The are of his backyard is 10.4 times 15.83 or 164.632 yd^2
the sod piecs are 1.33 by 1.33 or 1.78 yd^2
so divide 164.632 by 1.78 or
164.632/1.78=92.5 pieces of sod
if he is buying the sod in pieces, he will have to buy 93 pieces because he can't buy 1/2 sod
Remark
Make up a proportion that relates the tree and its properties to the stick and its properties.
Givens
Stick height (s_h) = 4
Stick shadow(s_s) = 2
Tree shadow = t_s = 18
Tree height = x
Formula
s_h / s_s = x / t_s
Substitute and solve.
4/2 = x / 18 Cross multiply
4*18 = 2 * x
72 = 2x Divide by 2
72/2 = x
x = 36
The height of the tree is 36 feet.
The inequality is still true! If you add a number, say 5 to both sides of the following inequality, does anything change?
3 < 6
3 + 5 < 6 + 5
8 < 11
The inequality is still true. We know the statement holds for subtracting the same number because, in a way, addition and subtraction are pretty much the same operation. If I subtract 5 from both sides, I can think of it like "I add negative 5 to both sides" or something along those lines. It's kind of backwards thinking.
Answer:
a) Null hypothesis:
Alternative hypothesis:
b) 
The degrees of freedom are given by:
The p value for this case taking in count the alternative hypothesis would be:
Step-by-step explanation:
Information given
represent the sample mean for the amount spent each shopper
represent the sample standard deviation
sample size
represent the value to verify
t would represent the statistic
represent the p value f
Part a
We want to verify if the shoppers participating in the loyalty program spent more on average than typical shoppers, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic for this case would be given by:
(1)
Replacing the info given we got:
The degrees of freedom are given by:
The p value for this case taking in count the alternative hypothesis would be:
The volume of the candle initially is:
V=Ab*h
Area of the base of the cylinder: Ab=pi*r^2
pi=3.14
Radius of the base: r=4 cm
Height of the cylinder: h=6 cm
Ab=pi*r^2
Ab=3.14*(4 cm)^2
Ab=3.14*(16 cm^2)
Ab=50.24 cm^2
V=Ab*h
V=(50.24 cm^2)*(6 cm)
V=301.44 cm^3
The candle melts at a constant rate of:
r=(60 cm^3)/(2 hours)=(120 cm^3)/(4 hours)=(180 cm^3)/(6 hours)
r=30 cm^3/hour
The amount of candle melted off after 7 hours is:
A=(30 cm^3/hour)*(7 hours)
A=210 cm^3
The percent of candle that is melted off after 7 hours is:
P=(A/V)*100%
P=[(210 cm^3)/(301.44 cm^3)]*100%
P=(0.696656051)*100%
P=69.66560510%
Rounded to the nearest percent
P=70%
Answer: 70%
