hich of the following is a case in which the area bounded by two curves is most easily found by integrating with respect to y?

Answer: You have a credit card that has a balance of $3,589.90 and a credit limit of $5,000. How much is the balance over the acceptable debt ratio percentage? $981.88.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the acceptable debt rate would be 43%

The values of z1 and z2 that will satisfy this equation are z1 = −8 and z2 = 6 and the vectors (2, −1, 3), (1, 2, 2), and (−4, −8, 6) do not span R3.

To find these values, we need to understand that for any three vectors to span R3, they must be linearly independent.

This means that none of the vectors can be expressed as a linear combination of the other two vectors.

We can start by finding the determinant of the matrix formed by the three vectors. If the determinant is not equal to 0, then the vectors are linearly independent and span R3.

However, if the determinant is equal to 0, then the vectors are linearly dependent and do not span R3.

Let's consider the matrix formed by the three vectors:

[tex]= > \begin{bmatrix}2 & 1 & -4 \\-1 & 2 & z1 \\3 & 2 & z2\end{bmatrix}[/tex]

The determinant of this matrix is equal to:

=> 2 * (2 * z2 - 2 * z1) - (-1) * (1 * z2 - 2 * -4) + 3 * (1 * z1 - 2 * -4)

=> 2z2 - 2z1 + 7z1 + 24 - 2z2 + 8z1 - 24

=> 9z1 + 2z2 - 24

So, the vectors will not span R3 if 9z1 + 2z2 - 24 = 0.

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The solutions of  Ax = 0 in parametric vector form, where A is a row equivalent to the given matrix are : x_1 = 2x_3 + 2x_2,x_2 = x_2 + x_3,x_3 = x_3,x_4 = 2x_3 + 6x_2,x_5 = -3x_3 - 6x_2,x_6 = -4x_3 - 2x_2

The given matrix is row equivalent, which means that it can be reduced to row echelon form using elementary row operations. To solve for the parametric vector, we start by performing the same operations to the identity matrix. First, we divide the first row by 2 to get the leading coefficient of 1 on the leftmost column. Then, we add the first row to the second row, and the third row to the fourth row to eliminate the elements below the leading coefficients.

Finally, we multiply the first row by -4 and add it to the third row to get the leading coefficient of 1 on the third column. After performing the same operations on the identity matrix, we get the parametric vector x_2 + x_3. This means that x_1 = 2x_3 + 2x_2, x_2 = x_2 + x_3, x_3 = x_3, x_4 = 2x_3 + 6x_2, x_5 = -3x_3 - 6x_2, and x_6 = -4x_3 - 2x_2. Essentially, the parametric vector is the sum of the two columns of the identity matrix that correspond to the two leading coefficients in the row echelon form of the original matrix.

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Step-by-step explanation:

The system of linear equations can be solved using elimination method or substitution method.

Here's the solution using elimination method:

Add the two equations to eliminate the y variable:

(7y + 10x - 8) + (2y - 5x - 18) = 0 + 0

9y + 5x - 26 = 0

Solve for y:

9y = 26 - 5x

y = (26 - 5x) / 9

Substitute this expression back into either of the original equations to solve for x:

7y + 10x - 8 = 0

7((26 - 5x) / 9) + 10x - 8 = 0

26 - 5x + 70x - 56 = 0

65x - 32 = 0

Solve for x:

65x = 32

x = 32/65

Finally, substitute the value of x back into the expression for y to find the value of y:

y = (26 - 5x) / 9

y = (26 - 5(32/65)) / 9

y = (26 - 160/65) / 9

y = (26 - 8/3) / 9

y = (26 - 8/3) / 9

y = (26 - 8/3) / 9

y = 18/9 - 8/3

y = (18 - 24) / 9

y = -6/9

The solution to the system of linear equations is:

x = 32/65

y = -6/9

The dimensions of a scale drawing of a rectangular flag that is 40 centimeters by 72 centimeters using the scale 1:8 is 4 cm by 7.2 cm. Option C.

This is because a 1:8 scale means that for every actual unit of length, the corresponding length on the scale drawing is 8 times smaller.

Therefore, in order to find the dimensions of the scaled drawing of the flag, we must divide the actual dimensions (40 cm by 72 cm) by 8. The result is 4 cm by 7.2 cm.

It is important to make sure that you use the correct scale when attempting to determine the dimensions of a scaled drawing. If you use a different scale than the one intended, your result will be incorrect.

For example, if you use a 1:4 scale instead of a 1:8 scale, you will end up with a scaled drawing that has dimensions of 20 cm by 36 cm, which is double the correct answer.

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To solve a series of linear equations by graphing them:

1. Visualize the initial equation.

2. Using the same rectangular coordinate system, graph the second equation.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

To develop a graph is to make a diagram that depicts the relationship between two or more objects.

Make a sequence of bars on graph paper as an example of a graph. YourDictionary, to express or give the form of using a graph.

To graph a set of linear equations and solve them:

1. Visualize the initial equation.

2. Using the same rectangular coordinate system, graph the second equation.

3. Establish if the lines are parallel, intersect, or are one and the same.

4. Determine the system's remedy. Find the intersection if the lines do indeed meet.

Therefore, to solve a series of linear equations by graphing them:

1. Visualize the initial equation.

2. Using the same rectangular coordinate system, graph the second equation.

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The probability that the student drinks soda, given that they drink coffee, is 0.25.

Let's designate the proportion of students who regularly consume soda as "S," those who frequently consume coffee as "C," and those who regularly consume both as "B."

Since 40% of students frequently consume soda, there are 0.4S kids who do the same.

Additionally, there are 0.3S students who consume coffee because 30% of students do it frequently.

Additionally, since 10% of students consume both beverages, there are 0.1S students who also consume soda and coffee.

Students in the class S = 0.4S + 0.1S = 0.5S either drink soda or both.

The pupils in C = 0.3S + 0.1S = 0.4S either consume coffee or both.

So, given that the student drinks coffee, the probability of drinking soda is:

P(soda | coffee) = P(soda and coffee) / P(coffee)

                          = 0.1S / 0.4S

                          = 0.25.

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An inequality to describe the constraints is x + 2y ≤ 30

What is inequality?

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than, or equal to, less than, or less than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.

Here, we have

Assume that a free throw is represented by f and that a Juli throw is represented by j.

We can then write an inequality equation as

10f + 10j = 30

Where 30 is the total number of points earned

F is the free throws made, in which each gives or earns one point

J is the jump shots made, in which each gives or earns two points.

Hence, an inequality to describe the constraints is x + 2y ≤ 30

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The formula for an exponential function is y = abx, where an is the value of y at x = 0 and b is the growth factor over each unit of time.

Consider the connection to be a function if each input value results in just one output value. Do not classify the relationship as a function if any input value results in two or more outputs.

Simple linear regression uses the equation Y = a + bX to connect X and Y. Both quantify the link between two numerical variables, including its intensity and direction.

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Y = abx is the equation for an exponential function, where b is the growth factor per unit of time and an is the value of y at x = 0.

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The equation ŷ = -3x + 15 best fits the given data sets.

The word linear function in mathematics refers to two separate but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

The linear function equation that best fits the data set is likely to be the one that minimizes the differences (or residuals) between the observed y-values (the data points) and the predicted y-values (calculated from the equation).

To find this equation, you can use the method of least squares, which involves finding the line that minimizes the sum of the squared residuals.

In this case, the equation ŷ = -3x + 15 minimizes the sum of the squared residuals and is therefore the best fit for the data set.

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The composite result function of (f( g(x) ) in the given functions f(x) = x+4 and g(x) = 12x + 1 is 12x + 5.

A function is simply a relationship that maps one input to one output.

Given that;

First, we set up the composite result function f(g(x))

f(x) = x + 4

f( g(x) ) = g(x) + 4

f( 12x + 1 ) = ( 12x + 1 ) + 4

Simplify

f( 12x + 1 ) = 12x + 1 + 4

Add 1 and 4

f( 12x + 1 ) = 12x + 5

Therefore, the composite function f( 12x + 1 ) is  12x + 5.

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The cosecant, secant, and cotangent functions are defined as the reciprocals of the sine, cosine, and tangent functions, respectively which have two parent trigonometric functions have a period of π and a range that consists of the set of all real numbers.

These functions also have a period of 2π and their ranges depend on the range of the corresponding parent function.

Therefore, correct answer will be a. sine, b. cosine and c. tangent.

The trigonometric functions are mathematical functions used to describe relationships involving lengths and angles of triangles. These functions include sine, cosine, tangent, cosecant, secant, and cotangent. Each of these functions has its own unique properties, including period and range.

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The transformation of polar coordinate into rectangular coordinate is r sec (theta) = 5 ⇒ x^2 - 5x + y^2.

Two real number lines that intersect at a right angle make up the rectangular coordinate system. The x-axis refers to the horizontal number line, and the y-axis to the vertical number line. Each point on this plane is connected to an ordered pair of real numbers by means of these two number lines, which constitute a flat surface known as a plane (x, y). The x-coordinate is the first number, while the y-coordinate is the second number.

Given that the polar equation is r sec (theta) = 5.

We can write the equation as follows:

r = 5 cos(theta)

Multiply both the sides of the equation with r:

r^2 = 5 cos(theta) r

We know that the value of r^2 = x^2 + y^2 and the value of cos(theta) r = x.

Substituting the values we have:

x^2 + y^2 = 5x

x^2 - 5x + y^2

Hence, the transformation of polar coordinate into rectangular coordinate is r sec (theta) = 5 ⇒ x^2 - 5x + y^2.

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The percentage of the corals at the dive site that Sarah observes died more than 12 months ago is 21%.

A percentage is a specification of the quantity of an item in a collection per 100 of all items in the  collection.

The observations of the corals are;

The percentage of the corals that are healthy = 30%

Percentage of the corals that are unhealthy = 40%

Percentage of the corals that are dead = 30%

Percentage of the dead corals that died in the past 12 months = 30%

The percentage of corals Sarah observed died more than 12 months ago; required.

The 30% of the dead corals that died in the last 12 months, indicatesa that the percentage of the dead corals that died more than 12 months ago = 100% - 30% = 70%

The percentage of the dead corals that died more than 12 months ago = 70%

Therefore, the percentage of the population of corals at the dive site that died more than 12 months ago = 70% × 30% = 21%

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180 lb to 140 kg conversion. The base unit of weight in the metric system is the kilograms, sometimes known as the kilograms.

Convert 140 Kilograms to Pounds.

kg             lb

140.00 308.65

140.01 308.67

140.02 308.69

140.03  308.71

Basically, to convert cost per kg to cost per lb, take the price for the kilogramme and divide it by 2.2046 to get the price for the pound. Fundamentally, 1 kilogramme equals 2.2046 pounds (there is a longer decimal position, but I shorten it to 2.2046).

Mathematical and technical fields frequently need to convert between kilogrammes and pounds; fortunately, this is a simple process. The majority of the time, all you have to do to convert is multiply the number of kilograms by 2.2 to get the number of pounds. Generally speaking, there are 2.2046 pounds in every kilograms.

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The probability of someone being the odd man out is 0.667

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Given,

3 persons toss a coin to decide who will buy refreshments for the group.

So, total no. of outcomes = (outcomes per each person) total persons

Total no. of outcomes = [tex]2^{3}[/tex]

Total no. of outcomes = 9

The outcomes that one person gets tails and others do not are = (THHH) + (HTHH) + (HHTH)+ (HHHT).

Here T = person getting tails, H = person getting heads.

Number of times one individual receives tails while another does not = 4.

Now, we try to calculate the number of outcomes for one person getting heads and others getting tails, and the results are as follows:

The chances of one individual getting tails while others do not = (HTTT) + (THTT) + (TTHT)+ (TTTH).

The number of possibilities that one individual gets heads while others do not = 3

So, total no. of possibilities that we get a loser = 3+3

Total no. of possibilities that we get a loss = 6.

We know that probability is defined as probability= total no. of possibilities / total no. of outcomes

Now, we have a probability that there is a loser in any game.

So, required probability = 6/9

Required probability = 0.667

∴ The required probability is 0.667

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The probability of someone being the odd man out is 0.667

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Given,

3 people toss a coin to decide who will buy refreshments for the group.

So, total no. of outcomes = (outcomes per each person) total persons

Total no. of outcomes = 2*2*2

Total no. of outcomes = 8

The outcomes that one person gets tails and others do not are = (THHH) + (HTHH) + (HHTH)+ (HHHT).

Here T = person getting tails, H = person getting heads.

The number of times one individual receives tails while another does not = 4.

Now, we try to calculate the number of outcomes for one person getting heads and others getting tails, and the results are as follows:

The chances of one individual getting tails while others do not = (HTTT) + (THTT) + (TTHT)+ (TTTH).

The number of possibilities that one individual gets heads while others do not = 3

So, the total no. of possibilities that we get a loser = 3+3

Total no. of possibilities that we get a loss = 6.

We know that probability is defined as probability= total no. of possibilities / total no. of outcomes

Now, we have a probability that there is a loser in any game.

So, required probability = 6/9

Required probability = 0.667

∴ The required probability is 0.667

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Step-by-step explanation:

The expression (2n^4)^-2 can be simplified as follows:

(2n^4)^-2 = 1 / (2n^4)^2

Using the rule that (a^b)^c = a^(bc), we can simplify further:

= 1 / (2^2 * n^4 * 2)

= 1 / (4 * n^4 * 2)

= 1 / (8 * n^4)

So (2n^4)^-2 = 1 / (8 * n^4) in simplified form using positive exponents.

Answer:

The probability that the individual has the disease is 1/500

Step-by-step explanation:

i found the fraction of 1 in 500 which is 1/500, hope this helps :)

Answer:

1/2 Bh

Step-by-step explanation:

find the area of the base (B) by multiplying.5 xlengthxwidth. The take this answer, multiply by .5 and the height of the pyramid.

The volume of a  triangular pyramid is 1/2 × area of the base× height.

What is a triangular pyramid?

A pyramid with a triangular base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids have four vertices. Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.

The volume of an object has defined as the space that is occupied by the object.

The volume of a triangular pyramid is 1/2 × B × h.

B =  area of the base of the triangular pyramid.

h = Height of  triangular pyramid

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the correct sample space for the gumball in her bag is option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive

Given, Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs.

The number of lemon limes in the bag = 2 lemon-lime

Number of watermelons in the bag = 3 watermelon

Number of grape gumballs in the bag = 5 grape gumball

Sample space is the set of all the possible outcomes of the experiment

Here there are 2 lemon-lime, 3 watermelons, and 5 grape gumball

Hence, if Julia had a bag filled with gumballs and there were 2 lemon-lime, 3 watermelon, and 5 grape gumballs, then the correct sample space for the gumball in her bag is an option (D) Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

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watermelon,lemon lime,lemon lime,grape,grape,grape

The equations have infinitely many solutions

-76x+76=-76x+76

76x + 76 = 76x +76

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. LHS = RHS is a common mathematical formula.

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:

When certain requirements are met, an equation can have an unlimited number of solutions.

We have the equation

76x+ 76 = -76x+76

So, 152x = 0

x = 0

and, -76x+76=-76x+76

0= 0

and, 76x + 76 = 76x +76

0 = 0

and, -76x + 76x = 76x - 76

-152x = -152

x= 1

So, the equation with 0=0 shows infinite many solution which are

-76x+76=-76x+76

76x + 76 = 76x +76

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The required quotient of the given expression -1/8 × 2/3 is given as -1/12.

