Answer:

Step-by-step explanation:
The formula of a volume of a cone:

<em>r</em><em> - radius</em>
<em>H</em><em> - height</em>
We have the diameter <em>2r = 10in → r = 5in</em>, and the height <em>H = 28in.</em>
Substitute:


The summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343
<h3>How to find the sum of consecutive integers?</h3>

<h3>
What are the properties of summation?</h3>
![\sum_{i=r}^s (a \times f(i) + b) = a \times [\: \sum_{i=r}^s f(i)] + (s-r)b](https://tex.z-dn.net/?f=%5Csum_%7Bi%3Dr%7D%5Es%20%20%28a%20%5Ctimes%20f%28i%29%20%2B%20b%29%20%3D%20a%20%5Ctimes%20%5B%5C%3A%20%5Csum_%7Bi%3Dr%7D%5Es%20f%28i%29%5D%20%2B%20%28s-r%29b)
where a, b, r, and s are constants, f(i) is function of i, i ranging from r to s (integral assuming).
For the given case, the considered summation can be written symbolically as:

It is evaluated as;
![\sum_{n=1}^{14} (3n + 2) = 3 \times [ \: \sum_{n=1}^{14} n ] + \sum_{n=1}^{14} 2\\\\\sum_{n=1}^{14} (3n + 2) = 3 \times \dfrac{(14)(14 + 1)}{2} + (2 + 2 + .. + 2(\text{14 times}))\\\\\sum_{n=1}^{14} (3n + 2) = 3 \times 105 + 28 = 343\\](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D1%7D%5E%7B14%7D%20%20%283n%20%2B%202%29%20%3D%203%20%5Ctimes%20%5B%20%5C%3A%20%5Csum_%7Bn%3D1%7D%5E%7B14%7D%20n%20%5D%20%2B%20%5Csum_%7Bn%3D1%7D%5E%7B14%7D%202%5C%5C%5C%5C%5Csum_%7Bn%3D1%7D%5E%7B14%7D%20%20%283n%20%2B%202%29%20%3D%203%20%5Ctimes%20%5Cdfrac%7B%2814%29%2814%20%2B%201%29%7D%7B2%7D%20%2B%20%282%20%2B%202%20%2B%20..%20%2B%202%28%5Ctext%7B14%20times%7D%29%29%5C%5C%5C%5C%5Csum_%7Bn%3D1%7D%5E%7B14%7D%20%20%283n%20%2B%202%29%20%3D%203%20%5Ctimes%20105%20%2B%2028%20%3D%20343%5C%5C)
Thus, the summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343
Learn more about summation here:
brainly.com/question/14322177
Answer:
Mandy should add the tens before she adds the ones.
Step-by-step explanation:
There are no other good answers and the correct answer is 82 pennies.
Answer:
7 ft
Step-by-step explanation:
The circumference of a circle is given by the formula ...
C = 2πr
The curved portion of a semicircle will be ...
C/2 = (2πr)/2 = πr
The straight portion of the semicircular shape will be the diameter, or 2r. That means the total perimeter of a semicircular shape is ...
P = πr +2r = r(π+2)
Then the radius is ...
r = P/(π+2) = (35.98 ft)/(3.14+2) = 7 ft
The radius of the patio is 7 ft.
Answer:
x=20
Step-by-step explanation:
(triangle angles must add up to 180º)
2x+10+2x+90=180
4x+100=180
4x=80
x=20