Evaluate and Simplify the expression: 13 + pwhen p =2

Answer:

There would be 18 girls in the class.

Step-by-step explanation:

Since 3/5 of the class are boys, that means 2/5 are girls. On a calculator, divide 2 by 5 since 2/5 are girls:

2 divided by 5 = 0.4

Now, we take the 0.4 and multiply it by the total of 45 students:

0.4 x 45 = 18 girls

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Work Shown:

x = number of boys

(3 boys)/(5 total) = (x boys)/(45 total)

3/5 = x/45

3*45 = 5x .......... cross multiply

135 = 5x

5x = 135

x = 135/5

x = 27

There are 27 boys in the class of 45 students total. That means there are 45-27 = 18 girls is the answer

------------------

Another approach:

3 out of every 5 students are boys

That must mean 2 out of every 5 students are girls

y = number of girls

(2 girls)/(5 total) = (y girls)/(45 total)

2/5 = y/45

2*45 = 5y

90 = 5y

y = 90/5

y = 18 is the answer

------------------

A third approach:

Consider a small class of 5 students. There are 3 boys and 5-3 = 2 girls. The ratio of boys to girls is 3:2

That ratio scales up to 3k:2k for some positive whole number k.

Those two subtotals of 3k and 2k must add to 45 total students.

3k+2k = 45

5k = 45

k = 45/5

k = 9

Then,

------------------

Feel free to explore other methods to solving this problem.

The denominator 6 in 3/6 is should not be changed when adding fractions if other fractions have a denominator of 6, to make the addition easy because 6 will be the lowest common multiple.

One of the reasons why the denominator will always stay the same when adding fraction is because the size of the equal pieces does not change when you combine the two fractions together.

For example say you want to add 3/6 + 1/6 + 2/6,

you will notice that all the fractions have equal denominator, so adding the fractions together will have the following result.

3/6 + 1/6 + 2/6 = (3 + 1 + 2 ) / 6

= 6/6

= 1

So the 6 in 3/6 should not be changed if all other fractions you wish to add to 3/6 have 6 as their denominator, because the 6 is lowest common multiple.

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part a: In order to determine and interpret the least squares regression line (LSRL), you need to have a set of data points and perform regression analysis.

The LSRL is a line that best fits the data points and represents the relationship between two variables. It is commonly used to predict or estimate values based on the given data.

To determine the LSRL, you will need to calculate the slope and the y-intercept of the line. The slope (m) represents the rate of change of the dependent variable for a one-unit increase in the independent variable.

The y-intercept (b) represents the value of the dependent variable when the independent variable is equal to zero.

Once you have determined the LSRL equation in the form of y = mx + b, you can interpret it.

For example, if the LSRL equation is y = 2x + 3, it means that for every one unit increase in the independent variable, the dependent variable is expected to increase by 2 units.

The y-intercept of 3 indicates that when the independent variable is zero, the dependent variable is expected to be 3.

part b: To predict the percent of children living in single-parent homes in 1991 for state 14, we can use the LSRL equation.

First, substitute the known value of the independent variable (1985) into the equation and solve for the dependent variable (percent of children living in single-parent homes). Let's say the LSRL equation is y = 0.5x + 10.

In this case, x represents the year and y represents the percent of children living in single-parent homes. So, when x is 1985, we can substitute it into the equation:

y = 0.5 * 1985 + 10
y = 993.5 + 10
y ≈ 1003.5

Therefore, the predicted percent of children living in single-parent homes in 1991 for state 14 would be approximately 1003.5 percent.

part c: To calculate the residual for state 14, we need to compare the observed percent of children living in single-parent homes in 1991 (21.5 percent) with the predicted value we obtained in part b (1003.5 percent).

The residual is calculated by subtracting the predicted value from the observed value:

Residual = Observed value - Predicted value
Residual = 21.5 - 1003.5
Residual ≈ -982

The negative value of the residual indicates that the observed value is significantly lower than the predicted value.

In other words, the actual percent of children living in single-parent homes in state 14 in 1991 is much lower than what was predicted based on the LSRL equation and the data from 1985.



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The solution to the initial value problem is dP dt molding sol = kP(1-P), where P(0) = 7 and P(2) = 4 is P(6.69) = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It involves the independent variable, the unknown function, and its derivatives. Differential equations are used to model various physical, biological, and social phenomena in the natural and social sciences.

Given,

the initial value problem as;

dP/dt = kP(1 - P),

P(0) = 7, P(2) = 4

To solve the initial value problem, we will integrate both sides of the given differential equation with respect to t;

we get,

P(t) / [P(t) - 1] = A * e^(kt)

where, A = P(0) / [P(0) - 1] = 7/6

Now, we can write

P(t) / [P(t) - 1] = 7/6 * e^(kt) ---(1)

Using P(2) = 4,

we have4 / (4 - 1) = 7/6 * e^(2k)6 / 7 = e^(2k)ln 6/7 = 2k

Therefore,

k = ln 6/14

Now, substituting k = ln 6/14 in equation (1),

we get

P(t) / [P(t) - 1] = 7/6 * e^(t * ln 6/14)P(t) / [P(t) - 1] = 7/6 * (e^(ln 6/14))^t

P(t) / [P(t) - 1] = 7/6 * (6/14)^(t/2)

P(t) / [P(t) - 1] = 7/12 * 3^(t/2)

Multiplying numerator and denominator by 3^(-t/2),

we get

P(t) / [P(t) - 1] = 7/12 * 3^(t/2) * 3^(-t/2) / (3^(-t/2) - 1)

P(t) / [P(t) - 1] = 7/12 * 3^(t/2) / (1 - 3^(-t/2))

Multiplying numerator and denominator by -1, we get

P(t) / [1 - P(t)] = 7/12 * [1 / (3^(-t/2) - 1)] - 1S

imilarly, using P(0) = 7,

we get

P(0) / [1 - P(0)] = 7/12 * [1 / (3^(0/2) - 1)] - 1 => P(0) = 7

Using the differential equation we can write,

P'(t) = kP(t)(1 - P(t))P'(t) = kP(t) - kP^2(t)P'(t) + kP(t) = kP(t) - kP^2(t) + kP(1 - P(t))U

sing P(t) = 7,

we have

P'(t) = k * 7 * (1 - 7) = -42k

Using P(t) = 4, we have

P'(t) = k * 4 * (1 - 4) = -12k

Therefore, the solution to the initial value problem is,

P(t) = [7e^(ln 6/14 * t)] / [7/6 + e^(ln 6/14 * t)]

Given, P(0) = 7,

we have

P(0) = [7e^(ln 6/14 * 0)] / [7/6 + e^(ln 6/14 * 0)] => 7 = 7/13

Solving for t, we have

4 = [7e^(ln 6/14 * 2)] / [7/6 + e^(ln 6/14 * 2)]

Multiplying numerator and denominator by e^(-ln 6/14 * 2), we get

4 = [7e^(-ln 6/14 * 2)] / [7e^(-ln 6/14 * 2)/6 + 1]24 + 7e^(-ln 6/14 * 2) = 42e^(-ln 6/14 * 2)31e^(ln 6/14 * 2) = 24e^(ln 6/14 * 2)e^(ln 6/14 * 2) = 24/31

Solving for t, we have;

\(t=\frac{2\ln (\frac{24}{31})}{\ln(\frac{6}{14})}\approx 6.69\)

Therefore, the solution to the initial value problem is P(6.69) = 4.

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Probability of people needing corrective shoes or dental work is 0.36.

The proportion of favorable cases to all possible cases used to determine how likely an event is to occur.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive".

Here, the two events getting corrective shoes and getting dental work are not mutually exclusive events.

P(corrective shoes or dental work) = P(corrective shoes) + P(dental work) - P(corrective shoes and dental work)

P(corrective shoes or dental work)  = 0.16 + 0.23 - 0.03

P(corrective shoes or dental work)  = 0.36

Hence, the probability of people needing corrective shoes or dental work is 0.36.

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The meaning to translate a triangle type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Lets take an example:

ΔXYZ with coordinates,

X(-9,6) , Y(2,3) AND Z(-2,-8).

Translation:

X - 3 units in x direction

Y - 3 units in x direction

Z - 3 units in x direction

After translation:

New coordinates are represented in yellow dots in the figure uploaded.

X(-9,6)→X(-9+3,6)→X(-6,6)

Y(2,3)→Y(2+3,3)→Y(5,3)

Z(-2,-8)→Z(-2+3,-8)→Z(1,-8)

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Answer:

potential to kinetic energy

Answer:

7

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

x- 41.5 = 13.5

Step-by-step explanation:

The normal rate is x and the sick rate is 41.5

The difference is 13.5

x- 41.5 = 13.5

The result is assigned tο variable x, sο the value stοred in x is 3.

The value stοred in x can be determined by evaluating the expressiοn οn the right-hand side οf the assignment statement.

Given the statement int x; x = 3 /static_cast<int>(1.5 + 2.4), the expressiοn inside the static_cast is evaluated first:

1.5 + 2.4 = 3.9

Then, the result οf the expressiοn is cast tο an int using static_cast<int>. This perfοrms a static cast, cοnverting the flοating-pοint value tο an integer by truncating the decimal pοrtiοn:

static_cast<int>(3.9) = 3

Finally, the result is assigned tο x, sο the value stοred in x is 3.

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Answer:

A- angle bisector

Step-by-step explanation:

The construction at the figure represents an angle bisector.

Angle bisector of an angle is defined as a straight line that divides the angle into two equal angles.

In the given figure, line AX bisect ∠ABC, which is ∠XAB =∠XAC

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Given:

Fabric required for each chair = 10 yards

Fabric required for each sofa = 20 yards.

Total available fabric = 300 yards.

The number of sofas must be at least twice the number of chairs.

Profit on each chair = $50

Profit on each sofa = $80.

To find:

The function that represents the manufacturer's profit, P.

Solution:

Let P represents the manufacturer's profit, x represent the number of chairs and y represent the number of sofas.

Profit on 1 chair = $50

Profit on x chairs = $50x

Profit on 1 sofa = $80

Profit on y sofas = $80y

Total profit = Profit on x chairs + Profit on y sofas

\(P=50x+80y\)

Therefore, the required profit function is \(P=50x+80y\).

Answer:

B on edge

Step-by-step explanation:

To approximate the volume of the cinder cone volcano, we can create a composite of different shapes that closely approximate the shape of the volcano. So, the approximate volume of the earth materials that make up the volcano is 3,428,520 cubic meters.

First, we can approximate the shape of the cone with a frustum (a truncated cone). We know that the height of the frustum is 230 m (the height of the volcano), the top diameter is 150 m, and the bottom diameter is 450 m. Using the formula for the volume of a frustum (V = 1/3πh(r₁² + r₂² + r₁r₂)), we can calculate the volume of the frustum to be approximately 3,026,400 cubic meters.

Next, we can approximate the shape of the base of the volcano with a circle. We know that the diameter of the base is 80 m, so using the formula for the volume of a cylinder (V = πr²h), we can calculate the volume of the base to be approximately 402,120 cubic meters.

Combining these two shapes, we can create a composite that approximates the volume of the volcano.

The reasoning for choosing these shapes is that they closely approximate the shape of the volcano. The frustum shape is used to approximate the cone shape of the volcano, while the circle shape is used to approximate the base of the volcano.

Adding the volumes of the frustum and the circle, we get an approximate volume of 3,428,520 cubic meters.

Therefore, the approximate volume of the earth materials that make up the volcano is 3,428,520 cubic meters. The units for volume are cubic meters.

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Answer:

Step-by-step explanation:

m - 9 = 12.

Answer:

If I have understood the problem correctly, your answer will be 8.6

Step-by-step explanation:

You will first subtract 6.3 from 2.5 resulting in you getting -3.8

Now your problem will look like this: 4.8-(-3.8)

Since there is two negatives side by side that negative becomes a positive.

Now your problem looks like this: 4.8+3.8

Now you just add the two together resulting in you getting 8.6

Your Welcome

The resultant of the given expression 4.8 – (2.5 – 6.3) is 8.6.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

The group's total number of items decreases or becomes lower when we subtract from it.

Given the expression,

4.8 – (2.5 – 6.3)

4.8 - (-3.8)

Since multiplication of two minuses is plus

So,

4.8 - (-3.8) = 4.8 + 3.8

⇒ 8.6

Hence "The resultant of the given expression 4.8 – (2.5 – 6.3) is 8.6".

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The AB latch is a digital circuit that has a state table and characteristic equation of Q = AB. It can be constructed using four two-input NAND gates and two inverters, where the output of the fourth NAND gate provides the signal Q'.

(a)

State Table:

A B Q

0 0 0

0 1 0

1 0 0

1 1 1

Characteristic Equation: Q = AB

(b)

(c) No, there are no transitions between input combinations that might cause unreliable operation.

(d) Yes, the output of the fourth NAND gate provides the signal Q'.

(e)

(f ) No, there are no transitions between input combinations that might cause unreliable operation. Yes, the output of the fourth NOR gate provides the signal Q'.

The AB latch is a digital circuit that has a state table and characteristic equation of Q = AB. It can be constructed using four two-input NAND gates and two inverters, where the output of the fourth NAND gate provides the signal Q'. Alternatively, it can also be constructed using four two-input NOR gates and two inverters, where the output of the fourth NOR gate provides the signal Q'. In both circuits, there are no transitions between input combinations that might cause unreliable operation.

The complete question us:

An AB latch operates as follows: If A = 0 and B = 0, the latch state is Q = 0; if either A = 1 or B = 1 (but not both), the latch output does not change; and when both A = 1 and B = 1, the latch state is Q = 1. (a) Construct the state table and derive the characteristic equation for this AB latch. (b) Derive a circuit for the AB latch that has four two-input NAND gates and two inverters. (c) In your circuit of part (b), are there any transitions between input combinations that might cause unreliable operation? Verify your answer. (d) In your circuit of part (b), is there a gate output that provides the signal Q′? Verify your answer. (e) Derive a circuit for the AB latch using four two-input NOR gates and two inverters. (f ) Answer parts (c) and (d) for your circuit of part (e).

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The hourly pay before the increase for marta and khalid is 21 and 17.5.

Given:

the ratio of martas hourly pay to khalids hourly pay is 6:5 both marta and Khalid get an increase of 1.50 in their hourly pay The ratio of Martas hourly pay to Khalid hourly pay after this increase is 13:11

Let x and y be the hourly pay before increase

x/y = 6/5

x = 6/5*y

x + 1.50 / y + 1.50 = 13/11

11(x+1.50) = 13(y+1.50)

11x + 16.5 = 13y + 19.5

11(6/5*y) = 13y + 19.5 - 16.5

66y/5 = 13y + 3.5

66y - 13*5y / 5 = 3.5

66y - 65y = 17.5

y = 17.5

x = 6/5*17.5

= 105/5

x = 21

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Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

y = - 2x + 5 ← is in slope- intercept form

with slope m = - 2

Parallel lines have equal slopes , then

y = - 2x + c ← is the partial equation

To find c substitute (- 3, 2 ) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = - 2x - 4 ← equation of parallel line

----------------------------------------------------------

(b)

y = 3x + 4 ← is in slope- intercept form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{3}\) , then

y = - \(\frac{1}{3}\) x + c ← is the partial equation

To find c substitute (3, 2 ) into the partial equation

2 = - 1 + c ⇒ c = 2 + 1 = 3

y = - \(\frac{1}{3}\) x + 3 ← equation of perpendicular line

The angle of CE is 5.5 units.

According to the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection

That means\($\cdots > $\) Triangles\($\mathrm{ODC}$\) and \($\mathrm{OEC}$\) are right triangles

In the right triangle OEC

we have

O E=O D=4.8 units \($\longrightarrow$\)radius of the circle

O C=7.3 units

Applying the Pythagorean Theorem

\($$O C^2=O E^2+C E^2$$\)

substitute the given values

\(& 7.3^2=4.8^2+C E^2 \\\)

\(& C E^2=7.3^2-4.8^2 \\\)

\(& C E^2=30.25 \\\)

\(& C E=5.5\) units

The complete questions is,

In the figure below, the segments cd and ce are tangent to the circle centered at o. Given that od= 4.8 and oc= 7.3, find ce

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The amount the building inspector may be entitled to from the prime contractor due to his injury is $150.00.

A subcontractor is a person or company that agrees to do some or all of another company's work as part of a larger project.

The original company, which is often referred to as the prime or principal contractor, delegates some part of the work to the subcontractor.

Typically, subcontractors have specialized knowledge or capabilities that the prime contractor does not have.

A subcontractor is an independent contractor who is employed by a prime contractor.

Because they are not employed by the principal contractor, they are not covered by the principal contractor's insurance policy for Workers' Compensation, General Liability, or automobile insurance.

If a subcontractor damages someone's property, the prime contractor may be liable if the subcontractor was performing work under the prime contractor's supervision or if the prime contractor was negligent in selecting or monitoring the subcontractor.

In this instance, the prime contractor may be held liable for any damage caused by a subcontractor or the subcontractor's worker.

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The amount the building inspector may be entitled to from the prime contractor due to his injury is $150.00.What is a subcontractor?A subcontractor is a person or business hired by a general contractor to carry out specific tasks on a construction site.

These individuals or businesses are often engaged in niche activities, such as painting, masonry, or electrical work, and are brought in on a temporary basis to complete a job. A subcontractor is not an employee of the contractor or project owner, but rather an independent contractor. What is the independent contractor rule?The independent contractor rule specifies that an employer is not responsible for injuries to independent contractors or their employees, such as a subcontractor's employees, on a job site. The rule is based on the assumption that independent contractors are responsible for their own protection and have the authority to provide for it. This indicates that the Prime Contractor will not be responsible for the Building Inspector's injuries caused by the Subcontractor. As a result, the inspector's claim against the prime is barred by the independent contractor rule.What is the outcome?The amount the building inspector may be entitled to from the prime contractor due to his injury is $150.00.

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Monthly Contribution = (Monthly Withdrawal Amount * (1 - (1 + Monthly Interest Rate)^(-Number of Months))) / Monthly Interest Rate

Monthly Interest Rate = 7.12% / 12

To help the employee plan their retirement savings contributions, we can calculate the monthly contribution they need to make to their 401(k) in order to achieve their retirement goals.

Here are the steps to calculate the monthly contribution:

Step 1: Calculate the ending salary at the time of retirement:

The employee's starting salary is $46,000 per year, and they receive an annual raise of 4.79%. We can calculate the ending salary at the time of retirement using the compound interest formula:

Ending Salary = Starting Salary * (1 + Annual Raise Rate)^Number of Years

Ending Salary = $46,000 * (1 + 0.0479)^(62 - 37)

Ending Salary = $46,000 * (1.0479)^25

Step 2: Calculate the annual withdrawal amount during retirement:

The employee plans to withdraw 30% of their ending salary each year they are retired. Since the retirement period is 25 years, the annual withdrawal amount is:

Annual Withdrawal Amount = 30% * Ending Salary

Step 3: Calculate the monthly withdrawal amount during retirement:

Since the employee will withdraw the money in monthly installments, we divide the annual withdrawal amount by 12:

Monthly Withdrawal Amount = Annual Withdrawal Amount / 12

Step 4: Calculate the monthly contribution to the 401(k):

We need to find the monthly contribution that, when compounded at an interest rate of 7.12% per year, will accumulate to the required retirement savings. We can use the future value of an ordinary annuity formula to calculate the monthly contribution:

Monthly Contribution = (Monthly Withdrawal Amount * (1 - (1 + Monthly Interest Rate)^(-Number of Months))) / Monthly Interest Rate

Monthly Interest Rate = 7.12% / 12

By plugging in the values and performing the calculations, we can determine the monthly contribution required for the employee to meet their retirement goals.

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Answer:

Step-by-step explanation:

Let the time taken to reach 12,000 feet = x

Distance traveled in 1 minute = 2000 ft

Distance traveled in 'x' minute = 2000 * x = 2000x

30,000 - 2000x = 12000

Add 2000x to both sides

30,000 = 12000 + 2000x

Now subtract 12,000 from both sides

30000 - 12 000 = 2000x

2000x =  18 000

Divide both sides  by 2000

x = 18000/2000

x = 9 minutes

If the equation be 2x² + 7x – 30 then the solution to this equation be 2.5.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Let the given equation be 2x² + 7x – 30 = 0

Factorizing it as

(2x – 5) (x + 6) = 0

then we get

2x – 5 = 0 or x + 6 = 0

simplifying the equation we get

2x = 5 or x = –6

x = 5/2 or x = –6

x = 2.5 or x = –6

Therefore, the correct answer is option a) 2.5.

The complete question is:

Which value of x is a solution to this equation?

2x² + 7x – 30

a) 2. 5

b) 5

c) -2. 5

d) -3

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Answer:

944cm²

Step-by-step explanation:

Area = Area of parallelogram + Area of trapezoid

Area of parallelogram= l× b= 16×26= 416cm²

Area of trapezoid= h/2(a+b)

where a=26cm, b=40cm, h=16cm

Area of trapezoid= 16/2(26+40)=8(66)=528cm²

Area= 416+528=944cm²

The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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Answer:

The answer would be Y= 1/4X -3

Step-by-step explanation:

Hope it was helpful .

Good luck ^.^

The function f(x) is greater than zero when the value of x lies in between -3 and 5 and this can be determined by using the given graph.

Graph is a mathematical representation of a Networks and it's describes the relation between lines and points.

The graph of the function f(x) is given.

The following steps can be used in order to determine the interval for f(x):

Step 1 - The value of f(x) means the value of y.

Step 2 - The value of f(x) is positive when the graph of f(x) is in the first or in the second quadrant.

Step 3 - So, according to the graph function f(x) is positive when the value of x is in between -3 and 5.

Therefore, the correct option is 3).

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Answer:

1/8 and 1/12

Step-by-step explanation: