5. The library is installing new
shelves. If the carpenter has
4/5 yard of wood to make
into 2 shelves of equal length,
how long will each shelf be?

The amount at the end of the 40 years calculated using compound interest at a rate of 10% is $1,357,777.67.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. The interest charged on a loan or deposit is known as compound interest. That is the idea that we employ the most frequently on a daily basis. The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Given,

The principal amount P = $30,000

The time period t = 40 years

The rate of interest r = 10%

The number of times compounded in a year n = 1

The compound interest formula can be used to calculate the amount at the end of 40 years.

[tex]A = P(1 + \frac{r}{n})^{nt} = 30000(1 + \frac{0.1}{1})^{1*40}[/tex]  = $1,357,777.67

Therefore the amount at the end of the 40 years calculated using compound interest at a rate of 10% is $1,357,777.67.

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Answer:

No

Step-by-step explanation:

from Pythagoras theorem, if the triangle is right angled square of largest side should be equal to sum of the squares of smaller two sides. the square of largest side is 18^2= 324  

9^2=81 and the last side is 17^2= 289

81+ 289= 370

This triangle is NOT a right triangle.

By answering the above question, we may infer that Due to the fact that equation we are multiplying a unit of money by a unit of time, the units for this product are dollars.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

$9/hour multiplied by 8 hours results in:

$8 × $9/hour = $72

Due to the fact that we are multiplying a unit of money by a unit of time, the units for this product are dollars.

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Using the arithmetic operations it is obtained that Russell ran 4 miles through his neighborhood every day after school.

To solve this problem, we can use the following equation -

total distance = distance per day x number of days

We know that Russell ran 2 miles around the football field before school every day.

Using multiplication,

Therefore, his total distance for the week from running around the football field is -

2 miles/day × 5 days = 10 miles

We also know that Russell ran a longer route through his neighborhood after school every day.

Let's call the distance of this route "x" miles.

Russell ran this route 5 times during the week, so his total distance from running through his neighborhood is -

Use multiplication,

x miles/day × 5 days = 5x miles

Finally, we know that Russell's total distance for the week was 30 miles. We can set up the equation -

Use addition,

10 miles + 5x miles = 30 miles

Simplifying, we get -

5x miles = 20 miles

x = 4 miles

Therefore, the distance value is obtained as 4 miles.

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Answer:

Step-by-step explanation:

Area of semi circle is 1/2 (πr²)

1/2 (3.14×6²)

56.52 unit²

9 is the equivalent value of x from the given triangle.

The angle bisector theorem is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into.

Applying the rule to solve the given question, we will have:

3x-7/12 = 3x +3/18

Cross multiply

12(3x+3) = 18(3x-7)36x + 36 = 54x - 126

Collect the like terms

36x-54x = -126 - 36

-18x = -162

x = 162/18

x = 9

Hence the value of x from the given figure is 9.

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The minute and second equivalent to [tex]13\frac{5}{10}[/tex] minutes is, 13 minutes 30 seconds.

A clock can be thought of as a circle having 12 steps and we know that circle is 360°,

So, the measure of each integer step of a clock is 30°.

We know, 1 minute is equal to 60 seconds.

Converting the mixed fraction into an improper fraction we have,

[tex]13\frac{5}{10} = \frac{135}{10}[/tex] minutes which is equal to,

[tex]\frac{135}{10}\times60[/tex] seconds.

= 810 seconds.

= 60×13 + 30 seconds.

= 13 minutes 30 seconds.

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As a result, after five years, the business makes $102.10 per hour of work performed by men.

The gains that a company makes are its earnings. They are obtained by deducting revenue from cost of products sold, running costs, and taxes. The creation and ongoing running of a company are primarily motivated by the desire to generate profits. Dividend payments to stockholders can then be made with the earnings.

If the factory earned $80 per man-hour of labor when it opened, and each year earns an additional 5% per man-hour, we can calculate the earnings for any given year using the formula:

E = $80 × (1 + r)ⁿ

where E is the earnings per man-hour, r is the annual rate of increase (5% = 0.05), and n is the number of years since the factory opened.

