Mabel's salary is 1/3 higher than Lens. Lens salary is 1/4 higher than the hiring rate. how will you represent Mabel's salary (in terms of the original hiring rate h) if the hiring rate will be increased by 40%

Answers

Answer 1

Answer:

points cuzo

but if i find it out i will edit

Step-by-step explanation:


Related Questions

which fractions are equivalent to 10/14

Answers

Step-by-step explanation:

20/28 = (20 ÷ 2) / (28 ÷ 2) = 10/14 = 5/7

15/21 = (15 ÷ 5) / (21 ÷ 5) = 5/7

25/35 = (25 ÷ 5) / (35 ÷ 5) = 5/7

So, 20/28, 15/21, and 25/35 are equivalent to 10/14.

A new employee at a woodworking repair shop is asked to remove some minor stains from a wooden patio table. He decides to use grade 1 steel wool thinking that a higher grade of steel wool will be most effective in quickly removing the stains.



What faulty inference did the employee use to make this decision?

There is little difference between grade levels of steel wool.
The coarser the steel wool grade, the less steel wool needed.
The higher the steel wool grade, the less muscle power required.
The coarser the steel wool, the better for all woodworking repair jobs

Answers

The higher the steel wool grade, the less muscle power required.

What faulty inference did the employee use to make this decision?

The faulty inference the employee used to make this decision is that a higher grade of steel wool will be more effective in quickly removing stains. In reality, higher grade steel wool is more abrasive and can actually damage the wood surface, leaving behind scratches and making the problem worse.

Grade 1 steel wool is the finest grade and is typically used for finishing and polishing wood. It is not suitable for removing stains, as it is not abrasive enough to remove the outer layer of the wood where the stain is located. To remove stains from wood, it is recommended to use a lower grade of steel wool or a non-abrasive cleaning solution specifically designed for wood.

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Margo borrows $2000 agreeing to pay it back with 8% annual

Answers

In response to the supplied query, we may state that Margo will thus interest have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.

what is interest ?

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The principle balance divided by the interest rate is the most typical approach to compute interest.

Margo will be required to repay the $2000 she borrowed plus an additional 8% of that sum as interest each year if she borrows the money at an 8% annual interest rate.

principle multiplied by the interest rate equals interest.

where "principal" refers to the initial loan amount and "rate" is the interest rate in decimal form. The interest rate in this situation is 8%, or 0.08 in decimal form.

Margo will so be required to pay the following interest each year:

interest: $160 x ($2,000 x 0.08)

Margo will thus have to repay a total of $2160 ($2000 + $160) every year until the debt is completely repaid.

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A container holds 2 pounds of peanuts. How many ounces of peanuts are in the container? (1 pound = 16 ounces)

Answers

I got 32 ounces of peanuts

Answer: 32 Ounces

Step-by-step explanation:

The container holds 32 ounces because if there are 2 pounds of peanuts, and 1 pound = 16 ounces, then you multiply 16 by 2.

16 x 2 = 32

Three research departments have 9, 7, 10 and members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done?

Answers

The number of ways that this can be done is given as follows:

272,160.

What is the Fundamental Counting Theorem?

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The number of ways for each department is given as follows:

Department 1: 9 delegates, 8 alternates.Department 2: 7 and 6.Department 3: 10 and 9.

Hence the total number of ways is given as follows:

9 x 8 x 7 x 6 x 10 x 9 = 272,160.

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2(d-3)+5(d+2) = 4(d+6)-11 ​

Answers

Given:-

[tex] \sf{2(d-3)+5(d+2) = 4(d+6)-11 }[/tex]

[tex] \: [/tex]

Solution:-

[tex] \sf{2(d-3)+5(d+2) = 4(d+6)-11 }[/tex]

[tex] \: [/tex]

[tex] \sf{2d - 6 + 5d + 10 = 4d + 24 - 11}[/tex]

[tex] \: [/tex]

[tex] \sf{2d + 5d - 4d = 24 - 11 + 6 - 10}[/tex]

[tex] \: [/tex]

[tex] \sf{7d - 4d = 13+6-10}[/tex]

[tex] \: [/tex]

[tex] \sf \: 3d = 19-10 [/tex]

[tex] \: [/tex]

[tex] \sf \: 3d = 9[/tex]

[tex] \: [/tex]

[tex] \sf \: d = \cancel \frac{9}{3} [/tex]

[tex] \: [/tex]

[tex] \underline{ \boxed{ \sf{ \color{pink}d = 3}}}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━

Hope it helps! :)

Find the value of the angle θ rounded to 1 DP.

The diagram is not drawn accurately.

Answers

Check the picture below.

[tex]\sin(24^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{17}}\implies 17\sin(24^o )=y \\\\[-0.35em] ~\dotfill\\\\ \sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{y}}\implies \theta =\sin^{-1}\left( \cfrac{4}{y} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{4}{17\sin(24^o )} \right)\implies \theta \approx 35.3^o[/tex]

Make sure your calculator is in Degree mode.

can someone please help me lean this crazy math please so i can learn

Answers

The slope of the lines are given as

a) m₁ = -2

b) m₂ = 4/3

c) m₃ = 5/2

d) The equation of line is y = ( 1/2 )x + 9/2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

a)

Let the first point be P ( 3 , 5 )

Let the second point be Q ( 7 , -3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = ( -3 - 5 ) / ( 7 - 3 )

Slope m₁ = -8/4

Slope m₁ = -2

b)

Let the first point be P ( 4 , 2 )

Let the second point be Q ( 10 , 10 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₂ = ( 10 - 2 ) / ( 10 - 4 )

Slope m₂ = 8/6

Slope m₂ = 4/3

c)

Let the first point be P ( -1 , -2 )

Let the second point be Q ( -3 , -7 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₃ = ( -7 - ( -2 ) ) / ( -3 - ( -1 ) )

Slope m₃ = -5/-2

Slope m₃ = 5/2

d)

Let the first point be P ( 5 , 7 )

The slope of the line is y = 1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 7 = ( 1/2 ) ( x - 5 )

y - 7 = ( 1/2 )x - 5/2

Adding 7 on both sides , we get

y = ( 1/2 )x + 9/2

e)

The slope of the line is y = 5/2 and the points are linear

Hence , the equation of line is y = ( 1/2 )x + 9/2

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The complete question is :

Determine the slopes between the points in lowest terms

a) ( 3 , 5 ) and ( 7 , -3 )

b) ( 4 , 2 ) and ( 10 , 10 )

c) ( -1 , -2 ) and ( -3 , -7 )

d) Draw and accurate graph of the line with the slope of ( 1/2 ) that passes through the point ( 5 , 7 )

Plot the following points in the plane: (2, 1), (-1/2, 0), (π, -3). Is there a point in the plane for which you need exactly three numbers to specify its location?

Answers

There is no such point that requires exactly three numbers to specify its location.

What is the Euclidean plane?

A mathematical notion known as the Euclidean plane symbolizes a two-dimensional environment in which points, lines, and forms may be specified and altered. The Greek mathematician Euclid, who originally described the geometry of the plane in his book Elements, is honoured by the name of the object. The Pythagorean theorem is used to calculate distance in the Euclidean plane, while degrees or radians are used to calculate angles.

The plane doesn't have any points that can be precisely located by three integers. Each point in the Euclidean plane may be found using only two integers, namely its x- and y-coordinates.

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Find the H.C.F by division method a) 30,45,60​

Answers

The H.C.F. of 30, 45, and 60 using the division method is 30.

What is the HCF of the numbers?

To find the H.C.F. (Highest Common Factor) of the given numbers using division method, we can follow these steps:

Step 1: Divide the larger number by the smaller number and find the remainder.Step 2: Now, divide the smaller number obtained in the previous step by the remainder.Step 3: Continue this process of dividing the previous divisor by the remainder until the remainder becomes zero.Step 4: The last divisor obtained in the above process is the H.C.F. of the given numbers.

Let's apply this method to find the H.C.F. of 30, 45, and 60.

Step 1: We start by dividing the larger number, 60, by the smaller number, 30.

60 ÷ 30 = 2 with a remainder of 0

Step 2: Now, we divide the smaller number, 30, by the remainder, which is 0.

30 ÷ 0 = undefined

Since the remainder is zero, we stop the process here. The last divisor we obtained is 30. Therefore, the H.C.F. of 30, 45, and 60 is 30.

