Question 40
5
NUMBER THEORY The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original
number. Find the number.

The moments of a variate 'X' are defined by the expected value of the variate raised to the power of r, where r is an integer. In this case, the moments of 'X' are defined by E(X^r) = 0.6, for r = 1, 2, 3. This means that the expected value of X, X^2, and X^3 are all equal to 0.6. The probability of an event occurring is represented by P(X). In this case, P(X > 0) = 0.4, P(X = 1) = 0.6, and P(X^2 = 1) = 0.2. Convergence in probability refers to the concept that a sequence of random variables converges to a specific value with a probability of 1 as the number of trials approaches infinity.

These probabilities represent the likelihood of X being greater than 0, equal to 1, and squared equal to 1, respectively. This means that the probability of the sequence being within a certain distance of the specific value approaches 1 as the number of trials increases.

Two laws of convergence in probability are the Law of Large Numbers and the Central Limit Theorem. The Law of Large Numbers states that the average of a sequence of random variables converges to the expected value as the number of trials approaches infinity. The Central Limit Theorem states that the distribution of the sum of a sequence of random variables approaches a normal distribution as the number of trials approaches infinity.

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Therefore , the solution of the given problem of triangle comes out to be NL =  √(100 + 20LM2) * 10 * 4 .

A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular. The intersection of a quadrilateral's three edges is known as an angle. The sum of a triangle's edges is 180 degrees.

Here,

By removing NP:, we can resolve this system of equations.

NL Equals NP(LM + NL + 5). (5 - LM)

NL = NP(LM - PQ + 5) (LM)

NL(5 - LM) = NP(LM + NL + 5)(LM - PQ + 5) (LM)

By enlarging and condensing, we obtain:

NP = 2NL Plus LM / 5LM

Now that we know this, we can put it into one of the equations to find NL:

(2NL Plus LM / 5LM)

NL = (LM Plus NL + 5) (5 - LM)

By condensing and rearrangeing, we obtain:

(2NL Plus LM) = 0 when (NL2 - 10NL - 5LM2)

The quadratic algorithm yields:

NL =  √(100 + 20LM2) * 10 * 4 alternatively,

=> NL = (10 -  √(100 + 20LM2)) / 4

NL can never be negative, so we pick the positive root:

NL =  √(100 + 20LM2) * 10 * 4

Now that we have this, we can put it into one of the equations to find NP:

NP = 2NL Plus LM / 5LM

NP = 5LM / (2(10 + √100 + 20LM^2)) / 4 + LM)

NP is equal to 5LM / (5 +  √(25 + 5LM2)).

The widths of NP and NL are as follows:

NP is equal to 5LM / (5 + sqrt(25 + 5LM2)).

NL = (10 -  √(100 + 20LM2)) / 4

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The length of the segment indicated is c = c = 9.92.

Pythagoras discovered that the square of the hypotenuse in a right-angled triangle with a 90° angle is equal to the sum of the squares of the other two sides.

The triangle has three sides: the hypotenuse, which is always the longest, the opposite, which doesn't touch the hypotenuse, and the adjacent (which is between the opposite and the hypotenuse).

a² = b² + c²

a = 19

b = 16.2

c or x =?

19² = 16.2² + c²

361 = 262.4 + c²

c² = 98.6

c = √98.6

c = 9.92

Therefore, the length of the segment indicated is c = 9.92.

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The domain of the expression is \( [-1,1] \).

To rewrite the quantity as an algebraic expression of \( x \), we need to use the definition of the cotangent function and the relationship between the sine and cosine functions. The cotangent function is defined as \[ \cot (\theta)=\frac{1}{\tan (\theta)}=\frac{\cos (\theta)}{\sin (\theta)} \]Using the relationship between the sine and cosine functions, \[ \cos^{2} (\theta)=1-\sin^{2} (\theta) \]we can rewrite the cotangent function in terms of the sine function as \[ \cot (\theta)=\frac{\sqrt{1-\sin^{2} (\theta)}}{\sin (\theta)} \]Substituting \( \arcsin (x) \) for \( \theta \) gives us \[ \cot (\arcsin (x))=\frac{\sqrt{1-\sin^{2} (\arcsin (x))}}{\sin (\arcsin (x))} \]Since \( \sin (\arcsin (x))=x \), we can simplify the expression to get \[ \cot (\arcsin (x))=\frac{\sqrt{1-x^{2}}}{x} \]This is the algebraic expression of the quantity in terms of \( x \).

