Eric works for a salary of $3,500 per month.

What is Eric’s gross pay for one year?

For the perimeter of a rectangle, the formula for w is

⇒ w = (p - 2L) / 2

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The formula for the perimeter of a rectangle is,

⇒ p = 2L + 2w

Hence, The formula for the width (w) is,

⇒ p = 2L + 2w

⇒ p - 2L = 2w

⇒ 2w = p - 2L

⇒ w = (p - 2L) / 2

Thus, For the perimeter of a rectangle, the formula for w is

⇒ w = (p - 2L) / 2

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The complete question is this,

The formula for the perimeter of a rectangle is P=2l+2w. Which is the equivalent equation solves for w?

P-2l/2=w

P+2l/2=w

P+l=w

P-1=w

A coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

a) Given that, the graph shows the equations y= - 1/2x+3 ------(i) and y=2x-2 ------(ii).

From the graph, the solution is (2, 2)

b) Put x=1 in equation (i), we get

y= -1/2(1)+3

y= 2.5

Put x=2 in equation (i), we get

y= -1/2(2)+3

y= 2

Put x=3 in equation (i), we get

y= -1/2(2)+3

y= -1/2 (3)+3

y= -1.5+3

y= 1.5

So, a coordinate that is a solution to the first equation is (3, 1.5)

Therefore, a coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).

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The short piece is 28 cm and the other piece is 43 cm longer or (28+15 = 43 cm).

Based on the question, One piece will be length x and the other piece will be 15 cm longer, so it will be x + 15 cm long.

Added together the length of these two boards will equal 71 cm. So the equation will be:

x + (x + 15) = 71

2x+15=71

2x=71-15

2x=56

x=28 cm

The short piece is 28 cm and the other piece is 43 cm longer or 28+15 = 43 cm.

Mathematical modeling can be done by taking the following steps, namely:

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Answer:

Step-by-step explanation:

You want the slope-intercept form equation for the tangent line at point (π/6, 1) on the curve y = 2·sin(x).

The slope of the line at the point of tangency is the derivative of the curve at that point:

  y' = 2cos(x) = 2·cos(π/6) = 2(√3/2)

  m = √3 . . . . . approximately 1.7321

Solving the line's equation for b, we have ...

  y = mx +b

  b = y -mx = 1 -(√3)(π/6)

  b = 1 -π√3/6 . . . . . approximately 0.0931

The equation of the line is ...

  y = mx +b

  y = (√3)x +1 -(π√3)/6

Answer:

tan60 = [tex]\frac{x}{6}[/tex]

      x = 6 x tan60

         = 10.4 ( cor to 3 significant figures)

cos60 = [tex]\frac{6}{y}[/tex]

        y = [tex]\frac{6}{cos60}[/tex]

           = 12

Answer:

Add 5 +4 × 6 ÷ 3 - 7 + 3and you will get 14 and that is your answer

The given fractions are sorted in ascending order following the rules of sorting fractions.

What are fractions?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. The number of components of a specific size is expressed as a fraction.

Some of the rules for arranging fractions are as follows:

Now following the above rules, we can solve each question.

        We will make the denominators the same.

      The LCM of 40, 40, 20,4,5 = 40

     So the fractions become,

         [tex]\frac{21}{40} , \frac{29}{40} ,\frac{34}{40},\frac{30}{40},\frac{32}{40}[/tex]

      Now sort them.

     [tex]\frac{21}{40} , \frac{29}{40} ,\frac{30}{40},\frac{32}{40},\frac{34}{40}[/tex]

  2. [tex]\frac{7}{9} , \frac{2}{9} ,\frac{5}{6},\frac{13}{18},\frac{3}{18}[/tex]

   LCM of 9,6,18 = 18

    So the fractions become,

      [tex]\frac{14}{18} , \frac{4}{18} ,\frac{15}{18},\frac{13}{18},\frac{3}{18}[/tex]

    Now sort them.

  [tex]\frac{3}{18} , \frac{4}{18} ,\frac{13}{18},\frac{14}{18},\frac{15}{18}[/tex]

3.  [tex]\frac{9}{4} , \frac{4}{3} ,\frac{5}{3},\frac{7}{4},\frac{7}{5}[/tex]

     LCM of 4,3,5 = 60

   [tex]\frac{135}{60} , \frac{80}{60} ,\frac{100}{60},\frac{105}{60},\frac{84}{60}[/tex]

Now sort them.

