Answer:
base angles each measure 68 degrees
third angle measures 34 degrees
Step-by-step explanation:
let '2x' = measure of each base angle
let 'x' = measure of third angle
the sum of all three must equal 180 degrees so you can write this equation:
2x + 2x + x = 180
combine 'like terms' to get:
5x = 180
divide each side by 5 to get:
x = 34
therefore, twice 'x' is 68
check:
68 + 68 + 34 = 180
180 = 180
Answer:
$177.38
Step-by-step explanation:
The first thing you want to do is figure out your variables. In A = Pe^(rt), "A" is the end amount (AKA however much money you have after however much time), "P" is the principle amount (AKA however much you have to start with), "r" is the rate, and "t" is the time. Take all the information they gave you in the problem and try to place it in one of these categories.
Tyler opened a savings account 6 years ago. Ding-ding, we've got a time. The account earns 2% interest, compounded annually. There's our rate. If the current balance is $200.00, how much did he deposit initially?
So, sort these out. t = 6 years. r = 2%, or r = .02. The current balance is $200.00, so is this your end amount or the money you had to start with? Well, since the question is asking you to find how much Tyler deposited initially, you know for sure $200.00 is your end amount ("A"). Let's find out what he started with.
200 = Pe^(.02)(6)
Note that e is not a variable, but a value. You won't ever replace it; it's part of your formula. What you want to solve for here is "P" to get your starting amount. Divide both sides by e^(.02)(6), and you'll see:
P = 200/[e^(.02)(6)] = 177.3840873
Since we're talking money, round that to the nearest cent like your question asked, and you get $177.38. You can check your answer by plugging this value back into A = Pe^(rt) with $177.38 being the principle amount. You get $200 back, so the answer is correct.
Given that a movie producer conducted a survey after a preview screening of her new
movie to find out how the film would be received by viewers from
different age groups.
Given the table that shows the numbers of viewers in
different age groups who rated the film excellent, good, average, and
poor.
Viewer's Age Group Excellent Good Average Poor Marginal Total
16–25 52 42 12 7 113
26–35 33 50 5 9 97
36–45 58 12 28 34 132
46–55 25 17 22 12 76
56+ 12 5 3 8 28
Marginal Total 180 126 70 70 446
<span>The number of viewers from the 46 - 55 age group who rated the film excellent is 25.
Therefore, the percentage of the total survey group who </span><span>rated the film excellent and also was from the 46-55 age group</span> = 25 / 446 x 100% = 5.61%