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By simplifying the above equation i.e 27^(3/4) we get, 9 x (3)^(1/4).

Simplification is the process of substituting a mathematical expression with a simpler (typically shorter) counterpart. A fraction is simplified to an irreducible fraction. In computer algebra, expressions are simplified.

In order to simplify the given equation we need to factorize the bases. You can see that in the following steps :

(a^b)^c=a^(bc)

a^(b+c)=a^b x a^c

By using this above equation, we can factorize the bases.

So, factorization would be equal to :

27 ^(3/4) = ((3^3) )^ (3/4)

       = 3^(9/4)

      = 3^ (2+1/4)

       = 3^2 x 3^(1/4)

      = 9 x 3^(1/4)

That’s how we simplified the given equation.

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Answer:13.77 cm.

Step-by-step explanation:

r = sqrt((3V)/(pih))

= sqrt((31758)/(pi29))

= sqrt((5274)/(pi*29))

= sqrt(182.16)/(pi/29)

= 13.77 cm

Answer:

Step-by-step explanation:300 mStep-by-step explanation:20 meters per minute. 15 minutes it dives. 20x15 is 300

Answer 3.8 x 104

Step-by-step explanation:

The vector <8,-5> when expressed in coordinate notation is (8, -5)

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

Notation = <8, -5>

The above expression is in vector notation

To express the vector notation in a coordinate notation, we simply express the <> as ()

So, we have the following representation

(8, -5)

Hence, the coordinate notation is (8, -5)

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The equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].

What is perpendicular lines?

When two geometric objects intersect at a right angle, they are considered to be perpendicular in elementary geometry. By using the perpendicular symbol,, the condition of perpendicularity can be graphically represented. Between two lines, a line and a plane, or between two planes can be used to define it.

Consider the given equation of line

5x + 4y = 10

Convert it into the form y = mx + c

⇒ 4y = -5x + 10

y = -5/4x + 10/4

y = -5/4x + 5/2

Here the slope of line is, -5/4.

The slope of perpendicular line is negative reciprocal of the slope of given line.

So, the slope of perpendicular line is,

[tex]-\frac{1}{(-5/4)} = \frac{4}{5}[/tex]

Also the line passes through the point (5, -4).

By using the point slope form to find the equation of line

[tex]y-y_1 = m(x-x_1)\\y-(-4) = \frac{4}{5}(x-5)\\ y+4=\frac{4}{5}x - 4\\ y = \frac{4}{5}x - 4 - 4\\ y = \frac{4}{5}x - 8[/tex]

Hence, the equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].

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If the area of the area of the base increases at rate of 2 cm²/sec then the rate at which the height of the box is decreasing is 0.11 cm/sec .

In the question ,

it is given that ,

the volume of the rectangular box having square base is 1100 cm³ ;

the rate of decrease of the area is (dA/dt) is = 2 cm²/sec ;

we know that ; Volume = Area × Height ;

the area of the square base of side 12 cm is = 12 × 12 = 144 ;

So , height = Volume/Area ;

= 1100/144 ;

Now , V = A × h ;

differentiating the above equation w.r.t. "t" ,

we get ;

dV/dt = A×(dh/dt) + h×(dA/dt)

0 = 144×(dh/dt) + (1100/144)×(2)

dh/dt = -2200/(144 × 144)

= -0.106095

≈ -0.11

Therefore , the rate of change of height is = 0.11 cm/sec .

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The probability that the entire batch will be accepted.

What is Acceptance Sampling?

Acceptance sampling is a statistical measure used in quality control. It allows a company to determine the quality of a batch of products by selecting a specified number for testing.

abc Electronics Company manufactured 1200 write-rewrite cds, and 150 are defective. Since 150 are defective, the number of write-rewrite cds that would be accepted is (1200 - 150 = 1050).

Since the items at selected without replacement, the number of write-rewrite cds will continue to decrease anytime a write-rewrite cds is taken out. For example if they are 1050 accepted write-rewrite cds if one is taken out they would then be 1049 accepted write-rewrite cds, and if another one is taken out they would be 1049 accepted write-rewrite cds and so on.

If 3 of these cds are randomly selected for testing without replacement,

The probability that the entire batch will be accepted

= (1050/1200) × (1049/1200) × (1048/1200) × (1047/1200)

= 0.8750 × 0.8742 × 0.8733 × 0.8725

=0.5828

The probability that the entire batch will be accepted is 0.5828 .