[tex]\frac{80}{60} , \frac{84}{60} ,\frac{100}{60},\frac{105}{60},\frac{135}{60}[/tex]

4. [tex]\frac{17}{7} , \frac{23}{7} ,\frac{24}{5},\frac{17}{5},\frac{11}{35}[/tex]

LCM of 7,5,35 = 35

[tex]\frac{85}{35} , \frac{115}{35} ,\frac{168}{35},\frac{119}{35},\frac{11}{35}[/tex]

Now sort them.

[tex]\frac{11}{35} , \frac{85}{35} ,\frac{115}{35},\frac{119}{35},\frac{168}{35}[/tex]

Therefore the above fractions are sorted in ascending order.

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The first truck did 62% of all the job.

First, from the problem we know that the first truck does its job at a rate per hour:

And, the second truck has a rate per hour of:

So, the rate per hour with both trucks working together will be the sum:

Now, we have to find the time it will take to do the whole job with both trucks, the whole job done will be represented by 100% or 1:

Where t is the unknown time that it takes to do all the job. Solving this we have:

This means that the whole job will be done after 3.08 hours using both trucks. However, the problem is asking just about the first truck. To find that answer we just have to multiply its rate with the time:

This decimal number represents the portion that the first truck finished to have the job done. 0.62 means that it did 62% of all the job.

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correct question:

The city just assigned a second garbage truck to empty the bins in Kat’s neighborhood on trash day. The crew from the first garbage truck used to empty all the bins by themselves in 5 hours. In their training, it took the crew from the second garbage truck 8 hours to empty all the bins. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty? To the nearest tenth, the first garbage truck will empty about of all the bins.

Answer:

Step-by-step explanation:

When the two crews start working together, the part of all the garbage bins that the first garbage truck will empty is; A: 0.6

We are told that the first truck empties all bins in 5 hours. Thus;

Rate of first truck per hour = ¹/₅

Second truck empties all bins in 8 hours. Thus;

Rate of second truck per hour = ¹/₈

If both trucks work together, their rate per hour is;

Combined rate per hour = ¹/₅ + ¹/₈

Combined rate per hour = ¹³/₄₀

Thus, number of hours it will take for both of them to do the whole job, we will solve as;

¹³/₄₀t = 1

where t is the time it will take both of them combined to finish the whole job.

Thus;

t = ⁴⁰/₁₃

The part that the first garbage truck will empty when they both work together = ¹/₅t = ¹/₅ * ⁴⁰/₁₃

⇒ Approximately 0.6

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a) The sets A, B and D form a partition of the real numbers, as each real number is present in exactly one of of these sets.

b) The sets B, D and E do not form a partition of the real numbers, as the element x = -2 belongs to both sets D and E.

The conditions for the partition of a set are given as follows:

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Answer:

x=-5

I think this is right

Step-by-step explanation:

Check the picture below.

Answer:

$80

Step-by-step explanation:

To find points on a Cartesian plane, you need to know the x and y coordinates of the point. The Cartesian plane has two axes, the x-axis and the y-axis, which intersect at the origin (0, 0).

The x-coordinate of a point tells you how far the point is from the y-axis, either to the right (if the coordinate is positive) or to the left (if the coordinate is negative).

The y-coordinate of a point tells you how far the point is from the x-axis, either up (if the coordinate is positive) or down (if the coordinate is negative).

So, to find a point on the Cartesian plane, you need to know both its x and y coordinates. For example, the point (3, 4) is located 3 units to the right of the y-axis and 4 units up from the x-axis.

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Answer: THE ANSWER IS 18/42 

Step-by-step explanation:

32.66 repeated :>))))))))))))))

Answer:

30.6666666667

Step-by-step explanation:

92÷3 = 30.6666666667

The amount of petrol left remaining in the car after Tuesday journey is (x/2) - 2

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

A car has x litres of petrol in its tank. One half is used on Monday. Therefore:

Amount of petrol remaining = x - (1/2) of x = x - x/2 = x/2

A further 2 litres on Tuesday, hence:

Amount of petrol left = (x/2) - 2

The amount of petrol left is (x/2) - 2

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It will take the inattentive driver 5.22 seconds to come to a complete stop, assuming the car's deceleration remains constant.

