Find the average rate of change of the given function on the interval [1,6]. g(x)=2x2−x

On October 28, Lee received proceeds of $71,153.66 from the discounted note.

Discounting a note involves receiving immediate cash by selling it to a financial institution at a discount.

The implication of discounting a note is that the receiver gets less than the maturity value.

The maturity value is the face value of the note plus the computed interest.

Face value of the note receivable = $70,000

Interest rate = 6.34%

Note period = 120 days

July 26 - October 28 = 94 days

Maturity value of the note receivable = The Face Value + Interest

= $71,459.07 [$70,000 + ($70,000 x 6.34% x 120/365)]

Bank discount rate = 6%

The discount period from October 28 to Nov 22 = 26 days (120 - 94)

Bank discount = Maturity Value x Discount Rate x Discount Period

= $305.41 ($71,459.07 x 6% x 26/365)

Proceeds = Maturity value - Bank discount

= $71,153.66 ($71,459.07 - $305.41)

Thus, by discounting the note receivable at LB Bank at 6%, Lee received $71,153.66 instead of the $71,459.07 it would have received at maturity.

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The next three terms in the sequence are  -1/16, 1/32, -1/64

The correct option is option C)

What is a sequence?

A sequence is an set of values separated by commas Referring to a generalized rule. They have a relation among them. One of the common sequences are arithmetic progression

We are given a sequence of -1, 1/2, -1/4, 1/8,

We have to describe the next three terms of the sequence

If we notice closely the given sequence is an geometric sequence

Hence they have a common factor known as common ratio

in it we divide a term by its previous term

Hence

Ratio= (1/2)/-1

Ratio = -1/2

Now to find the next terms we multiply this with the last term we get

1/8*-1/2= -1/16

Now Hence the next three terms are -1/16, 1/32, -1/64

The correct option is option c)

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Answer: Can't Say for sure but probably it is so I would Say Yes.

Answer:

they all are being multiplied by 10

Step-by-step explanation:

0.01 x 10 = 0.1

0.1 x 10 = 1

1 x 10 = 10

10 x 10 = 100

The width of the rectangle is given as w = p/2 - l which is derived from perimeter of rectangle

The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.

In this question, we simply need to make the width (w) the subject of formula.

The equation given is

p = 2w + 2l

p = 2w + 2l

p = 2(w + l)

p / 2 = w + l

w = p/2 - l

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The first and the second differences are shown in the table, the values of the second differences are constant, therefore, the relation is linear.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).

The first and the second differences are:

x            y              first differences                second differences

4            18                      ----

5            28                      10                                        ------

6            35                      7                                        -3

7            39                      4                                        -3

8            40                      1                                         -3

9            38                      -2                                        -3

The values of second differences are constant, therefore, the relation is linear.

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Answer: Look at the graph

Step-by-step explanation:

Addition of the given polynomial functions (5a³ + 4a² - 3a + 2) and (a³ - 3a² + 3a - 9)​ gives 8a³ + a² - 7

A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.

Addition of polynomial is achieved term by term

= (5a³ + 4a² - 3a + 2) + (a³ - 3a² + 3a - 9)​

= 5a³ + 3a³+ 4a² - 3a²- 3a + 3a + 2 - 9

= 8a³ + a² - 7

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Answer:

[tex] \sf Root \: of \: x \: are \: \dfrac{3}{2} \: and \: \dfrac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]

Step-by-step explanation:

[tex] \rm \implies 8 {x}^{3} - 27 = 0 \\ \\ \rm \implies (2 \times 2 \times 2) {x}^{3} - (3 \times 3 \times 3) = 0 \\ \\ \rm \implies {(2x)}^{3} - {3}^{3} = 0 \\ \\ \boxed{ \rm {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )} \\ \\ \rm \implies (2x - 3)( {(2x)}^{2} + (2x)(3) + {3}^{2} ) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: and \: 4 {x}^{2} + 6x + 9 = 0 \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{36 - 144} }{8} \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]

Answer:a, c and d

Step-by-step explanation:bc i got it right on edge

Using the z-score tables, the number of babies that weighed more than 10 pounds is; 43

A probability distribution that can be considered to be symmetric about the mean is the normal distribution, which can often be referred to as the Gaussian distribution. This depicts to us the concept of data being close to the mean occurring more often than data that are considered far from the mean. The normal distribution usually has a bell curve graph.

We are given that;

The total number of babies is 908.

Mean of the normal distribution is 7.2 pounds.

Standard deviation of the normal distribution is 1.5 pounds.

The formula of z score is given by;

z = (x - μ)/σ

where;

x is sample mean

μ is population mean

σ is standard deviation

We are given that;

x = 10

μ = 1.5

σ = 7.2

Thus;

z = (10 - 7.2)/1.5

z = 1.86667

The P-value from Z-Table gives us:

P(x > 10) = 1 - P(x < 10) = 0.030974

The number of babies that weighed more than 10 pounds is;

(0.030974 × 908) ≈ 43

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The expected value if you play this game will be -$0.205.

Let the number of gold, silver, and black marbles be P1, P2, and P3, respectively.

Given, The bag contains,

Number of gold marbles (P1)  = 3

Number of silver marbles (P2) = 5

Number of black marbles (P3) = 26

Also given,

The winning value if a gold marble is selected = $3

The winning value if a silver marble is selected = $2

The losing value if a black marble is selected = $1

Probability = Expected value/ Sum of the total number of events

Probability of picking a gold marble,

P1 = 3/ (3+ 5+ 26)

   = 3/34.

