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2 years ago

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A teacher has 15 students in his class, 8 girls and 7 boys. He wants to seat them in three rows of five, but knows that if any r

ow has two girls or two boys sitting next to each other, they will talk and won't pay attention. How many seating arrangements can he make that avoid this

1 answer:

andreyandreev [35.5K]2 years ago

5 0

Answer:

609638400

Step-by-step explanation:

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A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice th

icang [17]

Answer:

The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

$D = \sqrt{l^2+w^2}$ ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

$l = 2 \times w$ = 2w

Now, substitute these in [1] we have;

$\sqrt{(2w)^2+w^2} = w+5$

Squaring both the sides we get;

$4w^2+w^2 = (w+2)^2$

$5w^2 = w^2 + 4 + 4w$

or

$5w^2 -w^2 = 4w + 4$ or

$4w^2= 4w + 4$

Simplify:

$w^2-w-1 =0$ ......[2]

The quadratic equation is in the form of $ax^2+bx+c = 0$

the solution is given by: $x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}$

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

$w= \frac{-(-1) \pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$w =\frac{1 \pm\sqrt{1+4}}{2} = \frac{1 \pm\sqrt{5}}{2}$

Simplify:

$w \approx 1.62$ and $w \approx -0.62$

Then, the diagonal D = w+2

For $w \approx 1.62$

$D = 1.62 +2 \approx 3.62$

For $w \approx -0.62$

$D =-0.62 +2 \approx 1.38$

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

5 0

2 years ago

(14.14) larry reads that 1 out of 6 eggs contains salmonella bacteria. so he never uses more than 5 eggs in cooking. if eggs do

melomori [17]

we know that

The probability that "at least one" is the probability of exactly one, exactly 2, exactly 3, 4 and 5 contain salmonella.

The easiest way to solve this is to recognise that "at least one" is ALL 100% of the possibilities EXCEPT that none have salmonella.

If the probability that any one egg has 1/6 chance of salmonella

then

the probability that any one egg will not have salmonella = 5/6.

Therefore

for all 5 to not have salmonella

= (5/6)^5 = 3125 / 7776

= 0.401877 = 0.40 to 2 decimal places

REMEMBER this is the probability that NONE have salmonella

Therefore

the probability that at least one does = 1 - 0.40

= 0.60

the answer is

0.60 or 60%

6 0

2 years ago

Jordan used the distributive property to write an expression that is equivalent to 6c – 48. 6c - 48 is equivalent to 6(c - 48) I

Katyanochek1 [597]

It’s incorrect.

The correct answer is 6(c - 8)

8 0

2 years ago

Read 2 more answers

Jinghua hiked 4 1/2 miles through the woods in 2 1/4 hours. She hiked the return trip at the same average rate but by a differen

Anna007 [38]

Answer:

5 miles.

Step-by-step explanation:

Consider the question: Jinghua hiked 4 1/2 miles through the woods in 2 1/4 hours. She hiked the return trip at the same average rate but by a different route taking 2 1/2 hours. How many miles did Jinghua hike on the return trip ?

First of all, we will find Jinghua's speed using given information as:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Convert mixed fractions into improper fractions:

$4\frac{1}{2}\Rightarrow \frac{9}{2}$

$2\frac{1}{4}\Rightarrow \frac{9}{4}$

$\text{Jinghua's speed}=\frac{\frac{9}{2}\text{ Miles}}{\frac{9}{4}\text{ Hours}}$

Using property $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}$ :

$\text{Jinghua's speed}=\frac{9*4\text{ Miles}}{9*2\text{ Hours}}$

$\text{Jinghua's speed}=\frac{2\text{ Miles}}{\text{ Hour}}$

We know that distance is equal to the product of speed and time.

$\text{Distance}=\text{Speed}\times\text{Time}$

Since we have been given that Jingua hiked the return trip at the same average rate, so distance covered by her on return trip would be speed (2 miles her hour) times given time (2 1/2 hours).

$\text{Distance covered by Jingua on return trip}=\frac{2\text{ Miles}}{\text{ Hour}}\times 2\frac{1}{2}\text{ Hours}$

$\text{Distance covered by Jingua on return trip}=2\text{ Miles}\times \frac{5}{2}$

$\text{Distance covered by Jingua on return trip}=5\text{ Miles}$

Therefore, Jingua hiked 5 miles on her return trip.

8 0

2 years ago

Consider the polynomial: StartFraction x Over 4 EndFraction – 2x5 + StartFraction x cubed Over 2 EndFraction + 1 Which polynomia

Phoenix [80]

Answer:

$- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1$

Step-by-step explanation:

Given

$\frac{x}{4} - 2x^5 + \frac{x^3}{2} + 1$

Required

The standard form of the polynomial

The general form of a polynomial is

$ax^n + bx^{n-1} + cx^{n-2} +........+ k$

Where k is a constant and the terms are arranged from biggest to smallest exponents

We start by rearranging the given polynomial

$- 2x^5+ \frac{x^3}{2} +\frac{x}{4} + 1$

Given that the highest exponent of x is 5;

Let n = 5

Then we fix in the missing terms in terms of n

$- 2x^5+ 0x^{n-1} + \frac{x^3}{2} +0x^{n-3}+\frac{x}{4} + 1$

Substitute 5 for n

$- 2x^5+ 0x^{5-1} + \frac{x^3}{2} +0x^{5-3}+\frac{x}{4} + 1$

$- 2x^5+ 0x^{4} + \frac{x^3}{2} +0x^{2}+\frac{x}{4} + 1$

Hence, the standard form of the given polynomial is $- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1$

3 0

2 years ago