Similarity between concurrent and point of concurrency

A) The data modelling is an exponential function.

B) The explicit funciton that will be used to represent the data is;

f(n) = 2(2)^(n - 1)

C) The average rate of change here is; 7

A) We are given the coordinates as;

(1, 2), (2, 4), (3, 8), (4, 16)

From the given coordinates, we can observe a pattern which is that when x increases by 1, then y is multiplied by 2.

Thus, we can see that as the quotient between consecutive terms is the same, the data is a geometric sequence which is an exponential function.

B) The explicit formula that will be used for a geometric sequence with common ratio r and first term a is given by:

f(n) = ar^(n - 1)

Since first term ; a = 2

and common ratio r = 2, then we can say that;

f(n) = 2(2)^(n - 1)

C) The formula for average rate of change here is;

dy/dx = (y₂ - y₁)/(x₂ - x₁)

The coordinates of the 2nd and 4th day are;

(2, 4) and (4, 16)

Thus;

dy/dx = (16 - 4)/(4 - 2)

dy/dx = 14/2 = 7

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600 is the 80% of the the expected number

Number of people that expected to attend the concert = 750 people

Number of people that attended the concert = 600 people

600 is what percent of the expected number = ( Number of people that attended the concert ÷ Number of people that expected to attend the concert ) × 100

Substitute the values in the equation

600 is what percent of the expected number = (600 / 750) × 100

Divide the terms in bracket first

= 0.8 × 100

Multiply the given terms

= 80%

Hence, 600 is the 80% of the the expected number

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Answer:

the slope is 1.75

Step-by-step explanation:

Interpretation: The weight of newborn is 6 lb at birth, and every month baby gained 1.75 lb. You replace x with month you want to know the weight.  For example you can calculate the weight after 4 month : w= 1.75(4)+6= 13 lb

Answer:

x=19/24

Step-by-step explanation:

3/8=15/5x-2

3/8= 3x -2 |*8

3=24x-16

24x=19

x=19/24

The average rate of change of the resistance of the thermistor for each degree change in the temperature, when the temperatures changes from 0 °C and 2 °C is A. 4 ohms/°C

The average is calculated by adding the values in the dataset then dividing the result by the count of the numbers or values in the set. The average is also known as the arithmetic mean.

The function for finding the resistance of the thermistor is; R(t) = t³ + 5

The unit of the R = Ohms

The unit of t = Degrees Celsius, °C

The resistance of the thermistor when the temperature is t = 0 °C is found as follows;

R(0) = 0³ + 5 = 5

Therefore;

When the temperature is 0 °C the resistance of the thermistor is 5 Ohms

When the temperature is t = 2 °C, we have;

R(2) = 2³ + 5 = 13

The resistance of the thermistor at t = 2 °C is 13 Ohms

The average rate of change of a function, f(x), is found using the formula;

[tex]A(x) = \dfrac{f(x_2) - f(x_1) }{x_2-x_1}[/tex]

The average rate of change of the resistance per degree change in the temperature, between the temperature interval of 0 °C and 2 °C is therefore;

[tex]A(x) = \dfrac{R(2) - R(0)}{2 - 0}[/tex]

Which gives;

[tex]A(t) = \dfrac{13 -5}{2 - 0}= 4[/tex]

The average rate of change of the resistance of the thermistor between the temperatures of t = 0 °C and t = 2 °C is 4 Ohms/°C

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The length of the second rectangle is 8 in

Since we have painting with an area of 48 in.² and a length of 6 inches, since it is a rectangle, its area is A = LW where

So, making Wsubject of the formula, we have

W = A/L

Since

Substituting these into the equation, we have

W = A/L

W = 48 in²/6 in

W = 8 in

Now, since the  second painting with an area of 64 in.² it has the same width as the first painting, since it is also a rectangle, its area is A = LW where

So, making L subject of the formula, we have

L = A/W

Since

Substituting these into the equation, we have

L = A/W

L = 64 in²/8 in

L = 8 in

So, the length of the second rectangle is 8 in

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By solving a system of equations, we will see that the equation is:

-4*x - 3*y = -18

We know that the linear equation:

A*x + B*y = -18

We know that this linear equation passes through the points (-3, 10) and (6, -2), then replacing these values in the equation we will get two equations:

A*-3 + B*10 = -18

A*6 + B*-2 = -18

So we have a system of equations:

-3A + 10B = -18

6A - 2B = -18

if we add the two times the first equation and the second one we get:

2*(-3A + 10B) + 6A - 2B = 2*(-18) - 18

18B = -3*18

B = -3

by replacing that value of B in one of the equations we will be able to solve it for A.

