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Deffense [45]
3 years ago
5

Luguin

Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
7 0

Answer:

  • slant height: 6 units
  • lateral area: 108 square units

Step-by-step explanation:

<u>Given</u>

A right regular hexagonal pyramid with ...

  • base side length 6 units
  • base apothem 3√3 units
  • height 3 units

<u>Find</u>

  • lateral face slant height
  • pyramid lateral surface area

<u>Solution</u>

a) The apothem (a) and height (b) of the pyramid are two legs of the right triangle having the slant height as its hypotenuse (c). The Pythagorean theorem tells us the relationship is ...

  c = √(a² +b²) = √((3√3)² +3²) = √(27+9) = √36

  c = 6

The slant height of the pyramid is 6 units.

__

b) The lateral surface area of the pyramid is the area of each triangular face, multiplied by the number of faces. The area of one face will be ...

  A = (1/2)bh = (1/2)(6 units)(6 units) = 18 units²

Then the lateral surface area is 6 times this value:

  SA = 6(18 units²) = 108 units²

The lateral surface area of the pyramid is 108 square units.

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Are triangles ABC and EBD congruent? Explain
vladimir2022 [97]

Answer:

Yes, they are congruent!

Step-by-step explanation:

because they are the same shape meaning they will have the same angle/degree.

8 0
3 years ago
Read 2 more answers
Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical fact
scZoUnD [109]

Answer:

Explained below.

Step-by-step explanation:

The claim made by an expert is that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)².

(1)

The hypothesis for both the test can be defined as:

<em>H</em>₀: The variance of speeds does not exceeds 75 (mph)², i.e. <em>σ</em>² ≤ 75.

<em>Hₐ</em>: The variance of speeds exceeds 75 (mph)², i.e. <em>σ</em>² > 75.

(2)

A Chi-square test will be used to perform the test.

The significance level of the test is, <em>α</em> = 0.05.

The degrees of freedom of the test is,

df = n - 1 = 55 - 1 = 54

Compute the critical value as follows:

\chi^{2}_{\alpha, (n-1)}=\chi^{2}_{0.05, 54}=72.153

Decision rule:

If the test statistic value is more than the critical value then the null hypothesis will be rejected and vice-versa.

(3)

Compute the test statistic as follows:

\chi^{2}=\frac{(n-1)\times s^{2}}{\sigma^{2}}

    =\frac{(55-1)\times 94.7}{75}\\\\=68.184

The test statistic value is, 68.184.

Decision:

cal.\chi^{2}=68.184

The null hypothesis will not be rejected at 5% level of significance.

Conclusion:

The variance of speeds does not exceeds 75 (mph)². Thus, concluding that driving conditions are not dangerous on this highway.

7 0
3 years ago
Using any five itegers from 1 to 10 what is the greatest possible mean of the 5 numberes if the median is 4?
BartSMP [9]
That would  a set of 5 numbers in ascending order with  4 being the middle one and the other 4 being the highest possible So it is

2, 3, 4, 9, 10

Mean is 28/5  = 5.6 answer

( I am assuming that each number is different)

Of duplicates is allowed then its 4 4 4 10 10  whose mean is 6.4
5 0
3 years ago
250 people were asked to name their favorite fruit. Of those surveyed, how many people prefer peaches? 44% berries, 32% Peaches,
alexdok [17]

Answer:

80 people prefered peaches

Step-by-step explanation:

250-68%=80 people

6 0
3 years ago
April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 11 feet high. The height of t
kogti [31]

Answer:

Maximum height of the arrow is 203 feets

Step-by-step explanation:

It is given that,

The height of the arrow as a function of time t is given by :

h(t)=-16t^2+64t+11..........(1)

t is in seconds

We need to find the maximum height of the arrow. For maximum height differentiating equation (1) wrt t as :

\dfrac{dh(t)}{dt}=0

\dfrac{d(-16t^2+64t+11)}{dt}=0

-32t+64=0

t = 2 seconds

Put the value of t in equation (1) as :

h(t)=-16(2)^2+64(2)+11

h(t) = 203 feet

So, the maximum height reached by the arrow is 203 feet. Hence, this is the required solution.

8 0
3 years ago
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