At the store, 60% of the customers are parents and 40% of the customers are not. The average age of the parents is 52 years old. The average age of those not parents is 20 years old.

Thus, the area of the given trapezium is found toe be 37.8 sq. cm.

A trapezium is a quadrilateral in two dimensions with one pair of parallel sides. The non-parallel sides of a trapezium are referred to as the trapezium's "legs," while the parallel sides are referred to as its "bases." The length of the legs or the measuring of their angles are used to categorise trapeziums.

Given data:

area of trapezium = 1/2(sum of parallel side) * height

area  of trapezium = 1/2(PQ + CR)*PA

area  of trapezium = 1/2*(3.15 + 6.3)*8

area  of trapezium = 1/2*(9.45)*8

area  of trapezium = 37.8 sq. cm

Thus, the area of the given trapezium is found toe be 37.8 sq. cm.

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Answer:

  (a) ±{1, 2, 5, 10}

  (b) attached

  (c) {-2, -1, 5}

  (d) P(x) = (x +2)(x +1)(x -5)

Step-by-step explanation:

You want the possible and actual rational zeros for P(x) = x^3-2x^2-13x-10, and the factored form of the polynomial.

The rational root theorem tells you the possible rational zeros of a polynomial will be of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

The leading coefficient is 1, and the divisors of the constant are {1, 2, 5, 10}, so the possible rational zeros are ...

  {±1, ±2, ±5, ±10}

The attached graph shows the actual zeros of P(x) to be {-2, -1, 5}.

Each zero q corresponds to a factor (x -q). The factored form of the polynomial is ...

  P(x) = (x +2)(x +1)(x -5)

Answer:

24 + c = 40

C= Chau’s height

Let's call the amount of money Andy has "x".

According to the problem, Kelly has 7 pence more than Andy, so Kelly has x + 7 pence.

Georgia has a penny less than Andy, so Georgia has x - 1 pence.

The total amount of money they have is 1.48, which we can write as 148 pence.

So we can set up the equation:

x + (x + 7) + (x - 1) = 148

Simplifying and solving for x:

3x + 6 = 148

3x = 142

x = 47.33

Since we're dealing with pence, we'll round down to the nearest whole number:

x = 47

So Andy has 47 pence, Kelly has 54 pence (47 + 7), and Georgia has 46 pence (47 - 1).

Therefore , the solution of the given problem of expression comes out to be 6.5 is the abbreviated numerical expression.

Shifting numbers, which can be expanding, variable diminishing, or blocking, should be used instead of random estimations. Only through exchanging goods like tools, expertise, or answers to problems could they assist one another. The explanation on the reality equation may include the justifications, elements, or mathematical claims for tactics like increased argumentation, falsification, and blending.

Here,

The mathematical expression is expressed as follows:

=> 42 / 7 + (3 / 6)

We can use the division operations to make the expression simpler:

=> 7 /42 = 6

=> 6 / 3 = 0.5.

The statement is thus more easily expressed as follows:

=> 6 + 0.5

When we add the two numbers, we get:

=> 6.5

Therefore, 6.5 is the abbreviated numerical expression.

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The complete question is " Write and simplify this numerical expression. Forty-two divided by seven plus the quantity three divided by six"

according to the question, the PLUS Loan will have a higher balance due at the time of repayment by $233.80 ($11,966.11 - $11,732.31).

