Write a formula for the indicated rate of change. S(c, k) = c(34^k): dc/dk dc/dk =

The function that gives the amount of money in dollars, j(n), in Jamie’s account n years after the initial deposit is J(n) = P(1 + (r/3)/100)³ⁿ.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

Given, Jamie deposits $627 into a savings account and the account has an interest rate of 3.5%, compounded quarterly.

P = $627, r =  3.5%.

We know the formula for compound interest compounded quarterly is

A = P(1 + (r/3)/100)³ⁿ.

Or

J(n) = P(1 + (r/3)/100)³ⁿ. (here t is replaced by n).

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Answer:

\(m = \frac{2.90 - 2.50}{20 - 0} = \frac{.40}{20} = .02\)

\(f(x) = .02x + 2.50\)

\(f(30) = .02(30) + 2.50 \)

\(f(30) = 3.10\)

In 2030, the price of oil would be $3.10.

Answer:

x=-3

Step-by-step explanation:

The axis of symmetry is the line that separates a parabola directly in half. It is measure on x axis because it is being split in terms of that number. Next, you identify the origin and find exactly where the parabola is in half and that is your answer. Another way to do this would be to identify the vertex of the parabola. The answer is the x coordinate of the location of the vertex. (The highest point of a parabola.)

The two posters will cover 776 square inches of Melody's bedroom wall.

To find this, you add the area of the two posters together. Poster A has an area of 450 square inches, and poster B has an area of 326 square inches. By adding these two values together, we get 450 + 326 = 776 square inches. This is the total area that the two posters will cover on Melody's bedroom wall. It is important to note that this is assuming that the posters do not overlap each other and that they are placed next to each other, covering an equal area of the wall.

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The closest allowable distance that a randomly chosen datum falls within the required 2 standard deviations of the mean is 0.95.

The likelihood that a data is within two standard deviations of the mean

By observation, the distribution depicted in the task content above is a normal distribution.

One can tell the difference between the following .

In the case of a standard normal distribution, 68% of the observations (datum) are within one standard deviation of the mean, 95% are within two standard deviations of the mean, and 99.9% are within three standard deviations of the mean.

On this note, when expressed as a percentage; the probability that the randomly selected datum falls with 2 standard deviations is; 95/100 = 0.95.

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Answer:

2.24

Step-by-step explanation:

The rate of decrease at 10 seconds is - 0.642.

The formula for exponential growth is y = y₀.e^(kt).

The formula for exponential decay is y = y₀.e^(-kt).

From the graph, we conclude that it is an exponentially decaying function.

At t = 10, depth = 60 and at t = 0 depth = 112

                                                                   (as every box represents 4 units).

So, the rate of decrease can be obtained by,

112 = 60.e^(-10k).

e^(-10k) = 1.86.

lne^(-10k) = ln1.86.

- 10k = 6.42.

k = - 0.642.

The rate of decrease at 10 seconds is - 0.642.

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The valid reasons to use a sample instead of evaluating a much larger population are contacting the whole population would be only marginally more accurate than a sample. A sample can be chosen to validate a specific idea about the population.

Contacting the entire population would be time consuming.
1. Contacting the whole population would be only marginally more accurate than a sample: This is a valid reason because a well-designed sample can often provide an accurate estimate of the population, while using significantly fewer resources.
2. Sampling is a random process, and therefore more accurate than measuring the whole population: This statement is incorrect. A random sample can provide an unbiased estimate, but it is not necessarily more accurate than measuring the entire population.
3. A sample can be chosen to validate a specific idea about the population: This is a valid reason because sampling can be used to test hypotheses or ideas about the population without having to evaluate every member of the population.
4. Contacting the entire population would be time-consuming: This is a valid reason because sampling can save time and resources compared to attempting to gather data from every individual in a population.

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Answer:

True.

Step-by-step explanation:

\(\frac{(10)-2}{4}=2\\\\\frac{8}{4}=2\\\\2=2\)

Answer:

d

Step-by-step explanation:

the length of arc YPX is calculated as

YPX = circumference of circle × fraction of circle

the central angle of arc XY = 90° , then

central angle of arc YPX = 360° - 90° = 270°

YPX = 2πr × \(\frac{270}{360}\) ( r is the radius )

       = 2π × 8 × \(\frac{3}{4}\)

       = 16π × \(\frac{3}{4}\)

       = 4π × 3

       = 12π m

There are 330 ways to select 7 seed packets out of 11.

To count the number of ways to select 7 seed packets out of 11, we can use the combination formula:

\(( \frac {k}n )= k!(n-k)!n!\)

where n is the number of items to choose from, and k is the number of items to choose. In this case, n=11 and k=7.

Plugging these values into the formula, we get:

\(( \frac{7}{11})= 7!(11-7)!11!\)

Simplifying the factorials, we get:

\(( \frac{7}{11})= \frac{7\times 6\times 5\times 4\times 3\times 2\times 1}{11\times 10\times 9\times 8\times 7\times 6\times 5}\)

Simplifying further, we get:

\(( \frac{7}{11} )= \frac{4\times 3\times 2\times 1}{11\times 10\times 9\times 8}\)

Simplifying again, we get:

\((\frac{11}7)=330\)

Therefore, there are 330 ways to select 7 seed packets out of 11.