For example, if we want to find the earnings per man-hour after 3 years, we would plug in n=3:

E = $80 × (1 + 0.05)³

E = $80 × 1.157625

E = $92.61

Therefore, after 3 years, the factory earns $92.61 per man-hour of labor.

Similarly, if we want to find the earnings per man-hour after 5 years, we would plug in n=5:

E = $80 × (1 + 0.05)⁵

E = $80 × 1.276282

E = $102.10

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The correct question is:

A factory earned $80 per man-hour of labor when it opened Each year, the factory earns an additional 5% per man-hour

Answer:

i hope this helps

Step-by-step explanation:

Answer: the line will go through (0, -3) and for every x value it will go down one

Step-by-step explanation:

Example: (0, -3), (1, -5), (2, -7)

Fοr Marcus's situatiοn the prοbability value is οbtained as οptiοn B: 15%.

Prοbability is a way tο gauge hοw likely sοmething is tο happen. Many things are difficult tο fοrecast with absοlute cοnfidence. Using it, we can οnly make predictiοns abοut the likelihοοd οf an event happening, οr hοw likely it is. Prοbability can range frοm 0 tο 1, with 0 denοting an impοssibility and 1 denοting a certainty.

Tο find the prοbability that all 3 disks selected will be either all red οr all white, we need tο cοunt the number οf times that this οutcοme οccurs in the simulatiοn, and divide by the tοtal number οf pοssible οutcοmes.

Lοοking at the simulatiοn results, we can see that there are 2 times when all 3 disks are red -

There is alsο 1 time when all 3 disks are white -

Sο the tοtal number οf times that all 3 disks are either all red οr all white is 3.

There are a tοtal οf 20 pοssible οutcοmes in the simulatiοn, since there are 3 chοices fοr each οf the 3 selectiοns, and the selectiοns are made with replacement.

Sο, the prοbability οf selecting 3 disks that are all red οr all white is -

3/20 = 0.15 = 15%

Therefοre, the prοbability value is 15%.

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Marcus has a bag of plastic disks that are red (R) or white (W). He performs a simulation by randomly selecting 3 disks from the bag at one time and recording the results. He then puts the disks back in the bag. His results are shown.

RR   WW  WR  RW  WR

R       R      R    W    W

RW   RW  WW  RW  WW

 R      R     W      R      R

WR   RW  RR  RW  WR

W     W    W   W     W

WR   RW  WR  RW  RR

W     W    W     R     R

Based on the simulation, what is the probability that all 3 disks selected will be either all red or all white?

A. 85%

B. 15%

C. 10%

D. 5%

Answer:

10 points

Step-by-step explanation:

· The team was penalized 30 points in 3 plays.

· Suppose the team was penalized an equal number of yards each play.

To find the supposed amount of points for each penalty, find the unit rate.

Total points ÷ Total Plays

30 ÷ 3

10 points

Answer:

[tex]c+13 > 78[/tex]

Step-by-step explanation:

[tex]c+13 > 78[/tex]

They must collect over 78 coats. They already have 13 so they must either add that to the amount they still need to collect or subtract it from the number they're trying to beat.

The expression of the length of the arc is  4πb⁵

The circle has a radius of 9b³. An arc subtend an angle at the centre of 80b² degrees. Therefore, the expression for the length of the arc can be solved as follows:

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 80b² / 360 × 2 × π × 9b³

length of arc = 144b⁵π / 36

Therefore,

length of arc = 4πb⁵

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Answer:

6902

Step-by-step explanation:

divide through by multiples of the given values

Using arithmetic οperatiοns it is οbtained that Brandοn must mοw 15 lawns at $25 per lawn tο break even, meaning his revenue will cοver his cοsts.

