Answer:
The height of the pole is 105ft,
Step-by-step explanation:
Let us call 
the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is 
.
The wire length 
is 14 ft longer than height , hence
.
Thus we get a right triangle with hypotenuse 
, perpendicular , and base 
; therefore, the Pythagorean theorem gives
which upon expanding we get:
further simplification gives
,
which is a quadratic equation with solutions
Since the first solution 
will give the triangle base length of 
which is negative; therefore, we disregard it and pick the solution 
.
Hence, the height of the pole is 105ft.
1.4 in thousands is 1.400
Answer:
The calculated χ² = 0.57 does not fall in the critical region χ² ≥ 12.59 so we fail to reject the null hypothesis and conclude the proportion of fatal bicycle accidents in 2015 was the same for all days of the week.
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: proportion of fatal bicycle accidents in 2015 was the same for all days of the week
against the claim
Ha: proportion of fatal bicycle accidents in 2015 was not the same for all days of the week
2) the significance level alpha is set at 0.05
3) the test statistic under H0 is
χ²= ∑ (ni - npi)²/ npi
which has an approximate chi square distribution with ( n-1)=7-1= 6 d.f
4) The critical region is χ² ≥ χ² (0.05)6 = 12.59
5) Calculations:
χ²= ∑ (16- 14.28)²/14.28 + (12- 14.28)²/14.28 + (12- 14.28)²/14.28 + (13- 14.28)²/14.28 + (14- 14.28)²/14.28 + (15- 14.28)²/14.28 + (18- 14.28)²/14.28
χ²= 1/14.28 [ 2.938+ 5.1984 +5.1984+1.6384+0.0784 +1.6384+13.84]
χ²= 1/14.28[8.1364]
χ²= 0.569= 0.57
6) Conclusion:
The calculated χ² = 0.57 does not fall in the critical region χ² ≥ 12.59 so we fail to reject the null hypothesis and conclude the proportion of fatal bicycle accidents in 2015 was the same for all days of the week.
b.<u> It is r</u>easonable to conclude that the proportion of fatal bicycle accidents in 2015 was the same for all days of the week
Answer:
Average speed = 
miles per hour
Step-by-step explanation:
Formula to calculate the average speed of an object is,
Average speed = 
If I travel with the speed of x mph for t hours,
Total distance covered = Speed × Time
= 
= 
miles
Similarly, if I travel with the speed y mph for t hours,
Total distance covered = 
miles
Total distance covered by me = 
miles
Total time taken to cover this distance = 
= 
hours
Therefore, expression for the average speed will be,
Average speed = 
= 
= 
miles per hour
