What is the value of x in the equation

A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08 mm and stand

LenaWriter [7]

Answer:

10.20% probability that a randomly chosen book is more than 20.2 mm thick

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

250 sheets, each sheet has mean 0.08 mm and standard deviation 0.01 mm.

So for the book.

$\mu = 250*0.08 = 20, \sigma = \sqrt{250}*0.01 = 0.158$

What is the probability that a randomly chosen book is more than 20.2 mm thick (not including the covers)

This is 1 subtracted by the pvalue of Z when X = 20.2. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20.2 - 20}{0.158}$

$Z = 1.27$

$Z = 1.27$ has a pvalue of 0.8980

1 - 0.8980 = 0.1020

10.20% probability that a randomly chosen book is more than 20.2 mm thick

7 0

3 years ago

The function f(x) = g(x), where f(x) = 2x – 5 and g(x) = x2 – 6.

den301095 [7]

Answer:

$x=2.4$

Step-by-step explanation:

<u>Solving Equations Using Successive Approximations</u>

We need to find the solution to the equation

$f(x)=g(x)$

where

$f(x)=2x-5$

$g(x)=x^2-6$

The approximation has been already started and reached a state for x=2.5 where

$f(2.5)=0$

$g(2.5)=2.5^2-6=0.25$

The difference between the results is 0.25, we need further steps to reach a good solution (to the nearest tenth)

Let's test for x=2.4

$f(2.4)=-0.2$

$g(2.4)=2.4^2-6=-0.24$

The new difference is -0.2+0.24=0.04

It's accurate enough, thus the solution is

$\boxed{x=2.4}$

5 0

3 years ago

How much cardboard is needed to make the tissue box above? Square inches 8 3 3

Katen [24]

The amount of cardboard needed to make a cuboid box of dimensions 8 inch, 3 inches and 3 inches is 114 sq. inches.

<h3>What is the surface area of cuboid?</h3>

Let the three dimensions(height, length, width) be x, y,z units respectively.

The surface area of the cuboid is given by

$S = 2(a\times b + b\times c + c\times a)$

For this case, tissue box is almost cuboid shaped.

Also, its dimensions are given being 8 inches, 3 inches and 3 inches.

Suppose we measure the amount of cardboard needed in terms of area, then, the amount of cardboard needed to make that box(without any whole, full cuboid) is equal to the area of its surface(either outer or inner if we assume 0 inches thickness of cardboard),

Thus, we get:

Amount of cardboard needed = surface area of cuboid box with dimensions 8 by 3 by 3 (in inches)

= $2(8 \times 3 + 3 \times 3 + 3 \times 8) = 114 \: \rm in^2$

Thus, the amount of cardboard needed to make a cuboid box of dimensions 8 inch, 3 inches and 3 inches is 114 sq. inches.

Learn more about surface area of cuboid here:

brainly.com/question/13522634

#SPJ1

5 0

2 years ago

Help math sucks THESE MAKE MY BRAIN DIE

Flura [38]

Answer:

A ∩ B = {1, 3, 5}

A - B = {2, 4}

Step-by-step explanation:

The given problem regards sets and set notation, a set can simply be defined as a collection of values. One is given the following information:

A = {1, 2, 3, 4, 5}

B = {1, 3, 5, 6, 9}

One is asked to find the following:

A ∩ B,

A - B

1. Solving problem 1

A ∩ B,

The symbol (∩) in set notation refers to the intersection between the two sets. It essentially asks one to find all of the terms that two sets have in common. The given sets (A) and (B) have the values ({1, 3, 5}) in common thus, the following statement can be made,

A ∩ B = {1, 3, 5}

2. Solving problem 2

A - B

Subtracting two sets is essentially taking one set, and removing the values that are shared in common with the other set. Sets (A) and (B) have the following values in common ({1, 3, 5}). Thus, when doing (A - B), one will omit the values ({1, 3, 5}) from set (A).

A - B = {2, 4}

3 0

3 years ago

The ratio of triangle abc to the corresponding side of similar triangle def is 3:5. the perimeter of triangle def is 48in. what

Vlad1618 [11]

ABC : DEF
3: 5
3 x 9.6 : 5 x 9.6
28.8 : 48
Perimeter of triangle ABC = 28.8 inch

7 0

3 years ago