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notsponge [240]

3 years ago

13

A number cube with the numbers 1 through 6 is rolled. What is the theoretical probability, as a decimal, of the number cube show

ing a 3? Round the decimal to the nearest hundredth.

2 answers:

mixer [17]3 years ago

6 0

Answer:

The probability of the number cube showing a 3 = 0.1667

Step-by-step explanation:

A number cube with the numbers 1 through 6 is rolled.

So, The numbers which are marked on the cube : 1, 2, 3, 4, 5, 6

Total no. of numbers which are marked on the number cube = 6

No. of times the number cube is rolled = 1

We need to find the theoretical probability, as a decimal, of the number cube showing a 3.

Therefore, The probability of the number cube showing a 3 is given by :

$\text{Probability = }\frac{\text{No. of favorable outcomes}}{\text{Total no. of possible outcomes}}\\\\\implies\text{Probability = }\frac{1}{6}\\\\\implies \text{Probability }\approx =0.1667$

Zina [86]3 years ago

4 0

The theoretical probability of rolling a three would be 1/6.
1/6 expressed as a decimal would be 0.17.

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Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$ is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4}$

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

7 0

2 years ago

Can someone please awnser this for me i need to get a b in this class!!!!

Snezhnost [94]

The answer would be 30%

Explanation~

Well, you would have to add 27 and 23 first since, it says, “What percentage of the twelfth grade students have more than one college in mind” then, you’d have to figure out the percentage from there. And the percentage would be, 29.4117647059% of 170, round that to the nearest percent and it’s 30 I’m pretty sure.

3 0

3 years ago

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Ratling [72]

Answer:

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3 years ago

If “x” represents the full price of an item, write an expression to represent the final cost of an item that is 20% off.

zloy xaker [14]

The expression is x -20%

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3 years ago

Convert these please

Nezavi [6.7K]

Answer:

22.18mL
147.42kg
---
637.14 lbs
15.22mL
--
104 oz
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45.44 lbs
3.59 pt
43,000 mg
105 tsp
2,271.25 mL
18tsp
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219.99 kgs
3.79 L
3.96 g
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145.4 tbsp
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3 years ago