Given that f(x)= 2x+8 g(x)= 5x-2/4 and h(x)= 2x+6/x

find

a) g[f(0)]

b) f(-5)

c) f[h(3)]
d) h°f(x)
e) h⁻¹(x)

The expression that is equivalent to  ∛ 5 * [tex]\sqrt[5]{4}[/tex] is [tex]5^{1/3}*4^{2/5}[/tex]

A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.

The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.

This equation represents exponents in fraction form and the basics for the calculation is from

x^(b/n)

[tex]\sqrt[n]{x}^{b}[/tex]

Rewriting the expression is done as below

∛ 5

= [tex]5^{1/3}[/tex]

and

[tex]\sqrt[5]{4}[/tex]

[tex]= 4^{2/5}[/tex]

combining both gives

∛ 5 * [tex]\sqrt[5]{4}[/tex]

[tex]5^{1/3}*4^{2/5}[/tex]

[tex]5^{1/3}*4^{2/5}[/tex] is the equivalent expression

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The time needed for the account value to reach 11200 dollars is approximately 15.9 years.

Simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

A/P = 1 + rt

( A/P - 1 ) = rt

t = ( A/P - 1 ) / r

t = ( $11200/$5400 - 1 ) / 6.75%

t = ( $11200/$5400 - 1 ) / 6.75/100

t = ( 56/27 - 1 ) / 0.0675

t = ( 29/27 ) / 0.0675

t = 15.9 years.

Therefore, the required time to reach the accrued amount is 15.9 years.

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The complete sentence will be;

⇒ x² + x + 1/4 = ( x + 1/2)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x² + x + __ = (_____)²

Now,

Since, The expression is,

⇒ x² + x + __ = (_____)²

Hence, We can add the number to form the complete square as;

⇒ x² + x + 1/4 = x² + x + (1/2)²

                     = ( x + 1/2)²

Thus, The complete sentence will be;

⇒ x² + x + 1/4 = ( x + 1/2)²

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The point which satisfies equation is (-2,4)

What is circle?

A circle could be a form consisting of all purposes during a plane that are at a given distance from a given point, the centre.

Main body:

The center of circle formula is also known as the general equation of a circle. In a circle, if the coordinates of the center are (h,k), r is the radius, and (x,y) is any point on the circle, then the center of circle formula is given below:

Formula of circle =

(x - h)² + (y - k)² = r²

According to question:

center of circle = (2,1)

diameter of circle = 10 units

radius = 5 units

equation of circle ⇒

(x - 2)² + (y - 1)² = 25

for a point to lie on circle , it need to satisfy the equation of circle:

A) (1,-3)

⇒(1 - 2)² + (3 - 1)²

⇒(-1)² +2²

⇒5

so it does not lie on circle.

B) (-2,4)

⇒(-2 - 2)² + (4 - 1)²

⇒-4²+3²

⇒ 25

so, it satisfies the equation.

hence, the point which satisfies equation is (-2,4)

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Answer: There is no y-intercept on this equations

Step-by-step explanation:

so yes you were wrong

The equation, which represents the given condition x >= 6.2.

What is the inequality equation?

Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤, or ≥.

We have,

Six more than 5 times a number x is greater than or equal to 6.

So,

5x  >= 31

5x >= 31/5

x >= 6.2

Hence, the equation, which represents the given condition x >= 6.2.

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Complete equation:

Six more than 5 times a number x is greater than or equal to 6.

The confidence interval of this confidence level as calculate from the given data is 3.68 and 99% respectively.

Number of random sample (n)=28

Sample Standard deviation (S)=19.52

Confidence interval = 439.23 -  460.77 =  21.54

t = s/root of n

=19.52 /5.29

=3.68

v = n -1 = 27

now, confidence level

= 1 - alpha

= 99%

Confidence Interval, put simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.

The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.

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The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.

We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.

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We can estimate the number of adult partons at 2187 by solving equations.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

A function is an equation that has only one answer for y for every possible value of x.

When utilizing a function, each input of a specific type receives exactly one output.

A function is commonly referred to as f(x) or g instead of y. (x).

Because f(2) instructs us to do so, we should figure out the value of our function when x is equal to 2.

So, the total number of adults present was thus:

Let a be an adult, and b and c be kids.

Ticket totals:

a + c = 5200

c = (5200-a)

Total amount:

7.50a + 4.50c = 29961

In the first equation, swap out c with (5200-a).

7.5a + 4.5(5200-a) = 29961

7.5a + 23400 - 4.5a = 29961

7.5a - 4.5a = 29961 - 23400

3a = 6561

a = 6561/3

a = 2187

Therefore, we can estimate the number of adult partons at 2187 by solving equations.

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The value of f(5) When a polynomial f(x) is divided by x -5 is 4

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

If f(x) has a remainder of 4 when divided by x - 5

Then it means that if f(x -5) = f(0)

x -5 = 0

x = 5

so if you substitute 5 into f(x) which is f(5) it will give 4

so therefore f(5) = 4

In conclusion f(5) is same as 4

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For the function in the given case the constraint on domain can be written as  x ≥ 182. The correct option is (a).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

Suppose the amount of money spent be x.

And, the number of food items be y.

Now, as per the question the function can be written as follows,

y = x/182

As the number of food items can only be positive integers, the values of x must be the multiples of 182.

Thus, the expression for the domain can be written as x ≥ 182.

Hence, the constraint on the domain is given as x ≥ 182.

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Answer:

y=2x+8

Step-by-step explanation:

-6x+3y=24

-6x+6x+3y=24+6x  ==> isolate the y variable

3y=6x+24  ==> simplify

(3y=6x+24)/3

y=2x+8  <== y=mx+b  <== slope intercept form

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The expected value of this game will be 1,784.75.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

In a lottery game, a player picks six numbers from 1 to 28. Assuming the player matches each of the six numbers, they win 50,000 bucks. In any case, they lose $1.

Then the probability of winning (p) and losing (q) is given as,

p = 1 / 28

q = 27 / 28

Then the expected value is given as,

E(x) = 50,000 (1 / 28) - 1 (27 / 28)

E(x) = 1785.714 - 0.964

E(x) = 1,784.75

The expected value of this game will be 1,784.75.

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Answer:

Below

Step-by-step explanation:

2.42 x 10^4  = 24200

 24200

+ 23580

 47 780    or   4.778 x 10^4

In 2000, the population of the state was 23.1 million, After 13 years , the population of the state reach 28.3 million.

What is population?

The term "population" refers to all citizens who are present in a nation or who are temporarily absent from it, as well as all aliens who have made a nation their permanent home. The number of residents in a given area is depicted by this indicator. The annual changes in population brought on by births, deaths, and net migration are measured as growth rates.

Given:

[tex]A = 23.1e^0^.^0^1^5^2^t[/tex] models the population of US

where A is in million

t is years after 2000.

(a) We have to find the population in 2000.

In 2000, t = 0

Plug t = 0 in the above equation

[tex]A(0) = 23.1e^0^.^0^1^5^2^(^0^)\\A = 23.1[/tex]

Hence, in 2000 the population is 23.1 million.

(b) To find when the population of the state reach 28.3 million.

Plug A = 28.3 in above equation and solve for t.

[tex]28.3 = 23.1e^0^.^0^1^5^2^t\\e^0.0152t = \frac{28.3}{23.1} \\t*ln(0.0152) = ln( \frac{28.3}{23.1})\\t = 13.35718\\t = 13[/tex]

Hence, after 13 years the population of the state reach 28.3 million.

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Step-by-step explanation:

8x³ + 216

(2 * 2 * 2 * x * x * x) + (2 * 3 * 2 * 3 * 2 * 3)

The total weight of the water in a filled tank will be equal to 16,336 Pounds.

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.

As per the given data in the question,

Radius, r = 10/2 = 5 ft.

Use the equation of the volume of a sphere,

V = 4/3πr³

We only require half of it then,

V =  2/3πr³

V = 261.8 ft³

So, the total weight will be,

W = 261.8 × 62.4

W = 16,336 Pounds.

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Answer:

ANS:- 15.9

Step-by-step explanation:

5814/365 = 15.9

Answer:

c= 1.5t, c=t+0.5t and c=(1+0.5)t

Step-by-step explanation:

Given that, Clare scored 50% more points than Tyler, c is the number of points that Clare scored and t is the number of points that Tyler scored,According to question,c = 150% of tc = 1.5tHence, the correct options are c = 1.5t, c = t+0.5t and c = (1+0.5)t

Answer:

x> -10

Step-by-step explanation:

Hello,

I hope you and your family are doing well!

