What is the range of this box plot? Select one: 9 4 6 7

The probability distribution for the random variable x follows. x f(x) 20 0.20 25 0.15 30 0.30 35 0.35 (a) Is this probability d

Damm [24]

Answer:

(a) The probability distribution is valid.

(b) The probability that x = 30 is 0.30.

Step-by-step explanation:

The probability distribution of the random variable X is:

x: 20 | 25 | 30 | 35

f (x): 0.20 | 0.15 | 0.30 | 0.35

(a)

The properties of a probability distribution are:

0 ≤ P (X) ≤ 1
∑ P (X) = 1

All the probability value are more than 0 and less than 1.

Compute the sum of all the probabilities as follows:

$\sum P(X)=0.20+0.15+0.30+0.35=1$

The sum of all probabilities is 1.

Thus, the probability distribution is valid.

(b)

Consider the probability distribution table.

The probability of X = 30 is,

P (X = 30) = 0.30.

Thus, the probability that x = 30 is 0.30.

6 0

4 years ago

You are laying a concrete border around a circular pond ...The pond is 7 meters in diameter and is surrounded by a path 2 metres

nasty-shy [4]

Answer:

300 bags of 20 kg of premixed are required.

Step-by-step explanation:

Given:

diameter of pond 'd'= 7 m (given)

radius of inner border of pond 'r'= d/2= 7/2 m

The radius of outer circular border 'R'= r+2= 7/2+2= 11/2m

Area of concrete border around the circular pond= area of outer circle- area of inner circle

So, $\pi\times R^2-\pi\times r^2= \pi\times (R^2-r^2)$

=> 22/7 x ((11/2)²-(7/2)²)

=> 22/7 x (121/4-49/4)

=> $\frac{22}{7} \times \frac{72}{4}$

=> 56.57 m²

volume of concrete needed= area x height= 56.57 x 0.05= 2.8285 cubic meter

Since 1 cube meter requires 106 x 20 kg bags,

2.8285 cubic meters require bags= 2.8285x106x20 kg

20 kg bags of premixed concrete required= 2.8285x106x20/20

=> 2.8285x106

=> 299.821 or 300 approximately

5 0

4 years ago

Dr.Patterson just started an experiment .she will collect data for 8 days .How many hours is this

Allushta [10]

Answer:

192h

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Estimate the product by rounding In 2 times 6.254

Nadusha1986 [10]

Well it would equal 12.508 so, 13 I guess.

8 0

4 years ago

Could you make proof of "a > b" please ?

Sergio039 [100]

Answer:

See explanation

Step-by-step explanation:

Consider the first triangle:

1. From the right triangle with acute angle $\theta_1:$

$\dfrac{c}{h}=\tan\theta_1\Rightarrow c=h\tan\theta_1$

2. From the right triangle with acute angle $\alpha:$

$\dfrac{c+a}{h}=\tan\alpha\Rightarrow c+a=h\tan\alpha$

Thus,

$h\tan\theta_1+a=h\tan\alpha\Rightarrow a=h\tan\alpha-h\tan\theta_1$

Consider the second triangle:

1. From the right triangle with acute angle $\theta_2:$

$\dfrac{d}{h}=\tan\theta_2\Rightarrow d=h\tan\theta_2$

2. From the right triangle with acute angle $\beta:$

$\dfrac{d+b}{h}=\tan\beta\Rightarrow b+d=h\tan\beta$

Thus,

$h\tan\theta_2+b=h\tan\beta\Rightarrow b=h\tan\beta-h\tan\theta_2$

Now, since $\alpha>\beta,$ we have $\tan\alpha>\tan\beta$ and $\sin\alpha>\sin\beta.$

If

$\dfrac{\sin\alpha}{\sin\theta_1}=\dfrac{\sin\beta}{\sin\theta_2}$

and

$\sin\alpha>\sin\beta,$

then

$\sin\theta_1>\sin\theta_2.$

This means $\theta_1>\theta_2$ and $\tan\theta_1>\tan \theta_2.$

Hence,

$h\tan\theta_1>h\tan \theta_2\\ \\-h\tan\theta_1$

Now,

$h\tan\beta$

and

$-h\tan\theta_1$

so

$h\tan\beta-h\tan\theta_1$

Note that this solution is true only for acute angles $\alpha,\ \beta,\ \theta_1,\ \theta_2$

6 0

3 years ago