B) Write down an expression for the nth term of the following sequence.

There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If the total nu

Mashcka [7]

Answer:

<h2>There are 9 ducks and 3 swans in the pond.</h2>

Step-by-step explanation:

According to the problem, the number of swans in the pond is equal to the square root of the number of ducks, this can be expressed as

$s=\sqrt{x}$

Where $x$ represents the number of ducks in the pond.

If the total number of swans and ducks is 12, the expression would be

$s+x=12$

Now, we replace the first equation in the second one

$\sqrt{x} +x=12$

Then, we elevate each side to the square power

$\sqrt{x} =12-x\\(\sqrt{x} )^{2} =(12-x)^{2} \\x=144-24x+x^{2} \\x^{2} -25x+144=0$

Using a calculator, the roots are 9 and 16.

Let's evaluate each value.

For $x=9$ , $s=\sqrt{9}=3$ , and $9+3=12$ , which is true.

For $x=16$ , $s=\sqrt{16} =4$ , and $16+4=20$ , which is false.

Therefore, there are 9 ducks and 3 swans in the pond.

7 0

3 years ago

Read 2 more answers

16. From past experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain o

Lynna [10]

Answer:

E(x)=0.15

V(x)=0.3075

S(x)=0.5545

Step-by-step explanation:

The mean of a discrete variable is calculated as:

$E(x)=x_1*p(x_1)+x_2*p(x_2)+...+x_n*p(n)$

where $x_1,x_2,...,x_n$ are the values that the variable can take and $p(x_1),p(x_2),...,p(x_n)$ are their respective probabilities.

So, if we call x the number of defective transistors in cartons, we can calculate the mean E(x) as:

$E(x)=(0*0.92)+(1*0.03)+(2*0.03)+(3*0.02)=0.15$

Because there are 0 defective transistor with a probability of 0.92, 1 defective transistor with a probability of 0.03, 2 defective transistors with a probability of 0.03 and 3 defective transistors with a probability of 0.01.

At the same way, the variance V(x) is calculated as:

$V(x)=E(x^2)-(E(x))^2$

Where $E(x^2)=x_1^2*p(x_1)+x_2^2*p(x_2)+...+x_n^2*p(n)$

So, the variance V(x) is equal to:

$E(x^2)=(0^2*0.92)+(1^2*0.03)+(2^2*0.03)+(3^2*0.02)=0.33\\V(x)=0.33-(0.15)^2\\V(x)=0.3075$

Finally, the standard deviation is calculated as:

$S(x)=\sqrt{V(x)} \\S(x)=\sqrt{0.3075} \\S(x)=0.5545$

8 0

3 years ago

Read 2 more answers

Plz Answer ASAP! Thank you!

NARA [144]

Answer:

Step-by-step explanation:triangle P: 12, 24, and 30

triangle Q: 9, 40, and 41

triangle R: 5, 18, and 21

Which triangle is a right triangle? Explain your reasoning.

3 0

2 years ago

Of the students at Milton Middle School, 88 are girls. If 40% of the students are girls, how many total students are there at Mi

Zolol [24]

Answer:

220

Step-by-step explanation:

To find these types of answers use a calculator my friend. 'Tis so easy, just do

*88/.4 = 220

*must divide to multiply and 44% = .44 =)

8 0

3 years ago

D=xlx is a whole number)

prohojiy [21]

Answer:

Option (4)

Step-by-step explanation:

D = {x| x is a whole number}

D = {1, 2, 3, 4..........}

E = {x | x is a perfect square between 1 and 9}

E = {4}

F = {x | x is an even number greater than 2 and less than 9}

F = {2, 4, 6, 8}

(E ∩ F) = Set of common numbers of E and F

= {4}

D ∩ (E ∩ F} = Set of common numbers in the sets of D and (E ∩ F)

= {4}

Therefore, Option (4) will be the answer.

8 0

3 years ago