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Llana [10]
3 years ago
5

Find the mean for the following group of data items. 4.1, 8.9, 3.2, 1.9, 7.3, 6.3, 6.7, 8.6, 3.2, 2.3, 5.9 (Round to 3 decimal p

laces as needed.) The mean is
Mathematics
1 answer:
Alex787 [66]3 years ago
4 0

Answer:

The mean is 5.309.

Step-by-step explanation:

Given group of data,

4.1, 8.9, 3.2, 1.9, 7.3, 6.3, 6.7, 8.6, 3.2, 2.3, 5.9,

Sum = 4.1+ 8.9 + 3.2 + 1.9 + 7.3 + 6.3 + 6.7 + 8.6 + 3.2 + 2.3 + 5.9 = 58.4,

Also, number of observations in the data = 11,

We know that,

Mean=\frac{\text{Sum of all observation}}{\text{Total observations}}

Hence, the mean of given data = \frac{58.4}{11}=5.30909\approx 5.309

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The Surface Area of a square pyramid is 3600 ft. The slant height is 80 feet and the base is 20 feet. At most how many 1 foot cu
amm1812

Answer:

10,583 flexible cubes

9915 rigid cubes

Step-by-step explanation:

The equation for the surface area of a square pyramid is area of base plus perimeter of base multiplied by the slant height

Surface area = A + 1/2·p·s

The volume of the pyramid = 1/3×A×h

Where:

A = Area of the base = 20 × 20 = 400 ft²

h = The height of the pyramid = √((slant height)² - ((base side length)/2)²)

h = √(80² - (20/2)²) = 30·√7

The volume of the pyramid = 1/3*400*30·√7 = 4000·√7 ft³ = 10,583.005 ft³

If the cubes are flexible, approximately 10,583 cubes

For rigid cubes we have

Given that the height of the pyramid = 30·√7

The slope of the pyramid = 30·√7/10 = 3·√7

So an increase in height of 1 foot gives a reduction in width of 2/(3·√7)

The bottom can hold 400 cubes

The next layer can hold 19×19 = 361

3rd 361

4th 361

5th 324

6th 324

7th 324

8th 324

9th

Continuing, we get a total of about 9915 rigid cubes in the pyramid.

3 0
3 years ago
√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q. ​
frutty [35]

Answer:  

The smallest value of p+q is 11

It happens when p = 6 and q = 5.

=======================================================

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

I'll ignore the trivial factor of 1.

Here are the possible factorizations we could go with:

180 = 4*45

180 = 9*20

180 = 36*5

Those factorizations then lead to the following

\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\

Then we have

p+q = 2+45 = 47

p+q = 3+20 = 23

p+q = 6+5 = 11

The smallest value of p+q is 11 and it happens when p = 6 and q = 5.

Side note: p+q is smallest when we go with the largest perfect square factor.

6 0
1 year ago
box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the am
Naya [18.7K]

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

6 0
3 years ago
When tossing 2 coins, the probability of getting exactly 1 tail is 1/3. <br> A- true <br> B- false
Ghella [55]
The answer is b. False
3 0
3 years ago
Read 2 more answers
What assumption have you made in answering part b​
emmasim [6.3K]

You're assuming that this data set represents all of Mrs. Hassaan's pupils. Certain students could be missing from the histogram - for instance, there could be one or two students who missed the test, but for certain reasons will be taking a make-up exam. Their grade would not be recording in this data set, but they still contribute to the class size, and so would be unaccounted for here.

4 0
3 years ago
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