Answer: The correct answer is Choice B, 12.3 years.
A z-score of about -0.523 would corresponding to the area which divides the normal distribution at 70% and 30%.
Now, we just need to write and solve an equation for that z-score.
(x - 15) / 5.2 = -0.523
x - 15 = -2.7196
x = 12.283
We can round it to 12.3 years old.
Starts with 22.854...he then adds 5 times as much...
22.854 + 5(22.954) = 137.124
he divided mixture into 4 dishes
137.124/4 = 34.2810 grams <==
Answer:
AB = 32.6 in
Step-by-step explanation:
See the attached picture.
Triangle ABC is a right triangle, because this is a rectangular prism and height is perpendicular to top and bottom face.
Notice how we can use Pythagorean Theorem to find AB if we first calculate AC. To calculate AC we can use another right triangle ACD. (Perspective can be confusing, but angle ADC is right because this is a rectangular prism :)) From the angle ACD, AD is the opposite and AC is hypotenuse. Therefore we can use sine to find AC.
![\sin{(\text{angle})} = \frac{\text{opposite}}{\text{hypotenuse}}](https://tex.z-dn.net/?f=%5Csin%7B%28%5Ctext%7Bangle%7D%29%7D%20%3D%20%5Cfrac%7B%5Ctext%7Bopposite%7D%7D%7B%5Ctext%7Bhypotenuse%7D%7D)
![\sin{(m\angle ACD)} = \frac{\text{AD}}{\text{AC}}](https://tex.z-dn.net/?f=%5Csin%7B%28m%5Cangle%20ACD%29%7D%20%3D%20%5Cfrac%7B%5Ctext%7BAD%7D%7D%7B%5Ctext%7BAC%7D%7D)
![\sin{(50^\circ)} = \frac{24}{\text{AC}}](https://tex.z-dn.net/?f=%5Csin%7B%2850%5E%5Ccirc%29%7D%20%3D%20%5Cfrac%7B24%7D%7B%5Ctext%7BAC%7D%7D)
![\sin{(50^\circ)} \cdot {\text{AC}} = \frac{24}{\text{AC}} \cdot {\text{AC}}](https://tex.z-dn.net/?f=%5Csin%7B%2850%5E%5Ccirc%29%7D%20%5Ccdot%20%20%7B%5Ctext%7BAC%7D%7D%20%3D%20%5Cfrac%7B24%7D%7B%5Ctext%7BAC%7D%7D%20%5Ccdot%20%20%7B%5Ctext%7BAC%7D%7D)
![\sin{(50^\circ)} \cdot {\text{AC}} = 24](https://tex.z-dn.net/?f=%5Csin%7B%2850%5E%5Ccirc%29%7D%20%5Ccdot%20%20%7B%5Ctext%7BAC%7D%7D%20%3D%2024)
![\frac{{\sin{(50^\circ)}} \cdot \text{AC}}{\sin{(50^\circ)}} = \frac{24}{\sin{(50^\circ)}}](https://tex.z-dn.net/?f=%5Cfrac%7B%7B%5Csin%7B%2850%5E%5Ccirc%29%7D%7D%20%5Ccdot%20%5Ctext%7BAC%7D%7D%7B%5Csin%7B%2850%5E%5Ccirc%29%7D%7D%20%3D%20%5Cfrac%7B24%7D%7B%5Csin%7B%2850%5E%5Ccirc%29%7D%7D)
![{\text{AC}} = \frac{24}{\sin{(50^\circ)}}](https://tex.z-dn.net/?f=%7B%5Ctext%7BAC%7D%7D%20%3D%20%5Cfrac%7B24%7D%7B%5Csin%7B%2850%5E%5Ccirc%29%7D%7D)
![{\text{AC}} \approx 31.32977 \text{ in}](https://tex.z-dn.net/?f=%7B%5Ctext%7BAC%7D%7D%20%5Capprox%2031.32977%20%5Ctext%7B%20in%7D)
Now we can use pythagorean theorem in triangle ABC to find AB!
![\text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2](https://tex.z-dn.net/?f=%5Ctext%7Bhypotenuse%7D%5E2%20%3D%20%5Ctext%7Bleg%7D_1%5E2%20%2B%20%5Ctext%7Bleg%7D_2%5E2)
![\text{AB}^2 = \text{BC}^2 + \text{AC}^2](https://tex.z-dn.net/?f=%5Ctext%7BAB%7D%5E2%20%3D%20%5Ctext%7BBC%7D%5E2%20%2B%20%5Ctext%7BAC%7D%5E2)
![\text{AB}^2 = (9 \text{ in})^2 + (31.32977 \text{ in})^2](https://tex.z-dn.net/?f=%5Ctext%7BAB%7D%5E2%20%3D%20%289%20%5Ctext%7B%20in%7D%29%5E2%20%2B%20%2831.32977%20%5Ctext%7B%20in%7D%29%5E2)
![\text{AB}^2 = 1062.5545 \text{ in}^2](https://tex.z-dn.net/?f=%5Ctext%7BAB%7D%5E2%20%3D%201062.5545%20%5Ctext%7B%20in%7D%5E2)
![\sqrt{\text{AB}^2} = \pm\sqrt{1062.5545 \text{ in}^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Ctext%7BAB%7D%5E2%7D%20%3D%20%5Cpm%5Csqrt%7B1062.5545%20%5Ctext%7B%20in%7D%5E2%7D)
We are interested only in positive square root:
![\text{AB} = 32.5968 \text{ in}](https://tex.z-dn.net/?f=%5Ctext%7BAB%7D%20%3D%2032.5968%20%5Ctext%7B%20in%7D)
Rounded to one decimal place:
![\text{AB} = 32.6 \text{ in}](https://tex.z-dn.net/?f=%5Ctext%7BAB%7D%20%3D%2032.6%20%5Ctext%7B%20in%7D)
Answer:
Step-by-step explanation:
- One group goes to every 6th house
- Second group goes to every 8th house
<u>We need to find LCM of 6 and 8</u>
- LCM(6, 8) = LCM(3*2, 4*2) = 3*2*4 = 24
They will first meet at 24th house