The table below shows some values of a function g(x)

Which function represents the relationship shown in the table?

The volume of his large vase is 2,373.84cm^3 (option A)

The is 4 times the volume of the small verse. (option A)

A cylinder is a three-dimensional object. It is a prism with a circular base.

volume of a cylinder = nr^2h

Where:

Radius of the small verse = 6/2 = 3 cm

Volume of the small verse = 3.14 x 3² x 21 = 593.46 cm³

Radius of the large verse = (2 x 6) / 2 = 6cm

Volume of the large verse = 3.14 x 6² x 21 = 2,373.84 cm³

Difference in volumes =  2,373.84 cm³/  593.46 cm³ = 4

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Answer:

{x | x is a real number}

Step-by-step explanation:

x can have any real number value.

The simplified form of the first expression is -37 + 6i and the second expression is -16 - 14i.

What is the arithmetic operations?

Arithmetic operations are basic mathematical operations that can be performed on numbers, such as addition, subtraction, multiplication, and division.

The first expression is 7 - (3 + 41) + 6i. To simplify this expression, we need to first simplify the parentheses. Inside the parentheses, we have 3 + 41 = 44. So the expression becomes:

7 - 44 + 6i

Next, we can simplify the arithmetic operations by combining like terms:

7 - 44 + 6i = -37 + 6i

The second expression is -10 + (6 - 5i) - 9i. Similar to the first expression, we need to simplify the parentheses first. Inside the parentheses, we have 6 - 5i = 6 - 5i. So the expression becomes:

-10 + 6 - 5i - 9i

Next, we can simplify the arithmetic operations by combining like terms:

-10 + 6 - 5i - 9i = -16 - 14i

Hence, the simplified form of the first expression is -37 + 6i and the second expression is -16 - 14i.

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The linear function containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5) is given as follows:

y = -5x + 20.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The hypotenuse is composed by segment QR, hence the points are:

Q(3,5) and R(5,-5).

The slope is given by the change in y divided by the change in x, hence:

m = (-5 - 5)/(5 - 3)

m = -5.

Hence:

y = -5x + b.

When x = 3, y = 5, hence the intercept b is obtained as follows:

5 = -15 + b

b = 20.

Hence the equation is:

y = -5x + 20.

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The value of BD is 12cm.

What is  Pythagoras' theorem?

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 statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

BE = ED  (as E is the center of BD - property of a kite).

By Pythagoras' theorem:

10² = 8² + BE²

BE² = 10² - 8² = 36

BE = 6

So BD = 2*6 = 12.

Hence, the value of BD is 12cm.

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g(f(4)) means to first find f(4) and then use that result as the input for g(x).

So,

f(4) = 4 - 7 = -3

then we use the result, -3 as the input for g(x)

g(-3) = (-3)^2 = 9

Therefore, g(f(4)) = 9

There a rule for logarithms:

         [tex]\log_n(a^m) = m \cdot \log_n(a)[/tex]

So when you're working with [tex]\log_5(a^3)[/tex], we can use that rule to rewrite this as
        [tex]\log_5(a^3) = 3 \cdot \log_5(a)[/tex]

And since the first part tells us (on paper) that [tex]\log_5(a) = 2[/tex], then we can say
        [tex]\log_5(a^3) = 3 \cdot \log_5(a) = 3 \cdot 2 = 6[/tex]

Answer:

B 6

Step-by-step explanation:

Answer:

B. 6

Step-by-step explanation:

6 x -14 = 3x + 4

3x = 18

X = [tex]\frac{18}{3}[/tex] Which equals =

6

The probability of rolling a number greater than 1 on a six sided number cube is 5/6 therefore the likelihood that best describes the of this event is that it is Likely and is therefore denoted as option D.

This is referred to as the branch of mathematics which describes how likely an event is to occur or how likely it is that a proposition is true using numerical descriptions.

In this scenario we were told that the probability of rolling a number greater than 1 on a six sided number cube is 5/6 which means that is likely to occur due to the high percentage or ratio of the event being observed thereby making option D the correct choice.

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Answer:

-------------------------------------

Let the integers be:

Twice the sum of the second and third exceeds 3 times the first by 32:

Solve it for x:

Answer:

x

=

0

,

x

=

1

,

x

=

2

,

x

=

−

1

, and

x

=

−

2

Explanation:

Start off by factoring out an

x

as follows

x

(

x

4

−

5

x

2

+

4

)

=

0

We can factor

x

4

−

5

x

2

+

4

Doing so we have

x

(

x

2

−

4

)

(

x

2

−

1

)

=

0

So in order for this to be equal to zero

x

=

0

OR

x

2

−

4

=

0

OR

x

2

−

1

=

0

Well

x

=

0

x

2

=

4

x

=

±

√

4

=

±

2

x

2

=

1

x

=

±

√

1

=

±

1

Give the expression in terms of a, k, and t is g(t+1/k) = a2^(k(t+1/k)) = a2^kt * 2^(1/k)

The population doubles when P(t) = 2 * P(0), so we can set up the equation:

2 * 55 = 20^(5t)

Solving for t:

t = log(2)/(5 * log(20)) = log(2)/log(400)

The population doubles after approximately 0.173 years or 63.1 days.

g(t+1/k) = a2^(k(t+1/k)) = a2^kt * 2^(1/k)

Interpretation: g(t+1/k) is the population at time t+1/k, where a and k are positive constants. The population at t+1/k is equal to the population at time t multiplied by 2^(1/k). This means that if k is a large number, the population will change very little over time, if k is a small number, the population will change more quickly.

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Step-by-step explanation:

Money she makes=$140

since she saves 4/5 of the money she earns that means that: 4/5×140 = $32

This means that she saves $32 out of $140 she makes or earn

The Rate of plane in still air and rate of wind is 738 , 100 respectively .

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one

Given ,

An airplane travels 4466 kilometers against the wind in 7 hours and 5866 kilometers with the wind in the same amount of time.

Let speed of plane be Vp and Va

Now,

Vp - Va  = 4466 / 7

Vp+Va = 5866 / 7

So, Evaluating the equations,

we get,

2Vp = (4466+5866) / 7

Vp = 1476 / 2

Vp = 738

So substitute Vp =738 in Vp-Va = 4466/7

738 - Va = 638

Va = 738 - 638

Va = 100.

Hence, The Rate of plane in still air and rate of wind is 738 , 100 respectively .

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Answer:

46.05 years

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for t.

[tex]\implies 1000=100e^{0.05t}[/tex]

[tex]\implies 10=e^{0.05t}[/tex]

[tex]\implies \ln 10=\ln e^{0.05t}[/tex]

[tex]\implies \ln 10=0.05t\ln e[/tex]

[tex]\implies \ln 10=0.05t[/tex]

[tex]\implies t=\dfrac{1}{0.05}\ln 10[/tex]

[tex]\implies t=20\ln 10[/tex]

[tex]\implies t=46.0517018... \rm years[/tex]

Therefore, it will take 46.05 years for the initial investment of $100 to reach $1000.

Answer:

8.00

Step-by-step explanation:

First simplify the exponents 10^15 is 1000000000000000 or 1e+15 then 10^4 is 10000. Then multiply: 1e+15 x 3 = 3e+15 ------ 10000 x 7 = 70000. When you divide 3e+15 by 70000 you get 8.115 or 8 rounded to the decimal place.

The table 1  represent the function From the given figure.

What is function ?

The function in mathematical terms is the mapping of each member of a set (named as a domain) to another set of members (named as a codomain). This term has a different meaning from the same word that is used every day, such as "the tool works well." The concept of function is one of the basic concepts of mathematics and any quantitative science. The terms "function", "mapping", "map", "transformation" and "operator" are usually used synonymously.

In function, there are several important terms, including:

The domain is the area of ​​origin of the function f denoted by Df.

Codomain is the area where the f function area is denoted by Kf.

The range is the result area which is a subset of the codomain. The function range f is denoted by Rf.

PROPERTIES OF FUNCTIONS

1. INJECTIVE FUNCTION

Called one-on-one function. Suppose the function f represents A to B, then the function f is called a one-on-one function (injective), if each two different elements in A will be mapped to two different elements in B. Furthermore, it can be said briefly that f: A → B is injective function if a ≠ b results in f (a) ≠ f (b) or equivalent if f (a) = f (b) then the effect is a = b.

2. SURJECTIVE FUNCTION

Function f: A → B is called a function to or objective function if and only if for any b in the B domain can be at least one an in domain A so f (a) = b applies. In other words, a codomain of the objective function is the same as its range.

3. BIJECTIVE FUNCTION

A mapping off: A → B is such that f is both an injective and objective function at once, so it is said "f is a function of wisdom" or "A and B are in one-to-one correspondence".

Therefore, The table 1  represent the function From the given figure.

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Since the mid-points of opposite sides of a square are equal, the quadrilateral formed will also be a square.

A four-sided polygon whose all sides are equal is a square. This means that the opposite sides of a square are equal in length and the opposite angles are also equal. Furthermore, the diagonals of a square bisect each other at their mid-points. Therefore, if the mid-points of opposite sides of a square are joined, a quadrilateral is formed. Since the opposite sides and angles are equal, the quadrilateral formed is also a square. To prove this, we can draw a line from the mid-point of one side of the square to the mid-point of the opposite side. We can then draw a line from the mid-point of the other side of the square to the mid-point of the opposite side. This will form a quadrilateral, and due to the equal sides and equal angles, it will be a square.

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The limit in question is

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}$$[/tex]

This limit can be interpreted as the Riemann sum of a function defined on the interval [0, 16]. To calculate the sum, we need to first find the function that is being approximated. To do this, we can use the fact that the numerator of the limit can be rewritten as a single summation:

[tex]$$\sum_{k=1}^n k^3 = \frac{n^2 (n+1)^2}{4}$$[/tex]

This means that the function we are approximating is [tex]$f(x) = \frac{x^2 (x+1)^2}{4}$[/tex]

Now, to calculate the Riemann sum, we need to divide the interval [0, 16] into $n$ equal subintervals. The width of each subinterval is given by [tex]$\Delta x = \frac{16}{n}$\\The Riemann sum is given by $$\sum_{i=1}^n f\left(x_i\right) \Delta x = \sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}$$[/tex]

where [tex]$x_i = \frac{16i}{n}$[/tex]

Plugging this into the limit, we get

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}\\ = \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}}{n^4} = \\frac{16}{4} \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{n}}{n^3}$$[/tex]

Finally, we can take the limit of the above expression to get

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4} = \frac{16}{4} \cdot \frac{f(16)}{16^3} = \frac{1}{4}$$[/tex]

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A). The first term represents the total cost of the waffle irons and the second term represents the expenses.

B). The algebraic expression represents if the company sells 350 waffle irons per day will be 350x - 1500

C). The company's profit for a 5-day week is $250.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the algebraic expression 25x - 1,500 can be used to describe the daily profit of a company that makes waffle irons.

A). The first term represents the total cost of the waffle irons and the second term represents the expenses. Here 25 is the number of the waffle iron and the x is the number of days.

B). The algebraic expression represents if the company sells 350 waffle irons per day will be written as:-

350x - 1500

C). The company's profit for a 5-day week will be;-

Profit = 350x - 1500

Profit = ( 350 x 5 ) + 1500

Profit = 1750 - 1500

Profit = 250

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Answer:

9c + 0.8d + 1

Step-by-step explanation:

- (- 9c - 0.8d - 1) ← multiply each term in the parenthesis by - 1

= 9c + 0.8d + 1

On solving the function H(x) = 0.05x + 10.25, the plant's height after a period of 30 months is obtained as 11.75 m.

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 height of the plant is = 10.25 m

The rate at which plant grows is = 5 cm/month or 0.05m/month

The function for plant's height is given as - H(x) = 0.05x + 10.25

To find the plant's height after 30 months, substitute the value of x with 30 in the function -

H(30) = 0.05(30) + 10.25

Use the arithmetic operation of multiplication -

H(30) = 1.5 + 10.25

Use the arithmetic operation of addition -

H(30) = 11.75

Therefore, the plant's height after 30 months will be 11.75 m.

