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3 years ago

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Shawn's Breakfast Goodies recently sold 3 blueberry muffins and 3 other muffins. What is the experimental probability that the n

ext muffin sold will be a blueberry muffin?

1 answer:

katovenus [111]3 years ago

3 0

Answer:

The experimental probability can be expressed in three ways:

Fraction Form: 3/6 or 1/2

Decimal Form: 0.5

Percent Form: 50%

Step-by-step explanation:

Experimental probability is expressed as:

<em>(Favorable outcomes) / (Total outcomes)</em>

The favorable outcome in this situation is blubbery muffins. There were 3 blueberry muffins sold, so this is the <u>numerator</u> of our fraction.

To find the total outcomes we add 3 + 3, which equals 6. This will be the <u>denominator</u> of our fraction.

The fraction used to express experimental probability will look like this: 3/6

We can further simplify this to 1/2.

3 ÷ 3 = 1

6 ÷ 3 = 2

To find a decimal, we divide 1 ÷ 2 = 0.5

Multiply this by 100 to get a percentage, 0.5 x 100 = 50%

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The flagpole in front of VHS 50 feet tall. The angle of elevation from the end of its shadow to the top of the flagpole is 46°.

mamaluj [8]

Answer:

The length of the shadow is 48.28 feet.

Step-by-step explanation:

The flagpole at its shadow form a 46, 44, 90 triangle.

Let AB be the flagpole. AC is the shadow.

Let's use the sine law to calculate AC.

$\frac{AC}{sin(44)}=\frac{50}{sin(46)}\\AC=\sin(44)*\frac{50}{sin(46)}AC=48.28$

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3 years ago

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aliya0001 [1]

Answer:

$3x^{4}$

Step-by-step explanation:

I suggest looking lessons on it online if you don't understand... It's hard to do your work especially if you don't understand it. Or if your online, go to past lessons or something.

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Read 2 more answers

Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation

Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}$

$\Rightarrow x^{2}+y^{2}+z^{2}=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^{2}+z^{2}=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^{2}+(y-b)^{2}=p^{2}$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^{2}+y^{2}=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1$

$\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1$

$\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1$

$\Rightarrow \rho^{2} sin^{2}\phi=1$ (As $sin^{2}\theta+cos^{2}\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.

Thus, we can square root both sides and only consider the positive root as,

$\Rightarrow \rho sin\phi=1$

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is $r^{2}+z^{2}=25$

(b) The equation of the given cylinder in spherical coordinates is $\rho sin\phi=1$

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konstantin123 [22]

Answer:

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Step-by-step explanation:

complementary angles are two angles that add up to 180 degrees

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telo118 [61]

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Step-by-step explanation:

V represents volume and r represents radius

So V(r) represents the volume of the basketball with respect to radius

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