steven is cutting a board to use for a project.
the board is 10 feet long. he first has to cut off 1 1/2 feet from one end of the board. he has to cut the remaining section board into 3 pieces.
what is the length of each equal piece?
write and solve an equation to represent this situation. write answer as a mixed number

The linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).

What is proportional relationship?

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".

We are given points as (2,14.5), (4,29), (6,43.5) and the origin (0,0).

We know that in a proportional relationship the ratios are equal i.e.

[tex]\frac{y_{1} }{x_{1}} = \frac{y_{2} }{x_{2} } = \frac{y_{n} }{x_{n} }[/tex]

So,

⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25

Since, the ratios are same, therefore the linear relationship is a proportional relationship.

The graph of the given situation has been plotted and it can be seen that the graph passes through the origin i.e. (0,0)

Hence, the linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).

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The value of the variable x = π³ - π/π

Algebraic expressions are described as mathematical expressions that are comprised of variables, factors, constants, terms and coefficients.

These algebraic expressions are also comprised of arithmetic operations, such as;

From the information, we have that;

y = π³

y = πx + π

Substitute the values, we get;

π³ =  πx + π

collect like terms

π³ - π = πx

Divide both sides by the coefficient of x

x = π³ - π/π

Thus, the value is x = π³ - π/π

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There were 0-5 Listeners when the song was released.

The approximate number of listeners who had heard the song after the hour 5 was 15- below 50

The number of listeners was about 29,458 after hour 5842.62/

Alternative forms

Y= 4,637(1.26)ˣ

292131/50,5842,31/50,5.84262 =10³

5842.62

Including polynomial components, such as squared or cubed predictors, is the most popular technique to fit curves to data using linear regression. Typically, the model order is determined by the number of bends required in your line. Each exponent increment causes one additional bend in the curved fitting line.

Curve of Best Fit: a scatter plot curve that best approximates the trend. If the data looks to be quadratic, we use quadratic regression to get the equation for the best-fit curve. We do a cubic regression if it looks to be cubic.

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The solutions that match the given differential equation are a)y=0 and b)y=2x.

The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.

In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.

Therefore, the general solution to this differential equation is y = c1 + c2x.

y=0 is a solution of the differential equation since it satisfies the equation when plugged in.

y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.

y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.

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A power function is a type of function with a variable in the form of an exponent. An exponential function is a type of function that contains a variable in the form of an exponent.

The most common example of this is y = xn, where n is the exponent and x is the independent variable. For example, y = (π)x is a power function with an exponent of x and an independent variable of π.

Exponential Function: An exponential function is a type of function that contains a variable in the form of an exponent. The most common example of this is y = bx, where b is the base and x is the independent variable. For example, y = xy is an exponential function with a base of x and an independent variable of y.

Polynomial: A polynomial is a type of function that has a degree, which is the highest exponent of its variables. For example, y = x2 (2-x3) is a polynomial with a degree of 2 since the highest exponent of its variables is 2.

Trigonometric: A trigonometric function is a type of function that involves trigonometric ratios. The most common example of this is y = tan t â cos t, which uses the trigonometric ratios of tangent and cosine.

Algebraic Function: An algebraic function is a type of function that can be expressed as a combination of polynomials. The most common example of this is y = s / 1+s, which is a combination of polynomials with a numerator of s and a denominator of 1+s.

Root Function: A root function is a type of function that involves a root of a polynomial. The most common example of this is y = sqrt(x3 â 1) / 1+ 3sqrt(x), which uses the root of the polynomial x3 â 1 in the numerator and 3sqrt(x) in the denominator.

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Answer:

4/5 < 2/6

Step-by-step explanation:

Hope it helps! =D

The sample used in the study is b) the 4200 Florida residents surveyed. surveyed. To obtain the answer following steps are :
1. Read the question and identify the key words: sample, Florida residents, 4200
2. Consider the given options and eliminate those that don't match
3. Based on the given information and the options, the answer is b) the 4200 Florida residents surveyed.

This is because the sample used in the study was the 4200 Florida residents who were surveyed, and this sample was used to estimate the proportion of all Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters.

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Answer:

3/4 > 4/7

Step-by-step explanation:

1. Find the LCM of 4 and 7, which is 28

2. Take 3/4 and multiply the numerator and the denominator by 7 (because 7x4=28)

You will end up with 21/28

3. Take 4/7 and multiply the numerator and the denominator by 4 (because 4x7=28)

You will end up with 16/28

Now that the denominators are the same,  the fraction with the bigger numerator is the greater fraction. Therefore, 3/4 is the greater than 4/7.

Number of shingles in the 6th row is 110.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_{n+1} - T_n

for all positive integer values of n

Given;

Each row has 7 fewer shingles than the row below it

First row has 75 shingles

Now,

a=75

D=7

n=6

a_{n}=a_{1}+(n-1)d

a6=75+(6-1)7

a6=75+35

a6=110

Therefore, the answer of arithmetic sequence will be 110.

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Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. (75 -7)  On the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33

The two equivalent expressions to the given one are the ones in options C and E.

C (100y + 32) - (200y + 16)

E -(-100y + 16 + 200y - 32)

We want to see which expressions are equivalent to:

-4*(-25y + 4 + 50y - 8)

Let's distribute that product so we will get:

-4*(-25)*y - 4*4 - 4*50y - 4*-8

100y - 16 - 200y + 32 = -(-100y + 16 + 200y - 32)

Then option E is a correct option

And also is C: (100y + 32) - (200y + 16)

If we keep simplifying this we wil get:

100y - 16 - 200y + 32 = -100y + 16

And here we end.

The only two equivalent expressions are E and C.

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The probability of a person that has the disease and indication of the test also shows the presence of the disease is given by 0.92.

Let us consider 'A' represents the test indicate the presence of disease when it was actually present

A = 96%

  = 0.96

And 'B' represents the population percent actually has the disease

B = 2%

  = 0.02

A' represents the population who represents the disease when actually disease is not present.

A' = 0.08

Probability of a person that has the disease when test also indicates its presence is given by :

P ( A/ B) = P( A∩B) / [ P(A∩B) + P(A'∩B) ]

             = ( 0.02 × 0.96 ) / [ ( 0.02 × 0.96 ) + ( 0.02 × 0.08 ) ]

             = 0.0192 / 0.0208

             = 0.92

Therefore, the required probability of a person having disease when test also indicates it is equal to 0.92.

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The area a of the window as a function of the width x of the window 12x -(4 + π)x2/8

Let y be the height of the window's rectangular part, and let P represent the window's perimeter.

P then equals x plus 2y plus the length of the semicircular part. The radius of the semicircular part is x/2.

So, P = x + 2y + (1/2)(circumference)

     P = x + 2y  + (1/2)(2)π(x/2)

     P = x + 2y +πx/2 = 24

2y = 24 - x - πx/2

y = 12 - x/2 - πx/4 = 12 - (2 + π)x/4

A = xy + (1/2)π(x/2)2

   = x(12 - (2 + π)x/4) + πx2/8

   = 12x -(2 + π)x2/4 + πx2/8

    = 12x - (4 + 2π)x2/8 + πx2/8

   = 12x - 4x2/8 - πx2/8

   = 12x -(4 + π)x2/8

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The number of teachers who teach:

(a) science but not humanities = 45

(b) Humanities but not science = 10  

(c) Humanities or science = 70

To find the number of teachers that teach only Science we can subtract the number of teachers who teach both subjects from the number of teachers that teach science.

Similarly, to find the number of teachers that teach only Humanities we can subtract the number of teachers who teach both subjects from the number of teachers that teach Humanities.

