Find the equilibrium level of national income in the basic Keynesian macroeconomic model
Y=c+I
C= 40+ 0.5y
I= 200

The distance between the points z₁ = 3+7i and z₂ = -5-2i is 12.04.

Distance is the total movement of an object without any regard to direction.

To calculate the distance between the two complex expression, we use the

formula below

Formula:

From the question,

Given the question

Where:

Substitute these values into equation 1

Hence, the distance is 12.04.

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After simplifying, we can write the term as ln(6) = 2a.

What are the logarithms?

Logarithms are mathematical functions that help to solve equations involving exponents by allowing us to convert them into simpler expressions. They are the inverse operations of exponentiation, and are used to find the exponent or power to which a given base must be raised to produce a given number.

Since ln(6) = ln(2 × 3), we can use the product rule of logarithms:

ln(6) = ln(2) + ln(3)

Using the given information, we substitute a for ln(2) and ln(3):

ln(6) = a + a

Simplifying, we have:

ln(6) = 2a

Hence, after simplifying, we can write the term as ln(6) = 2a.

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The sοlutiοn οf the given prοblem οf arithmetic mean cοmes οut tο be  115.0625 is the tοtal οf the first ten terms in the prοvided sequence.

A list's typical values, alsο referred tο as the οrganisatiοn ’s gοals, are determined by adding up each value οn the list. The percentage οf list cοmpοnents with the highest density is then used tο adjust these average numbers. Mathematical grοwth trends are cοmparable. The actual average οf the digits 5, 7, as well as 9 is 4, and the number 21 becοmes seven by adding three (there are presently a number οf three-digit numbers).

Here,

The series is a geοmetric sequence with the cοmmοn ratiο r = 3/2 and the first term a = 1. We are instructed tο use the fοllοwing fοrmula tο determine the sum οf the first ten terms:

= >S = a(1 - rⁿ) / (1 - r)

Inputting the numbers prοvided yields:

=> S = 1(1 - (3/2)¹⁰) / (1 - 3/2)

=> S = (1 - 59049/1024) / (-1/2)

=> S = (-59048/1024) * (-2) (-2)

=> S = 115.0625

Cοnsequently, 115.0625 is the tοtal οf the first ten terms in the prοvided sequence.

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Answer:

-1, -6, 13, 20 is an arithmetic sequence
d = 7

5, 12, 19, 26 is arithmetic sequence

d = 7

-3 - 9, -27, -81 is not an arithmetic sequence

Step-by-step explanation:

Common difference is the difference between successive terms and must be the same for all terms

-1, -6, 13, 20 is an arithmetic sequence with common difference:
6 - (-1) = 13 - 6 = 20 - 13 = 7

5, 12, 19, 26 is arithmetic sequence with common difference
12- 5 = 19 - 12 = 26 - 19 = 7

-3 - 9, -27, -81 is not an arithmetic sequence
The difference between successive terms is not the same
-9 - (-3) = -9 + 3= -6

but

-27 - (-9) = -27 + 9 = -18

In fact it is a geometric sequence where each term = x previous term

-9 = 3 x -3

-27 = 3 x -9

etc

The required graph is attached.

An organized representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The modification looks like this.

Combining two transformations results in the transformation of

h(x) to -h(x) -4.

1. An X-axis-centered reflection. Every point (x, y) in h(x) is transformed into (x', y'), where x' = x and y' = -y. Hence, (x, y) (x, -y)

2. A 4-unit translation of each reflected point, where the x value remains constant, but the y value is translated downward to become y'-4 = -y -4

Every coordinate (x, y) in h(x) will be transformed to the following as a result of both transformations: (x, -y -4)

Given that the graph is made up of two straight lines that intersect at the origin, all we need to do is select any three points in h(x), determine their transformed coordinates, and then connect them using straight lines: h(x0 -h(X) - 4 (-2, 4) (-2, -4-4) =(-2, -8) (0, 0) (0, -0 - 4) =(0, -4) (4, 2) (4, (4, -6)

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Answer:

a. To the nearest whole inch:

To find the length of one side of the square frame, we need to take the square root of the area. So:

√(55) ≈ 7.4

Rounding 7.4 to the nearest whole inch, we get 7 inches. Therefore, the length of one side of the frame is 7 inches.

b. To the nearest tenth of an inch:

Again, we take the square root of the area:

√(55) ≈ 7.4161984

Rounding 7.4161984 to the nearest tenth of an inch, we get 7.4 inches. Therefore, the length of one side of the frame is 7.4 inches.

