Answer:
Step-by-step explanation:
![75^{30}\\\\75=3\cdot5\cdot5=3\cdot5^2\\\\75^{30}=(3\cdot5^2)^{30}=3^{30}\cdot(5^2)^{30}=3^{30}\cdot5^{60}](https://tex.z-dn.net/?f=75%5E%7B30%7D%5C%5C%5C%5C75%3D3%5Ccdot5%5Ccdot5%3D3%5Ccdot5%5E2%5C%5C%5C%5C75%5E%7B30%7D%3D%283%5Ccdot5%5E2%29%5E%7B30%7D%3D3%5E%7B30%7D%5Ccdot%285%5E2%29%5E%7B30%7D%3D3%5E%7B30%7D%5Ccdot5%5E%7B60%7D)
![45^{45}\cdot15^{15}\\\\45=3\cdot3\cdot5=3^2\cdot5\\15=3\cdot5\\\\45^{45}=(3^2\cdot5)^{45}=(3^2)^{45}\cdot5^{45}=3^{90}\cdot5^{45}\\15^{15}=(3\cdot5)^{15}=3^{15}\cdot5^{15}\\\\45^{45}\cdot15^{15}=3^{90}\cdot5^{45}\cdot3^{15}\cdot5^{15}=3^{90+15}\cdot5^{45+15}=3^{105}\cdot5^{60}\\\\=3^{75+30}\cdot5^{60}=3^{75}\cdot\underbrace{3^{30}\cdot5^{60}}_{75^{30}}=3^{75}\cdot75^{30}](https://tex.z-dn.net/?f=45%5E%7B45%7D%5Ccdot15%5E%7B15%7D%5C%5C%5C%5C45%3D3%5Ccdot3%5Ccdot5%3D3%5E2%5Ccdot5%5C%5C15%3D3%5Ccdot5%5C%5C%5C%5C45%5E%7B45%7D%3D%283%5E2%5Ccdot5%29%5E%7B45%7D%3D%283%5E2%29%5E%7B45%7D%5Ccdot5%5E%7B45%7D%3D3%5E%7B90%7D%5Ccdot5%5E%7B45%7D%5C%5C15%5E%7B15%7D%3D%283%5Ccdot5%29%5E%7B15%7D%3D3%5E%7B15%7D%5Ccdot5%5E%7B15%7D%5C%5C%5C%5C45%5E%7B45%7D%5Ccdot15%5E%7B15%7D%3D3%5E%7B90%7D%5Ccdot5%5E%7B45%7D%5Ccdot3%5E%7B15%7D%5Ccdot5%5E%7B15%7D%3D3%5E%7B90%2B15%7D%5Ccdot5%5E%7B45%2B15%7D%3D3%5E%7B105%7D%5Ccdot5%5E%7B60%7D%5C%5C%5C%5C%3D3%5E%7B75%2B30%7D%5Ccdot5%5E%7B60%7D%3D3%5E%7B75%7D%5Ccdot%5Cunderbrace%7B3%5E%7B30%7D%5Ccdot5%5E%7B60%7D%7D_%7B75%5E%7B30%7D%7D%3D3%5E%7B75%7D%5Ccdot75%5E%7B30%7D)
![\text{therefore it is divisible by}\ 75^{30}](https://tex.z-dn.net/?f=%5Ctext%7Btherefore%20it%20is%20divisible%20by%7D%5C%2075%5E%7B30%7D)
![Used:\\\\(ab)^n=a^nb^m\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}](https://tex.z-dn.net/?f=Used%3A%5C%5C%5C%5C%28ab%29%5En%3Da%5Enb%5Em%5C%5C%5C%5C%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5Ca%5En%5Ccdot%20a%5Em%3Da%5E%7Bn%2Bm%7D)
Answer: the z score is 1
Step-by-step explanation:
Since the head circumference for boys at birth is normally distributed,
we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = head circumference for boys at birth.
µ = mean head circumference
σ = standard deviation
From the information given,
µ = 34.5cm
σ = 1.3 cm
For a boy born with a head circumference of 35.8cm, the z score is
z = (35.8 - 34.5)/1.3
z = 1
Answer:
Yes to both.
Step-by-step explanation:
It is true that
![\dfrac{x}{y}=1 \iff x=y](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7By%7D%3D1%20%5Ciff%20x%3Dy)
In fact, if you know that x/y=1, just multiply both sides by y to get x=y. On the other hand, if you know that x=y (and they are not zero), you can divide both sides by y to get x/y=1.
Since the two expressions are equivalent, you can always use Phil's or Don's expression, at will.
Answer:
a ratio between two different units
for example 60miles per 5 hours
Step-by-step explanation:
let me know if you need unit rate yoo :)