Answer: 22.0.6%
Step-by-step explanation:
Given : According to a human modeling project, the distribution of foot lengths of women is approximately Normal with 
and 
.
In the United States, a woman's shoe size of 6 fits feet that are 22.4 centimeters long.
Then, the probability that women in the United States will wear a size 6 or smaller :-
![P(x\leq22.4)=P(z\leq\dfrac{22.4-23.4}{1.3})\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\\approx P(z\leq-0.77)\\\\=1-P(z\leq0.77)\\\\=1-0.77935=0.2206499\approx0.2206=22.06\%](https://tex.z-dn.net/?f=P%28x%5Cleq22.4%29%3DP%28z%5Cleq%5Cdfrac%7B22.4-23.4%7D%7B1.3%7D%29%5C%20%5C%20%5B%5Cbecause%20z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5D%5C%5C%5C%5C%5Capprox%20P%28z%5Cleq-0.77%29%5C%5C%5C%5C%3D1-P%28z%5Cleq0.77%29%5C%5C%5C%5C%3D1-0.77935%3D0.2206499%5Capprox0.2206%3D22.06%5C%25)
Hence, the required answer = 22.0.6%
Answer: 12
Step-by-step explanation:
One yard is three feet. So three times four is 12 because it makes four yards in total with each side being a yard.
-3x+4=-17
subtract -4 from both sides
divide -3 from both sides
the answer is 7
Answer:
z = -12
Step-by-step explanation:
The given system of equations is:
xy/(x + y) = 1 ...........................(1)
xz/(x + z) = 2...........................(2)
yz/(y + z) = 3...........................(3)
From (1): x + y = xy
=> y = xy - x
y = x(y - 1)
x = y/(y - 1).......................................(4)
From (2): 2(x + z) = xz
=> 2x + 2z = xz
2x = xz - 2z
2x = z(x - 2)
z = 2x/(x - 2) ....................................(5)
From (3): 3(y + z) = yz
=> 3y + 3z = yz
3y = yz - 3z
3y = z(y - 3)
z = 3y/(y - 3)....................................(6)
Comparing (5) and (6)
2x/(x - 2) = 3y/(y - 3)
2x(y - 3) = 3y(x - 2)
2xy - 6x = 3xy - 6y
6(y - x) = xy .................................(7)
But from (1): xy = x + y
Using this in (7), we have
6(y - x) = x + y
6y - y - 6x - x = 0
5y - 7x = 0
5y = 7x
x = 5y/7................................................(8)
Using this in (4)
5y/7 = y/(y - 1)
1/(y - 1) = 5/7
(y - 1) = 7/5
y = 1 + 7/5
y = 12/5..........................................(9)
Using this in (8)
x = 5(12/5)/7 = 12/7 .......................(10)
Using (10) in (5)
z = 2x/(x - 2)
z = 2(12/7) ÷ (12/7 - 2)
= 24/7 ÷ -2/7
= 24/7 × (-7/2)
= -24/2 = -12
z = -12.
Answer:
m∠6 = 116°
Step-by-step explanation:
<u>first find x:</u>
7x - 17 = 2x + 78
subtract 2x from both sides: 5x - 17 = 78
add 17 to both sides: 5x = 95
divide by 5: x = 19
<u>plug x into 7x - 17</u>
7(19) - 17 = 116
∠6 and 7x - 17 are vertical angles and therefore congruent, so m∠6 also = 116°
