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2 years ago

Find the domain of the following function f(x)=sqrt x-4. write your answer in interval notation.

Mathematics

2 answers:

AlladinOne [14]2 years ago

8 0

X has to be equal or greater than four, so the interval notation would be [4,∞)

zvonat [6]2 years ago

3 0

Answer:

$[4,\infty)$

Step-by-step explanation:

We have been given a function $f(x)=\sqrt{x-4}$ . We are asked to find the domain of our given function.

We know that domain of a function is all values of independent variable for which function is defined.

We also know that square root of negative numbers is not defined.

The domain of our given function will be all non-negative values of x as:

$x-4\geq 0$

$x-4+4\geq 0+4$

$x\geq 4$

Therefore, the domain of our given function is all values of x greater than or equal to 4 that is $[4,\infty)$ in interval notation.

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Suppose that the probability of a baseball player getting a hit in an at-bat is 0.3089. If the player has 25 at-bats during a we

klio [65]

Answer:

$P(X>9) = 0.3593$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=25, p=0.3089)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

For this case we want this probability:

$P(X >9)$

And we can use the complement rule like this:

$P(X>9) = 1-P(X \leq 8)= 1-[P(X=0) + P(X=1) +....+P(X=8)]$ And we can find the individual probabilities like this:

$P(X=0) =(25C0)(0.3089)^0 (1-0.3089)^{25-0} =0.0000974$

$P(X=1) =(25C1)(0.3089)^1 (1-0.3089)^{25-1} =0.0011$

$P(X=2) =(25C2)(0.3089)^2 (1-0.3089)^{25-2}=0.00584$

$P(X=3) =(25C3)(0.3089)^3 (1-0.3089)^{25-3}= 0.02$

$P(X=4) =(25C4)(0.3089)^4 (1-0.3089)^{25-4}=0.049$

$P(X=5) =(25C5)(0.3089)^5 (1-0.3089)^{25-5}=0.092$

$P(X=6)=(25C6) (0.3089)^6 (1-0.3089)^{25-6} = 0.138$

$P(X=7) =(25C7)(0.3089)^7 (1-0.3089)^{25-7}=0.167$

$P(X=8) =(25C8)(0.3089)^8 (1-0.3089)^{25-8}=0.168$

And in order to do the operations we can use the following excel code:

"=1-BINOM.DIST(8,25,0.3089,TRUE)"

And we got:

$P(X>9) = 0.3593$

4 0

2 years ago

For the problem 1/5g- 1/10- g + 1 3/10g -1/10, Tyson created an equivalent expression using the following steps. 1/5g+-1g+1 3/10

professor190 [17]

The true statements are:

Tyson's expression is not equivalent to the original expression
The equivalent expression is: $\frac{1}{2}g- \frac 1{5}$

<h3>What are equivalent expressions?</h3>

Equivalent expressions are expressions that have equal values

The original expression is given as:

$\frac 15g- \frac 1{10}- g + 1 \frac{3}{10}g -\frac{1}{10}$

Collect like terms

$\frac 15g- \frac 1{10}- g + 1 \frac{3}{10}g -\frac{1}{10} = \frac 15g - g + 1 \frac{3}{10}g- \frac 1{10} -\frac{1}{10}$

Evaluate the like terms

$\frac 15g- \frac 1{10}- g + 1 \frac{3}{10}g -\frac{1}{10} = \frac{1}{2}g- \frac 1{5}$

Tyler's equivalent expression is given as:

$\frac15g-g+ 1 \frac3{10}g-\frac 1{10}-\frac 45g+1 \frac{1}{10}$

Collect like terms

$\frac15g-g+ 1 \frac3{10}g-\frac 1{10}-\frac 45g+1 \frac{1}{10} = \frac15g-g+ 1 \frac3{10}g-\frac 45g-\frac 1{10}+1 \frac{1}{10}$

Evaluate the like terms

$\frac15g-g+ 1 \frac3{10}g-\frac 1{10}-\frac 45g+1 \frac{1}{10} = -\frac 3{10}g$

The simplified expressions of the original expression, and Tyson's equivalent expressions are not equal.

Hence, Tyson's expression is not equivalent to the original expression

Read more about equivalent expressions at:

brainly.com/question/9603710

3 0

1 year ago