Answer:
Step-by-step explanation:
Apply the weights to the scores and add them up:
5% × midterm + 15% × project + 35% × homework + 45% × final
= 0.05(75) +0.15(93) +0.35(78) +0.45(70)
= 76.5
The student has a solid letter grade of C.
<u>Answer:</u>
The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north.
<u>Step-by-step explanation:</u>
• To find the magnitude of the resultant vector, we have to use Pythagoras's theorem:
![\boxed{a^2 = b^2 + c^2}](https://tex.z-dn.net/?f=%5Cboxed%7Ba%5E2%20%3D%20b%5E2%20%2B%20c%5E2%7D)
where:
a ⇒ hypotenuse (= resultant vector = ? mi)
b, c ⇒ the two other sides of the right-angled triangle (= 452 mil North, 767 mi West).
Using the formula:
resultant² = ![452^2 + 767^2](https://tex.z-dn.net/?f=452%5E2%20%2B%20767%5E2)
⇒ resultant = ![\sqrt{452^2 + 767^2}](https://tex.z-dn.net/?f=%5Csqrt%7B452%5E2%20%2B%20767%5E2%7D)
⇒ resultant = 890.3 mi
• To find the direction, we can find the angle (labeled <em>x</em> in diagram) that the resultant makes with the north direction:
![tan (x) =\frac{767}{452}](https://tex.z-dn.net/?f=tan%20%28x%29%20%3D%5Cfrac%7B767%7D%7B452%7D)
⇒ ![x = tan^{-1} (\frac{767}{452} )](https://tex.z-dn.net/?f=x%20%3D%20tan%5E%7B-1%7D%20%28%5Cfrac%7B767%7D%7B452%7D%20%29)
⇒ ![x = \bf{59.5 \textdegree}](https://tex.z-dn.net/?f=x%20%3D%20%5Cbf%7B59.5%20%5Ctextdegree%7D)
∴ The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north .
Answer:
The perimeter is 16 units
Step-by-step explanation:
Add up all the sides together
1+1+7+7 = 16
Answer:
When multiplying a number by 10, move the decimal to the right. Whenever a number is multiplied by 10, the decimal is shifted to one place in the right.
Like : ![7.36\times10=73.6](https://tex.z-dn.net/?f=7.36%5Ctimes10%3D73.6)
When multiplying a number by 0.1, move the decimal to the left. This means the number is multiplied by
or we can say the number is simply divided by 10.
So, when a number is divided by 10, the decimal is shifted to one place on the left.
Like : ![44.56\times0.1=4.456](https://tex.z-dn.net/?f=44.56%5Ctimes0.1%3D4.456)
or ![\frac{44.56}{10}=4.456](https://tex.z-dn.net/?f=%5Cfrac%7B44.56%7D%7B10%7D%3D4.456)
D because the radical simplified is -sqrt of 6 / 3 and when you multiply D with the radical it gives you that answer.