Divide the principal times the interest rates, the length of time, and various other factors to arrive at simple interest. Simple return = principle + interest + hours is the marketing formula. The easiest way to compute interest is with this method. The most typical technique to figure out interest is to use a portion of the principal sum. He is only going to pay his share of the 100% interest, for example, if he loans $100 form a friend then agrees to pay it off with 5% interest. $100 (0.05) corresponds to $5. Interest must be paid as you borrow money and must be added to any loans you make. Interest is often determined as a yearly proportion of the loan total. The interest on the loan is this percentage.

given,

To compare the two loans, we need to calculate the total balance due for each loan at the time of repayment. We can start by calculating the balance due for the Unsubsidized Stafford Loan:

Principal: $10,720

Interest rate: 5.95% per year, compounded monthly

Time: 6 months grace period + 6 months repayment = 1 year

Number of periods: 12 months x 1/12 month per period = 12 periods

Using the formula for compound interest, the balance due on the Unsubsidized Stafford Loan after 1 year is:

B = P(1 + r/n)^(nt) + I [(1 + r/n)^(nt) - 1]/(r/n)

where B is the balance due, P is the principal, r is the annual interest rate, n is the number of times per year the interest is compounded, t is the time in years, and I is the monthly payment.

Plugging in the numbers, we get:

B = $10,720(1 + 0.0595/12)^(121) + $0 [(1 + 0.0595/12)^(121) - 1]/(0.0595/12)

B = $11,732.31

Now, let's calculate the balance due for the PLUS Loan:

Principal: $11,443.63

Interest rate: 6.55% per year, compounded monthly

Time: 6 months repayment

Number of periods: 6 periods

Using the same formula for compound interest, the balance due on the PLUS Loan after 6 months is:

B = $11,443.63(1 + 0.0655/12)^(120.5) + $0 [(1 + 0.0655/12)^(120.5) - 1]/(0.0655/12)

B = $11,966.11

Therefore, the PLUS Loan will have a higher balance due at the time of repayment by $233.80 ($11,966.11 - $11,732.31). Thus, the Unsubsidized Stafford Loan will have a lower balance due at the time of repayment compared to the PLUS Loan.

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The answer of the given question based on the graph coordinate is , the rule for the values in the table is: Y = 7X - 0.

In mathematics, a coordinate is a set of values that specifies the position of a point in space. Coordinates are used to locate points, lines, and other geometric objects in a plane, a three-dimensional space, or even higher dimensions.

X    Y

5    35

1     7

4    28

2    14

One possible way to do this is to calculate the differences between successive pairs of X and Y values, and then see if there is a constant difference or ratio between them.

Taking the first two rows as an example, we have:

X Y

5 35

1 7

The difference between the X values is 5 - 1 = 4, and the difference between the Y values is 35 - 7 = 28. Dividing the difference in Y by the difference in X gives us:

(35 - 7) / (5 - 1) = 28 / 4 = 7

This means that for every increase of 1 in X, the corresponding increase in Y is 7. We can check this for the other pairs of values in the table and see that it holds true:

X Y

5 35

4 28 (decrease of 1 in X, decrease of 7 in Y)

2 14 (decrease of 2 in X, decrease of 14 in Y)

So the rule for the values in the table is:

Y = 7X - 0.

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The measure of arc angle QT is determined as 142 ⁰.

The measure of m∠STR is determined as 23⁰.

The measure of angle subtended by the arc QT is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠QST = ¹/₂( arc QT )

arc QT = 2 (m∠QST)

arc QT = 2 x 71⁰

arc QT = 142⁰

m∠STR = ¹/₂( arc SR )

m∠STR = ¹/₂ x 46⁰

m∠STR = 23⁰

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The surface area of the pyramid is 64 square feet.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To find the surface area of the pyramid, we need to find the area of each face and add them together.

First, let's find the area of the base, which is a square with side length 4 feet:

Area of base = 4 feet x 4 feet = 16 square feet

Next, we need to find the area of each triangular face. We know that the height of each triangular face is 6 feet, and the base of each triangular face is one of the sides of the square base, which is 4 feet. To find the area of a triangle, we use the formula:

Area of triangle = 1/2 x base x height

Area of each triangular face = 1/2 x 4 feet x 6 feet = 12 square feet

There are 4 triangular faces, so the total area of all the triangular faces is:

Total area of triangular faces = 4 x 12 square feet = 48 square feet

Now we can find the total surface area by adding the area of the base and the area of the triangular faces:

Total surface area = area of base + area of triangular faces

Total surface area = 16 square feet + 48 square feet

Total surface area = 64 square feet

Therefore, the surface area of the pyramid is 64 square feet.

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To find the LCM of 24 and 6, we can use the prime factorization method.

First, we find the prime factorization of each number:

24 = 2 x 2 x 2 x 3

6 = 2 x 3

Then, we identify the highest power of each prime factor that appears in either number.

The prime factor 2 appears three times in 24, but only once in 6. Therefore, we take the highest power of 2, which is 2 x 2 x 2 = 8.

The prime factor 3 appears once in both numbers, so we take the highest power of 3, which is 3.

Finally, we multiply these together to get the LCM:

LCM(24, 6) = 8 x 3 = 24

Therefore, the LCM of 24 and 6 is 24.

~~~Harsha~~~

Answer: LCM of  24 and 6 is 24

Step-by-step explanation:

To the right of 1.61, 9.24, and 15.09, the area under the X² curve with five degrees of freedom is 0.078, 0.0001, and 0, respectively.

A surface's area can be measured in two dimensions by multiplying its length by its breadth. It is employed to determine the size of a room or a plot of land. The size of a shape, like a circle or a square, can also be determined using area. Area is frequently expressed in square metres or square feet.

Here in the question,

(a)1.61

The following formula can be used to determine the area under the 1.61-degree curve with five degrees of freedom to the right:

Area = 1 - Φ(x; df)

Where df stands for the degrees of freedom and (x; df) is the cumulative distribution function of the chi-square distribution.

For df = 5, Φ(1.61; 5) = 0.922.

As a result, 1 - 0.922 = 0.078 represents the area under the 1.61-degree curve with 5 degrees of freedom to the right.

(b) 9.24

For df = 5, Φ(9.24; 5) = 0.9999.

As a result, 1 - 0.9999 = 0.0001 is the value of the area under the X² curve with 5 degrees of freedom to the right of 9.24.

(c) 15.09

For df = 5, Φ(15.09; 5) = 1.

As a result, 1 - 1 = 0 represents the area under the 15.09-based X² curve with 5 degrees of freedom to the right.

The area under the X² curve with five degrees of freedom to the right of 1.61, 9.24, and 15.09, respectively, is 0.078, 0.0001, and 0.

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1. The solution set can be written as:

{x = [t, s, (3/2)t + (3/2)s] : t, s ∈ R}

2. The solution set can be written as:

{x = [t, s, (3/2)t + (3/2)s - 3] : t, s ∈ R}

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

To find the solution set in parametric vector form for the equation x₁ + 3x₂ - 2x₃ = 0, we can write:

x₁ = t      (arbitrarily setting x1 = t)

x₂ = s

x₃ = (3/2)t + (3/2)s

where t and s are arbitrary parameters.

Therefore, the solution set can be written as:

{x = [t, s, (3/2)t + (3/2)s] : t, s ∈ R}

This is a set of infinitely many vectors that lie on a plane in three-dimensional space.

Part 2

For the equation x₁ + 3x₂ - 2x₃ = -6, we can rewrite it as x₁ + 3x₂ - 2x₃ = 0 - 6, which is of the same form as the equation in Part 1, but with a constant on the right-hand side.

Using the same method as in Part 1, we can find the solution set as:

x₁ = t

x₂ = s

x₃ = (3/2)t + (3/2)s - 3

where t and s are arbitrary parameters.

Therefore, the solution set can be written as:

{x = [t, s, (3/2)t + (3/2)s - 3] : t, s ∈ R}

This is also a set of infinitely many vectors that lie on a different plane in three-dimensional space.

Comparing the two solution sets, we can see that they are both sets of infinitely many vectors and have a similar form (parametric vector form). However, they lie on different planes in three-dimensional space, and the second set is shifted downward by 3 units along the third axis.

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Answer:

C. 84.8 m

Step-by-step explanation:

Circumference of circle = D x 3.14

D = 27 m

Let's solve

27 x 3.14 = 84.78 m

So, the circumference of the circle is C. 84.8 m

Answer:

Option C) 84.8 is the correct answer.

Step-by-step explanation:

