In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?

Answer:

[tex] \rm \: f(x) = \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } [/tex]

Differentiating both sides with respect to x

[tex] \rm \dfrac{d}{dx} ( {f}( x) = \dfrac{d}{dx} \bigg( \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } \bigg)[/tex]

Using u + v rule

[tex] \rm \: {f}^{ \prime} x = \dfrac{d}{dx} \bigg( \dfrac{5}{x} \bigg) + \dfrac{d}{dx} \bigg( \dfrac{7}{ {x}^{2} } \bigg)[/tex]

[tex] \rm \: {f}^{ \prime} x = 5. \dfrac{d}{dx} ( {x}^{ - 1} ) + 7. \dfrac{d}{dx} ( {x}^{ - 2} )[/tex]

[tex] \rm \: {f}^{ \prime} x = 5.( - 1. {x})^{ (- 1 - 1)} + 7.( - 2. {x})^{ - 2 - 1} [/tex]

[tex] \rm \: {f}^{ \prime} x = { - 5x}^{ - 2} { - 14x}^{ - 3} [/tex]

[tex] \rm \: {f}^{ \prime} x = - \dfrac{5}{ {x}^{2} } - \dfrac{14}{ {x}^{3} } [/tex]

[tex] \rm \: {f}^{ \prime} x = - \bigg(\dfrac{5}{ {x}^{2} } + \dfrac{14}{ {x}^{3} } \bigg)[/tex]

Hense The required Derivative is answered.

[tex]\boxed{\begin{array}{c|c} \rm \: \underline{function}& \rm \underline{Derivative} \\ \\ \rm \dfrac{d}{dx} ({x}^{n}) \: \: \: \: \: \: \: \: \: \ & \rm nx^{n-1} \\ \\ \rm \: \dfrac{d}{dx}(constant) &0 \\ \\ \rm \dfrac{d}{dx}( \sin x )\: \: \: \: \: \: & \rm \cos x \\ \\ \rm \dfrac{d}{dx}( \cos x ) \: \: \: & \rm - \sin x \\ \\ \rm \dfrac{d}{dx}( \tan x ) & \rm \: { \sec}^{2}x \\ \\ \rm \dfrac{d}{dx}( \cot x ) & \rm- { \csc }^{2}x \\ \\ \rm \dfrac{d}{dx}( \sec x ) & \rm \sec x. \tan x \\ \\\rm \dfrac{d}{dx}( \csc x ) & \rm \: - \csc x. \cot x\\ \\ \rm \dfrac{d}{dx}(x) \: \: \: \: \: \: \: & 1 \end{array}}[/tex]

Therefore , the solution of the given problem of equation comes out to be  f(x) = sin(/2 x) (when x = 1 or 2).

Variable words are commonly used in complex algorithms to show consistency between two statements that are not compatible. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization yields b + 7 as opposed to a single formula the fact that split 12 into two parts, which can be used with data collected from y + 7.

Here,

The goal is to construct a trigonometric equation with only answers at

x = 1 and x = 2.

f(x) = A sin(Bx+C+D)

=> B + C + D + A = 0 (equation 1)

=> Equation 2: A sin(2B + C + D) = 0

=> B + C sin A = 0 (equation 3)

=> Sin(2B+C) = A = 0 (equation 4)

Since sin(x) = 0 when x is a multiple of, formulae 3 and 4 can be rewritten as follows:

=> B + C = nπ (equation 5)

=> 2B + C = mπ (equation 6)

with numbers n and m. When we simultaneously solve equations 5 and 6 for B and C, we obtain:

=> B = (m - n)π/2 (equation 7)

=> C = nπ - B (equation 8)

=> When x = 1, C = /2 - /2 = 0.

=> When x = 2, C =  − /2 = 3/2.

Thus, the result is as follows:

when f(x) = sin(/2 x) (when x = 1 or 2)

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the profit function is positive, producing 164 units of the new product line would yield a profit of $600.

We should proceed with the product line since it is profitable and we can reasonably expect to meet our break-even quantity.
To find the break-even quantity, we need to set the cost function equal to the revenue function and solve for x:
C(x) = R(x)
55x + 3500 = 80x
25x = 3500
x = 140
Therefore, the break-even quantity is 140 units.
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
P(x) = 80x - (55x + 3500)
P(x) = 25x - 3500
Now we can evaluate the profit function at different values of x to see if producing these products is profitable or not.
If we plug in x = 164, the expected sales quantity, we get:
P(164) = 25(164) - 3500
P(164) = 4100 - 3500
P(164) = 600

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The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.

The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

For the given question:

Triangle with degree angles - 45-45-90

It means two legs are of same length 5 units.

Then, hypotenuse H will be:

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 5√2

Thus, the correct third side of the triangle will be 5√2.

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Step-by-step explanation:

No, the ratio in a 30-60-90 triangle is

::

[tex]1:1:\sqrt{2} [/tex]

not

1:1:2

Answer:

Step-by-step explanation:

To determine the amount that Buggiero Brothers Oil must deposit today in order to have enough money to pay the R85 000 liability four years from today, we can use the present value formula:

Present Value (PV) = Future Value (FV) / (1 + r)^n

where:

- FV is the future value, which is R85 000

- r is the annual interest rate, which is 6%

- n is the number of years until the liability needs to be paid, which is 4

To calculate the future value of the annual deposits of R16 000, we can use the future value of an annuity formula:

FV = PMT x [(1 + r)^n - 1] / r

where:

- PMT is the annuity payment, which is R16 000

- r is the annual interest rate, which is 6%

- n is the number of years of the annuity, which is 3 (since the first payment is made one year from today)

Plugging in the numbers:

FV = R16 000 x [(1 + 0.06)^3 - 1] / 0.06

FV = R61 719.56

Therefore, the total future value that Buggiero Brothers Oil will have in four years, including the initial deposit and the annual payments, will be:

FV = R85 000 + R61 719.56

FV = R146 719.56

Plugging in the numbers to the present value formula:

PV = R146 719.56 / (1 + 0.06)^4

PV = R116 442.12

Thus, Buggiero Brothers Oil needs to deposit R116 442.12 today to have enough money to pay the R85 000 liability four years from today, assuming a 6% rate of return.

The ranking from greatest to least goes on Nick, Olivia, Grace, and Brandon.

So in this, we have to rank the person who got most of the candy bars first and that is Nick.

After Nick Olivia has 94 candy bars so she is second in order.

Then on the third Grace had 75 candy bars.

And at the least Brandon is there with 53 candy bars.

Nick sold 100 candy bars

Olivia sold 94 candy bars

Grace sold 75 candy bars

Brandon sold 53 candy bars

Therefore, the ranking from greatest to least is Nick, Olivia, Grace, and Brandon.

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Answer:

height = 12 m

Step-by-step explanation:

We can assume from the problem that the movie screen is rectangular and the formula for perimeter (P) of a rectangle is

P = 2h + 2w, where l is the length and w is the width.

Thus, we can plug in 70 for P and 23 for w and solve for h:

[tex]70=2h+(2*23)\\70=2h+46\\24=2h\\12=h[/tex]

Comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.

A multiple of the denominators of two or more fractions can be used as a common denominator to add, subtract, or compare the fractions. As fractions with dissimilar denominators cannot be added together or directly compared, they must be changed into comparable fractions with the same denominator. We must determine the least common multiple (LCM) of the fraction denominators in order to determine a common denominator. The lowest number that is a multiple of both denominators is known as the LCM. Once we have the common denominator, we may multiply the numerator and denominator by the same factor to change each fraction to an equal fraction with the same denominator.

The two values are 9/10 and 3/2.

Taking the LCM we have:

9/ 10 and 15/10

Now comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.

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On number line we can compare 9/10 and 3/2 as 9/10 < 3/2.

What is number line?

A number line is a visual representation of numbers in order, usually shown horizontally. It is a line with a starting point and an endpoint that represent the smallest and largest numbers, respectively.

To compare 9/10 and 3/2 on a number line, we need to first convert them to the same denominator. The least common multiple of 10 and 2 is 10, so we can convert 3/2 to 15/10:

9/10 = 0.9

3/2 = 15/10 = 1.5

Now, we can plot these two numbers on a number line:

We can see that 9/10 is to the left of 3/2 on the number line.

Therefore we can compare 9/10 and 3/2 as 9/10 < 3/2.

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Answer:

Null Hypothesis (H0): There is no significant difference in life span for people in the two towns.

Alternative Hypothesis (H1): There is a significant difference in life span for people in the two towns.

Answer:

The null and alternative hypotheses that should be used to test this claim are:

Null hypothesis: There is no significant difference in lifespan for people in the two towns. Symbolically, this can be represented as H0: μ1 = μ2, where μ1 and μ2 are the population mean lifespans of Town A and Town B, respectively.

Alternative hypothesis: There is a significant difference in lifespan for people in the two towns. Symbolically, this can be represented as Ha: μ1 ≠ μ2.

To test this claim, the researcher can conduct a two-sample t-test using the data collected from the two towns. The test statistic can be calculated as:

t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^0.5

where x1 and x2 are the sample mean lifespans of Town A and Town B, respectively, s1 and s2 are the sample standard deviations of Town A and Town B, respectively, and n1 and n2 are the sample sizes of Town A and Town B, respectively.

Using the given data, the test statistic can be calculated as:

t = (78.5 - 74.4) / (11.2^2/20 + 12.3^2/20)^0.5 = 1.02

At a significance level of 0.05 with 38 degrees of freedom (df = n1 + n2 - 2), the critical value for a two-tailed test is ±2.024. Since the calculated t-value (1.02) falls within the acceptance region (-2.024 < t < 2.024), the null hypothesis cannot be rejected. Therefore, we do not have enough evidence to conclude that there is a significant difference in lifespan for people in the two towns.

Step-by-step explanation:

hope its help <:

The area of the shaded region under normal distribution is: 3.51

The standard normal distribution is defined as the normal distribution with a mean of 0 and a standard deviation of 1.

The z-table or the  standard normal table is one that provides the area under the standard normal curve to the left of a specified value, or "z-value". The value for the area is also the probability that the variable is less than the specified z-value.

To the right of -2.25 and to the left of -0.35

From standard normal table, we have the p-values as:

Area to the left of -0.35 = 0.3632

Area to the left of -2.25 = 0.0122

Area of the shaded region = 0.3632 - 0.0122 = 0.351

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Answer:

Step-by-step explanation:

subtract 20-3.50 you will get 16.50

Multiply 2.50x6 you will get 15

Subtract 16.50-15.00 you will get 1.50

If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, -4).

In Mathematics, a translation is a type of rigid transformation which is used in moving every point of an object in the same direction, as well as for the same distance.

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (3, 1) → Coordinate B' = (1, (-3)) = (1, -3)

Lastly, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, -3) → (1 + 2, -3 - 1) = B' (3, -4).

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Answer:

Compound shapes can also be called composite shapes. To find the area of compound shapes we must divide the compound shape into basic shapes and find the area of each of the basic shapes and add them together.

the answer is m + n = 24 + 55 = 79.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.

First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.

This can be simplified by dividing the numerator and denominator by 2:

48/110 = 24/55

So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.

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Answer:

To simplify the inequality x - 10 > 3, we can isolate x by adding 10 to both sides:

x - 10 + 10 > 3 + 10

Simplifying, we get:

x > 13

Therefore, the simplified inequality is x > 13.

Answer:

=6.96969e+29

Step-by-step explanation:

The height of the pole to the nearest foot, given the angle of elevation and the surveyor distance, is C. 135 ft

To find the height of the pole, we can use the tangent function from trigonometry. The tangent of the angle of elevation (44°) is equal to the ratio of the height of the pole (h) minus the transit height (4 feet) to the distance between the transit and the pole (140 feet).

So, we have:

tan(44°) = (h - 4) / 140

h - 4 = 140 × tan(44°)

h = 140 × tan(44°) + 4

h = 140 × 0.965 + 4

h = 135.1

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On the graph we have to ensure that the data points are seen, the text and design on the graph are meaningful along with keeping the alignment on a common scale.

The graph only presents the facts in an organised manner. It facilitates our understanding of the facts. The numerical information gleaned via observation is referred to as data.

For the given question,

In a graph the data should be shown clearly.

Now, displaying the data clearly entails making sure the data points are visible while also including relevant language on the graph itself.

Designing of the graph should be in a simple manner.

The alignment to be used has to be on a common scale.

The visual encoding has to be transparent.

Use of standard-forms are welcomed.

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Answer:

4/9

Step-by-step explanation:

4 sandwiches in between 9 friends

4 sandwiches must be divided in between 9 people

- > [tex]\frac{4 sandwiches}{9 people}[/tex] = [tex]\frac{4}{9}[/tex]

Answer:

Step-by-step explanation:

2/3

Andrew needs to choose a captain creature and a partner creature for his expedition to a mysterious dungeon. Each creature belongs to the grass, fire, or water group, and each group has 6 creatures, hence there are 216 ways

If the captain and partner creatures cannot be from the same group, how many ways can Andrew choose a captain creature and a partner creature?" by using combinatorial techniques.

Since Andrew cannot choose a captain and partner creature from the same group, there are 3 choices for the captain creature and 2 choices for the partner creature.

Therefore, the number of ways that Andrew can choose a captain and partner creature is: 3 * 2 * 6 * 6 = 216

Therefore, there are 216 ways that Andrew can choose a captain creature and a partner creature for his expedition to the mysterious dungeon

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Answer:

75%

Step-by-step explanation:

3/4 =75%

If you divide 3 by 4 you get 0.75

1=100%

0.75=75%

Answer:

.75

Step-by-step explanation:

think of 3 quarters

Answer:

4/8 in lowest terms is 1/2.

Step-by-step explanation:

Answer: 1/2

4/8 is equivalent to 1/2

Answer:

-2 and 3 is the required answer

Answer: The answer is: -2 or 3

Step-by-step explanation:

x^2 -x -6 = 0

x^2 -3x +2x -6 = 0

x(x-3) + 2(x-3) = 0

(x-3)(x+2) = 0

So x-3 = 0 :: x = 3

or x+2 = 0 ::  x=-2

Answer: i think its A and B

Step-by-step explanation: 33 divided by 2 is 16.5

                                             50 divided by 3 is 16.6667

                                             72 divided by 4 is 18 so that would be to much

                                             89 divided by 5 is 17.8 which is also to much

Answer:

2301 / 100

Step-by-step explanation:

We take

23.01 time 100 which makes 2301/100 fraction.

Answer:

The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money accumulated after n years

P = the principal (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $2,500, r = 0.05 (since 5% = 0.05), n = 2 (since interest is compounded semiannually), and t = 15. Substituting these values into the formula, we get:

A = 2500(1 + 0.05/2)^(2*15)

A ≈ $5,551.33

Therefore, Lyla's investment will be worth approximately $5,551.33 after 15 years if interest is compounded semiannually.

To calculate the total purchase price for Martin Pincher, we need to calculate the total amount of taxes he must pay and then add the purchase price of the items.

Let's start by calculating the taxes.

State Tax:

State Tax = 0.05 x (28.61+23.27+7.96)

State Tax = 0.05 x 59.84

State Tax = 2.99

County Tax:

County Tax = 0.005 x (28.61+23.27+7.96)

County Tax = 0.005 x 59.84

County Tax = 0.30

City Tax:

City Tax = 0.025 x (28.61+23.27+7.96)

City Tax = 0.025 x 59.84

City Tax = 1.50

Total taxes = 2.99 + 0.30 + 1.50

Total taxes = 4.79

Now let's calculate the total purchase price.

Total purchase price = 28.61+23.27+7.96 + 4.79

Total purchase price = 64.63

Answer:

  $64.63

Step-by-step explanation:

You want to know the total with tax of purchases of $28.61, 23.27, and 7.96 when they are subject to taxes of 5%, 0.5% and 2.5%.

The sum of the individual prices is subject to tax that is the sum of the individual tax rates. The tax rate sum is ...

  5% +0.5% +2.5% = 8%

Then the multiplier of the price is ...

  total = subtotal × (1 +8%) = 1.08×subtotal

A calculator can do all the computations at once, so we don't actually need to know the subtotals in order to find the total sale amount.

  (28.61 +23.27 +7.96) × 1.08 = 64.6272

The tax is generally rounded to the nearest cent, so ...

  the total purchase price is $64.63.

__

Additional comment

In the days before smart cash registers, the amount of sales tax was found by looking in a table supplied by the tax authority. It was always the same for any given purchase amount.

These days, the tax may be computed on the fly in such a way that the total tax collected is as near as possible to the total tax that needs to be collected.

That means a hundred instances of this purchase might have a total price of $64.63 for 72 of them, and $64.62 for the remaining 28 of them. That way, the total of the 100 sales would be $6462.72 and exactly the right amount of tax will have been collected. (At least one pizza chain collects tax this way.)

However, we need to choose the positive value for t, since time cannot equation be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

So we have:

[tex]-16t^2 + 170t + 30 = 20\\-16t^2 + 170t + 10 = 0\\8t^2 - 85t - 5 = 0\\t = (-b + \sqrt(b^2 - 4ac)) / 2a\\t = (-(-85) + \sqrt((-85)^2 - 4(8)(-5))) / 2(8)\\t = (85 + \sqrt(7225 + 160)) / 16\\t = (85 + \sqrt(7385)) / 16[/tex]

However, we need to choose the positive value for t, since time cannot be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.

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