Answer: (0.093,0.267)
Step-by-step explanation:
The confidence interval for the difference in proportion is given by :-
![(p_1-p_2)\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}](https://tex.z-dn.net/?f=%28p_1-p_2%29%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cdfrac%7Bp_1%281-p_1%29%7D%7Bn_1%7D%2B%5Cdfrac%7Bp_2%281-p_2%29%7D%7Bn_2%7D%7D)
Given :
; ![n_2=300](https://tex.z-dn.net/?f=n_2%3D300)
Proportion of men said they wore seatbelts =![p_1=\dfrac{130}{200}=0.65](https://tex.z-dn.net/?f=p_1%3D%5Cdfrac%7B130%7D%7B200%7D%3D0.65)
Proportion of women said they wore seatbelts =![p_2=\dfrac{140}{300}\approx0.47](https://tex.z-dn.net/?f=p_2%3D%5Cdfrac%7B140%7D%7B300%7D%5Capprox0.47)
Significance level : ![\alpha=1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3D1-0.95%3D0.05)
Critical value : ![z_{\alpha/2}=z_{0.025}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.025%7D%3D1.96)
Now, the 95% confidence interval for the difference in proportion of men and women who wear seatbelts will be :-
![(0.65-0.47)\pm (1.96)\sqrt{\dfrac{0.65(1-0.65)}{200}+\dfrac{0.47(1-0.47)}{300}}\\\\\approx0.18\pm0.087\\\\=(0.093,0.267)](https://tex.z-dn.net/?f=%280.65-0.47%29%5Cpm%20%281.96%29%5Csqrt%7B%5Cdfrac%7B0.65%281-0.65%29%7D%7B200%7D%2B%5Cdfrac%7B0.47%281-0.47%29%7D%7B300%7D%7D%5C%5C%5C%5C%5Capprox0.18%5Cpm0.087%5C%5C%5C%5C%3D%280.093%2C0.267%29)
Hence, the 95% confidence interval for the difference in proportion of men and women who wear seatbelts = (0.093,0.267)
So she walked during this time with <span>4 miles per hour (x*4)
during
the rest of the way (which is 0.7-x, as the whole way took her 42
minutes, so the rest is 0.7-x) she walked with 5 miles per hour - the
distance was (0..7-x)*5 m/h
the total distance was 3 miles, so if we sum the two distances, we will get 3 miles:
x*4+ (0.7-x)*5=3
let's remove the bracket:
4x+0.7*5-5x=3
</span>
<span>4x+3.5-5x=3
subtract 3.5 from both sides:
4x-5x=3-3.5
-x=-0.5
multiply both sides by (-1)
x=0.5:
so she walked for half an hour alone, that is for 30 minutes!</span>
B. Decreases
(Hopefully I’m right!)
Answer:
<em><u>-10</u></em>
Step-by-step explanation:
Alright, let me explain negative multiplcation.
A negative number multiplied by another negative number becomes a positive number. But a negative number multiplied by a positive number is still negative. <u>Every pair of 2 negatives become positive.</u> This is important. Make sure to remember that.
That's it! If you need more help then reach out to your teacher. I'm sure that they will be more than happy to help!
Hope this helped! :)
Answer:
Spencer and Abigail are correct
Lauren is incorrect
Step-by-step explanation:
Spencer and Abigail are correct
Slope = change in y ÷ change in x
Or ![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Let
= (3, -1)
Let
= (5, 4)
![\implies m=\dfrac{4-(-1)}{5-3}=\dfrac52](https://tex.z-dn.net/?f=%5Cimplies%20m%3D%5Cdfrac%7B4-%28-1%29%7D%7B5-3%7D%3D%5Cdfrac52)
This is Spencer's method
Let
= (5, 4)
Let
= (3, -1)
![\implies m=\dfrac{-1-4}{3-5}=\dfrac52](https://tex.z-dn.net/?f=%5Cimplies%20m%3D%5Cdfrac%7B-1-4%7D%7B3-5%7D%3D%5Cdfrac52)
This is Abigail's method
It doesn't matter which point you label as point 1 and point 2, as long as you carry out the slope calculation correctly.
Lauren's calculation is wrong as she calculated her slope as:
where it should have been ![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)