2. How much interest is earned on a principal of $267 invested at an interest rate of 6% for six years?

The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

\(\implies {\blue {\boxed {\boxed {\purple {\sf { (5x + 6y)(5x - 6y) }}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( ={25x}^{2} - 36 {y}^{2} \)

\( = ({5 \times 5)x}^{2} - (6 \times 6){y}^{2} \)

\( = ({5x})^{2} -( {6y})^{2} \)

\( = (5x + 6y)(5x - 6y)\)

\( {a}^{2} - {b}^{2} = (a + b)(a - b)\)

\(\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}\)

Answer:

chemical energy to produce light energy

The percentage by which the cost is increasing will be 75%.

The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.

The percentage of the 8th graders who want to go to the water slides is found from;

In the year 2000, a house was valued at $60 000.

In 2010, the same house was valued at $80 000.

The percentage value is found as;

\(\% = \frac{60000}{80000} \times 100 \\\\ \% =75 \%\)

Hence the percentage by which the cost is increasing will be 75%.

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Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

m=21/8

Step-by-step explanation:

5 /38+m=8
Move the constant to the right.
43/8+m=8

m=8-43/8

m=21/8

Answer:

Step-by-step explanation:

1/2 ÷ 2/3 = 1/2 x 3/2 = 3/4 -_- so easy

Answer:

The first one is three the second is four

Step-by-step explanation:

1/2÷2/3 (do copy, dot, flop)

1/2·3/2

1·3=3

2·2=4

3/4

The two numbers in bold are the answers

Answer:

(a)  Domain:  (-∞ ,∞)    Range:  (-∞ ,∞)

     \(\textsf{As} \; x \rightarrow -\infty, \; f(x) \rightarrow - \infty\)

     \(\textsf{As} \; x \rightarrow +\infty, \; f(x) \rightarrow + \infty\)

(b)  x = 6

(c)  See below.

(d)  g(x) = (x - 6)(x² - 4x + 1)

(e)  x = 6,   x = 2 + √3,   x = 2 - √3

Step-by-step explanation:

Given polynomial:

\(g(x)=x^3-10x^2+25x-6\)

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Both the domain and range are unrestricted, therefore:

As the leading coefficient is positive and the degree of the polynomial is odd, the end behavior of the function is:

Rational Root Theorem

\(\dfrac{p}{q}=\dfrac{\textsf{a factor of the last term $(a_0)$}}{\textsf{a factor of the first term $(a_n)$}}\)

where:

\(f(x)=a_n x^n+a_{n-1} x^{n-1} +... + a_2 x^2+a_1 x +a_0\)

Identify the factors (both positive and negative) of the constant of the polynomial.  The factors are the possible values of p:

Identify the factors (both positive and negative) of the leading coefficient of the polynomial. These factors are the possible values of q.

Find each possible value of p/q

\(\implies \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 2}{\pm 1}, \dfrac{\pm 3}{\pm 1}, \dfrac{\pm 6}{\pm 1}=\pm1, \pm2, \pm 3, \pm6\)

Therefore, the possible rational roots of g(x) are:

Substitute each of the possible roots into g(x).  Any root that results in f(x) = 0 is an actual rational root.

\(x=-1 \implies g(-1)=(-1)^3-10(-1)^2+25(-1)-6=-42\)

\(x=1 \implies g(1)=(1)^3-10(1)^2+25(1)-6=10\)

\(x=-2 \implies g(-2)=(-2)^3-10(-2)^2+25(-2)-6=-104\)

\(x=2 \implies g(2)=(2)^3-10(2)^2+25(2)-6=12\)

\(x=-3 \implies g(-3)=(-3)^3-10(-3)^2+25(-3)-6=-198\)

\(x=3 \implies g(3)=(3)^3-10(3)^2+25(3)-6=6\)

\(x=-6 \implies g(-6)=(-6)^3-10(-6)^2+25(-6)-6=-732\)

\(x=6 \implies g(6)=(6)^3-10(6)^2+25(6)-6=0\)

Therefore, the actual rational root is x = 6.

Descartes' Rule of Signs tells us the maximum number of positive and negative roots.

Positive root case

\(g(x)=+x^3-10x^2+25x-6\)

As there are 3 sign changes, the maximum possible number of positive roots is 3.

Negative root case

\(\begin{aligned}g(-x)&=(-x)^3-10(-x)^2+25(-x)-6\\ &=-x^3-10x^2-25x-6 \end{aligned}\)

As there are no sign changes, there are no negative roots.

Remainder Theorem

When we divide a polynomial f(x) by (x − c) the remainder is f(c).

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x).

From part (b) we know that f(6) = 0, so (x - 6) is a factor of g(x):

Use long division to find the other factor:

\(\large \begin{array}{r}x^2-4x+1\phantom{)}\\x-6{\overline{\smash{\big)}\,x^3-10x^2+25x-6\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-6x^2)\phantom{-b000000)}}\\-4x^2+25x-6\phantom{)}\\-~\phantom{()}\underline{(-4x^2+24x)\phantom{))..)}}\\x-6\phantom{)}\\-~\phantom{()}\underline{(x-6)\phantom{}}\\0 \phantom{)}\end{array}\)

(x² - 4x + 1) cannot be factored further.

Therefore the factored polynomial is:

The zeros of a polynomial are the values of x when f(x) = 0:

\(\implies g(x)=0\)

\(\implies (x-6)(x^2-4x+1)=0\)

Therefore:

\(\implies x-6=0\)

\(\implies x^2-4x+1=0\)

We have already established that x = 6 is a zero.

To find the other zeros, use the quadratic formula.

\(\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}\)

\(x^2-4x+1 \implies a=1, \;\;b=-4, \;\;c=1\)

Therefore:

\(\implies x=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(1)}}{2(1)}\)

\(\implies x=\dfrac{4 \pm 2\sqrt{3}}{2}\)

\(\implies x=2 \pm \sqrt{3}\)

Therefore, the zeros of the given polynomial are:

Note: There are no complex zeros.

Answer:D

Step-by-step explanation:

The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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1.5 inches of steel is needed to make one string

Here, we want to know the number of inches of steel wire that is needed to amke one spring

Let the number be x;

We can have a relation as follows;

Answer:

Step-by-step explanation:

The bell boy added $270 and $20 incorrectly. The $20 bill was something that was returned due to overcharching. On the other hand, $270 was the amount that they paid for their room. This only means that $20 should be deducted from $270 and that's the amount that they paid for their room while $30 and $20 are the amount that the bell boy received as a tip

Total money of the three men: 3($100) = $300

They paid $270 for the room: $300 - $270 = $30

Tip for the bell boy: $30 - $30 = $0

Amount overcharged to them: $0 + $20 = $20

Tip to the bell boy: $20 - $20 = $0

They were left with no more money from the original $300.

By using the graph of g, the solution to g(3) is equal to 8.

In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In Mathematics and Geometry, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.

When the domain (input value) of the given function g(x) shown in the graph is 3, the output value (range) is given by;

g(3) = 8.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Let's call the rectangle's length x and its width, x - 6.

Since a rectangle has 4 sides and the perimeter of the rectangle

is just the distance around the outside of the figure,

we can create an equation.

This equation will be x + x + x - 6 + x - 6 = 72.

Simplifying on the left gives us 4x - 12 = 72.

Add 12 to both sides to get 4x = 84.

Now divide both sides by 4 to get x = 21.

Since x represents our length, we know that the length is 21 inches.

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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Answer:

0.62kg or 620g.

Step-by-step explanation:

If there are 25 newspapers in a stack that weighs 15.5kg, 15.5 divided by 25 would give you the weight of one newspaper, which is 0.62kg.

To convert kilograms to grams:

0.62kg x 1000 = 620g

Answer:

0.62 kg

Step-by-step explanation:

25 newspaper = 15.5kg

1  newspaper = ? Y

cress cross

25 newspaper Y = 15.5 kg × 1 newspaper

25 newspaper         25 newspaper

Y = 15.5 kg

     25

Y = 0.62 kg

Answer:

All numbers that are in the decimal places are significant.

Step-by-step explanation:

A decimal is a digit after the decimal dot.

E.g. 1 in 2.31 is a decimal. 1 in 2.13 is also a decimal.

(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2  - (5x + 2) is simplified as -4.

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2  - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

= (5x - 5x) + (-2 - 2)

= 0 - 4

= - 4

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Answer:

22050 J

Step-by-step explanation:

Answer:

c. 0.55

Step-by-step explanation:

A chosen acre of land is forested and not forested are complimentary event , so let :

F = Chosen land is forested

F = Chosen land is not forested

....and we know  F+F = S

where S is sample space and we know probability ocer whole sample space is 1 , that is P(S)=1 , and we know F and F are independent so

P(F+F) = P(S)

P(F) + P(F)=1

We have given that probability of forest land in randomly chosen an acre land in Canada have probability 0.45 so P(F)=0.45 so ,

0.45 + P(F) = 1

P(F) = 1 - 0.45

P(F) = 0.55

Hence, the probability that the chosen acre is not forested is 0.55

Answer:

4c less than -5c because 5is greater that 4 either way.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

(<) this means less than

(>) this means greater than

So since the question doesnt say anything about -4°C we can automatically cross out A and B

They are both negative! but when you have a negative. Its going to be less than a positive

So this means 4°C is greater than -5°C

or in other words

D.) 4°C > -5°C

hope this helps!

and dont forget 2

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The given value, 1,503 passengers which represents the number of individuals that died according to the task content is; Choice B; The value is a parameter because it describes some characteristic of a population.

A parameter, in its simplest definition is a measure which describes a characteristic or feature of a population, for instance, the mean of the population.

A statistic on the other hand is a measure of the characteristic or feature of a sample such as a sample standard deviation.

On this note, the number 1503 as given in the task content is a parameter as it describes some characteristic of a population.

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Answer:

Step-by-step explanation:

The answer is B

Answer:

Step-by-step Explanation:

According to the graph given in the attachment, the no. of launches made in those years are:

The no. of launches was greatest in the year 1985 and the line graph touches the highest peak in 1985\(.\)

The average rate of change for the snowfall amount is given as follows:

2.4 inches per hour.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The change in the output is given as follows:

8.1 - 3.3 = 4.8.

(output is the amount of snow).

The change in the input is given as follows:

2 - 0 = 2.

(input is the time in hours).

Hence the average rate of change of the snowfall over time is given as follows:

4.8/2 = 2.4 inches per hour.

(change in the snowfall divided by the change in time).

The table is given by the image presented at the end of the answer.

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Answer:

-15228

Step-by-step explanation:

Given the expression :

-4(14)6x for X = 13

To evaluate ; simply substitute 13 for X in the equation :

-14(14)6(13)

-14 * 14 * 6 * 13 = - 15228

Check the picture below.

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~4 - (-2)~~)^2 + (~~1 - (-4)~~)^2} \implies d=\sqrt{(4 +2)^2 + (1 +4)^2} \\\\\\ d=\sqrt{( 6 )^2 + ( 5 )^2} \implies d=\sqrt{ 36 + 25 } \implies d=\sqrt{ 61 }\)