Probability of picking a silver marble,

P2 = 5/ (3+ 5+ 26)

   = 5/34.

Probability of picking a black marble,

P3 = 26/ (3+ 5+ 26)

   = 26/34.

The expected value if you play the game will be,

Value = ($3) P1 + ($2) P2 + (-$1) P3

         = ($9/34) + ($10/34) - ($26/34)

         = - ($7/34)

         = -$ 0.205

Thus, you will face a loss of 0.205 cents.

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Answer:

Step-by-step explanation:

There are four different color marbles.

Probability of blue:

Next, there are 3 marbles left in the bag since no replacement.

Probability of red after blue:

The probability of these two steps in order:

Complement of R is:

The proof to the above diagram is ∠1 + ∠3 = 180

Supplementary angles are angles whose sum equals 180°

If angle A + angle B = 180°, then both angles are said to be supplementary, meaning angle A is the supplement of Angle B.

∠2 ≅ ∠3. This means ∠2 is approximately equal to ∠3

Also ∠1 + ∠2 = 180°( sum of angles on a straight line)

making ∠2 the subject of the equation

∠2 = 180 - ∠1

But ∠2 ≅ ∠3, which we can say that ∠2 = ∠3

substituting ∠2 for ∠3 in the equation, we have

∠3 = 180 - ∠1

which is further simplified as,

∠1 + ∠3 = 180°

Which  means both angles are also supplementary.

In conclusion,  both angles are supplementary as ∠1 + ∠3 = 180

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The exponential function that can model the county population, y, x decades after Tiana was born, is:

[tex]y = 641000(0.99)^x[/tex]

The population will fall below 600,000 in 6.6 decades after Tiana was born.

The definition of the exponential function is presented as follows:

[tex]y = a(b)^x[/tex]

In which the parameters of the exponential function are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the function is:

[tex]y = 641000(0.99)^x[/tex]

The population will fall below 600,000 when y = 600000, hence:

[tex]y = 641000(0.99)^x[/tex]

[tex]600000 = 641000(0.99)^x[/tex]

[tex](0.99)^x = \frac{600000}{641000}[/tex]

[tex]\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}[/tex]

[tex]x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}[/tex]

[tex]x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}[/tex]

x = 6.6 decades.

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The equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.

Given function:

g(x) = 6/x-1

vertical asymptote for any function is denominator is equal to zero.

x - 1 = 0

x = 1.

Therefore the equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.

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To have $600,000 for retirement in 35 years at 5% interest, one would need to deposit $528.13 in the account each month.

Periodic deposits are monthly cash inflows into a retirement account that accumulates interest by compounding.

To find periodic deposits, we can use an online finance calculator, defining the parameters as follows.

N (# of periods) = 420 months (35 years x 12)

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $600,000

Results:

Monthly Deposits (PMT) = $528.13

Sum of all periodic deposits = $221,814.60

Total Interest = $378,185.40

Thus, monthly deposits of $528.13 can accumulate to $600,000 in 35 years at 5% interest.

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Answer:

x=1

Step-by-step explanation:

Answer: x=1

Step-by-step explanation:

2x + 5 = 7

2x + 5 - 5 = 7 - 5

2x = 2

2x/2 = 2/2

x=1

Answer:

Step-by-step explanation:

The expression equivalent to [tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex] is m - 2.

Equivalent expressions are expressions that work the same even though they look different.

In other words, equivalent expressions are expressions that have the same value.

Therefore, the expression that is equivalent can be calculated as follows:

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex]

Hence, let's simplify the expression to find it's equivalent,

open the bracket

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m[/tex]

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m = -\frac{21}{2}+\frac{17}{2}+2m-m[/tex]

[tex]-\frac{21}{2}+\frac{17}{2}+2m-m=-\frac{4}{2} + m[/tex] = m - 2

Therefore,

[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = m-2[/tex]

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The completion of the inventory table is as follows:

Some of the inventory methods that are used in completing the inventory table are:

                                    Units    Unit Cost    Total Cost

Jan. 1      Beg. Inventory  10       $7.00            $70

Apri. 11    Purchases        30     $12.00          $360

May 17    Purchases        40     $13.00          $520

Dec. 5    Purchases        20    $15.00           $300

Total                              100                        $1,250

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Step-by-step explanation:

why ? the same pattern your saw yourself, as the handwritten numbers indicate.

it is 1:118.

event on the left is multiplied by 118 to create the numbers on the right.

From the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).

As given in the question,

Given equation is :

y = A(x-h)² +k

Standard basic parabola equation is y = x² where parabola pass through (0, 0) .

In the given quadratic function y = A(x-h)² +k , it represent equation of parabola which is U shaped .

Value of A > 0 then it open in upward direction .

Value of A <0 then it is open in downward direction.

Vertex of the given parabola y = A(x-h)² +k  is (h, k).

Line of symmetry is given by vertical line x =h.

Therefore, from the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).

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Answer:

d the last one I think

Step-by-step explanation:

I am not really sure

Answer:

D.) 6.67 X 10^2

Answer:

Step-by-step explanation:

A. -1/3x

B. -x

c.-5/4x

Answer:

x=-1,x=3/5

Step-by-step explanation:

Those are the two values of x