What is the range of the function on the graph

The expression that gives the closest estimate of 327+171 is  325+175.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Here, we have

Given: 327+171

We have to find the closest estimate of the given expression.

We concluded that the closest estimate of the given expression is 325+175.

327 is close to 325.

175 is close to 325.

Hence, The expression that gives the closest estimate of 327+171 is  325+175.

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Answer:

x² - 8x

Step-by-step explanation:

The least degree polynomial with two roots has to be a quadratic polynomial.

Since the roots are 0 and 8, the factors are, (x - 0)(x - 8) = x² - 8x

Cheers

Answer:

The polynomial of least degree with roots 0 and 8 is x(x-8)=0. This can be written in standard form as x2 - 8x = 0.

Answer:

33 15/16

Step-by-step explanation:

Answer: 185 yards

Divide it by 3 to convert to yards

Here 30% is an example of descriptive statistics.

Brief informative coefficients known as descriptive statistics are used, to sum up, a particular data set, which may be a sample of a population or a representation of the complete population. Measurements of central tendency and measures of variability make up descriptive statistics (spread).

The mean, median, and mode are measurements of central tendency, while the standard deviation, variance, minimum and maximum variables, kurtosis, and skewness are measures of variability. While inferential statistics assist the user in testing a hypothesis or evaluating, descriptive statistics aid in the summary of a data set's properties.

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The mean of the sampling distribution of the sample mean for samples of size 16 is 3.2 V16, which is equal to the population mean of 3.2 divided by the square root of 16 (V16). This represents the expected mean of the sample mean when samples of 16 are taken from the population.

Step 1: Calculate the population mean (μ):

μ = 3.2 pets per student

Step 2: Calculate the standard deviation of the population (σ):

σ = 1.7 pets per student

Step 3: Calculate the sample size (n):

n = 16 students

Step 4: Calculate the mean of the sampling distribution (μx):

μx = μ / √n

μx = 3.2 / √16

μx = 3.2 / 4

μx = 0.8

Therefore, the mean of the sampling distribution of the sample mean for samples of size 16 is 0.8.The mean of the sampling distribution of the sample mean for samples of size 16 is 3.2 V16. This is calculated by dividing the population mean (3.2 pets per student) by the square root of the sample size (16). The square root of 16 is 4, which gives us a final result of 0.8. This means that the expected mean of the sample mean when samples of 16 are taken from the population is 0.8. This is a useful measure for understanding the variability of the sample mean, as it indicates how much the sample mean is likely to vary from the population mean.

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After using proportion the enlarged photo length is C)15 inches.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here According to the question before enlargement the width is 4 inches and length is 6 inches. Taking proportion between before and after enlargement of the measurements then,

=> [tex]\frac{ width}{length}[/tex]

=> [tex]\frac{4}{6}=\frac{10}{x}[/tex]

=> x = [tex]\frac{10\times 6}{4}[/tex]

=> x = 5 × 3 = 15

Hence after enlargement the photo length is 15 inches.

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The system is a consistent system with an infinite solutions.

There are two types of system of equations - consistent and inconsistent.

Inconsistent means that it has no solution , i.e. the solution does not exist.

Consistent system means a solution of the equation exists.

Further, this is of type , a consistent system may have a unique solution or an infinite number of solutions where we need to assign an arbitrary value to a free variable.

For e.g. let us consider the system -

x + y+ z = 0

2x + 3y + 4z = 1

Since , (0,0,0) is a solution to this system , we can't say its an inconsistent system .

Also, for a system to be consistent , either a unique solution exists or an infinite solutions exist. There is no particular number of solutions.

Also, we see that (-1,1,0) is also a solution other than the zero solution.

So, such a system is a consistent system with infinite solutions.

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318/38=9.

What are compatible numbers?

The term "compatible numbers" refers to those that are simple or complimentary. It indicates that the numbers are compatible if they are simple to add, subtract, multiply, or divide. It is also simpler to estimate the answer and solve difficulties because these numbers are near to the real numbers in value.

Step by step explaination:

318/38=8.3

to round of 8.3 to 9

The equation to the compatible number 318/38 is 9

(318/38=9).

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Due of the greater legroom, the exit row seats are reserved for the airline's most valuable passengers.

A United Airlines representative told Travel + Leisure that although the end row used to be standardized by skipping row 33 on some maps, it is no longer the case. A mathematical formula, in essence, underlies the justification for having a consensus seating chart.

Airlines frequently omit certain row numbers in order to accommodate more passengers because airplanes are intended to carry the maximum number of passengers possible.

Due of the greater legroom, the exit row seats are reserved for the airline's most valuable passengers.

The complete question is,

How come airlines don't use Row 9?

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Answer: The sample formed by the people who are recounted in the U.S. Census Bureau's accuracy check is a random sample. This is because the census districts are selected in a random manner, with each district having an equal chance of being selected. Random sampling is a method of selecting a sample from a larger population in which each member of the population has an equal chance of being selected. This ensures that the sample is representative of the population as a whole and allows for the estimation of population characteristics with a known degree of precision.

Step-by-step explanation:

The linear inequality that models this scenario is 3x + 5y ≤ 480

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Inequalities are used to show that an expression containing numbers and variables are not equal.

Let x represent the number of 15 inch laptops and y represent the number of 17 inch laptops.

It takes 3 hours to manufacture a 15 inch laptop and 5 hours to manufacture a 17 inch laptop.

The company has 480 hours T of manufacturing time available, hence:

3x + 5y ≤ 480

The linear inequality is 3x + 5y ≤ 480

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The answer of 10 more than 90 is 100.

The answer of 10 more than 90 is 100 which can be derived using simple mathematical calculations.

To find 5 more than 5, you can add 5 to the original number 5.

10 + 90 = 100

It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 10 more than 90 is 100.

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Answer: 2x-5

Step-by-step explanation: twice=2  the lenght=x We don't know the length, and  decreased= subtract sign  

2x-5

We can easily equalize the arguments in an equation if it has a logarithm with the same base on both sides.

Step 1: Isolate a base-identical logarithmic expression on both sides of the problem using the exponentiation rules.

Step 2: Equip the arguments with one another.

Step 3. Finally, resolve the resulting equation.

Step 4: Verify your conclusions.

The logarithm of a number is the power of 10 that must be increased in order to equal that number. Simple examples include:

[tex]10^2[/tex] = 100 , therefore log100 = 2

[tex]10^3[/tex] = 1000, therefore log1000 = 3

log200 = 2.301 (between log100 and log1000)

Mathematicians discover that the following statements are constant:

log(a×b) = loga + logb

log(ab) = loga - logb

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A function is a mathematical relation between two sets of values that assigns a unique output to each given input.

What is a function?

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

I) f(x)- 2G(x) = 5x³-8x²+18x-13

II) 2f(x)+3G(x) = 31x³+26x²-34x+30

III) 1/2f(x)+ G(x)​ = 17/2x³+8x²-12x19/2

Here, we have

f(x)= 11x³+4x²-2x+3, G(x)= 3x³+6x²-10x+8

We have to find  I) f(x)- 2G(x), ii) 2f(x)+3G(x), iii) 1/2f(x)+ G(x)​

I) f(x)- 2G(x) = 11x³+4x²-2x+3 -2(3x³+6x²-10x+8 )

= 11x³+4x²-2x+3 - 6x³-12x²+20x-16

= 5x³-8x²+18x-13

Hence, the value of f(x)- 2G(x) is 5x³-8x²+18x-13.

II) 2f(x)+3G(x) = 2(11x³+4x²-2x+3)+3(3x³+6x²-10x+8 )

= 22x³+8x²-4x+6+9x³+18x²-30x+24

= 31x³+26x²-34x+30

Hence, the value of 2f(x)+3G(x) is 31x³+26x²-34x+30.

III)  1/2f(x)+ G(x)​ = 1/2(11x³+4x²-2x+3) + (3x³+6x²-10x+8)

= 11/2x³+2x²-2x+3/2+3x³+6x²-10x+8

= 17/2x³+8x²-12x19/2

Hence, the value of 1/2f(x)+ G(x)​ is 17/2x³+8x²-12x19/2.

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The probability that the fair die must be cast more than 5 times is 0.4315 or 43.15%.

The probability that it must be cast more than five times is the complement of the probability that it will be cast five or less times.

The probability of getting a 6 on the first roll is 1/6, the probability of not getting a 6 on the first roll is 5/6. The probability of getting a 6 on the second roll, given that it was not obtained on the first roll, is 1/6. The probability of getting a 6 on the third roll, given that it was not obtained on the first and second rolls is 1/6 and so on.

The probability of not getting a 6 in five rolls is (5/6)⁵. The probability of getting a 6 on the fifth roll is 1/6. The probability of getting a 6 on the fifth roll or not getting it on the first five rolls is (5/6)⁵ + 1/6.

So the probability of getting a 6 in five rolls or less is (5/6)⁵ + 1/6.

Therefore, the probability of getting a 6 in more than five rolls is 1 - ((5/6)⁵ + 1/6) = 0.4315

So the probability of having to cast the die more than five times to get a 6 is 0.4315 or 43.15%.

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Answer: C. -2/3

Step-by-step explanation:

The log value of 7 base 10 is approximately 0.8451.

What is logarithm ?

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.

The logarithm of a number is the power to which a certain base (in this case we can consider it as base 10) must be raised to produce that number.

The log value of 7 base 10 is approximately 0.8451.

You can calculate it using log10(7) in most of the calculators or programming languages and get the same result.

The log value of 7 base 10 is approximately 0.8451.

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Answer: The absolute value of the difference

Step-by-step explanation:

Hope this helps

The car with the better mileage is the hybrid car.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

Compact car:

288 miles with 9 gallons of gas.

This means,

y = 32x

Where y is the distance traveled with x gallons

The distance traveled per gallon.

= 288/9

= 32 miles

Hybrid car:

y = 42x represents the distance traveled with x gallons.

