What are the coordinates of the vertex of the graph of the function y 3x² 12x 3?.

The var() function in R is used to calculate sample variance. In those uncommon situations where you want a populace change, utilize the populace mean to work out the example difference and duplicate.

The outcome by (n-1)/n; Take note of the fact that sample variance converges on population variance as sample size increases.

R's sample variance and standard deviation are specified by var(y), which tells R to calculate the sample variance of Y by employing n-1 "degrees of freedom," where n is the number of observations in Y. On the other hand, sd(y) tells R to return the sample standard deviation of y by employing n-1 degrees of freedom. sqrt(var(y)) equals sd(y).

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Her displacement is 9.43 miles, and her office is 5 miles west and 8 miles north from her house

Let's use the notation (x, y) to denote Beth's position, we assume she starts at the point (0, 0).

First she travels 9 miles west and 9 miles north, so the new position is:

(0 - 9, 0 + 9) = (-9, 9)

Then travels 6 miles west and 6 miles nort

(-9 - 6, 9 + 6) = (-15, 15)

then travel 10 miles east and 7 miles south to their office

(-15 + 10, 15 - 7) = (-5, 8)

So the office is 5 miles west and 8 miles north from her house, and the displacement is equal as the absolute value of that point.

dispacement = √( (-5)² + 8²) = 9.43

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They sell 21 pizzas for $321 in one evening.

A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation. It is a mathematical problem expressed entirely in words typically used as an educational tool.

Word problems are regarded as an important aspect of the basic curriculum because they require students to apply their understanding of various concepts to real-life settings.

Let us assume that,

small size pizza =x

medium size pizza =y

large size pizza =z

so, x+y+z=21

6x+9y+10z= 321

y=z+1

x+y+z=21

6x+9y+10z= 321

y-z=1

6x+9y+10z= 321

y+4z=31

5z=30

z=6

y=z+1

y=7

x+y+z=21, x=8

{8,7,6}

8*$6=$48

7*$9=$56

6*$10=$60

Thus, they sell 21 pizzas for $321 in one evening.

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Yes, a probability distribution is given.

The mean of this probability distribution is 1.62 and the standard deviation is 0.84.

Mean = ΣxP(x) = 0*0.108 + 1*0.354 + 2*0.390 + 3*0.148 = 1.62

Standard Deviation = √Σ(x-mean)2P(x) = √(0-1.62)2*0.108 + (1-1.62)2*0.354 + (2-1.62)2*0.390 + (3-1.62)2*0.148 = 0.84

This is a probability distribution for a situation in which college students are randomly elected and arranged in groups of three. The number of people in the group who claim to take one or more online courses is the random variable, or x. The probability distribution is given by the values of x and the probabilities associated with them (P(x)). From the given values, we can calculate the mean and standard deviation of the distribution. The mean of the distribution is 1.62, and the standard deviation is 0.84. This means that, on average, 1.62 students in the groups of three will say that they take one or more online courses. The standard deviation of 0.84 implies that the actual number of students in the groups who say that they take online courses will vary from the mean value by about 0.84 students

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The four methods of solving a quadratic equation are Factoring, Completing the square, Quadratic formula, Graphing.

A quadratic equation is a type of polynomial equation that can be written in the form of ax^2 + bx + c = 0, where x is the variable, and a, b, and c are constants. The degree of the equation is 2, and it creates a parabolic shape when graphed. The solutions of a quadratic equation are also known as roots, and there can be zero, one or two distinct solutions. The solutions can be real or complex numbers. The most common method to find the roots of quadratic equation is using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

The four 4 methods of solving quadratic equation are :

Factoring: This method involves factoring the quadratic equation into the product of two binomials. Once factored, you can set each binomial equal to zero and solve for the roots (x-values) of the equation.

Completing the square: This method involves rearranging the equation into a perfect square trinomial and then solving for the roots. The basic idea is to add and subtract the square of half the coefficient of the x^2 term to both sides of the equation.

Quadratic formula: This method utilizes the quadratic formula to find the roots of the equation. The formula is: x = (-b ± √(b^2 - 4ac)) / 2a

Graphing: This method involves plotting the equation on a coordinate plane and finding the x-values (roots) of the equation by observing where the graph intersects the x-axis.

All four method are used to find the x-intercepts(root) of the quadratic equation, which is the main goal of solving the quadratic equation.

Hence, The four methods of solving a quadratic equation are Factoring, Completing the square, Quadratic formula, Graphing.

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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After solving, the solution of the pair of equation is (2, 1).

In the given question, we have to find the solution of pair of equation 2x + y = 5 and 3x - 2y = 4.

The given equation are:

2x + y = 5.........(1)

3x - 2y = 4.........(2)

Multiply equation 1 by 2 then add by equation 2.

4x + 2y + (3x - 2y) = 10 + 4

Now simplifying

4x + 2y + 3x - 2y = 14

7x = 14

Divide by 7 on both side, we get

x = 2

Now putting the value of x in equation 1

2(2) + y = 5

4 + y = 5

Subtract 4 on both side, we get

y = 1

Hence, the solution of the pair of equation is (2, 1).

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The complete question is:

What is the solution of pair of equation 2x + y = 5 and 3x - 2y = 4?

No. of hours, hourly employee need to work to get earnings as the standard employee = 50 hours.

What is an equation?

An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

Given, weekly salary of an employee = $500

Hourly earning of another employee = $10

Let the hourly employee work for x hours to earn the same earnings as weekly employee

By the question,

$10 x = $500

x = $500/$10

x = 50 hrs.

Hence, the hourly employee has to work around 50 hours make same weekly earnings as the standard employee.

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On solving the exponential function A(t) = 80 (0.965)^t, the number of animals will drop to 15 after 47 years.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The number of animals studied for the research = 80

The decrease rate of certain species = 3.5%

The rate of decay in exponential term = (1 - 0.035) = 0.965

The exponential function for the situation is -

A(t) = 80 (0.965)^t

Where, t is the number of time periods in years and A(t) = change in the population of animals.

The number of animals drop to 15.

So, substitute the value of A(t) = 15 in the equation -

A(t) = 80 (0.965)^t

15 =  80 (0.965)^t

15/80 = 0.965^t

0.1875 = 0.965^t

ln(0.1875) = t ln(0.965)

t = ln(0.1875)/ln(0.965)

t = -1.6739/-0.0356

t = 47.01

Therefore, the time period value is obtained as t=41 years.

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Step-by-step explanation:

if x and y vary directly, they are defined as

y = kx

with k being a constant for all x.

now, if they vary inversely, they are defined as

y = k/x

so,

6/5 = k/4

24/5 = k

y = f(x) = 24/5 / x = 24/(5x)

f(7) = 24/(5×7) = 24/35

when x = 7, y = 24/35

When x and y vary inversely, their product is always a constant, k. In this case, we know that x = 4 and y = 6/5, so we can use this information to find the value of k:

k = xy = (4)(6/5) = 24/5

The function that models this inverse variation is:

xy = k

We can find y when x = 7 by substituting this value into the equation and solving for y:

xy = k

(7)y = 24/5

y = 24/5*(1/7)

y=24/35

So when x = 7, y = 24/35.

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The solution to log base 7 of 1 is x=0, which is the value of the power to which 7 must be raised to get the value 1.

The logarithm function is an inverse function of the exponential function, and it is defined as log_b(x) = y means b^y = x. In other words, it represents the power to which the base b must be raised to get the value x.

In this case, we are solving log_7(1), which means we are looking for the power to which 7 must be raised to get the value 1.

Since any number raised to the power of 0 is 1, we can say that 7^0 = 1, which means that log_7(1) = 0.

To solve log base 7 1, you need to find the value of x that satisfies the equation log_7(x) = 1.

Using the definition of logarithm, log_b(x) = y means b^y = x.

So to solve log7(1), we can set 1 = 7^x and get x = log7(1) = 0

So the solution to log base 7 of 1 is x=0.

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Answer: 63 gingerbread cookies

Step-by-step explanation: Okay, to find the answer to this problem, we shall use this formula:

Final amount = Whole # * Part % / 100

So, now let's plug in the numbers to find the answer:

Final amount = 90 * 70 / 100

= 6300/ 100

= 63

Therefore, Kenny ordered a total of 63 gingerbread cookies. I hope this helped!

Answer: liner

Step-by-step explanation:

Answer:

Step-by-step explanation:

linear, because the slope intercept fomat is y=mx+b it's just that the y intercept is zero so they just excluded it. So the equation would be y=8.75x+0 but they just removed the zero to simplify. So yes, it is linear

Answer:

1 [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

Both blocks contain 9 stars

left block has all 9 shaded = [tex]\frac{9}{9}[/tex] = 1

right block has 5 shaded = [tex]\frac{5}{9}[/tex]

mixed number = 1 + [tex]\frac{5}{9}[/tex] = 1 [tex]\frac{5}{9}[/tex]

Answer:

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

Use slope equation:

Substitute coordinates and solve for n:

The polynomial f(x) = x³ + 9x² + 23x + 15 has a factor of x + 3

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

The degree of a polynomial is the power is the highest exponent. The cubic polynomial have a degree of 2.

Given that the linear function x + 3 is a factor of f(x), hence f(-3) = 0. Therefore:

f(-3) = 0

f(-3) = (-3)³ + 9(-3)² + a(-3) + 15 = 0

(-3)³ + 9(-3)² + a(-3) + 15 = 0

-27 + 81 - 3a + 15 = 0

69 - 3a = 0

3a = 69

a = 23

The value of a is 23

The polynomial becomes f(x) = x³ + 9x² + 23x + 15

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The 4 types of symmetry in biology is spherical, radial, biradical, and bilateral.

The term symmetry is defined as the balanced arrangement of body parts or shapes around a central point or axis

As we all know that the 4 types of symmetry in biology is defined as the size, shape, and relative location on one side of a dividing line mirrors the size, shape, and relative location on the other side.

Here we have also know that animals can be categorized on the basis of their symmetry.

And the basic classification includes Levels of organization, Symmetry, Diploblastic and Triploblastic Organization, Coelom, Segmentation, and Notochord in biology.

Therefore all these categories must be kept in mind while classifying an animal.

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The value of x is 3.67 in the given right angled triangle.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

In the given triangle ,

Triangle STU ,

T = 90

S = 69

So, U = 180 - 90-69

U = 180 - 159

U = 21

And US  = 10

sin69 = TU/US

sin69 = TU / 10

0.93 = TU/ 10

93 / 100 = TU / 10

93/10 = TU

TU = 9.3

So, in the triangle

as per pythagores theorem ,

SU^2  = ST^2 + TU^2

10*10 = x*x + 9.3*9.3

x*x = 100-86.49

x*x = 13.51

x = 3.67  (Approx)

Hence, The value of x is 3.67 in the given right angles triangle.

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A dot serves to depict a point, which is a place in any space (.). Nothing about it is long, tall, shaped, or big.Therefore, the snail finally arrives at the point (6,5).

What is a point and line?

To indicate an accurate location in space, a point is denoted by a dot (.). It has no height, width, or any dimension. It is hence sizeless.

The simplest basic object in geometry is a point. A dot and a capital letter are used to identify it. Only position is represented by a point, which has no size (that is, zero length, zero width, and zero height).

A dot serves as a visual representation of a point, which is a place in any space (.). It lacks all dimensions—length, height, shape, and size. With capital letters, it denotes the start of drawing any figure or shape. Line. a collection of points together along a straight path.

The snail moves 1 unit North, 2 units East, 3 units South, 4 units West, 5 units North, 6 units East, 7 units South, 8 units West, 9 units North, and 10 units East.

Starting at (0,0), the snail moves:

Therefore, the snail finally arrives at the point (6,5).

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So, the given system will have a unique solution when k=,1

A system of linear equations in two variables will have a unique solution when the equations are consistent and independent.

In this case, the system of equations is kx + 3y = k and 3x + ky = k.

One way to check for consistency and independence is by using the determinant of the coefficient matrix and comparing it to the determinant of the system. The determinant of the coefficient matrix is (kk) - (3ky) = k^2 - 3ky and the determinant of the system is k^2 - k.

For the system to have a unique solution, the determinant of the coefficient matrix must be non-zero and equal to the determinant of the system.

Therefore, the system will have a unique solution when k^2 - 3ky = k^2 - k.

Which means that k=1.

This system will have a unique solution when k=1, and the pair of linear equations will be 1x + 3y = 1 and 3x + ky = 1.

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Answer:

9/12 + 4/12

Step-by-step explanation:

Find the lowest common denominator. 12 is divisible by 4 and 6.

4 x 3 =12 and 6x2 =12

3/4 x 3/3 =9/12

2/6 x 2/2= 4/12

The images are formed when two plane mirrors are placed at 36 is 9

The term plane in math defined as a two-dimensional doubly ruled surface spanned by two linearly independent vectors.

Here we need to find the number of images are formed when two plane mirrors are placed at 36.

Here we have given that the generalization of the plane to higher dimensions is called a hyperplane.

And here we also know that the angle between two intersecting planes is known as the dihedral angle.

The by using the formula we have calculated as,

=> n = (360 / 36) - 1

=> n = 10 - 1

=> n = 9

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Answer:

7/9

Step-by-step explanation:

Multiply [tex]\frac{2}{3}[/tex] by 3 to get the common denominator of 9. Whatever you do to the top, you do to the bottom too.

So you would do [tex]\frac{2}{3}[/tex] x [tex]\frac{3}{3}[/tex]  to get [tex]\frac{6}{9}[/tex]

Add [tex]\frac{1}{9}[/tex] to [tex]\frac{6}{9}[/tex] to then get [tex]\frac{7}{9}[/tex]

So your answer would be [tex]\frac{7}{9}[/tex]

Total number of outcomes (n) = 2

Let E be the event of getting a yellow colored side of the coin.

Therefore, n(E) = 1

Therefore, P(E) = n(E)/n = 1/2

Answer:

1/2

Hope it helps.

If you have any query, feel free to ask.

Answer: 1 1/4 mile

Step-by-step explanation:

Solving 3 equations with 3 variables using substitution involves using one equation to solve for one variable in terms of the other variables, and then substituting that expression into the other equations. Here is the general process:

   1. Choose one of the equations and solve for one of the variables in terms of the other variables. For example, if the equation is 2x + 3y - z = 5, you can solve for x by isolating it on one side of the equation: x = (5 + z - 3y)/2

  2.Substitute the expression for the solved variable into the other equations. For example, if you have the equations 2x + 3y - z = 5, x + y + z = 7, and 3x - 2y + z = 6, you would substitute x = (5 + z - 3y)/2 into the other equations.

  3.For the remaining variables, solve the resulting equations. For instance, you would obtain y + z = 7 - (5 + z - 3y)/2 and 3(5 + z - 3y)/2 - 2y + z = 6 after inserting x = (5 + z - 3y)/2 into the other equations.

  4.By putting the remaining variables on one side of the equation, you can solve for them. After that, you can solve for the variable's value.

 5.Check to see if the solution is valid by substituting it back into the original equation.

It's crucial to remember that this approach could not always result in a singular solution; in certain circumstances, you might discover that the system has neither a solution nor an unlimited number of solutions.

  therefore, using these 5 steps we can solve the equations using substitution .

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CI will yield more amount, because simple interest generates earnings from principal only.

Interest rate is the amount charged over and above the principal amount by the lender from the borrower.

Given that, A recent college graduate is looking to begin saving for retirement. Option A is a savings account with 3.5% annual simple interest. Option B is a savings account with 3.5% annual interest compounded monthly.

Let the principal amount be, $20000

Solving for simple interest, we get,

SI = PRT / 100

= 20000×3.5×10 / 100

= 7000

Therefore, amount = $27000

Now, CI =

A = P(1+r)ⁿ

A = 20000(1+0.035/12)¹²⁰

A = 1241286.32

Therefore, we see that CI will yield more amount.

Hence, CI will yield more amount, because simple interest generates earnings from principal only.

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Answer:

Step-by-step explanation: