Round each number to the nearest hundredth.

If 6/7 of 28 is divided by 2/9 of 21, what is the quotient?

Alja [10]

Answer: 5.150

Step-by-step explanation:

1. Multiply 28 by 6/7

2. Multiply 21 by 2/9

3. Divide 24 by 4.66

6 0

1 year ago

Which intergers in each pair is greater? a.+12 or -21 b.+17 or -20

Annette [7]

Answer:

b is the answer by solomon

4 0

3 years ago

A particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls invol

Phoenix [80]

Answer:

0.1091 or 10.91%

Step-by-step explanation:

We have been given that a particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls involve fax messages and consider a sample of 20 calls. We are asked to find the probability that exactly 6 of the calls involve a fax message.

We will use Bernoulli's trials to solve our given problem.

$P(X=x)=^nC_x\cdot P^x(1-P)^{n-x}$

$P(X=6)=^{20}C_6\cdot (0.20)^6(1-0.20)^{20-6}$

$P(X=6)=\frac{20!}{6!(20-6)!}\cdot (0.20)^6(0.80)^{14}$

$P(X=6)=\frac{20!}{6!(14)!}\cdot (0.000064)(0.04398046511104)$

$P(X=6)=38760\cdot (0.000064)(0.04398046511104)$

$P(X=6)=0.1090997009730$

$P(X=6)\approx 0.1091\\$

Therefore, the probability that exactly 6 of the calls involve a fax message would be approximately 0.1091 or 10.91%.

4 0

3 years ago

Need this worked out please so I can understand it

Afina-wow [57]

9514 1404 393

Answer:

a) 12

b) y +5 = 12(x +2)

Step-by-step explanation:

The slope of a function is its derivative.

a) The slope of y = x^3 +3 at any point is y' = 3x^2. So, at the point where x=-2, the slope of the curve is ...

m = 3(-2)^2 = 12 . . . . slope at (-2, -5)

__

b) The equation of the tangent line is most easily written using the point-slope form of the equation of a line.

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y +5 = 12(x +2) . . . . line with slope 12 through point (-2, -5)

3 0

3 years ago

A rectangle has width that is 6 meters less than the length. The area of the rectangle is 280 square meters. Find the dimensions

salantis [7]

Dimensions are length 20 meter and width 14 meter

Solution:

Let "a" be the length of rectangle

Let "b" be the width of rectangle

Given that,

A rectangle has width that is 6 meters less than the length

Width = length - 6

b = a - 6

The area of the rectangle is 280 square meters

The area of the rectangle is given by formula:

$Area = length \times width$

Substituting the values we get,

$Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0$

Solve the above equation by quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}$

$a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14$

Since, length cannot be negative, ignore a = -14

Thus solution of length is a = 20

Therefore,

width = length - 6

width = 20 - 6 = 14

Thus dimensions are length 20 meter and width 14 meter

6 0

3 years ago