Use the graph of f(x) to find the indicated function values.



If x = 0, then f(0) =
.



If f(x) = 0, then x =
.

Answer: 0.1875

Step-by-step explanation: ..

The measure of each interior angle of a decagon is 144 degrees.

1. A decagon is a 10 sided polygon.

2. The sum of the interior angles of any polygon with n sides is (n - 2) * 180 degrees.

3. For a decagon, n = 10, therefore the sum of the interior angles is (10 - 2) * 180 degrees = 8 * 180 degrees = 1440 degrees.

4. Therefore, the measure of each interior angle of a decagon is 1440 degrees / 10 = 144 degrees.

The measure of each interior angle of a decagon is 144 degrees.

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Yes, 0.5 - 3(-2x - 1 over 3 + 4 + 8x) and -1.5(12x + 7) are equivalent expressions.


To prove this, we can use the distributive property:

0.5 - 3(-2x - 1 over 3 + 4 + 8x)

= 0.5 - 3(-2x/3 - 1/3 + 4/3 + 8x/3)

= 0.5 - (-6x - 1 + 4 + 24x)/3

= (0.5*3 + 6x + 1 - 4 - 24x)/3

= (-1.5*12x - 1.5*7)/3

= -1.5(12x + 7)
No, 0.5 - 3(-2x -1 over 3 +4 + 8x) and -1.5(12x +7) are not equivalent expressions.

To determine if two expressions are equivalent, we can simplify both expressions and compare them.

For the first expression, 0.5 - 3(-2x -1 over 3 +4 + 8x), we can distribute the -3 and combine like terms:

0.5 - 3(-2x) - 3(-1) - 3(3) - 3(4) - 3(8x)
= 0.5 + 6x + 3 - 9 - 12 - 24x
= -18x - 7.5

For the second expression, -1.5(12x +7), we can distribute the -1.5:

-1.5(12x) - 1.5(7)
= -18x - 10.5

As we can see, the simplified expressions are not the same, so they are not equivalent expressions.

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The solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) [tex]e^{\frac{22t}{3} }[/tex] - (4/3) [tex]e^{\frac{-16t}{3} }[/tex]

y(t) = (-13/3) [tex]e^{\frac{22t}{3} }[/tex] + (2/3) [tex]e^{\frac{-16t}{3} }[/tex]

To solve the system of differential equations, we can use matrix exponential. The system can be written in matrix form as follows:

X' = AX, where X = [x y], A = [22 60; -6 -16]

The matrix exponential of A can be calculated as follows:

[tex]e^{(At)}[/tex] = I + At + [tex]\frac{(At)^{2}}{2!}[/tex] + [tex]\frac{(At)^{3}}{3!}[/tex] + ...

where I is the identity matrix and t is the variable of integration.

We can substitute A and t = 1 into the formula to get:

[tex]e^{A}[/tex]= I + A + [tex]\frac{(A)^{2}}{2!}[/tex] + [tex]\frac{(A)^{3}}{3!}[/tex]+ ...

= [1 0; 0 1] + [22 60; -6 -16] + [44 192; -36 -104]/2! + [ -256 -768; 96 272]/3! + ...

= [1 + 22 + [tex]\frac{44}{2!}[/tex] - [tex]\frac{256}{3!}[/tex]*60 + [tex]\frac{192}{2!}[/tex] - [tex]\frac{768}{3!}[/tex];

-6 + [tex]\frac{(-6)}{2!}[/tex] + [tex]\frac{96}{3!}[/tex] - 16 + [tex]\frac{(-104)}{2!}[/tex]+ [tex]\frac{272}{3!}[/tex]]

= [[tex]\frac{29}{3}[/tex] [tex]\frac{102}{3}[/tex];

[tex]\frac{-13}{3}[/tex]  [tex]\frac{-4}{3}[/tex] ]

Now we can use the initial conditions to find the constants of integration. We have:

X(0) = [x(0) y(0)] = [5 3]

So,

[[tex]e^{A}[/tex]] [[tex]c_{1}[/tex]] = [5]

[[tex]c_{2}[/tex]] [3]

Multiplying both sides by the inverse of [tex]e^{A}[/tex], we get:

[[tex]c_{1}[/tex]] = [29/3 102/3]^(-1) [5]

