What are the types of Discontinuities?

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:

The ratio is 1:16 or (30 minutes:480 minutes).

What is the ratio of lunch interval to the total period in office?

The theory used in this question is the ratio of two numbers.

A ratio is a comparison of two numbers, usually expressed as a fraction or as a decimal. Ratios can be used to compare two numbers and identify relationships between them.

In this case, the ratio is being used to compare the lunch interval (30 minutes) to the total time the office is open (450 minutes).

Given:

The total time the office is open in minutes: 9 am - 5 pm = 8 hours = 8 x 60 minutes = 480 minutes.

Divide the lunch interval (30 minutes) by the total time the office is open (450 minutes): 30 minutes / 480 minutes.

= 1: 16

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Answer:

[tex]\boxed{\mbox \large a = \dfrac{9}{10} = 0.9}[/tex]

Step-by-step explanation:

Equation to be solved is
[tex]\dfrac{5}{3}a + \dfrac{4}{5} = a + \dfrac{7}{5}[/tex]

Step 1

Get rid of those annoying denominators by multiplying throughout 15. We choose 15 because it is the lowest common multiple of 3 and 5. Since 3 and  are prime numbers the LCM is 3 x 5 = 15

[tex]15 \cdot \dfrac{5}{3}a +15 \cdot \dfrac{4}{5} = 15\cdot a + 15\cdot \dfrac{7}{5}}[/tex]
==> [tex]25a + 12 = 15a + 21}\\[/tex]

Step 2

Subtract 15 from both sides:

==> [tex]25a -15a + 12 = 15a -15a + 21}\\\\\\ 10a + 12 = 21}\\[/tex]

Step 3

Subtract 21 from both sides
[tex]10a + 12 -12 = 21 - 12\\\\[/tex]

[tex]10a = 9[/tex]

Step 4

Divide by 10 both sides

[tex]\dfrac{10a}{10} = \dfrac{9}{10}\\\\\implies a = \dfrac{9}{10} = 0.9[/tex]

let f be a differentiable function such that f(1)=2 and f′(x)=x2 2cosx 3 then f(4)= 4.1414

if a function is differential at x if the limit of a function exists at a pint x and the function is continuous at x point also then the function is differentiable at the point x

since sin and cos function are differentiable and their limit exists

Given that f is  a function given by

f(x) =2cosx +1

Here x is taken in radians.

Hence when x =1.5

we have cos 1.5 = 0.0707

2cosx = 0.1414

And hence

2cosx+1=1+0.1414

=1.1414

Thus we get

f(1.5) = 1.1414 apprxy

f( 4) = 0.1414 +4

      = 4.1414

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Answer:

C) 10.790

Step-by-step explanation:

we are given:

[tex]f(1)=2\\[/tex]

[tex]\frac{dy}{dx} =\sqrt{x^2+2cos(x)+3}[/tex]

we need to find:

[tex]f(4)=?[/tex]

integrate the function by using a TI-84 calculator (math > 9:fnInt( > input)

[tex]\\\int\limits^4_1 {\sqrt{x^2+2cos(x)+3} } \, dx \\\\\\=8.789[/tex]

since we are looking on the interval [1, 4] we need to add our two limiting values together:

[tex]F(4)+F(1)=2+8.789\\\\=10.790[/tex]

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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expression by 8 in the third case, giving us 12*(-7)*8 = -672. Finally, we divide the expression by g(x) to find the fourth limit, giving us 12/(-7) = -1.714.

a. limx→3[f(x)g(x)] = limx→3[12*(-7)] = -84

b. limx→3[3f(x)g(x)] = limx→3[3*12*(-7)] = -252

c. limx→3[f(x) 8g(x)] = limx→3[12*(-7)*8] = -672

d. limx→3[f(x)/g(x)] = limx→3[12/(-7)] = -1.714

The given limits are limx→3f(x)=12 and limx→3g(x)=−7. We can calculate the following limits by substituting x=3 in the given expressions: limx→3[f(x)g(x)] = -84, limx→3[3f(x)g(x)] = -252, limx→3[f(x) 8g(x)] = -672 and limx→3[f(x)/g(x)] = -1.714. To find these limits, we first multiply the two expressions, f(x) and g(x). This gives us 12*(-7) = -84 in the first case. In the second case, we multiply this expression by 3, giving us 3*12*(-7) = -252. We then multiply this expression by 8 in the third case, giving us 12*(-7)*8 = -672. Finally, we divide the expression by g(x) to find the fourth limit, giving us 12/(-7) = -1.714.

