The given expression is a difference of squares, so we have
16 (<em>a</em> + <em>b</em>)² - 49 (<em>a</em> - <em>b</em>)² = 4² (<em>a</em> + <em>b</em>)² - 7² (<em>a</em> - <em>b</em>)²
… = (4 (<em>a</em> + <em>b</em>))² - (7 (<em>a</em> - <em>b</em>))²
… = (4 (<em>a</em> + <em>b</em>) - 7 (<em>a</em> - <em>b</em>)) (4 (<em>a</em> + <em>b</em>) + 7 (<em>a</em> - <em>b</em>))
… = (4<em>a</em> + 4<em>b</em> - 7<em>a</em> + 7<em>b</em>) (4<em>a</em> + 4<em>b</em> + 7<em>a</em> - 7<em>b</em>)
… = (-3<em>a</em> + 11<em>b</em>) (11<em>a</em> - 3<em>b</em>)
Whenever number less than 1 is raised to the power of "t" , the equation is exponentially decaying.
This is because as time increases the decimal is being raised to a higher and higher power causing it to decay. For example, when
t= 0 sec in eq 1 the H= 5.9(0.82)^0 = 5.9(1). So, at time= 0 seconds H= 5.9.
but, if time increases to t=2secs, then H= 5.9(0.82)²= (5.9)(0.6724)= 3.96716.
At time = 2 seconds H= 3.96716.
In the other case, where a value greater than 1 is raised to the power of time(t) the equation is an exponential growth equation.
ANSWER:
Exponential Decay:
H= 5.9(0.82)^t
A= (3/4)^t
H= 7/2(5/6)^t
Exponential Growth:
y=0.8(3.6)^t
f(t)= 0.72(15)^t
A= 4/9 (8)^t
Niether:
g(x)= 0.3x - Neither growth nor decay because nothing in the equation is being raised to an exponential power of "t" (time)
Answer:
0.88% probability that the sample proportion will differ from the population proportion by more than 5%
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For proportions p in a sample of size n, we have that
In this problem:
What is the probability that the sample proportion will differ from the population proportion by more than 5%?
Less than 0.19 - 0.05 = 0.14 or greater than 0.19 + 0.04 = 0.24. Since the normal distribution is symmetric these probabilities are equal, which means that we can find one of them and multiply by 2. So
Probability of being less than 0.14.
pvalue of Z when X = 0.14. So
has a pvalue of 0.0044
2*0.0044 = 0.0088
0.88% probability that the sample proportion will differ from the population proportion by more than 5%
Answer:
The lines are parallel
Step-by-step explanation:
y = -2x+1 and y = -2x+4 are in the form y = mx +b
Both have a slope of -2
If the slopes are the same the lines are parallel