Answer: 78
Step-by-step explanation:
- [6 (2) (4)] + [5 (2) (3) ]
- The first bracket, 6*2* = 12, 12 * 4 = 48
- The second bracket, 5*2 = 10, 10 * 3 = 30
- Add the answers of both brackets. 48 + 30 = 78
Answer:
4.8%
Step-by-step explanation:
The population that grows with an annual percentage rate compounded continuously is given by: H = H° e^rt
Let the population be represented by H
The population reaches 1.1 times its previous size in 2 years.
So when t=2,
H = 1.1 H°
We substitute to obtain:
1.1 H° = H° e^r2
1.1 = e^2r
Take natural log to get:
In 1.1 = 2r
r = In 1.1 /2
r = 0.0477
Therefore the annual percentage rate is 4.8%
This is a two step problem. First, you need to find the difference (or increase) in the rent using subtraction.
616-560 = $56 increase
Now we need to figure what percent 56 is to the original amount (560)
We voice it like this:
56 is to 560 as x is to 100.
The equation looks like this:
56/560 - x/100
Cross multiply to cancel out the denominators.
56 x 100 = 560 x
5600 = 560 x
x = 10 percent.
Check it!
What is 10 percent of 560?
560 x .1 = $56
Was that your increase? ... yes.
Answer:
99% Confidence interval: (0.185,0.375)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 150
Number of cars that have faulty catalytic converters, x = 42
99% Confidence interval:
Putting the values, we get:
The 99% confidence interval for the true proportion of new cars with faulty catalytic converters is (0.185,0.375)
Answer:
Given: A triangle ABC and a line DE parallel to BC.
To prove: A line parallel to one side of a triangle divides the other two sides proportionally.
Proof: Consider ΔABC and DE be the line parallel to Bc, then from ΔABC and ΔADE, we have
∠A=∠A (Common)
∠ADE=∠ABC (Corresponding angles)
Thus, by AA similarity, ΔABC is similar to ΔADE, therefore
AB/AD= AC/AE
⇒AD+DB/AD = AE+EC/AE
⇒1+DB/AD = 1+ EC/AE
⇒DB/AD = EC/AE
Therefore, a line parallel to one side of a triangle divides the other two sides proportionally.
⇒Therefore Proved
Hope this helps!!!