Answer:
1.4
Step-by-step explanation:
Sample size: 3
Lowest value: 2.89
Highest value: 4.29
Range: 1.4
formula for calculating the range:
Range = maximum(x_i) - minimum(x_i)
where x_i represents the set of values.
From information given, we know
208 miles was at rate of 65 mph. so divide total mileage by speed to get time spent.
208 ÷ 65 = 3.2 hours
So the rest of the trip took 6 - 3.2 = 2.8hours to travel another 348 total miles minus the 208 miles driven at 65mph is 140 miles.
140 miles divided by 2.8 hours gives speed
140 ÷ 2.8 = 50 miles per hour
Answer:
10^2 × 10^2
Step-by-step explanation:
Given that
Write 100 times 100 that would be multiplying to the power by 10
So based on the above information
The equation that would be developed is
10^2 × 10^2
The same would be represented as an answer
Answers:
(a) p + m = 5
0.8m = 2
(b) 2.5 lb peanuts and 2.5 lb mixture
Explanations:
(a) Note that we just need to mix the following to get the desired mixture:
- peanut (p) - peanuts whose amount is p
- mixture (m) - mixture (80% almonds and 20% peanuts) that has an amount of m; we denote this as
By mixing the peanuts (p) and the mixture (m), we combine their weights and equate it 5 since the mixture has a total of 5 lb.
Hence,
p + m = 5
Note that the desired 5-lb mixture has 40% almonds. Thus, the amount of almonds in the desired mixture is 2 lb (40% of 5 lb, which is 0.4 multiplied by 5).
Moreover, since the mixture (m) has 80% almonds, the weight of almonds that mixture is 0.8m.
Since we mix mixture (m) with the pure peanut to get the desired mixture, the almonds in the desired mixture are also the almonds in the mixture (m).
So, we can equate the amount of almonds in mixture (m) to the amount of almonds in the desired measure.
In terms mathematical equation,
0.8m = 2
Hence, the system of equations that models the situation is
p + m = 5
0.8m = 2
(b) To solve the system obtained in (a), we first label the equations for easy reference,
(1) p + m = 5
(2) 0.8m = 2
Note that using equation (2), we can solve the value of m by dividing both sides of (2) by 0.8. By doing this, we have
m = 2.5
Then, we substitute the value of m to equation (1) to solve for p:
p + m = 5
p + 2.5 = 5 (3)
To solve for p, we subtract both sides of equation (3) by 2.5. Thus,
p = 2.5
Hence,
m = 2.5, p = 2.5
Therefore, the solution to the system is 2.5 lb peanuts and 2.5 lb mixture.
