Answer: The correct option is
(D) 60.
Step-by-step explanation: Given that the number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively.
After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5.
We are to find the number of stamps that Kaye had more than Alberto.
Let the number of stamps Kaye and Alberto has are 5x and 3x respectively.
Then, according to the given information, we have
![(5x-10):(3x+10)=7:5\\\\\Rightarrow \dfrac{5x-10}{3x+10}=\dfrac{7}{5}\\\\\Rightarrow 25x-50=21x+70\\\\\Rightarrow4x=120\\\\\Rightarrow x=\dfrac{120}{4}\\\\\Rightarrow x=30.](https://tex.z-dn.net/?f=%285x-10%29%3A%283x%2B10%29%3D7%3A5%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B5x-10%7D%7B3x%2B10%7D%3D%5Cdfrac%7B7%7D%7B5%7D%5C%5C%5C%5C%5CRightarrow%2025x-50%3D21x%2B70%5C%5C%5C%5C%5CRightarrow4x%3D120%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B120%7D%7B4%7D%5C%5C%5C%5C%5CRightarrow%20x%3D30.)
So, the number of stamps that Kaye had = 5 × 30 = 150
and
the number of stamps that Alberto had = 3 × 30 = 90.
Therefore, the number of stamps that Kaye had more than Alberto is
![150-90=60.](https://tex.z-dn.net/?f=150-90%3D60.)
Thus, Kaye had 60 stamps more than Alberto.
Option (D) is CORRECT.
Answer:
$158.75
Step-by-step explanation:
Given:
The Maple Car Rental Comany charges a flat fee of $45 plus 35 cents per mile
And we have to write a linear equation that gives the total cost in terms of numbers of miles driven then find the total cost if the renter drives 325 miles.
Solution:
Total cost = 35 cents of renter drives in miles + fixed charge of the car
Total cost = ![0.35\times325 +45](https://tex.z-dn.net/?f=0.35%5Ctimes325%20%2B45)
![= 113.75 + 45\\= 158.75](https://tex.z-dn.net/?f=%3D%20113.75%20%20%2B%2045%5C%5C%3D%20158.75)
Thus, total cost is $158.75, when the renter drives 325 miles.
Y = mx + b
b is y intercept
Solution: y intercept is 3
Answer: 0.8
Step-by-step explanation:
Using the Cosine formula :
![Cos A = \frac{b^{2}+c^{2}-a^{2}}{2bc}](https://tex.z-dn.net/?f=Cos%20A%20%3D%20%5Cfrac%7Bb%5E%7B2%7D%2Bc%5E%7B2%7D-a%5E%7B2%7D%7D%7B2bc%7D)
![a = 6](https://tex.z-dn.net/?f=a%20%3D%206)
![b = 8](https://tex.z-dn.net/?f=b%20%3D%208)
![c = 10](https://tex.z-dn.net/?f=c%20%3D%2010)
substituting into the formula , we have
![Cos A = \frac{8^{2}+10^{2}-6^{2}}{2(8)(10)}](https://tex.z-dn.net/?f=Cos%20A%20%3D%20%5Cfrac%7B8%5E%7B2%7D%2B10%5E%7B2%7D-6%5E%7B2%7D%7D%7B2%288%29%2810%29%7D)
![Cos A = \frac{64+100-36}{160}](https://tex.z-dn.net/?f=Cos%20A%20%3D%20%5Cfrac%7B64%2B100-36%7D%7B160%7D)
![Cos A = \frac{164-36}{160}](https://tex.z-dn.net/?f=Cos%20A%20%3D%20%5Cfrac%7B164-36%7D%7B160%7D)
![Cos A = \frac{128}{160}](https://tex.z-dn.net/?f=Cos%20A%20%3D%20%5Cfrac%7B128%7D%7B160%7D)
Therefore :
Cosine of angle A = 0.8