Conditional Probability?</h3>
We are given;
P(E) = 0.2
P(F|E) = 0.6
Now, P(F/E) is known as conditional probability and it means the probability of event F given the probability of another event E. This can be expressed as; P(F|E) = P(E and F)/P(E)
Thus;
P(E and F) = 0.2 * 0.6
P(E and F) = 0.12
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Explanation:
Linear escale factor 1.
In this case the original volume of the parallelepiped is:
24 cubic units and the new volume must be:
So in this case the ratio of volumes is 1:1
Linear escale factor 2.
In this case the original volume of the parallelepiped is the same: 24 cubic units.
The new voume must be:
So in this case the ratio of volumes is 24:192, that is 1:8
Linear escale factor 3.
In this case the original volume of the parallelepiped is the same: 24 cubic units.
The new voume must be:
So in this case the ratio of volumes is 24:648, that is 1:27
Linear escale factor 4.
In this case the original volume of the parallelepiped is the same: 24 cubic units.
The new voume must be:
So in this case the ratio of volumes is 24:1536, that is 1:64
Linear escale factor r.
In this case the original volume of the parallelepiped is the same: 24 cubic units.
The new voume must be:
So in this case the ratio of volumes is 24:24r^3, that is:
