Length (L): L
width (w): (2/3)L
Perimeter (P) = 2L + 2w
390 = 2(L) + 2(2/3)(L)
1170 = 6L + 4L
1170 = 10L
117 = L
width (w): (2/3)L = (2/3)(117) = 2(39) = 78
Answer: width = 78 ft, length = 117 ft
Answer:
w = 3
Step-by-step explanation:
8 • (w + 2) - 40 = 0
Pulling out like terms :
3.1 Pull out like factors :
8w - 24 = 8 • (w - 3)
Equation at the end of step 3 :
8 • (w - 3) = 0
Step 4 :
Equations which are never true :
4.1 Solve : 8 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.2 Solve : w-3 = 0
Add 3 to both sides of the equation :
w = 3
One solution was found :
w = 3
Processing ends successfully
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Population = 135 students
Mean score = 72.3
Standard deviation of the scores = 6.5
Part (a): Students from 2SD and 3SD above the mean
2SD below and above the mean includes 95% of the population while 3SD includes 99.7% of the population.
95% of population = 0.95*135 ≈ 129 students
99.7% of population = 0.997*135 ≈ 135 students
Therefore, number of students from 2SD to 3SD above and below the bean = 135 - 129 = 6 students.
In this regard, Students between 2SD and 3SD above the mean = 6/2 = 3 students
Part (b): Students who scored between 65.8 and 72.3
The first step is to calculate Z values
That is,
Z = (mean-X)/SD
Z at 65.8 = (72.3-65.8)/6.5 = 1
Z at 72.3 = (72.3-72.3)/6.5 = 0
Second step is to find the percentages at the Z values from Z table.
That is,
Percentage of population at Z(65.8) = 0.8413 = 84.13%
Percentage of population at (Z(72.3) = 0.5 = 50%
Third step is to calculate number of students at each percentage.
That is,
At 84.13%, number of students = 0.8413*135 ≈ 114
At 50%, number of students = 0.5*135 ≈ 68
Therefore, students who scored between 65.8 and 72.3 = 114-68 = 46 students
Do you understand how to solve or do you want me to explain
Total tickets sold = 800
Total revenue = $3775
Ticket costs:
$3 per child,
$8 per adult,
$5 per senior citizen.
Of those who bought tickets, let
x = number of children
y = number of adults
z = senior citizens
Therefore
x + y + z = 800 (1)
3x + 8y + 5z = 3775 (2)
Twice as many children's tickets were sold as adults. Therefore
x = 2y (3)
Substitute (3) into (1) and (2).
2y + y + z = 800, or
3y + z = 800, or
z = 800 - 3y (4)
3(2y) + 8y + 5z = 3775, or
14y + 5z = 3775 (5)
Substtute (4) nto (5).
14y + 5(800 - 3y) = 3775
-y = -225
y = 225
From (4), obtain
z = 800 - 3y = 125
From (3), obtain
x = 2y = 450
Answer:
The number of tickets sold was:
450 children,
225 adults,
125 senior citizens.
