Write an equation involving absolute value for the following graph:

Answer:

The total number of pencils is 76 x 3 = 228 pencils

If each teacher receives an equal amount of pencils, we can divide the total number of pencils by the number of teachers to find how many pencils each teacher receives:

228 pencils / 4 teachers = 57 pencils/teacher

Each teacher receives 57 pencils.

If Sarah has a 20% discount, her total cost after the discount in dollars and cents be 31.40.

Therefore the answer is $31.40

Sarah has a 20% discount, so the percentage of the cost she needs to pay is

100 - 20 = 80%.

To calculate the total cost after the discount, we need to multiply the original total cost by the percentage of the cost Sarah needs to pay:

= $39.25 x 0.8

= $31.40

So, after the discount, Sarah would pay $31.40 before tax.

To round it to the nearest cent we have $31.40 so the answer is 31.40

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By solving a linear equation we will see that there are 20 games left.

We know that there is a total of 100 games, and the ratio of wins to loses for the rockets is:

3:2

The ratio for the rangers is:

7:13

We know that if the rockets loses all the remaining games, and the rangers win all the remaining games then both teams will win the same number of games.

Let's define X as the number of games left, the number of games won by the rockets is:

(100 - X)*(3/5)

The number of games won by the rangers is:

(100 - X)*(7/20)

We know that if the rangers win the X games left, they will have the same number of wins than the rockets (if the rockets don't win any more game)

Then we can write the linear equation:

(100 - X)*(7/20) + X = (100 - X)*(3/5)

we can solve this for X.

X = (100 - X)*(3/5) - (100 - X)*(7/20)

X = (100 - X)*(3/5 - 7/20)

X = (100 - X)*(12/20 - 7/20)

X = (100 - X)*(5/20)

(20/5)*X = 100 - X

4*X = 100 - X

4*X + X = 100

5*X = 100

X = 100/5

X = 20

There are 20 games left for the rockets.

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Answer:Volume of Pipe Formula. The pipe volume formula is: Volume = pi x radius² x length. To do piping size calculation, follow these steps: Find the inner diameter and length of the pipe, in inches or millimeters. Calculate the inner diameter of the pipe by measuring

Step-by-step explanation:

On solving the provided question, we can say that the value of the expression will be as - [tex]1/ ( 36a^4b^{10} )[/tex]

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

here,

the expression is -

[ [tex][( 2a{-3}b^4)^2 / (3a^5b){-2}]^{-1}[/tex] ]

[tex][( 1 /2a{-3}b^4)^2 (3a^5b){2}]^{-1}[/tex]

[tex]1/ ( 36a^4b^{10} )[/tex]

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The solution of the given equation is x = -3,3. Hence option C is the correct option.

What is a quadratic equation?

A quadratic equation is any equation in algebra that can be rearranged in a standard form where x represents an unknown value and a, b, and c represent known numbers, with a ≠ 0.

The number of solutions of a quadratic equation is 2. The degree of a quadratic equation is also 2.

Given equation is

25x² +64 = 289

Subtract 64 from both sides of the equation:

25x² +64 -64 = 289 -64

25x² = 225

Divide both sides by 25:

25x²/25 = 225/25

x² = 9

Take square root on both sides:

√x² = √9

x = ±3.

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Tomas drove the fastest with the speed of 70 miles per hour.

What is speed?

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

The formula for calculating speed is -

Speed = Distance / Time

Maren travels 60 miles in 1 hour.

Speed of Maren = 60/1

Speed of Maren = 60 miles per hour

Safiya travels 120 miles in 3 hour.

Speed of Safiya = 120/3

Speed of Safiya = 40 miles per hour

Tomas travels 84 miles in 1.2 hour.

Speed of Tomas = 84/1.2

Speed of Tomas = 70 miles per hour

Cam travels 75 miles in 1.5 hour.

Speed of Cam = 75/1.5

Speed of Cam = 50 miles per hour

Therefore, the fastest driver is Tomas.

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The answer is CalcETS 1.1.058.

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The difference between the 51st term of a and the 51st term of b is 1000.

the nth term of an arithmetic series is given by [tex]a_{n}= a_{0}+(n-1)*d[/tex]

where [tex]a_{0}[/tex] is the first term of the arithmetic series, [tex]a_{n}[/tex] is the nth term of the series and d is the common difference

Given that,

[tex]a_{0}=b_{0}=30[/tex]

Common difference of both series that have absolute value = 10

common difference of series a is 10 as this series is increasing

similarly, the common difference of series b is -10 as it is decreasing

Putting the values in the above equation we get:

[tex]a_{51}= a_{0}+(n-1)*d\\[/tex]

=> 30 + (51-1)*10

=> 30 + 500 = 530

Thus, the value of [tex]a_{51}[/tex] is 530.

[tex]b_{51}= b_{0}+(n-1)*d\\[/tex]

=> 30 + (51-1)*-10

=> 30 -500 = -470

Thus, the value of [tex]b_{51}[/tex] is -470.

so we have to find the value of [tex]a_{51}-b_{51}[/tex] which is 530 - (-470) =530 +470 =1000

Therefore, The difference between the 51st term of a and the 51st term of b is 1000.

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The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne in the simplest form, will be 4:3

The ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 28:21.

To simplify this ratio, we can divide both numbers by their greatest common factor (GCF). The GCF of 28 and 21 is 7.

So, the simplified ratio is 28/7: 21/7 = 4:3

So the ratio of the number of tickets sold by Jake to the number of tickets sold by Jeanne is 4:3 in simplest form.

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As per the remainder that the greatest possible value of 17

The term remainder in math defined as if a number is not completely divisible by another number  then we are left with a value once the division is done

Here we have if x is a positive integer, then r is the remainder when x is divided by 4 and r is the remainder when x is divided by 9.

As we all know that the remainder is always smaller than the divisor.

Here we have also know that it will be 0 if the dividend is evenly divisible or a positive integer less than the divisor.

So, when we divided by 4 then the largest remainder will be 3 and then here we have to  divided by 9, then the largest remainder will be written as

=> r² + R = 32 + 8

=> 9 + 8 = 17

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An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives is[tex]-1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\[/tex].

The terms antiderivative and primal are additional terms for integral. Something that is essential is crucial or required. If you are an essential member of the team, it signifies that you are necessary for the team to work. To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context.

The set of functions (the antiderivative) whose derivative is the integrand is represented by the integral, which is referred to as an indefinite integral. Calculus' fundamental theorem connects the assessment of definite integrals to that of indefinite integrals.

From 1 to 3:

[tex]sqrt(x^2+9)=t+x\\x=(9-t^2)/(2*t)\\anddx=-(t^2+9)/(2t^2)dt\\= 1/2int (t^2+9)^2/t^3dt\\= -1/2int (t+18/t+81/t^3)dt\\= -1/2*(t^2/2+18ln(t)-81/(2t^2))+C\\[/tex]

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Therefore , selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.

Calculating the probability of an event happening or a declaration being true is the focus of the mathematical field of probability theory. A chance is just a number between 0 and 1, with 1 denoting certainty and 0 roughly indicating the likelihood of an event occurring. Probability is a mathematical expression of the likelihood or probability that because an event will take place. The percentage ranges of 0% to 100% as well as the numerals 0 and 1 can be used to describe probabilities. the percentage of times an event occurs in a perfect collection of equally likely alternatives, out of all possible outcomes.

Here,

Given The likelihood of selecting a paperback book at random from either a bookshelf is 2/5, as stated.

In order to determine whether picking a paperback book is more likely to be strange,

So, using the information provided, we observe it.

that the odd favor of picking a paperback book is 2:1.

Option D is the proper choice.

Since selecting a paperback book has an odd favor of 2:5, this probability problem's solution indicates that.

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Answer:

2:3

Step-by-step explanation:

1. There is a correlation that exists between the average number of hours of internet browsing and the average score on the math test.

2. The function that best fits the data is: Y = f(X)

3. The slope and the intercept tells us that a student would be at their best in a test if they spent 0 hours browsing.

1. The correlation that exists in this data set tells us that as a person spends more time on the computer, they would spend less time on their test preparation. This would eventually affect their score.

When the student did not browse the internet, they had their highest score in math. As they started to spend more time on the internet, the score started to drop.

2. The function is given as

math test score Y = function of X: hours spent browsing the internet

this is written mathematically as:

Y = f(X)

3. The Y intercept is at the point where the student spent 0 hours browsing. this is the point where they did their best in this test. This tells us that if a student spent 0 hours on the internet, they would do their best in the test.

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The slope-intercept form of the given equation is y = -3/5x - 5

From the question, we are to write the given equation in the slope-intercept form

From the given information,

The given equation is

3x + 5y = -25  

The general form for the slope-intercept form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

Writing the equation in the slope-intercept form of a line

3x + 5y = -25

5y = -3x - 25

Divide through by 5

5y/5 = -3/5x - 25/5  

y = -3/5x - 5

The equation is y = -3/5x - 5

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The length of the side overline(FH) when Triangle FGH is formed by connecting the midpoints of the side of triangle CDE is 5.

This problem can be solved using the Median Line theorem. The Median Theorem states that the medians of a triangle intersect at a point called the centroid which is two-thirds of the distance from the vertices to the midpoint of the opposite sides. This is what we will use to solve the given problem.

From the problem, we can conclude that points H and F are the midpoints of the sides CE and CD respectively. Hence, line HF is the median line of the triangle CDE. So, the length of the line HF/FH is going to be -

= (1/2)*ED

= 5

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Answer:

To the nearest tenth of an inch, the length of the arc is 54.0 inches

Step-by-step explanation:

To determine the length of the arc, x, we need to use the formula for arc length, which is:

arc length = radius * angle (in radians)

Therefore,

arc length = 30 inches * 1.8 radians = 54 inches

The first statement is correct. The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31.62% and 52.38%. However, the rest of the statements are incorrect.

"There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between 31.62% and 52.38%." is incorrect, this statement is about a probability of a single student, but the confidence interval is about a probability of the whole population.

"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238)." is correct, this statement is true, but it doesn't add any additional information.

"The 99% confidence interval is (0.4762, 0.6838)." is incorrect, this value is not the correct confidence interval.

"We are 99% confident that the true proportion of students attending the Winter Formal is between 47.62% and 68.38%." is incorrect, this statement is not true, as the confidence interval is not (0.4762, 0.6838) but (0.3162, 0.5238)

"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838)." is incorrect, as this is not the correct confidence interval.

In conclusion, the faculty members at McAdenville High School can be 99% confident that the true proportion of students who will attend the Winter Formal is between 31.62% and 52.38%.

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The eight interior angle based on the information given will be 728°.

From the information, the sizes of seven of the exterior angles of an octagon are 42˚, 110˚, 13˚, 67˚, 55˚, 11˚ and 53˚ and.we.wany to eork out the size of each of the eight interior angles

In this case, it should be noted the octagon has with sides. This will be Illustrated as:

= (n - 2) × 180

= (8 - 2) × 180

= 1080

The eight interior angle will be:

= 1080 - (42 + 110 + 13 + 67 + 55 + 11 + 54)

= 1080 - 352

= 728

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The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.

A line's slope or gradient is a number that defines both its direction and its steepness. The slope may be calculated using the following formula: slope = (y2-y1)/ (x2-x1). The coordinate points on the equation of line g(x) are (0, 2), (5, 4) and (10, 6) while the coordinate points on the equation of line f(x) are (3, 1) and (0, -1).

The slope of the line g(x) is now (4-2)/(5-0) =2/5.

The slope of a line f(x) is (-1)/. (0-3)

=2/3

The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.

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Correct option is: b

The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.

This can e solved using the concept of null-hypothesis.

Using a single observable variable to compare two sets of observed data and measurable phenomena, the null hypothesis is a common statistical theory that contends that no statistical link and significance exists.

A hypothesis that a link of some sort exists between the variables is where scientists start their inquiry. The alternative, known as the null hypothesis, claims that there isn't any such link. Despite its uninteresting appearance, null hypothesis is a crucial component of research.

The correct hypotheses to test the owner's claim is as follows:

H0: pExpress  - pCoffee = 0

Ha: pExpress - pCoffee < 0

Since p-value = 0.0330 < 0.05, we reject the null hypothesis.

Thus, the correct option for this hypothesis test is:

The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.

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Since 0.033 < 0.05, the owner should reject the null hypothesis. The genuine percentage of customers who drink espresso and bring their own cups is clearly lower than the true percentage of customers who drink coffee and bring their own cups.

The null hypothesis is a widely used statistical theory that asserts that no statistical relationship and significance exists when two sets of observed data and measurably occurring occurrences are compared.

Scientists begin their investigation with the presumption that there is some form of relationship between the factors. The alternative, often known as the null hypothesis, contends that such a connection doesn't exist. The null hypothesis, although appearing dull, is an essential part of the research.

The following are the proper assumptions to test the owner's assertion:

H0: pExpress  - pCoffee = 0

Ha: pExpress - pCoffee < 0

Since p-value = 0.0330 < 0.05, we reject the null hypothesis.

Thus, the correct option for this hypothesis test is:

Since 0.033 < 0.05, the owner should reject the null hypothesis. There is strong proof that the actual percentage of consumers who order an espresso and bring their own cups is far lower than the actual percentage of customers who order coffee and bring their own cups.

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The quantity of units that the company needs to sell in order for the net income to equal $0 would be = 8.

The net income of the company in thousands of dollars is represented with the function;

f(x) = 9x2 – 54x – 144,

It can be simplified as follows:

f(x) = 9(x² - 6x - 16)

Then:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0, hence:

x + 2 = 0 -> x = -2.

x - 8 = 0 -> x = 8.

The positive value and not a negative shows that there are amount of products sold which should be = 8.

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A polynomials is a mathematical statement made up of real number coefficients and a sum of power in one or so more parameters (indeterminates) having non-negative integer exponents.

SOLUTION:

Three terms with non-negative integers exponents (x2, x1) make up Option "polynomial, "'s which has real numbers (x3, -2x3, and 3) as coefficients.

Option "c" x+1/x is a rational function; it is not a polynomials because of the fraction in it. It consist of one polynomials divided by another polynomial. 1/x

Option "d" is a polynomial that has real numbers (5, -3, and 2) as coefficients and terms with non-negative integers exponents (x2, x1) as its exponents.

Consequently, option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2).

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Option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2). A polynomials is a mathematical statement made up of real number coefficients and a sum of power in one or so more parameters (indeterminates) having non-negative integer exponents.

Three terms with non-negative integers exponents (x2, x1) make up Option "polynomial, "'s which has real numbers (x3, -2x3, and 3) as coefficients.

Option "c" x+1/x is a rational function; it is not a polynomials because of the fraction in it. It consist of one polynomials divided by another polynomial. 1/x

Option "d" is a polynomial that has real numbers (5, -3, and 2) as coefficients and terms with non-negative integers exponents (x2, x1) as its exponents.

Consequently, option "b" 3x3/2-5x2-1/2x-1 is not a polynomial due to the fraction and non-integer exponent (3/2).

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There are three main types of solutions found in mathematics for a given problem or equation: No solution, Unique solution, and Infinitely many solutions.

Solutions in mathematics are a set of values that can be assigned to the variables of an equation or a system of equations so that it holds true. In other words, it is a set of values that satisfies the equation or system of equations.

Types of solutions:

No solution: In this situation, there is no set of values that can be assigned to the variables of an equation or system of equations so that it holds true.

Unique solution: In this situation, there is only one set of values that can be assigned to the variables of an equation or system of equations so that it holds true.

Infinitely many solutions: In this situation, there are infinitely many sets of values that can be assigned to the variables of an equation or system of equations so that it holds true. This situation arises when the given equation is not independent.

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The solutions are x = ±1.73, ±3.87.

Given equation: x4 − 10x2 + 9 = 0

Rewrite equation as (x2 - 9)(x2 + 1) = 0

Set each factor equal to 0 and solve for x

x2 - 9 = 0

⇒ x2 = 9

⇒ x = ±3.87

x2 + 1 = 0

⇒ x2 = -1 ⇒

x = ±1.73

The given equation is x4 − 10x2 + 9 = 0. This can be rewritten as (x2 - 9)(x2 + 1) = 0. By setting each factor equal to 0 and solving for x, we get x2 - 9 = 0 which implies x2 = 9 and x = ±3.87. Similarly, x2 + 1 = 0 implies x2 = -1 and x = ±1.73. Therefore, the solutions of x4 − 10x2 + 9 = 0 are x = ±1.73, ±3.87.

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Answer:

Step-by-step explanation:

The constant of proportionality from the number of bottles of juice bought to the total cost is 1.15 dollars and cents.