lim (1 - 1/(n + 1)) ^ (n ^ 2)

Answer:

[tex](0,-2)[/tex]

Step-by-step explanation:

Let the coordinates of the desired point be [tex](a, -a^2-2)[/tex]. Let the distance of this point from [tex](0,1)[/tex] be [tex]f(a)[/tex].

By the distance formula, [tex]f(a)=\sqrt{a^2+(a^2+3)^2}[/tex].

Clearly, [tex]f(a)[/tex] is minimized when the radicand is minimized.

Clearly, the radicand is always increasing, so the minimum is achieved at the left endpoint of the maximal domain of [tex]f(a)[/tex], which is [tex]a=0[/tex].

So, the coordinates are [tex](0,-2)[/tex].

The point on the curve y = -x^2 - 2 that is closest to the point (0, 1) will be (0, -2)

From the information, we want to know the point on the curve y = -x^2 - 2 that is closest to the point (0, 1).

Let the coordinates of the desired point be illustrated as (a - a² - 2).

The distance of the point from (0, 1) is depicted as f(a).

When the radicand is minimized, f(a) is minimized.

In this case, the minimum will be achieved at the left endpoint of the maximal domain of f(a) which is a = 0.

Therefore, the coordinates will be (0, -2).

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Using the Time-Distance Formula, it will take Adbi 2 hours.

We can use the time-distance formula to find how long it will take for Abdi to catch up with Bashir. The time-distance formula is distance = speed x time.

Let t be the time in hours that it takes for Abdi to catch up with Bashir.

We know that the distance Abdi has covered is 4 miles more than Bashir, and the relative speed between the two runners is 8mph - 6mph = 2mph.

So we can write the equation:

4 = (8 - 6) * t

Solving for t, we get t = 4/2 = 2 hours.

So it will take Abdi 2 hours to catch up with Bashir.

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Answer: The total bill including tax and gratitude is $35.20

And each one of the 5 friends paid $10 for the bill.

So the total amount paid is $10*5 = $50

If each person paid $10 and the total bill was $35.20

then the change will be $50-$35.20 = $14.80

And since they split the bill equally then each one of them will get back $14.80/5 = $2.96

So each person will get back $2.96

Step-by-step explanation:

The value of the variable , x is 10. 33

It is important to note that in mathematics, complementary angles are defined as angles that sum up to 90 degrees.

Some properties of complementary angles are;

From the information given, we have the angles as;

Equate the angles to 90 degrees

8x - 9 + x + 6 = 90

collect like terms

8x + x = 90 +3

add the like terms, we get;

9x = 93

Make 'x' the subject of formula by dividing both sides by 9

x = 93/9

x = 10. 33

Hence, the value is 10.33

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So, only option C is a counterexample of the conditional statement "If a number is divisible by 4, then it is divisible by 8."

A counterexample of a conditional statement is a specific case or example that contradicts the statement or goes against its logical implications.

In this case, the conditional statement is "If a number is divisible by 4, then it is divisible by 8."

Option C, 36, is a counterexample of this conditional statement.

This is because 36 is divisible by 4 (9 x 4 = 36), but it is not divisible by 8 (36 / 8 = 4.5). This contradicts the statement that if a number is divisible by 4, it must also be divisible by 8.

Option A, 12, is not a counterexample of the conditional statement because 12 is divisible by 4 (12 / 4 = 3) and also divisible by 8 (12 / 8 = 1.5).

Option B, 32, is not a counterexample of the conditional statement because 32 is divisible by 4 (32 / 4 = 8) and also divisible by 8 (32 / 8 = 4).

Option D, 20, is not a counterexample of the conditional statement because 20 is not divisible by 4 (20 / 4 = 5)

So, in summary, only option C is a counterexample of the conditional statement "If a number is divisible by 4, then it is divisible by 8."

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To solve the system of equations using elimination, we can follow these steps:

Multiply the first equation by 4, and the second equation by 2:

20x + 8y = 12

8x - 16y = 24

Add the two equations together:

20x + 8y = 12

8x - 16y = 24

28x - 8y = 36

Solve for x by dividing both sides of the equation by 28:

x = 36/28 = 9/7

Substitute the value of x back into one of the original equations:

5x + 2y = 3

5(9/7) + 2y = 3

45/7 + 2y = 3

2y = -42/7

Solve for y by dividing both sides by 2:

y = -21/7

So the solution of the system of equations is (x,y) = (9/7, -21/7)

It is also worth noting that we could have also multiplied the first equation by -2 and the second equation by 5 and added them together, this will also lead us to the same solution.

Step-by-step explanation:

(6n+5)°(4n-5)°

use the method of expand

6n(4n-5)+5(4n-5)

24n²-30n+20n-25

24n²- 10n -25

use middle term/ quadratic formula

n=5/4 (1.25) or n= -5/6 (-0.833333)

Through the given data points the domain of the function is 1 ≤ n ≤ 5.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The domain of a function is the complete set of all possible values of independent variable.

The points associated with the graph is (1,15) and (5,11).

The formula for equation is (y - y1) =  (y2-y1)/(x2-x1) (x - x1).