The domain of the expression is the set of values of \( x \) for which the expression is defined. Since the expression involves a square root, we need to ensure that the radicand is non-negative. This gives us the inequality \[ 1-x^{2}\geq 0 \]Solving for \( x \) gives us the inequality \[ -1\leq x\leq 1 \]Therefore, the domain of the expression is \( [-1,1] \).

In conclusion, the quantity can be rewritten as an algebraic expression of \( x \) as \[ \cot (\arcsin (x))=\frac{\sqrt{1-x^{2}}}{x} \]and the domain on which the equivalence is valid is \( [-1,1] \).

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The answer is sin(2x) = 0.8824.

If cot(x) = 5/3, we can use the identity cot(x) = 1/tan(x) to find the value of tan(x). Therefore, tan(x) = 1/(5/3) = 3/5.

Now, we can use the identity sin(2x) = 2sin(x)cos(x) to find the value of sin(2x). First, we need to find the values of sin(x) and cos(x).

Since tan(x) = 3/5, we can use the Pythagorean identity 1 = sin^2(x) + cos^2(x) to find the values of sin(x) and cos(x).

Let's assume sin(x) = 3/a and cos(x) = 5/a. Then, we can plug these values into the Pythagorean identity and solve for a:

1 = (3/a)^2 + (5/a)^2

1 = 9/a^2 + 25/a^2

1 = 34/a^2

a^2 = 34

a = √34

Therefore, sin(x) = 3/√34 and cos(x) = 5/√34.

Now, we can plug these values into the identity sin(2x) = 2sin(x)cos(x) to find the value of sin(2x):

sin(2x) = 2(3/√34)(5/√34)

sin(2x) = 30/34

sin(2x) = 0.8823529411764706

To 4 decimal places, sin(2x) = 0.8824.

the answer is sin(2x) = 0.8824.

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It took 24 days for the bank balance to increase from -$75 to $81 with daily deposits of $6.50.

Let's start by figuring out how much the bank balance increased by each day.

If the starting bank balance was -$75 and the ending bank balance was $81, then the total increase was:

$81 - (-$75) = $156

If she deposited $6.50 per day, then the bank balance increased by $6.50 each day.

So we can divide the total increase by the daily increase to find out how many days it took to reach $81:

$156 ÷ $6.50 per day = 24 days

Hence, the number of days is 24

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Answer and Step-by-step explanation:

1 cm: 12 m

This scale reduces the size of an actual object. For example, if a car is 4 meters long in real life, it would be represented as 0.33 cm on a map that uses this scale (4 meters divided by 12).

6 ft: 10 in

This scale enlarges the size of an actual object. For example, if a room is 10 feet wide in real life, it would be represented as 60 inches on a blueprint that uses this scale (10 feet multiplied by 6).

1 km: 1000 m

This scale preserves the size of an actual object. For example, if a park is 2 kilometers wide in real life, it would be represented as 2000 meters on a map that uses this scale.

The center of the ellipse is,

⇒ (3, 1)

An expression which is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division is called an mathematical expression.

We have to given that;

The equation of ellipse is,

⇒ (x - 3)²/4 + (y - 1)²/9 = 1

Now, We know that;

General form of the ellipse is,

⇒ (x - h)²/a + (y - k)²/b = 1

Where, (h, k) = the center of the ellipse.

Hence, We get;

The equation of ellipse is,

⇒ (x - 3)²/4 + (y - 1)²/9 = 1

By comparing;

The center of the ellipse is,

⇒ (h, k) = (3, 1)

Thus, The center of the ellipse is,

⇒ (3, 1)

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The probability of Steve picking a lime at random from the fruit bowl is 1/3.

Using the ratio given to find the proportion of oranges and kiwis in the fruit bowl. Let the number of oranges be 3x and the number of kiwis be 5x. Then the total number of fruits in the bowl is 3x + 5x + L, where L is the number of limes.

