Answer:
21 feet
Step-by-step explanation:
You could either do
3 + 3 + 3 + 3 + 3 + 3 + 3 = 21
or
3 x 7 = 21
Answer:
a) w = 8; y = 5.25
b) x = 10; z = 7.2
Step-by-step explanation:
a) Dimensions on the smaller figure are FA/F'A' = 3/4 times those on the larger figure.
6 = (3/4)w
w = 24/3 = 8
y = (3/4)·7 = 21/4 = 5.25
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b) Dimensions on the smaller figure are ER/E'R' = 9/15 = 3/5 times those on the larger figure.
6 = (3/5)x
x = 30/3 = 10
z = (3/5)12 = 36/5 = 7.2
Answer:
40 ft²
Step-by-step explanation:
Let the length of the original rectangle be L and original Breadth be B
it is given that the original area is 5/8 ft²
i.e.
Original Length x Original Breadth = Original Area, or,
LB = 5/8 ft² ------------------(1)
Given that the dilation factor is 8,
Hence,
New Length = 8L and New Breadth = 8B
THerefore,
New Area = 8L x 8B
= 64 LB (from (1) above , we know that LB = 5/8 ft², substitute into expression)
= 64 (5/8)
= 40 ft²
Answer:
1 hour
Step-by-step explanation:
I find these easiest to work by considering the initial difference in distance and the speed at with that gap is closing.
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The gap is 15 miles, the distance the first ship is from harbor when the second ship starts.
The rate of closure is the difference in the speeds of the two ships:
60 mph -45 mph = 15 mph
Then the closure time is ...
time = distance/speed
time = (15 mi)/(15 mi/h) = 1 h
It will take the second ship 1 hour to catch up to the first ship.
Answer:
The probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,

And the standard deviation of the distribution of sample mean is given by,

The information provided is:
<em>μ</em> = 144 mm
<em>σ</em> = 7 mm
<em>n</em> = 50.
Since <em>n</em> = 50 > 30, the Central limit theorem can be applied to approximate the sampling distribution of sample mean.

Compute the probability that the sample mean would differ from the population mean by more than 2.6 mm as follows:


*Use a <em>z</em>-table for the probability.
Thus, the probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.