To find the number of teachers who teach Humanities or science we use the elementary set formula,

Here we have

Total number of teachers = 100

No of teachers who teach Humanities, n(H)= 25

No of teachers who teach Science, n(S) = 60

No of teachers who teach both Science and Humanities, n(H ∩ S) = 15  

The number of teachers who teach science but not humanities

= No of teachers who teach Science - No of teachers who teach both

= 60 - 15 = 45  

The number of teachers who teach Humanities but not science

= No of teachers who teach Humanities - No of teachers who teach both

= 25 - 15 = 10

The number of teachers who teach Humanities or Science  

As we know n(A ∪ B) = n(A) + n(B) - n(A ∩ B)  

The number of teachers who teach Humanities or Science

= n(S) + n(H) - n(S ∩ H)    

= 60 + 25 - 15

= 70

Therefore,

The number of teachers who teach:

(a) science but not humanities = 45

(b) Humanities but not science = 10  

(c) Humanities or science = 70

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Answer:

0.2142857143

Step-by-step explanation:

4/7 × 3/8

=12/56

=0.2142857143.

The value of N would be N = q/(9 + 4uz).

What is algebraic manipulation?

Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.

Given:

q - 4Nuz = 9N

To find the value of N, we can use algebraic manipulation.

9N + 4Nuz = q

N(9 + 4uz) = q

N = q/(9 + 4uz)

Hence, the value of N would be N = q/(9 + 4uz).

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When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.

Division is the process of splitting a number or an amount into equal parts.

Given is an expression, 3x³+x-200 which is divided by x-4,

Therefore,

(3x³+x-200) / (x-4)

Divide the leading term of the dividend by the leading term of the divisor:

3x³/x = 3x²

Multiply it by the divisor: 3x²(x−4)=3x³−12x²

Subtract the dividend from the obtained result:

(3x³+x−200)−(3x³−12x2) = 12x²+x−200

Divide the leading term of the obtained remainder by the leading term of the divisor: 12x²/x = 12x

Multiply it by the divisor: 12x(x−4) = 12x²−48x

Subtract the remainder from the obtained result:

(12x²+x−200)−(12x²−48x) = 49x−200

Divide the leading term of the obtained remainder by the leading term of the divisor: 49x / x = 49

Multiply it by the divisor: 49(x−4) = 49x−196

Subtract the remainder from the obtained result:

(49x−200)−(49x−196) = −4

Hence, When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.

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a) ∀x∃y(x < y): For all values of x there exist number y such that all x are less than y.

b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0)) : For any numbers x and y if x is greater tha or equal to 0 and y is greater than or equal to 0 then their product is greater than or equal to 0.

c) ∀x∀y∃z(xy = z) : For any numbers x and y there exist number z such that the product of x and y is equal to z.

We know that  a mathematical statement is nothing but a sentence which is either true or false.

We need to translate these statements into English.

The meaning of some mathematical symbols:

∀ : for all

∃ : there exists exactly one

∧ : and

Here, x, y, z are real numbers.

Consider given mathematical statements.

a) ∀x∃y(x < y)

For all values of x there exist number y such that all x are less than y.

b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))

For any numbers x and y if x is greater tha or equal to 0 and y is greater tha or equal to 0 then their product is greater than or equal to 0.

c) ∀x∀y∃z(xy = z)

For any numbers x and y there exist number z such that the product of x and y is equal to z.

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The average speed throughout the given time was [1,2] = -2.00 cm/sii. -0.26 cm/siii for [1,1.1]. [1.1,1.01] = 0.17 cm/siv. [1.1,1.001] = 0.02 cm/s

The particle's displacement divided by the passage of time represents its average velocity at each time interval. The displacement of the particle for the above motion equation is given by s = 2 sint + 4 cost. By subtracting the displacement at the beginning and end of the period and dividing it by the change in time, we can determine the average velocity for each time period. As an illustration, the displacement for the time period [1,2] is 2 sin + 4 cos at the beginning of the period and 2 sin + 4 cos at the end of the period. These two figures differ by -4, and one second has passed between them.

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If you look at this rationally I believe it will be 7.0 with the odd number.

Expressed the answers to the given operations with the proper number of significant figures:

(a) (1.600 × 10-¹)(2.1 × 10³) = 336

(b) (1.33)³ = 2.352637

(c) 1.93.x 2.651 = 5.11643

(d) 4.4/2.200 = 2

In calculation, single integers called integers are used to represent values. To represent all fine values, the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in colorful combinations and reiterations.