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When the domain of x is restricted, the function x2 becomes one-to-one, and the inverse function is x.

It is true that limiting a function's domain might cause it to become invertible. Because it is not one-to-one in the example, the function x2 is not invertible across its complete domain of real numbers (i.e., it assigns multiple outputs to some inputs). However, x2 becomes one-to-one and invertible when the domain of x is constrained to or any subset of that interval. The range of x2, which is, is used to define the inverse function in this situation, which is

The function x2 becomes one-to-one when the domain of x is constrained, and the inverse function is

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The concept of linear pairs from the given diagram shows that; GKH =  90°

A linear pair is formed when two straight lines intersect to form two angles that are adjacent to each other and are on a straight line.

Now, what this means is that ∠F KG and ∠GKH will sum up to 180 degrees because they are linear pairs from the question.

Due to the fact that ∠F KG = 90°, then we can say that;

∠F KG + ∠GKH = 180°

90° + ∠GKH = 180°

∠GKH = 180° - 90°

∠GKH =  90°

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The solution of m+n+p = 462+40+3 = 505.

The set is divided into several parts: the large 3x4x5 parallelepiped, 6 external parallelepipeds that share a face with the large parallelepiped and have a height of 1, 1/8 spheres (one at each vertex of the large parallelepiped), and 1/4 cylinders connecting each adjacent pair of spheres.

The parallelepiped has a volume of $3 times 4 times 5 = 60 cubic units.

The external parallelepipeds have a volume of $2(3 times 4 times 1)+2(3 times 5 times 1)+2(4 times 5 times 1)=94$.

Each of the 1/8 spheres has a radius of 1. Their combined volume is [tex]\frac{4}{3} \pi[/tex].

There are 12 of the 1/4 cylinders, allowing for the formation of 3 complete cylinders. Their volumes are 3[tex]\pi[/tex], 4[tex]\pi[/tex], and 5[tex]\pi[/tex], totaling 12[tex]\pi[/tex].

The total volume of these parts is 60+94+ [tex]\frac{4}{3} \pi[/tex] +12[tex]\pi[/tex] = [tex]\frac{462 + 40\pi }{3}[/tex]. Thus, the solution is m+n+p = 462+40+3 = 505.

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The time(s) that the projectile will​ (a) reach a height of 192 ft is 4 seconds  and (b) return to the ground when is 8 seconds

Time is the continued sequence of existence and event that can occur in an apparently inevitable succession from the past through the present

The set height, s=192

(a) 192=-16t²+112t

-16t^2+112t-192=0

-t^2+8t-16=0

t^2-8t+16=0

(t-4)(t-4)=0

t=4 twice

The projectile will reach a height of 192ft after 4 sec on the way up and after 4 sec again  on the way down

..

Also, set height, s=0

(b) -16t^2+128t=0

-t^2+8t=0

-t(t-8)=0

t=0 (reject)

or

t=8

The projectile will return to the ground after 8 sec

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Correct question:

A projectile is launched from the ground with an initial velocity of V0 feet per second. Neglecting air resistance, its height in feet per seconds after launch is given by s = -16t^2 +V0t. Find the time(s) that the projectile will

(a) reach a height of 192ft and

(b) return to the ground when V0= 112 feet per second.

Answer: $385.50

Step-by-step explanation: 25,700x1.5% = 385.50

When an occurrence is so common that it shouldn't be the result of chance or external influences on the study, it is said to be "statistically significant."

Different clinical significance exists. It alludes to tangible results. It frequently refers to the actual impact of a medical problem (or medical treatment) on a patient's health. The effects of a medicine are clinically meaningful if they provide alleviation. A medical problem is also considered clinically significant if it affects a patient's quality of life or expected lifespan.

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Answer:

The function's minimal value is m = A |B|. When either sin x or cos x is equal to 1, this minimum is reached. Create a graph for the first example, y = 1 + 2 sin x.

Step-by-step explanation: