suppose that g is a continuous function, 3_integral^5
g(x)dx=18, and 3_integral^10 g(x)dx =36. Find
5_ integral^10 g(x)dx
those are intergral symbols with numbers on
top and bottom. please show work. thanks

The triangle ABC seems to be an scalene triangle since all of the sides AB, BC and CA have different lengths, and also the triangle is not a right angled triangle.

A scalene triangle is a type of triangle in which all three sides have different lengths. In other words, none of its sides are of equal length. As a result, all three angles in a scalene triangle are also different. It is different from an Isosceles triangle, where at least two sides are of equal length and an equilateral triangle where all sides are of equal length.

A right triangle is a type of triangle in which one angle is a right angle (90 degrees). This makes it different from other types of triangles such as acute triangle and obtuse triangle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. This theorem is used to determine if a triangle is a right triangle or not.

The triangle ABC is a scalene triangle, as its sides have different lengths.

To determine whether it is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).

To find the side lengths, we can use the distance formula, which is

d = √((x2 - x1)² + (y2 - y1)²)

AB = √((9 - 6)² + (3 - 6)²) = √(3² + (-3)²) = √18 = 3√2

BC = √((9 - 2)² + (3 - 2)²) = √(7² + 1²) = √50 = 5√2

AC = √((2 - 6)² + (2 - 6)²) = √(4² + 4²) = √32 = 4√2

We know that in a right triangle, one of the side should be the hypotenuse and the other two should be the legs. We can check if any one of the side is satisfying that. But in this case, we can see that none of the sides are satisfying that condition, therefore the triangle ABC is not a right triangle.

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Answer: W = 7

Step-by-step explanation:

do PEMDAS and then follow the order of operations rule

Answer:

z + 4 × 9

Sorry if this is wrong.

Answer:

a

Step-by-step explanation:

to find the zeroes let f(x) = 0 , that is

- 2(x - 5)(x + 6)(x + 7) = 0

equate each factor to zero and solve for x

obviously multiplying any value by - 2 will not give zero

so only consider the binomial factors

x + 7 = 0 ⇒ x = - 7

x + 6 = 0 ⇒ x = - 6

x - 5 = 0 ⇒ x = 5

Answer: Synthetic division and synthetic substitution are both methods used to divide polynomials, but they are used for different types of polynomials and have different steps and procedures.

Synthetic division is a method used to divide a polynomial by a linear binomial of the form (x-c), where c is a constant. It is used to find the quotient and remainder of the division, and it involves a process of simplifying the polynomial using a specific set of steps.

Synthetic substitution, on the other hand, is a method used to divide a polynomial by a polynomial of higher degree. It is used to find the quotient and remainder of the division, and it involves replacing a variable in the polynomial with an expression and then simplifying.

In summary, Synthetic Division is used when dividing a polynomial by a linear binomial and Synthetic Substitution is used when dividing a polynomial by a polynomial of higher degree.

Step-by-step explanation:

Synthetic division is used for polynomial division by a linear factor, resulting in a quotient polynomial. Synthetic substitution, however, is used to find the value of a polynomial function at a given x-coordinate.

Synthetic division and synthetic substitution are both methods used in algebra to evaluate polynomials. However, they differ in their specific applications and the outcomes they provide.

Synthetic division is a method used to divide a polynomial by a linear factor of the form (x - c). It allows for quick and efficient division without the need for long division. The process involves setting up a synthetic division table and performing a series of calculations based on the coefficients of the polynomial. The result is a simplified quotient polynomial.

On the other hand, synthetic substitution is a technique used to evaluate a polynomial function at a specific value of x. It involves substituting the given value into the polynomial and using synthetic division to perform the calculations. The result obtained is the value of the polynomial at that particular x-coordinate.

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At the end of 28years the neurosurgeon will have an amount of $115875.00

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

The amount earned or paid after compounded interest is given as A = P(1+r/100)^t

Where P is the principal saved

t is the time for saving

and r is the rate of interest

Here t = 28 years

P = 25,000

and r = 5.63% per annum

therefore A = P(1+r/100)^t

A = 25000(1+5.63/100)^28

A = 25000(1+0.0563)^28

A = 25000(1.0563)^28

A = 25000× 4.635

A= $115875.00

This means at the end of 28 years, the neurosurgeon will have a amount of $115875.00

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Answer:

-20 beacause - x + = - and you do 2x10

You can use the formula y=mx+b, where m is the slope.

Your gradient is -3/2.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

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.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

According to our question-

y=-3/2x+1

Your slope in the second equation is -3/2 since y=-3/2x+5 is already in the form y=mx+b and m is the slope.

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Elise average pay per hour in 2017 is 13.73 pounds

Elise earned 2100 as a monthly salary in 2016.In 2017, she got a 3% pay increase on her monthly salary.

