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3 years ago

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There are 4 boys and 2 girls from the 7th grade and 3 boys and 5 girls from the 8th grade on the soccer team. The coach will pic

k one captain from each grade. What is the probability that he will pick a boy from the 7th grade and a girl from the 8th grade?

1 answer:

kaheart [24]3 years ago

5 0

Answer:

5/12

Step-by-step explanation:

P(b,7) = 4/6

P(g,8) = 5/8

4/6 x 5/8 = 20/48 (or 5/12 reduced)

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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

<em><u>Solution:</u></em>

Let "a" be the length of rectangle

Let "b" be the width of rectangle

Given that,

<em><u>A rectangle has width that is 6 meters less than the length</u></em>

Width = length - 6

b = a - 6

The area of the rectangle is 280 square meters

<em><u>The area of the rectangle is given by formula:</u></em>

$Area = length \times width$

<em><u>Substituting the values we get,</u></em>

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

<em><u>Solve the above equation by quadratic formula</u></em>

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

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

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

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

<em><u>Thus solution of length is a = 20</u></em>

Therefore,

width = length - 6

width = 20 - 6 = 14

Thus dimensions are length 20 meter and width 14 meter

6 0

3 years ago

The diameter of a cylinder is 4 centimeters. The height is 12 centimeters. Using 3.14 for pi, what is the volume of the cylinder

erica [24]

Answer:

V = 150.72 cm³.

Step-by-step explanation:

First, get the volume of a cylinder.

V = πr²h

Where:

π = 3.14 (given)

r = radius (half of diameter, or 2)

h = height (12)

Knowing this, substitute the known values.

V = πr²h

V = (3.14)(2²)(12)

Square 2.

V = (3.14)(4)(12)

Multiply 3.14 and 4.

V = (12.56)(12)
Multiply 12.56 and 12.

V = 150.72.

Since it is already rounded to the nearest hundredth, that is your answer.

7 0

2 years ago

Simplify: 0.9(2b-1)-0.5b+1

Nutka1998 [239]

Answer:

Step-by-step explanation:

0.9*2b = 1.8b

0.9*-1 = -0.9

So far we have 1.8b-0.9. It can't be simplified further.

Then, we add the 2nd part, -0.5b+1.

We have:

1.8b-0.9-0.5b+1. Next we combine like terms.

1.8b-0.5b = 1.3b.

-0.9+1 = 0.1

Then we put it together.

1.3b+0.1 is our answer.

Hope this helped! Have a nice day :D

5 0

2 years ago

Read 2 more answers

Estimate the quotient 63.5 dividend by 5

Contact [7]

The estimate is twelve because five goes into sixty roughly twelve times.

3 0

2 years ago

(with steps please) Find the inverse Laplace transform, f(t), of the function: s/((s^2+9)*(s^2+16))

sveta [45]

Answer:

Step-by-step explanation:

Given is a Laplace transform of f(t) as

$F(s) = \frac{s}{(s^2+9)(s^2+16)}$

Let

$\frac{s}{(s^2+9)(s^2+16)}=\frac{As+B}{(s^2+9)}+\frac{Cs+D}{(s^2+16)}$

Solving we get $\:s=s^3\left(A+C\right)+s^2\left(B+D\right)+s\left(16A+9C\right)+\left(16B+9D\right)$

$A+C=0: B+D=0: 16A+9C=1 and 16B+9D=0$

Solving B=0=D

$A=\frac{1}{7} \\C=\frac{-1}{7}$

Hence we have

f(t) = inverse Laplace of

$\frac{1}{7}[ \frac{s}{(s^2+9)}-\frac{s}{(s^2+16)}]$

= $\frac{1}{7} (cos 3t-cos 4t)$

4 0

3 years ago