The numbers of courses taught per semester by a random sample of university professors are shown in the histogram. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard
deviation of the data set.
Make a frequency distribution for the data.
x f

1 _
2 _
3 _
4 _

Kindly check explanation

Step-by-step explanation:

Given the plot above :

X (f)fxf * x²

1 222

21734___68

32163___189

41664___256

56 163 ___515

Sample mean = Σfx / Σf

Σfx = 163 ; Σf = 56

Hence sample mean = 163 / 56

= 2.91

Standard deviation (s) :

Sqrt[(Σf*x² - (Σfx)²/Σf)) / Σf]

Sqrt [(515 - 474.45) / 56]

= sqrt(40.55 / 56)

= 0.851

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

step-by-step explanation:

given perimeter: 28cm

length: 9cm

atp,

2(l+w)=p of the reactangle

2(9+x)=28

18+2x=28

2x=28-18

x=10/2

x=5

therefore width is 5 cm