6*A - 2*(-3) = -18

6*A + 6 = -18

6*A = -18 - 6 = -24

A = -24/6 = -4

The equation is:

-4*x - 3*y = -18

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Answer:

5x=325+160

Step-by-step explanation:

this was very easy but i guess with so many words it could confuse people

By solving a linear equation, it is obtained that Warren has drawn 30 pictures of animals

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let Warren has drawn 5x pictures of animals and 2x pictures of people

Warren has drawn 18 more pictures of animals than people in his notepad

By the problem,

5x - 2x = 18

3x = 18

x = [tex]\frac{18}{3}[/tex]

x = 6

Number of pictures of animals Warren has drawn = [tex]5 \times 6 = 30[/tex]

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Answer: candidate 2 has 90 votes

Step-by-step explanation:

165-75=90

Pygmy rabbit is 22.61-10 meters longer than the wasp.

Given:

A wasp is 1.39-10 meters long.

A pygmy rabbit is 24-10¹ meters long.

Pygmy rabbit longer than the wasp = size of pygmy rabbit - size of wasp.

= (24 - 1.39)-10meters

= 22.61-10 meters.

Therefore pygmy rabbit is 22.61-10 meters longer than the wasp.

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Let the number be n.

Then the expression is:

Answer:

Step-by-step explanation:

Forming the expression,

→ 4x + x

Let's solve the expression,

→ 4x + x

→ 5x

Hence, the answer is 5x.

Function g(x) is a translation of one unit to the left and 3 units down of f(x), then the correct option for the graph of g is B.

Here we start with a function f(x), and we also have the graph of this function.

And we want to find the graph of the function defined as:

g(x) = f(x + 1) - 3

Notice that:

g(x)=  f(x + 1)

Is a translation of one unit to the elft of f(x).

g(x) = f(x) - 3

Is a translation of 3 units down of the graph of f(x).

Then:

g(x) = f(x + 1)- 3

Is a translation of one unit to the left and 3 units down.

With that in mind, we can see that the correct option for the graph of g(x) is option B.

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If  a vegetarian dish will be first. The number of different ways that are there to place the dishes on the table is 576.

There are 4 vegetarian dishes = P4 = 4!

There are 4 meat dishes =P4 =4!

Now let find the number of different  ways

Number of different  ways = 4! × 4!

Number of different  ways = 24 × 24

Number of different  ways = 576 different ways

Therefore the number of different ways  is 576.

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Answer:

D) 16

Step-by-step explanation:

A=4

[tex]a^3[/tex]/a=?

[tex](4^3)[/tex]/(4)=?

64/4=16

Answer:

a = 7

Step-by-step explanation:

Substitute x for 2 and f(x) for 14

14 = -2(2³) + a(2²) + 2

14 = -16 + 4a + 2

14 = -14 + 4a

14 + 14 = 4a

28 = 4a

4a = 28

Divide both sides by 4

4a/4 = 28/4

a = 7

Alternative:

Since from the question, you're already told that f(2) = 14, you just have to find the number that can be multiplied by 2 with a resultant of 14; that number is 7. To confirm, substitute a for 7 in the equation.

Answer:

Never

Because for example; 25(the multiple of 5) + 20(the multiple of 10) equals 45

Answer:

Step-by-step explanation:

never

The linear regression equation from the given scatter plot is:

y = -1.62x + 215.64.

Using this function, the estimate of his weight 15 weeks into the diet is:

191.34 pounds.

The linear regression equation is obtained inserting the points of the scatter plot of the situation into a linear regression calculator.

From the given scatter plot, the points are given as follows:

(0,216), (1,214), (2,213), (3,210), (4,210), (5,207), (6,206), (7,202), (8,203), (9,202), (10,200)

Inserting these points into a calculator, the line of best fit is given as follows:

y = -1.62x + 215.64.

