Can someone please help?? I know how to get this problem started but I can't seem to do the entire thing. Thank you.

Whole numbers are written on cards and then placed in a bag. Pilar selects a single card, writes down the number, and then place

tatuchka [14]

Answer:

The answer is A (i just took the test)

Step-by-step explanation:

Answer: The outcomes do not appear to be equally likely, so a uniform probability model is not a good model to represent probabilities in Pilar's experiment

The outcomes are: 1 2 3 4 5

The Relative Frequency: 0.05 0.35 0.26 0.13 0.21

As you can see the outcomes do not appear to be equally likely since 0.05 and 1 are not close in number range along with the other options

6 0

2 years ago

Read 2 more answers

Let a and b be two positive numbers. If 2a + 3b=6 then the maximum product of these a and b is:

VikaD [51]

Answer:

a= 3/2

b= 1

a*b= 3/2

Step-by-step explanation:

For getting this problem we need to think in terms of only one unknown. Lets start by looking at our equation:

2a + 3b=6

No, we need to see what happens to a*b. Lets get the value of one of these unknowns in terms of the other, this is, a in terms of b or b in terms of a. Here, I will get a in terms of b (if you like, do the other way and compare):

2a + 3b=6

Subtract 3b in both sides:

2a = 6 - 3b

Now divide both sides by 2 to get a alone:

a = (6 - 3b)/2

a = 3 - 3/2 b

Now lets try to multiply a by b, using this a we found above:

a*b = (3 - 3/2 b)*b

Using distributive:

a*b = 3b - 3/2 b^2

So, we have an expression for a*b that depends only on b. Notice that this expression is a parabola with negative coefficient on the square term, what makes it a negative parabola that MUST have a maximum value. So, we have an expression for a*b that can be maximized, so we can find the maximum of a*b by the derivative of the expression. Lets derive in b:

(3b - 3/2 b^2)' = (3b)' - (3/2 b^2)' = 3 - 3b

So, the derivative equal to 0 gives us the maximum:

3 - 3b = 0

Suming 3b in both sides:

3 = 3b

Dividing by 3:

1 = b

So, we maximize our expression a*b when b is equal to 1. Now, we can replace it on a = 3 - 3/2 b to find b:

a = 3 - 3/2(1) = 3 - 3/2 = 3/2

Thus, a is equal to 3/2 and the product a*b is maximized when:

a = 3/2

b = 1

And the product is a*b= (3/2) * 1 = 3/2

5 0

2 years ago

Use Gauss's Law to find the charge contained in the solid hemisphere x2 + y2 + z2 ≤ a2, z ≥ 0, if the electric field is E(x, y,

Anit [1.1K]

Answer: $\frac{16}{3}$ π $a^{3}$ . 

Given:

$x^{2}+y^{2}+z^{2} \leq a^{2}, z \geq 0$

Using Gauss's Law = ∫∫s E ·dS

= ∫∫∫ div E dV,

⇒ Divergence (Gauss') Theorem

= ∫∫∫ (1+1+6) dV

= 8×(volume of the hemisphere, radius "a")

= 8× ( $\frac{1}{2}$ )(4/3)π $a^{3}$

= $\frac{16}{3}$ π $a^{3}$ . 

6 0

2 years ago

A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s.

Alex777 [14]

Answer:

$Sequence = 120$

Step-by-step explanation:

Given

6 rolls of a die;

Required

Determine the possible sequence of rolls

From the question, we understand that there were three possible outcomes when the die was rolled;

The outcomes are either of the following faces: 1, 2 and 3

Total Number of rolls = 6

Possible number of outcomes = 3

The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;

$Sequence = \frac{6!}{3!}$

$Sequence = \frac{6 * 5 * 4* 3!}{3!}$

$Sequence = 6 * 5 * 4$

$Sequence = 120$

Hence, there are 120 possible sequence.

7 0

2 years ago

Find the length of side AB Give answer to 3 significant figures

Rina8888 [55]

Answer:

AB = 8.857 cm

Step-by-step explanation:

Here, we are given a right angle $\triangle ABC$ in which we have the following things:

$\angle A = 90 ^\circ\\\angle C = 41 ^\circ\\\text{Side }BC = 13.5 cm$

Side BC is the hypotenuse here.

We have to find the side AB.

Trigonometric functions can be helpful to find the value of Side AB here.

Calculating $\angle B$ :

Sum of all the angles in $\triangle ABC$ is $180^\circ$ .

$\Rightarrow \angle A + \angle B + \angle C = 180^\circ\\\Rightarrow 90^\circ + \angle B + 41^\circ = 180^\circ\\\Rightarrow \angle B = 49^\circ$

We know that cosine of an angle is:

$cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\Rightarrow cos B = \dfrac{AB}{BC}\\\Rightarrow cos 49^\circ = \dfrac{AB}{13.5}\\\Rightarrow AB = 13.5 \times 0.656\\\Rightarrow AB = 8.857 cm$

So, side AB = 8.857 cm .

6 0

1 year ago