A subject οf mathematics knοwn as arithmetic οperatiοns deals with the study and use οf numbers in all οther branches οf mathematics. Basic οperatiοns including additiοn, subtractiοn, multiplicatiοn, and divisiοn are included.

Let x be the number οf lawns Brandοn mοws.

Use the arithmetic οperatiοn οf multiplicatiοn.

His revenue frοm mοwing × lawns at $25 per lawn is -

Revenue = Price per lawn × Number οf lawns

Revenue = $25 × x

Revenue = $25x

Use the arithmetic οperatiοn οf additiοn.

His tοtal cοst includes the equipment cοst οf $300 and the variable cοst οf $5 per lawn, sο his tοtal cοst is -

Cοst = Equipment cοst + Variable cοst

Cοst = $300 + $5x

Tο break even, his revenue must be equal tο his cοst.

Use the arithmetic οperatiοn οf additiοn.

Sο we can set the revenue equal tο the cοst and sοlve fοr x -

Revenue = Cοst

$25x = $300 + $5x

$20x = $300

x = 15

Therefοre, Brandοn must mοw 15 lawns at $25 per lawn.

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The translation that occurred to the segment is: B. The segment was shifted to the right four units and up five units.

Translation is a transformation in which an object is moved without being rotated, resized or distorted. It involves sliding the object a certain distance in a certain direction, while maintaining its shape and size. The resulting image of the object is congruent to the original object, meaning that they have the same size and shape.

To find the translation that occurred to the segment, we need to calculate the distance between point A and its image A' and the direction in which the translation occurred.

The distance between A and A' is given by:

√((7-3)² + (2-(-3))²) = √(16 + 25) = √(41)

So the segment was translated by a distance of √(41).

To find the direction of the translation, we can subtract the coordinates of A from the coordinates of A':

(A'x - Ax, A'y - Ay) = (7-3, 2-(-3)) = (4, 5)

So the segment was shifted to the right four units and up five units.

Therefore, the correct answer is B. The segment was shifted to the right four units and up five units.

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The measure of angle ABC in the triangle inscribed in the circle is given as follows:

m < ABC = 84º.

The sum of the measures of the interior angles of a triangle is of 180º.

The internal angles for the triangle are given as follows:

Then the measure of angle ABC is obtained as follows:

m < ABC + 2 x 48 = 180

m < ABC = 180 - 96

m < ABC = 84º.

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Answer:[tex]\frac{1}{8}[/tex]<[tex]\frac{3}{20}[/tex]

Step-by-step explanation:

The highest temperature on record belongs to California's Death Valley which, in 1913, reached a temperature of 134 degrees Fahrenheit, or 56.7 degrees Celsius, Al Jazeera reports.

The highest temperature in India is found in this city, situated at a height of 178 metres in Rajasthan, the country's biggest state. There, 50 degrees Celsius has been recorded as the greatest temperature to date. Extreme weather may be found in the city both in the summer and the winter.

However, according to the India Meteorological Department, the highest temperature ever recorded in India was 51°C (123.8°F) in the town of Phalodi, Rajasthan on May 19, 2016. It's important to note that temperatures can vary greatly depending on the location and time of year.

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Therefore, the prime trinomials are: 5x² + 4x + 4 and 5x² – 8x + 2.

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using the operations of addition, subtraction, and multiplication. Polynomials are widely used in mathematics and other fields to model a wide range of phenomena and processes. In a polynomial, the variables are usually represented by letters such as x, y, or z, while the coefficients are numbers that multiply the variables. The exponents indicate the power to which each variable is raised.

Here,

To determine which trinomials are prime, we need to factor each trinomial and check if it can be factored further into linear factors with integer coefficients. If a trinomial can be factored further, then it is not prime. On the other hand, if a trinomial cannot be factored further, then it is prime.

Let's factor each trinomial and see which ones are prime:

x² + 11x + 18

This trinomial can be factored into (x + 2)(x + 9), so it is not prime.

x²  + 11x + 18

This trinomial can be factored into (x + 2)(x + 9), so it is not prime.

x² – 3x – 2

This trinomial can be factored into (x – 2)(x + 1), so it is not prime.

x²  – 3x – 2

This trinomial can be factored into (x – 2)(x + 1), so it is not prime.

5x² + 4x + 4

This trinomial cannot be factored further, so it is prime.

5x² – 8x + 2

This trinomial cannot be factored further, so it is prime.

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In the given situation, one snack bar has 14 carbohydrates.

Let's denote the number of carbs in one snack bar as "x".

From the given information, we can set up a system of two equations:

2x + 3y = 73 (where y is the number of carbs in one glass of milk)

4x + 2y = 86

We can then solve for x by using elimination or substitution.

Using elimination, we can multiply the first equation by 2 and subtract it from the second equation:

4x + 2y = 86

(4x + 6y = 146) (2 times the first equation)

-4y = -60

Dividing both sides by -4, we get:

y = 15

Substituting this value of y into the first equation, we can solve for x:

2x + 3y = 73

2x + 3(15) = 73

2x + 45 = 73

2x = 28

x = 14

Therefore, there are 14 carbs in one snack bar.

Step-by-step explanation:

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of carbohydrates in one snack bar.

Now, we can use the given information to set up a system of equations:

2x + 3y = 73 (where y is the number of carbohydrates in one glass of milk)

2y + 4x = 86

We have two equations and two unknowns, so we can solve for x and y using any method we prefer. Here, we will use the substitution method:

Rearrange the first equation to solve for y: y = (73 - 2x)/3

Substitute this expression for y in the second equation: 2((73 - 2x)/3) + 4x = 86

Simplify: (146 - 4x)/3 + 4x = 86

Multiply both sides by 3 to eliminate the fraction: 146 - 4x + 12x = 258

Simplify: 8x = 112

Solve for x: x = 14

Therefore, one snack bar has 14 carbohydrates.

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In the given situation, one snack bar has 14 carbohydrates.

Let's denote the number of carbs in one snack bar as "x".

From the given information, we can set up a system of two equations:

2x + 3y = 73 (where y is the number of carbs in one glass of milk)

4x + 2y = 86

We can then solve for x by using elimination or substitution.

Using elimination, we can multiply the first equation by 2 and subtract it from the second equation:

4x + 2y = 86

(4x + 6y = 146) (2 times the first equation)

-4y = -60

Dividing both sides by -4, we get:

y = 15

Substituting this value of y into the first equation, we can solve for x:

2x + 3y = 73

2x + 3(15) = 73

2x + 45 = 73

2x = 28

x = 14

Therefore, there are 14 carbs in one snack bar.

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of carbohydrates in one snack bar.

Now, we can use the given information to set up a system of equations:

2x + 3y = 73 (where y is the number of carbohydrates in one glass of milk)

2y + 4x = 86

We have two equations and two unknowns, so we can solve for x and y using any method we prefer. Here, we will use the substitution method:

Rearrange the first equation to solve for y: y = (73 - 2x)/3

Substitute this expression for y in the second equation: 2((73 - 2x)/3) + 4x = 86

Simplify: (146 - 4x)/3 + 4x = 86

Multiply both sides by 3 to eliminate the fraction: 146 - 4x + 12x = 258

Simplify: 8x = 112

Solve for x: x = 14

Therefore, one snack bar has 14 carbohydrates.

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The correct answer is f(m)=5230(1.015)m12.

A function is a self-contained block of code that takes inputs, performs specific operations on those inputs, and produces an output. It is a subprogram that performs a specific task, and helps to break down larger programs into smaller, more manageable pieces. Functions are also reusable, meaning that once a function is written, it can be used over and over again in different places in the program.

This function can be used to represent the student enrollment m months after the study began, as it takes into consideration the number of years (t) represented by the number of months (m) and incorporates it into the equation. The equation multiplies the number of months (m) by 12 to convert it into the number of years (t) used in the original equation, f(t)=5230(1.015)t. This ensures that the correct student enrollment is calculated based on the number of months since the study began.

