Answer:
(8.213 ; 8.247)
Step-by-step explanation:
Given the data :
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24
Sanple size, n = 15
Sample mean, xbar = Σx / n = 123.45 / 15 = 8.23
The sample standard deviation, s = √(x -xbar)²/n-1
Using calculator :
Sample standard deviation, s = 0.03116
s = 0.031 (3 decimal places)
The 95% confidence interval :
C.I = xbar ± (Tcritical * s/√n)
Tcritical at 95%, df = 15 - 1 = 14
Tcritical = 2.145
C.I = 8.23 ± (2.145 * 0.031/√15)
C.I = 8.23 ± 0.0171689
C.I = (8.213 ; 8.247)
1 step: Divide the polynomial
by the polynomial
with remainder:

Here
is quotient and
is remainder.
2 step: Substitute previous result into the fraction:

Answer: correct choice is A.
<u>Given</u>:
The coordinates of the points A, B and C are (3,4), (4,3) and (2,1)
The points are rotated 90° about the origin.
We need to determine the coordinates of the point C'.
<u>Coordinates of the point C':</u>
The general rule to rotate the point 90° about the origin is given by

Substituting the coordinates of the point C in the above formula, we get;

Therefore, the coordinates of the point C' is (-1,2)
So prime factorization is what it seems, <u>finding the prime factors of a number.</u> Using prime factorization, we can break down 254 as such:

Since 2 and 127 are prime,<u> the prime factorization of 254 is 2 × 127.</u>
Answer:
C. 5√3
Step-by-step explanation:
To figure this out, we need to apply the Pythagorean Theorem, <em>a</em><em>²</em><em> </em><em>+</em><em> </em><em>b</em><em>²</em><em> </em><em>=</em><em> </em><em>c</em><em>²,</em><em> </em>where <em>c</em><em> </em>is the "HYPOTENUSE". In this case, <em>c</em><em> </em>is already found for us [10], so the operation we use whenever the hypotenuse is defined is deduction, or subtraction. Apply the Pythagorean Theorem: a² + 25 = 100; 75 = a². Now, to find <em>a</em><em>,</em><em> </em>we need to find two numbers that multiply to 75, where one of them is a PERFECT SQUARE, and in this case, they are 3 and 25. Since the square root of 25 is 5 [in this case, NO NON-NEGATIVE root], that gets moved to the outside of the radical, and 3 [NON-PERFECT SQUARE] stays wrapped under the radical, ending up with <em>5</em><em>√</em><em>3.</em><em> </em>You understand?
I am joyous to assist you anytime.