The length of a rectangle is three times its width what is the width if the area is 147 square
Answer:
P = 0.0008 (non rounded answer is 0.000771605)
Step-by-step explanation:
You first need to determine how many different ways you can roll a 7 using 2 dice. You options are...
First Die Second Die
1 6
2 5
3 4
4 3
5 2
6 1
There are six different ways to roll a 7. If you do the same for all possible numbers, you will see that there are 36 total options when rolling two dice. The first die has six options, and the second die also has 6 options. 6x6 = 36. (This is the fundamental counting principal you have have leared in statistics)
So the chances of rolling a 7 one time with two dice is 1/6. Since repeated rolling of dice is an independent event (any roll has no effect on the next roll), you multiply the probabilities of each event.
So the probability of rolling a 7 four times in a row is
(1/6)(1/6)(1/6)(1/6), which simplifies to 1/6^4, or 1/1296,
Probability is written in decimal form, and usually rounded to 4 decimal places.
1/1296 = 0.000771605, or 0.0008 rounded to 4 decimals
The answer to the system of equations is x = 3, y = -2 and z = 5.
In order to find this you can use elimination to create two equations with only x and y. First we will add equation one with equation 2 multiplied by 2.
-x + 2y + 2z = 3
6x + 2y - 2z = 4
---------------------
5x + 4y = 7
Then we can add equation 2 with equation 3.
3x + y - z = 2
2x + y + z = 9
------------------
5x + 2y = 11
Now we can use these two equations together to solve for y. It will be easiest if we multiply the second one by -1.
5x + 4y = 7
-5x - 2y = -11
------------------
2y = -4
And then we can solve for y.
2y = -4
y = -2
With that answer we can go back to any equation with just y and x and solve for x.
5x + 4y = 7
5x + 4(-2) = 7
5x - 8 = 7
5x = 15
x = 3
Now we can use x and y in any equation to find z.
2x + y + z = 9
2(3) + (-2) + z = 9
6 - 2 + z = 9
4 + z = 9
z = 5
Answer:
(230.21 ; 233.13)
Step-by-step explanation:
Given the data :
230.66, 233.05, 232.58, 229.48, 232.58
To calculate the 90% CI
WE obtain the mean and standard deviation of the sample data :
Mean of sample, ΣX /n = 1158.35/5 = 231.67
The standard deviation of the sample, s = 1.531 (Using calculator).
(The 90% Tcritical value, 2 sided, df = 4) = 2.132
The confidence interval, CI :
Mean ± Tcritical * s/√n
C.I = 231.67 ± (2.132 * (1.531/√5)
C. I = 231.67 ± 1.4597
(231.67 - 1.4597) ; (231.67 + 1.4597)
(230.21 ; 233.13)