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y = 5(10)ˣ is the equation for the  exponential function

The general form of the exponential function is y = abˣ

From the table, when x = 0, y = 5. Substitute the values into the function:

y = abˣ

5 = ab⁰             (Note: b⁰ = 1)

5 = a(1)

5= a

a = 5

Also, from the table, when x = 1, y = 50. Substitute the values into the function:

y = abˣ

50 = 5 × b¹

50 = 5b

5b = 50

b = 50/5 = 10

We can now write the equation for the exponential function:

y = abˣ

y = 5(10)ˣ

Therefore, the equation for the exponential function is y = 5(10)ˣ

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The area of the painting, frame and painting, frame are 84 square inches, 174 square inches and 90 square inches. respectively.

Length = 10.5 in

Width = 8 in

Area of the painting = Length × Width

= 10.5 in × 8 in

= 84 square inches

Length = 14.5 in

Width = 12 in

Area of the frame and painting = Length × width

= 14.5 in × 12 in

= 174 square inches

Area of the frame = Area of the frame and painting - Area of the painting

= 174 square inches - 84 square inches

= 90 square inches

In conclusion, the areas are 84 square inches, 174 square inches and 90 square inches. respectively.

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Answer:

1 = 36

2. = 32

3 = 10

4.= 21

5. = 14

6 =7456200

Step-by-step explanation:

In response to the query, we can state that As a result, interest accounted for $6.23 of Kyle's payment in month 2.

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 most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.  

The yearly interest rate must be divided by 12 to obtain the monthly interest rate since it is given:

1.5% each month divided by 12 equals 0.125%.

initial balance is $5,020.

Amount paid: $45.08

Interest added equals 0.125% * $5,020 = $6.27

Principle paid equals $45.08 minus $6.27, or $38.81.

Final balance: $5,020 minus $38.81 equals $4,981.19

As a result, interest accounted for $6.27 of Kyle's payment in month 1.

Total starting balance: $4,981.19

Money received: $45.08; Interest owed: 0.125% * $4,981.19; Total: $6.23

Principal paid equals $45.08 minus $6.23, or $38.85.

Final balance: $4,981.19 minus $38.85 equals $4,942.34

As a result, interest accounted for $6.23 of Kyle's payment in month 2.

The amortisation table might look like this:

Month Starting Balance Payment: To Principal Ending Balance: To Interest Payment

[tex]1 $5,020.00 $6.27 $38.81 $4,981.19\s2 $4,981.19 $6.23 $38.85 $4,942.34\s3 $4,942.34 ...[/tex]

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The decimal calculation for Arturo's is 18.97, Bonnie's is 20.51, Courtney's is 31.42, Dawson's is 35.00.

Measurement is the process of assigning a numerical value to a physical quantity, such as length, weight, temperature, or time. Measurements are used to quantify and compare different aspects of the world around us, and they play a crucial role in many areas of science, engineering, and everyday life.

Measurements can be made using a variety of tools and techniques, ranging from simple rulers and scales to sophisticated scientific instruments. The accuracy and precision of a measurement depend on many factors, including the quality of the measuring instrument, the skill of the person making the measurement, and the conditions under which the measurement is taken.

In order for measurements to be meaningful and useful, they must be expressed in units that are well-defined and universally accepted. The International System of Units (SI) is the most widely used system of units in the world, and it is based on seven fundamental units of measurement, including the meter for length, the kilogram for mass, the second for time, and the kelvin for temperature.

Student           Measurement (yards)    Decimal Calculation

Arturo           6√28                            18.97

Bonnie           8√17                            20.51

Courtney   10π                            31.42

Dawson           3.5√100                    35.00

To calculate the decimals, we can use a calculator to evaluate the square roots and π, and then multiply by the given constant factor, and round the result to the nearest hundredth yard.

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The complete question is:

Answer:

89.974

Step-by-step explanation: