Answer:
Step-by-step explanation:
Perimeter of rectangle = 208 m
2*(l + w) = 208 {divide both sides by 2}
l +w = 208/2
l +w = 104
l = 104 - w
Area of rectangle = 2415 square meters
l*w = 2415
Substitute l = 104 - w in the above equation,
(104 - w ) *w = 2415
104w - w² = 2415
0 = 2415 - 104w + w²
w² - 104w + 2415 = 0
Sum = -104
Product = 2415
Factors = (-69) , (-35)
w² - 35w - 69w + (-69)*(-35) = 0
w(w - 35) - 69(w - 35) = 0
(w -35)(w -69)
w - 35 = 0 ; w -69 = 0
w = 35 ; w = 69
The dimensions of the building: 35 , 69
Answer:
20, 30
Step-by-step explanation:
let the intergers be x and y
x = 2/3y
from this eqn, we know that y is larger.
hence, y-x=10
y-2/3y=10
1/3y=10
y=30
x=2/3y =2/3(30) = 20
Answer:
Null hypothesis: 
Alternative hypothesis: 
Step-by-step explanation:
For this question we need to take in count that the the claim that they want to test is "if the proportion is greater than 0.3". Our parameter of interest for this case is 
and the estimator for this parameter is given by this statistic 
obtained from the info of sa sample obtained.
The sample proportion would be given by:
Where X represent the success and n the sample size selected
The alternative hypothesis on this case would be specified by the claim and the complement would be the null hypothesis. Based on this the system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
And in order to check the hypothesis we can use the one sample z test for a proportion with the following statistic:
Answer:
Associative property
Step-by-step explanation:
This property states that when three or more numbers are added (or multiplied), the sum (or the product) is the same regardless of the grouping of the addends (or the multiplicands).
eg. a+(b+c) is same as (a+b)+c