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Answer:

4.5

Step-by-step explanation:

You calculate it. look 1 yard is 36 inches. so 1/8 of a yard is 36 divided by 8. 4.5!

180 people would the elevator carry than if all the passengers were​ adults.

What is the meaning of times?

The mathematical symbol is used to represent the multiplication operation and the consequent product. It is often referred to as the times sign or the dimension sign.

Given an elevator can carry 25 adults or 30 children at one time.

One day the elevator carries a full passenger load 36 times.

If the elevator carries all adults, then it carries (25 × 36) = 900 adults.

If the elevator carries all children, then it carries (30 × 36) = 1080 adults.

If all the passengers were​ children, then the elevator carry more than (1080 - 900) = 180 people if all the passengers were​ adults.

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Oliver travelled the distance of 21.5 ft

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

As shown in the figure, we need to find the perimeter of the triangle ABC.

Perimeter = g + h +f ............(1)

g=f = 6.3 ft

Finding h using pythogoras theorem formula:

h² = g² + f²  

    = 6.3² +  6.3²

   =  79.38

h =√79.38  = 8.909 ≈ 8.9 ft  

So, (1) => Perimeter = 6.3 + 6.3 + 8.9 = 21.5 ft

Thus, Oliver travelled the distance of 21.5 ft

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The number of apples obtained from the product of the fraction represented by the apples and the total number of fruits is 5 apples.

A fraction is a representation of the proportion or part of a whole quantity.

The fraction of the fruit that are apples = One quarter = 1/4

The fraction of the fruit that are oranges = One quarter of the number of fruits

The number of bananas = 4

Number of pear = 3

Number of plums = 3

The fraction of the whole fruit are represented by  apples and oranges = (1/4) + (1/4) = 1/2

The fraction of the total number of fruits represented by the bananas, pear and plum = 1 - (1/4 + 1/4)) = 1/2

Therefore;

Half of the total number of fruits = 4 + 3 + 3 = 10 fruits

Half of the fruits = 10

The total number of fruits is therefore, n = 2 × 10 = 20

The number of fruits that are apples = (1/4) × The total number of fruits

Therefore, the number of apples = (1/4) × 20 = 5

The number of fruits that are apples are 5 fruits

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(A) cylindrical coordinate = (r, θ, z) = (√2, -π/4, 1)

(B) cylindrical coordinate = (r, θ, z) = (14, -π/3, 7)

In the given question, we have to change from rectangular to cylindrical coordinates. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A) (-1,1,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

So we find the value of r and θ one by one.

r = √x^2+y^2

r = √(-1)^2+(1)^2

r = √1+1

r = √2

θ = [tex]\tan^{-1}[/tex](y/x)

θ = [tex]\tan^{-1}[/tex](1/-1)

θ = [tex]\tan^{-1}[/tex](-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√2, -π/4, 1)

B) (-7,7√3,7)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

So we find the value of r and θ one by one.

r = √x^2+y^2

r = √(-7)^2+(7√3)^2

r = √49+147

r = √196

r = 14

θ = [tex]\tan^{-1}[/tex](y/x)

θ = [tex]\tan^{-1}[/tex](7√3/-7)

θ = [tex]\tan^{-1}[/tex](-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 7)

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Answer: 8

Step-by-step explanation:

=(1) ^3×(2) ^3

=1×1×1×2×2×2

=1×8

=8

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The probability that the battery lasts between 12,000 and 14,000 miles is approximately 0.084.

The number of miles that a car can run before its battery wears out follows an exponential distribution with an average value of 11,000 miles. The probability that the battery lasts between 12,000 and 14,000 miles can be calculated as follows:

P(12,000 < x < 14,000) = P(x < 14,000) - P(x < 12,000)

To calculate the probabilities on the right-hand side of the equation, we can use the formula for the cumulative distribution function (CDF) of an exponential distribution:

F(x) = 1 - e^(-x/λ)

where λ is the mean value of the distribution. In this case, λ = 11,000 miles.

Plugging in the values and solving, we get:

P(12,000 < x < 14,000) = F(14,000) - F(12,000)

= (1 - e^(-14,000/11,000)) - (1 - e^(-12,000/11,000))

= e^(-12,000/11,000) - e^(-14,000/11,000)

≈ 0.242 - 0.158

≈ 0.084

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The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.

Given that,

We have to find the system of linear equation in which (2,-1) is a solution of the first equation but not for the second equation and (5,5) is a solution for system of equation.

We know that,

To find the system of equation we have a formula that is

y=mx-mx₁+y₂

Here m is slope

m=-1-5/2-5

m=-6/-3

m=2

The equation is

y=2x-2(5)+5

y=2x-10+5

y=2x-5

Therefore, The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.

