Answer:
The cumulative frequency table displays the scores that some students achieved in a test. (a) Create a cumulative frequency graph based on this data on the grid provided. [2]...
Step-by-step explanation:
Solution Procedure
Considering the spool as a cylindrical shape, and calculating the circumference based on the area cited, we establish the connection between circumference and area as follows:
... C = 2√(πA)
To find ten times this circumference, we calculate:
... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm
Derivation of Formulas
The standard formulas for circumference and area are:
... C = 2πr
... A = πr²
Multiplying the area formula by π and extracting the square root yields:
... πA = (πr)²
... √(πA) = πr
Doubling this value results in the circumference formula:
... C = 2√(πA) = 2πr
You can utilize the Pythagorean theorem expressed as a^2 + b^2 = c^2... if b is unknown, you can rearrange the formula. Hence, c^2 - a^2 = b^2. Squaring 47 gives 2209 and squaring 13 yields 169... Subtracting gives you 2209-169, which results in 2040. Taking the square root of that yields approximately 45.166359, which can be rounded to 45 or as 45.167 when expressed to two decimal places. I hope this helps!:)
Answer:
The four odd numbers in sequence are 89, 90, 91, and 93.
Step-by-step explanation:
Designate the four consecutive numbers as x, x+2, x+4, and x+6.
Based on the information given in the question
x + (x + 2) + (x + 4) + (x + 6) = 368
4x + 12 = 368
4x = 356
x = 89
Consequently, the numbers are 89, 90, 91, and 93.
Hope this is helpful:)
Answer:
Upon solving for y, we find:
By substitution, we have:
Thus, we arrive at:
And for x, we determine:
This gives us a length of 76 and a width of 12.5.
Step-by-step explanation:
We are dealing with a rectangle. The formula for the perimeter is:
Here, x denotes the length and y the width. The following conditions can be established:
Substituting these values yields:
When we solve for y, we find:
By substitution, we obtain:
Thus, we conclude:
The length is found to be 76, while the width measures 12.5.
