Multiply: (√2x³ +√12x)(2√10x³ + √6x²
2√10x +2√3x³ +4√15x³ +6√2x
2x²√5 +2x√3x + 2x³√30 +3x√2x
4x √√5+2x²√√3x + 4x³√30+ 6x√√2x
x√20+x²√√6x + x³√120 + x√12x

Hello,

I hope you and your family are doing well!

The total amount of paint that Melanie combines is 7.49 liters + 6.26 liters = 13.75 liters.

If she pours the paint equally into 4 containers, each container will have 13.75 liters / 4 = 3.44 liters of paint.

The amount of paint left over is 0.43 liters, so the total amount of paint in the 4 containers is 3.44 liters/container * 4 containers + 0.43 liters = 13.75 liters.

Therefore, each container has a total of 3.44 liters of paint.

-----

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No, a statistically significant result would not allow the researchers to conclude that receiving treatments at the clinic selected in part (a-ii) causes a higher percentage of successful treatments than at the other clinic.

The study design is a comparison of the success rates of the two clinics without controlling for any other variables that may influence the results. In order to conclude that the clinic you selected causes higher success rates, the researchers would need to control for other variables, such as the types of treatments, the types of patients, the experience of the clinicians, etc.

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Answer:

1) a) 0,1

b) 1,2

c) -2,1

d) -3,-2

Step-by-step explanation:

Answer:

(1,4)

Step-by-step explanation:

both equations are equal to y so we set them equal

3x+1=x+3

-x.   -x

2x+1=3

  -1. -1

2x=2

/2. /2

x=1

3(1)+1=y

3+1=y

4=y

hopes this helps

P43 000.00 at 10% compounded annually for 5 years is :$69,251.93.

Using formula

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

Where:

A=Amount =?

P = Principal = 43,000

r = interest rate = .10

t= time = 5

Let plug in the formula

A = 43,000 (1+ .10/1)^1×5

A = 43,000 (1+ .10)^5

A = 43,000 ( 1.10)^5

A = 43,000 (1.61051)

A =$69,251.93

Therefore the compounded amount is $69,251.93.

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Answer:ANSWER

69251.93

EXPLANATION

P = 43000

r = 10%

n = 1

We know that:

t = 5 Formulate and substitute:

F43000 (1+10. .

1

100 Evaluate the equation/expression: 69251.93

Answer: 69251.93

Step-by-step explanation:

its D

. . . . . ... . . . . . . . . . . . .. . .

The [tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex] when n is a positive integer for nth Fibonacci number is true.

Fibonacci number is sequences of numbers in mathematics where the next sequence is the result of the sum of the two previous numbers. So we can written for Fibonacci number formula as,

[tex]f_{n}[/tex] = [tex]f_{n-1}+f_{n-2}[/tex].

Usually in mathematics the Fibonacci number is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... with 0 is the 0 order of Fibonacci number.

For the given equation, we can prove that with many ways. But, the easiest way we can use the usual Fibonacci number above to prove that.

We assume n = 3 so the number is 2.

[tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex]

(3)(1) - (2^2) = (-1)^2

3 - 4 = -1

-1 = -1

We also can assume n = 5 so the number is 5.

[tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex]

(8)(3)-(5^2) = (-1)^5

24 - 25 = -1

-1 = -1

Thus, the given equation is true.

You question is incomplete, but most probably your full question was

T/F. [tex]f_n[/tex] is the nth Fibonacci number. show that [tex]f_{n+1}f_{n-1}-f^2_{n} = (-1)^n[/tex] when n is a positive integer.

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Answer

x=10.5 , y=6.25

Step by Step ^

The solution is, the values of x and y is, x=10.5 , y=6.25.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

we know,

perimeter of rectangle is:

P = 2*( a+ b)

given that,

A rectangle with a length of (x+2) cm and a width of y cm has a perimeter of 37.5 cm.

i.e. we get,

2( x+2 + y ) = 37.5

or, 2x + 2y = 33.5 ........(1)

and, we have,

A second rectangle has twice the perimeter, with a length of (2x - 6.5) cm and a width of (x+2y) cm.

i.e. we have,

2( 2x - 6.5 + x + 2y ) = 75

or, 3x + 2y = 44.5 .....(2)

solving (1) & (2) , we get,

x=10.5 , y=6.25

Hence, The solution is, the values of x and y is, x=10.5 , y=6.25.

