Consider the following function. g ( x ) = x 3 − 6 A) Find its average rate of change over the interval [ − 2 , 2 ] . B) Compare this rate with the instantaneous rates of change at the endpoints of the interval.

Divide 30 by 29.5735 to get the liquid ounce equivalent of 30 ml or around 1.0144 fluid ounces.

When measuring liquid components for cooking or baking, for example, it might be useful to convert milliliters (ml) to fluid ounces (fl oz).

It's vital to keep in mind that, depending on the amount of accuracy required by the recipe or activity at hand, it's typical when working with liquid measurement to round to the next tenth or hundredth of an ounce or milliliter.

To achieve precise and consistent findings, it's also crucial to utilize the proper measurement equipment and units.

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Answer: The Addition Rule for disjoint events is the sum of the probabilities of 2 events, while the General Addition Rule says if 2 are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).

Step-by-step explanation: The Addition Rule states that for two disjoint events, the probability that one or the other occurs is the sum of the probabilities of the two events. (Book example on p. 280 about the probability that a randomly selected student is either a sophomore (A) or a junior (B) therefore P(A or B). The addition of probabilities for disjoint events is the third basic rule of probability: Rule 3: If two events A and B are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).

Answer: The Addition Rule for disjoint events is the sum of the probabilities of 2 events, while the General Addition Rule says if 2 are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).

Step-by-step explanation: hope this helps0^0

Answer:  In trigonometry, the unit circle has a radius of 1 and is centered at the origin. It’s useful for learning ratios like sine and cosine. It also illustrates the relationship between angles in degrees and radians.

Step-by-step explanation:

Which of the following is not an equivalent fraction of 1830, the correct answer is (option A)

Fractions that represent the same value

Equivalent fractions are fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake.

To find equivalent fractions, you just need to multiply the numerator and denominator of that reduced fraction (35) by the same natural number, ie, multiply by 2, 3, 4, 5, 6... Important: 1830 looks like a fraction, but it is actually an improper fraction. 610 is equivalent to 1830 because 3 × 25 × 2 = 610.

Hence, Which of the following is not an equivalent fraction of 1830, the correct answer is (option A)

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Answer:23/10

Step-by-step explanation:

you move the comma and  how many times you have to move it is how many zeros in the denominator

The cube root of 36 is a number between 3 and 3.5, and can be represented mathematically as ∛36.

Square roots are simply the opposite operation of squaring a number. For example, the square root of 9 is 3 because 3 x 3 = 9.

Similarly, the cube root is the opposite operation of cubing a number. The cube root of a number is the value that, when cubed, gives the original number. For instance, the cube root of 27 is 3 because 3 x 3 x 3 = 27.

Now, to answer your question, "What is 36 cube root?" - this can be written as ∛36 or as the cube root of 36. To find the cube root of 36, we need to find a number that, when cubed, gives 36.

We can start by using trial and error. We know that 2 x 2 x 2 = 8, which is less than 36. We also know that

=> 3 x 3 x 3 = 27, which is less than 36.

So, we can try a number between 3 and 4. Let's try 3.5.

If we cube 3.5, we get 42.875, which is greater than 36.

If we try a number lower than 3.5, we will get an even greater value. Therefore, the cube root of 36 is between 3 and 3.5.

We can use more precise methods to find the cube root of 36, such as using a calculator or estimating with decimal approximations. However, using trial and error is a simple and effective way to find an approximate answer.

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The NumPy matrix inverse is a function that calculates the inverse of a given square matrix.

The NumPy matrix inverse function is a strategy that works out the opposite of a square grid involving the NumPy library in Python. The inverse of a matrix is a matrix that, when duplicated by the first grid, creates the identity matrix.

In NumPy, the matrix inverse function is executed as the linalg.inv() technique, which takes a NumPy cluster as information and returns its converse as an exhibit. The matrix should be square and invertible, the importance of its determinant isn't equivalent to nothing. The matrix inverse is utilized in different fields of math, designing, and science to solve systems of linear equations, track down the eigenvalues and eigenvectors of a network, and perform different procedure on matrices.

