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3 years ago

If 588 digits were used to number the pages of a book, how many pages are in this book?

Mathematics

2 answers:

gregori [183]3 years ago

4 0

Answer:

294 pages are in this book

Step-by-step explanation:

jeka57 [31]3 years ago

3 0

Answer: 232 pages are in this book.

Step-by-step explanation:

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Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when $M = 0.5$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.5 = 1.96\frac{2}{\sqrt{n}}$

$0.5\sqrt{n} = 2*1.96$

Dividing both sides by 0.5

$\sqrt{n} = 4*1.96$

$(\sqrt{n})^2 = (4*1.96)^2$

$n = 61.5$

Rounding up

We would have to take a sample of 62 to achieve this result.

8 0

3 years ago

The present age of the father is twice the age of his daughter. Ten years ago, the

Elenna [48]

Answer:

<h3> The father is 40 and the daughter is 20.</h3>

Step-by-step explanation:

x - the present age of the daughter

2x - the present age of the fathter

x - 10 - the age of the daughter ten year ago

2x - 10 - the age of the fathter ten year ago

Father is older than his dauther, so:

2x - 10 = (x - 10) + 20

2x - 10 = x - 10 + 20

2x - 10 = x + 10 {subtract x from both sides}

x - 10 = 10 {add 10 to both sides}

x = 20

2x = 2·20 = 40

6 0

3 years ago

A circle is centered at J(3, 3) and has a radius of 12.

stealth61 [152]

Answer:

$(-6,\, -5)$ is outside the circle of radius of $12$ centered at $(3,\, 3)$ .

Step-by-step explanation:

Let $J$ and $r$ denote the center and the radius of this circle, respectively. Let $F$ be a point in the plane.

Let $d(J,\, F)$ denote the Euclidean distance between point $J$ and point $F$ .

In other words, if $J$ is at $(x_j,\, y_j)$ while $F$ is at $(x_f,\, y_f)$ , then $\displaystyle d(J,\, F) = \sqrt{(x_j - x_f)^{2} + (y_j - y_f)^{2}}$ .

Point $F$ would be inside this circle if $d(J,\, F) < r$ . (In other words, the distance between $F\!$ and the center of this circle is smaller than the radius of this circle.)

Point $F$ would be on this circle if $d(J,\, F) = r$ . (In other words, the distance between $F\!$ and the center of this circle is exactly equal to the radius of this circle.)

Point $F$ would be outside this circle if $d(J,\, F) > r$ . (In other words, the distance between $F\!$ and the center of this circle exceeds the radius of this circle.)

Calculate the actual distance between $J$ and $F$ :

$\begin{aligned}d(J,\, F) &= \sqrt{(x_j - x_f)^{2} + (y_j - y_f)^{2}}\\ &= \sqrt{(3 - (-6))^{2} + (3 - (-5))^{2}} \\ &= \sqrt{145} \end{aligned}$ .

On the other hand, notice that the radius of this circle, $r = 12 = \sqrt{144}$ , is smaller than $d(J,\, F)$ . Therefore, point $F$ would be outside this circle.

5 0

3 years ago

(6 x 10^2) divide (3 x 10^-5)

Hunter-Best [27]

Answer:

=20000000 (let me know if it's incorrect)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Help plz!! The function h(t)=-16t^2+22t+4 models the height (h) of a football t seconds after it is thrown. The question ask to

Black_prince [1.1K]

If you're familiar with the quadratic equation
$\frac{ -b \pm \sqrt{b^2-4ac}}{2a}$

well, $\frac{ -b}{2a}$ is the x component of the vertex, in your case, the vertex is the highest point

figure out what t is at the highest point, and then substitute that back into the equation in order to determine height

x=t in this problem

8 0

3 years ago