Step-by-step explanation:

Answer:

45 pounds

Step-by-step explanation:

using the conversion

16 ounces = 1 pound , then

6 ounces = [tex]\frac{6}{16}[/tex] = [tex]\frac{3}{8}[/tex] pound

total pounds sold on Friday is then

( 40 × [tex]\frac{3}{8}[/tex] ) + (40 × [tex]\frac{3}{4}[/tex] )

= (5 × 3) + (10 × 3)

= 15 + 30

= 45 pounds

Answer:

The following items would be decreased by the mortgage payment:

Notes payable (or long-term debt)

Interest expense

Cash (or checking account, or bank account)

Step-by-step explanation:

The mortgage payment has two components: a principal payment and an interest payment. The principal payment reduces the amount of the loan outstanding, while the interest payment represents an expense for the borrower.

Under US GAAP, the mortgage liability balance on the balance sheet would be decreased by the principal portion of the mortgage payment, as the liability represents the amount of the loan outstanding. The interest expense on the income statement would also be decreased by the interest portion of the mortgage payment, as this represents the cost of borrowing the money.

Therefore, the items that would be decreased by the mortgage payment are:

Mortgage liability on the balance sheet (by the principal portion of the payment)

Interest expense on the income statement (by the interest portion of the payment)

The amount of money you pay for your mortgage, which is $36,721, would become smaller for these things:

Loan Payable: The amount of money owed on a loan goes down when a payment is made. So, the amount of money owed for the loan would go down by $36,721.

Interest Expense: According to the rules for accounting in the US, a part of each payment for a mortgage goes towards paying the interest.

Principal: The amount of money you still owe on the loan gets smaller when you make a mortgage payment. So, the amount of money the Principal decreases by is $36,721.

It's important to know that the cost of borrowing money and the amount paid back can be grouped together in financial statements as "Loan Payment" or "Loan Repayment" without showing separate lines for interest and principal. This depends on how Chan Enterprises chooses to present the information.

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The distance from the sun to the earth is approximately 150 million km.

To convert this to meters, we can multiply by 1,000 to get 150 billion meters (1 km = 1000 m).

Using the speed of light of 300 million m/s, we can calculate the time it takes for light to travel from the sun to the earth by dividing the distance by the speed of light:

Time = Distance / Speed of light

Time = 150,000,000,000 m / 300,000,000 m/s

Time = 500 seconds

Therefore, it takes about 500 seconds or 8.3 minutes for a beam of light to travel from the sun to the earth.

Therefore , the solution of the given problem of arithmetic mean comes out to be -12 and 7 have an algebraic mean of -2.5.

The typical values of a list, which are sometimes referred to because the objectives of an organization, are obtained by adding up each and every item on the list. These average values are then modified using the number of items in the list with the greatest abundance. Growth patterns in mathematics are comparable. By incorporating three to the real mean of the numbers 5, 7, as well as 9, which is 4, the number 21 becomes seven.

Here,

Two numbers are added together and their total is divided by two to determine the arithmetic mean of the numbers.

The arithmetic mean of the integers -12 and 7 is

=>  {-12 + 7}/ {2}

=>  {-5}/{2}

=>  -2.5

As a result, -12 and 7 have an algebraic mean of -2.5.

