Answer:
the probability that 0≤x≤1/2 and 1/4≤y≤1/2 is 3/64 (4.68%)
Step-by-step explanation:
assuming that X and Y are independent variables for the probability density function f(x,y) :
f(x,y) = 4*x*y for 0≤x≤1 and 0≤y≤0
f(x,y) = 0 elsewhere
then the probability is calculated through:
P(x,y)= ∫f(x,y) dx dy = ∫4xy dx dy
for 0≤x≤1/2 and 1/4≤y≤1/2 we have
P(0≤x≤1/2,1/4≤y≤1/2 ) = ∫4xy dx dy = ∫4xy dx dy = 4*∫x dx ∫y dx = 4*[((1/2)²/2-0²/2)] *[(1/2)²/2-(1/4)²/2)] = 1 * 1/4 * (1/4-1/16) = 1 * 1/4 * 3/16 = 3/64
then the probability that 0≤x≤1/2 and 1/4≤y≤1/2 is 3/64 (4.68%)
Answer: $112.50 ; $4612.5
Step-by-step explanation:
a) Determine how much interest Christine paid at the end of 1 year.
This will be:
Simple interest = PRT/100
where
P = principal = $4500
R = rate = 2.5%
T = time = 1 year
Interest = (4500 × 2.5 × 1)/100
= 11250/100
= $112.50
b) Determine the total amount Christine will repay the bank at the end of 1 year.
Total amount = Principal + Interest
= $4500 + $112.50
= $4612.5
Answer:
Option c) is correct.
That is x-5y=12 and 3x+2y=-15 are the system of linear equations satisfies the point (-3,3) so this is the solution.
Step-by-step explanation:
To verify that which system of linear equations having the solution (-3,-3)
Let
and
To solve it we have to use elimination method
First multiply the equation(1) into 3 we get
Now subtracting the equations (2)and (3) the signs may vary in the second equation we get
________________
_______________
Now substitue the value y=-3 in equation (1) we get
Therefore x=-3
Therefore the solution is (-3,-3)
Therefore Option c) is correct.
That is x-5y=12 and 3x+2y=-15 are the system of linear equations satisfies the point (-3,3) so the solution is (-3,-3).
Answer:
The new mean is: 11.8
Step-by-step explanation:
Given the data set
2.4 1.6 3.2 0.3 1.5
Sum of terms = 2.4 + 1.6 + 3.2 + 0.3 + 1.5 = 9
Number of terms = 5
We know that the mean of a data set is the sum of the terms divided by the total number of terms, so
Mean = Sum of terms / Number of terms
substituting Sum of terms = 9 and Number of terms = 5
= 9/5
= 1.8
Thus, the Mean = 1.8
We need to determine the mean when each piece of data is increased by 10.
All we need is to add 10 in the determined mean to determine the new mean.
New Mean = Mean + 10
= 1.8 + 10
= 11.8
Therefore, the new mean is: 11.8
<u>VERIFICATION:</u>
When each piece of data is increased by 10
so,
The sum of angles of any triangle is always 180 degrees
Now here
Angle A = 25° , Angle C = 90°
Now A+B+C= 180
25° +B + 90°=180°
115° +B = 180°
Subtract 115° from both sides
115°-115° +B = 180°-115°
B=65°
Angle B = 65 degrees