0<x<1 and 0<y<1
x>0 so x is positive and y>0 so y is also positive.
When you multiply two positive numbers you always get a positive number, so the product of x and y must be positive, or greater than 0.
xy>0 - it must be true
xy<0 - it can't be true
Also when you divide a positive number by a positive number you always get a positive number, so the quotient of x and y must be positive.
x/y<0 - it can't be true
D and E can be true, but don't have to. It depends on the values of x and y. If x>y, then x-y>0 is true and x-y<0 isn't true; if x<y, then x-y>0 isn't true and x-y<0 is true.
Therefore, only A <u>must</u> be true.
The new mean is 11
Step-by-step explanation:
The mean = sum of the numbers ÷ numbers
- The mean of a set of 5 numbers is 12
- One of the number is 16
- We need to find the new mean if 16 is removed from the set of numbers
∵ The set has 5 numbers
∵ The mean of the 5 numbers is 12
- Substitute these values in the rule of the mean above
∴ 12 = sum of the numbers ÷ 5
- Multiply both sides by 5
∴ 60 = sum of the numbers
∵ One of the number is 16
∵ 16 is removed from the set of the number
- Subtract 16 from the sum and the numbers will be four numbers
∵ The new sum = 60 - 16
∴ The new sum = 44
∵ The set has 4 numbers
∴ The new mean = 44 ÷ 4 = 11
The new mean is 11
Learn more:
You can learn more about the mean in brainly.com/question/5069437
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Answer:
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+ 
Step-by-step explanation:
To verify the identity:
sinx/1-cosx = cscx + cotx
we will follow the steps below;
We will take just the left-hand side and work it out to see if it is equal to the right-hand side
sinx/1-cosx
Multiply the numerator and denominator by 1 + cosx
That is;
= 
open the parenthesis on the right-hand side of the equation at the numerator and the denominator
sinx(1+cosx) = sinx + sinx cosx
(1-cosx)(1+cosx) = 1 - cos²x
Hence
= 
But 1- cos²x = sin²x
Hence we will replace 1- cos²x by sin²x
=
=
= 
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+ 
=
+ 
=
+ 
=
+ 
Note that;
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Answer:
<h3>
Therefore total amount of money that he got is = $(5+0.50x) [ x = number of correct math]</h3>
Step-by-step explanation:
Given, Gilberto's grandfather gives him $5 for his birthday and then$0.50 for each math he answers correctly on his math exam for the year.
Let , the number of math that he answers correctly on his his math exam for the year is x
Therefore he got = $(0.50× x) =$ 0.50x for doing correct math.
Therefore total amount of money that he got is = $(5+0.50x) [ x = number of correct math]