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Aleonysh [2.5K]

3 years ago

7

Need help in this mathquestion. The function h(x)=(x+2)^2 can be expressed in the form f(g(x)) where f(x)=x^2 , and g(x) is defi

ned below:

1 answer:

blsea [12.9K]3 years ago

4 0

Answer:

In a nutshell, $g(x) = x+2$ .

Step-by-step explanation:

A composition is operation between function that consist in replacing the independent variable of the first function, $f(x)$ in this case, for $g(x)$ . Common notations for composition between functions are $f(g(x))$ and $f\circ g (x)$ . If we know that $h(x) = f\circ g (x) = (x+2)^{2}$ and $f(x) = x^{2}$ , then $g(x) = x+2$ .

In a nutshell, $g(x) = x+2$ .

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According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

blagie [28]

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5.1% of burglaries are cleared with arrests.

This means that $p = 0.051$

A new detective is assigned to six different burglaries.

This means that $n = 6$

What is the probability that at least one of them is cleared with an arrest?

Either none are cleared, or at least one is. The sum of the probabilities of these events is 100% = 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.051)^{0}.(0.949)^{6} = 0.7305$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7305 = 0.2695$

26.95% probability that at least one of them is cleared with an arrest

8 0

2 years ago

If ∠x= 55, then find the values of a, b, c and d

AnnyKZ [126]

Answer:

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8 0

2 years ago

What is the value of x in the equation x - 2/3 + 1/6 = 5/6?<br><br> 1) 4<br> 2) 6<br> 3) 8<br> 4) 11

Licemer1 [7]

Answer:

$\large\boxed{x=\dfrac{4}{3}=1\dfrac{1}{3}}$

Step-by-step explanation:

$x-\dfrac{2}{3}+\dfrac{1}{6}=\dfrac{5}{6}\qquad\text{multiply both sides by 6}\\\\6x-6\!\!\!\!\diagup^2\cdot\left(\dfrac{2}{3\!\!\!\!\diagup_1}\right)+6\!\!\!\!\diagup^1\cdot\left(\dfrac{1}{6\!\!\!\!\diagup_1}\right)=6\!\!\!\!\diagup^1\cdot\left(\dfrac{5}{6\!\!\!\!\diagup_1}\right)\\\\6x-(2)(2)+1=5\\\\6x-4+1=5\\\\6x-3=5\qquad\text{add 3 to both sides}\\\\6x=8\qquad\text{divide both sides by 6}\\\\x=\dfrac{8}{6}\\\\x=\dfrac{8:2}{6:2}\\\\x=\dfrac{4}{3}$

3 0

3 years ago

Read 2 more answers

An isosceles trapezoid is a quadrilateral with two congruent legs, a pair of parallel bases, and congruent base angles. Prove th

seraphim [82]

Answer:

The answer is below

Step-by-step explanation:

We must first define the concepts a little:

We have that when the sides are congruent that is to say that they have the same direction and the same size and also the two opposite sides are parallel, the angles will be the same.

Now, in an isosceles triangle, two angles are congruent, because their two sides are congruent.

3 0

3 years ago

The height of the plant is given by the equation h = 0.5d + 4. Rewrite this as a function rule where f(x) is the height, in cent

ad-work [718]

Answer:

Here's what I get

Step-by-step explanation:

h = 0.5d + 4

A function rule tells you how to convert an input value (x) into an output value (y).

Your function rule is

ƒ(x) = 0.5x + 4

An easy way to represent your function is to make a graph.

The easiest way to make a graph is to make a table containing some inputs and their corresponding outputs.

Here's a typical table.

$\begin{array}{cc}\textbf{x} &\textbf{y} \\0 & 4 \\2 & 5 \\4 & 6 \\6 & 7\\6 & 8 \\\end{array}$

The graph is like the one below.

4 0

3 years ago