The procedure in mathematics to work and crack the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= -1/8 × 2/3
= -1/ [4×3]
= -1/12

Thus, the needed quotient of the given expression -1/8 × 2/3] is given as -1/12.

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The fraction of the given equation would be 2/3.

locating the Original number.

The outcome is one less than the original number when a two-digit number with its digits reversed is subtracted from the same number. The number itself can be obtained by adding three times the tens digit and four times the units digit of the original integer.

Suppose that x is the initial or positive number.

(x - 4/7)* 7 = x

7(x) - 7(4/7) = x

7x - 4 = x

7x-x = 4

6x = 4

x = 4/6 = 2/3

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The interquartile range of the data represented in the box-and-whisker plot is given as follows:

IQR = 3.

The measures represented in the box-and-whisker plot are given as follows:

The interquartile range is calculated as the difference between the third quartile and the first quartile.

Hence the correct value is given as follows:

IQR = 18 - 15

IQR = 3.

Meaning that the last option is the correct option.

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The  situations that could be represented by two numbers whose product is equal to 20 are options A, B, D, E and F

Recall that the product of two numbers is the result you get when you multiply them together/

The Factors of 20 are: 1,2,4,5,10,20

From the analysis,

Option A: The change in the balance of a checking account after a man spends $4 a day for five days. = $4*5 = 20

Option B: The miles traveled after a sailor makes two trips of 10 miles each. = 2*10 = 20

Option D: The difference in altitude after a kite loses altitude four times by 5 feet each time.

⇒4*5 = 20

Option E: The amount of sugar in a recipe if it calls for 2  cups per pitcher and Martha is making 10 pitchers.

⇒2*10 = 20

Option F: The total charge created from twenty electrons each with a 1 charge

⇒1*20 = 20

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The multiplication rule is used to calculate joint probability.

Joint probability is the probability of two events happening simultaneously. The multiplication rule states that the probability of two independent events happening together is equal to the product of their individual probabilities.

The formula can be expressed as: P(A and B) = P(A) x P(B). For example, if the probability of event A is 0.3 and the probability of event B is 0.4, then the joint probability of both events happening together is 0.3 x 0.4 = 0.12. The multiplication rule is only applicable for independent events, meaning that the occurrence of one event does not affect the probability of the other event.

When events are dependent, the calculation of joint probability is more complicated and may involve conditional probability.

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Answer:

Yes, the set of ordered pairs (1, 7), (3, 8), (3, 6), (6, 5), (2, 11), (1, 4) represents a relation. This relation is a function since each input (x-value) has a single output (y-value).

Step-by-step explanation:

There is point i.e., value of x where the function  f(x) = x³ - 4x² - 7x +12 is not continuous.

Consider the polynomial function f(x) = x³ - 4x² - 7x +12

As we know if a function f be a function defined on an open interval containing point a where t a ∈ R be a constant, a function f is continuous at a if lim_(x→a) f(x) = f(a).

Here, the domain of polynomial function  f(x) = x³ - 4x² - 7x +12  is set of all real numbers, as the function is well defined for all real values of x.

We know that every polynomial function is continuous in their domain.

This means, the polyomial function f(x) = x³ - 4x² - 7x +12  is continuous on set of all real numbers.

Therefore, there is no value of x where the polynomial function f(x) = x³ - 4x² - 7x +12 is not continuous.

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The length of the fabric is 15cm.

What is Pythagoras' theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given: Elijah takes a rectangular piece of fabric and makes a diagonal cut from one corner to the opposite corner. The cut he makes is 17 inches long and the width of the fabric is 8 inches.

We have to find the fabric's length.

We apply here Pythagoras theorem and we get

a² + b² = c²

a² +  (8)² = (17)²

a² +64 = 289

a²  = 289 - 64

a²  = 225

a = 15

Hence, the length of the fabric is 15cm.

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