Explain how to solve the compound dependent event question.

Complete the square to find the minimum value of the expression 4x2 + 8x + 23.

Tcecarenko [31]

So you need to come up with a perfect square that works for the x coefficients.
like.. (2x + 2)^2
(2x+2)(2x+2) = 4x^2 + 8x + 4
Compare this to the equation given. Our perfect square has +4 instead of +23. The difference is: 23 - 4 = 19

I'm going to assume the given equation equals zero..

So, If we add subtract 19 from both sides of the equation we get the perfect square.

4x^2 + 8x + 23 - 19 = 0 - 19
4x^2 + 8x + 4 = - 19
complete the square and move 19 over..
(2x+2)^2 + 19 = 0
factor the 2 out becomes 2^2 = 4
ANSWER: 4(x+1)^2 + 19 = 0

for a short cut, the standard equation
ax^2 + bx + c = 0 becomes a(x - h)^2 + k = 0
Where "a, b, c" are the same and ..
h = -b/(2a)
k = c - b^2/(4a)

Vertex = (h, k)
this will be a minimum point when "a" is positive upward facing parabola and a maximum point when "a" is negative downward facing parabola.

3 0

2 years ago

The product of two rational numbers is 9⁄7 and one of them is 15⁄14. Then the other rational number is

Rasek [7]

Answer:

The other rational number in the operation given is:

<u>6/5</u>

Step-by-step explanation:

To obtain the number in the operation given, we're gonna represent the operation:

r * 15/14 = 9/7

Where:

r = the other rational number.

Now we are going to solve r to identify its value in numbers:

r * 15/14 = 9/7

$r = \frac{\frac{9}{7} }{\frac{15}{14}}$ (We pass a number that is multiplying to the left of the equal, to divide to the right of the equal symbol)

$r = \frac{6}{5}$

As you can see, when we operate, <u>the result is 6/5</u>, and we can prove this multiplying as we had in the original equation, replacing r by 6/5:

r * 15/14 = 9/7
6/5 * 15/14 = 9/7
9/7 = 9/7

In this form, we know the result is correct.

8 0

3 years ago

Kevin made 4 of his 6 shots on goal at soccer practice.

mafiozo [28]

Answer:

48

Step-by-step explanation:

4/6 = 2/3

2/3 times 72 = 48

8 0

2 years ago

Select the correct answer. robin randomly selects a number between 1 and 20. what is the probability that the number selected is

Vlada [557]

The probability that the number selected is the square of a natural number will be $\frac{1}{5}$ .

<h3 /><h3>What is probability?</h3>

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.

Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

P is the probability

F(E) is the favorable event

T(E)is the total event

The probability is found as;

$\rm P = \frac{F(E)}{T(E)} \\\\ \rm P = \frac{4}{20)} \\\\ \rm P = \frac{1}{5}$

Hence the probability that the number selected is the square of a natural number will be $\frac{1}{5}$ .

To learn more about the probability link is given below.

brainly.com/question/795909

8 0

2 years ago

Isabella averages 152 points per bowling game with a standard deviation of 14.5 points. Suppose Isabella's points per bowling ga

Serga [27]

Answer:

The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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.

In this question:

$\mu = 152, \sigma = 14.5$

The z-score when x=187 is ...

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{187 - 152}{14.5}$

$Z = 2.41$

The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.

3 0

2 years ago