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Answer:

the answer is 878888293389349

Respuesta:

Los enteros positivos, o números enteros, se utilizan de muchas maneras durante la vida diaria. Los números de carretera se contabilizan junto con los límites de velocidad de la carretera. Los enteros se utilizan para comprender qué velocidad conducir en una carretera determinada. Los números en los relojes se utilizan para entender la hora y para configurar las alarmas del reloj. Hay números en edificios y casas para identificar direcciones y números para los niveles de piso dentro de los edificios. Los mapas utilizan enteros para proporcionar dirección e información. Los enteros negativos pueden ser menos obvios para su uso en la vida cotidiana. Algunos ejemplos de uso negativo de enteros incluyen las lecturas del termómetro, manteniendo la puntuación en un juego de hockey, altitud y bancos. Aunque todos estos ejemplos utilizan enteros positivos, también utilizan enteros negativos. Un termómetro utiliza negativo enteros para representar temperaturas por debajo de cero. En hockey, cuando el otro equipo anota en la línea del primer equipo, es un menos, pero cuando el primer equipo anota, es un plus. La altitud que está por debajo del nivel del mar está representada con números negativos. Los bancos y las cooperativas de crédito representan débitos con enteros negativos y créditos con enteros positivos.

Teo can fill 28 glasses in  4 2/3 pitches of juice.

Teo  has 4 2/3 pitches of juice.

First we write the improper fraction (mixed fraction) as a proper fraction.

4 2/3

= [(4 × 3) + 2] / 3

= (12 + 2) / 3

= 14/3

One glass holds 1/6 of a pitcher.

Let m number of glasses hold 14/3 pitches of juice.

By unitary method,

m × (1/6) =  14/3

To find the value of m we need to divide fractions.

m = (14/3) / (1/6)

m = (14/3) × (6/1)

m = 14 × 2

m = 28

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The value of x in (8^x/5) (8^x/4)=8^4 is 80/9

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

The equation;(8^x/5) (8^x/4)=8^4

LHS=(8^x/5) (8^x/4)

=(8^x/5) (8^x/4)

=8^(x/5+x/4)

=8^((4x+5x)/20)

=8^(9x/20)

Now, by comparing LHS to RHS

We will get;

9x/20=4

9x=80

x=80/9

Therefore the answer of the equation will be 80/9

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Answer:

The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:

f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4

f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6

The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.

To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."

The inverse function as g⁻¹ (h)  = [(h+6)/10]² which is the correct answer would be an option (E).

The inverse function is defined as a function obtained by reversing the given function.

To determine the inverse of a function, all you have to do is switch where h and g are and resolve for g.

So after switching h and g,

g = g(h) = 10√h - 6

becomes

h = 10√g - 6

Now, we solve for h regularly.

h + 6 = 10√g

(h + 6)/10 = √g

[(h+6)/10]² ⇒ g = [(h+6)/10]² = g(x)

Therefore the inverse of g(x) is g⁻¹ (h)  = [(h+6)/10]²

Hence, the inverse function as g⁻¹ (h)  = [(h+6)/10]²

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The car will travel approximately 11.829 if its wheels revolve 10,000 times without slipping.

First, we need to find the circumference of the wheel, which is given by the formula:

circumference = pi x diameter

where pi is approximately equal to 3.14.

So, the circumference of the wheel = 3.14 x 24 = 75.36 inches.

Next, we need to find the distance traveled by the car in one revolution of the wheel, which is equal to the circumference of the wheel.

Distance traveled by the car in one revolution of the wheel = 75.36 inches = 0.0011829 miles (1 inch = 0.000015783 miles).

Therefore, the distance traveled by the car in 10,000 revolutions of the wheel = 0.0011829 x 10,000 = 11.829 miles.

Rounding this answer to two decimal places, we get the final answer as approximately 11.829.

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The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.

The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.

In this case, applying the EDD rule, the sequence of jobs would be as follows:

D (Due on Friday 10th June)

F (Due on Tuesday 14th June)

E (Due on Wednesday 15th June)

C (Due on Friday 17th June)

G (Due on Thursday 16th June)

H (Due on Saturday 18th June)

A (Due on Monday 13th June)

B (Due on Monday 20th June)

By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.

Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.

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Answer:

73.12 ft²

Step-by-step explanation:

area = (8 x 6) + [(1/2)(3.14)(4²)] = 73.12 ft²

i believe it’s 42 but we’ll see if im wrong.

Answer: 42

Step-by-step explanation:

Plug 10 in for x

-4(10-15)2+2

(-40+60)2+2

(20)2+2

40+2

p(10)=42

Answer: Falling

Step-by-step explanation:

Once you rearrange this equation into y-intercept form and you get y = -4x-3, you then graph the line and the line appears to be decreasing down.

The area under the curve is \(\frac{6 \sqrt{3}}{5}\).

Consider the following parametric equations:\($$x=t^2-3 t \text { and } y=\sqrt{t} \text { and the } y \text {-axis. }$$\)

The objective is to find area enclosed by the curve using the formula.

The area under the curve is given by parametric equations x=f(t), y=g(t),  and is traversed once as t increases from α to β, then the formula for calculating the area under the curve:

\($$A=\int_\alpha^\beta g(t) f^{\prime}(t) d t$$\)

The curve has intersects with y-axis. so x=0

\($$\begin{aligned}t^2-3 t & =0 \\t(t-3) & =0 \\t & =0 \text { or } t=3\end{aligned}$$\)

Now we have to draw the graph,

Let f(t)=\(t^2-3 t, g(t)=\sqrt{t}$\)

Differentiate the curve f(t) with respect to t.

\(f^{\prime}(t)=2 t-3\)

Now, find the area under the curve use the above formula.

\(\begin{aligned}A & =\int_0^3(\sqrt{t})(2 t-3) d t \\& =\int_0^3(2 t \sqrt{t}-3 \sqrt{t}) d t \\& =\int_0^3\left(2 t^{\frac{3}{2}}-3 t^{\frac{1}{2}}\right) d t \\& =\left[2 \frac{t^{\frac{5}{2}}}{\frac{5}{2}}-3 \frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right]_0^3 \\& \left.\left.=\left[\frac{4 t^{\frac{5}{2}}}{5}-2 t^{\frac{3}{2}}\right]_0^3\right]^{\frac{5}{2}}\right] \\\\\end{aligned}$$\)

\(& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right]\)

\($\begin{aligned}& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right] \\& =\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}-0 \\& =\frac{6 \sqrt{3}}{5}\end{aligned}\)

Therefore,  the area of the curve is \(\frac{6 \sqrt{3}}{5}\).

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Answer: 60 %

Step-by-step explanation:

To find what percent 144 is of 240, we can use the following proportion:

part/whole = percent/100

Let x be the percentage we are trying to find, then we can write:

144/240 = x/100

To solve for x, we can cross-multiply:

14400 = 240x

Dividing both sides by 240, we get:

x = 14400/240 = 60

Therefore, 144 is 60% of 240.

Answer:

60%

Step-by-step explanation:

Percent proportion:

240 - 100%

144 - x%

Cross-multiply to find x:

\( \frac{144 \times 100\%}{240} = \frac{14400}{240} = 60\%\)

So, 144 is 60% of 240

a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

To write a rational number as a decimal, you need to divide the numerator by the denominator. Let's go through each option to determine which decimal is repeating or terminating.

a. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

b. 0: This decimal is also terminating because there are no numbers after the decimal point. The rational number is 0.

c. 0.16 overbar: This decimal has a line over the 16, indicating that it is repeating. The rational number is 0.161616...

d. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

So, to summarize:

a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

.

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Use long division to the quotient is \(5 x^5+90 x^2-134 x+3\)

What is quotient?

A quotient in mathematics is the amount created by dividing two numbers. In mathematics, the term "quotient" is frequently used to refer to the integer portion of a division, as well as to a fraction or a ratio.A fraction's quotient is the whole number that results from simplifying the fraction. The quotient is the fraction's decimal form if the simplified fraction yields a non-whole number.

\(\begin{aligned}& \text { Simplify }\left(5 x^5+90 x^2-135 x\right)+(x+3): \quad 5 x^5+90 x^2-134 x+3 \\& \text { Steps } \\& \left(5 x^5+90 x^2-135 x\right)+(x+3)\end{aligned}\)

\(Simplify $\left(5 x^5+90 x^2-135 x\right)+(x+3): \quad 5 x^5+90 x^2-135 x+x+3$\)

\(=5 x^5+90 x^2-135 x+x+3\)

\(Add similar elements: $-135 x+x=-134 x$\)

\(=5 x^5+90 x^2-134 x+3\)

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For the function  f(x)=Asin(2x)+D where A and D are positive real numbers. The value of f((π)/(12)) is 17.

We are given that the function f(x) = Asin(2x) + D has a maximum value of 22 and a minimum value of 2.

The maximum value of the function occurs when sin(2x) takes its maximum value of 1. Similarly, the minimum value occurs when sin(2x) takes its minimum value of -1.

So, we have:

f(x) = Asin(2x) + D

f(x_max) = A(1) + D = 22

f(x_min) = A(-1) + D = 2

From these two equations, we can form a system of equations:

A + D = 22

-A + D = 2

Adding the two equations together, we eliminate the variable A:

2D = 24

Dividing both sides by 2, we find:

D = 12

Substituting this value back into one of the equations, we can solve for A:

A + 12 = 22

A = 22 - 12

A = 10

Now, we have the values of A = 10 and D = 12.

To find the value of f((π)/(12)), we substitute x = (π)/(12) into the function:

f((π)/(12)) = 10sin(2(π)/(12)) + 12

= 10sin(π/6) + 12

= 10(1/2) + 12

= 5 + 12

= 17

Therefore, the value of f((π)/(12)) is 17.

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