X=2
Do you want to see how to solve it?
Answer:
Step-by-step explanation:
Given : Suppose an urn has r red and w white marbles.
To find : Determine the probability that the marble is white ?
Solution :
Number of red marbles = r
Number of white marbles = w
Total number of marbles in an urn = r+w
Favorable outcome is getting the marble is white = w
So, Probability that the marble is white is given by
See the picture attached to better understand the problem
we know that
in the right triangle ABC
cos A=AC/AB
cos A=1/3
so
1/3=AC/AB----->AB=3*AC-----> square----> AB²=9*AC²----> equation 1
applying the Pythagoras Theorem
BC²+AC²=AB²-----> 2²+AC²=AB²---> 4+AC²=AB²----> equation 2
substitute equation 1 in equation 2
4+AC²=9*AC²----> 8*AC²=4----> AC²=1/2----> AC=√2/2
so
AB²=9*AC²----> AB²=9*(√2/2)²----> AB=(3√2)/2
the answer isthe hypotenuse is (3√2)/2
Answer:
Step-by-step explanation:
Required
Match each expression to their simplified form
1.
Simplify the expression in bracket by using the following law of indices;
The expression becomes
Split the fraction in the bracket
Simplify the fraction by using the following law of indices;
The expression becomes
Further simplify the expression in bracket by using the following law of indices;
The expression becomes
Hence,
2.
Simplify the expression in bracket by using the following law of indices;
The expression becomes
Further simplify the expression in bracket by using the following law of indices;
The expression becomes
Hence,
3.
Simplify the numerator as thus:
Simplify the denominator as thus:
Simplify the expression in bracket by using the following law of indices;
The expression becomes
Hence,
4.
Simplify the expression in bracket by using the following law of indices;
The expression becomes
Hence
Answer: 76 baseballs and 24 bats were ordered.
Step-by-step explanation:
Let x represent the number of baseballs that were ordered for the summer basketball camp.
Let y represent the number of bats that were ordered for the summer basketball camp.
Bakersfield parks and recreation department ordered a total of 100 baseballs and bats for the summer basketball camp. This means that
x + y = 100
Baseballs cost $4.50 each and bats cost $20 each. The total purchase was $822. This means that
4.5x + 20y = 822 - - - - - - - - - - -1
Substituting x = 100 - y into equation 1, it becomes
4.5(100 - y) + 20y = 822
450 - 4.5y + 20y = 822
- 4.5y + 20y = 822 - 450
15.5y = 372
y = 372/15.5
y = 24
x = 100 - y = 100 - 24
x = 76