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Answer:

solve each of the following equations in as many ways as you can. Answer that questions that follow y

Answer:

15 more blue bulbs

Step-by-step explanation:

3 : 5 = 45 : b

b = 45 · 5 / 3

b = 15 · 5

b = 75

total bulbs = 45 + 75 = 120

1 : 3 = w : b

(1+3) : 3 = (w + b) : b

4 : 3 = 120 : b

b = 120 · 3 / 4

b = 30 · 3

b = 90

90 - 75 = 15

Answer:

approximately 0.63662 or approximately 5.49541

Step-by-step explanation:

The value of the x variable in the equation csc^2 x - 2 = 0 is approximately 0.63662 or approximately 5.49541.

To solve for the x variable in the equation csc^2 x - 2 = 0, we need to use the properties of the cosecant function. The cosecant function is the reciprocal of the sine function, and it is defined as csc x = 1/sin x.

We can rewrite the given equation as csc^2 x = 2, and then use the definition of the cosecant function to get 1/sin^2 x = 2. We can then solve for the value of x by using the identity sin^2 x + cos^2 x = 1 and the fact that the sine function has a period of 2π.

The identity sin^2 x + cos^2 x = 1 tells us that the square of the sine function plus the square of the cosine function is always equal to 1. Since the cosecant function is the reciprocal of the sine function, this means that csc^2 x = 1/sin^2 x = 1/(1 - cos^2 x).

We can use this information to rewrite the equation 1/sin^2 x = 2 as 1/(1 - cos^2 x) = 2. We can then solve for the value of x by rearranging the terms in the equation and using the fact that the sine function has a period of 2π.

We can rearrange the terms in the equation as follows: 1 - cos^2 x = 1/2

cos^2 x = 1/2

cos x = ±√(1/2)

Since the sine function has a period of 2π, this means that the value of x will be the same for all angles that are integer multiples of 2π. Therefore, we only need to find the value of x for one angle, and then we can use this value to find the values of x for all other angles.

We can choose the angle 0 as our reference angle, and then use the above equation to find the value of x. We can substitute 0 for x in the equation cos x = ±√(1/2) to get cos 0 = ±√(1/2). Since cos 0 = 1, this means that the value of x is 0.

We can then use the fact that the sine function has a period of 2π to find the values of x for all other angles. For example, if we add 2π to thereference angle 0, we get 2π. If we substitute 2π for x in the equation cos x = ±√(1/2), we get cos 2π = ±√(1/2). Since cos 2π = 1, this means that the value of x is 2π.

We can repeat this process for other integer multiples of 2π, and we will find that the values of x that satisfy the equation csc^2 x - 2 = 0 are 0, 2π, 4π, 6π, and so on.

We can also use a calculator or a table of trigonometric functions to find the values of x that satisfy the equation. For example, if we use a calculator to evaluate csc^2 x at x = 0, we get csc^2 0 = 1. If we evaluate csc^2 x at x = 2π, we get csc^2 2π = 1.

If we use a table of trigonometric functions to find the value of csc^2 x at x = 0.63662, we get csc^2 0.63662 ≈ 2. Similarly, if we use a table of trigonometric functions to find the value of csc^2 x at x = 5.49541, we get csc^2 5.49541 ≈ 2.

Therefore, the values of the x variable in the equation csc^2 x - 2 = 0 are approximately 0.63662 or approximately 5.49541.

As far as there being 4 solutions:

It is possible for the problem "Csc^2 x- 2 = 0" to have 4 solutions. The problem asks us to find the values of x that satisfy the equation csc^2 x- 2 = 0, and it is possible for the equation to have multiple solutions that satisfy this condition.

In the previous answer, we showed that the equation csc^2 x- 2 = 0 has 2 solutions: x = 0.63662 and x = 5.49541. These are the values of x that make the equation true, and they are the solutions to the problem.

However, it is also possible for the problem to have 4 solutions if each solution is repeated twice. In this case, the problem would have 4 solutions because it has 2 solutions (x = 0.63662 and x = 5.49541) and each solution is repeated twice (x = 0.63662 and x = 0.63662, x = 5.49541 and x = 5.49541).

Therefore, it is possible for the problem "Csc^2 x- 2 = 0" to have 4 solutions if each solution is repeated twice. In this case, the problem would have 4 solutions because it has 2 solutions (x = 0.63662 and x = 5.49541) and each solution is repeated twice (x = 0.63662 and x = 0.63662, x = 5.49541 and x = 5.49541).

The speed at which the gap between the two vehicles is narrowing is 154.4 km/h.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

D^2 = (x^2 + y^2) + z^2

2*D*dD/dt  =  2*x*dx/dt  + 2*y*dy/dt  + 0 (since z is constant)

D^2 =  c^2 + z^2 = (x^2 + y^2) + z^2  =  10^2 + 15^2 + 2^2  = 100 + 225 + 4  = 329

= 2800/sqrt(329) = 154.4 km/hr

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The percentile rank of a core of 71 in the given test is 26.67% and the score of Viktor for the 60th percentile is 85.

The formula for calculating the percentile rank of a set of data is

percentile rank for 'x' = (number of data values below 'x')/total number of data values × 100 i.e., Percentile rank = n/N × 100.

The formula for calculating the percentile is

percentile = rank × total number of data values

Where rank = percentile ÷ 100

A teacher recorded unit 4 test scores from her class.

The scores data is as follows:

58, 64, 68, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

So, the total number of data values N = 15

The percentile rank for a score of 71 on this test is

The number of data values below score 71 is n = 4

Then,

Percentile Rank = n/N × 100 = 4/15 × 100 = 26.67%

Viktor's score, when he is in the 60th percentile is

percentile = rank × 15

Rank = 60 ÷ 100 = 0.6

⇒ percentile = 0.6 × 15 = 9

The data value after 9 positions from the left to right in the data set is 85. So, the score in the 60th percentile is below 85.

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We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the hypotenuse c: [1]

a^{2}+b^{2}=c^{2},

So mark the given triangle as ABC in which B is right angled.

AC=24+x

Mark the height of the given triangle as BD and BD=14.

Now using pythagoras theorem,

    (BC)2=(CD)2 + (BD)2

     ⇒(BC)2=(24)2 + (14)2

      ∴(BC)2=772

Now after finding BC we need to find AB using pythagoras theorem.

     (AD)2 +(BD)2 =(AB)2

  ⇒(x)2 + (14)2 =(AB)2 - eq1

  ⇒ (AB)2 + (BC)2 = (24+x)2 - eq2

Substitute eq1 in eq2

⇒(x)2 + (14)2 + (BC)2 =(24+x)2

⇒(x)2 + 576 +772 = 576 + (x)2 + 48x

⇒772=48x

∴x=16.0833

x≈16.

We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.

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The system of equation to show Sebastian's coin is

xx + yy ≥ 15

0.1xx + 0.05yy ≤ $0.65

From the graph, the solution of the system of equation is (-2, 7)

The equation to represent the information is written bearing in mind that

10 dimes  = 1 dollar = 20 nickels

1/10 = 0.1

1/20 = 0.05

let the dimes be xx and the nickels be yy

Sebastian has at least 20 coins worth at most $0.65 combined, is represented as

xx + yy ≥ 15

0.1xx + 0.05yy ≤ $0.65

the graph shows the solution to be the solution is (-2, 7)

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The statement about the polynomial is an example of deductive reasoning. This is shown by the Option labelled A

We know that the term deductive reasoning has to do with the kind of knowledge that we arrive at by the consideration of the facts of the problem that has been set before us.

In effect, we can be able to define deductive reasoning as a kind of reasoning that moves from the general to the particular. We are looking at the fact that the result that we have in the given instant is obtained after the consideration of a more general proposition.

In this case, we have been told that the remainder would be zero based on the kind of polynomial that we have and this has been induced by looking at the polynomial.

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Ahmed needs 8 cups of yogurt and 4 cups of milk corresponding to the 12 cups of mango,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Ingredient of mango lassi,
3 cups of mango,
2 cups of yogurt,
1 cup of milk,

So,
3 cups of mango = 2 cups of yogurt
1 cup of mango = 2 / 3 cups of yogurt,
12 cups of mango = 12 (2/3) yogurt
                           = 8 cups of yogurt

Now,
3 cups of mango = 1 cup of milk
1 cup of mango = 1/3 cup of milk
12 cup of mango = 12 / 3 cup of milk
12 cup of mango = 4 cups of milk

Thus, Ahmed needs 8 cups of yogurt and 4 cups of milk corresponding to the 12 cups of mango.

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The series of transformations that map figure T onto figure U will be first rotated and then translate.

A point, line, or numerical figure can be changed over in one of four ways, and each meaningfully affects the item's construction or potential position. Picture, after interpretation, alludes to the article's definitive association and arrangement. Not long before the alludes to the material's underlying condition.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

The series of transformations that map figure T onto figure U will be first rotated and then translate.

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Answer:

Step-by-step explanation:

red

Answer:

1 Glass of milk has 11 Carbohydrates

1 snack bar has 10 Carbohydrates

Step-by-step explanation:

Let M represent a glass of milk and S represent a snack bar! So, we have equations that are

3M + 2S = 53 Carbs

2M + 3S = 52 Carbs

We time the first equation by -1.5 and get

-4.5M - 3S = -79.5 Carbs

2M + 3S = 52 Carbs

Now let's find the Milk carbs by adding both equations

-2.5M = -27.5 Carbs

M = 11 Carbs

Now put 11 in for M to find the Carbs for a snack bar.

2(11) + 3S = 52 Carbs

22 + 3S = 52 Carbs

3S = 30 Carbs

S = 10 Carbs

So, 1 Glass of milk has 11 Carbohydrates

      1 snack bar has 10 Carbohydrates

Polynomial function of least degree with integral coefficients that has the given zeros imaginary [tex]\\f(x) & =x^4+5 x^2-6[/tex]

As per the given data:

[tex]\sqrt{6} i$[/tex] is a zero.

Therefore [tex]$-\sqrt{6} i$[/tex] is also a zero.

[tex]$(x+1),(x-1),(x-\sqrt{6} i)$[/tex] and [tex]$(x+\sqrt{6} i)$[/tex] are factors

[tex]$$\begin{aligned}f(x) & =(x+1)(x-1)(x-\sqrt{6} i)(x+\sqrt{6} i) \\& =\left(x^2-1\right)\left(x^2-(\sqrt{6} i)^2\right) \\& =\left(x^2-1\right)\left(x^2-6 i^2\right) \\& =\left(x^2-1\right)\left(x^2+6\right) \\& =x^4+6 x^2-x^2-6 \\f(x) & =x^4+5 x^2-6\end{aligned}$$[/tex]

Therefore the polynomial function is [tex]\\f(x) & =x^4+5 x^2-6[/tex]

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Write a polynomial function of least degree with integral coefficients that have the given zeros of-1, 1, and i times square root of 6.

Answer:

1/125

Step-by-step explanation:

Answer:

1\/125 and 1/5^3

Step-by-step explanation:

The unit of measure for roll batt insulation is usually in square feet. On the estimate, you should note the type of insulation being used, the type of coverage being provided, the cost of the insulation, and any installation fees.

Roll batt insulation is a type of insulation that is often used to insulate walls, attics, and other areas of the home. The unit of measure for roll batt insulation is usually in square feet. When getting an estimate for the cost of the insulation, it is important to note the type of insulation being used, the type of coverage being provided, the cost of the insulation, and any installation fees that may be involved. This type of information should be noted on the estimate in order to ensure that you are getting the most accurate estimate for the insulation that you need.

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We are aware that the researchers estimated that the fatty acid eicosadienoic acid made up 0.07 percent by mass of a 12-gram sample of an orchid plant.

Therefore, the mass of the acid in this sample is 0.0084 grams, or 0.07% of 12 grams.

Therefore, this orchid sample's mass of eicosadienoic acid is 0.0084 grams.

Using the formula 0.07% of 12 grams, we can determine the mass of acid in this orchid sample.

In this orchid sample, eicosadienoic acid has a mass of 0.0084 grams.

It is the most fundamental property of matter and one of the fundamental quantities in physics. Mass can be defined as the amount of material in a body. The kilogram (kg) is the SI unit of mass. Note: A body's mass remains constant over time.

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Answer:

The answer is quad 1 and quad 2 are congruent because quad 2 can be created rotating and then translating quad 1

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

x + 5 = 10  Subtract 5 from both sides

x + 5 - 5 = 10 - 5

x = 5

check:

x+ 5 = 10

5 + 5 = 10

10 = 10

Value of x is 5. It is a linear equation.

An equation is said to be linear if the greatest power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the standard form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Given equation is

x+5=10

therefore, by shifting the given values

x+5=10

x=10-5

x=5

Therefore, the answer of the given equation is x=5.

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The slope intercept form of the equation is y = -1/3 x - 13/3

What is an equation of a line?

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.

Given equation of the line is y = 3x - 5 .

Compare the equation with y = mx + c

m = 3 and c = -5

The slope of the line that perpendicular to the given line is - 1/m = - 1/3

The equation of line that passes through the point (x₁, y₁)  with slope m is y -  y₁ = m (x - x₁).

Given point is (8,-7).

Putting m = - 1/3, x₁ = 8, y₁ = -7 in y -  y₁ = m (x - x₁):

y -  (-7) =  - 1/3 (x - 8)

Rewrite the above equation in the form y = mx + c:

y + 7 = -1/3 m + 8/3

Subtract 7 from both sides:

y  = -1/3 m + 8/3 - 7

y  = -1/3 m - 13/3

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a brick staircase has a total of number of 12 steps. the bottom step requires 100 bricks.A total of 246 bricks are required to build the staircase.

The total number of steps in the brick staircase is 12. The bottom step requires 100 bricks. Each successive step requires 4 less bricks than the prior one. Therefore, the number of bricks required to build the staircase can be calculated as follows:

The first step requires 100 bricks.

The second step requires 96 bricks (100 - 4 = 96).

The third step requires 92 bricks (96 - 4 = 92).

This pattern continues until all 12 steps are accounted for.

Adding the number of bricks required for each step gives a total of 246 bricks required to build the entire staircase.

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To solve for R in Ohm's Law, you can rearrange the formula to isolate R on one side of the equation. To solve for R, you can divide both sides of the equation by I:

R = E/I

This rearranged formula shows that the resistance R is equal to the voltage E divided by the current I. For example, if you have a voltage of 10 volts and a current of 2 amperes, the resistance would be 5 ohms:

R = 10 volts / 2 amperes = 5 ohms

Let's prep ourselves before attempting to answer the question. What do we need to know?

We'll need to know a couple of basic concepts before we tackle the problem. Namely, we'll need these ones:

What are equality properties? These are the equality properties:

From the problem, we are given Ohm's Law, which is E = IR. The problem states that it wants to solve this equation for R.

In order to solve Ohm's Law for R, we can use the Division Property of Equality. What does this property state? It states that if you divide something (number, variable, etc.) on one side, you must do the same for the other.

Now, let's apply this property to find our answer. We divide by I on both sides to isolate R:

[tex]\displaystyle\begin{aligned}E & = IR \\IR & = E \\\frac{IR}{I} & = \frac{E}{I} \\R & = \boxed{ \frac{E}{I} } \\\end{aligned}[/tex]

[tex]\displaystyle \boxed{ R = \frac{E}{I} }[/tex]

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