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help with this please youll get 65 points​

Answers

Answer:

105 or 40500

Step-by-step explanation:

you have too add or mutilple

help pls offering 100 POINTS!!! nonsense will be reported and Banned. and offering brainiest

Answers

To find the area of the given circle we have to use the formula πr², where π=22/7 and r is radius of the circle. The area of the circle is 1519.76 square feet.

What is a circle?

A circle is a closed two-dimensional figure in which all sets of points in the plane are equidistant from a specific point called the "center". A line passing through the circle forms a line of specular symmetry. It is also rotationally symmetrical about the center at any angle. 

Solution for the area of the circle:

Given, radius = 22 feet

∴Area of the circle = πr²

                               = (22/7)×22²

                               = 3.14 × 484

                               = 1519.76 square feet

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- Find the truth set of 4x +2 = 3(2x)​

Answers

Answer:

y = −x2 + 2x −5

Step-by-step explanation:

To find the truth set of the equation 4x + 2 = 3(2x), we need to solve for x and then determine the values of x that make the equation true.

Starting with the equation:

4x + 2 = 3(2x)

Distribute the 3 on the right-hand side:

4x + 2 = 6x

Subtract 4x from both sides:

2 = 2x

Divide both sides by 2:

1 = x

Therefore, the truth set of the equation 4x + 2 = 3(2x) is {1}. In other words, the equation is only true when x is equal to 1.

Write 2 multiplication or division expressions that equal -360

Answers

This expression divides 360 by -1 to get -360.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.

Here are two possible multiplication/division expressions that equal -360:

18 x (-20) = -360

This expression multiplies 18 by -20 to get -360.

360 ÷ (-1) = -360

Therefore, This expression divides 360 by -1 to get -360.

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What is the answer to Justify Conclusions One side of a square is
10 units. Which is greater, the number of square units for the area of the square or the number of units for the perimeter? Give me an Explain. Please

Answers

Therefore , the solution of the given problem of square comes out to be the square's perimeter is higher than the number of square units for the square's surface.

Exactly what is a square?

A square, according to Euclidean mathematics, is a quadrilateral with four equal sides and four equal angles. Another term for a rectangle is a shape with two neighboring sides that are the same length. A quadrilateral is said to be equilateral if one of its 4 triangular edges and four equal corners is a square. A cubical angle refers to one that's 90 ° or straight. The square's diagonals are evenly spaced and split in half at a 90-degree angle.

Here,

We can use the formulas for area and perimeter of a square to decide which is greater: its area or perimeter with sides that are 10 units long.

A = s², where s is the extent of one edge, calculates the area of a square. The square's size in this instance is

=> 102 = 100 square units.

P = 4s, where s is the length of one edge, calculates the perimeter of a square. In this instance, the square's circumference is

=> 4(10)

=> 40 units.

We can see that the perimeter is larger than the area by comparing the two values.

Consequently, we can draw the conclusion that the number of units for the square's perimeter is higher than the number of square units for the square's surface.

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you enclose a field using sections of fence with lengths of 9, 12, and 15 meters. Estimate the area of the field.

Answers

The estimated area of the field enclosed by the fence is approximately 220.5 square meters.

What is the Pythagorean theorem?

A basic geometry theorem that explains the relationship between a right triangle's three sides is known as the Pythagorean theorem.

We can employ the following strategy to determine how much of the field the fence is enclosing:

Include the lengths of the fence sections in a rough sketch of the field.

Make a straightforward polygon that resembles the field's shape using the fence sections.

To calculate the area of the triangle-shaped portion of the field, use the triangle's area formula ([tex]A = 1/2 \times base \times height[/tex]). We must identify the triangle's base and height in order to accomplish this.

The Pythagorean theorem can be used to calculate the triangle's height: [tex]a^2 + b^2 = c^2[/tex]where a and b are the triangle's two shorter sides (9 meters and 12 meters, respectively), and c is the longest side (15 meters). When we solve for (a), we see that it is equal to

(a)

[tex]= \sqrt{(c^2 - b^2)} \\= \sqrt{(15 2 - 12 2}) \\= \sqrt{(81)} \\= 9 meters.\\[/tex]

The triangle is therefore 9 meters tall. The 9-meter fence portion serves as the triangle's base.

When we apply the triangle's area formula, we obtain:

A is equal to half of the base plus the height, or 9 meters plus 9 meters, or 40.5 square meters.

The area of the remaining field must be increased by the area of the triangle. This estimate may not be very exact because we have just estimated the field's form, but it should at least give us a general notion of the field's size.

If the remaining area of the field has a roughly rectangular form, we can calculate its area by multiplying the rectangle's length and width. The 12-meter and 15-meter fence sections can be used as a guide to determine the rectangle's size.

By dividing the width by the length, we obtain:

180 square meters is the size of the remaining part (12 meters times 15 meters).

To determine the approximate total size of the field, add the areas of the rectangle and triangle portions:

Total area estimated: 40.5 square meters plus 180 square meters, which equals 220.5 square meters.

As a result, the field's approximate area inside the barrier is 220.5 square meters.

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I need help with there’s problems

Answers

Answer:

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

4. x = 2, y = 1 --> = (2,1)

Step-by-step explanation:

3.

x+5y =8

x = 8-5y

-x+2y=-1

-8+5y+2y=-1

7y-8=-1

7y=-1+8

7y=7

Divide 7 from both sides

y = 1

x=8-5y

x=8-5(1)

x = 3

4.

y=x-1

y=-2x+5

-2x+5=x-1

5=x-1+2x

5=3x-1

5+1=3x

6=3x

Divide 3 from both sides

2=x

x=2

Mary has 7 cups of flour. It takes 5/6 cup of flour to make one cake. How many cakes can Mary make?

Answers

Mary can bake 8 cakes the with 7 cups of flour she possesses because we are unable to create a quarter of a cake.

What is the flour recipe?

Starch, a polymer, is one of the ingredients in all-purpose flour, which has the chemical formula (C6H5O10)n (C 6 H 5 O 10) n.

We need to divide Mary's total flour supply by the quantity of flour required for creating one cake in order to determine how many cakes she can produce.

First, we must divide 5 by 6 to get the fraction 5/6 in decimal form:

5 ÷ 6 = 0.8333...

Hence, 0.8333 cups of flour are required to produce one cake.

We're able to divide Mary's entire flour supply by the quantity of flour needed to produce one cake:

7 cups of flour ÷ 0.8333 cups of flour per cake = 8.4 cakes

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You would like to retire 25 years from now and have a retirement fund from which you can draw
an income of $50,000 per year – forever! How can you do it? Assume a constant APR of 7%.
(What balance do you need to earn $50,000 from interest? How can you get to that balance?)

Answers

The future value earning need to save $527.13.

What is future value?

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

Here  $50,000 now at 3% inflation will become 50000*1.03^250 after 20 years.

i.e.  $121,363 is required in retirement years (for 20 years)

Calculate the PV of these payments 7% is calculated as below.

FV = 0; 1/y = 7%; n=20; PMT = 121363; calculate PV = $1,191,560

Now we want to get $1,191,560 at the start of retirement by saving per year  to get the per month amount.

FV = 1191560; PV = 0; n= 12*35; 1/y = 7%/12; calculate PMT  = $527.13

Hence you have to save $527.13 dollar per month.

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Hello, I need help with this problem. Thanks

Answers

A about 0.76 miles per hour

Mayerlin wraps a gift box in the shape of a cube 5.5. How much wrapping paper did she use in square inches

Answers

Check the picture below.

so we really have six 5.5x5.5 squares

[tex]\stackrel{ \textit{Area for 6 squares} }{(6)(5.5)(5.5)}\implies \text{\LARGE 181.5}[/tex]

Graph the following functions and determine where F(x) = G(x). State the x values only. Select all that apply.
f(x)= -x^2+8x-13 and g(x)= x+3

a. 4
b. no solution
c. all real numbers
d. -13

Answers

For the specified functions, there is no answer. By graphing the functions, the answer has been discovered.

What does graphing a function mean?

The method of graphing a function begins with creating the graph of a pertinent function. The function equation will be satisfied at a point on a curve if it reflects the function at that location.

According to the given information:

We are given two functions as f(x) = -x² + 8x - 13 and g(x) = x + 3

The graph of the given functions has been plotted and attached below.

In the graph, the red function represents the f(x) function and the blue line represents the g(x) function.

