Answer:
The equation for the number free throws for the best player is 0.90 times by 40 you get 36 shots made If you need a explanation on how I did it then comment on the answer. From a fellow 5th grader
Step-by-step explanation:
The total number of children in Stephan's school prefer pepperoni pizza where 375 children in Stephan's school is 310.
<h3>What is equivalent ratio?</h3>
Equivalent ratio is the ratio which is same in the value as the original ratio, but the numerator and denominator is different for both the ratios.
Stephan read that 62 out of every 75 children prefer pepperoni pizza. Thus, the ratio of children who prefer pepperoni pizza to the total children is,
![n=\dfrac{62}{75}\\](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7B62%7D%7B75%7D%5C%5C)
Let suppose there are <em>x </em>children in Stephan's school prefer pepperoni pizza. There are 375 children in Stephan's school. The ratio of children who prefer pepperoni pizza to total 375 children is,
![\dfrac{x}{375}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B375%7D)
Both the above ratio are for the same condition, and are equivalent ratio. Thus,
![\dfrac{x}{375}=\dfrac{62}{75}\\x=\dfrac{62}{75}\times375\\x=310](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B375%7D%3D%5Cdfrac%7B62%7D%7B75%7D%5C%5Cx%3D%5Cdfrac%7B62%7D%7B75%7D%5Ctimes375%5C%5Cx%3D310)
Thus, the total number of children in Stephan's school prefer pepperoni pizza where 375 children in Stephan's school is 310.
Learn more about the equivalent ratio here;
brainly.com/question/2914376
#SPJ1
Answer: The sample is 13414 years old.
Step-by-step explanation:
Expression for rate law for first order kinetics is given by:
where,
k = rate constant
t = age of sample
a = let initial amount of the reactant= 100
a - x = amount left after decay process=
a) for completion of half life:
Half life is the amount of time taken by a radioactive material to decay to half of its original value.
b) for completion of 20% of reaction
The sample is 13414 years old.
Answer:
The value of m is 6.
Step-by-step explanation:
Here, the given equation,
![x^4-(3m+2)x^2+m^2=0](https://tex.z-dn.net/?f=x%5E4-%283m%2B2%29x%5E2%2Bm%5E2%3D0)
![x^4+0x^3-(3m+2)x^2+0x+m^2=0](https://tex.z-dn.net/?f=x%5E4%2B0x%5E3-%283m%2B2%29x%5E2%2B0x%2Bm%5E2%3D0)
Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )
Thus, we can write,
![a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}](https://tex.z-dn.net/?f=a-3b%2Ba-b%2Ba%2Bb%2Ba%2B3b%3D%5Cfrac%7B%5Ctext%7Bcoefficient%20of%20%7Dx%5E3%7D%7B%5Ctext%7Bcoefficient%20of%20%7Dx%5E4%7D)
![=\frac{0}{1}=0](https://tex.z-dn.net/?f=%3D%5Cfrac%7B0%7D%7B1%7D%3D0)
![\implies a=0----(1)](https://tex.z-dn.net/?f=%5Cimplies%20a%3D0----%281%29)
![(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}](https://tex.z-dn.net/?f=%28-3b%29%28-b%29%2B%28-b%29%28b%29%2B%28b%29%283b%29%2B%283b%29%28-3b%29%2B%28-b%29%283b%29%2B%28-3b%29%28b%29%3D%5Cfrac%7B%5Ctext%7Bcoefficient%20of%20%7Dx%5E2%7D%7B%5Ctext%7Bcoefficient%20of%20%7Dx%5E4%7D%7D)
![=\frac{-3m-2}{1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-3m-2%7D%7B1%7D)
![3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2](https://tex.z-dn.net/?f=3b%5E2-b%5E2%2B3b%5E2-9b%5E2-3b%5E2-3b%5E2%3D-3m-2)
![-10b^2=-3m-2](https://tex.z-dn.net/?f=-10b%5E2%3D-3m-2)
![\implies b^2=\frac{3m+2}{10}-----(2)](https://tex.z-dn.net/?f=%5Cimplies%20b%5E2%3D%5Cfrac%7B3m%2B2%7D%7B10%7D-----%282%29)
![(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2](https://tex.z-dn.net/?f=%28-3b%29%28-b%29%28b%29%283b%29%3D%5Cfrac%7B%5Ctext%7BConstant%20term%7D%7D%7B%5Ctext%7Bcoefficient%20of%7Dx%5E4%7D%3D%20m%5E2)
![9b^4=m^2](https://tex.z-dn.net/?f=9b%5E4%3Dm%5E2)
![9(\frac{3m+2}{10})^2=m^2](https://tex.z-dn.net/?f=9%28%5Cfrac%7B3m%2B2%7D%7B10%7D%29%5E2%3Dm%5E2)
![9(\frac{9m^2+4+12m}{100})=m^2](https://tex.z-dn.net/?f=9%28%5Cfrac%7B9m%5E2%2B4%2B12m%7D%7B100%7D%29%3Dm%5E2)
![81m^2+36+108m=100m^2](https://tex.z-dn.net/?f=81m%5E2%2B36%2B108m%3D100m%5E2)
![-19m^2+108m+36=0](https://tex.z-dn.net/?f=-19m%5E2%2B108m%2B36%3D0)
![19m^2-108m-36=0](https://tex.z-dn.net/?f=19m%5E2-108m-36%3D0)
![19m^2-114m+6m-36=0](https://tex.z-dn.net/?f=19m%5E2-114m%2B6m-36%3D0)
![19m(m-6)+6(m-6)=0](https://tex.z-dn.net/?f=19m%28m-6%29%2B6%28m-6%29%3D0)
![(19m+6)(m-6)=0](https://tex.z-dn.net/?f=%2819m%2B6%29%28m-6%29%3D0)
![\implies m=-\frac{6}{19}\text{ or }m=6](https://tex.z-dn.net/?f=%5Cimplies%20m%3D-%5Cfrac%7B6%7D%7B19%7D%5Ctext%7B%20or%20%7Dm%3D6)
But m > 0,
Hence, the value of m is 6.
Answer:
45th term is 85
Step-by-step explanation:
We use the definition of the nth term of an arithmetic sequence:
![a_n=a_1+(n-1)\,d](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29%5C%2Cd)
which for our case gives:
![a_n=a_1+(n-1)\,d\\a_n=-3+(45-1)\,2\\a_n=-3+44*2\\a_n=-3+88\\a_n=85](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29%5C%2Cd%5C%5Ca_n%3D-3%2B%2845-1%29%5C%2C2%5C%5Ca_n%3D-3%2B44%2A2%5C%5Ca_n%3D-3%2B88%5C%5Ca_n%3D85)