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The integration of 1/ln(x) is not possible as We permit y = lnx, we then recognize that x = ey.

By differentiating each aspects of this equation with admire to y we get:dx/dy = ey, because the exponential characteristic differentiates to itself whilst differentiated with admire to its power.

In mathematics, the logarithmic quintessential characteristic or quintessential logarithm li(x) is a unique characteristic. It is applicable in issues of physics and has variety theoretic significance. In particular, in keeping with the high variety theorem, it's far a excellent approximation to the high-counting characteristic, that is described because the variety of high numbers much less than or same to a given value x.

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The decimal number 24.7 represents the average mileage of the vehicle.

Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.

A famous magazine tests vehicles and trucks for mileage out and about and around the city. the magazine reports that half of the vehicles tried had mileages beneath 24.7 mpg out and about, and the other half of the vehicles tried had mileages above 24.7 mpg.

The decimal number 24.7 means the vehicle can cover 24.7 miles with each gallon of gas.

The decimal number 24.7 represents the average mileage of the vehicle.

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The new coordinates after a reduced scale factor of 0.77 with the origin will be equal to (−10, 10), (20, 40), (30, 30). Hence, option B is correct.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the data given in the question,

We will combine the x and y dimensions even by scale factors to shrink the picture by a multiplier of 0.77 with both the origins as that of the center of dilatation because the figure's vertices are (-13, 13), (26, 52), and (39, 39).

So, the first point is (-13, 13)

-13 × 0.77 = -10 and,

13 × 0.77 = 10

So, the new point is (-10, 10).

The second point is (26, 52).

26 × 0.77 = 20

52 × 0.77 = 40

So, the new point is (20, 40)

The third point is (39, 39)

39 × 0.77 = 30

39 × 0.77 = 30

So, the new point is (30, 30).

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Answer:

x = - 4

Step-by-step explanation:

A line with an undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (- 4, 2 ) with x- coordinate - 4 , then

x = - 4 ← equation of line

Answer:

X=1

Step-by-step explanation:

For step one you have to Distribute

2x-1(4x+3)=-7x+2 --> 2x-4x-3=-7x+2

For step two you have to Combine Like Terms

2x-4x-3=-7x+2 --> -2x-3=-7x+2

For step three you have to Add Three To Both Sides

-2x-3=-7x+2 --> -2x=-7x+5

For step four you have to Add 7x To Both Sides

-2x=-7x+5 --> 5x=5

For step 5 you have to Divide Both Sides By The Same Factor (5)

5x=5 --> x=1

Hope This Helps!

The classification model is used to define the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.

Percentage:

In math,  number or ratio that can be expressed as a fraction of 100 refers the percentage.

Given,

Here we have a dollar general sends out a $5 off coupon to its email subscribers.

And we need to find the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.

Then the model used to define the this type of situation is refers as the classification model, because in this model, we have classify the given group of people based on the constraint.

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Answer:

11[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

15-1/2 = 31/2

(31/2)(3/4) = 93/8 = 11[tex]\frac{5}{8}[/tex]

The exponential generating function is,

G(x) = (x¹/1! + x²/2! + ...)(x¹/1! + x³/3! + x⁵/5! +...)(x°/0! + x¹/1! + x²/2! + ...)²

where the first factor describes the pennies, the second describes the quarters, and the last describes nickles and dimes.

We want the coefficient of [tex]x^{r}[/tex]/r!.

Using exponential identities we get,

G(x) = ([tex]e^{x}[/tex] - 1)([tex]\frac{e^{x}-e^{-x} }{2}[/tex]) ([tex]e^{x}[/tex])² = [tex]\frac{1}{2}[/tex] ([tex]e^{4x} - e^{2x} - e^{3x} + e^{x}[/tex]),

and the coefficient is

[tex]\frac{1}{2} (4^{r} - 2^{r}- 3^{r} + 1 )[/tex]

The generating function is

G(x) = (x¹/1! + x²/2! + ...)⁴(x°/0! + x¹/1! + x²/2!+...)²² = ([tex]e^{x}-1[/tex])⁴[tex]e^{22x}[/tex],

and we again want the coefficient of [tex]x^{10}[/tex]/10!.

