The coordinates of vertex A of ABC are

A survey was conducted that asked 1003 1003 people how many books they had read in the past year. results indicated that x overb

kirill115 [55]

The confidence interval is

$10.5\pm1.35 = (9.15, 11.85)$ . This means that we can be 99% confident that the mean number of books people read lies between 9.15 and 11.85.

To find the confidence interval, we first find the z-score associated with it:

Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995

Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.

We calculate the margin of error using

$ME=z*\frac{s}{\sqrt{n}}
\\
\\=2.575*\frac{16.6}{\sqrt{1003}}=1.35$

This means that the confidence interval is
$10.5\pm1.35$

The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85

5 0

3 years ago

Pleaseee help What choices are real numbers? Check all that apply.

7nadin3 [17]

Answer:

what you arest mine but the other one says no answer what

Step-by-step explanation:

6 0

3 years ago

A sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standa

nignag [31]

For this problem, the confidence interval is the one we are looking for. Since the confidence level is not given, we assume that it is 95%.

The formula for the confidence interval is: mean ± t (α/2)(n-1) * s √1 + 1/n

Where:

α= 5%

α/2 = 2.5%

t 0.025, 19 = 2.093 (check t table)

n = 20

df = n – 1 = 20 – 1 = 19

So plugging in our values:

8.41 ± 2.093 * 0.77 √ 1 + 1/20

= 8.41 ± 2.093 * 0.77 (1.0247)

= 8.41 ± 2.093 * 0.789019

= 8.41 ± 1.65141676

= 6.7586 < x < 10.0614

3 0

3 years ago

12-(-19)= HELP ME OUT PLZ

Vikentia [17]

Answer:

31

Step-by-step explanation:

A negative negative is a positive

12- (-19)

12+19

31

6 0

3 years ago

A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.

irakobra [83]

Answer:

The integral is equal to $5\sec^2(2x)+C$ for an arbitrary constant C.

Step-by-step explanation:

a) If $u=\tan(2x)$ then $du=2\sec^2(2x)dx$ so the integral becomes $\int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C$ . (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case $u=\sec(2x)$ hence $du=2\tan(2x)\sec(2x)dx$ . We rewrite the integral as $\int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C$ .

c) We use the trigonometric identity $\tan(2x)^2+1=\sec(2x)^2$ is part b). The value of the integral is $5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C$ . which coincides with part a)

Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.

3 0

3 years ago