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3 years ago

If (c) were f(k) = -3/k+2, what value of k would be excluded from the domain?

Mathematics

1 answer:

9966 [12]3 years ago

6 0

k = - 2 is excluded from the domain

the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that k cannot be

solve k + 2 = 0 ⇒ k = - 2 ← excluded value

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For X a binomial random variable with n=5 and p=1/4, answer the following

mash [69]

Recall that for $X\sim\mathrm{Bin}(n,p)$ , i.e. a random variable $X$ following a binomial distribution over $n$ trials and with probability parameter $p$ ,

$\mathbb P(X=x)=f_X(x)=\begin{cases}\dbinom nx p^x(1-p)^{n-x}&\text{for }x\in\{0,1,\ldots,n\}\\\\0&\text{otherwise}\end{cases}$

So you have

$\mathbb P(X=2)=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac34\right)^{5-2}=\dfrac{135}{512}\approx0.26$

$\mathbb P(2\le X\le4)=\displaystyle\sum_{x=2}^4\mathbb P(X=x)$
$=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac14\right)^{5-2}+\dbinom52\left(\dfrac14\right)^3\left(1-\dfrac14\right)^{5-3}+\dbinom52\left(\dfrac14\right)^4\left(1-\dfrac14\right)^{5-4}$
$=\dfrac{375}{1024}\approx0.37$

The expected value of $X\sim\mathrm{Bin}(n,p)$ is simply $np$ , while the standard deviation is $\sqrt{np(1-p)}$ . In this case, they are $\dfrac54=1.25$ and $\sqrt{\dfrac{15}{16}}\approx0.97$ , respectively.

7 0

3 years ago

Enter the solutions from least to greatest.<br> (2x+4)(3x-2)=0

MArishka [77]

Answer:

From least to greatest: -2, 2/3

Step-by-step explanation:

Set each factor equal to 0 and solve

2x + 4 =0

2x = -4

x = -2

3x - 2 = 0

3x = 2

x = 2/3

4 0

2 years ago

If 0° ≤ θ ≤ 90° and cosθ = 11/15 , what is the value of sin (90° - θ)?

igor_vitrenko [27]

$11/15=0.7333$
$cos^{-1}(0.7333) =42.83342$
$sin(90-47.166572) = 0.7333$

first, find the numeric value for 11/15
second to find theta, simply do the <em>inverse</em> cos (which is cos^-1) of the first answer.
now you know theta, just do the sin of 90 - theta and that's it!

since you know whatr cos(theta) is, you just take the inverse cos of that number to get theta and 'reverse' cos, essentially. you are just solving for theta, by reversing the cos function with cos^-1
please mark as brainliest!

7 0

3 years ago

Read 2 more answers

Find the slope of the line going through the points (11,5) and (20,5)

Pani-rosa [81]

So remember the formula for working out the slope:

(y2 - y1) ÷ (x2 - x1)

We already know two points:

(11, 5) and (20, 5) (Remember points are like (x, y)

Therefore y2 = 5 and y1 = 5 and x2 = 20 and x1 = 11

Substitute these into the formula from the start:

(y2 - y1) ÷ (x2 - x1)
(5 - 5) ÷ (20 - 11)
0 ÷ 9

And we can determine the slope is equal to 0 as 0 ÷ 9 = 0

4 0

3 years ago

You have 55,000 in your savings account that pays 2.5% annual interest and the inflation rate is 3.4%. How much buying power wil

diamong [38]

We solve the question as follows:
Simple interest=Principle×Rate×Time
Thus given:
p=$55000, R=2.5%, time= 1 year
thus
Interest=55000×0.025×1=$1375

To evaluate the amount required to keep up with the inflation, your interest rate should match the inflation rate otherwise prices are going up faster than the savings.
Required interest rate=55000×0.034×1=$1870

The buying power lost will be the difference between your required interest and actual interest.

Thus:
Buying power lost=1870-1375=$495

8 0

3 years ago