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Black_prince [1.1K]
3 years ago
7

Teje ratio of adulta to children attedening a new exhibit at the museum was found 8:5 based on this ratio if 390 people attended

one day how many would be children
Mathematics
1 answer:
Ratling [72]3 years ago
8 0
8x - adults
5x - children

8x+5x=390\\
13x=390\\
x=30\\\\
5x=5\cdot30=150
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Step-by-step explanation:

x=22°(alternate angles are equal)

y=50°(angle sum in triangle is 180°)

z=108°

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Pens come in packages of 6. Pencils come in
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Find the product of 51 and -2.5. Use the distributive property to rewrite and solve. The first step is done for you. 51(-2.0) +
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The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price
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Answer:

A)  3%

B)  Product A

Step-by-step explanation:

<u>Exponential Function</u>

General form of an exponential function: y=ab^x

where:

  • a is the initial value (y-intercept)
  • b is the base (growth/decay factor) in decimal form
  • x is the independent variable
  • y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

<u>Part A</u>

<u>Product A</u>

Assuming the function for Product A is <u>exponential</u>:

f(x) = 0.69(1.03)^x

The base (b) is 1.03.  As b > 1 then it is an <u>increasing function</u>.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, <u>product A is increasing by 3% each year.</u>

<u>Part B</u>

\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%

Check using different two consecutive values of f(t):

\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%

Therefore, as 3% > 1%, <u>Product A recorded a greater percentage change</u> in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

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  • b = 1.01
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\implies f(t) = 10100(1.01)^{t-1}

To check this, substitute the values of t for 1 through 4 into the found function:

\implies f(1) = 10100(1.01)^{1-1}=10100

\implies f(2) = 10100(1.01)^{2-1}=10201

\implies f(3) = 10100(1.01)^{3-1}=10303.01

\implies f(4) = 10100(1.01)^{4-1}=10406.04

As these values match the values in the given table, this confirms that the found function for Product B is correct and that <u>Product B increases by 1% per year.</u>

4 0
2 years ago
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