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vagabundo [1.1K]
2 years ago
13

34.

Mathematics
2 answers:
poizon [28]2 years ago
6 0

Answer:

The lateral surface area of the triangular prism is 379.5sq units

Step-by-step explanation:

The side lengths of the base of the triangular prism are 5 meters, 8 meters, and 10 meters.

It is given that the height of the prism is 16.5 meters.

To determine the lateral surface area of the prism, let us use the formula  

where a, b,c are the side lengths of the base of the triangular prism and h is the height of the prism.

Here  and  

Substituting these values in the formula, we have,

Simplifying, we get,

Multiplying, we get,

Thus, the lateral surface area of the triangular prism is

xxMikexx [17]2 years ago
3 0

Answer:

379.5

Step-by-step explanation:

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Alice, Bernice, and Cheryl shared some stamps in the ratio 8 : 9 : 18. Alice received 184 stamps. Find the number of stamps that
faust18 [17]
184/8=23
8=alice
9=bernice
18=cheryl

8:9:18=184:207:414
6 0
2 years ago
A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues,
EleoNora [17]

Answer:

  •   <u> 7,692 moose.</u>

Explanation:

The table that shows the pattern for this question is:

Time (year) Population

  0                   40

  1                     62

  2                    96

  3                   149

  4                   231

A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.

Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.

Thus you must find both P₀ and r.

<u>1) P₀ </u>

  Using the first term of the sequence (0, 40) you get:

   P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀

Then, P₀ = 40

<u>  2) r</u>

Take two consecutive terms of the sequence:

  • P(0) = 40 r⁰ = 40
  • P(1) = 40 r¹ = 40r = 62
  • P(1) / P(0) = 40r / 40 = 62/40
  • r = 62/40 = 1.55

 

You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55

<u>3) Model</u>

 

Thus, your model is P(x) = 40(1.55)ˣ

<u> 4) Population of moose after 12 years</u>

  • P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692, which is round to the nearest whole number.
7 0
2 years ago
the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . wri
Y_Kistochka [10]

The pattern in the given series of amount in the account are in the form of

arithmetic and geometric progression.

  • The function for Option 1 is;  \underline{ f(n) = 1,100 + (n - 1) \cdot 100}
  • The function for Option 2 is; \underline{f(n) = 1,100 \times  1.1^{(n - 1)}}

Reasons:

The given table of values is presented as follows;

\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right]

In Option 1, the amount in dollars for each year has a common difference of d = 100

The first term, a = 1,100

Therefore;

The Option 1 can be represented as an arithmetic progression , A.P. in the

form, tₙ = a + (n - 1)·d as follows;

For the Option 1, we have;

  • The amount in dollars after <em>n</em> years, \underline{ f(n) = 1,100 + (n - 1) \cdot 100}

For Option 2, it is possible to find;

1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1

Therefore;

The terms in the Option 2 have a common ratio of r = 1.1

The Option 2 is a geometric progression, G.P.

The first term in Option 2 is a = 1,100

Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾

Therefor;

  • The function for the Option 2 is; \underline{f(n) = 1,100 \times  1.1^{(n - 1)}}

Learn more about arithmetic and geometric progression here:

brainly.com/question/8932895

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4 0
2 years ago
How do I solve this? Person to help gets brainliest.
REY [17]

Answer:

I believe its C?

Step-by-step explanation:

8 0
2 years ago
Solve for x: 8x - 2 - 5x = 8
Travka [436]

Answer:

3 1/3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x = 10 /3

Decimal Form:

x = 3. 3 3

Mixed Number Form:

x  =  3  1/3

6 0
3 years ago
Read 2 more answers
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