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andrew11 [14]
3 years ago
5

4

Mathematics
1 answer:
Nana76 [90]3 years ago
8 0

Answer:

154838455387+6785+++56

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In ΔABC, if the length of side b is 3 centimeters and the measures of ∠B and ∠C are 45° and 60°, respectively, what is the lengt
Umnica [9.8K]
Answer is 3.67 centimeters
3 0
3 years ago
Read 2 more answers
solve |5x - 1| < 1 a. {x|0 < x < 2/5} b. {x|x < 0 or x > 2/5} c. {x|-2/5 < x < 2/5}
aliina [53]
<span>|5x - 1| < 1
-1 < 5x - 1 < 1
-1 + 1 < 5x < 1 + 1
0 < 5x < 2
0/5 < x < 2/5
0 < x < 2/5
</span>
8 0
3 years ago
Emmanuel carves a cone-shaped hollow out of a solid clay cylinder. What is the approximate volume of the solid portion of the cy
bixtya [17]

Answer:

3.14r^2(h-\frac{1}{3}h_1)

Step-by-step explanation:

Let h be the cylinders height and r the radius.

-The volume of a cylinder is calculated as:

V=\pi r^2h

-Since the cone is within the cylinder, it has the same radius as the cylinder.

-Let h_1be the height of the cone.

-The area of a cone is calculated as;

V=\pi r^2 \frac{h}{3}\\\\=\frac{1}{3}\pi r^2h_1

The volume of the  solid section of the cylinder is calculated by subtracting the cone's volume from the cylinders:

V=V_{cy}-V_{co}\\\\=\pi r^2h-\frac{1}{3}\pi r^2 h_1, \pi=3.14\\\\=3.14r^2(h-\frac{1}{3}h_1)

Hence, the approximate area of the solid portion is 3.14r^2(h-\frac{1}{3}h_1)

5 0
3 years ago
Jenny bought a 5 notebooks and 2 pencils, and the total was 9 dollars.
weeeeeb [17]
You would solve this with simultaneous equations, so if we write it as:
5n + 2p = 9
3n + 2p = 6
(subtract)
2n = 3
÷ 2
notebooks = 1.5

Now you would substitute it in:
(3 × 1.5) + 2p = 6
4.5 + 2p = 6
- 4.5
2p = 1.5
÷ 2
pens = 0.75

So your final answer is notebooks are $1.50 and pens are $0.75, I hope this helps!
6 0
3 years ago
2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati
Ket [755]

Answer:

\sigma = 11.28 --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

<u>Start by calculating the mean</u>

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

\bar x = \frac{\sum fx}{\sum f}

So, we have:

\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}

\bar x = \frac{7531}{91}

\bar x = 82.76

Next, calculate the variance using the following formula:

\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}

\sigma^2 = \frac{11580.6816}{91}

\sigma^2 = 127.26

Lastly, take the square root of the variance to get the standard deviation

\sigma = \sqrt{\sigma^2}

\sigma = \sqrt{127.26}

\sigma = 11.28 --- approximated

<em>Hence, the standard deviation is approximately 11.28</em>

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.

8 0
2 years ago
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