If m(x) = x+5/x-1, and n(x) = x-3, which function has the same domain as m of n of x?

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

ollegr [7]

Answer: a. A point estimate for p is 0.597 .

b. The 95% confidence interval for p.

Lower limit = 0.48

Upper limit = 0.71

Step-by-step explanation:

Given : Sample size of professional actors : n= 67

Number of extroverts : x= 40

Let p represent the proportion of all actors who are extroverts.

a. The point estimate for p = sample proportion = $\hat{p}=\dfrac{x}{n}$

$=\dfrac{40}{67}=0.597$

b. Confidence interval for population proportion :

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

Since the critical value for 95% confidence interval is 1.96 , so the 95% confidence interval for p would be

$0.597\pm (1.96)\sqrt{\dfrac{0.597(1-0.597)}{67}}$

$0.597\pm (1.96)\sqrt{0.0036}$

$0.597\pm (1.96)(0.06)$

$0.597\pm 0.1176$

$(0.597-0.1176,\ 0.597+0.1176)\\\\=(0.4794,\ 0.7146)\\\\\approx(0.48,\ 0.71)$

In the 95% confidence interval for p.

Lower limit = 0.48

Upper limit = 0.71

8 0

2 years ago

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Enter the expression N0e−λt, where N0 is N-naught (an N with a subscript zero) and λ is the lowercase Greek letter lambda.

Natali5045456 [20]

So the question tells to express the expression in your problem where N0 is N-naught and the symbol represent the lower case Greek letter lambda. So the best answer or expression would be that the lambda is the wavelength of the expression. I hope you are satisfied with my answer

7 0

2 years ago

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Barbara is tiling her craft room floor with square tiles. She wants 6/10 of squares tiles to be red. If she uses 18 red tiles, h

Sveta_85 [38]

Answer:

6 and 18 are common because 6x3=18. Remember the rule to multiply all numbers by 3. So multiply 10 by 3 and you will get 30. The total number of square tiles needed is 30 tiles. If you are putting it into a ratio it would be 18:30.

5 0

2 years ago

The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = y minus 1 equals StartFract

Zina [86]

Answer:

The equation of the line in standard form is

$x-4y=8$

Step-by-step explanation:

The equation of the line in point slope form is

$y-y1=m(x-x1)$

we have

$y-1=(1/4)(x-12)$

so

$m=1/4$

$(12, 1)$

step 2

Find the equation of the line in standard form

The equation of the line in standard form is

$Ax+By=C$

where

A is positive integer

B and C are integers

we have

$y-1=(1/4)(x-12)$

Multiply by 4 both sides to remove the fraction

$4y-4=(x-12)$

$x-4y=12-4\\x-4y=8$

8 0

2 years ago

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Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist

Lera25 [3.4K]

Answer:

$Sum = -81$

Step-by-step explanation:

See the comment for complete question.

Given

$c = 36$ ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

$x^2 + ax + 36 = 0$

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

$x = -\alpha$ and $x = -\beta$

Using the above roots, the equation can be represented as:

$(x + \alpha)(x + \beta) = 0$

Open brackets

$x^2 + (\alpha + \beta)x + \alpha \beta = 0$

To compare the above equation to $x^2 + ax + 36 = 0$ , we have:

$a = \alpha + \beta$

$\alpha \beta = 36$

Where: $\alpha, \beta$ and $\alpha \ne \beta$

The values of $\alpha$ and $\beta$ that satisfy $\alpha \beta = 36$ are:

$\alpha = -1$ and $\beta = -36$

$\alpha = -2$ and $\beta = -18$

$\alpha = -3$ and $\beta = -12$

$\alpha = -4$ and $\beta = -9$

So, the possible values of a are:

$a = \alpha + \beta$

When $\alpha = -1$ and $\beta = -36$

$a = -1 - 36 = -37$

When $\alpha = -2$ and $\beta = -18$

$a = -2 - 18 = -20$

When $\alpha = -3$ and $\beta = -12$

$a = -3 - 12 = -15$

When $\alpha = -4$ and $\beta = -9$

$a = -4 - 9 = -13$

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

$Sum = -37 -20 -15 - 9$

$Sum = -81$

7 0

2 years ago