1) If Keith drove 259 miles of a 500-mile trip and his wife drove the rest of the way, what percent of the trip did his wife drive?
a) 25.9%
b) 48.2%
c) 49.8%
d) 51.8%
e) 74.1%
2) If 150% of J is equal to half of K, and K is not equal to 0, then J/K =
a) 1/5
b) 1/3
c) 1/2
d) 2
e) 3
3) The length of a radius of a circle is decreased by 10%. This causes the area to be decreased by
a) 19%
b) 20%
c) 21%
d) 25%
1. find what percentage of the trip Keith drove, then his wife must have driven the remaining percentage
2.
1.5J = (1/2)K
3J = K
divide by K
3J/K = 1
divide by 3
J/K = 1/3
3. with radius r, area = πr^2
reduce radius by 10% ---> new radius = .9r
new area = π(.9r)^2 = .81π
decrease = .19π
.19π/π = .19 or 19%
asdwa
1) Well, if Keith drove 259 miles out of a 500-mile trip, we can calculate the percent that his wife drove by dividing her distance by the total distance and multiplying by 100. So, (500 - 259) / 500 * 100 = 241 / 500 * 100 = 48.2%. So, the answer is b) 48.2%. Keith can take a break now and let his wife do the driving!
2) Ah, the good old algebra problem. Let's see if I can solve it without getting tangled up. If 150% of J equals half of K, we can write it as 1.5J = 0.5K. Now, let's solve for J/K by dividing both sides of the equation by K. We get 1.5J / K = 0.5K / K, which simplifies to 1.5J / K = 0.5. Finally, by dividing both sides of the equation by 1.5, we can find that J/K = 0.5 / 1.5 = 1/3. So, the answer is b) 1/3. Math, it's as easy as pie... or should I say, pi?
3) Oh, the circle is getting smaller! If the length of the radius is decreased by 10%, we need to figure out how it affects the area. The formula for the area of a circle is A = πr^2, but since we're dealing with percentages here, let's make it A = π(0.9r)^2. If we simplify that, we get A = π(0.81r^2), which means the new area is 0.81 times the original area. To find the percentage decrease, we subtract this from 1 and multiply by 100: (1 - 0.81) * 100 = 0.19 * 100 = 19%. So, the area is decreased by a) 19%. Smaller radius, smaller area – that's how circles roll!
1) To find the percent of the trip Keith's wife drove, we need to calculate the remaining distance she drove and express it as a percentage of the total distance.
Total distance of the trip = 500 miles
Keith drove 259 miles
Remaining distance = Total distance - Distance Keith drove = 500 miles - 259 miles = 241 miles
To find the percent, we divide the remaining distance by the total distance and multiply by 100.
Percent of the trip Keith's wife drove = (Remaining distance / Total distance) * 100
= (241 miles / 500 miles) * 100
≈ 0.482 * 100
≈ 48.2%
Thus, the answer is (b) 48.2%.
2) We are given that 150% of J is equal to half of K. Mathematically, this can be expressed as:
150% of J = (1/2)K
To find J/K, we need to divide J by K.
Divide both sides of the equation by K:
(150% of J) / K = (1/2)
Simplify the left side by converting 150% to its decimal form:
(1.5 * J) / K = (1/2)
Now, divide both sides of the equation by 1.5:
((1.5 * J) / K) / 1.5 = (1/2) / 1.5
Simplify the left side:
J / K = 1/3
Thus, J/K = 1/3, so the answer is (b) 1/3.
3) When the length of the radius of a circle is decreased by 10%, the new radius becomes 90% of the original radius.
If we assume the original radius is 100 units, the new radius would be 90 units.
The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
Original area = π * (100^2) = 10,000π
New area = π * (90^2) = 8,100π
To find the percent decrease, we compare the difference between the original and new areas to the original area.
Percent decrease = ((Original area - New area) / Original area) * 100
= ((10,000π - 8,100π) / 10,000π) * 100
= (1900π / 10,000π) * 100
= 19%
Therefore, the area is decreased by 19%, so the answer is (a) 19%.