[[tex]c_{2}[/tex]] [-13/3 -4/3] [3]

Solving this system of linear equations, we get:

[tex]c_{1}[/tex] = -4/3

[tex]c_{2}[/tex] = 2/3

Therefore, the solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) [tex]e^{\frac{22t}{3} }[/tex] - (4/3) [tex]e^{\frac{-16t}{3} }[/tex]

y(t) = (-13/3) [tex]e^{\frac{22t}{3} }[/tex] + (2/3) [tex]e^{\frac{-16t}{3} }[/tex]

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Answer:

Answered By Unish ©

Verified Answer ✅

Step-by-step explanation:

Multiply the following rational expressions. Remember to fully simplify your answer.

(x^2-1)/(2x-3) ∙ (2x^2+x-6)/(x^2+3x+2)

First, let's factor the expressions in both numerators and denominators to simplify the multiplication:

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(x^2 - 1)/(2x - 3) = (x + 1)(x - 1)/(2x - 3)

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(2x^2 + x - 6)/(x^2 + 3x + 2) = (2x - 3)(x + 2)/(x + 1)(x + 2)

Notice that the factor (x + 2) appears in both the numerator and denominator of the second expression. We can cancel this factor and simplify the expression:

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(x^2 - 1)/(2x - 3) ∙ (2x^2 + x - 6)/(x^2 + 3x + 2)

= [(x + 1)(x - 1)/(2x - 3)] ∙ [(2x - 3)/(x + 1)]

= (x - 1)

Therefore, the simplified product of the two rational expressions is x - 1.

Answer: 34

Step-by-step explanation:

The result of multiplying the numbers 17 by 2 is 34.

When you multiply two numbers, you are essentially adding the first number to itself a certain number of times, determined by the second number.

In this case, when you multiply 17 by 2, you are adding 17 to itself two times:

17 + 17 = 34

Therefore, the result of multiplying 17 by 2 is 34.

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As per the conversion factor, 50 meters is equal to 54.6805 yards

Before we dive into the mathematical process of converting meters to yards, it is essential to understand the basic concept of these two units of distance. Meters and yards are both units of length used to measure distances, and they are both commonly used in different parts of the world.

Now, to convert 50 meters to yards, we need to know the conversion factor between meters and yards. A conversion factor is a mathematical relationship between two units of measurement. In this case, the conversion factor between meters and yards is 1 meter equals 1.09361 yards.

Using this conversion factor, we can easily convert 50 meters to yards. To do this, we simply multiply the distance in meters by the conversion factor. So,

50 meters x 1.09361 yards/meter = 54.6805 yards.

In conclusion, converting 50 meters to yards involves understanding the conversion factor between these two units of distance and using it to multiply the given distance in meters. With a little bit of practice, you can easily convert distances between meters and yards or any other units of measurement.

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The solution is, the cost of each ticket is $21.25.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

each of them bought a game ticket and a $16.50 team jersey.

together, they paid a total of $75.50.

now, we get,

total cost of jersey = 16.50 * 2

                               =33

so, total cost of ticket = 75.50 - 33

                                    =42.50

so, we get,

the cost of each ticket = 42.50 / 2

                                     =21.25

Hence, The solution is, the cost of each ticket is $21.25.

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A system of linear equations can have exactly one solution, infinitely many solutions, or no solutions. It cannot have exactly s solutions, where s is an integer strictly greater than 1.

To see why this is the case, let's consider a system of linear equations with m equations and n variables, where m ≤ n. We can represent the system as an augmented matrix A = [A|B], where A is the coefficient matrix of the system and B is the constant vector.

If the system has exactly one solution, then the rank of the coefficient matrix A is equal to the rank of the augmented matrix A = [A|B], which is n. This means that the number of pivots in the row echelon form of A is equal to n, and there are no free variables.

If the system has infinitely many solutions, then the rank of the coefficient matrix A is less than n, and there are one or more free variables. In this case, the number of solutions is not a fixed number, but rather a family of solutions that can be represented parametrically.

If the system has no solutions, then the rank of the coefficient matrix A is less than the rank of the augmented matrix A = [A|B], which is n + 1. In this case, there is a contradiction in the equations, and there is no solution.

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a) The economic order quantity is 300 units.

b) The annual holding costs are 3,750.

c) The annual ordering costs are 3,750.

d) The reorder point is 117 units.

To solve this problem, we can use the Economic Order Quantity (EOQ) model, which helps determine the optimal order quantity to minimize total inventory costs. The formula for EOQ is:

[tex]EOQ = \sqrt{((2DS/H)}[/tex]

where D is the annual demand, S is the setup cost per order, and H is the annual holding cost per unit.

a) Find the economic order quantity:

D = 15,000 units

S = 75 per order

H = 25 per unit per year

Substituting into the formula for EOQ:

[tex]EOQ = \sqrt{((2\times15000\times75)/25)} = \sqrt{90000} = 300 units[/tex]

Therefore, the economic order quantity is 300 units.

b) Find the annual holding costs:

To find the annual holding costs, we need to multiply the average inventory level by the holding cost per unit. Half of the EOQ can be used to compute the average inventory level.

Average inventory level = [tex]EOQ/2 = 300/2 = 150 units[/tex]

Annual holding costs = Average inventory level x Annual holding cost per unit

= [tex]150 \times25 = 3,750[/tex]

Therefore, the annual holding costs are 3,750.

c) Find the annual ordering costs:

To find the annual ordering costs, we need to divide the annual demand by the EOQ and then multiply by the setup cost per order:

Number of orders per year = Annual demand / EOQ =[tex]15,000 / 300 = 50[/tex] orders per year

Annual ordering costs = Number of orders per year x Setup cost per order

=[tex]50 \times75 = 3,750[/tex]

Therefore, the annual ordering costs are 3,750.

d) What is the reorder point?

The inventory level at which a new order ought to be placed is known as the reorder point. It is calculated as the lead time demand plus safety stock. The lead time demand is the demand during the lead time, which is 2 working days in this case. We can assume that the demand is evenly distributed over the 300 working days per year, so the lead time demand is:

Lead time demand = (Annual demand / 300) x Lead time = [tex](15,000 / 300) \times 2 = 100 units[/tex]

The safety stock is the buffer inventory kept to cover unexpected demand during the lead time. The safety stock depends on the desired service level and the variability of demand and lead time. Assuming a 95% service level and a normal distribution of demand and lead time, we can use the z-score corresponding to a 95% service level, which is 1.645. The standard deviation of demand during the lead time can be estimated as the square root of the lead time demand:

Standard deviation of demand during lead time = [tex]\sqrt{100}[/tex] = 10 units

The safety stock is then:

Safety stock = z-score x Standard deviation of demand during lead time

= [tex]1.645 \times 10 = 16.45[/tex] units (rounded up to 17 units)

Therefore, the reorder point is:

Reorder point = Lead time demand + Safety stock

= [tex]100 + 17 = 117[/tex]units

Therefore, the reorder point is 117 units.

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the perimeter of the equilateral triangle with a side length of 12√3 is 36√3 units.

In order to find the perimeter of the given triangle, we have to find the side of the triangle. The altitude of the triangle  = 18 inches. Let us assume the side of the triangle as a. The formula for calculating the altitude of an equilateral triangle is : Altitude  =√3/2×a  (side)

18 =√3/2 × a

a = 18 × 2√3

a = 36√3

a = 36 ×√3 / √3×√3

a =36√3/3

a = 12√3 inches.

If the side of an equilateral triangle is 12√3, then all three sides of the triangle are of equal length, since it is an equilateral triangle. Therefore, the perimeter of the triangle is simply the sum of the lengths of its three sides. Since each side of the triangle has a length of 12√3, the perimeter is: Perimeter = 3 x (12√3) = 36√3.

Therefore, the perimeter of the equilateral triangle with a side length of 12√3 is 36√3 units.

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a) It is a continuous random variable.

b) It is a discrete random variable.

c) It is not a random variable nor discrete.

d) It is a continuous random variable

e)  It is a discrete random variable

f) It is a discrete random variable

A continuous variable has an uncountable range of possible values.

Any value falling inside an interval is acceptable.

They cannot be stated as decimal numbers and can only accept a discrete value. Counting is used to obtain them rather than measuring.

a). The height of a randomly selected giraffe is a continuous random variable.

b). The random variable is discrete. You can count how many people are sitting at a computer.

c). The gender of college students ⇒ Gender is categorical data. It is neither continuous nor discrete.

d). The number of people in a restaurant that has a capacity of 300 is a continuous random variable

e). The number of bald eagles in a country Since the number of people cannot be expressed as decimals, thus it is a discrete random variable

f). it is a discrete random variable as a number of people is a discrete count, which takes values such as 0 or 1 or 2.

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x must be a whole number, the maximum whole number of gigabytes of data Piper can use while staying within her budget is 4.

What is the inequality?

An inequality is a mathematical statement that compares two expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

Let x be the number of whole gigabytes of data Piper can use while staying within her budget.

Her cost for data usage would be $5 per gigabyte, so her total cost would be:

Total Cost = $38.50 + $5x

The problem states that she wants to keep her bill under $60 per month, so we can set up an inequality:

$38.50 + $5x ≤ $60

Subtracting $38.50 from both sides, we get:

$5x ≤ $21.50

Dividing both sides by $5, we get:

x ≤ 4.3

Hence, x must be a whole number, the maximum whole number of gigabytes of data Piper can use while staying within her budget is 4.

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The correct option is (A) The ordinal level of measurement is most appropriate because the data can be ordered, but differences cannot be found or are meaningless.

The ordinal level of measurement is most commonly used when dealing with data that can be ordered, but the differences b/w the data points are not significant or cannot be determined. This type of data is commonly used when looking for ranking or grading data.

For example In customer satisfaction surveys, or when categories are assigned values, like when a student's performance in a class is assigned a letter grade. With the ordinal data, the values ​​are ordered in a meaningful way, but the differences between the values ​​are not necessarily significant.

For example, if you assign a letter grade to a student's performance, difference between an A and a B is not importantly difference among C and D. This type of data is useful for finding a quick and easy way to compare data points, but this gives no information about the actual differences between the data points.

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The value of the expressions are not equal

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

p = -3²

q = ( -3 )²

On simplifying the equations , we get

The value of p = -9

The value of q = 9

So , the value of p and q are not equal

Hence , the equations are not equal

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One U.S. ounce (oz) is equal to 0.0296 litre. Simply multiply any number of oz with the given value of litre to convert and find volume.

Using a volumetric unit of measurement, the three-dimensional extent of an object or space can be determined. Volume is used to determine capacity. The volumetric unit is therefore essentially a unit for measuring the size or extent of an object or space.

The unit is typically used to describe the volume of goods or liquids. Use the International System of Units to calculate a quantity of something. The SI Units are used globally to communicate the measurements used in research settings despite the fact that people speak various languages.

For measuring volume, the three most widely used SI units are cubic meters, liters, and milliliters. specifically, the SI system's cubic meter as the unit of volume.

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Answer:

p = 29 and q = -3.

Step-by-step explanation:

Using long division, the remainder when we divide by x − 1 is p+q−16.  The remainder when we divide by x + 1 is p−q−20.

Answer:

sum of all side of Pentagon= 540

10x+6x+4x+3x+x=540

According to question

The correct inequality written in factored form represents the graphed region is,

⇒ y ≥ (x + 6) (x - 18)

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The graph shows the inequality.

And, The point on the graph is, (- 4, - 44)

Now, By all options;

The correct inequality is satisfy the given point on the graph.

From (i);

The inequality is,

⇒ y ≥ (x + 6) (x - 18)

Put x = - 4, y = - 44

⇒ - 44 ≥ (- 4 + 6) (- 4 - 18)

⇒ - 44 ≥ (2) (- 22)

⇒ - 44 ≥ - 44

Hence, It is the correct inequality written in factored form represents the graphed region.

Thus, The correct inequality written in factored form represents the graphed region is,

⇒ y ≥ (x + 6) (x - 18)

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Answer:

A

Step-by-step explanation:

(f - g )(x)

= f(x) - g(x)

= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1

= 3x + 2 - 2x + 2 ← collect like terms

= x + 4

The value of the function (f-g)(x) is x+4.

A function in math is a rule or expression that defines a relationship between one variable (the input or independent variable) and another variable (the output or dependent variable).

Given are two functions, f(x) = 3x+2 and g(x) = 2x-2, we need to find the value of (f-g)(x)

So,

(f-g)(x) = f(x) - g(x)

= 3x+2 - (2x-2)

= x+4

Hence, the value of the function (f-g)(x) is x+4.

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The numbers on the mailboxes could be considered either categorical or quantitative data. The correct Option is C: Either categorical or quantitative data.

The numbers on the mailboxes can be considered either categorical or quantitative data, depending on the context in which they are being used.

If the numbers are simply labels for the mailboxes, with no inherent numerical value or order, then they can be considered categorical data. In this case, the numbers would be treated as labels for the different categories or groups, rather than as measurements with numerical significance.

On the other hand, if the numbers are being used to represent a quantity or a position in a sequence, then they can be considered quantitative data. For example, if the numbers represent the physical location of the mailbox within a building, or the order in which mail is sorted and delivered, then they can be treated as numerical measurements.

Therefore, without further context, the numbers on the mailboxes could be considered either categorical or quantitative data.

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Answer and Step-by-step explanation:

120 kg is approximately 264.55 lbs (pounds).

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.

The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.

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It is wrong to say that the probability of getting two red cards is the same as the probability of getting one red card because the two events are not independent.

The probability of getting a red card on the first draw is 26/52 or 1/2. However, the probability of getting a red card on the second draw depends on what card was drawn first. If a red card was drawn first, there are now only 25 red cards left in the deck and the probability of getting a red card on the second draw is 25/51. If a black card was drawn first, there are still 26 red cards left in the deck and the probability of getting a red card on the second draw is 26/51. Therefore, it is wrong to say that the probability of getting two red cards is the same as the probability of getting one red card.

The correct way to calculate the probability of getting two red cards is to multiply the probability of getting a red card on the first draw by the probability of getting a red card on the second draw given that a red card was drawn first. This gives us:

P(two red cards) = P(red card on first draw) * P(red card on second draw | red card on first draw)

= (26/52) * (25/51)

= (1/2) * (25/51)

= 25/102

So the probability of getting two red cards is 25/102 or approximately 0.2451.

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Answer: 9 laps in 1 day = 18 laps in 2 days

Step-by-step explanation:

To complete the proportion, we can use the fact that the number of laps is directly proportional to the number of days:

9 laps in 1 day = 18 laps in x days

To solve for x, we can use the property of proportions that the product of the means equals the product of the extremes:

9 laps × x days = 1 day × 18 laps

Simplifying, we get:

9x = 18

Dividing both sides by 9, we get:

x = 2

Therefore, the missing number to complete the proportion is 2. The complete proportion is:

9 laps in 1 day = 18 laps in 2 days

Answer: 2 days

Step-by-step explanation: 9 + 2 equals 18 therefor 18 laps in 2 days

Answer:

Hi! This question tells us that the book costs $18 and that it costs 3 times more than a DVD. In order to determine the cost of the DVD, all we have to do is divide 18 by 3. 18 divided by 3 is 6. Therefore, the DVD costs $6.

Hope this helps!

Answer:$6

Step-by-step explanation: 18÷3=6

The converted value of the currency 350 euros to dollars is equal to 374.1493 dollars.

The value of One Euro in dollars in todays time is equal to:

1 Euro = 1.068998 U.S. dollars

Now substitute the required converted Euro value we get ,

⇒ 350 Euros = ( 350 ×  1.068998 ) dollars

⇒ 350 Euros = ( 374.1493 ) dollars

Therefore, the value of the currency after conversion 350 euros to dollars is equal to 374.1493  dollars.

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The key feature that is NOT present in the function h(x) is "The x-intercept of h(x) is (5, 0)".

To find the x-intercept of a function, we need to set the y-value to 0 and solve for x. In the case of h(x), we have two different equations for different ranges of x:

h(x) = (x - 5)² when 0 ≤ x ≤ 4

h(x) = -log₄(x + 6) when x > 4

Setting the first equation to 0 and solving for x, we get:

0 = (x - 5)²

0 = x - 5

x = 5

However, this value of x does not fall within the range of 0 ≤ x ≤ 4, so it is not a valid x-intercept for this equation.

Setting the second equation to 0 and solving for x, we get:

0 = -log₄(x + 6)

log₄(x + 6) = 0

4⁰ = x + 6

1 = x + 6

x = -5

This value of x also does not fall within the range of x > 4, so it is not a valid x-intercept for this equation either.

Therefore, the function h(x) does not have an x-intercept of (5, 0), and this is the key feature that is NOT present in the function.

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