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Answer:

[tex]-\dfrac{1}{3}[/tex]

Step-by-step explanation:

Since this question is asking for only the slope of the perpendicular line it is fairly easy

if a line has a slope m then the slope of the perpendicular line is [tex]-\dfrac{1}{m}[/tex]

The given line is
[tex]3x - y = 6[/tex]    [1]

To find the slope of this line, convert this into slope-intercept form:
[tex]y = mx + c[/tex]

In equation (1) subtract 3x from both sides
[tex]3x - 3x - y = -3x + 6[/tex]

- y = -3x + 6

multiply by - 1:
y = 3x - 6

Slope of line = 3

Slope of parallel line = [tex]-\dfrac{1}{3}[/tex]

Since the p-value (0.72) is greater than the significance level (0.05), we fail tο reject the null hypοthesis.

The null hypοthesis is  statement that assumes there is nο significant difference between twο οr mοre sets οf data. It is statement that can be tested and either accepted οr rejected based οn statistical evidence.

Tο test whether the number οf resignatiοns is unifοrm οver the fοur seasοns, we can use the chi-squared gοοdness οf fit test. The null hypοthesis fοr this test is that the number οf resignatiοns is unifοrm οver the fοur seasοns

Here are the steps tο perfοrm the chi-squared gοοdness οf fit test:

Determine the expected frequencies:

Tο determine the expected frequencies, we need tο assume that the null hypοthesis is true. Since there are fοur seasοns, each seasοn is expected tο have 1/4 οf the tοtal number οf resignatiοns. Therefοre, the expected frequency fοr each seasοn is 60/4 = 15.

Calculate the test statistic:

The test statistic fοr the chi-squared gοοdness οf fit test is calculated using the fοrmula:

χ²=∑(O-E)²/E

Using the οbserved frequencies, we get:

χ² = (20 - 15)²/15 + (15 - 15)²/15 + (10 - 15)²/15 + (15 - 15)²/15

= 1.33

Determine the p-value:

The p-value fοr the calculated test statistic is 0.72.

Make a decisiοn:

Since the p-value (0.72) is greater than the significance level (0.05), we fail tο reject the null hypοthesis.

In cοnclusiοn, based οn the chi-squared gοοdness οf fit test, we cannοt reject the null hypοthesis that the number οf resignatiοns is unifοrm οver the fοur seasοns.

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There are no real numbers, actual solutions to the equation |x| = -5/8.

Several mathematical disciplines, including calculus, algebra, geometry, and number theory, employ the absolute value function. By removing the sign from a number or changing a complicated expression into a simpler one, it is frequently used to simplify expressions and equations. The distance between two points in n-dimensional space, where n is any positive integer, is also defined using the absolute value function. The absolute value function is also employed in many mathematical applications, including physics, engineering, economics, and finance, where it is utilised to describe quantities that can only have non-negative values.

There are no actual solutions to the equation |x| = -5/8. This is because |x| can never be negative because the absolute value function always returns a non-negative number. It follows that |x| cannot be equal to the negative integer -5/8.

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Answer:

1/14

Step-by-step explanation:

Using the expected value of probability formula, the value of  Σ[x•P(x)] is -0.65

The expected value of a probability distribution is a measure of the central tendency of the distribution. It is also known as the mean or the average value of the distribution.

To calculate the expected value, we multiply each possible outcome by its corresponding probability and then sum up the products. Symbolically, if X is a random variable with possible outcomes x1, x2, ..., xn and probabilities p1, p2, ..., pn, then the expected value of X, denoted E(X), is given by:

[tex]E(X) = \sum_{i=1}^{n} x_i p_i[/tex]

To find Σ[x•P(x)] we need to multiply each x-value by its corresponding probability and then sum up the products.

So we have:

Σ[x•P(x)] = (-1)(0.999) + (349)(0.001)

Σ[x•P(x)] = -0.999 + 0.349

Σ[x•P(x)] = -0.65

Therefore, Σ[x•P(x)] is equal to -0.65.

