Answer:
Use a calculator for this like desmos graphing
Step-by-step explanation:
Step-by-step explanation:
Let grandson's age be x.
Let grandpa's age be y {equation : y = 8+5x}
so,
x + y = 88
or, x + 8+ 5x = 88 (substituting the value of y)
or, 6x + 8 =88
or, 6x = 88-8
or, 6x = 80
or, x = 80/6
so, x = 13.33
so grandson's age = 13.33
grandpa's age = 8 + 5x = 8 + (5×13.33) = 74.65 yrs
Answer: 0.2872
Step-by-step explanation:
Given : In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product, 260 of these people said they never did so.
i.e. n= 1000 and x= 260
⇒ Sample proportion : ![\hat{p}=\dfrac{260}{1000}=0.26](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B260%7D%7B1000%7D%3D0.26)
z-value for 95% confidence interval : ![z_c=1.960](https://tex.z-dn.net/?f=z_c%3D1.960)
Now, an upper confidence bound at the 95% confidence level for the true proportion of such consumers who never apply for a rebate. :-
![\hat{p}+ z_c\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%2B%20z_c%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D)
![=0.26+ (1.96)\sqrt{\dfrac{0.26(1-0.26)}{1000}}](https://tex.z-dn.net/?f=%3D0.26%2B%20%281.96%29%5Csqrt%7B%5Cdfrac%7B0.26%281-0.26%29%7D%7B1000%7D%7D)
![=0.26+ (1.96)(0.01387)=0.26+0.0271852=0.2871852\approx0.2872](https://tex.z-dn.net/?f=%3D0.26%2B%20%281.96%29%280.01387%29%3D0.26%2B0.0271852%3D0.2871852%5Capprox0.2872)
∴ An upper confidence bound at the 95% confidence level for the true proportion of such consumers who never apply for a rebate : 0.2872
The fraction form is 11/25
Hope this helps!!!!:)
9u means you're multiplying 9 into that vector, both components. Same with the 2v. 9*3 = 27 and 9*-1 = -9, so your new vector u is <27, -9>. Now let's do v. 2* -6 (twice) = -12, so your new v vector is <-12, -12>. Add those together now, first components of each and second components of each. 27 + (-12) = 15; -9+(-12)=-21. So the addition of those gives us a final vector with a displacement of <15, -21>