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: 9.3x10-11
Step-by-step explanation:
Answer:
y = -2x - 3
Step-by-step explanation:
Please look carefully at this graph. There are two red dots on the graph. The x- and y-coordinates of one are (-5,7) and those of the other are (0,-3).
Now as we move to the right, from (-5,7) to (0,-3), x increases by 5 and y decreases by 10 (note that 7-10 is -3). Thus, the slope of this line is
m = rise / run = -10/5, or m = -2.
Then the equation of this line, in point-slope form, is
y-7 = -2(x-[-5])x, or y-7 = -2(x+5). This is in point-slope form.
If you'd like to have it in slope-intercept form, manipulate y-7 = -2(x+5) as follows: (a) add 7 to both sides, obtaining y = -2(x+5) + 7, and (b) perform the indicated multiplication: y = -2x - 10 + 7, or y = -2x - 3.
Answer:
B
Step-by-step explanation:
Answer:
Hello!
To solve for x, you need to follow SADMEP. SADMEP is subtraction, addition, division, multiplication, exponents, and parentheses. It follows the same rules as PEMDAS, but SADMEP is only used when solving algebraic equations.
x - 5 = 0.1(x + 5) (use the distributive property)
x - 5 = 0.1x + 0.5 (subtract 0.1x to both sides)
0.9x - 5 = 0.5 (add 5 to both sides)
0.9x = 5.5 (divide both sides by 0.9)
x = 6.1111... | This can be rounded to 6.11 km/hour.
Therefore, Kelli can swim about 6.11 kilometers per hour.
Hope this helps :D
Mark me brainliest if its good, i know its right though (:
