Exponents are hard but think about it like addition, that number tells you how many times to add that number to itself. To write the equation put the number and then the exponent on the top right of that number. Your welcome!
Answer:
Yes, both np and n(1-p) are ≥ 10
Mean = 0.12 ; Standard deviation = 0.02004
Yes. There is a less than 5% chance of this happening by random variation. 0.034839
Step-by-step explanation:
Given that :
p = 12% = 0.12 ;
Sample size, n = 263
np = 263 * 0.12 = 31.56
n(1 - p) = 263(1 - 0.12) = 263 * 0.88 = 231.44
According to the central limit theorem, distribution of sample proportion approximately follow normal distribution with mean of p = 0.12 and standard deviation sqrt(p*(1 - p)/n) = sqrt (0.12 *0.88)/n = sqrt(0.0004015) = 0.02004
Z = (x - mean) / standard deviation
x = 22 / 263 = 0.08365
Z = (0.08365 - 0.12) / 0.02004
Z = −1.813872
Z = - 1.814
P(Z < −1.814) = 0.034839 (Z probability calculator)
Yes, it is unusual
0.034 < 0.05 (Hence, There is a less than 5% chance of this happening by random variation.
Answer:
<h2>
25metres</h2>
Step-by-step explanation:
Given the area of the garden in terms of the width modeled by the equation A(x) = -(x-25)²+625 where x is the width of the garden. The side with that will produce the maximum garden area is occurs at when d[A(x)]/dx = 0
Given A(x) = -(x-25)²+625
d[A(x)]/dx =-2(x-25) + 0
Since d[A(x)]/dx = 0
-2(x-25) = 0
open the parenthesis
-2x+50 = 0
-2x = 0-50
-2x = -50
Divide both sides by -2;
-2x/-2 = -50/-2
x = 25metres
<em>Therefore the width of the garden that will produce the maximum garden area is 5metres.</em>
<em></em>
Answer:
a)$15.95
b) 8kg
Step-by-step explanation:
a)Approach this question by finding how much does it cost for 1g
So,
$2.1/50=$0.042per gram
then, multiple 380 to get the cost of sweets for 380 g
$0.042/gram*380gram=$15.96(Note: the gram cancel out each other)
Which is $15.95 as the question requested
b)This question stated that 3/4 of the metal has 15 kg
So, in order to find the total mass of metal we invert the 3/4 fraction
e.g 4/3*15=20kg
now we have the total mass we can find the mass for 2/5 of the metal
2/5*20kg=8kg