(y2-y1)/(x2-x1) = (11 - 15)/(5 - 1)

m = -4/4

m = -1

Now, the equation can be written as -

y - y1 = m(x - x1)

y - 15 = -1(x - 1)

y - 15 = -x + 1

y = -x + 16

From the graph k = -n + 16

The independent variable 'n', taking the values between 1 and 5, in that interval graph is continuous.

Therefore, the domain is 1 ≤ n ≤ 5.

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Elizabeth will practice piano for 252 minutes in one week by solving function f(x)=504x where x = time in multiple of 2years.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

As given

f(x)=504x where x = time in multiple of 2 years

For 1 year x=1/2

Hence,

y=504*1/2

y=252 minutes

Elizabeth will practice piano for 252 minutes in one week.

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The amount of codeine that Ken is being prescribed every day, given the Tyelenol 3 being prescribed is 165. 47 milligrams of Codeine

The amount of codeine in 30 ml of Tylenol 3 is:

= ( 17 x 73 ) / 30

= 41. 37 mL of Codeine

The number of 6 hour periods in a day is:

= 24 / 6

= 4

The amount of codeine that Ken is being prescribed a day is therefore:

= 4 x 41. 37

= 165. 47 milligrams of Codeine

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The number of the people with headaches to the nearest whole number is 3100

Percentage can be defined as the number or ratio expressed as fraction of 100.

It is represented using the mathematically sign"%".

Due to this, percentage is a dimensionless number.

it is known to have no unit of measurement.

They are also seen as fractions with 100 as their denominators. It is the relative value of a quantity with 100.

From the information given, we have that;

Then,

6.6/100 × 46785

Multiply the values, we get

3087. 81 people

Hence, the value is 3100 people in the nearest whole number.

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Simplify all:

The volume of the metal sphere is 4π/3(R^3 - r^3)

The volume of the solid generated is 2π cubic units.

The volume of the ring can be found by subtracting the volumes of two spheres with radii R and r:

V = (4/3) * π * (R^3 - r^3)

So, the volume of the ring is given by:

V = (4/3) * π * (R^3 - r^3) cubic units.

Evaluate

V = 4π/3(R^3 - r^3)

We have the equation to be

y = 1/x

The volume of the solid is given by the definite integral:

V = 2π ∫[a,b] x * y dx

where a and b are the lower and upper limits of the interval over which we are integrating.

In this case, a = 1 and b = 2, so the volume of the solid is given by:

V = 2π ∫[1,2] x * 1/x dx = 2π ∫[1,2] dx = 2π (x)|[1,2] = 2π (2 - 1) = 2π.

So, the volume is to 2π cubic units.

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The standard form of a related quadratic function is,

⇒ (x² - 5x - 36)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The solutions of a quadratic equation are -4 and 9.

Let the factors of the quadratic equation are,

⇒ (x - (-4)) (x - 9)

⇒ (x + 4) (x - 9)

⇒ (x² - 9x + 4x - 36)

⇒ (x² - 5x - 36)

Thus, The quadratic function is,

⇒ (x² - 5x - 36)

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Answer:

110

Step-by-step explanation:

180-70 =110

Hector has to put the fixed point of the compass on points A and C.

Option (C) is correct.

What is the angle bisector of an angle?

The angle bisector of an angle is a line, ray, or segment that divides an angle into two congruent angles. It is a line that bisects (divides into two equal parts) the angle.

For example, if you have a right angle of 90 degrees, the angle bisector would be a line that divides the angle into two 45-degree angles.

In the given figure, Hector is using a compass and straightedge to construct the bisector of angle CEB.

So he has to put the fixed point of the compass on points A and C.

Hence, Hector has to put the fixed point of the compass on points A and C.

Option (C) is correct.

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Using the empirical rule, 95% of vehicles travel between 60 miles per hour and 80 miles per hour.

Generally, Given that

To find the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour

60 = 70-(2*5) ,

this shows that the 58 value is 2 standard deviations below the mean

and

80 = 70 +( 2*5)

This shows that the 74 value is 2 standard deviations above the mean

Using the empirical rule, we know that 95% of data fall within 2 standard deviations from the mean.

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Answer:

Step-by-step explanation:

The investment below is compounded semi-annually, while an investment of the same principal at the same rate compounded annually would have interest compounded once per year.

The formula for compound interest is A = P(1 + r/n)^nt where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year and t is the number of years.

In the case of the semi-annual investment:

A = 9000(1 + 0.04/2)^(2*15) = $21,831.62

In the case of the annual investment:

A = 9000(1 + 0.04)^15 = $21,812.30

As we can see, the semi-annual investment yields a slightly larger return than the annual investment, $19.32 more. Compounding interest more frequently results in a larger return due to the interest earning interest.

Answer:

Step-by-step explanation:

50% of 200 is =100

If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000. The probability of unscheduled maintenance in exactly 5,000 hours is:.7135.

Using this formula to the probability of unscheduled maintenance in exactly 5,000 hours

P ( X < 5000) = 1 - e^(-λx)

Where:

e = exponent

-λ = Operating hour

x = Number of hours

Let plug in the formula

P ( X < 5000) = 1 - e^(-(1/4000) × 5000)

P ( X < 5000) = 1- e^-1.25

P ( X < 5000)  = 1 - .2865

P ( X < 5000)  = .7135

Therefore the probability is .7135.

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The result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.

f(x)   | -2 | -1 | 0 | 1 | 2

-------|----|----|----|----|----

f(x)   | 5  | -3 | 0 | -3 | 5

g(x)   | -2 | -1 | 0 | 1 | 2

-------|----|----|----|----|----

g(x)   | 6  | 0  | 0 | 0  | 6

h(x)   | -2 | -1 | 0 | 1 | 2

-------|----|----|----|----|----

h(x)   | 6  | 0  | 0 | 0  | 6

h(x) = g(f(x))

For x = -2, h(x) = g(f(-2)) = g(5) = 6

For x = -1, h(x) = g(f(-1)) = g(-3) = 0

For x = 0, h(x) = g(f(0)) = g(0) = 0

For x = 1, h(x) = g(f(1)) = g(-3) = 0

For x = 2, h(x) = g(f(2)) = g(5) = 6

Since f is an odd function and g is an even function, then h(x) = g(f(x)) will be an even function. This means that for any given x, h(x) will always equal 0 or a positive value. For the set of values provided above, the result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.

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add and then subtract them m

It represents the output values, hence the claim that "The notation "f(x)" (f of x) is another means of encoding y-values in a function" is accurate.

An expression that can be used to define and depict the relationship between two or more variables in a data collection is referred to as a function in mathematics.

In conclusion, this means that a function typically illustrates the link between a data set's input values (x-values or domain) and output values (y-values or range), as well as demonstrating how the components in a table are uniquely paired (mapped).

Generally speaking, the output values (y-values or range) of a data set (function) are displayed on the y-coordinate of a graph, and they are typically denoted by either the notation f(x) or y.

The complete question is:

The notation "f(x)" (f of x) is another way of representing y-values in a function. True or False?

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The value of g(2) = -1/4 and the value of g(-2) is π/2 - 3/2

Consider function g(x)

[tex]g(x) = \int\limits^x_1 {f(t)} dt[/tex]

Here, function f be the continuous function defined on interval [-4, 3]

The graph of function f is shown below.

It consists of three line segments and a semicircle centered at the origin, is given above.

For x = 2,

g(2)

[tex]=\int\limits^2_1 {f(t)} dt[/tex]

= -(1/2) × 1 × (1/2)                .........(From the graph of function f)

= -1/4

For x = -2,

g(-2)

[tex]=\int\limits^{-2}_1 {f(t)} dt\\\\=-\int\limits^{1}_{-2} {f(t)} dt[/tex]

= -(3/2 - π/2)                .........(From the graph of function f)

= π/2 - 3/2

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The complete question is:

Let f be the continuous function defined on [-4, 3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by [tex]g(x) = \int\limits^x_1 {f(t)} dt[/tex]

Frin dthe values of g(2) and g(-2)

Answer:

8 days

Step-by-step explanation:

I assume you meant $0.15/day late fee (15 cents per day)?  If so, the answer is:

x = # of days late

$2.00 + ($0.15/day)x = $3.20

($0.15/day)x = $3.20 - $2.00 = $1.20

x = $1.20/ ($0.15/day) = 8 days

The solution to the system of equations 3x - y = 17 and 5x + 3y = 5 is (4, -5)

An equation is an expression showing the relationship between numbers and variables.

Given the equations:

3x - y = 17 ;    multiplying by 3:

9x - 3y = 51     (1)

5x + 3y = 5     (2)

To solve by elimination method, subtract add 2 to equation 1, hence:

14x = 56

Dividing by 14:

x = 4

Put x = 4 in equation 2:

5(4) + 3y = 5

20 + 3y = 5

3y = -15

y = -5

The solution is (4, -5)

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The quadrilaterals in a and b have the missing values of x as 85° and 57° respectively and can be best described as a scalene quadrilateral.

A scalene quadrilateral is a four-sided polygon in which all four sides have different lengths and all four angles have different measures. This is also known as an asymmetric quadrilateral.

we shall evaluate for the missing values of x as follows:

x + 109° + 96° + 70° = 360° {sum of interior angles of a quadrilateral}

x + 275° = 360°

x = 360° - 275° {subtract 275° from both sides}

x = 85°

x + 85° + 94° + (180° - 58°) = 360° {sum of interior angles of a quadrilateral}

x + 301 = 360°

x = 360° - 303° {subtract 303° from both sides}

x = 57°

Therefore, the missing values of x for quadrilaterals in a and b are 85° and 57° respectively, and can be best described as a scalene quadrilateral.

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The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The fundamentals of algebra taught us a way to express an unknown price using letters which includes x, y, z, and so on. these letters are referred to as here as variables. An algebraic expression can be a combination of both variables and constants. Any value this is located earlier than and accelerated with the aid of a variable is a coefficient.

Given

expression ,

4^-3 / 4^-1

= 4 ^ (-3-(-1))

= 4^ (-3+1)

= 4^(-2)

= 1/4^2

= 1/16 .

Therefore , The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .

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