An inattentive driver traveling 16.0 m/s when he notices a red light ahead and his car is capable of decelerating at a rate of [tex]3.06 m/s^2[/tex]. To determine how much time it will take for the car to come to a complete stop, we can use the following equation of motion:

v = v0 + at

where v is the final velocity (in this case, 0 m/s), v0 is the initial velocity (16.0 m/s), a is the acceleration (negative, because the car is slowing down), and t is the time.

Rearranging and solving for t, we get:

t = -v0 / a

t = -16.0 / (-3.06)

t = 5.22 seconds

So, it will take the inattentive driver 5.22 seconds to come to a complete stop, assuming the car's deceleration remains constant. This time can be used to determine the minimum distance the driver needs to maintain between himself and the vehicle in front of him to avoid a collision.

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Answer:

y=1/5x+10

Step-by-step explanation:

The variable y as the subject formula in the equation (2/3)y + v = x is y = (3/2)(x) - (3/2)(v)

Given the equation in the question;

(2/3)y + v = x

y = ?

Solve for y, we make 'y' the subject of the formula.

(2/3)y + v = x

Subtract v from both sides

(2/3)y + v - v = x - v

(2/3)y = x - v

Multiply both sides by 3/2

(3/2)(2/3)y = (3/2)(x - v)

y = (3/2)(x - v)

Apply distributive property.

y = (3/2)(x) - (3/2)(v)

Therefore, y equals (3/2)(x) - (3/2)(v).

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Answer:

D

Step-by-step explanation:

diff y / diff x = slope

so -6/2 = -3

Y intercept is where x= 0, so it's 6

D

The other lengths we can determine for this diagram are;

A rhombus is a flat shape that has four sides that are the same length with the opposite sides parallel to each other and not perpendicular to each other. The four sides of a rhombus are the same length because a rhombus is formed from two congruent isosceles triangles.

The image above includes a rhombus with 90 degree angles between its diagonals.

So that the four outer sides are the same length, namely DE=EF=FG=DG= 6

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Answer: To project the population in 2020, we can use the linear trend line equation.

First, we need to find the equation of the line. Let's use the two given points, (2000, 220,000) and (2010, 252,000), to find the slope of the line:

slope = (252,000 - 220,000) / (2010 - 2000) = 32,000

Next, we can use the slope-intercept form of the line equation: y = mx + b, where m is the slope and b is the y-intercept.

Plug in the first point: 220,000 = 32,000 * 2000 + b

Solve for b: b = 220,000 - 32,000 * 2000 = -44,000,000

The equation of the line is: y = 32,000x - 44,000,000

Finally, we can use the equation of the line to project the population in 2020:

y = 32,000 * 2020 - 44,000,000 = 264,000

So, the projected population in 2020 is 264,000.

Step-by-step explanation:

Answer:

The Pythagorean Theorem states that, for a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Therefore, if we have a right triangle with angles A, B, and C, then:

$$A^2 + B^2 = C^2$$

Now, let's consider a triangle with angles of 75°, 45°, and 30°. We know that the sum of the angles must equal 180°, so these three angles add up to 180°.

We can now plug in the angles into the formula above and solve for the hypotenuse C:

$$(45^2) + (30^2) = C^2$$

$$2025 = C^2$$

$$\sqrt{2025} = C$$

Therefore, the length of the hypotenuse C is 45 units.

Now, let's look at the cosine of angle A, which is 75°. By definition, the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Therefore, for this triangle:

$$\cos 75° = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{\text{Adjacent side}}{45}$$

We can now find the length of the adjacent side by subtracting the length of the opposite side from the hypotenuse:

$$\text{Adjacent side} = 45 - \text{Opposite side}$$

The length of the opposite side is equal to the length of the other leg, which is 30 units in this case. Therefore, the length of the adjacent side is 15 units.

Putting this all together, we can now solve for the cosine of 75°:

$$\cos 75° = \frac{15}{45} = \frac{\sqrt{2} (\sqrt{3}-1)}{4}$$

Therefore, cos 75° = √2 (√3-1)÷4.