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The greatest common factor from the terms of the polynomial 8x4 − 12x3 + 16x is 4x(2x3 − 3x2 + 4). Option B

Algebraic expressions are described as mathematical expressions that are comprised of terms, variables, coefficients, factors and constants.

These algebraic expressions are also composed of mathematical or arithmetic operations, such as;

From the information given, we have that;

8x⁴ − 12x³ + 16x

Factor the common terms

4x(2x³ - 3x² + 8)

Hence, the expression is 4x(2x³ - 3x² + 8)

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y=x+1 and y=x-5 are the equations of the lines in the given graph.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Considering the two lines are parallel, they both have the same slope.

let m be the slope of the two lines:

y=mx+y₀

y=mx+y₁

y₀, y ₁ are the value on y axis where the two lines cross the axis.

Because the lines are parallel, there exists no point that lies on both lines, therefore the system has 0 solution.

Hence, y=x+1 and y=x-5 are the equations of the lines in the given graph.

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Answer:

9

Step-by-step explanation:

7 x (9 x 2) = (7 x 9) x 2  This is the associative property.

7 x ( 18) = (63) x 2

126 = 126

The probability of choosing 2 students who both play soccer from a class of 10 students, where 5 students play soccer, is 5/6 or 0.83.

The probability of choosing 2 students who both play soccer from a class of 10 students, where 5 students play soccer, can be calculated using the formula for combinations:

[tex]C(5,2) =\frac{5!}{(2! * (5-2)!)}[/tex]

           [tex]= \frac{10}{(2 * 3!)} \\ \\=\frac{10}{(2 * 6) } \\\\= \frac{5}{6}[/tex]

So, the probability of choosing 2 students who both play soccer is 5/6 or 0.83.

This means that if the teacher randomly selects 2 students from the class, there is an 83% chance that both of them play soccer.

In conclusion, the probability of choosing 2 students who both play soccer from a class of 10 students, where 5 students play soccer, is 5/6 or 0.83.

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Two non-functions could be (a,a) -> a and (a,b) -> a and (a,a) -> b and (a,b) -> b, meaning that both inputs can result in either a or b.

A set is a collection of distinct objects, which can be anything, such as numbers, letters, or even other sets.

The set-roster notation is a way to write a set by listing its elements inside curly brackets {}.

(a) To write the set (XXX) XY, we need to repeat the set X three times, which would be X = {a,a,a}.

Then we can join it with the set Y to form (XXX) XY = {a,a,a,a,b}.

(b) To find two functions and two non-function relations from X x Y to Y, we need to understand what a function and a relation are. A function is for every element in the domain (X x Y), there is exactly one corresponding element in the codomain (Y) where as a non-function, or a relation, is a set of ordered pairs where the same input can have different outputs.

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30 degrees Celsius in Fahrenheit is 86

What is 30 degrees Celsius in Fahrenheit?

      30ºC = 86ºF

calulation:

           T(ºF) = 30ºC × 9/5 + 32 = 86ºF

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Answer: 7, 7, 19, and 19

Recall that a rectangle has congruent parallel sides, meaning the sides opposite are equivalent in length. Therefore, 2 sides are both 12 cm longer than the other two sides. Let's write an equation:

Let x be the shorter side, and x + 12 be the longer side.

x + x + (x + 12) + (x + 12) = 52

Combine like terms.

4x + 24 = 52

4x = 28

x = 7

Therefore, the shorter sides are 7, and the longer sides are 19

The subscriber will pay $0.40 more if they pay using a credit card with a 27.999 APR instead of using cash.

Here are the steps to calculate the amount paid more when paying using a credit card instead of cash:

Take the annual percentage rate (APR) of 27.999 and divide it by 12 to get the monthly interest rate.

Multiply the monthly interest rate by the balance ($16.99) to get the monthly interest charge.

Add the monthly interest charge to the balance ($16.99).

This gives you the total amount paid after one month of interest charges.

Subtract the original balance ($16.99) from the total amount paid after one month of interest charges.

This gives you the amount paid more due to the interest charges.

The final answer would be the amount paid more, which is $0.40 in this case.

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a) Using the linear equation 68000 + 2000t, Alyssa would make a salary of $86,000 after 9 years of working for the company.

b) Based on the same linear equation, Alyssa's salary after t years would be 68000 + 2000t.

A linear equation is a mathematical equation written in the form of y=mx+b.

Linear equations involve a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The offered annual salary of Alyssa = $68,000

Annual salary raise = $2,000

The number of years Alyssa would work for the company = t years

The number of years Alyssa worked in the company = 9 years

68000 + 2000t

68000 + 2000(9)

68000 + 18000

= 86,000

= $86,000

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The total number of student that plotted the number of book they read is 18.

