Check the picture below.
so notice, their perimeter is the same, because the perimeter is just one rod anyway, and all rods are the same length, thus
Answer:
The value of the test statistic is t=1.12.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that the mean amount of time required to reach a customer service representative significantly differs between the two hotels.
Then, the null and alternative hypothesis are:
The sample 1, of size n1=20 has a mean of 2.65 and a standard deviation of √2.952=1.72.
The sample 2, of size n2=20 has a mean of 2.01 and a standard deviation of √2.952=1.89.
The difference between sample means is Md=0.64.
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the t-statistic as:
Answer: The correct option is 1.
Explanation:
The given piecewise function is,
It means if x<0, then
If 
, then
Since the f(x) is defined for x<0 and , therefore the function f(x) is not defined for 
.
From the graph 2, 3 and 4 we can easily noticed that for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.
Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for , hence the first option is correct.
Answer:
1) 120
2) E (Z) = 12 and Variance of Z = 90
a) 5 liters
Step-by-step explanation:
1. We can find this by suing combinations.
Here n= 10 and r= 3 so n C r
= 10 C 3= 120
2. E(X) = 8 and E(Y) = 3
Z = 2X - 3Y +5
E(Z ) = 2 E (X) - 3(E)(Y) +5 ( applying property for mean)
= 2(8) - 3(3)+ 5 = 16+5-9= 21-9= 12
V(X) = 9 and V(Y) = 6.
V(Z) = E(Z )²- V(X) *V(Y) (applying property for Variance for two variables )
= 144- 54= 90
3. 55 liters contain adulterated milk in 7: 4.
So it contains 4/ 11*55= 20 liters of water
But we want to make it a ratio of 7:6
the water will be 6/13 *55= 25.38 when rounded gives 25 liters of water
So 25- 20 = 5 liters must be added to make it a ratio of 7:6
For us to determine the number of points that is needed in order to surpass or succeed the hardest setting of the game level 5, we use first the function g(x) to determine the total points required for the lower level.
g(x) = 8(2)(x) + 1
We substitute the x of the function with 5 since we are in level 5.
g(5) = 8(2)(5) + 1 = 81
Then, to determine the points for the hardest setting, we multiply the points by 3 as given in function h(x).
h(x) = 3(81) = 243
Hence, to succeed the hardest setting of level 5, one needs a total of 243 points.