The estimate weight at the 15th week of the diet is the numeric value of the function when x = 15, that is, the lone instance of x in the function is replaced by 15, as follows:

y = -1.62(15) + 215.64 = 191.34 pounds.

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The piece of information does he need is  ∠F ≅ ∠J.

What is triangle?

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides.

Properties of triangle?

Given,

ΔFGH = ΔJKL

By SAS property of triangle;

[tex]\bar{FH}[/tex] ≅ [tex]\bar{JL}[/tex],     FG ≅ JK

third property ,

                         ∠F = ∠J

By SAS property at least two side their ratio must be equal and one angle.

[tex]\frac{FG}{JK} = \frac{FH}{JL}[/tex]

∠F = ∠J

So, option A is correct.

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Answer:

Joseph's present age=3 yrs

David's present age=9 yrs

Step-by-step explanation:

Let Joseph's present age be x.

David's present age=3x

__________________

Ater 3 yrs,

Joseph's age=x+3

David's age=2(x+3)

Also, we can add 3 to David's present age to get age After 3 yrs. So, David's age after 3 yrs would also be 3x+3.

Now, balance them.

3x+3=2(x+3)

3x+3=2x+6

x=3

D"s prsent age=9

J's present age=3

The slope-intercept form is

    y = - x + 1

Given points are  (2, - 1)

          and  y = x + 4

The product of slopes of perpendicular lines is  - 1

   so ,  m = - 1/1  =  -1

     ∴ y = -1 (x) + b

       y  = - x + 1

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The ratio of the areas of these two photos is equal to 9:16.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities.

This ultimately implies that, a ratio is generally expressed as a quotient of two numerical quantities or variables.

Generally speaking, the corresponding ratio of the areas of two geometric figures (shapes) is equal to the square of the ratio of their corresponding side length:

Area of photos = (a:b)²

Substituting the given parameters into the formula, we have;

Area of photos = (3:4)²

Area of photos = 9:16

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If the plumber charges a customer $45 , then the visit was 0.5 hours long .

In the question ,

it is given that

the fixed charge to visit a client's home is = $35

additional per hour charge of plumber is = $20 .

let the time taken by plumber in the customer house be "x" .

So , according to the question

the equation for total charge is

total charge = 35 + 20x

given the customer paid $45 ,

So , 45 = 35 + 20x

20x = 45 - 35

20x = 10

x = 10/20 = 0.5

Therefore , If the plumber charges a customer $45 , then the visit was 0.5 hours long .

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The difference in lengths is 9 cm and the length of the carrot is 9 cm longer than the pea pod.

Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have to determine the difference in lengths

The length of the carrot = 14 cm

The length of the pea pod = 5 cm

The difference in lengths = maximum length - minimum length

The difference in lengths = 14 cm - 5 cm

Apply the subtraction operation, and we get

The difference in lengths = 9 cm

We conclude that the length of the carrot is 9 cm longer than the pea pod.

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Answer:

D? I'm not sure tho so don't be mad if it's wrong

Answer:

Tuition and Fees = $5,992.93

Room = $5,115.92

Board = $4,044.01

Computer Costs = $1,088.15

The 160 feet range and 70 feet height of the path of Gunter Money which can be described with a quadratic equation, gives;

(a) The path is; y = -1.09375×10²·x² + 1.75·x

(b) The vertex form of the equation is; y = -1.09375·(x - 80)² + 70

(c) The angle at the start is approximately 60.3°

A quadratic equation is a single variable polynomial equation of the second degree.

The points in the path which is a path of a projectile and has a shape of a parabola are;

(0, 0), (80, 70), and (160, 0)

The equations are;

y₁ = a·x₁² + b·x₁ + c

y₂ = a·x₂² + b·x₂ + c

y₃ = a·x₃² + b·x₃ + c

Plugging in the coordinates of the three points in the path gives;

The matrix becomes;

[tex]A = \begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}[/tex]

[tex]X = \begin{bmatrix}a \\b \\c\end{bmatrix}[/tex]

[tex]Y = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]

We have;

A·X = Y, which gives;

[tex]\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}\cdot \begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}0 \\70 \\0\end{bmatrix}[/tex]