From the graph, we can see that the two does not meet.

Hence, there is no solution for the given functions.

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Sin2x. Cos x plus Cos2x. Sinx

Answers

So, the simplified form of the given expression is cosxsinx(3cosx - sinx).

What is a mathematical expression?

A statement, at least two parameters or integers, and one or more calculations make up a mathematical expression. It is possible to multiply, divide, add, or subtract quantities using this mathematical operation. The following is the expression's structure: An expression is (total count, numerical operator, number, or variable).

We can simplify the given expression using the product-to-sum identities:

sin2x × cosx + cos2x × sinx

= 2sinx × cosx × cosx + (cos²x - sin² x) × sinx [using the identity sin2x

= 2sinx × cosx and cos²x = cos² x - sin² x]

= 2sinx × cos² x + cos²x × sinx - sin² x × sinx [expanding the brackets]

= cosx × sinx(2cosx + cosx - sinx)

= cosx × sinx(3cosx - sinx)

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14 1/2 x 6 1/2 x 6 1/2

Answers

14[tex]\frac{1}{2}[/tex] x 6[tex]\frac{1}{2}[/tex] x 6[tex]\frac{1}{2}[/tex]

= 14[tex]\frac{1}{2}[/tex] x 36[tex]\frac{1}{4}[/tex]

= 504[tex]\frac{1}{8}[/tex]

Answer:

273/2

Step-by-step explanation:

What are at least two ways you can determine if an exponential function is a growth?

Answers

Answer:

a and b

Step-by-step ex

XPO Corporation has a minimum tax credit of $51,000 from 2017. XPO’s 2018 tax liability before any MTC carryover is $30,500. What is XPO’s minimum tax credit carryover to 2019, if any?

Answers

XPO's minimum tax credit carryover to 2019 is $20,500.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

XPO's minimum tax credit from 2017 is $51,000. This means that they are allowed to reduce their 2018 tax liability by up to $51,000 using this credit.

Since their 2018 tax liability before any MTC carryover is $30,500, they have not used the entire minimum tax credit for 2017. Therefore, they can carry over the remaining credit to 2019.

To calculate the minimum tax credit carryover to 2019, we need to subtract the amount of the minimum tax credit that XPO used in 2018 from the total minimum tax credit of $51,000:

Minimum tax credit carryover = $51,000 - $30,500 = $20,500

Therefore, XPO's minimum tax credit carryover to 2019 is $20,500.

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Mario was studying right angles and wondered if during his math class the minute and hour hands of the clock formed a right angle. If his class meets from 2:00 p.m. to 2:50p.m. is a right angle formed? If it is determine the nearest second when the hands form the right angle.​

Answers

the hands do form a right angle during Mario's math class, at 2:35:17.5 p.m. (rounded to the nearest half-second).

What is the right-angle triangle?

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

During the class from 2:00 p.m. to 2:50 p.m.,

the hour hand will move from the 2 to the 3 and will be halfway between the 2 and 3 at 2:30 p.m. The minute hand will make one full revolution around the clock face, from the 12 to the 12, during this time.

Let's calculate the positions of the hour and minute hands at 2:30 p.m.:

The hour hand moves 1/12 of the way around the clock face for each hour or 30 degrees for each hour. At 2:30 p.m.,

it will have moved 2.5 hours, so it will be 2.5 * 30 = 75 degrees past the 2 o'clock mark.

The minute hand moves 360 degrees in 60 minutes or 6 degrees per minute. At 2:30 p.m.,

it will have moved 30 minutes, so it will be 30 * 6 = 180 degrees past the 12 o'clock mark.

To determine if the hands form a right angle, we need to calculate the angle between them. Let's call this angle "A".

The angle between the hour and minute hands is the absolute difference between their positions, which is 105 degrees in this case (180 degrees - 75 degrees).

If the minute hand is ahead of the hour hand by exactly a quarter of a revolution or 90 degrees, then the hands will form a right angle.

So, we need to check whether angle A is equal to 90 degrees. If A = 90 degrees, then the hands form a right angle, and we can calculate the time when this happens by finding the time at which the minute hand is exactly 90 degrees ahead of the hour hand.

Let's set up an equation to solve for the time t:

A = 90 = 180 - 75 - 6t

Solving for t, we get:

t = 17.5

Therefore, the hands do form a right angle during Mario's math class, at 2:35:17.5 p.m. (rounded to the nearest half-second).

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Calc for business!
Please help!


A chemical substance has a decay rate of 8.8% per day. The rate of change of an
dN
amount N of the chemical after t days is given by =-0.088N
dt
(i) Let No represent the amount of the substance present at to. Find the exponential function
that models the decay.
(ii) Suppose that 400g of the substance is present at to. How much will remain after 3 days?
(iii) What is the rate of change of the amount of the substance after 3 days?
(iv) After how many days will half of the original 400 g of the substance remain?

Answers

(i) N(t) = No e^(-0.088t) (ii) approximately 323.3 g of the substance(iii) the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.(iv) approximately 7.88 days.

Describe Rate of change?

The rate of change can be positive, indicating an increase in the value of the variable, or negative, indicating a decrease. It can also be constant, indicating a steady increase or decrease, or it can vary over time, indicating a more complex pattern of change. Understanding the rate of change of a variable is important in many fields, including engineering, economics, and finance, among others.

(i) Since the decay rate is given by -0.088 per day, the exponential function that models the decay is:

N(t) = No e^(-0.088t)

where No is the initial amount of the substance present at t=0.

(ii) If 400g of the substance is present at t=0, then we have No = 400. Substituting this value into the exponential function, we get:

N(t) = 400 e^(-0.088t)

To find how much will remain after 3 days, we need to evaluate N(3):

N(3) = 400 e^(-0.088*3) ≈ 323.3 g

Therefore, approximately 323.3 g of the substance will remain after 3 days.

(iii) The rate of change of the amount of the substance after t days is given by:

dN/dt = -0.088N

To find the rate of change after 3 days, we need to evaluate dN/dt at t=3:

dN/dt | t=3 = -0.088N(3) = -0.088(323.3) ≈ -28.4 g/day

Therefore, the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.

(iv) We want to find the value of t such that half of the original 400 g of the substance remains. In other words, we want to solve the equation:

N(t) = 200

Substituting No = 400 into the exponential function, we get:

400 e^(-0.088t) = 200

Dividing both sides by 400, we get:

e^(-0.088t) = 0.5

Taking the natural logarithm of both sides, we get:

ln(e^(-0.088t)) = ln(0.5)

Simplifying, we get:

-0.088t = ln(0.5)

Solving for t, we get:

t ≈ 7.88 days

Therefore, after approximately 7.88 days, half of the original 400 g of the substance will remain.

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Tommy goes to the video store and rents 2 video games for $3.99 each. He also rents the latest Sonic The Hedgehog movie for $3.50. He gives the clerk a twenty-dollar bill. How much change should Tommy receive?

Answers

Answer:

8.52

Step-by-step explanation:

add the two 3.99 making 7.98 then add 3.50 making 11.48 then substract that from 20.00 making the final answer 8.52

who would make the most money in one week? a head mechanic working 25 hours, an assistant mechanic working 30 hours, a sales manager working 35 hours, a front desk clerk working 40 hours?

Answers

The one making the most money in one week is by sales manager which is an amount of $1006.25.

What is Unit Rate?

Unit rate is the amount of one quantity for a unit amount of the other quantity.

Given that,

Hourly rate of a head mechanic = $37.52 per hour

Number of hours worked in a week = 25 hours

Money made = 25 × 37.52 = $938

Hourly rate of a assistant mechanic = $30.42 per hour

Number of hours worked in a week = 30 hours

Money made = 30 × 30.42 = $912.6

Hourly rate of a sales manager = $28.75 per hour

Number of hours worked in a week = 35 hours

Money made = 35 × 28.75 = $1006.25

Hourly rate of a front desk clerk = $15.09 per hour

Number of hours worked in a week = 40 hours

Money made = 40 × 15.09 = $603.6

Money most made is by sales manager.

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Your question is incomplete. The complete question is given as,

Who would make the most money in one week? a head mechanic working 25 hours with an hourly rate $37.52 per hour, an assistant mechanic working 30 hours with an hourly rate $30.42 per hour, a sales manager working 35 hours with an hourly rate $28.75 per hour, a front desk clerk working 40 hours with an hourly rate $15.09 per hour?

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