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4 years ago

Is 3,198 a reasonable product for 727x44?Why or why not?

Mathematics

1 answer:

Umnica [9.8K]4 years ago

5 0

3,198 is not a reasonable product for 727 × 44.

727 × 44 = 31,998

Even if we wanted to round 727 to 730 and round 44 to 50, our estimate would still be very far off. 3,198 is very far off for a reasonable estimate.

Therefore, this would not be a good estimate.

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Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the pop

Andreyy89

Answer:

The smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.

Step-by-step explanation:

The complete question is:

The mean salary of people living in a certain city is $37,500 with a standard deviation of $2,103. A sample of n people will be selected at random from those living in the city. Find the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income. Round your answer up to the next largest whole number.

Solution:

The (1 - α)% confidence interval for population mean is:

$CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$

The margin of error for this interval is:

$MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$

The critical value of z for 90% confidence level is:

z = 1.645

Compute the required sample size as follows:

$MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\cdot\sigma}{MOE}]^{2}\\\\=[\frac{1.645\times 2103}{500}]^{2}\\\\=47.8707620769\\\\\approx 48$

Thus, the smallest sample size n that will guarantee at least a 90% chance of the sample mean income being within $500 of the population mean income is 48.

3 0

3 years ago

Evalue 6C4. A) 1/30 B)5 C) 15 D) 360

Margarita [4]

6C4 = 6!/(4!2!)= 720/(2*24)=15

7 0

3 years ago

Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three

RSB [31]

Answer:

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Step-by-step explanation:

we have

$f(x)=x^{2}$

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

$g(x)=-5x^{2}+100x-450$

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

Convert to vertex form

$g(x)=-5x^{2}+100x-450$

Complete the square

$g(x)=-5(x^{2}-20x)-450$

$g(x)=-5(x^{2}-20x+100)-450+500$

$g(x)=-5(x^{2}-20x+100)+50$

$g(x)=-5(x-10)^{2}+50$

The vertex is the point (10,50)

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

5 0

3 years ago

Read 2 more answers

A tree is broken at a height of 9m from the ground and its top touches the ground at distance of 12m from the base of the tree.

KatRina [158]

Answer: i took the test its number 555555

Step-by-step explanation:

3 0

3 years ago

How do I set this up?

eimsori [14]

So find out Y first with the equation 2y+6=8y-102 which is y=18

Then plug in y for 8y-102 which is 42

Finally make the equation 3x+42=180 to find x which is 46

8 0

4 years ago