[tex]X = \dfrac{Y}{A} = A^{-1}\cdot Y[/tex]

Where;

A⁻¹ = The inverse of the matrix A

[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \frac{ \begin{bmatrix}0 \\70 \\0\end{bmatrix}}{\begin{bmatrix}0 & 0 & 1\\80^2 &80 & 1\\160^2 &160 &1 \\\end{bmatrix}} = \begin{bmatrix}\dfrac{1}{12800} & -\dfrac{1}{6400} & \dfrac{1}{12800} \\\\-\dfrac{3}{160} &\dfrac{1}{40} & -\dfrac{1}{160} \\\\1 &0 &0 \\\end{bmatrix}\bullet \begin{bmatrix}0\\ \\70\\ \\0\end{bmatrix}=\begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]

[tex]\begin{bmatrix}a \\b \\c\end{bmatrix} = \begin{bmatrix}-\dfrac{7}{640} \\ \\\dfrac{7}{4} \\ \\0\end{bmatrix}[/tex]

[tex]a = -\dfrac{7}{640}[/tex]

[tex]b = \dfrac{7}{4}[/tex]

c = 0

The equation for Gunter Money's path is therefore;

[tex]y = -\dfrac{7}{640} \cdot x^2 + 1\dfrac{3}{4} \cdot x + 0 = -1.09375\times 10^2 \cdot x^2 + 1.75\cdot x[/tex]

(b) The vertex of the path is (h, k) = (80, 70)

The vertex form of a quadratic equation is; y = a·(x - h)² + k

The equation of Gunter Money's path in vertex form is therefore;

[tex]y = -\dfrac{7}{640} \cdot \left(x - 80)^2 + 70 = -1.09375\times 10^2\cdot (x - 80)^2+70[/tex]

(c) The angle of the parabolic path of Gunter Money's motion at a point is given by the value of the arctangent of the differentiation of the function for the motion at the point as follows;

[tex]y' = -\dfrac{7\times 2}{640} \cdot x + 1\dfrac{3}{4}[/tex]

At the point Gunter Money takes off,  (0, 0), we have;

[tex]tan(\theta) = y' = -\dfrac{7\times 2}{640} \times 0 + 1\dfrac{3}{4} = 1\dfrac{3}{4} = 1.75[/tex]

[tex]\theta = arctan(1.75) \approx 60.3^{\circ}[/tex]

The angle is approximately 60.3°

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The amount of Tritium that bottle contains now will be 439,421.

Consider the function:

y = a (1 - r)ˣ

Where x is the number of times this decay occurs, a = initial amount, and r = fraction by which this decay occurs.

Tritium is a radioactive isotope of hydrogen that rots by around 5% each year. An enormous container of water that contained 856,000 tritium iotas stayed undisturbed for a very long time.

Then the amount of Tritium that bottle contains now will be given as,

y = 856,000 (1 - 0.05)¹³

Simplify the equation, then we have

y = 856,000 (1 - 0.05)¹³

y = 856,000 (0.95)¹³

y = 856,000 (0.51334)

y = 439,421

The amount of Tritium that bottle contains now will be 439,421.

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Answer:

Step-by-step explanation 2/3 is the answer :

The required probability, that she chooses low-fat yogurt is 2/3.

Given that, a cooler is filled with containers of yogurt. Some of the containers have low-fat yogurt and some have non-fat yogurt. There are three flavors for each type of yogurt, as shown in the table.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,

From the given,
Sample space = 24

Low Fat =16
Non-fat = 8

The probability that she chooses low-fat yogurt
= 16/24
= 2/3

Thus, the required probability, that she chooses low-fat yogurt is 2/3.

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The rate of change for cost is =  $2 per hour .

In the question ,

it is given that

the fixed rent for the bicycle is =$20

per hour charge of the bicycle is = $2

let the number of hours we rent a bicycle is = x

and let the total cost for renting the bicycle is = y

So , the equation to represent the cost becomes

y = 20 + 2x

to find the rate of change we differentiate the equation with respect to x .

we get

dy/dx = 2

Therefore , The rate of change is $2 per hour .

The given question is incomplete , the complete question is

You rent a bicycle for $20 plus $2 per hour. What is the rate of change of Cost ?

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