Let's call Sydney's age x and Devaughn's age y. We know that y = 3x and x + y = 116.

Substituting the first equation into the second equation gives:

3x + x = 116

4x = 116

x = 29

So Sydney's age is 29.

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Happy Holidays!

The type of the function for the given graph f(x) on the right is odd function.

An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.

The link between varying amounts and other variables was the foundational idea behind functions. The effect of time on a planet's position serves as an example of this. The infinitesimal calculus was used to develop the concept in the past, beginning at the end of the 17th century and continuing through the 19th century.

An odd function's graph possesses rotational symmetry with respect to the origin, which means that it doesn't change after being rotated by 180 degrees around the origin.

Therefore, The type of the function for the given graph f(x) on the right is odd function.

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The value of x for the triangle is equal to 17.32.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Calculate the perpendicular side for both triangles by using the Pythagorean theorem.

H² = P² + B²

Here, H is the hypotenuse, P is perpendicular and B is the base.

For the first triangle, the perpendicular is calculated as,

P² = x² - 10²......................................................1

For the second triangle, the perpendicular will be,

P² = ( 30² - x² ) - 20²  .......................................2

Equate the equation 1 and 2 and solve,

x² - 10² = ( 30² - x² ) - 20²

x² - 100 = 900 - x² - 400

2x² = 900 - 400 + 100

2x² = 600

x√ = 300

x =√300

x = 17.32

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Answer:

Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40

Marie is $10 000 richer

Step-by-step explanation:

Albert

(a) $1000 at 1.2 % compounded monthly

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

A = 1000(1 + 0.001)¹²⁰ = $1127.43

(b) $500 losing 2%

0.98 × 500 = $490

(c) $500 compounded continuously at 0.8%

A = Pe^rt

  = 500e^0.008 * 10

 =  $541.64

(d) Balance

Total = 1127.43 + 490.00+ 541.64 = $2159.07

Marie

(a) 1500 at 1.4 % compounded quarterly

A = 1500(1 + 0.0035)⁴⁰ = $1724.99

(b) $500 gaining 4 %

1.04 × 500 = $520.00

(c) Balance

Total = 1724.99 + 520.00 = $2244.99

Hans

$2000 compounded continuously at 0.9 %

A = 2000e^0.009 * 10

  = $ 2188.35

Max

(a) $1000 decreasing exponentially at 0.5 % annually

A = 1000(1 - 0.005)¹⁰= $951.11

(b) $1000 at 1.8 % compounded biannually

A = 1000(1 + 0.009)²⁰ = $1196.29

(c) Balance

Total = 951.11 + 1196.29 = $2147.40

Marie is $10,000 richer at the end of the competition.

Hope this helps!!! :)

Answer:

[tex]\huge\boxed{\sf 157.1 \ units^2}[/tex]

Step-by-step explanation:

Diameter = 20

Radius = Diameter/2 = 20/2 = 10

[tex]\displaystyle =\frac{\pi r^2}{2} \\\\r = 10\\\\= \frac{\pi (10)^2}{2} \\\\= \frac{100 \pi}{2} \\\\= \frac{314.2}{2} \\\\= 157.1 \ units^2\\\\\rule[225]{225}{2}[/tex]

Answer:I hope this helpful mark me brainlist if correct then no if wrong

Step-by-step explanation:

P times 3 =-0.0027

Use the commutative property to reorder the terms

3p=-0.0027

Divide both sides of the equation by 3

p=-0.009 or p=-9/1000

Answer:

a. [tex]1 * 10^{-10}[/tex]

Explanation:

A converted to standard notation is the same number.

Answer:

Step-by-step explanation:

Let x be the number.

The square of the number is x2

Increased by twice the number means add 2x.

So your equation is :

X2 +2x = 48.

Can you take it from here?

The asked number is 12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, When the square of a certain number is added to the number, the result is the same as when 48 is added to three times the number.

Let the number be x,

x²+x = 48X3 + x

x² = 144

x = 12

Hence, The asked number is 12.

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Answer:

6790 km

Step-by-step explanation:

move the decimal 3 places to the right.

Answer:

203 dollars

Step-by-step explanation:

100 percent = 145

10 percent = 14.5

30 percent = 43.5

43.5 + 14.5 + 145 = 203