Answer:
25.2294 feet
Step-by-step explanation:
We can solve this question drawing a triangle using the values given and then using the law of sines. (See image attached to know how to draw the triangle and use the values).
First we need to find the third angle of the triangle, that is, the angle in the vertix where the bird is:
y + 55 + 63 = 180
y = 62°
The relation between the angles and the distances are:
25 / sin(y) = x / sin(63)
25 / 0.8829 = x / 0.8910
x = 25 * 0.8910 / 0.8829 = 25.2294 feet
Answer:
1. ![\bar X=5.10](https://tex.z-dn.net/?f=%5Cbar%20X%3D5.10)
2. ![\sigma=0.47](https://tex.z-dn.net/?f=%5Csigma%3D0.47)
3.![\sigma^2=0.22](https://tex.z-dn.net/?f=%5Csigma%5E2%3D0.22)
Step-by-step explanation:
<u>QUESTION 1</u>
The given data set for the expenditure is
![4.85,5.10,5.50,4.75,4.50,5.00,6.00](https://tex.z-dn.net/?f=4.85%2C5.10%2C5.50%2C4.75%2C4.50%2C5.00%2C6.00)
The formula for calculating the mean is given by,
![\bar X=\frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%20X%3D%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
We need to add all the expenditure and divide by the total number of days.
![\bar X=\frac{4.85+5.10+5.50+4.75+4.50+5.00+6.00}{7}](https://tex.z-dn.net/?f=%5Cbar%20X%3D%5Cfrac%7B4.85%2B5.10%2B5.50%2B4.75%2B4.50%2B5.00%2B6.00%7D%7B7%7D)
This gives us,
![\bar X=\frac{35.7}{7}](https://tex.z-dn.net/?f=%5Cbar%20X%3D%5Cfrac%7B35.7%7D%7B7%7D)
to the nearest hundredth.
<u>QUESTION 2</u>
The standard deviation of the data set is given by the formula;
![\sigma =\sqrt{\frac{\sum(x-\bar X)^2}{n} }](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Csqrt%7B%5Cfrac%7B%5Csum%28x-%5Cbar%20X%29%5E2%7D%7Bn%7D%20%7D)
This implies that,
![\sigma =\sqrt{\frac{(4.85-5.10)^2+(5.10-5.10)^2+(5.50-5.10)^2+(4.75-5.10)^2+(4.50-5.10)^2+(5.00-5.10)^2+(6.00-5.10)^2}{7} }](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Csqrt%7B%5Cfrac%7B%284.85-5.10%29%5E2%2B%285.10-5.10%29%5E2%2B%285.50-5.10%29%5E2%2B%284.75-5.10%29%5E2%2B%284.50-5.10%29%5E2%2B%285.00-5.10%29%5E2%2B%286.00-5.10%29%5E2%7D%7B7%7D%20%7D)
This will give us,
![\sigma =\sqrt{\frac{(-0.25)^2+(0.00)^2+(0.40)^2+(-0.35)^2+(-0.60)^2+(-0.10)^2+(0.90)^2}{7} }](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Csqrt%7B%5Cfrac%7B%28-0.25%29%5E2%2B%280.00%29%5E2%2B%280.40%29%5E2%2B%28-0.35%29%5E2%2B%28-0.60%29%5E2%2B%28-0.10%29%5E2%2B%280.90%29%5E2%7D%7B7%7D%20%7D)
![\sigma =\sqrt{\frac{0.0625+0+0.16+0.1225+0.36+0.01+0.81}{7} }](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Csqrt%7B%5Cfrac%7B0.0625%2B0%2B0.16%2B0.1225%2B0.36%2B0.01%2B0.81%7D%7B7%7D%20%7D)
![\sigma =\sqrt{\frac{61}{280} }](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Csqrt%7B%5Cfrac%7B61%7D%7B280%7D%20%7D)
![\sigma =0.466775](https://tex.z-dn.net/?f=%5Csigma%20%3D0.466775)
to the nearest hundredth,
.
<u>QUESTION 3</u>
The variance is the square of the standard deviation.
![\sigma^2 =(0.46675)^2](https://tex.z-dn.net/?f=%5Csigma%5E2%20%3D%280.46675%29%5E2)
![\sigma^2 =0.217857](https://tex.z-dn.net/?f=%5Csigma%5E2%20%3D0.217857)
To the nearest hundred gives,
![\sigma^2 =0.22](https://tex.z-dn.net/?f=%5Csigma%5E2%20%3D0.22)
A) Luis
When there’s a negative number you’d change it to be a positive
Answer:
14 gallons = 23 days
Step-by-step explanation:
14/6