Choose the function whose graph is given by:

Answer:

P(0) = 0.6825

P(1) = 0.2607

Step-by-step explanation:

Based on the provided data, there were 107 homicide incidents and a total of 280 city-years recorded.

Let us denote the variable representing homicides per city-year as X.

The mean value of X can be calculated with the following formula:

\begin{array}{c}\\{\rm{Mean}} = \frac{{107}}{{280}}\\\\ = 0.382\\\end{array}

Mean=   107/280 = 0.382

The average number of homicides per city-year \left( {\lambda = \mu } \right)(λ=μ) is 0.382.

a. To find the probability of no homicides occurring:

\begin{array}{c}\\P\left( {X = 0} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^0}}}{{0!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {\rm{1}} \right)}}{1}\\\\ = 0.6825\\\end{array}

P(X=0) =  e  −0.382  (0.382)⁰​/1

= (0.6825)(1) /1

P(X=0) = 0.6825

Thus, the chance of experiencing zero homicides P(0) is 0.6825.

b. To determine the probability of one homicide occurring:

\begin{array}{c}\\P\left( {X = 1} \right) = \frac{{{e^{ -0.382}}{{\left( {0.382} \right)}^1}}}{{1!}}\\\\ = \frac{{\left( {0.6825 \right)\left( {0.382} \right)}}{1}\\\\ = 0.2607\\\end{array}

P(X=1) =  e  −0.382  (0.382)¹​/1

= (0.6825)(0.382)/1

P(X=1) = 0.2607

Thus, the probability of having one homicide P(1) is 0.2607.

​

To solve this problem, we need to convert the measurements so we can carry out the necessary calculations. A ton equals 2000 pounds, therefore, 3/4 ton translates to 1500 pounds. Since there are 16 ounces in a pound, 4 pounds and 14 ounces amounts to 4.875 pounds. To find the number of bricks, we divide:
                                     number of bricks = 1500 lbs / 4.875 lbs
                                                            = 307.7

Consequently, this is the number of bricks required. The final answer is approximately.

Response:

PQ's slope is 0

MN's slope equals infinity

The lines PQ and MN are perpendicular to one another

Detailed explanation:

For two points in the coordinate plane, denoted as (x1, y1) and (x2, y2), the slope is determined as follows:

If a line has a slope of zero, it runs parallel to the X-axis and stands perpendicular to the Y-axis

If a line's slope is infinite, it is parallel to the Y-axis and perpendicular to the X-axis

Moreover, it is established that X and Y are perpendicular to each other.

As PQ's slope is zero, it runs parallel to the X-axis and perpendicular to the Y-axis

With MN having an infinite slope, it runs parallel to the Y-axis and perpendicular to the X-axis.

Therefore, lines PQ and MN are indeed perpendicular.

This can be expressed using the general formula for a² – b².

Answer:

                          π

V-foam = 4r³( 2 - ----- )

                             3

Step-by-step explanation:

Let r denote the radius of the sphere. The volume of the sphere is expressed as

V = (4/3)(π)(r³).

Next, understand that the cube's side length is 2r, hence the cube's volume is

V = (2r)³, which equals 8r³.

The volume of the foam is derived from the cube's volume subtracting that of the sphere:

V-foam = 8r³ - (4/3)(π)(r³). This can be simplified to

                          π

V-foam = 4r³( 2 - ----- )

                             3