So, in 2017 she got a monthly salary of (1+3/100)*2100= 2163

Then her yearly salary in the year 2017 became (2163 × 12) =25956

In 2017, Elise worked for 1890hours.

Therefore, her average pay per hour for the year 2017 will be:

= 25956 / 1890

= 13.73

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Complete question

in 2016, she earned a monthly salary of £2100

In 2017, she earned a 3% pay increase on her monthly salary.

Given that in 2017 Elise worked 42 hours per week for 45 weeks work out her average pay per hour for the year.

The amount of ingredient that is needed to make just 2 portions are:

Generally, the term "portion" refers to how much food is served to you or how much you eat. Portion sizes can differ from meal to meal. For example, you might serve yourself two small pancakes in one portion at home, but at a restaurant, you might get a stack of four pancakes as one portion.

Data

Needed 2 portions

Recipe: 250 g oats, 1.4 litres milk, 90 g suga

Portion of Oat:

250/5 * 4 = 50 *2 = 100g oats

Portion of milk:

1.2/5 * 2 = 0.48l milk

Portion of sugar:

90/5 * 2 = 18*2 = 36g sugar

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Todd's conclusion is therefore incorrect, not all linear relationships are proportional, they can be represented by a linear equation but they don't need to have a constant ratio between the two variables.

What is a linear relationship?

A linear relationship is a relationship between two variables in which the change in one variable is directly proportional to the change in the other variable. Linear relationships can be represented by a linear equation, which is an equation that can be written in the form of y = mx + b, where m and b are constants.

Proportional relationships also have a constant ratio between the two variables, but the relationship between the variables is not always linear. Proportionality can be represented by the equation y = kx, where k is a constant.

In general, it is not true that all linear relationships must be proportional. While it is true that a proportional relationship will always result in a linear graph, there are also many other types of linear relationships that do not fit this definition. For example, the equation y = 2x + 3 describes a linear relationship, but it is not proportional because the ratio between y and x is not constant.

Hence, Todd's conclusion is therefore incorrect, not all linear relationships are proportional, they can be represented by a linear equation but they don't need to have a constant ratio between the two variables.

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The correct statement is,

⇒ - 8/5 < 3/5

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The numbers are,

⇒ 3/5 and - 8/5

Now, By comparing, we get;

⇒ 3/5 and - 8/5

⇒ 3/5 > - 8/5

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Therefore , the solution of the given problem of inequality comes out to be  -17 is the figure that meets the inequality .

When both sides of a mathematical expression are not equal, an inequality exists. In inequality, we compare values in contrast to equations. The equal sign is substituted by the signs smaller than (or lower than or identical to), wider than (or greater or comparable to), or even not equal to. Olivia, for instance, is selected for the 12U Softball level. How old is Olivia? You don't know Olivia's age because "equals" is missing from the sentence. But since you know she needs to be less than or similar to 12, so can enter Olivia's Age 12.

Given:

-3q ≤ 51

Currently, -17 is the figure that meets the inequality out of all the numbers that have been provided.

Due to the fact that a negative integer has a higher value the smaller it is, -3 5 1.

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Answer:

7/9

Step-by-step explanation:

Simplify the following:

(2/3)/(6/7)

Multiply the numerator by the reciprocal of the denominator, (2/3)/(6/7) = 2/3×7/6:

(2×7)/(3×6)

2/6 = 2/(2×3) = 1/3:

7/(3×3)

3×3 = 9:

Answer:7/9

To evaluate x/y for x = 2/3 and y = 6/7, you need to substitute these values into the expression x/y and simplify the result.

x/y = (2/3) / (6/7)

To simplify the fraction, you can cross multiply the numerator and denominator by 7, which is the denominator of the second fraction:

(2/3) / (6/7) = (2/3) * (7/6) = (27) / (36) = 14/18

The fraction can be simplified further by dividing both the numerator and denominator by their greatest common divisor (GCD) which is 2:

14/18 = (14/2) / (18/2) = 7/9

So x/y = 7/9 when x = 2/3 and y = 6/7

It's important to note that the result is a fraction, if you want to express it as decimal you can divide 7 by 9 or use a calculator to get 0.7777 repeating.

The required distinct roots of the following equation using the quadratic formula is x = -3±√5i.

Any quadratic problem can be solved using the quadratic formula.

The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients.

After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

So, the quadratic formula:

x = -b±√b²-4ac/2a

Now, insert values and calculate for roots as follows:

x = -b±√b²-4ac/2a

x = -b±√b²-4*4(1)*14/2(1)

x = -b±√36/56/2

x = -b±√-20/2

Discriminant: b² - 4ac < 0

Now,

x = -6± 2√5i/2

x = -6/2 ± 2√5i/2

x = -3±√5i

Therefore, the required distinct roots of the following equation using the quadratic formula is x = -3±√5i.

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Answer: The new value of the sum of N1,500 investment at a simple rate of 15% per annum for 2 years is N1950

Step-by-step explanation:

Simple interest is calculated by multiplying the principal amount, interest rate, and time.

The formula for simple interest is:

Simple Interest = (principal x rate x time) / 100

In this case, the principal amount is N1,500, the interest rate is 15% per annum and the time is 2 years.

So the simple interest earned on the investment is:

Simple Interest = (1500 x 15 x 2) / 100

Simple Interest = N450

To find the new value of the investment, we add the simple interest earned to the principal amount.

New value = Principal + Simple Interest

New Value = 1500 + 450

New Value = N1950

Explanation: Simple interest is calculated by multiplying the principal amount, interest rate, and time. By using this formula, the interest earned on the investment was N450. And by adding the interest to the principal amount, we can find the new value of the investment which is N1950.

Let x be the time (in hours) it takes Meredith to edit a textbook alone. We know that Phil takes 4x hours to edit a textbook alone, since he takes four times as long as Meredith.

We also know that it takes them 16 hours to edit a textbook together. We can use this information to set up the equation:

x + 4x = 16

5x = 16

x = 16/5

So it takes Meredith 16/5 hours to edit a textbook alone.

We know that Phil takes 4x to edit a textbook alone, so we can substitute in the value we found for x to find his time:

4x = 4(16/5) = 16/5 * 4 = 64/5

So it takes Phil 64/5 hours to edit a textbook alone.

To prove this statement, we will use the following definitions and properties:

A finite dimensional vector space is a vector space that has a finite number of basis vectors.

A basis for a vector space is a set of vectors that span the space, meaning that any vector in the space can be written as a linear combination of the basis vectors.

A linear combination of a set of vectors is an expression of the form a_1v_1 + a_2v_2 + ... + a_nv_n, where v_1, v_2, ..., v_n are the basis vectors and a_1, a_2, ..., a_n are scalars from the field.

A non-zero element of a finite dimensional vector space is a vector that is not equal to the zero vector, the additive identity of the space.

Now, let's assume that V is a finite dimensional vector space over a field F, and let B be a basis for V. We will show that every non-zero element of V can be expressed as a unique linear combination of the basis vectors in B.

Let v be a non-zero element of V. Since B spans V, there exists a set of scalars a_1, a_2, ..., a_n from the field F such that v = a_1v_1 + a_2v_2 + ... + a_nv_n, where v_1, v_2, ..., v_n are the basis vectors in B. This is a valid linear combination representation of v with respect to B.

To show that this linear combination representation of v is unique, let's assume that there exists another set of scalars b_1, b_2, ..., b_n from the field F such that v = b_1v_1 + b_2v_2 + ... + b_nv_n. Then, subtracting the second equation from the first one, we get:

0 = (a_1 - b_1)v_1 + (a_2 - b_2)v_2 + ... + (a_n - b_n)v_n.

Since B is a basis for V, the only way for the left-hand side of the equation to be the zero vector is for all the scalars in the linear combination to be equal, i.e. a_1 = b_1, a_2 = b_2, ..., a_n = b_n. Thus, v can be expressed as a unique linear combination of the basis vectors in B, which completes the proof.

Therefore the slope of the line passes through  (5, 9) and (3, -5) comes out to be 7.

By computing the ratio of the vertical to horizontal distance (rise over run) between two points, the slope—a numerical value that defines how steep a line is—is often calculated.a number that indicates how inclined a line is, is frequently determined by dividing the vertical distance (rise over run) between two places by the horizontal distance (run over rise).

The slope of line that passes through  (5, 9) and (3, -5)

Slope= gradient between the two points

Slope= (y2-y1)/(x2-x1)

Where y2= -5

Y1= 9

X2= 3

X1= 5

(-5-9)/(3-5)

-14/-2

7

Therefore the slope of the line passes through  (5, 9) and (3, -5) comes out to be 7.

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The ratio of the mystery novel to all novels from Addison's novel collection, is D. 4 to 11.

Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

The ratio of the mystery novels to all novels can therefore be found by first finding the total number of novels :

= 2 + 4 + 5

= 11 novels

The ratio would then be:

Number of mystery novels : Number of all novels

                  4                         :               11

Which is 4 to 11.

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Since the ordered pair (a, b) satisfies the inequality y > x + 3, a statement which is true include the following: C. b is greater than a.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) data points or elements that are commonly written in a fixed order within parentheses as (x, y).

This ultimately implies that, an ordered pair is typically used for representing the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

Based on the given ordered pair (x, y) which satisfies this inequality y > x + 3, this can be rewritten in terms of a and b as follows;

y > x + 3

b > a + 3

In this context, we can reasonably infer and logically deduce that b is greater than a i.e b > a.

