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Digiron [165]
3 years ago
13

Determine the value(s) of k such that the system of linear equations has the indicated number of solutions. (Enter your answers

as a comma-separated list.) An infinite number of solutions
9x + ky = 24
kx + y = 8
Mathematics
1 answer:
Ratling [72]3 years ago
8 0

Answer:

k=3

Step-by-step explanation:

The given system of equations are

9x+ky=24

kx+y=8

We need to find the value of k if the given system of equation have infinite number of solutions.

If two equations a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 have infinite number of solutions, then

\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}

Using this we get

\dfrac{9}{k}=\dfrac{k}{1}=\dfrac{-24}{-8}

\dfrac{9}{k}=\dfrac{k}{1}=3

\dfrac{k}{1}=3

k=3

Therefore, the value of k is 3.

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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
likoan [24]

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:

  • a = 10,100
  • b = 1.01
  • n = t - 1 (as the initial value is for t = 1 not t = 0)

\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
A bank manager is interested in the average length of time that customers are willing to wait in line before they give up and le
Fynjy0 [20]

Answer: The average length of time that the 25 customers waited before leaving the bank.   <u> e. Statistic</u>

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The average length of time that all customers will wait before leaving the bank <u>a. Parameter</u>

Step-by-step explanation:

A data is a list of observations.

In statistics, a variable is an attribute that defines  a person, place, thing, or thought.

A large group that have similar individuals as per the researcher's point of view is known as population, where its subset is known as sample.

The measure of certain characteristic in population is known as parameter, where for sample it is known as statistic.

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Answer:

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5 0
3 years ago
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