Answer:
b= 2 over 7
Step-by-step explanation:
exact form b= 2 over 7
decimal form b= 0.285714
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = mean sale amount for mail order sales = 82.70
x2 = mean sale amount for internet sales = 66.9
s1 = sample standard deviation for mail order sales = 16.25
s2 = sample standard deviation for internet sales = 20.25
n1 = number of mail order sales = 17
n2 = number of internet sales = 10
For a 99% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (17 - 1) + (10 - 1) = 25
z = 2.787
Margin of error =
z√(s²/n1 + s2²/n2) = 2.787√(16.25²/17 + 20.25²/10) = 20.956190
Answer:
The required polynomial is f(x)=
Step-by-step explanation:
Given that polynomial is passing through points (-1,-1) (0,7) ( 1,9) and (2,17)
Let, The required polynomial be f(x)=
For point (-1,-1)
f(x)=
f(-1)=
(-1)a+b-c+d=(-1) Equation 1
For point (0,7)
f(x)=
f(0)=
d=7 Equation 2
For point ( 1,9)
f(x)=
f(1)=
a+b+c+d=9 Equation 3
For point (2,17)
f(x)=
f(2)=
8a+4b+2c+d=17 Equation 4
Replacing value of d of equation 2 in equation 1,3,4
For equation 1:
(-1)a+b-c+d=(-1)
(-1)a+b-c=(-8)
For equation 3:
a+b+c+d=9
a+b+c=2
For equation 4:
8a+4b+2c+d=17
8a+4b+2c=10
Now,
On adding equation 1 and 3
For equation 1: (-1)a+b-c=(-8)
For equation 3: a+b+c=2
((-1)a+b-c)+(a+b+c)=(-8)+2
2b=(-6)
b=(-3)
Replacing value of b in equation 1 and 4:
For equation 1: (-1)a+b-c=(-8)
(-1)a+(-3)-c=(-8)
(-1)a-c=(-5) Equation 4
For equation 4: 8a+4b+2c=10
8a+4b+2c=10
8a+4(-3)+2c=10
8a+2c=22 Equation 5
For value of a and c:
Equation 4 can be write as
(-1)a-c=(-5)
a+c=5
a=5-c
Replacing value of a in equation 5
8a+2c=22
8(5-c)+2c=22
40-8c+2c=22
-6c=-18
c=3
So,
a=5-c=5-3=2
a=2
Thus,
The value of
a=2, b=(-3), c=3 and d=7
The required polynomial is
f(x)=
f(x)=
Answer:
1820 ways
Explanation:
Use combination method. where order does not matter.
: combination formula
Solve:
From the first two inference, it takes her phone 1 minute to charge 2% i.e 1 minute of charge = 2% of battery.
Therefore; charging from scratch,
1 min = 2%
x mins = 50%.
using cross multiplication,
x mins = (50% × 1 min) ÷ 2%.
x = 25 mins.
For 90%, applying the same formula,
y min = (90% × 1 min) ÷ 2%
y = 45 mins.
So from zero percent, it will take Dana's phone 25 minutes to charge to 50% and 45 minutes to charge to 90%.