Where y is the distance traveled with x gallons

The distance traveled per gallon.

y = 42 x 1 = 42 miles

Thus,

The hybrid car gets better mileage.

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The complete question is:

A new compact car can travel 288 miles on nine gallons of gas. The distance driven in miles y varies directly with the number of gallons of gas x. This situation can be represented by the equation y= 32x.

The distance y traveled by a hybrid car using x gallons of gas can be represented by y = 42x. Which car gets better gas mileage? Explain.

Answer:

where the probleme to help

Answer:

71.11 km/h

Step-by-step explanation:

D = S/T

D = distance

S = Speed

T = Time

The motorist is going 80km/h and takes 4.5 hours to reach his destination.

80/4.5 = 17.77km

The motorist travels 17.77km

Now find how fast he'll have to go to reach 17.77km in 4 hours.

17.77 * 4 = [71.11 km/h]

Answer:

f(x) = x² - 4x - 5

Step-by-step explanation:

given the roots of a parabola x = a and x = b , then the factors are

(x - a) and (x - b)

the function is then the product of the roots , that is

f(x) = (x - a)(x - b)

from the graph the roots ( where graph crosses the x- axis ) are

x = - 1 and x = 5 , then corresponding factors are

(x - (- 1) ) and (x - 5) , that is (x + 1) and (x - 5) , then

f(x) = (x + 1)(x - 5) ← expand using FOIL

     = x² - 5x + x - 5

f(x) = x² - 4x - 5

The domain of the function represented by the graph include the following: D. x ≥ -7.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = x ≥ -7 or [-7, ∞].

Range = y ≥ 0 or [0, ∞].

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The four properties of equality are alike as all the expression on LHS is equal to all the expression on RHS, x = y.

What are Properties of Equality?

The relationship between two equal quantities is described by the property of equality, and if an operation is used on one side of the equation, it must also be used on the other side to keep the equation balanced.

There are four properties of equality -

Addition Property of Equality

Example - x - 3 = 8

⇒ x - 3 + 3 = 8 + 3

⇒ x = 8 + 3

⇒ x = 11

Subtraction Property of Equality

Example - x + 4 = 7

⇒ x + 4 - 4 = 7 - 4

⇒ x = 7 - 4

⇒ x = 3

Multiplication Property of Equality

Example - x/4 = 6

⇒ (x/4) × 4 = 6 × 4

⇒ x=24

Division Property of Equality

Example - 3x = 6

⇒ (3x/3) = 6/3

⇒ x=2

They are alike as they need to keep the equations balanced.

The left-hand side of the equation and the right-hand side of the equation is always equal in all the properties of the equality.

Therefore, the properties of equality are alike.

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The new temperature of a gas will be 324.38k .

The Ideal Gas Equation defines the four gas variables and one constant for a better understanding. The four gas variables are pressure (P), volume (V), number of moles of gas (n), and temperature (T). Lastly, the constant in the equation shown below is R, known as the gas constant.

PV=RT

at constant pressure

    V∝T

   [tex]\frac{V_{1} }{V_{2} } = \frac{T_{1} }{T_{2} }[/tex]

According to the question,

[tex]V_{1} = 7.3 litres[/tex] , [tex]V_{2} = 7.4 litres, T_{1} = 320k[/tex]

⇒ [tex]\frac{7.3}{7.4} = \frac{320}{T_{2} }[/tex]     (substitute the values)

⇒ [tex]T_{2} =\frac{320 * 7.4}{7.3}[/tex]

⇒ [tex]T_{2} =324.38[/tex]

Hence, the new temperature will be 324.38k.

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So, our estimate for the number of students at the school who would say they play a sport or game outdoors 4 hours per week is 160 students.

In order to estimate the number of students at the school who would say they play a sport or game outdoors 4 hours per week, we can use the sample data provided and make an assumption about the larger population.

First, we can see from the table that 4 students out of the 25 surveyed, or 16%, reported playing a sport or game outdoors for 4 hours per week.

If we assume that this sample is representative of the larger population of 1000 students at the school, we can use this percentage to estimate the number of students who would report playing a sport or game outdoors for 4 hours per week.

To do this, we can multiply the total number of students at the school (1000) by the percentage of students in the sample who reported playing a sport or game outdoors for 4 hours per week (0.16).

1000 x 0.16 = 160

So, our estimate for the number of students at the school who would say they play a sport or game outdoors 4 hours per week is 160 students.

Keep in mind that this is an estimation based on a sample and there could be some degree of error. To reduce the error, it's better to survey a larger sample.

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The Round-off of 15 nearest to the 10th is 20. This process is called rounding off the numbers.

The process is used to simplify the numbers so that the number can easily be calculated, this is called round-off. The Round-off process can take place to the nearest 10, 100,1000, and so on.

In round-off, the numbers 0,1,2,3,4 are considered as nearest to the "0" and the numbers 5,6,7,8,9,10 are considered as nearest to the "10". Just like that, 15 is considered as nearest to the "20".

It can also be used for numbers as well as decimal numbers so that we can write the decimal number in simplified form.

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