Here we have given that the diameter of circle is 27 m and we have to find the circumference of circle. The formula to find circumference of circle is :

[tex]\dashrightarrow\sf{C = \pi d}[/tex]

Where :

Thus, finding the circumference of circle by substituting the given values in the formula :

[tex]\dashrightarrow\sf{C = \pi d}[/tex]

[tex]\dashrightarrow\sf{C = \pi \times d}[/tex]

[tex]\dashrightarrow\sf{C = 3.14 \times 27}[/tex]

[tex]\dashrightarrow\sf{C = 84.78 \: m}[/tex]

[tex]\dashrightarrow\sf{C \approx 84.8\: m}[/tex]

Hence, the circumference of circle is 84.8 m.

The scale factor of the dilation is 48.

The scale factor is a mathematical concept that describes the ratio of the lengths, areas, or volumes of two similar geometric figures. Similar figures have the same shape but may have different sizes.

When one figure is a dilation (a type of transformation that changes the size of a figure without changing its shape) of another figure, the scale factor is the ratio of the corresponding side lengths or dimensions of the two figures.

The scale factor of the dilation is the ratio of the length of the image to the length of the original object. In this case, the length of the image is 12 millimeters and the length of the original object is 0.25 millimeters. Therefore, the scale factor is:

scale factor = length of image/length of the original object

scale factor = 12 mm / 0.25 mm

scale factor = 48

So the scale factor of the dilation is 48.

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The length of the missing diagonal is 4 miles.

Step-by-step explanation:

GIVEN :

TO FIND :

USING FORMULA :

[tex] \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}[/tex]

SOLUTION :

Substituting the given values in the formula to find the length of the missing diagonal :

[tex] \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}[/tex]

[tex] \longrightarrow{\sf{20 = \dfrac{10 \times d_2}{2}}}[/tex]

[tex] \longrightarrow{\sf{20 \times 2= 10 \times d_2}}[/tex]

[tex] \longrightarrow{\sf{40= 10 \times d_2}}[/tex]

[tex] \longrightarrow{\sf{d_2 = \dfrac{40}{10}}}[/tex]

[tex] \longrightarrow{\sf{d_2 = \cancel{\dfrac{40}{10}}}}[/tex]

[tex]\longrightarrow{\sf{\underline{\underline{d_2 = 4 \: miles}}}}[/tex]

Hence, the length of the missing diagonal is 4 miles.

Answer:

The length of the missing diagonal is 4 miles.

Step-by-step explanation:

To find the length of the missing diagonal, we can use the formula for the area of a rhombus, which is:

[tex]\sf\qquad\dashrightarrow Area_{(Rhombus)} = \dfrac{(Diagonal_1 \times Diagonal_2)}{2}[/tex]

We know that the area is 20 square miles and one of the diagonals is 10 miles, so we can substitute these values into the formula as follows:

[tex]\sf\qquad\dashrightarrow20 = \dfrac{(10 \times Diagonal_2)}{2}[/tex]

Simplifying the equation, we get:

[tex]\sf\qquad\dashrightarrow 40 = 10 \times Diagonal_2[/tex]

Dividing both sides by 10, we get:

[tex]\sf\qquad\dashrightarrow \boxed{\bold{\:\:Diagonal_2 = 4\:\:}}\:\:\:\bigstar[/tex]

Therefore, the length of the missing diagonal is 4 miles.

The value of measure of ∠ RST is,

⇒ ∠ RST = 34°

We have to given that;

In circle S with m ∠RUT = 17°

Hence, We get;

⇒ ∠ RST = 2 × ∠ RUT

⇒ ∠ RST = 2 × 17°

⇒ ∠ RST = 34°

Thus, The value of measure of ∠ RST is,

⇒ ∠ RST = 34°

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Answer:

101

Step-by-step explanation:

substitute 5 in the x:

=18(5)+11

=90+11

=101

Answer:

no solution

Step-by-step explanation:

3r + 10 - 3r = 15 ← collect like terms on left side

10 = 15 ← false statement

this false statement indicates the equation has no solution

Answer:

Okay, based on your previous question and the analysis, the 3 statements that are true about the function f(x) = x2 – 5x + 12 and its graph are:

   The graph of the function is a parabola.

   The graph contains the point (0, 0).

So the options you should select are:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

Let me know if selecting options 2 and 5 makes sense! I can provide any additional details or clarification if needed.

Please let me know if you have any other questions! I'm happy to help explain any other concepts related to this quadratic function and its graph.

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 .The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Okay, just to reiterate, based on the previous analysis, the 3 statements that are TRUE about the quadratic function f(x) = x2 – 5x + 12 and its graph are:

   The graph of the function is a parabola. (true)

   The graph contains the point (0, 0). (true)

   The graph of the function opens down. (false, unknown without seeing graph)

   The value of f(–10) = 82 (false)

   The graph contains the point (20, –8). (false)

So you should select options:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

Please let me know if selecting these 3 options makes sense and matches the analysis. I can re-explain anything if needed.

Your selected options should be:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

   The graph of the function opens down.

Let me know if these look correct or if you have any other questions! I'm happy to help explain further or go over any part of the analysis.

Please select options 2, 5 and 3 as the statements that are true about the quadratic function and its graph.

Step-by-step explanation:

Answer:

AM and AR

Step-by-step explanation:

A is the center, AR is a radius and so is AM

Answer: GL = [tex]\sqrt{61}[/tex]

Step-by-step explanation:

     Since this is a right triangle, we can use the Pythagorean theorem. GL is the hypotenuse.

Given:

     a² + b² = c²

Substitue:

     AL² + AG = GL²

Find side lengths (count via the coordinate plane given):

     6² + 5² = GL²

Square:

     36 + 25 = GL²

Add:

     61 = GL²

Square root both sides:

     [tex]\sqrt{61}[/tex] = GL

The inequality that represents all possible values for the amount of money that Joann has is 21 ≤ J ≤ 50.

Let's call the amount of money that Joann has in her wallet "J" and the amount of money that Shana has in her wallet "S".

We know that the total amount of money they have is at least $56 and at most $85. Therefore, we can write two inequalities:

J + S ≥ 56 (the total is at least $56)

J + S ≤ 85 (the total is at most $85)

We also know that Shana has only $35 in her wallet. We can substitute this value for S in the inequalities to get an inequality that represents all possible values for the amount of money that Joann has:

J + $35 ≥ 56 (substituting S = $35 in the first inequality)

J + $35 ≤ 85 (substituting S = $35 in the second inequality)

Simplifying these inequalities by subtracting $35 from both sides, we get:

J ≥ 21 (the amount of money Joann has is at least $21)

J ≤ 50 (the amount of money Joann has is at most $50).

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Asnwer: 30 minutes

Explanation:

10 laps in 20 minutes is 1 lap every 2 minutes.

So we get this:

1 lap = 2 minutes

But we want 15 laps, so multiply both sides by 15 to get:

15 laps = 30 minutes

The resort should sell a number of 255 packages at a price of $2400 per person to maximize their monthly profit and the maximal profit is $613,400.

Maximal profit refers to the highest level of profit that a business or organization can achieve given certain constraints such as cost, demand, or pricing. It is the point at which a company or business generates the most revenue after accounting for all expenses associated with production and distribution of goods or services. To determine the maximal profit, a business will need to find the optimal balance between costs and revenue, while also taking into account factors such as competition and market demand. This involves analyzing a variety of financial metrics such as revenue, cost of goods sold, gross profit margin, and net profit margin, among others.

Let's begin by defining some variables:

P = price of the package

Q = number of packages sold

R = revenue

C = cost

Profit = revenue - cost

Based on the information given, we can create the following equations:

R = P * Q

C = 1600 + 2000 * Q

Profit = R - C = P * Q - (1600 + 2000 * Q)

We want to find the price that will maximize the monthly profit. To do this, we need to find an expression for profit in terms of P only. We can use the equation for C to substitute Q in the expression for profit:

C = 1600 + 2000 * Q

Q = (C - 1600) / 2000

Profit = P * Q - (1600 + 2000 * Q)

Profit =

Profit = P * ((C - 1600) / 2000) - C + 1600

Now we can find the derivative of profit with respect to P:

dProfit/dP = (C - 1600) / 2000

To find the value of P that maximizes profit, we need to set the derivative equal to 0:

dProfit/dP = 0

(C - 1600) / 2000 = 0

C = 1600

This means that profit is maximized when revenue equals cost, which makes sense. Substituting C = 1600 into the expression for profit, we get:

Profit = P * ((1600 + 2000 * Q - 1600) / 2000) - 1600

Profit = P * Q - 1600

Now we need to find the corresponding values of P and Q. We know that for every increase of $100 in price, there will be a decrease of 5 in the number of packages sold. This means that:

Q = 300 - (P - 2000) / 100 * 5

Substituting this into the expression for profit, we get:

Profit = P * (300 - (P - 2000) / 100 * 5) - 1600

To find the maximum profit, we can take the derivative of this expression with respect to P and set it equal to 0:

dProfit/dP = 300 - (P - 2000) / 20 = 0

P = 2400

This means that the price that will maximize the monthly profit is $2400 per person. To find the corresponding number of packages sold, we can substitute this into the equation for Q:

Q = 300 - (2400 - 2000) / 100 * 5 = 255

Therefore, the resort should sell 255 packages at $2400 per person to maximize their monthly profit. To find the maximal profit, we can substitute these values into the expression for profit:

Profit = 2400 * 255 - 1600 = $613,400.

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Answer:

  A.  X

Step-by-step explanation:

You want to know which graph is decreasing for x > 3.

A graph is decreasing when it slopes down to the right. The only graph in the group that has any decreasing portion is graph X. The decreasing part of that graph is to the right of x = 3, where x > 3.

Graph X is the one you want.

__

Additional comment

All the other graphs are increasing everywhere, so aren't even worth any consideration.

Five points on the inverse function g(x) = log₄(x) are: (1, 0), (4, 1), (16, 2), (1/4, -1/2), and (2, 0.5).

Given that

f(x) = 4^x.

To find the inverse of the function f(x) = 4^x,

We need to interchange the positions of x and y and solve for y. So, we have:

x = 4^y

Taking the logarithm base 4 of both sides, we get:

y = log₄(x)

Therefore, the inverse of the function f(x) = 4^x is g(x) = log₄(x)

To find five points on the inverse function g(x), we can choose five x-values and find the corresponding y-values:

If x = 1, then g(x) = log₄(1) = 0, so the point is (1, 0).

If x = 4, then g(x) = log₄(4) = 1, so the point is (4, 1).

If x = 16, then g(x) = log₄(16) = 2, so the point is (16, 2).

If x = 1/4, then g(x) = log₄(1/4) = -1/2, so the point is (1/4, -1/2).

If x = 2, then g(x) = log₄(2) ≈ 0.5, so the point is (2, 0.5).

Therefore, five points on the inverse function g(x) = log₄(x) are: (1, 0), (4, 1), (16, 2), (1/4, -1/2), and (2, 0.5).

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Answer: 4

Step-by-step explanation:

Answer:

Scientific notation = 8.434 × 10^5

Scientific e notation = 8.434e5

Engineering notation = 843.4 × 10^3 ---> (thousand; prefix kilo- (k) )

Standard form = 8.434 × 10^5

The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.