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Complete Question:

The ordered pair (a, b) satisfies the inequality y>x+3. Which statement is true?

A.if you add 3 to b , it will equal a

B. a is greater than b

C. b is greater than a

D. If you subtract 3 from b, it will equal a

The length of the one of the leg of the triangle is 12√2 in. Thus, option B is correct.

The longest side of a right triangle in geometry is called the hypotenuse. Moreover, it is the side that faces the right angle. The definition of hypotenuse is "length under" or "stretch under." Plato was said to have used it for the first time around 400 BC.

In many applications of geometry and trigonometry, the hypotenuse plays a significant role. The Pythagorean Theorem is the most widely known. Using the Pythagorean Theorem, a2 + b2 = c2, one can determine the length of the hypotenuse.

The Right angles triangle is also a isosceles angled triangle which means two of the angles are equal.

When two angles are equal the corresponding sides are equal too.

a = b

Given that the measure of the triangles' hypotenuse is 24 inches

c² = a² + b²

24² = a² + b²

576 = a² + b²

But the sides are equal i.e.

a = b

Giving us

576 = a² + a²

576 = 2a²

a² = 576/2

a² = 288

a = √288

a = 12√2

Thus, the length of the one of the leg of the triangle is 12√2 in. Thus, option B is correct.

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Answer:

Step-by-step explanation:

b e2020

Since there is a 0.45 chance of winning a prize at the carnival game, the likelihood that he will win one is 0.04 out of every five games.

Probability theory, a subfield of mathematics, analyzes the likelihood that an event will occur or a statement is true. The probability of an event occurring is a number between 0 and 1, where approximately 0 indicates how unlikely the event is and 1 indicates how certain it is. A probability is a quantitative expression of the likelihood that a particular event will occur. Probabilities can also be expressed as percentages between 0% and 100% or as percentages between 0 and 1. the ratio of the total number of outcomes to the number of events in a complete collection of equally likely outcomes that result in a certain occurrence.

given

= (0.45 )* 1*5 / 5

= 0.04

Since there is a 0.45 chance of winning a prize at the carnival game, the likelihood that he will win one is 0.04 out of every five games.

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It would take 2.69 minutes for both machines to complete the project at the same time

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Machine A completes a project every 5.5 minutes. Machine B completes a project every 5.25 minutes.

Let t represent time it would take both machines to complete the project, hence:

(1/5.5 + 1/5.25)t = 1

86t/231 = 1

t = 2.69 minutes

It would take 2.69 minutes to complete

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Answer:

21/4 * 11/2=5.25*5.5

Step-by-step explanation:

21/4 * 11/2=5.25*5.5

= 28.875

The function for the monthly bill can be written as y = 7 + 4x.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a music streaming service charges $7 per month for the first user and $4 more per month for each additional user.

The equation can be written as,

y = 4x + 7

Here, y is the monthly charge and x is the number of months.

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Answer:

To calculate the number of yards of ribbon Christine bought, we need to determine how much money she spent on the ribbon. We know that the card had $20 on it initially and that $18.42 was left on the card after her purchase, so we can subtract the remaining balance from the original balance to find out how much she spent:

$20 - $18.42 = $1.58

We also know that the ribbon was 14 cents per yard, so we can divide the amount spent on the ribbon by the price per yard to find out how many yards Christine bought:

$1.58 / $0.14 = 11.285714285714286

So, Christine bought 11.285714285714286 yards of ribbon.

For the m/m/1 queuing model, the average number in the system is equals to the four. So, the correct answer is option (c).

This is the most widely used queuing system in analytics. M/M/1 is a good approximation for a large number of

mass service systems. The M/M/1 quening system assumes a Poisson arrival process. This assumption is a very good approximation for the process of arriving at real systems that satisfy the following rules,

We have, customer service is every 4 minutes. So, the Service rate μ = 1 customer/4 minutes = 0.25 customer/minute or 15 per hour.

Customers arrive individually at a rate of one customer every 5 minutes according to the distribution of poisons.

Number of customer service= 1

The arrival rate is 1/ (mean time between arrivals) . Here, the rate of arrival of customers/5 minutes is λ = 0.2 customers/min or 12 per hour. Therefore,

Utilization factor = (arival rate /service rate)100 = λ/μs

Utilization factor = (12/15) 100%

= (4/5)100 = 80%

Utilization factor = 80%

Average number in the system = λ/( μ - λ)

= (60/5)/[ (60/4)-(60/5)]

= 12/3 = 4

So, the average number in the system is 4.

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Complete question:

A queuing model that follows the m/m/1 assumptions. a customer can be served every 4 minutes. customers arrive independently at the rate of one customer every 5 minutes according to a poisson distribution. the average number in the system is

a) 7

b) 5

c) 4

d) 6