Part B: If GA = 29 and a major arc mDUG = 185°, then determine the minor arc length of


GD.

The correct answer is (4x^3 - 8x^2 )

Solve by using Foil's Method

Multiply (x - 3)(4x^2)

Begin, by multiplying together, the first terms of binomial

= x * 4x^2 = 4x^3

Now, multiply the last term of binomial.

= -3 * 4x^2 = -12x^2

Sum up the partial products starting from the first to last product from the first to last product and collect it:

=(4x^3 - 8x^2 )

Now, Let us know

What is Foil's Method ?

FOIL a mathematical series of steps used to multiply two binomials.

By definition we have the meaning of FOIL is given by:

F: First

O: Outer

I: Inner

L: Last

Binomial is simply an expression that consist of two variables or terms separated by either the addition sign (+) or subtraction (-).

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Answer:

B) y = -5x + 7

Step-by-step explanation:

Pick 2 points on the line:  (10, 5) and (15, 4)

slope = change in y ÷ change in x = (15 - 10) ÷ (4 - 5) = -5

from inspection, the y-intercept is (0, 7)

Therefore, using slope-intercept formula:  y = mx + b

(where m is the slope and b is the y-intercept)

y = -5x + 7

Answer:

does it say like x=_

Step-by-step explanation:

Answer:

x = 105°

Step-by-step explanation:

Every triangle is equal to 180°. You can find two angles in the triangle in which the x angle is located.

To find the right lower angle, subtract 65 and 90 from 180, to get 25. Then find the lower left angle by subtracting 50 and 80 from 180, to get 50.

You now know that two angles in the overlapped triangle are 50 and 25, which you can subtract from 180 to find the final angle, 105°.

Hope this helped!

Answer:

594

Step-by-step explanation:

You multiply 18 by 3 by 11 :)

Given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.

So, the likelihood that a pupil is between the ages of 6 and 8 can be calculated using the techniques below:

P = 28/89

Therefore, given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.

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The complete question is given below:

Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age group. One student from the school will be selected at random. What is the probability that the student is in the age group of 6 to 8 years given that the selected student responded with joy?

Noel delivered an average of 500 yards of ribbon per day from Tuesday to Monday.

The central value represents the typical or average value of all the numbers in the set.

From Tuesday to Friday, Noel delivered 350 yards of ribbon per day, a total of 4 days. So, the total length of ribbon that he delivered during this period is

=> 4 * 350 = 1400 yards.

From Saturday to Monday, he delivered 700 yards of ribbon per day, a total of 3 days. So, the total length of ribbon that he delivered during this period is

=> 3 * 700 = 2100 yards.

To find the average length of ribbon that Noel delivered per day, we need to find the total length of ribbon he delivered in both periods and divide it by the total number of days.

The total length of ribbon he delivered in both periods is

=> 1400 + 2100 = 3500 yards.

The total number of days is

=> 4 + 3 = 7 days.

So, the average length of ribbon that Noel delivered per day is

=> 3500/7 = 500 yards.

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Answer:

13

Step-by-step explanation:

To find the distance between two points in a coordinate plane, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the points (-3, 6) and (-8, -6) as follows:

d = sqrt((-8 - (-3))^2 + (-6 - 6)^2)

= sqrt((-5)^2 + (-12)^2)

= sqrt(25 + 144)

= sqrt(169)

= 13

Therefore, the distance between the two points in simplest radical form is 13.

Answer:

Comencemos por encontrar el número total de monedas en el frasco. Sabemos que hay 15 centavos, 18 monedas de diez centavos y 21 cuartos, así que:

Número total de monedas = número de centavos + número de monedas de diez centavos + número de cuartos

Número total de monedas = 15 + 18 + 21

Número total de monedas =

También sabemos que hay 83 monedas en total, por lo que el número de monedas de cinco centavos se puede encontrar restando el número de centavos, monedas de diez centavos y cuartos del total:

Número de monedas = número total de monedas - número de centavos - número de monedas de diez centavos - número de cuartos

Número de níquel = 83 - 15 - 18 - 21

Número de níqueles = 29

Por lo tanto, hay 29 monedas de cinco centavos en el frasco.

Para encontrar el número de monedas que no son níqueles, podemos restar el número de monedas del total:

Número de monedas sin níquel = número total de monedas - número de monedas

Número de monedas sin níquel = 83 - 29

Número de monedas sin níquel = 54

Así que hay 54 monedas en el frasco que no son monedas de cinco centavos.

Podemos usar la ecuación "n = número total de monedas - número de centavos - número de monedas de diez centavos - número de cuartos" para encontrar el número de monedas de cinco centavos en el frasco, donde n representa el número de monedas de cinco centavos. Sustituyendo los valores dados, obtenemos:

n = 83 - 15 - 18 - 21

n = 29

Por lo tanto, la ecuación es n = 29.

Step-by-step explanation:

espero te ayude en algo

An electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

The circuit underneath is composed of:

A battery as a supply of direct modern-day which materials electricity within side the circuit for modern-day to go with the drift. Direct modern-day affords uni-directional modern-day. Here it has cells. Here 4 cells are linked in collection for the battery.

Two bulbs A and B linked in parallel connection. Each bulb has been parallel connected with a voltmeter.

A voltmeter measures the voltage throughout the element that it's miles linked with. It is continually linked in parallel with the additives.

Main circuit has an ammeter in collection with the battery and connection of bulb.

An ammeter measures the modern-day flowing within side the circuit. It is continually linked in collection.

Therefore, an electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

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In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

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By using the power rule of integration, the solution for F(x) is: F(x) = \(4x^4 + 7x^2 + 7x - 23\)

To find F, we need to integrate F'(x) with respect to x.
So, F(x) = ∫(16x³ + 14x + 7) dx
Using the power rule of integration, we can integrate each term separately.
∫(16x³) dx = \(4x^4\) + C1
∫(14x) dx = 7x² + C2
∫(7) dx = 7x + C3
Adding all of these results, we get:
F(x) = \(4x^4\) + 7x² + 7x + C
Now, we need to use the initial condition F(1) = -5 to solve for the constant C.
F(1) = \(4(1)^4\) + 7(1)² + 7(1) + C = -5
Simplifying this equation, we get:
4 + 7 + 7 + C = -5
C = -23
Therefore, the solution for F(x) is: F(x) = \(4x^4 + 7x^2 + 7x - 23\)

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Answer:

0.78

used a calculator

The  examples that would constitute a discrete random variable are;

I. Total number of points scored in a football game

III. Number of near collisions of aircraft in a year

A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.

A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.

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Answer:

-3 ,-2 ,-1, 0

Step-by-step explanation:

x is the smallest integer then, x+x+1+x+2+x+2=-6
4x+6= -6   4x=-12 x= -3 so the integers are..

Answer:

48ft.

Using the area formula of length times width, (8x6), we can easily get 48ft, which is how much area the carpet takes up.

To find the values of z that make the product with the complex number 5-6i a real number, we need to consider the imaginary part of the product.

The product of z and 5-6i can be written as:

z * (5 - 6i)

Expanding this expression, we get:

5z - 6zi

For the product to be a real number, the imaginary part (-6zi) must be equal to zero. This means that the coefficient of the imaginary unit i, which is -6z, must be zero.

Setting -6z = 0, we find:

z = 0

So, one possible nonzero value of z is 0.

However, since we are looking for nonzero values of z, we need to find another value that satisfies the condition.

Let's consider the equation for the imaginary part:

-6z = 0

Dividing both sides of the equation by -6, we have:

z = 0/(-6)

z = 0

Again, we find z = 0, which is not a nonzero value.

Therefore, there are no other nonzero values of z that make the product with the complex number 5-6i a real number. The only value that satisfies the condition is z = 0.

Option D correctly states that a function can't satisfy all the given conditions simultaneously.

If a function satisfies f(x) > 0, it means the function takes positive values on the interval. If f'(x) > 0, it indicates that the function is increasing on the interval, meaning its slope is positive. Conversely, if f'(x) < 0, it implies that the function is decreasing on the interval, meaning its slope is negative.

For a function to satisfy both f'(x) > 0 and f'(x) < 0 on the same interval, it would require the function to change from increasing to decreasing or vice versa within that interval. However, such a situation is not possible because if the function is increasing, its derivative (slope) cannot suddenly become negative, and if the function is decreasing, its derivative cannot suddenly become positive.