Given probability of picking an orange is 1/4, probability of picking a particular fruit from the bowl is calculated as:

number of that fruit / total number of fruits

1/4 = 3x / (3x + 5x + L)

Simplifying this equation, we get:

3x + 5x + L = 12x

L = 4x.

Substituting L = 4x and simplifying, we get:

probability of picking a lime = 4x / (3x + 5x + 4x) = 4/12 = 1/3

Therefore, the probability of picking a lime from the fruit bowl is 1/3.

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Two comparations can be done:

I understand that we want to compare the numbers:

√144 and 12.9329...

Notice that the second number has infinite decimals after the decimal point (and there is no a clear pattern), so it is an irrational number.

For the first one, we know that:

12*12 = 144

So 144 is a perfect square, then when we apply the square root we will get:

√144 = 12

Then the two comparations are:

√144 is rational and 12.9329... is irrational.

And:

12.9329...> √144

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Answer: p = (3.6 x 10^4)(0.03)^2

Step-by-step explanation:

According to the Pythagorean theorem, |AC| = 10 * sqrt(5/3)

The Pythagorean Theorem states that the square on the tangent line (the side across from the right angle) of a right triangle, or, in standard algebraic form, a2 + b2, are equal to a square just on legs.

The following are some significant applications of the Pythagoras theorem in daily life: used in architecture and building. used to determine the shortest distance in two-dimensional navigation.

Since the diagonals of a rectangle are identical, the Pythagorean theorem states that AB = CD and BC = AD.

Using the Trigonometry once more, but this times with the edges of the rectangle, we can get d.

Lastly, by applying the right triangle's sides to the Pythagorean theorem, we may determine AC. ACD:

[tex]AC=\frac{500}{3}=10*\frac{5}{3}[/tex]

Therefore, |AC| = 10*(5/3)

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Answer:

16.1 is the closest asnwer

Step-by-step explanation:

if you didn't understand feel free to send me a message bro

The exponential function that satisfies the given conditions is y = 2ˣ- 6.

An exponential function with a parent base of 2 can be written as y = 2ˣ. To ensure that the range is {y|y>-5}, we need to add a constant term to the function.

We can write the exponential function as y = 2ˣ + k, where k is a constant term.

To find the value of k, we can plug in the smallest value in the range, which is -5, and solve for k:

-5 = 2ˣ + k

k = -5 - 2ˣ
Since the domain is {x|x∈R}, we can plug in any value for x. Let's plug in 0 for x:

k = -5 - 2⁰

k = -5 - 1

k = -6

So, the exponential function with a parent base of 2 that has a domain of {x|x∈R} and a range of {y|y>-5} is y = 2ˣ - 6.

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The exact solutions to the equation sin^2(x) - cos^2(x) - sin(x) = 0 in the interval [0, 2π) are π/2, 7π/6, and 11π/6.

Given that

sin^2(x) - cos^2(x) - sin(x) = 0

Let's use the identity cos^2(x) + sin^2(x) = 1 to rewrite the equation:

sin^2(x) - (1 - sin^2(x)) - sin(x) = 0

Open the bracket and evaluate the like terms

2sin^2(x) - sin(x) - 1 = 0

Now we can solve for sin(x) using the quadratic formula:

sin(x) = [-b ± √(b² - 4ac)]/2a

Where

a = 2, b = -1 and c = -1

So, we have

sin(x) = [1 ± √((-1)² - 4 * 2 * -1)]/2*2

sin(x) = [1 ± √9]/4

sin(x) = (1 ± 3) / 4

Evaluate and split

sin(x) = 1 or sin(x) = -1/2.

If sin(x) = 1, then x = π/2.

If sin(x) = -1/2, then we can use the unit circle to find the solutions in the interval [0, 2π):

sin(x) = -1/2 when x = 7π/6 or 11π/6.

Therefore, the solutions in the interval [0, 2π) are π/2, 7π/6, and 11π/6.

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The given operation (x²-11x+30)/(x-6)-(x²-12x+35)/(9x³)  expressed in simplest form is x - 11 + 29.89x⁻¹- 2x⁻²+ 8x⁻³ - (3.89)x⁻⁴.

To express this operation in simplest form, we need to find the common denominator and combine the numerators.

Find the common denominator. The common denominator of (x-6) and (9x^(3)) is (9x^(3))(x-6).

Multiply each fraction by the common denominator to get the same denominator for both fractions.

(x²-11x+30)/(x-6) * (9x³)/(9x³) = (9x³)(x²-11x+30)/(9x³)(x-6)

(x²-12x+35)/(9x³) * (x-6)/(x-6) = (x-6)(x²-12x+35)/(9x³)(x-6)

Combine the numerators and keep the same denominator.

(9x³)(x²-11x+30) - (x-6)(x²-12x+35) / (9x³)(x-6)

Simplify the numerator by distributing and combining like terms.

(9x⁵-99x⁴+270x³) - (x³-18x₂+72x-35) / (9x³)(x-6)

9x⁵-99x⁴+269x³-18x²+72x-35 / (9x³)(x-6)

Simplify the denominator by multiplying.

9x⁵-99x⁴+269x³-18x²+72x-35 / 9x⁴-54x³

Simplify the fraction by dividing each term in the numerator by the term in the denominator with the highest power.

(9x⁵/9x⁴)-(99x⁴/9x⁴)+(269x³/9x⁴)-(18x²/9x⁴)+(72x/9x⁴)-(35/9x⁴)

Simplify each term.

x - 11 + (269/9)x⁻¹- (18/9)x⁻²+ (72/9)x⁻³ - (35/9)x⁻⁴

Combine like terms.

x - 11 + (29.89)x⁻¹ - (2)x⁻² + (8)x⁻³- (3.89)x⁻⁴

Therefore, the operation  (x²-11x+30)/(x-6)-(x²-12x+35)/(9x³)   expressed in simplest form is  x - 11 + 29.89x⁻¹- 2x⁻²+ 8x⁻³ - (3.89)x⁻⁴.

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Answer:

X=5

Step-by-step explanation:

instructions refer to the image

37. sec x / tan x = (1/cos x) / (sin x/cos x) = cos x / sin x = cot x
38. cot x / csc x = (cos x/sin x) / (1/sin x) = cos x / sin^2 x = cos x * (1/sin^2 x) = cos x * (csc^2 x)
39. sin x / csc x + cos x / sec x = (sin x / 1/sin x) + (cos x / 1/cos x) = sin^2 x + cos^2 x = 1
40. 1/sin²x - 1/tan^2 x = (1/sin^2 x) - (1/(sin^2 x/cos^2 x)) = (1/sin^2 x) - (cos^2 x/sin^2 x) = (1 - cos^2 x)/sin^2 x = sin^2 x/sin^2 x = 1
41. (1 - sin a)(1 + sin a) = 1 - sin^2 a = cos^2 a
42. (sec a - 1)(sec a + 1) = sec^2 a - 1 = tan^2 a
43. (cos B tan B + 1)(sin B - 1) = (cos B * sin B/cos B + 1)(sin B - 1) = (sin B + 1)(sin B - 1) = sin^2 B - 1 = -cos^2 B
44. (1 + cos B)(1 - cot B sin B) = (1 + cos B)(1 - cos B/sin B * sin B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B - cos^2 B/sin^2 B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B) = (1 + cos B) * 1 = 1 + cos B
45. 1 + cos a tan a csc a / csc a = 1 + (cos a * sin a/cos a * 1/sin a) / (1/sin a) = 1 + (sin a / sin a) / (1/sin a) = 1 + 1/(1/sin a) = 1 + sin a = sin a + 1
46. (cos a tan a + 1)(sin a - 1) / cos^2 a = (cos a * sin a/cos a + 1)(sin a - 1) / cos^2 a = (sin a + 1)(sin a - 1) / cos^2 a = (sin^2 a - 1) / cos^2 a = -cos^2 a / cos^2 a = -1

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Answer:

To graph y = 1/2x and y = x + 2, follow these steps:

Make a table of values for each equation. Choose several values of x, plug them into the equation, and solve for y. For y = 1/2x, you might choose x = -2, -1, 0, 1, and 2. For y = x + 2, you might choose the same values of x.

For y = 1/2x:

x | y

-2 | -1

-1 | -1/2

0 | 0

1 | 1/2

2 | 1

For y = x + 2:

x | y

-2 | 0

-1 | 1

0 | 2

1 | 3

2 | 4

Plot the points from each table on a graph. For y = 1/2x, plot the points (-2, -1), (-1, -1/2), (0, 0), (1, 1/2), and (2, 1). For y = x + 2, plot the points (-2, 0), (-1, 1), (0, 2), (1, 3), and (2, 4).

Draw a line through each set of points. The line for y = 1/2x should have a slope of 1/2 and pass through the point (0, 0). The line for y = x + 2 should have a slope of 1 and pass through the point (0, 2).

Label the axes and the lines. You can label the x-axis "x" and the y-axis "y". Label the line for y = 1/2x "y = 1/2x" and the line for y = x + 2 "y = x + 2".

Check your graph. Make sure each point is plotted correctly and the lines are drawn accurately. You can also check your graph by plugging in other values of x and making sure the corresponding points are on the lines.

Use simultaneously equation to eliminate one value and find the other then you find the value of the other one by substituting the value that u find from the other one eg: eliminate X find the value of y and then substitute y in one of your equation to find the value of X.

Answer:

  50 people

Step-by-step explanation:

Given a research project that take 16 people 125 days to complete, you want to know the number of people needed to complete the project in 40 days.

In math, project effort is measured in people×days. That value is considered to be a constant for a given project. This makes the number of people inversely proportional to the number of days, and vice versa.

  (16 people)×(125 days) = 2000 people·days = (p people)×(40 days)

Dividing by 40 days, we have ...

  p people = (2000 people·days)/(40 days) = 50 people

50 people are needed to complete the research in 40 days.

__

Additional comment

In real life, more people may get in each other's way. Or too few people may cause motivation, cooperation, and synergy to be lost. The maxim, "adding people to a late project makes it later" has a certain basis in reality.

The runner should choose the second cooler, because the probability of selecting a sports drink and a water from the first cooler is about 24.98% and the second cooler is about 25.86%.

To calculate the probability of selecting a sports drink and a water bottle from each cooler, we need to use the following formula:

Probability of selecting a sports drink and a water bottle = (number of sports drinks / total number of bottles) x (number of water bottles / (total number of bottles - 1))

For the first cooler, the probability of selecting a sports drink and a water bottle is:

(19/39) x (20/38) = 0.2498, or about 24.98%

For the second cooler, the probability of selecting a sports drink and a water bottle is:

(14/29) x (15/28) = 0.2586, or about 25.86%

Therefore, the runner should choose the second cooler, because it has a slightly higher probability of selecting a sports drink and a water bottle.

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3a and 4b are not like terms, hence they cannot be added, and the result of the expression is 3a + 4b and not 7ab.

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted.

3a and 4b on this problem are not like terms, as the letters, in this case a and b, are different.

Thus, the expression cannot be simplified, as only like terms, which are terms whose definition we gave in this explanation, can be simplified.

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We can write P(x) as P(x) = (x - 2)(x + 3)Q(x), where Q(x) is another polynomial.

This is the factored form of P(x), and it can be used to find other roots or to simplify the polynomial equation.

The factor theorem is a useful tool in finding the factors of a polynomial equation. The theorem states that if k is a root of the polynomial equation P(x) = 0, then x - k is a factor of P(x).

In our problem, we have P(2) = 0 and P(-3) = 0. This means that 2 and -3 are both roots of the polynomial equation P(x) = 0. According to the factor theorem, this means that x - 2 and x + 3 are both factors of P(x).

Therefore, we can write P(x) as P(x) = (x - 2)(x + 3)Q(x), where Q(x) is another polynomial. This is the factored form of P(x), and it can be used to find other roots or to simplify the polynomial equation.

In conclusion, the factor theorem is a useful tool in finding the factors of a polynomial equation. In our problem, we used the factor theorem to find the factors x - 2 and x + 3 of the polynomial equation P(x) = 0.

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Answer:

Mate show the full picture please..half of the question is not shown.

Step-by-step explanation:

Perimeter would not be used to solve the problem of determining the cost of replacing a linoleum floor with a wood floor. Perimeter is a measure of the boundary of a two dimensional shape, such as a square, rectangle, or triangle. This measure would not be useful in calculating the cost of replacing a floor, as the cost of the flooring materials will depend on the total area of the floor, rather than its perimeter.

Area is the measure of the two dimensional space of a shape, and would be the correct measure to use when calculating the cost of replacing a floor. Area is calculated by measuring the length and width of the floor, then multiplying them together. The cost of the flooring materials can then be calculated by multiplying the area of the floor by the cost of the materials per square foot. This would give an accurate figure for the total cost of the flooring materials.

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The Cartesian equation ( y = f(x)) for the curve is y = -x.

To find the Cartesian equation of the curve, we need to eliminate the parameter θ from the given parametric equations. We can do this by rearranging the equations and solving for θ in terms of x or y, and then substituting that value into the other equation.

First, let's rearrange the first equation to solve for cotθ:
2x = cotθ - cscθ
2x + cscθ = cotθ
cscθ - cotθ = -2x

Next, let's rearrange the second equation to solve for cscθ:
4y = 2cscθ - 2cotθ
2cscθ = 4y + 2cotθ
cscθ = 2y + cotθ

Now, let's substitute the value of cscθ from the second equation into the first equation:
2y + cotθ - cotθ = -2x
2y = -2x
y = -x

Therefore, the Cartesian equation of the curve is y = -x.

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The  product of 3∛6 and 2∛6 is equals to 18.

What is underroot ?

In mathematics, the symbol "√" is called the radical symbol, and the expression written under it is called a radicand.

To simplify 3∛6, we can use the fact that the cube root of a number can be written as a power of that number with an exponent of 1/3. Therefore, 3∛6 can be rewritten as 6^(1/3) raised to the power of 3.

D) To add 3∛6 and 2∛6, we can first factor out the common term of ∛6:

3∛6 + 2∛6 = (3 + 2)∛6 = 5∛6

So the sum of 3∛6 and 2∛6 is 5∛6.

E) To subtract 2∛6 from 4∛6, we can again factor out the common term of ∛6:

4∛6 - 2∛6 = (4 - 2)∛6 = 2∛6

So the difference between 4∛6 and 2∛6 is 2∛6.

F) To multiply 3∛6 by 2∛6, we can use the fact that the product of two roots with the same index can be found by multiplying the radicands together:

3∛6 x 2∛6 = (3 x 2)∛(6 x 6) = 6∛36

Since the cube root of 36 is 3 (3 x 3 x 3 = 27 and 4 x 4 x 4 = 64), we can simplify this further:

6∛36 = 6 x 3 = 18

Therefore, the product of 3∛6 and 2∛6 is equals to 18.

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To graph a quadratic function, follow the steps explained to obtain the smooth curve of the quadratic function.

Graphing quadratic functions involves plotting the points on a coordinate plane that satisfy the equation of the function. Quadratic functions are typically written in the form:

f(x) = ax^2 + bx + c

where;

To graph a quadratic function, you can follow these steps:

x = -b / 2a

y = f(x)

You can find the x-coordinate of the vertex by using the formula above, and then substitute it into the function to find the corresponding y-coordinate.

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The volume of a right rectangular prism is given by the formula below

[tex]V=whl[/tex]

Thus, in our case,

[tex]V=2.5\times13.5\times9=303.75[/tex]

The volume of the container is 1116.5ft^3.

Finally, multiply the total volume by the density given in the problem, as follows

[tex]weight=303.75\times0.28=85.05[/tex]

             ⇒ [tex]weight[/tex] ≈ [tex]85[/tex]

Rounded to the nearest pound, the answer is 85 pounds.

A dog eats soft food out of a 16oz packet. Every day the dog eats its meals split into three dishes breakfast, lunch, and dinner. If the dog needs to eat 11oz daily, each dish would have 3.67oz of food.

To find out  oz would be in each dish, we need to divide the total amount of food the dog needs to eat daily (11oz) by the number of dishes (3). This will give us the amount of food in each dish.

Here's the math:

11oz ÷ 3 dishes = 3.67oz per dish

So, each dish would have 3.67oz of food.

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