The smallest positive value for (a+b)/(a-b)+(a-b)/(a+b) where a and b are integers is 2.

In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.

Now

For given expression (a+b)/(a-b)+(a-b)/(a+b)

where a>b and both are integers.

solving the expression

((a+b)(a+b)+(a-b)(a-b))/((a+b)(a-b))

=2(a²+b²)/a²-b²                  

As (a+b)²=a²b²+2ab and a²-b²=(a+b)(a-b)

So for given expression negative and positive values for a,b gives same result then smallest values will be a=1, b=0

Then

=2*1/1

=2

Hence, The smallest positive value for (a+b)/(a-b)+(a-b)/(a+b) where a and b are integers is 2.

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Answer:

183

365/2

you get 182.5 but you round up because you don't have half a person in the room.

Step-by-step explanation:

Answer:

[tex](x, y ) \rightarrow (\boxed{\dfrac{x}{3}}, \boxed{-\dfrac{y}{3}})[/tex]

Step-by-step explanation:

The image(the smaller inverted triangle) obtained from the pre-image(the larger triangle) by compressing it by a factor of -1/3(called a dilation) and then reflected across the y-axis

If you examine the two triangles you will see that

Point A(-3, -3) ==> Point X(-1, 1)

Point B(-3, 3) ==> Point Z(-1, -1)

Point C(3, -3) ==> Point Y(1, 1)

So the x coordinates and y coordinates of the image are transformed as follows:

x' =  x/3

y' =   - y/3

The statistical test to be chosen depends on the nature of the data and the research question being answered. There are several statistical tests available, each with different assumptions and purposes.

A statistical test is a method used to evaluate data and make inferences about a population based on a sample of the population. The purpose of a statistical test is to determine if the results of an experiment or survey are statistically significant, which means that they are unlikely to have occurred by chance. Statistical tests use mathematical models to determine the likelihood of an event occurring and provide a level of confidence in the results.

Here are some common statistical tests and when they might be used:

T-test: A t-test is used to compare the means of two groups to determine if there is a significant difference between them. This test is often used in experiments where one group is treated differently from another.

ANOVA: ANOVA (Analysis of Variance) is used to compare the means of three or more groups to determine if there is a significant difference between them.

Chi-square test: A chi-square test is used to determine if there is a significant relationship between two categorical variables.

Linear Regression: Linear regression is used to study the relationship between a dependent variable and one or more independent variables.

Logistic Regression: Logistic regression is used to predict a binary outcome based on one or more independent variables.

It is important to choose the right statistical test to ensure that the results are meaningful and accurate. The choice of the test depends on the research question, the nature of the data, and the assumptions of the test. It is advisable to consult with a statistician to determine the appropriate test for a given situation.

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The difference between the median and mean income can be explained by the distribution of the data.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When data collection is ranked from least to greatest, the median is the midpoint. The mode is the number that occurs most often in a data set.

The median and mean are both measures of center used to describe a distribution of data. In this case, the median income of American households in 2021 is reported as $70,000, which means that half of the households have an income below $70,000 and a half have an income above $70,000.

On the other hand, the mean income of these same households in 2021 is reported as $100,000. This means that if we were to add up the income of all households and divide by the total number of households, we would get an average of $100,000 per household.

The difference between the median and mean income can be explained by the distribution of the data. If the data is symmetrically distributed around the center (i.e., the median), the mean and median will be similar. However, if the data is skewed, meaning it is not evenly distributed, then the mean and median will be different.

In this case, it is possible that a small number of households have very high incomes, which would pull up the mean income while not affecting the median income as much. This could explain why the mean income is higher than the median income.

It's also worth noting that while the median and mean income are both useful measures, they do not tell the whole story about income distribution.

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Answer:

f(0) = -3

Step-by-step explanation:

1. Insert f(0) into the function of f(x) = 3x-6

2. f(0) = 3 x 0 - 6

3. f(0) = 3 - 6 =  -3

Answer:

5

Step-by-step explanation:

We can set up an equation.
Let x be the number.

So 5x+5 would be equal to 30.

5x+5 = 30

Subtract 5 on both sides:
5x = 25

Divide by 5 on both sides:

x = 5