Which number produces a rational number when added to 1/5

Find the area of the shaded regions. Give your answer as a completely simplified

Pavel [41]

The area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.

<h3>What is a circle?</h3>

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have a circle in which the shaded region is shown.

The radius of the small circle r = 3 cm

The radius of the large circle R = 3+4 = 7 cm

The area of the shaded region:

= area of the large circle sector - an area of the small circle sector

= (120/360)[π7²] - (120/360)[π3²]

= 49π/3 - 3π

= 40π/3 square cm or

= 13.34π square cm

Thus, the area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.

Learn more about circle here:

brainly.com/question/11833983

#SPJ1

5 0

2 years ago

2.) Which expression has a value of -4?<br> A. (-4) B. |-4| C. |4|<br> D. -|4|

Liono4ka [1.6K]

Answer:

A and D both have a value of -4

Step-by-step explanation:

A. (-4) = -4

B. |-4| = positive value of what is inside = 4

C. |4| = positive value of what is inside = 4

D. -|4| = -positive value of what is inside = -4

5 0

3 years ago

Read 2 more answers

To determine the price of servicing a car, a

Serggg [28]

Answer:

Hey there!

We can write this equation, where x is the hourly rate and y is the fixed fee.

4x+y=270

7x+y=420

4x+y=270

-7x-y=-420

-3x=-150

x=50

4(50)+y=270

200+y=270

y=70.

The fixed fee is G. $70.

Let me know if this helps :)

7 0

4 years ago

Read 2 more answers

Darren wants to estimate the mean age in a population of trees. He'll sample nnn trees and build a 90\%90%90, percent confidence

Alchen [17]

Using the z-distribution, as we have the standard deviation for the population, it is found that the smallest sample size required to obtain the desired margin of error is of 77.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

The margin of error is given by:

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

In this problem, we have that the parameters are given as follows:

$M = 3, z = 1.645, \sigma = 16$ .

Hence, solving for n, we find the sample size.

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

$3 = 1.645\frac{16}{\sqrt{n}}$

$3\sqrt{n} = 1.645 \times 16$

$\sqrt{n} = \frac{1.645 \times 16}{3}$

$(\sqrt{n})^2 = \left(\frac{1.645 \times 16}{3}\right)^2$

$n = 76.97$

Rounding up, the smallest sample size required to obtain the desired margin of error is of 77.

More can be learned about the z-distribution at brainly.com/question/25890103

4 0

2 years ago

A function $f$ has a horizontal asymptote of $y = -4,$ a vertical asymptote of $x = 3,$ and an $x$-intercept at $(1,0).$ Part (a

Masja [62]

1. $f$ has a horizontal asymptote at $y=-4$

This means that

$\displaystyle\lim_{x\to\pm\infty}f(x)-(-4)=0$

(for at least one of these limits)

2. $f$ has a vertical asymptote at $x=3$

This means that $f$ has a non-removable discontinuity at $x=3$ . Since $f$ is some rational function, there must be a factor of $x-3$ in its denominator.

3. $f$ has an $x$ -intercept at (1, 0)

This means $f(1)=0$ .

(a) With

$f(x)=\dfrac{ax+b}{x+c}$

the second point above suggests $c=-3$ . The first point tells us that

$\displaystyle\lim_{x\to\pm\infty}\frac{ax+b}{x-3}+4=0=\lim_{x\to\pm\infty}\frac{ax+b+4x-3}{x-3}=0$

In order for the limit to be 0, the denominator's degree should exceed the numerator's degree; the only way for this to happen is if $a=-4$ so that the linear terms vanish.