(-3,7); (-10,0)



For 20 points

The minimum value of the given function f(x) = 16x² −16x+28 is 24.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.

To find the minimum value of the function f(x) = 16x² −16x+28 using the derivative method, you can start by taking the derivative of the function. The derivative of a quadratic function is given by:

f'(x) = 2ax + b

In this case, the derivative of the function f(x) is:

f'(x) = 2×16x - 16

To find the minimum value, we need to find the x value that makes the derivative equal to zero. Setting the derivative equal to zero and solving for x gives us:

216x - 16 = 0

32x = 16

x = 0.5

Now that we have the value of x that minimizes the function, we can plug this value back into the original function to find the minimum value:

f(0.5) = 16×(0.5)² - 16(0.5) + 28 = 4 - 8 + 28 = 24

Therefore, the minimum value of the function is 24.

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Sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.

Now, According to the question :

Sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}. For example, set A is a collection of all the natural numbers, such as A = {1,2,3,4,5,6,7,8,…..∞}. Also, check sets here.

Sets can be represented in three forms:

1. Roster Form: Example- Set of even numbers less than 8={2,4,6}

2. Statement Form: Example-A = {Set of Odd numbers less than 9}

3. Set Builder Form: Example: A = {x: x=2n, n ∈ N and 1 ≤ n ≤ 4}

What are the types of Sets?

A set has many types, such as;

1. Empty Set or Null set

2. Finite Set

3. Infinite Set

4. Equal Set

5. Subsets

6. Universal Set

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Yes , it Is the equation that is a linear equation in two variables √ 2x √ 5y 16

The equation of standard linear equation in two variables can be expressed as

ax + by + c = 0

here,

a, b,c are real numbers.

Power of x and y are 1,So named linear equation.

It must be sure that non of a and b is equal to zero.

If either of a and b is equal to zero,then the equation becomes linear equation in one variable.

Solution of linear equation in two variables:

If only one equation is given,then infinite many solutions are present.

If two equations are given,then three type of solutions are present:

Unique situation

Infinite many solutions

No solution

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Addition, subtraction, multiplication and division are four type of arithmetic

Beside mentioned above exponential and modulus operations are also arithmetic

The Greek noun arithmos, which means "number," is where the word arithmetic ultimately comes from. Along the way, it also appeared in Latin, Anglo-French, and Middle English. Even elementary mathematics has a rich vocabulary. Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations.

So addition,multiplication, subtraction and division are 4 types of arithmetic

2+2=4

2*2=4

2/2=1

2-2=0

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The level of a line's slope indicates its steepness, here θ = [tex]tan^{-1/3}[/tex] is the slope angle of Y = 3x + 1.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

Now, given that,  

Y = 3x + 1 ........ (1)

slope intercept form equation is: y = mx+c ........... (2)

next, if we compare (1) and (2)

it comes out to be

m = 3 representing slope

and c = 1 representing y-intercept.

now, slope angle: tan θ = m (slope)

tan θ = 3              [putting the value of m]

θ = [tex]tan^{-1/3}[/tex]

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The complete question is as follows:

What is the slope angle of Y = 3x + 1?

Answer:

Step-by-step explanation:

Sample Space

off  even numbers

= {2,4,6,8,10}.

There are 5 outcomes in the sample space,

The law of cosines generalizes the Pythagorean formula to all triangles. It says that c^2, the square of one side of the triangle, is equal to a^2 + b^2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

c^2=a^2 + b^2 - 2abcosC

Pythagorean formula

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

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The expected number that will arrive on time is; 151.23

The standard deviation of this distribution is; 6.62

We are given;

Percentage of the flights involved in the study arrived on time; p = 71% = 0.71

Sample size; n = 213

Now, the formula for the mean which is the expected number that will arrive on time is;

μ = np

μ = 213 * 0.71

μ = 151.23

The formula for the standard deviation of the distribution is;

σ = √(np(1 - p))

σ = √(213*0.71(1 - 0.71))

σ = 6.62

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To prove two triangles are similar in the given circles need to prove that intercepted arc formed by the pair of angles should be equal or same.

As given in the question,

Two triangles formed in the circle are similar required following steps to prove it correct:

Therefore, to prove the two triangles are similar in the circle need to prove they have same intercepted arc formed by the pair of angles.

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The given values are 2,6,5,3,0,3,4,3,2,4,5,2,4

There are the following values as shown in the given data.

To find the mode first we have to assign each value that how many times it appears.

1. 2-3 the number 2 appears only Three times.

2. 6-1 the number 6 appears one time.

3. 5-2 the number 5 appears only two times.

4. 3-3 the number 3 appears only three times.

5. 0-1 the number 1 appears only one time.

6. 4-3 the number 4 appears only Three times.

So, the mode of the given data is 4,3,2 as it appears the most number of times.

If a given set of values with two modes is bimodal, a given set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal.

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The vertical asymptote of y = 1x - 5 is x = 5, since the denominator becomes zero when x = 5 and the function is undefined at this point.

The vertical asymptote of y = 1x - 5 is x = 5. This is because when x = 5, the denominator of the function (1x - 5) becomes zero, and the function is undefined at this point. As a result, the vertical asymptote is x = 5. This can be seen by taking the limit of the function as x approaches 5 from either side. As x approaches 5 from the left, the limit of the function is negative infinity, and as x approaches 5 from the right, the limit of the function is positive infinity. Thus, the vertical asymptote of y = 1x - 5 is x = 5, since the denominator becomes zero when x = 5 and the function is undefined at this point.

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Answer:

Step-by-step explanation:

Determine an algebraic expression for the nth term of the following sequence.

A set of 3 figures are connected squares. Figure 1 is a column of 5 squares next to a column of 3 shaded squares. Figure 2 is figure 1 with an additional column of 3 shaded squares to the right. Figure 3 is figure 2 with an addition column of 3 shaded squares to the right to make 9 shaded squares.

The number of choices the gardener has is 440440

It is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

The formula for combination is [tex]^nC_r[/tex] = n! / r!(n - r)1

We have,

Number of geranium = 14

Number of lilies = 12

Number of geranium bought = 5

Number of lilies bought = 3

The number of choices.

= [tex]^{14}C_5 \times ^{12}C_3[/tex]

= (14 x 13 x 12 x 11 x 10)/(5 x 4 x 3 x 2) x (12 x 11 x 10)/(3 x 2)

= 14 x 13 x 11 x 2 x 11 x 10

= 440440

Thus,

The number of choices is 440440.

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Expression is a constant, variable or constant multiplied by a variable separated by operator.

Identity, as we all know, is equality, which holds true regardless of the variable's value. These identities are algebraic formulas that show that for all possible values of the variable, the Left-Hand Side (LHS) and the Right-Hand Side (RHS) of the equation are equal. A phrase that can have any value is called a variable.

Monomial, polynomial and binomial are the three types of algebraic expression.

An expression with variables, constants, and algebraic operations is known as an algebraic expression (like subtraction, addition, multiplication, etc.). Terms comprise expressions. For instance: 5x+20y, 6-8x.

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Area: The total space covered by the two-dimensional surface of an object, or a flat shape is called an area.

Many different area formulas are available to get the area of various two-dimensional shapes. We can also get a shape's area by counting the number of unit squares that cover the whole surface of the object.

This method helps us to learn and make out the concept of area.

The unit of area is forever measured in square units like square centimeters, square meters, square inches, and so on.

Volume: The space enclosed within the object or the space covered by any three-dimensional solid object is known as volume.

To find the volume, we divide the occupied space into equal cubical units and calculate the total occupied cubical units, The unit of volume can be in a cubic centimeter, cubic meter, cubic inches, and so on.

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The solution of the given system of equations 3x + y = 10 ,  x - y = 2 is equal to x = 3 and y = 1.

As given in the question,

Given system of equations are :

3x + y = 10      ____(1)

x - y = 2    _____(2)

Add equation (1) and  (2) to eliminate y and get the value of x we have,

3x + y = 10

x - y = 2

4x      = 12

⇒x = 12 / 4

⇒ x = 3

Substitute value of x = 3 in equation (1) to get the value of y for the given equation,

3(3) + y = 10

⇒ 9 + y = 10

⇒ y = 10 - 9

⇒ y = 1

Therefore, the solution of the given system of equations is equal to x = 3 and y =1.

The above question is incomplete, the complete question is:

What is the solution of the system of equations 3x + y = 10 ,  x - y = 2?

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The median for the data is 24.

Median is the middle value of the set of data when the data is arranged in an ascending order.

The median of a data has a higher frequency if the data is distributed symmetrically.

We will arrange the given data in ascending order as 21, 23, 24, 25 and 27.

Also, the number of values here is 5, which is an odd number. As we know if the number of values is odd in a data, then the middle value will be the median.

For 5 numbers, the middle value will be the number from either side.

In the given data, as we can see that the value is 24, so 24 will be the median for the data.

Hence, the median for the data is 24.

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The required real proportion's 95% confidence interval is (0.301; 0.359).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

So, the sample size is 1000.

Phat = 0.33

(1 - phat) = 1 - 0.33 = 0.67

Zcritical = 1.96 at 95%

The confidence range is as follows:

Phat ± margin of error

Margin of Error = Zcritical * sqrt[(phat(1 - phat)) /n]

Margin of Error = 1.96 * sqrt[(0.33 * 0.67) / 1000]

Margin of Error = 1.96 * 0.0148694

Margin of Error = 0.0291440

Lower boundary = (0.33 - 0.0291440) = 0.300856

Upper boundary = (0.33 + 0.0291440) = 0.359144

Therefore, the required real proportion's 95% confidence interval is (0.301; 0.359).

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Correct question:
Cyber Monday Shopping A survey of 1000 U.S. adults found that 33% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 95% confidence interval of the true proportion.

Answer:

Below

Step-by-step explanation:

1/a + 1/r = 1/3        a = aaron rate   r = rosa rate    3 = rate of both

1/5 + 1/r = 1/3

1/r = 2/15

r = 15/2 = 7.5 hr for rosa alone

Answer:

2

Step-by-step explanation:

Any number to the power of 1 is that number itself, thus 2 to the power of 1 is 2.

Step-by-step explanation:

an exponent always means how often the base (or base number) is multiplied by itself.

like

3⁴ = 3×3×3×3

5³ = 5×5×5

x⁵ = x×x×x×x×x

so,

x¹ = x

for every value of x.

and therefore

2¹ = 2

In mixed number form, the change in the distance when using the new road instead of the dirt roads is 2 1/12 miles lesser.

To determine the change in the distance when using the new road instead of the dirt roads, we need to find the difference between the distance of the new road and the distance of the dirt roads.

The distance of the dirt roads is the sum of the two measurements given, which is 2 3/8 + 3 5/6 = 5 15/24 miles.

The change in the distance when using the new road instead of the dirt roads is the difference between the distance of the new road and the distance of the dirt roads, which is 4 1/3 - 5 15/24 = -2 2/24 miles.

In mixed number form, the change in the distance when using the new road instead of the dirt roads is -2 and 2/24 = -2 1/12 miles.

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Answer:

11.1

Step-by-step explanation:

sin 46 · x = 8

0.71934 x = 8

x  = 8/0.71934

x = 11.121306

Answer:

Hence, x=28.

Step-by-step explanation:

The approximate volume of the greenhouse will be 1,527 ft³.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Ellen's greenhouse is in the shape of a hemisphere.

And, The diameter of the floor is 18 feet.

Now,

Since, Ellen's greenhouse is in the shape of a hemisphere.

We know that;

⇒ The volume of Hemisphere = (2/3) πr³

Here, The diameter of the floor is 18 feet.

Hence, The radius of the floor = 18/2

                                               = 9 feet

So, We get;

⇒ The volume of Hemisphere = (2/3) πr³

⇒ The volume of Hemisphere = (2/3) × 3.14 × 9³

                                               = 1,527 ft³

Thus, The approximate volume of the greenhouse =  1,527 ft³

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The advantages of being a multinational corporation are mentioned below.

Multinational corporations (MNCs) have several advantages:

Expansion into new markets: MNCs can expand their operations into new markets around the world, which can increase their revenues and profits.

Access to cheaper labor: MNCs can take advantage of lower labor costs in different countries by setting up operations in those countries. This can help them reduce their overall production costs and increase their competitiveness.

Creation of a trade surplus: MNCs can create a trade surplus by exporting more than they import. This can benefit the economies of the countries where they operate by generating foreign exchange and creating jobs.

Lower tax payments: MNCs can reduce their tax payments by taking advantage of lower tax rates in different countries and by using tax havens.

Note that relying on unskilled workers is not necessarily an advantage of being an MNC, as it may not be the most efficient or effective way to operate. In fact, many MNCs rely on skilled workers in order to produce high-quality products and services.

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Below are some benefits of working for a multinational firm.

Multinational businesses (MNCs) benefit from a number of factors:

Expansion into new markets: MNCs can broaden their business activities into other geographies, which can boost their earnings.

Access to cheaper labor: By establishing operations there, MNCs can benefit from lower labor costs in other nations. They can become more competitive and lower their overall production costs as a result.

Making a trade surplus: By exporting more than they import, MNCs can make a trade surplus. Through the production of foreign exchange and the creation of jobs, this can help the economy of the nations where they are present.

Lower tax obligations: MNCs can lower their tax obligations by utilizing tax havens and nations with lower tax obligations.

The equation of a line in different forms are:

1. The slope-intercept form: y = mx + b.

2. The point-slope form: y - y₁ = m(x − x₁).

3. The standard form: ax + by = c.

There are three ways that an equation that represents a line can be written in, they are as follows:

1. The slope-intercept form: this is expressed as y = mx + b. In this form, we have the following values and what they each represent:

m = the slope of the line.

b = the y-intercept of the line,

x and y are the coordinates of a point on the line.

2. The point-slope form: this is expressed as y - y₁ = m(x − x₁). In this form, the variables represented are:

m = the slope of the line.

x₁ and y₁ are the coordinates of a point that the line passes through.

3. The standard form: this is expressed as ax + by = c. In this form, the variables a, b, and c are integers.

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x=1/2 and x=-4 are zeros of the polynomial 2x²+7x-4=0.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is 2x²+7x-4=0

To find the zero of 2x²+7x-4=0 we need to find the roots of polynomial.

2x²+7x-4=0

2x²+8x-x-4=0

Take 2x as common from first two terms

2x(x+4)-(x+4)=0

(2x-1)(x+4)=0

2x-1=0

2x=1

x=1/2 and x=-4 are zeros.

Hence, x=1/2 and x=-4 are zeros of the polynomial 2x²+7x-4=0.

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The yield of stock at yesterday's closing price is 3.43%.

Annual dividend is the profit of the stock which is divided among the shareholders, both common and preferred shareholders annually.

Given,

Annual dividend = $1.20

Today's closing price = $34.50

Net change = -$0.50

Let x be yesterday's closing price.

Net change = Today's closing price - yesterday's closing price

⇒ -0.50 = 34.50 - x

⇒ x = 34.50 + 0.50

⇒ x = 35

Yield = [tex]\frac{Annual dividend}{Price}[/tex] × 100

         = [tex]\frac{1.2}{35}[/tex] × 100

         = 3.4286 % ≈ 3.43 %

Hence the stock's yield at yesterday's closing price of preferred stock is 3.43 %.

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Answer:

B

Step-by-step explanation

Multiplying by 0.97 will decrease $200,000 to $194,000.

^c is x years after the purchase, so having (0.97)^c will make the $200,000 value decrease more and more.