Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi. (4 points)
2 answers:
Answer:
The circumference of a circle is and the area of a circle is
.
Option (c) is correct .
Step-by-step explanation:
Formula
Where r is the radius of a circle .
As given
Diameter is 10 inches.
Radius = 5 inches
Put values in the above formulas .
Therefore the circumference of a circle is and the area of a circle is
.
Option (c) is correct .
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Answer:
A. x = 11/16
Step-by-step explanation:
For the purpose here, it is convenient to rearrange the equation to f(x) -g(x) = 0. We know the root will be in the interval [0, 1] because (f-g)(0) = -3 and (f-g)(1) = +3. At each iteration, we evaluate (f-g)(x) at the midpoint of the interval to see which of the interval end points can be moved and still bracket the root.
Using the bisection method starting with the interval [0, 1] we find f(1/2)-g(1/2) < 0, so we can move the interval limits to [1/2, 1].
For the next iteration, we find f(3/4) -g(3/4) > 0, so we can move the interval limits to [1/2, 3/4].
For the third iteration, we find f(5/8) -g(5/8) < 0, so we can move the interval limits to [5/8, 3/4].
Then the root is approximately the middle of that interval:
x ≈ (5/8 +3/4)/2 = 11/16
_____
This value of x is 0.6875. The root is closer to 0.639802004233. The bisection method takes about 3 iterations for each decimal place of accuracy. Other methods can nearly double the number of accurate decimal places on each iteration.
Answer:
Step-by-step explanation:
Hello!
<em>The table shows the daily sales (in $1000) of shopping mall for some randomly selected days </em>
<em>Sales 1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 3.1-3.5 3.6-4.0 4.1-4.5 </em>
<em>Days 18 27 31 40 56 55 23 </em>
<em>Use it to answer questions 13 and 14. </em>
<em>13. What is the approximate value for the modal daily sales? </em>
To determine the Mode of a data set arranged in a frequency table you have to identify the modal interval first, this is, the class interval in which the Mode is included. Remember, the Mode is the value with most observed frequency, so logically, the modal interval will be the one that has more absolute frequency. (in this example it will be the sales values that were observed for most days)
The modal interval is [3.1-3.5]
Now using the following formula you can calculate the Mode:
Li= Lower limit of the modal interval.
c= amplitude of modal interval.
fmax: absolute frequency of modal interval.
fprev: absolute frequency of the previous interval to the modal interval.
fpost: absolute frequency of the posterior interval to the modal interval.
<em>A. $3,129.41 B. $2,629.41 C. $3,079.41 D. $3,123.53 </em>
Of all options the closest one to the estimated mode is A.
<em>14. The approximate median daily sales is … </em>
To calculate the median you have to identify its position first:
For even samples: PosMe= n/2= 250/2= 125
Now, by looking at the cumulative absolute frequencies of the intervals you identify which one contains the observation 125.
F(1)= 18
F(2)= 18+27= 45
F(3)= 45 + 31= 76
F(4)= 76 + 40= 116
F(5)= 116 + 56= 172 ⇒ The 125th observation is in the fifth interval [3.1-3.5]
Li: Lower limit of the median interval.
c: Amplitude of the interval
PosMe: position of the median
F(i-1)= accumulated absolute frequency until the previous interval
fi= simple absolute frequency of the median interval.
<em>A. $3,130.36 B. $2,680.36 C. $3,180.36 D. $2,664</em>
Of all options the closest one to the estimated mode is C.