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3 years ago

Find the average rate of change of the function f(x)=(3/-3x-5), on the interval x ∈ [0,3]

Mathematics

1 answer:

vivado [14]3 years ago

8 0

Answer:

9/70

Step-by-step explanation:

Mathematically;

Average rate of change on an interval [a,b] is;

f(b) - f(a)/b-a

f(0) = -3/5

f(3) = -3/14

a = 0

b = 3

Making the substitution, we have

-3/14-(-3/5)/3-0

= 3/5-3/14/3

= (42-15)/70/3

= 27/70/3

= 27/70 * 1/3 = 9/70

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Use technology and the given confidence level and sample data to find the confidence interval for the population mean mu. Assume

Sphinxa [80]

Answer: (1.55, 6.45)

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\overline\ {x}\pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Significance level : $\alpha: 1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

Sample size : n=41

Sample mean : $\overline{x}=4.0\text{ kg}$

Standard deviation : $\sigma=6.1\text{ kg}$

Then, 99% confidence interval for population mean will be :_

$4\pm\ (2.576)\dfrac{6.1}{\sqrt{41}}\\\\\approx4\pm2.45\\\\=(4-2.45, 4+2.45)=(1.55, 6.45)$

8 0

4 years ago

Employees of the store in the example wear shirts with the logo on the back. The scale from the original logo in inches to the s

bagirrra123 [75]

Answer:

72 in²

Step-by-step explanation:

The original logo is a triangle and has dimensions of

1.5 in x 1.5 in

The scale factor is

Original to shirt = 1:8

Area of the logo on shirts

A = 1/2bh
A = 1/2*(1.5*8)(1.5*8) =72 in²

6 0

3 years ago

In △ABC , line AB is extended up to point E and line BC is extended up to D . The measure of some of the angles is given as; ∠BA

Over [174]

Answer:

$\angle ACD = 130 ^\circ$ .

Step-by-step explanation:

$\angle ABC$ and $\angle EBC$ are supplementary angles. Their sum should be $180^\circ$ . $\angle EBC = 120^\circ$ $\implies \angle ABC = 180^\circ - \angle EBC = 180^\circ - 120^\circ = 60^\circ$ .

The sum of the three angles in triangle $\triangle ABC$ : $(\angle ABC + \angle BAC + \angle ACB)$ should be equal to $180^\circ$ .

$\angle ABC = 60^\circ$ and $\angle BAC = 70^\circ$ $\implies \angle ACB = 180^\circ - \angle ABC - \angle ACB = 180^\circ - 70^\circ - 60^\circ = 50^\circ$ .

$\angle ACB$ and $\angle ACD$ form another pair of supplementary angles. Their sum should also be $180^\circ$ . $\angle ACB = 50^\circ$ $\implies \angle ACD = 180^\circ - \angle ACB = 180^\circ - 50^\circ = 130^\circ$ .

8 0

4 years ago

If f(x)=x+7 and g(x)= <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bx%20-%2013%7D%20" id="TexFormula1" title=" \frac{

Sergio [31]

Hi,

$f(x)=x+7\\

g(x)= \dfrac{1}{x-13} \\

(fog)(x)=f(g(x))=f(\dfrac{1}{x-13})=\dfrac{1}{x-13}+7\\


$
Domain of (fog)(x) is R \ {13} =(-oo 13[ U ]13 +oo)

8 0

3 years ago

Slope of (0,45) (6,33) (15,15)

Vladimir [108]

Answer:

The slope is -2

Step-by-step explanation:

Given

$(x_1,y_1) = (0,45)$