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The width W of the island will be 3.75 ft by given scaling factor.

What exactly is scaling factor?

The Scale Factor is used to scale shapes in various dimensions. Geometry teaches us about various geometrical shapes in both two and three dimensions. The scale factor is a statistic for figures that seem similar but have different scales or measures. Imagine two circles have the same appearance but different radii.

The scale factor specifies how much larger or smaller a figure is than the original figure. With the use of a scale factor, you may design an expanded or smaller version of any original form.

Now,

Here given that 1 inch=1.5 ft

and as w=2.5 inches then the actual width W will be =2.5*1.5

=3.75 ft

and we can find scaling factor by  length of the actual object divided by length of scale drawing i.e.

S=length of object/length of drawing

hence,

          The width W of the island will be 3.75 ft.

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The two planes that have created the parallel traits would be airplane 3 and airplane 5

To get the parallel lines, we would have to check the angles that are formed

for angle 3 angles on a line is 180

x + 110 = 180

x = 70 degrees

For angle 5

we can see that the position of x in 3 is the same position in 5

hence we can see that in plane 5, x = 70

hence these two would be parallel

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Answer:

3x13=39

Step-by-step explanation:

ellie=13

kid 1=13

kid 2 =13

Answer:

its 320

Step-by-step explanation:

The total number of many sixth-grade students at Luehrs Middle School found using the percentage is 320.

What is meant by percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. There is no dimension to percentages. As a result, it is known as a dimensionless number.

Given,

Number of students in sixth grade who has a pet dog = 112

The percentage of sixth grade students who has a pet dog = 35%

Let the number of total sixth grade students be x.

Percentage

= (Number of students with pet dog/Total number of sixth grade students *    100

35 = (112/x) * 100

35/100 = 112/x

x = (100/35) * 112 = 320

Therefore the total number of many sixth-grade students at Luehrs Middle School found using the percentage is 320.

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When tossing a fair coin, the possible outcomes are a head (H) or a tail (T), each with a probability of 1/2.

To find the probability of getting at least one head in two coin tosses, we can first find the probability of getting no heads (i.e., two tails) and then subtract that from 1 to get the probability of getting at least one head.

The probability of getting two tails is (1/2) * (1/2) = 1/4, since the probability of getting a tail on the first toss is 1/2 and the probability of getting a tail on the second toss is also 1/2, and we multiply these probabilities together to get the joint probability.

Therefore, the probability of getting at least one head in two coin tosses is:

1 - 1/4 = 3/4

So the probability of at least one head in two coin tosses is 3/4 or 0.75.

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The ratio of cars to trucks is 1 to 3, which means that for every three trucks, there is one car. Since there are 51 trucks, this means that there is 17 cars (51/3 = 17). Therefore, the dealer has 17 cars for sale.

The automotive dealer sells both cars and trucks and the ratio of cars to trucks on the lot is 1 to 3. This means that for every three trucks, there is one car. Therefore, if there are 51 trucks currently for sale, then the number of cars can be determined by dividing this number by 3. This equals 17 cars. Thus, the dealer has 17 cars for sale.

The ratio of cars to trucks is 1 to 3, which means that for every three trucks, there is one car. Since there are 51 trucks, this means that there is 17 cars (51/3 = 17). Therefore, the dealer has 17 cars for sale.

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The present ages are the Boy is 17 years old and his sister's age is 14 years old.

Since the ratio of ages is 4: 3 take them as 4x and 3x and form an equation as given in the problem. Solve the resultant equation for the values of 'x'. And calculate the ages 5 years ago and add 5 to get the present ages.

Here we have

A boy is older than his sister by 3 years  

Then the difference is both ages = 3

Given that five years ago the ratio of ages = 4: 3  

Let 4x and 3x be the age of a boy and his sister five years

As we know the difference between them = 3 years

=> 4x - 3x = 3

=> x = 3 years

=> 4x = 4(3) = 12

Boy's age after '5' years = 12 + 5 = 17 years

His sister's age = 17 - 3 = 14 years

Therefore,

The present ages the Boy is 17 years old and his sister's age is 14 years old.

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Complete Question:

A boy is older than his sister by 3 years, five years ago the ratio was 4:3. Find his present age.

The nth derivative of each function is n!.

Taking the nth derivative of a function is the process of calculating successive derivatives and observing the patterns that occur.

In your example, the function given is f(x) = xⁿ. To find the nth derivative, you need to calculate the first few derivatives and observe the pattern that occurs.

The first derivative of the function f(x) = xⁿ is f'(x) = [tex]nx^{n-1}[/tex]

The second derivative is f''(x) = [tex]n(n-1)x^{n-2}[/tex]

From here, you can see that the pattern is that the exponent of x decreases by 1 each time, and the coefficient of x increases by n-1 each time.

Therefore, the nth derivative of

f(x) = xⁿ => f^(n)(x) = [tex]n(n-1)(n-2)...(n-(n-1))x^{n-n}[/tex] = n!x⁰ = n!.

This result is true for any value of n, so the nth derivative of f(x) = xⁿ is always equal to n.

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Using a calculator, we find that b ≈ 3.9 inches (rounded to the nearest 10th of an inch).

What is the Law of Sines?

The Law of Sines, also known as the sine rule, is a trigonometric formula used to find unknown sides or angles in a triangle.

To solve this problem, we can use the Law of Sines, which states that for any triangle ABC,

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the side lengths opposite the corresponding angles A, B, and C, respectively.

Using this formula, we can set up the following proportion:

b/sin(B) = a/sin(A)

Plugging in the values we know, we get:

b/sin(36°) = 6/sin(121°)

Solving for b, we get:

b = (6 sin(36°))/sin(121°)

Using a calculator, we find that b ≈ 3.9 inches (rounded to the nearest 10th of an inch).

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Any system of geometry that is not based on the principles of Euclidean geometry is known as non-Euclidean geometry.

Many geometrical systems that are not based on the parallel postulate or other Euclidean axioms are referred to as non-Euclidean geometry.

The parallel postulate asserts that given a line and a point off the line, there is only one line that can be drawn through the point parallel to the provided line.

Attempts to establish or refute this postulate gave rise to non-Euclidean geometries. Contrarily, non-Euclidean geometries are founded on diverse axioms that allow for various kinds of parallel lines, including multiple parallel lines in hyperbolic geometry and no parallel lines in elliptic geometry.

Non-Euclidean geometry is important to many fields of mathematics and science, including relativity theory and cosmology.

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If Seshni wants to cover six cushions, each measuring 36 cm x 36 cm, with fabric.  

a. Seshni needs to buy 0.84375 square meters of fabric.

b. It will cost R64.66 including VAT.

a. The dimensions of each cushion are 36 cm x 36 cm, and with the added 1.5 cm seam allowance, each cushion will require fabric with dimensions of (36 + 1.5) cm x (36 + 1.5) cm = 37.5 cm x 37.5 cm.

The total area of fabric required to cover all six cushions is:

6 cushions x (37.5 cm x 37.5 cm) = 8437.5 square centimeters

To convert to square meters, we need to divide by 10000:

8437.5 square centimeters / 10000 = 0.84375 square meters

So, Seshni needs to buy 0.84375 square meters of fabric.

b. Next, we can calculate the cost of the fabric.

0.84375 square meters / 0.9 meters = 0.9375 meters

The cost per meter is R59.99 excluding VAT, so the cost of the fabric is:

0.9375 meters x R59.99/meter = R56.23

To calculate the cost including VAT, we need to add the VAT amount. Assuming the VAT rate is 15%, the VAT amount is:

0.15 x R56.23 = R8.43

So the total cost including VAT is:

R56.23 + R8.43 = R64.66

Therefore, Seshni needs to buy 0.84375 square meters of fabric, and it will cost R64.66 including VAT.

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Since we want the equation in the form y = kx, we need to find the value of k that will make this equation fellow to the bone we just wrote.

We can rewrite the equation as

y = ( m/ x) x b

Now, we can see that if we set k = m/ x, the equation will be in the form y = kx.

So, the equation that describes the relationship between the number of square yards( x) of ground to be covered and the number of scoops( y) of bean seed demanded is y = kx

where k = m/ x, and m and b are constants that depend on the specific situation.

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The population of Medway, Ohio, is expected to be approximately 3728 in the year 2020.

From the question, we have the following parameters that can be used in our computation:

Initial, a = 4007

Rate = 0.36% per year

The decay function is represented as

y = a(1 - rate)^x

So, we have

y = 4007 * (1 - 0.36%)^x

This gives

y = 4007 * (0.9964)^x

The year 2020 is 20 years from 2000

So, we have

x = 20

Substitute the known values in the above equation, so, we have the following representation

y = 4007 * (0.9964)^20

Evaluate

y = 3728

Hence, the approximate solution is 3728

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[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =177 \end{cases}\implies n(177)=180n-360 \\\\\\ 177n=180n-360\implies 0=3n-360\implies 360=3n \\\\\\ \cfrac{360}{3}=n\implies 120=n[/tex]

The automobile is currently worth Rs 52,488. four years ago, it was worth 80,000.

Present Value A = Rs. 52,488

Depreciation rate r = 10 % per annum

Time t = 4 years

Let initial value be P

We know the formula, A =[tex]$\mathrm{P}\left(1-\frac{\mathrm{r}}{100}\right)^t$[/tex]

We obtain by substituting the supplied values.

52,488 =[tex]$\mathrm{P}\left[1-\frac{10}{100}\right]^4 \\[/tex]

52,488 = [tex]$\mathrm{P}(0.9)^4 \\[/tex]

[tex]$\mathrm{P}=\frac{52488}{0.6561} \\[/tex]

P = 80,000

The complete question is:

The value of a car depreciates every year at the rate of 10% on its value at the beginning of the year. If the present value of the car is Rs 52,488 its worth four years ago was

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The perimeter of the trapezoid ABFE and the prove that the triangle ΔABC is an isosceles are as follows;

First question;

The perimeter of the trapezoid ABFE is 100 units

Second question;

The sides AB and BC in the triangle ΔABC are congruent, therefore, triangle ΔABC is an isosceles triangle

An isosceles triangle is a triangle that has two sides that have the same lengths.

The specified parameters are;

The segment joining the midpoints of the side [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex] of the equilateral triangle ΔABC = EF

EF = 2·x + 8 and AB = 7·x - 2

The midsegment theorem applied to the triangle ΔABC indicates that we get;

EF = (1/2) × AB

Therefore; 2·x + 8 = (1/2) × (7·x - 2)

(1/2) × (7·x - 2) = 2·x + 8

7·x - 2 = 2 × (2·x + 8)

7·x - 2 = 4·x + 16

7·x - 4·x = 16 + 2 = 18

3·x = 18

x = 18/3 = 6

x = 6

EF = 2·x + 8

Therefore; EF = 2 × 6 + 8 = 20

EF = 20

AB = 7·x - 2

Therefore; AB = 7 × 6 - 2 = 40

AB = 40

AB = AC = BC (Definition of an equilateral triangle)

Therefore;

AC = BC = AB = 40 (symmetric property)

The midpoints E and F, indicates that we get;

AE = CE and BF = CF

AC = AE + CE and BC = BF + CF (segment addition property)

Therefore; AC = AE + AE = 2 × AE

40 = 2 × AE

AE = 40/2 = 20

BC = 2 × BF

40 = 2 × BF

BF = 40/2 = 20

The perimeter of the trapezoid ABFE, P = AB + BF + EF + AE

P = 40 + 20 + 20 + 20 = 100

Second question

The coordinates of the vertices of the triangle are;

A(1, 2), B(-5, 3), and C(-6, -3)

The lengths of the sides of the triangle found using the distance formula are;

AB = √((-5 - 1)² + (3 - 2)²) = √(37)

BC = √((-6 - (-5))² + (-3 - 3)²) = √(37)

AC = √((-6 - 1)² + (-3 - 2)²) = √(74)

The lengths of the sides AB and BC in the triangle ΔABC are the same, therefore, the triangle ΔABC is an isosceles triangle.

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Therefore, the lateral surface area of the cube is 35/2 square inches.

In mathematics, area is the measure of the size of a two-dimensional region or surface. It is usually measured in square units, such as square meters, square feet, or square centimeters. The area of a shape or surface is determined by the amount of space it covers in a plane or on a flat surface. Areas are commonly used to describe the size of objects or spaces in a variety of contexts, including geometry, architecture, engineering, and physics. They are also used in everyday life, such as calculating the amount of carpet needed to cover a floor or the amount of paint needed to cover a wall.

Here,

Since the package is a cube, all of its faces are identical squares. Therefore, the area of one face is equal to the length of one side squared.

Let x be the length of one side of the cube. Then we have:

x² = 7(5)/8

Solving for x, we get:

x = √(7(5)/8) = sqrt(35/8)

The lateral surface area of the cube is the sum of the areas of the four non-base faces. Since the cube has six faces in total, the lateral surface area is:

Lateral surface area = 4 * (side length)²

Lateral surface area = 4 * x²

Lateral surface area = 4 * (√(35/8))²

Lateral surface area = 4 * 35/8

Lateral surface area = 35/2

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The measure of ∠VWX in this triangle VWX is, 68.9°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, The cosine rule of triangles,

Here, cosW = (VW² + XW² - VX²)/2(WX×WV).

cosW = (36² + 23² - 35²)/2(36×23).

cosW = 600/1656.

W = cos⁻¹(0.36).

∠W = 68.9°.

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$12,960 is the answer I believe

1% of 12,000 is 120

120 times 8 is 960

12,000 plus the tax (960) = 12,960

The value after converting the length 178 cm  to inches , is 178 cm is equivalent to 70 inches .

The Centimeters (cm) and inches are both the units of measurement that  are used to measure length .

They both belong to different systems of measurement. Centimeters are used in the International System of Units (SI), whereas  inches are used in the Imperial and US Customary systems.

We know that 1 centimeter is = 0.3937 inches .

that means that conversion factor is 0.3937 ,

So , we can write ; 178 cm = 178 × 0.3937 inches ;

⇒ 178 cm = 70.0786 inches ≈ 70 inches .

Therefore , 178 cm is approximately equal to 70 inches .

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Step-by-step explanation:

hence proved...

The answer mentioned in above pdf.

missing part is (. OC is correct option of cubic formula)...

So, in response to the above question, we can state that We obtain the inequality following system of inequalities by combining these three constraints:

[tex]x + y \geq 10\\x \leq 7\\y \leq 6[/tex]

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

[tex]x + y \geq 10[/tex]

Next, we know that Sam works out his cardiovascular system for no more than 7 hours. Thus, x must be less than or equal to 7. This restriction can be shown by the inequality:

[tex]x \leq 7[/tex]

Finally, we are aware that Sam only devotes a maximum of 6 hours to weight training. This implies that y should be between -6 and -6. This restriction can be shown by the inequality:

[tex]y \leq 6[/tex]

We obtain the following system of inequalities by combining these three constraints:

[tex]x + y \geq 10\\x \leq 7\\y \leq 6[/tex]

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