Answer:
The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 27 - 1 = 26
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of 
. So we have T = 2.7787.
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 4.9 - 3.7 = 1.2.
The upper end of the interval is the sample mean added to M. So it is 4.9 + 3.7 = 8.6.
The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).
The probability that the sum of Michelle's rolls is 4 is 0.083
∴ P(A)=0.083
Step-by-step explanation:
Given that Michelle is rolling two six-sided dice, numbered one through six.
To find the probability that the sum of her rolls is 4:
∴ n(s)=36
Let P(A) be the probability that the sum of her rolls is 4
Then the possible rolls with sums of 4 can be written as
n(A)=3
The probability that the sum of her rolls is 4 is given by
=0.083
∴ P(A)=0.083
∴ the probability that the sum of Michelle's rolls is 4 is 0.083
-please give brainliest if correct!
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
"THIS MESSAGE IS TOP SECRET."
We need to use the Caesar cipher.
As in general we always take a shift of 3 keys in Caesar cipher.
so, According to shift of 3 keys it becomes,
T→W
H→K
I→L
S→V
M→P
E→H
A→D
G→J
O→R
C→F
R→U
P→S
So, it can be written as
"THIS MESSAGE IS TOP SECRET."
WKLVP HVVDJ HLVWR SVHFU HW.
we make a set of 5 letters in a word after Caesar cypher.
Hence, Option 'a' is correct.
Answer:
m<PTR = 140°
Step-by-step explanation:
First, find the value of x. To find the value of x, derive an equation which you'd use in solving for x.
m<PTQ = (x + 28)°
m<RTS = (2x + 16)°
m<PTQ = m<RTS (vertical opposite angles are congruent)
Therefore:
x + 28 = 2x + 16
Solve for x. Combine like terms
28 - 16 = 2x - x
12 = x
x = 12
Find m<PTQ
m<PTQ = (x + 28)
plug in the value of x
m<PTQ = 12 + 28 = 40°
m<PTR + m<PTQ = 180° (supplementary angles)
m<PTR + 40° = 180° (substitution)
m<PTR = 180 - 40 (subtracting 40 from each side)
m<PTR = 140°
