Answer:
a) Null hypothesis:
Alternative hypothesis:
b) 
(1)
Where 
c) 
d) In this scenario, we notice that 
thus the conclusion for this case would indicate
Step-by-step explanation:
Information provided
denote the number of men possessing smartphones
signify the number of women possessing smartphones
group of men sampled
group of women sampled
symbolize the proportion of men with smartphones
symbolize the proportion of women with smartphones
denote the pooled estimate of p
z would denote the test statistic
signify the value
Part a
The objective is to evaluate if there is a disparity in smartphone ownership between men and women; the hypothesis statements would be:
Null hypothesis:
Alternative hypothesis:
Part b
The statistic relevant to this case is expressed as:
(1)
Where
Part c
By substituting the provided information, we find:
Part d
In this instance, it is evident that thus the conclusion for this case would seem
Solution Procedure
Considering the spool as a cylindrical shape, and calculating the circumference based on the area cited, we establish the connection between circumference and area as follows:
... C = 2√(πA)
To find ten times this circumference, we calculate:
... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm
Derivation of Formulas
The standard formulas for circumference and area are:
... C = 2πr
... A = πr²
Multiplying the area formula by π and extracting the square root yields:
... πA = (πr)²
... √(πA) = πr
Doubling this value results in the circumference formula:
... C = 2√(πA) = 2πr
Honestly, I find Mrs. Garcia's method easier to perform mentally. It hinges on how familiar you are with your multiples of 5. (5*15 = 75 is a multiplication I often use)
Melissa's approach involves calculating 5*20 = 100 and 5*9 = 45, then combines the 3-digit result 100 with the 2-digit result 45, yielding 145. Adding 45 to 00 is simple and doesn’t require carrying digits, thus the arithmetic is fairly straightforward.
Mrs. Garcia's technique involves computing 5*14 = 70 and 5*15 = 75, then summing these two-digit results. Many people may not readily recall that 5*15=75, which complicates forming that product. The addition of 70 and 75 requires a carrying operation, making the math somewhat more complex. The resulting total is 145.
(The rationale behind my preference for Mrs. Garcia's method is that I can achieve the final sum by simply doubling 7 tens, followed by adding 5. The only 3-digit number to remember mentally is the ultimate total.)
_____Subtraction introduces a slight complication, yet reshaping it as $5(30 -1) = $150 - 5 = $145 is possible.
Or, you may reframe it as $5(28 +1) = $140 +5 = $145.
Dividing an even number by 2 to find the product of 5 is straightforward when you append a zero.
5*14 = 10*7 = 70
5*28 = 10*14 = 140.
Her phrasing suggests that she would sell numerous water bottles and just a single iced tea. The accurate equation should be 1.25x + 1.49y = 100, as she may offer varying quantities of both.
<span>Denote x as the interval, then:
186 = 50 + 3 + (3+x) + (3+2x) + (3+3x) + (3+4x) + (3+5x) + (3+6x) + (3+7x)
186 = 74 + 28x
x = 4
Age of the eldest son = 3+7x = 3+28 = 31.</span>
