Marika solved the equation (6x + 15)2 + 24 = 0. Her work is below. 1. (6x + 15)2 = –24 2. = 3. 6x + 15 = 4. 6x = – 15 5. x = Ana
2 answers:
Given equation:
First step Marika applied to get rid 24 from left side.
24 is added on left side of the equation.
The reverse operation of addition is subtract.
So, we need to subtract 24 from both sides in first step.
On simplifying it gives:
.
Then she took square root to get rid square from left side .
But we can see that 24 is a negative number.
So, we can't take square root of 24.
Therefore, in second step the did some mistake:
<h3><em>There are no real solutions to this equation because the square root of a negative number is not a real number.</em></h3>You might be interested in
Answer:
31.82% probability that you will receive 2 apples.
Step-by-step explanation:
The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
5 + 7 = 12 total fruits, which means that
7 apples, which means that
You receive 2 fruits, which means that
What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?
This is, as a proportion, P(X = 2). So
0.3182*100% = 31.82%
31.82% probability that you will receive 2 apples.
Answer:
The 95% confidence interval for the true proportion of university students who use laptop in class to take notes is (0.2839, 0.4161).
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population proportion <em>P</em> is:
The information provided is:
<em>x</em> = number of students who responded as"yes" = 70
<em>n</em> = sample size = 200
Confidence level = 95%
The formula to compute the sample proportion is:
The R codes for the construction of the 95% confidence interval is:
> x=70
> n=200
> p=x/n
> p
[1] 0.35
> s=sqrt((p*(1-p))/n)
> s
[1] 0.03372684
> E=qnorm(0.975)*s
> lower=p-E
> upper=p+E
> lower
[1] 0.2838966
> upper
[1] 0.4161034
Thus, the 95% confidence interval for the true proportion of university students who use laptop in class to take notes is (0.2839, 0.4161).