A number is a symbol that can be used to represent any of the ten integers ranging from 0 to 9. an illustration of a two- number.

When a number has two integers, it's called a 2- number . 2- number figures have two integers and range from 10 to 99.

They're unfit to begin with zero since it'll also be regarded as a single- number .

Any number between 1 and 9 can be used as the number in the knockouts place. For case, the figures 45, 78, and 12 have two integers.

a) (1.600 × 10-¹)(2.1 × 10³)

= 1.6 × 2.1 × 10⁻¹⁺³

= 3.36 × 10²

= 336

b) (1.33)³

= 2.352637

c) 1.93 × 2.651

= 5.11643

d) 4.4/2.200

= 2.0

= 2

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The expression to represent how much Jamie spends in all. we may state,0.40x + 0.40y is 8, 0.30x + 0.30y is 6

Set variables to represent the amounts we wish to identify.

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Answer:this is so ez

Step-by-step explanation: 2/5

Answer:

656 cm sq

Step-by-step explanation:

2 x 10 x 2 x 10 = 400

8 x 2 x 8 x 2 =256

256+400 = 656

The measure of an exterior angle of the regular polygon shown in the figure is 60°.

The angle between a side of a polygon and an extended adjacent side is called its exterior angle.

Given is a polygon, since, it has six vertices, so we can say it is a regular hexagon,

We know that, the sum of interior angles of regular hexagon is 720°

Therefore, one interior angle = 720 / 6 = 120°

If we extend a side of the hexagon, (refer to figure attached in solution)

Then, the interior angle and an exterior angle "A" will make a linear pair,

Therefore,

120° + A = 180°

A = 60°

Hence, the measure of an exterior angle of the regular polygon shown in the figure is 60°.

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Answer:

5 tickets for $12.50

Step-by-step explanation:

because in that deal the ticket only costs $2.05

and in the second deal which is 8 tickets for $20.60 the ticket costs 2.57

I think you want to know what written out means? If yes it means when someone writes something down on a book or paper.

The public increased the amount of currency it held and that banks increased the reserve-deposit ratio is $0.66 million.

Now, According to the question:

December 1921

-Currency held by public: $4.59

-Reserve Deposit ratio: 0.095

-Bank reserves: $3.11

-Money supply: $37.3

December 1932

-Currency held by public: $4.82

-Reserve Deposit ratio: 0.109

-Bank reserves: $3.18

-Money supply: $34.0

We know that:

Bank deposits = (Bank reserves)/(Desired reserve-deposit ratio).

The Fed injected $0.30 billion (the public held $0.23 billion as currency and reserves increased by $0.07 billion was held as reserves). However, the money supply still fell by $3.3 billion.

It would have taken an additional 0.109 × $3.3 billion = $0.36 billion in reserves to support $3.3 in additional deposits.

So the answer is $0.30 billion + $0.36 billion = $0.66 billion.

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The given question is incomplete, complete question is :

Based on the information in the table, what quantity of reserves would the Federal Reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?

December 1921

-Currency held by public: $4.59

-Reserve Deposit ratio: 0.095

-Bank reserves: $3.11

-Money supply: $37.3

December 1932

-Currency held by public: $4.82

-Reserve Deposit ratio: 0.109

-Bank reserves: $3.18

-Money supply: $34.0

The inequality that is graphed on the number line is:

x > -2

Here we can see the graph of an inequality on a number line, on it, we can see a blue line that starts with a open circle (which means that we need to use the symbols < or >) at x = -2

Then the line extends to the right of that number, so the allowed values of x are larger than -2, then the inequality graphed is:

x > -2

Thus the correct option is the fourt one.

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Answer:

Step-by-step explanation:

[tex]-63y^2+27y[/tex]

[tex]-63yy+27y[/tex]

[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]

[tex]9y\left(-7y+3\right)[/tex]