Multiplying we get,

G(x) = ([tex]e^{4x}-4e^{3x}+2e^{2x}+1[/tex])[tex]e^{22x}[/tex] = [tex]e^{26x}-4e^{25x}+2e^{24x}+e^{22x}[/tex]

so the coefficient of [tex]x^{10}[/tex]/10! is

26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰

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Answer:0.038

Step-by-step explanation:

The ordinary number equivalent of 3.8x10⁻² is expressed as 0.038.

To express the number 3.8x10⁻² as an ordinary number, we need to understand scientific notation. In scientific notation, numbers are written in the form of a coefficient (a decimal number greater than or equal to 1 but less than 10) multiplied by 10 raised to a certain power (positive or negative). This notation is commonly used to represent very large or very small numbers in a concise and standardized way.

Let's break down 3.8x10⁻² step by step:

The coefficient: 3.8

The coefficient is the decimal part of the number, which should be greater than or equal to 1 but less than 10. In this case, the coefficient is 3.8.

The exponent: -2

The exponent indicates the power of 10 to which the coefficient is raised. If the exponent is negative, it means the number is less than 1. In this case, the exponent is -2, which means we are dividing the coefficient by 100 (10 raised to the power of -2 is 1/100).

Now, to express 3.8x10⁻² as an ordinary number, we simply perform the calculation:

3.8 × 10⁻² = 3.8 ÷ 100 = 0.038

So, the ordinary number equivalent of 3.8x10⁻² is 0.038.

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An approximate 95% confidence interval for the difference in the mean tooth damage is  (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

For sweetened samples

The value of n = 10

The mean of the samples = 6.14

The standard deviation of the sample = 5.0

For unsweetened samples

The value of n = 15

The mean of  the sample = 5.20

The standard deviation of the sample = 15.0

We have to assume that necessary conditions for inference are met

The confidence interval = 95%

The equation will be

(6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

Therefore, the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

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The numbers are 10 and 10. And the sum of their squares will be 200.

For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.

The maximum and minimum value of the function is at f'(x) = 0.

The sum of the two numbers is 20.

Let the first number be 'x'. Then the other number is (20 - x). Then the equation is given as,

y = x² + (20 - x)²

Differentiate the function, then we have

y' = 0

2x + 2(20 - x)(-1) = 0

x - 20 + x = 0

2x = 20

x = 10

Then the other number is given as,

⇒ 20 - 10

⇒ 10

The sum of their squares is given as,

⇒ 10² + 10²

⇒ 100 + 100

⇒ 200

The numbers are 10 and 10. And the sum of their squares will be 200.

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The equation x² + y² = 49 can be written in standard form as (x-0)² + (y-0)² = 49, which is the equation for a circle with a center at (0, 0) and a radius of 7.

The equation for a circle is (x-h)² + (y-k)² = r², where (h, k) represents the center of the circle and r represents the radius.

In order to find the center (h, k) and radius (r) of the circle, we need to rearrange the equation to put it in the standard form. To do this, we subtract 49 from each side of the equation, which will give us x² + y² - 49 = 0. Then, we can factor the equation to get (x² + y²) - 7(7) = 0. This can be further simplified to (x + 7)(x - 7) + (y + 7)(y - 7) = 0.

Since there are no solutions for (x + 7) or (x - 7) when set equal to 0, we can conclude that the equation for the circle is (x-0)² + (y-0)² = 49, which is the equation for a circle with a center at (0, 0) and a radius of 7.

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Answer:

Step-by-step explanation:

The correct option is A 6

×

4 = 24

Closure property of multiplication for whole numbers states that product of two whole numbers a and b is always a whole number c.

Only options B and C have a multiplication sign. Of them, option B is of the form a

×

b = b

×

a

So 6

×

4 = 24 is an example for closure property of multiplication.

The first and fourth quadrant of a coordinate grid should be used to display the given data .

In the question ,

it is given that ,

from the time the storm has started the temperature change is from 0° to - 20° .

we know that time cannot be in negative , and temperature can be both negative and positive .So only quadrant 1 and 4 can be used for representation .

Y = temperature

X = time

Quadrant 1 = (+x , +y) this can be used because x can only be positive and y is also positive.

Quadrant II = (-x , +y) this cannot be used because x cannot be negative

Quadrant III = (-x , -y) this cannot be used because x cannot be negative

Quadrant IV = (+x , -y) this can be used because x can only be positive and y can be negative.

Therefore , only 1 and 4 quadrants can be used .

The given question is incomplete , the complete question is

An equation is written to represent the relationship between the temperature in Alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. if the storm lasted five hours and the temperature saw a drop from 0° to - 20°, which quadrant(s) of a coordinate grid should be used to display this data ?

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