A dot blot the caption Book Read Over the Summer goes from 0 to 7. 0 ha 1 dot, 1 ha 3 dot, 2 ha 6, 3 ha 2, 4 ha 3, 5 ha 1 dot, 6 ha 2, and 7 ha 0 dot are the numbers. Using a dot plot

the total number of students who tracked how many books they read

add total dots  

1 dot + 3 dot +  6 dot +  2 dot + 3 dot +1 dot + 2 dot + 0 dot = 18.

The total number of student that plotted the number of book they read is 18.

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The equation Ax = b has a solution for each b in R4 if and only if the columns of A span R4.

The equation Ax = b is a linear equation that is commonly used in linear algebra. This equation is used to find the solution of a system of linear equations. The equation consists of a matrix A and a vector b.

Spanning refers to the ability of a set of vectors to generate all other vectors in a given space. If the columns of A span R4, then for each vector b in R4, there exists a unique solution x in R4 such that Ax = b.

On the other hand, if the columns of A do not span R4, then there are some vectors in R4 that cannot be generated by the columns of A and thus the equation Ax = b will not have a solution for each b in R4.

In conclusion, the set of vectors in the matrix A must be able to generate all other vectors in R4 for the equation to have a solution for each b in R4.

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s = {(-5, 7)} cannot be a basis for R^2 because it does not satisfy the three requirements of a basis: having at least two linearly independent vectors, containing only linearly independent vectors, and spanning the entire vector space.

The set s = {(-5, 7)} is not a basis for R^2 (the two-dimensional real vector space) for several reasons:

Cardinality: A basis for a vector space must contain at least two linearly independent vectors. Since s contains only one vector, it cannot be a basis for R^2, which has dimension 2.

Linear independence: A basis must contain linearly independent vectors. If a vector in the basis can be written as a linear combination of the other basis vectors, it is not linearly independent, and the set cannot be a basis.

Spanning: A basis must span the entire vector space, meaning that every vector in the vector space can be written as a linear combination of the basis vectors. The set s = {(-5, 7)} does not span R^2 because it contains only one vector, and not every vector in R^2 can be written as a scalar multiple of this vector.

Therefore, s = {(-5, 7)} cannot be a basis for R^2 because it does not satisfy the three requirements of a basis: having at least two linearly independent vectors, containing only linearly independent vectors, and spanning the entire vector space.

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The vector v with a magnitude of 9 and in the same direction as u = <18 / √29, 45 / √29>.

What is the vector?

A vector quantity has both a magnitude and a direction. Speed only has a magnitude, but no direction. Velocity has both.

Given a vector u = <2, 5>, the magnitude of the vector v that is in the same direction as u and has a magnitude of 9 can be found as follows:

Step 1: Find the unit vector in the direction of u

A unit vector in the direction of u can be found by dividing each component of u by its magnitude:

magnitude of u = √(2^2 + 5^2) = √(4 + 25) = √29

unit vector in the direction of u = u / magnitude of u = <2 / √29, 5 / √29> = <2 / √29, 5 / √29>

Step 2: Multiply the unit vector by the desired magnitude

To find the vector v with a magnitude of 9 and in the same direction as u, we can multiply the unit vector by 9:

v = magnitude * unit vector in the direction of u = 9 * <2 / √29, 5 / √29> = <18 / √29, 45 / √29>

Therefore, the vector v with a magnitude of 9 and in the same direction as u = <18 / √29, 45 / √29>.

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The only value of c that satisfies the initial condition g(2) = 5 is c = -3.

The graph of a function f consists of three line segments, with points (1,2), (2,3), and (3,4).

An antiderivative of f is a function g such that g'(x) = f(x). That is, g is the "opposite" of the derivative of f. The values of c in an antiderivative g(x) = f(x) + c are determined by the initial condition g(2) = 5, since g'(2) = f(2) = 3.

So, in order to determine the value of c, we need to integrate f(x) and find the value of g(2). The integral of f(x) is

g(x) = x² + 2x + c

Substituting x = 2 into this equation, we get

g(2) = 4 + 4 + c = 8 + c

Now, since g(2) = 5, we can solve for c:

5 = 8 + c

c = -3

Therefore, the only value of c that satisfies the initial condition g(2) = 5 is c = -3.

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For given functions, f(g(4)) = 2, f(f(8)) = ∛2 and f(g(x)) = ∛ ( x² - 8 ).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range and a co-domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In math, various function types exist. Among the crucial kinds are:

When there is a mapping for a range for each domain between two sets, this is known as an injective function or one to one function.

When more than one element is mapped from domain to range, the function is said to be surjective or to be an onto function.

a polynomial function is a function made by of polynomials

Now,

For functions f(x) = ∛ x and g(x) = x²-8

f(g(x)) = ∛ (x²-8)

f(f(x)) = ∛ ∛ x

g(f(x)) = ( ∛ x ) ² - 8

Therefore,

f(g(4))=∛4²-8= ∛16 - 8

= ∛8 = 2

f(f(8)) = ∛ ∛ 8 = ∛2

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Right function are

f(x)=∛x and g(x)=x^2-8

There are six orange marbles for every one green marble in the bag.

Step 1: Understand the question.

The question asks us to determine which statement must be true about a bag of colored marbles with a ratio of orange to green marbles of 6:1.

Step 2: Determine the ratio of orange to green marbles.

The ratio of orange to green marbles is 6:1, which means that for every one green marble, there are six orange marbles.

Step 3: Determine the statement that must be true.

Therefore, the statement that must be true about this bag of marbles is that there are six orange marbles for every one green marble in the bag.

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The geometric form known as a pentagon has five sides and five angles.

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The given coordinates make a right angled triangle.

Scaling is defined as the process of changing the dimensions of the original figure as per some specific proportional rule.

If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. Similarly, if the initial coordinates are (x, y) then after scaling the coordinates would be {Kx, Ky}.

Scale factor is a dimensionless quantity that tells by how much time a specific dimension of a figure is enlarged or reduced. Mathematically, it is the ratio of two similar quantities. In case of length scaling, we can write -

{K} = L{final}/L{initial}

Given are the coordinates of the triangle as -

P(-1, 3)

Q(9, - 1)

R(-3, - 2)

The distance formula is given as -

d² = (x₂ - x₁)² + (y₂ - y₁)²

PQ = 2√29

QR = √145

RP = √29

QR² = RP² + PQ²

145 = 29 x 4 + 29

145 = 145

Therefore, the given coordinates make a right angled triangle.

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Based on the graph, in year 4 there were 1.16 times more burglaries if compared to year 1.

Based on the graph, the number of burglaries these years was:

This shows a growing trend in the number of burglaries over the years.

number in year 4/ 1

255/220 = 1.159 which can be rounded to 1.16

Based on this, year 4 had 1.16 times more burglaries than year 1.

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Chloe is 31 years old while Tino is 17 years old.

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Let x represent Chloe present age and y represent Tino present age. Chloe and Tino have a combined age of 48. Hence:

x + y = 48     (1)

Also, Three years ago Chloe was double the age Tino, hence:

x - 3 = 2(y - 3)

x - 2y = -3    (2)

From both equations:

x = 31, y = 17

Chloe is 31 years old.

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(a) The future value is $18,971.06, which is closest to option D) $64,521.06

(b) So the present value of the estimated payments is $317,375, which is closest to option A) $350,623.10

(c) The present value of the savings is $25,620.51, which is closest to option C) $73,734.84

A) The future value of the deposits can be calculated using the formula for compound interest:

FV = PV * (1 + r/n)^(nt)

where

PV = $7,000

r = 12% = 0.12

n = 2 (compounded semiannually)

t = 5 years = 10 semiannual periods

Plugging in these values, we get:

FV = $7,000 * (1 + 0.12/2)^(2 * 10)

FV = $7,000 * (1.06)^20

FV = $7,000 * 2.667532622

FV = $18,971.06

B) The present value of the estimated payments can be calculated using the formula for the present value of an annuity:

PV = PMT * (1 - (1 + r)^(-n)) / r

where

PMT = $31,000

r = 8% = 0.08

n = 20 payments (from age 70 to 90)

Plugging in these values, we get:

PV = $31,000 * (1 - (1 + 0.08)^(-20)) / 0.08

PV = $31,000 * (1 - 0.170811153) / 0.08

PV = $31,000 * 0.83 / 0.08

PV = $31,000 * 10.375

PV = $317,375

C) The present value of the savings can be calculated using the formula for present value of a lump sum:

PV = FV / (1 + r/n)^(nt)

where

FV = $12,000 * 10 (total savings)

r = 10% = 0.1

n = 2 (compounded semiannually)

t = 10 years = 20 semiannual periods

Plugging in these values, we get:

PV = ($12,000 * 10) / (1 + 0.1/2)^(2 * 20)

PV = ($120,000) / (1.05)^40

PV = $120,000 / 4.68

PV = $25,620.51

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