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3 years ago

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Renee scores an average of 153 points in a game of bowling, and her points in a game of bowling are normally distributed. Suppos

e Renee scores 175 points in a game, and this value has a z-score of 2. What is the standard deviation

1 answer:

drek231 [11]3 years ago

7 0

Answer:

The standard deviation is 11 points

Step-by-step explanation:

To calculated the z-score of a value x, we use the following equation:

$z=\frac{x-m}{s}$

Where m is the mean, s is the standard deviation and z is the z-score.

If we solve this equation for s, we get:

$s=\frac{x-m}{z}$

So, replacing z by 2, m by 153 and x by 175, we get:

$s=\frac{175-153}{2}=11$

Therefore, the standard deviation is 11 points

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Please help i need help on question b

anzhelika [568]

There are 12 possible outcomes.....three of these will be a "7" ...so...

A "7" should occur 1/4 of the time

If each player pays 20p to play.....the school will take in 120 * 20 = 2400p

However.......1/4 of the players should win = 30 players.....and each lollipop costs 30p.....so......the school should spend 30 * 30 = 900p for the prizes

So......the school should raise 2400 - 900 = 1500p if 120 people play the game

3 0

4 years ago

Read 2 more answers

Solve for qqq. 3\left(q+\dfrac43\right) = 23(q+ 3 4 )=2<br>pls answer this

enyata [817]

Answer:

<h2>19/3</h2>

Step-by-step explanation:

Given the expression $3\left(q+\dfrac43\right) = 23$ , we are to find the value of q;

$3\left(q+\dfrac43\right) = 23\\on\ expansion\\\\3q + 4/3(3) = 23\\\\3q+4 = 23\\\\subtract \ 4\ from \ both\ sides \ of \ the \ equation\\\\3q+4-4 = 23-4\\\\3q = 19\\\\Diviide \both\ sides \ by \ 3\\\\3q/3 = 19/3\\\\q = 19/3$

Hence the value of q is 19/3

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3 years ago

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 $\rho sin\phi=1$

7 0

3 years ago

What is the slope of a line perpendicular to the line whose equation is 2x-y=5 ?

mariarad [96]

Answer:

-1/2

Step-by-step explanation:

the slope of the line 2x-y=5 is 2

a perpendicular line has the negative reciprocal of the slope of the other line

hopefully this helps :)

3 0

3 years ago

Find the ordered pair that makes both the equations below true

NNADVOKAT [17]

Answer:

(3, 1)

Step-by-step explanation:

(a) Algebraic solution

(1) y = -⅔x + 3

(2) y = 2x - 5

Set Equation (1) equal to Equation (2)

-⅔x + 3 = 2x - 5

Multiply each side by 3

-2x + 9 = 6x - 15

Add 15 to each side

-2x + 24 = 6x

Add 2x to each side

24 = 8x

Divide each side by 3

(3) x = 3

Substitute (3) into (2)

y = 2×3 - 5 = 6 - 5 = 1

The ordered pair that makes both equations true is (3, 1).

(b) Graphical solution

In the diagram below, the red line is the graph of Equation (1). The blue line is the graph of Equation (2). The point of intersection is at (3, 1).

7 0

3 years ago