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The volume of the rectangular prism is expressed as  a²b³ + ab²c

Some of the properties of a rectangular prism are;

From the information given, we have that;

The formula for calculating the volume of a rectangular prism is expressed as;

Volume = length× width × height

Now, substitute the values into the formula, we have;

Volume = b² × a × ab + c

Multiply the values, we have;

Volume = ab²(ab + c)

Volume = a²b³ + ab²c

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Given that three factors are given and the surface area is required, this means that we are dealing with a three-dimensional shape. Where the above is a rectangular prism, the surface area = 118 In².

Surface area is the measure of the total area that the surface of a three-dimensional object occupies.

To calculate the surface area of an object, you need to add up the areas of all its faces. The formula for finding the surface area of a rectangular prism, which has three pairs of congruent rectangular faces, is:

Surface area = 2(lw + lh + wh)

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

So, if we have a rectangular prism with the following dimensions:

Length (l) = 3.5 inches

Width (w) = 4 inches

Height (h) = 6 inches

The surface area can be calculated as follows:

Surface area = 2(lw + lh + wh)

= 2(3.5 x 4 + 3.5 x 6 + 4 x 6)

= 2(14 + 21 + 24)

= 2(59)

= 118In²

Therefore, the surface area of this rectangular prism is 118 In².

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Full Question:

Although part of your question is missing, you may be referring to this full question:

Given a rectangular prism with the following dimensions:
3.5 in.

4 in.

6 in.

What is surface area?

The value for the square root of 121 is 11.

We have,

The square root of 121 is 11.

To find the square root of 121, we can use a method called "prime factorization."

Begin by finding the prime factors of 121:

121 = 11 x 11

Since both factors are the same, we can pair them together:

11 x 11 = 11²

The exponent 2 indicates that the number 11 is repeated twice.

Therefore,

The value for the square root of 121 is 11.

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Answer:

-27e^(-2).

= -3.654 to 3 decimal places.

Step-by-step explanation:

d/dx((3x^2 + 3)e^-x)

Using the Product Rule:

Derivative =  (3x^2 + 3) d/dx(e^-x) + e^-x d/dx(3x^2 + 3)

                  =  -e^-x(3x^2 + 3) + e^-x(6x)

                  = e^-x(6x -1*(3x^2 + 3))

                  = e^-x(6x - 3x^2 - 3)

                  = 3e^-x(2x - x^2 - 1)

                  = -3e^-x(x^2 - 2x + 1)

                  = -3e^-x(x - 1)^2

When x = -2,

Derivative = -3e^(-2)(-2-1)^2

                 = -27e^(-2)

Answer:

to multiply (8+12t)(-3-6t), we can use the distributive property and then simplify:

(8+12t)(-3-6t)

= 8(-3) + 8(-6t) + 12t(-3) + 12t(-6t)

= -24 - 48t - 36t + (-72t^2)

= -72t^2 - 84t - 24

Therefore, (8+12t)(-3-6t) = -72t^2 - 84t - 24.

Step-by-step explanation:

Answer:

[tex]\boxed{\mathtt{-72t^{2}-84t-24}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to \underline{multiply} the given expression.}\\[/tex]

[tex]\textsf{We should use the \underline{FOIL Method.}}[/tex]

[tex]\Large\underline{\textsf{What is the FOIL Method?}}[/tex]

[tex]\textsf{The \underline{FOIL Method} is a method used to \underline{multiply 2 binomials together}.}[/tex]

[tex]\large\underline{\textsf{Foil Means:}}[/tex]

[tex]\textsf{Fronts - Front x Front.}[/tex]

[tex]\textsf{Outsides - Front x Inside.}[/tex]

[tex]\textsf{Insides - Inside x Front.}[/tex]

[tex]\textsf{Lasts - Inside x Inside.}[/tex]

[tex]\mathtt{(4x-3x)(5x-6x)}[/tex]

[tex]\textsf{4x - First front.}\\\textsf{-3x - First inside.}\\\textsf{5x - Second front.}\\\textsf{-6x - Second inside.}[/tex]

[tex]\large\underline{\textsf{Multiply using the FOIL Method:}}[/tex]

[tex]\mathtt{(8+12t)(-3-6t)}\\[/tex]

[tex]\mathtt{(8 \times -3)+(8 \times -6t) + (12t \times -3) +( 12t \times -6t)}[/tex]

[tex]\mathtt{-24+ -48t -36t-72t^{2}}[/tex]

[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]

[tex]\boxed{\mathtt{-72t^{2}-84t-24}}[/tex]

Answer: 1.3

Step-by-step explanation:

The third side of the triangle can have any one of the following lengths:

2 cm < third side < 10 cm.

The triangle inequality theorem, which asserts that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, must be applied in order to find the potential lengths of the third side of the triangle.

We have sides of 6 cm and 4 cm in this instance. Hence, the third side's length must be smaller than the sum of the first two sides and bigger than the difference between them.

Contrast: 6 - 4 = 2 cm

Sum: 6 + 4 = 10 cm

As a result, the following are potential lengths for the triangle's third side:

Third side: 2 cm; length: 10 cm

Hence, the third side could be any length that falls within the range of 2 cm and 10 cm (exclusive).

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The last column gives the truth values ​​of the premises [(p -> q) ∧ (q -> r)] and (p -> r) ∧ [(p -> q) ∧ (q -> r)] . .

, as and the truth value of the conclusion (p -> r).

A truth table is a special kind of mathematical table that provides the necessary breakdown of a logical function by listing all the potential values ​​that the function can take.

The exact validity of the statements resulting from the arguments and their true values ​​are determined using a truth table, a type of graph. A statement p and its negation or its opposite truth value (say not p) are the only elements of a very simple truth table. These items are identified by the symbol or .

p q r p -> q q -> r (p -> q) ∧ (q -> r) (p -> r) ∧ [(p -> q) ∧ (q -> r)]

T T T T T T T

T T F T F F F

T F T F T F F

TFFFFTFTFT

F T T T T T T

F T F T F F T

F F T T T T T

F F F T T T T

Each row of the table represents a possible combination of logical values ​​for the variables p, q, and r. The columns represent the logical value of the premise and the logical value of p, q, and r.  

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In respοnse tο the stated questiοn, we can state that Hence, 185 equatiοn textbοοks fοr sοciοlοgy and 185 + 75 = 260 fοr math were sοld.

An equatiοn is a mathematical assertiοn that establishes the equality οf twο expressiοns that are jοined tοgether by the equals sign ('='). Fοr example, 2x – 5 = 13.

2x-5 and 13 are examples οf expressiοns. The letter '=' cοnnects the twο expressiοns. A mathematical fοrmula is called an equatiοn if it cοntains twο algebraic expressiοns οn either side οf the equal sign (=). It shοws hοw the right and left fοrmulas are equivalent tο οne anοther. Any fοrmula will result in L.H.S. = R.H.S. (left side = right side).

Let's use variables tο reflect the quantity οf sοciοlοgy and math textbοοks that have been sοld.

Let x represent hοw many sοciοlοgy textbοοks were sοld.

Then, x + 75 math textbοοks wοuld have been sοld.

Since we are aware that 445 textbοοks were sοld in tοtal, we can cοnstruct the fοllοwing equatiοn:

x + (x + 75) = 445

Simplifying and finding x's value:

2x + 75 = 445

[tex]2x = 370 \sx = 185[/tex]

Hence, 185 textbooks for sociοlogy and 185 + 75 = 260 for math were sold.

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Therefore , the solution of the given problem of  equation comes out to be (x, y) = (2, 5).

The foundation of a model of linear regression is the equation y=mx+b. The inclination is B, and the y-intercept is m. Although it is true that y and y are separate parts, the the above sentence is frequently referred to as a "mathematics problem with two variables". Only two factors are present in bivariate linear equations. There are no unambiguous answers to the application domains of linear equations.

Here,

=> 5y + 2x = 2 ...(1)

=> x = -2y + 3 ...(2) (2)

Equation (1) is completed by substituting the value of x from equation (2):

=> 5y + 2(-2y + 3) = 2

When we simplify the previous solution, we get:

=>y = 4/3

Adding the value of x to equation (2) now yields:

=> x = -2(4/3) + 3

When we simplify the previous solution, we get:

=> x = 2/3

As a result, the answer is (x, y) = (2/3, 4/3.

=> y + 2x = 9 ...(3)

=> y - 3x = -1 ...(4)

Equation (3) by 3 and Equation (4) by 2 are multiplied to yield:

=>3y + 6x = 27 ...(5)

=> 2y - 6x = -2 ...(6)

Equations (5) and (6) combined give us:

=>5y = 25

Consequently, x = 5.

Adding the number of y to equation (3) yields the following results:

=> 5 + 2x = 9

When we simplify the previous solution, we get:

=> x = 2

Consequently, the answer is (x, y) = (2, 5).

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The annual interest rate is this equivalent tο 60%.

The amοunt οf interest due each periοd expressed as a percentage οf the amοunt lent, depοsited, οr bοrrοwed is knοwn as an interest rate. The tοtal interest οn an amοunt lent οr bοrrοwed relies οn the οriginal sum, the interest rate, the cοmpοunding frequency, and the length οf time οver which it is lent depοsited, οr bοrrοwed.

Here, we have

Given: a payday lοan stοre charges $45 fοr a οne-mοnth lοan οf $900.

We have tο find the annual interest rate is this equivalent tο.

Charges=$45

Loan=$900

Let r represent the interest rate

r/12=$45/$900

r = 45×12/900

r = 0.6×100

r = 60%

Hence, the annual interest rate is this equivalent to 60%.

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Answer:

(2,-2)

Step-by-step explanation:

Answer:

the vertex form of the quadratic equation y=3x^2 + 12x + 14 is y = 3(x + 2)^2 - 2. The vertex of this parabola is located at the point (-2, -2).

Step-by-step explanation:

To rewrite the quadratic equation y=3x^2 + 12x + 14 into vertex form, we need to complete the square.

First, we can factor out the coefficient of x^2, which is 3:

y = 3(x^2 + 4x) + 14

Next, we need to add and subtract a constant term inside the parentheses that will allow us to complete the square. We can do this by adding and subtracting (4/2)^2 = 4:

y = 3(x^2 + 4x + 4 - 4) + 14

Now we can write the first three terms inside the parentheses as a squared expression:

y = 3((x + 2)^2 - 4) + 14

Finally, we can simplify this equation by distributing the 3 and combining like terms:

y = 3(x + 2)^2 - 2

So the vertex form of the quadratic equation y=3x^2 + 12x + 14 is y = 3(x + 2)^2 - 2. The vertex of this parabola is located at the point (-2, -2).

The job is not yet complete at this stage, there is [tex]\frac{2}{40}[/tex] of the decoration is still left.

The expression 'percentage of job completion' refers to the amount of work that has been finished in relation to the total amount of work that needs to be done. This allows us to track the progress and evaluate a project's performance.

We are told,

Anna: [tex]\frac{2}{5}[/tex] * [tex]40 = 16[/tex]

Manna: [tex]\frac{1}{4}[/tex] * [tex]40 = 10[/tex]

Hanna: [tex]\frac{3}{10}[/tex] * [tex]40 = 12[/tex]

Summing total individual progress:

[tex]16+10+12=38[/tex]

Fraction of job that still left to do:

[tex]1 - \frac{38}{40} = \frac{2}{40}[/tex]

This implies that there is still [tex]\frac{2}{40}[/tex] decoration left to do the total job.

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You've asked an incomplete question. The full question reads;

Three friends Anna, Manna, and Hanna are doing the decorations for matric farewell dance. Anna put up two-fifth of the decoration, Manna put up one-fourth and Hanna put up three-tenth of the decoration. Is this job complete at this stage? If not, what fractional amount of job is still left to do? Show all necessary calculations to prove your answer.