Answer:
18 inches.
Step-by-step explanation:
If the ratio for inches to miles is
,
then you multiply the top and bottom by 6 to get to 30. This gets the numerator to 18 inches.
<span>Representing in fraction for the best understanding
</span>
<span>
When the exponent is negative, the inversion is made, the numerator becomes the denominator, and the denominator becomes the numerator, and the change of signal from the exponent, which was negative, becomes positive.
</span>
Answer:
c.-1/6
Answer:
We can find the volume of a sphere using the volume of a cylinder. Cylinder is a solid which has a circular base. We know the fact that the volume of any solid is equal to the product of base area and height of the solid. So, the volume of a right circular cylinder of base radius ‘r’ and height ‘h’ is given by
Step-by-step explanation:
Transform <em>Y</em> to <em>Z</em>, which is distributed N(0, 1), using the formula
<em>Y</em> = <em>µ</em> + <em>σZ</em>
where <em>µ</em> = -16 and <em>σ</em> = 1.21.
Pr[-15.043 < <em>Y</em> ≤ <em>k</em>] = 0.1546
Pr[(-15.043 + 16)/1.21 < (<em>Y</em> + 16)/1.21 ≤ (<em>k</em> + 16)/1.21] = 0.1546
Pr[0.791 < <em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.1546
Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] - Pr[<em>Z</em> < 0.791] = 0.1546
Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] = 0.1546 + Pr[<em>Z</em> < 0.791]
Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.1546 + 0.786
Pr[<em>Z</em> ≤ (<em>k</em> + 16)/1.21] ≈ 0.940
Take the inverse CDF of both sides (<em>Φ(x)</em> denotes the CDF itself):
(<em>k</em> + 16)/1.21 ≈ <em>Φ⁻¹</em> (0.940) ≈ 1.556
Solve for <em>k</em> :
<em>k</em> + 16 = 1.21 • 1.556
<em>k</em> ≈ -14.118
Answer:
A) x = 3 or -1
B) x = -7
C)x = -7
Step-by-step explanation:
A) x² + 2x + 1 = 2x² - 2
Rearranging, we have;
2x² - x² - 2x - 2 - 1 = 0
x² - 2x - 3 = 0
Using quadratic formula, we have;
x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)
x = (2 ± √16)/2
x = (2 + 4)/2 or (2 - 4)/2
x = 6/2 or -2/2
x = 3 or -1
B) ((x + 2)/3) - 2/15 = (x - 2)/5
Multiply through by 15 to get;
5(x + 2) - 2 = 3(x - 2)
5x + 10 - 2 = 3x - 6
5x - 3x = -6 - 10 + 2
2x = -14
x = -14/2
x = -7
C) log(2x + 3) = 2log x
From log derivations, 2 log x is same as log x²
Thus;
log(2x + 3) = logx²
Log will cancel out to give;
2x + 3 = x²
x² - 2x - 3 = 0
Using quadratic formula, we have;
x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)
x = (2 ± √16)/2
x = (2 + 4)/2 or (2 - 4)/2
x = 6/2 or -2/2
x = 3 or -1
