16.) A. B. C. Algebra 2 chapter 7
1 answer:
Your equation for exponential growth is of the form 
, where a is the initial or starting value and b is the multiplier. DO NOT EVER EVER MULTIPLY A TIMES B AND THEN RAISE IT TO THE X POWER! This is not the way you do these. A and B remain separate. In our situation, we have an equation that looks like this 
. That's part a. Now we need to find how many bacteria are on it 5 hours later, which will be subbed in for our x in the equation. 
. Raise 4 to the 5th power first to get 1024, then multiply that by 8 to get a total of 8192 bacteria on your cookie 5 hours later. That's part b. Now for part c, you're going to have to use some of the properties of logs to solve this. This time they're asking for the time it takes to get 100,000 bacteria on the cookie, which is your x value. You need to get it out from being an exponent to being a "regular" variable we can solve for. So our equation now uses the number of bacteria as our y: 
. Begin by dividing both sides by 8 to get rid of it on the right: 
. Now take the log of both sides to bring down that x: 
, and using the power property we have log(12,500) = x log(4). Now we will divide both sides by log(4) to isolate the x and do the work on our calculator to find that x= 6.80. In other words, it will take just short of 7 hours for your cookie to have 100,000 bacteria on it. I'd suggest cafeteria food, but that might kill you quicker!
You might be interested in
Answer:
So the p value obtained was a very low value and using the significance level assumed for example we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of circuits that show evidence of undercutting is significantly less than 0.05.
Step-by-step explanation:
1) Data given and notation
n=1000 represent the random sample taken
X=33 represent the number of circuits that show evidence of undercutting
estimated proportion of circuits that show evidence of undercutting
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that they reduce the rate of undercutting to less than 5%.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
So the p value obtained was a very low value and using the significance level assumed for example we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of circuits that show evidence of undercutting is significantly less than 0.05.
Answer:
67 degrees
Step-by-step explanation:
It is given that,
The measures of the three angles of a triangle are 43°, 70°, and xº.
We need to find the value of x.
We know that, the sum of angles of a triangle is equal to 180 degrees. Applying this theorem, we get :
Hence, the value of x is 67 degrees.