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Answer:

-4/1

Explanation:

you have 2 points so you are counting the slope of the line based of those 2 points

1st point (X1=0 Y1= -1) (0,-1)

2nd point (X2= -1 Y2= -4) (-1, -4)

using the slope formula Y2 - Y1/X2 - X1

(-4 -(-1)) / (0 -(-1)) =

-4/1

the slope is -4/1

Answer:

248

Step-by-step explanation:

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

The expression is not factorable with rational numbers.

x² − 4x + 7

\(\textit{volume of a rectangular prism}\\\\ V=Lwh ~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ h=1.8\\ L=4.2\\ V=26.46 \end{cases}\implies \begin{array}{llll} 26.46=(4.2)w(1.8)\implies 26.46=7.56w \\\\\\ \cfrac{26.46}{7.56}=w\implies 3.5=w \end{array}\)

Answer:

Nominal decisions can be broken into two distinct categories: dichotomous decisions and polychotomous decisions.

segment EH and segment E'H' both pass through the center of dilation.

A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.

The center, which may be found within, outside, or on a figure, is the only invariant (not changing) point under a dilation (k 1).

In the figure attached, triangle EFG is shown.

H is located at (0, 1)

The center of dilation is located at (0, 2)

Then, H' is located at (0, 0), so that the distance between the center of dilation and H' is twice the distance between the center of dilation and H.

E is located at (0, 5)

Then, E' is located at (0, 8), so that the distance between the center of dilation and E' is twice the distance between the center of dilation and E.

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The total cost of materials and labor for the office space, considering a tile unit cost of P300 and labor cost equal to the materials cost, amounts to P63,000.

To calculate the total cost of materials and labor, we first need to determine the cost of the tiles. Given that the unit cost of a certain tile is P300, we can multiply this by the area of the office space to find the total cost of the tiles. The office space has an area of 63 sqm, so the total cost of the tiles is P300 * 63 = P18,900.

Next, we need to calculate the labor cost, which is 100% of the materials cost. Since the materials cost is P18,900, the labor cost will be equal to P18,900. Therefore, the total cost of labor is also P18,900.

To find the total cost of materials and labor, we add the cost of the tiles (P18,900) and the labor cost (P18,900): P18,900 + P18,900 = P37,800.

Therefore, the total cost of materials and labor for the office space is P37,800.

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The given equation 5x² - 7x + 2 can be factorized using the factorization method as;(5x - 2)(x-1)

Factorization in mathematics refers to the process of expressing a given number or expression as a product of two or more factors. In other words, it is the method of breaking down a number or an expression into simpler parts or factors.

Given that 5x² - 7x + 2 =0 whic can be seen as a quadratic equation, from this we can see that (x-1) is one of the factor.

We can re wrirte the expression as 5x² - 5x - 2x + 2 =0, we can see that the new expression is still the same with the original expression , then we can factor out as :

5x(x-1) -2(x-1)

(5x - 2)(x-1)

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From this Triangle

Taking Triangle XZH, wanting to find HZ

From the Second triangle, ZHY

XY = x + 8

= 11.83 + 8

=19.83

Answer:

2nd choice i belive

Step-by-step explanation:

The solution to this system of equations is infinitely many solutions

The system of equations is given as:

-5.9x  -3.7y = -2.1.

5.9x + 3.7y = 2.1.

Add both equations to eliminate a variable

-5.9x + 5.9x - 3.7y + 3.7y = -2.1 + 2.1

Evaluate

0 +0 = 0

Evaluate the sum of zeros

0 = 0

Both sides of the equations are the same

Hence, the solution to this system of equations is infinitely many solutions

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Answer:

Option C is correct. The system of linear equation -5.9x - 3.7y =  -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.

What is system of linear equation?

The system of linear equations is "a set of two or more linear equations or   variables is called system of linear equation".

What is infinitely many solutions?

An equation has infinitely many solutions only if "the two lines are coincident and having the same y-intercept".

According to the question,

The system of linear equation,

-5.9 x - 3.7y = -2.1            →  (1)

5.9 x + 3.7y = 2.1              →  (2)

The equation (1) is same as the equation (2) only the difference equation (1) is multiplied by (-1). Both equation give the same line. To check if above equations have same y-intercept, the equation can be written in slope intercept form y = m x +c where 'm' is the slope of the line, 'c' is the 'y-intercept'.

y = - (5.9/3.7) x + 2.1   [From equation (1)]

y = -(5.9/3.7) x + 2.1      [From equation (2)]

The both equation have same y-intercept. Therefore, the system of linear equations have infinitely many solution.

Hence, the system of linear equation -5.9x - 3.7y =  -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.  

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Step-by-step explanation: