How do you use the definition of continuity and the properties of limits to show that the function h(t) = (2t-3t^2)/(1+t^3) is continuous at the given number a=1?

The overall balance after 2 years on the account after taxes have been paid is 40.00.

The formula for simple interest is:

I=P*T*R

where P is the principal amount of money, R is the interest rate as a decimal, and T is the time.

We know the principal amount is 2000, the interest rate is 5%, and the time is 2 years.

We must convert the interest rate to a decimal.

Divide by 100 or move the decimal place to two spots to the left.

6/100=0.05 or 5.0 --> 0.5 --> 0.05

Now we know all the values.

P=2000

T=2

R=0.05

Substitute the values into the simple interest formula.

I=2000*2*0.05

Multiply.

I=2000*0.1

I=200

The simple interest is 200.00

Now, every year must also pay 20% income tax on the interest earned annually, for that we have to subtract 20% in simple interest.

overall balance =200*20/100

overall balance=40.

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Answer:3

Step-by-step explanation:

Answer: Jimmy has 3 apples left.

Step-by-step explanation: 5-2=3

-1 = 4

-2 = 3

If x = 4, y = 5, z = 1/2 , then

(a) It will take 3 minutes  to secure door ,

(b) It will take 56 minutes to complete system check ,

(c) It will take 44 minutes to fill pantry with astronaut food .

The values of x , y and z are x = 4, y = 5, z = 1/2 ;  

Part(a) ;

The Number of minutes to secure door is calculated the by expression

⇒ 7x - 5y .

Substituting values as x = 4 and y = 5 ,

we get ;

⇒ 7(4) - 5(5) = 28 - 25 = 3 minutes .

Part(b) ;

The Number of minutes to fill pantry with astronaut food is calculated the by expression :

⇒ 12z + 2y² ,

Substituting values as z = 1/2 and y = 5 ,

we get ;

⇒ 12z + 2y² = 12(1/2) + 2(5)² = 6 + 2×25 = 6 + 50 = 56 minutes .

Part(c) ;

The Number of minutes to complete system check is calculated the by expression

⇒ 2xy + 8z ,

Substituting values as x = 4 , z = 1/2 and y = 5 ,

we get ;

⇒ 2xy + 8z = 2(4)(5) + 8(1/2) = 40 + 4 = 44 minutes .

The given question is incomplete , the complete question is

Evaluate the following expressions to help the astronauts prepare for take off. These numbers will help calculate the amount of time it will take to prepare for take off.

In this case x = 4, y = 5, z = 1/2 ;  

(a) Number of minutes to secure door is found by expression ⇒ 7x - 5y .

(b) Number of minutes to complete system check is found by expression ⇒ 12z + 2y² ,

(c) Number of minutes to fill pantry with astronaut food is found by expression ⇒ 2xy + 8z .

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The given function is continually increasing at an interval (3, ∞)

An interval is a set of (real) numbers with the property that for every pair of numbers y and z that it contains, it contains also every number between y and z.

Given that, a function f(x) = 2/3|x - 3| + 2

Plot the graph for the function. we get that, the graph is continuously decreasing from ∞ to -3 and continuously  increasing in 3 to ∞

Hence, the given function is continually increasing at an interval (3, ∞)

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Greta’s capital allocation is 0.37 for the S& P 500 and whereas  for the  hedge fund the captial allocation is  0.63. it is done using the  Capital Allocation formula.

The calculation was done using the Capital Allocation formula, which is Risk Aversion multiplied by Risk Premium divided by the sum of the squared standard deviations of the two portfolios plus the correlation between the two portfolios multiplied by the standard deviation of portfolio 1 times the standard deviation of portfolio 2.

for  S& P 500 : Capital Allocation = Risk Aversion x Risk Premium / (SD^2 + (Correlation x SD1 x SD2)) = 3 x 5.6% / (20.6^2 + (0.3 x 20.6 x 35.6)) = 0.37 .

whereas Hedge Fund: Capital Allocation = Risk Aversion x Risk Premium / (SD^2 + (Correlation x SD1 x SD2)) = 3 x 10.6% / (35.6^2 + (0.3 x 20.6 x 35.6)) = 0.63

The Risk Aversion was given as 3, the Risk Premiums of the S& P 500 and the Hedge Fund were given as 5.6% and 10.6% respectively, and the standard deviations of the S& P 500 and the Hedge Fund were given as 20.6% and 35.6% respectively. The correlation between the two portfolios was given as 0.3. The calculation yielded a capital allocation of 0.37 for the S& P 500 and 0.63 for the Hedge Fund.

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Answer:

1/12

Step-by-step explanation:

An hour consists of 60 minutes and 5 minutes would be 1/12 of an hour.

5 minutes / 60 minutes

divide both sides by 5

1/12 of an hour

Answer:

x = +4 , -4

Step-by-step explanation:

    x² - 16 = 0

           x² = 16

           [tex]\sf x = \sqrt{16}\\\\x = \sqrt{4*4}\\\\[/tex]

          x = ±4

Answer: NOT Parallel because 98 /= 82  (Alternate angles are equal)

Answer:

it should be

Step-by-step explanation:

no.c half - open

The factorized expressions are (4x - 1)(4x + 5), (2z - 7)(z + 10) and (3x - 8)(2x + 5)

The pair factors of -80 are (-1, 80), (-2, 40), (-4, 20), (-5, 16) and (-8, 10).

The pair factors of -80 in this category is

(-4, 20)

This is so because

-4 + 20 = 16

We have

16x^2 + 16x - 5

So, we have

16x^2 + 20x - 4x - 5

Factorize

4x(4x + 5) -1(4x + 5)

So, we have

(4x - 1)(4x + 5)

For the other expressions, we have

2z^2 + 13z - 70

2z^2 + 20z -7z - 70

So, we have

(2z - 7)(z + 10)

6x^2 - x - 40

6x^2 + 15x -16x - 40

So, we have

(3x - 8)(2x + 5)

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1) Note the line of best fit is indicated in the attached graph.

2) Based on the line, the total score (on the y-axis) for the person who didn't study for the test (that is whose hours of homework are zero) is 38.

3) The y-intercept of the line of best fit in graph two is 8

4) The slope of the line of best fit for the scatter plot in graph 2 is -1/2

5) the equation of the line of best fit is given as y = -0.5x + 8

A straight line with the best fit is one that minimizes the distance between it and certain data. In a scatter plot of multiple data points, the line of best fit is used to express a connection.

It is a result of regression analysis and may be used to forecast indicators and price changes.

Note that most of the answers above are self-explanatory.

1) When drawing a line of best fit, you try to keep the line in such a way that it captures as many points as possible while balancing the number of points to the left and to the right of the line as much as possible.

2) Note that the person who didn't study is the person with zero hours of homework. Thus identifying the corresponding grade

3) to determine the y-intercept, just look at the point on the y-axis where the line is touching. The total score that corresponds with zero on the y-axis is 38.

4) the formula for slope is ΔY/ΔX

Since we have the two corresponding points each on the y-axis and on the x-axis, that is:

X1 = 0

X2 = 2

Y1 = 8

Y2 = 7

ΔX = 2 – 0 = 2

ΔY = 7 – 8 = -1

Thus,

Slope (m) = ΔY/ΔX

= -1/2

=-0.5

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There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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According to the formula of area of rectangle, the dimensions of the rectangle is 3.6 x 18

The term called area of rectangle is calculated by using the formula

=> A = l x w

where l refers the length of rectangle and w refers the width of the rectangle.

Here we have know that the area of the rectangle is 66 square inches.

And let us consider that W refers the width of rectangle and here we know that the length is 5 inches longer than it is wide so it can be written as 5W.

Then the dimensions of the rectangle is calculated as,

=> 66 = (W x 5W)

=> 66 = 5 W²

=> W² = 13.2

=> W = 3.6

Then the value of length is calculated as,

=> L = 5 x 3.6

=> L = 18

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Answer: 2.4 x 10^-2

Step-by-step explanation:

6 x 4 = 24 (you can do this because powers are the same)
24 x 10^-3
2.4 x 10^-2

X intercept is none , y intercept is (0,1)

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

the distance from the origin to a point where a graph crosses a coordinate axis. : interception.

The x- and y-intercepts of a line, or linear equation intercepts, are often used in problems involving lines and their graphs. Linear equation intercepts are important points to be able to understand and decipher in applications of linear equations problems and can also be used when graphing lines.

f(x)=x^2+1=0

so the x intercept is none and y intercept is (0,1)

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Answer:

#1 is 2.56

#2 is 2374.32

#3 is 19

#4 is 2,007.62

Step-by-step explanation:

3.2 x 0.8 = 2.56

Solve 22.83 x 104 =2374.32

The aquarium in Key West has a display of 486 fish. How many fish would be in 25 displays=12150

542.6 x 3.7 =2007.62

6,325 x 48 =303600

Answer: The game piece is a right trapezoid and its area can be calculated by using the formula:

Area = (b1 + b2) * h / 2

Where b1 and b2 are the lengths of the bases (the parallel sides of the trapezoid) and h is the height.

We can use the information given to find the area of the game piece:

A square with sides measuring 3 inches is attached to a triangle, giving a total combined length on one side of 10 inches.

So, the length of the base of the triangle is 7 inches (10 inches - 3 inches) and the height of the trapezoid is 3 inches.

Now we can substitute these values into the formula:

Area = (3 + 7) * 3 / 2

Area = 10 * 3 / 2

Area = 15 in²

So the area of the game piece is 15 square inches.

Step-by-step explanation:

20 : 7 is already the simplest term and  there is no need to further simplify.

Ratio can be defined as the given value divided by total value.

When presenting a ratio as an answer:

1. It has to be in the form of integer, it cannot be in the form of fraction or decimals

2. There should be of the equivalent units.

3. It must be in its simplest form

Convert the units in cm

Coloured Fabric = 70 mm

Coloured Fabric = 70 ÷ 10 cm

Coloured Fabric = 7 cm

Find the ratio of the Colour Fabric to White Fabric:

Coloured Fabric = 7 cm

White Fabric = 20 cm

Ratio of  White Fabric : Colour Fabric = 20 cm : 7 cm

Ratio of  White Fabric : Colour Fabric = 20 : 7

Therefore, 20 : 7 is already the simplest term and  there is no need to further simplify.

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The integer that makes the sentence true is -200

From the question, we have the following parameters that can be used in our computation:

50 - 250

The above expression is not a division sentence

Instead, it is a subtraction sentence

using the above as a guide, we have the following:

50 - 250

Evaluate the difference in the sentence above

50 - 250 = -200

Hence, the integer is -200

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Answer:

Solution:

Let another number be x.

Then positive number = 5x

According to the question,

5

�

+

21

=

2

(

�

+

21

)

5x+21=2(x+21)

⇒

5

�

+

21

=

2

�

+

42

⇒5x+21=2x+42

⇒

5

�

−

2

�

=

42

−

21

⇒5x−2x=42−21

⇒

3

�

=

21

⇒3x=21

⇒

�

=

21

3

=

7

⇒x=

3

21

​

=7

Hence another number = 7 and positive number = 7 x 5 = 35.

The number of years it would take for $1500 to earn $350 will be 5.43 years.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

The amount of $1500 is invested to earn $350 in simple interest at a rate of 4.3%.

Then the number of years is given as,

350 = (1500 x 4.3 x T) / 100

350 = 15 x 4.3 x T

64.5T = 350

T = 5.43 years

The number of years it would take for $1500 to earn $350 will be 5.43 years.

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The inverse function takes the output of the original function and gives the input that would produce that output.

In mathematics, the inverse function (f^-1) of a function f(x) is a function that "undoes" the action of the original function. The relationship between a function f(x) and its inverse function f^-1(y) is such that if f(x) = y, then f^-1(y) = x. In other words, the inverse function takes the output of the original function and gives the input that would produce that output.

It's important to note that not all functions have inverse functions, a function may not have an inverse if it's not one-to-one function, that is, if it's output has more than one input that produces it.

Correct Question :

How does each inverse function  f^(-1)y  relate to its original function? Describe the relationship in terms of the context for each situation.

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The number of years until the town will have 100 students is given as follows:

22.68 years.

A decaying exponential function is modeled as follows:

y = a(1 - r)^x.

In which:

The parameter values for this problem are given as follows:

a = 320, r = 0.05.

