Which ratio is equivalent to 21:56

Use counting to determine the whole number that corresponds to the cardinality of these sets:______. (a) A= (xl x € Nand 20.<

Harlamova29_29 [7]

Answer:

Step-by-step explanation:

Cardinality of a set is defined as number of element in a set. It is represented as n(X) where X is any set.

a) Given the set A =(x l x € N and 20.< x<27). According to the set, the set contains the values of natural numbers between 20 and 27. The values are 21, 22, 23, 24, 25 and 26

A = (21, 22, 23, 24, 25, 26)

According to the set A, it can be seen that there are 6 elements in the set, this means n(A) = 6.

b) Given B=(x | xeN and x+1=x)

Since natural numbers starts from 1, the first element in the set is 2 i.e 1+1

The elements of the set B = (2, 3, 4, 4...)

The number of whole number in the set is therefore infinite.

c) For the set C={x l xe N and (x- 1)(x - 9) = 0)

We need to get the root of the equation (x- 1)(x - 9) = 0

x-1 = 0 and x-9 = 0

x = 1 and x = 9

Hence the element C = (1,9)

The number of whole number in the set is n(C) = 2

d) D={xlx E N, H X 5 100, and x is divisible by both 5 and 8)

Given the value of x between 5 and 100, the values of x divisible by 5 = (10, 15, 20, 25, 30, 35, 40, 45, 50 , 55, 60 , 65, 70, 75, 80 85, 90, 95)

values of x divisible by 8 = (16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96)

The total number of elements in both set = 29 i.e n(D) = 29

3 0

4 years ago

You borrow $600. You pay 5% interest compounded annually. How much do you owe at the end of 4 years?

beks73 [17]

I want to say C, but im not completely positive :/ sorry. C sounds right though. Hope this helps!

7 0

3 years ago

Read 2 more answers

Find the quotient and remainder: 6, 489 ÷ 46 = ?

valentina_108 [34]

The answer to this question is 141 R3.

5 0

3 years ago

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to d

k0ka [10]

Part A:

From the central limit theorem, since the number of samples is large enough (up to 30), the mean of the the mean of the average number of moths in 30 traps is 0.6.

Part B:

The standard deviation is given by the population deviation divided by the square root of the sample size.

$standard \ deviation= \frac{\sigma}{\sqrt{n}} = \frac{0.4}{\sqrt{30}} = \frac{0.4}{5.477} =0.073$

Part C:

The probability that an approximately normally distributed data with a mean, μ, and the standard deviation, σ, with a sample size of n is greater than a number, x, given by

$P(X\ \textgreater \ x)=1-P(X\ \textless \ x) \\ \\ =1-P\left(z\ \textless \ \frac{x-\mu}{\sigma/\sqrt{n}} \right)$

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 given by:

$P(X\ \textgreater \ 0.7)=1-P(X\ \textless \ 0.7) \\ \\ =1-P\left(z\ \textless \ \frac{0.7-0.6}{0.073} \right)=1-P(z\ \textless \ 1.369) \\ \\ =1-0.91455=\bold{0.0855}$

7 0

4 years ago

Consider the function.

Mariana [72]

Answer: (2 1/2, 0) (the last option)

Step-by-step explanation:

I guess the function is:

f(x) = (2 1/2) - (3 1/2)*x

now, the rule for f-1(x) that we know is:

f-1( f(x) ) = x.

So if we want to find the x-intercept of f-1(x), we must evaluate it in f(0)

f-1(f(0)) = 0.

And we have that f(0) = (2 1/2) - (3 1/3)*x = 2 1/2

This means that the x-intercept of f-1(x) will be when x= 2 1/2, so the intercept is:

(2 1/2, 0)

5 0

3 years ago