Hence the function is given as follows:

y = 320(0.95)^x.

The time it will take for the population to have 100 students is x when y = 100, hence:

100 = 320(0.95)^x

(0.95)^x = 100/320

(0.95)^x = 0.3125

x log(0.95) = log(0.3125)

x = log(0.3125)/log(0.95)

x = 22.68 years.

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The comparable word in Bryan's pattern is 28 whereas the number in Liam's pattern is 49.

The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the. sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d

Given this, we must first determine what is the position of 49 in Liam's pattern. Since Liam's pattern starts at 7 and increases by 7 each time, we can say that

d = 7

a₁ = 7

Substituting these values, we will get

49 = 7 + (n - 1) * 7

49 = 7 + 7n - 7

49 = 7n

n = 7

we are asked what is the corresponding term in Bryan's pattern when the number in Liam's pattern is 49. Since 49 is the 7th term in Liam's pattern, we need to find the 7th term in Bryan's pattern. As stated in the problem, Bryan's pattern starts at 4 and increases by 4 each time. This means that

d = 4

a₁ = 4 n = 7

Substituting these values, we will get

a₇= 4 + (7 - 1) * 4

a₇ = 4 + (6) * 4

a₇ = 4 + 24

a₇ = 28

Therefore, when the number in Liam's pattern is 49, the corresponding term in Bryan's pattern is 28.

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The percentage change is by 30% and it indicates percentage increase due to increase in new quantity.

The percent change will be calculated using the formula -

Percentage change = difference in quantity ÷ original quantity × 100

Difference in quantity will further be expressed by the formula -

Difference in quantity = New quantity - original quantity

Keep the values in formula for calculation. Firstly finding the difference in quantity.

Difference in quantity = 39 - 30

Performing subtraction

Difference in quantity = $9

Percentage change = 9/30×100

Performing division and cancelling zero

Percentage change = 30%

The mentioned scenario represents percentage increase.

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The answer is [tex]\frac{55}{96}[/tex] .

If A, B, and C  are three dependent events,

P(A∩ B∩C) =P(A). P(A|B) .P(C|A∩B)

Let us use your birthday as a starting point.

Let A be the first friend who has a different birth month than you. Let B be the second friend who has a different birth month than friend 1  and you

Let C be the third friend who has a different birth month than friend 1, friend 2, and you

there are 12 months in a year

P(A∩ B∩C) =P(A). P(A|B) .P(C|A∩B)

P(A∩ B∩C)  [tex]= \frac{11}{12} .\frac{10}{12} .\frac{9}{12}[/tex]

P(A∩ B∩C) [tex]= \frac{990}{1728} =\frac{55}{96}[/tex]

So, the result is [tex]\frac{55}{96}[/tex] .

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The correct statements to the given polynomials are  x²-5, x³, x⁴+3x+6, 1,x+2

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given; To find a polynomial for each of the example.

A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients). You call an expression with a single term a monomial, an expression with two terms is a binomial, and an expression with three terms is a trinomial. An expression with more than three terms is named simply by its number of terms.

Thus we have the examples to the required polynomial accordingly:

1. A binomial of degree 2 is : x²-5

2. A monomial of degree 3 is: x³

3. A trinomial of degree 4 is: x⁴+3x+6

4. A monomial of degree 0 is: 1

5. A binomial of degree 1 is: x+2

Hence, The examples are x²-5, x³, x⁴+3x+6, 1,x+2

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[tex]1\frac{5}{12}[/tex] liter of water Gabriella drink altogether.

A fraction represents a part of a whole.

Gabriella drank 2/3L water before jog

Gabriella drank 3/4L water after her jog

Altogether water she drank (2/3+3/4)

2/3+3/4

LCM of 3 and  4 is 12

8+9/12

17/12

17/12 can be written as mixed fraction [tex]1\frac{5}{12}[/tex].

Hence,  [tex]1\frac{5}{12}[/tex] liter of water Gabriella drink altogether.

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Answer: I don't know

Step-by-step explanation: good luck

Answer:

A. 3/4

Step-by-step explanation:

[tex]\frac{8}{1}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{24}{4}[/tex] = 6

6 is less than 8