quick! find the solution to the following system
x-y=6
x=11
(show all work)

Part A:

From the given frequency table, we can determine the number of students who have a job and are enrolled in at least three courses:

Job and at least three courses: 37

Similarly, we can calculate the number of students who do not have a job and are enrolled in at least three courses:

No job and at least three courses: 9

To find the proportions, we need to divide these counts by the total sample size, which is 150:

Proportion of students with a job and at least three courses: 37/150 = 0.2467 or 24.67%

Proportion of students without a job and at least three courses: 9/150 = 0.06 or 6%

Part B:

The segmented bar graph provides a visual representation of the association between employment status and the number of courses in which students are enrolled among the 150 students in the sample.

The graph shows three categories of courses: Two Courses, Three Courses, and Four Courses. The y-axis represents the percentage of students in each category, ranging from 0% to 100%.

For the students with a job, the graph indicates that the majority of them (80%) are enrolled in either two or three courses, with a smaller proportion (20%) enrolled in four courses.

For the students without a job, the graph reveals that a significant portion (40%) are enrolled in three courses, while the remaining students are evenly distributed between two courses (20%) and four courses (40%).

Overall, the graph suggests a relationship between employment status and the number of courses. Students with a job tend to have a higher proportion enrolled in two or three courses, while those without a job are more evenly distributed across the different course categories, with a slightly higher percentage in three courses.

All of the coordinates in the attached screenshot are in the second quadrant.

The domain and range of the relation shown in the table include the following: A. domain:{−3, −1, 2, 4}, range:{0, 2, 4}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined.

This ultimately implies that, a domain is the set of all possible input values (x-values) to a relation, and the domain of a graph comprises all the input values which are located on the x-coordinate from the least to the greatest.

Additionally, a range is the set of all real numbers that is associated with the elements of a domain i.e all of the y-values shown on the y-coordinate of the graph of a relation, from the least to the greatest.

By critically observing the table of this relation shown, we can reasonably infer and logically deduce the following:

Domain = {−3, −1, 2, 4}.

Range = {0, 2, 4}.

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Answer:

(a) 0.15866

(b) Clustered, with two peaks

(c) Point estimate is 6.3 inches

Margin of error is 0.7 inches

(d) Yes

(e) Stratified sampling method

Step-by-step explanation:

(a) The given information are as follows

Mean diameter of Aspen trees, μ = 8 inches

Standard deviation, σ = 2.5 inches

\(z = \frac{x - \mu}{\sigma} = \frac{5.5 - 8 }{2.5} = -1\)

Therefore;

p(x < 5.5) = p(z < -1)

From the z score table, we have p = 0.15866

Therefore, the probability that a randomly selected aspen tree in this park in 1975 would have a diameter less than 5.5 inches = 0.15866

(b) The distribution of the Aspen trees can be described as clustered and having two peaks around 9.25 inches and 5.25 inches

(c) The point estimate is 5.6 + (7.0 - 5.6)/2 = 6.3

The margin of error = (7.0 - 5.6)/2 = 0.7 inches

(d) Yes, because the 8 inches is outside the range

(e) Stratified sampling method

Here, the Aspen trees are separated into the highland and lowland samples such that the measurement required will be representative of both highlands park and lowlands park.

We will have the following:

From the problem we will have the following expressions:

Now, from this we determine the value for the bill on september:

Now, since there are 3 people, the payment for each one is:

So, the payment for each one is $26.87 in September.

Answer:

y = 4

Step-by-step explanation:

an horizontal line has always the same y (in this case is 4)

Answer:

-120, -90, -85

Total;

-295

Step-by-step explanation:

Here, we want to write the sum of negative integers in order of the turns given in the question

We have these orders as follows;

-120-90-85

The sum of these is;

-295

Answer:

\( \: \)

Step-by-step explanation:

Let us assume A, B, C and D are the four angles of the parallelogram. Where, ∠A = 20° and we have to find the measure of ∠B, ∠C and ∠D

So, If ∠A = 20°, then So, also ∠C = 20°.

Therefore,

⠀

And, ∠A and ∠B are adjacent angles. We know,

So,

⇒ ∠A + ∠B = 180°

⇒ 20° + ∠B = 180°

⇒ ∠B = 180° – 20°

⇒ ∠B = 160°

So,

⠀

So, If ∠B = 160°, then So, also ∠D = 160°.

Therefore,

After seven years, the maturity value of Prabhjot's investment in the mutual fund was $1,804.94. This value takes into account the initial investment of $1,450 and the compounding of interest at different rates over the course of seven years.

To calculate the maturity value of Prabhjot's investment, we need to consider the compounding of interest at different rates for the first three years and the last four years.

For the first three years, the interest is compounded semi-annually at a rate of 4.8%.

This means that the investment will grow by 4.8% every six months. Since there are two compounding periods per year, we have a total of six compounding periods for the first three years.

Using the compound interest formula, the value of the investment after three years can be calculated as:

\(A=P*(1+\frac{r}{n})^{nt}\)

Where:

A = Maturity value

P = Principal amount (initial investment)

r = Annual interest rate (4.8%)

n = Number of compounding periods per year (2)

t = Number of years (3)

Using the above formula, we can calculate the value of the investment after three years as $1,450 *\((1 + 0.048/2)^{2*3}\) = $1,577.94.

For the last four years, the interest is compounded quarterly at a rate of 4.5%.

This means that the investment will grow by 4.5% every three months. Since there are four compounding periods per year, we have a total of sixteen compounding periods for the last four years.

Applying the compound interest formula again, the value of the investment after the last four years can be calculated as:

A = $1,577.94 * \((1 + 0.045/4)^{4*4}\)= $1,804.94.

Therefore, the maturity value of Prabhjot's investment after seven years is $1,804.94.

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a. the equation for the object's velocity is v(t) = -6 cos(t) - 1. b. the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

a) To find the equation for the object's velocity, we need to integrate the acceleration function with respect to time.

The integral of a(t) = 6 sin(t) with respect to t gives us the velocity function v(t):

v(t) = ∫(6 sin(t)) dt

Integrating sin(t) gives us -6 cos(t), so the equation for the object's velocity is:

v(t) = -6 cos(t) + C

To find the constant C, we use the initial velocity v(0) = -7 m/s:

-7 = -6 cos(0) + C

-7 = -6 + C

C = -1

Therefore, the equation for the object's velocity is:

v(t) = -6 cos(t) - 1

b) To find the object's displacement from time 0 to time 3, we need to integrate the velocity function over the interval [0, 3]:

Displacement = ∫[0,3] (-6 cos(t) - 1) dt

Integrating -6 cos(t) gives us -6 sin(t), and integrating -1 gives us -t. Applying the limits of integration, we have:

Displacement = [-6 sin(t) - t] from 0 to 3

Plugging in the upper and lower limits:

Displacement = [-6 sin(3) - 3] - [-6 sin(0) - 0]

Displacement ≈ -6 sin(3) + 3

Therefore, the object's displacement from time 0 to time 3 is approximately -6 sin(3) + 3 meters.

c) To find the total distance traveled by the object from time 0 to time t, we need to integrate the absolute value of the velocity function over the interval [0, t]:

Total Distance = ∫[0,t] |(-6 cos(t) - 1)| dt

Since the absolute value function makes the negative part positive, we can rewrite the equation as:

Total Distance = ∫[0,t] (6 cos(t) + 1) dt

Integrating 6 cos(t) gives us 6 sin(t), and integrating 1 gives us t. Applying the limits of integration, we have:

Total Distance = [6 sin(t) + t] from 0 to t

Plugging in the upper and lower limits:

Total Distance = [6 sin(t) + t] - [6 sin(0) + 0]

Total Distance = 6 sin(t) + t

Therefore, the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

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Answer:

Daily pay= $18

5 days pay = $90

Step-by-step explanation:

Archer's daily pay =p

Pay for 5 days= 5p

Gas = 1/2 of 5p

= 1/2 × 5p

= 5p/2

Water = $5

Balance = $40

5p = 5/2p + 5 + 40

5p - 5/2p = 45

10p -5p /2 = 45

5/2p = 45

p= 45÷ 5/2

= 45 × 2/5

= 90/5

P= $18

5p= 5 × $18

=$90

The equation to determine Archer's daily pay is

5p = 5/2p + 5 + 40

Divide both sides by 5

p = 5/2p + 45 ÷ 5

= (5/2p + 45) / 5

p= (5/2p + 45) / 5

As per area of rectangle, the dimensions of the box that yield the lowest cost is (1,1,6)

Area of rectangle:

The standard formula for area of rectangle is calculated as,

A = length x breadth

Given,

A closed rectangular box with volume 6 cubic feet is made from two different types of cardboard. the top and bottom are made with a heavy-duty cardboard that costs 30 cents per square foot. The sides are made from a light-weight cardboard that costs 5 cents per square foot.

Here find the dimensions of the box that yield the lowest cost.

Here let's consider the dimensions of the rectangular box be length l, breadth is b, and height is h.

Now, from the given information, the total cost can be derived as,

=> C=2lb×48+(2bh+2lh)×8

=> C=96lb+16bh+16lh

=> C=16(6lb+bh+lh) -----------------→(1)

Then the given volume is, V = lbh = 6 ---------------→(2) cubic feet.

Then the equation 2,

=> lbh = 6h = 6/lb

And then we have to substitute the value of h in equation 1, we get

=> C(l,b,h)=16(6lb+6/l+6/b)

Now we need to minimize the resulting function of two variables.

Therefore, we need to partially derivative the above function with respect to l,b. And set these equal to zero.

And the for l=0,b is undefined. So we can eliminate l=0.

Here we have to substitute l=1,b=112⇒1 in equation 2, we get

=> lbh=6(1)(1)h=6h=6h=6

Therefore, the critical point is, (1,1,6)

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354 Valencia student tickets and 133 non-student tickets were sold.

Let's use algebra to solve the problem. Let

x be the number of Valencia student tickets sold

y be the number of non-student tickets sold

We know that

x + y = 487 (the total number of tickets sold is 487)

14x + 25y = 8391 (the total receipts from ticket sales is $8391)

We can use the first equation to express one of the variables in terms of the other. For example, we can solve for y

y = 487 - x

Here we have to use the substitution method, we can then substitute this expression for y into the second equation

14x + 25(487 - x) = 8391

Simplifying and solving for x

14x + 12275 - 25x = 8391

-11x = -3884

x = 354

So, 354 Valencia student tickets were sold. We can use the first equation to find y

x + y = 487

354 + y = 487

y = 133

So, 133 non-student tickets were sold.

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The given differential equation by undetermined coefficients y"" 8y' + 16y= 20x + 4 y(x) = C₁e^(-4x) + C₂xe^(-4x) + x³ - x² + x - 1 and the given differential equation by undetermined coefficients. y""+y' + y = x²-3x y(x) = C₁e^(-x) + C₂e^(-x) + x - 3x².

Given differential equation is y'' + 8y' + 16y = 20x + 4

To solve the given differential equation by undetermined coefficients, assume that

y_p = A + Bx+ Cx² + Dx³ + Ex⁴ + Fx⁵ … (1)

Differentiating equation (1) with respect to x, we get

y_p' = B + 2Cx + 3Dx² + 4Ex³ + 5Fx⁴ + … (2)

Again differentiating equation (1) with respect to x, we get

y_p'' = 2C + 6Dx + 12Ex² + 20Fx³ + … (3)

Putting equation (1), (2) and (3) in the given differential equation, we get

2C + 6Dx + 12Ex² + 20Fx³ + 8B + 16(B + Cx + Dx² + Ex³ + Fx⁴) + 16(A + Bx + Cx² + Dx³ + Ex⁴ + Fx⁵) = 20x + 4

Simplifying, we get

16A + 8B + 2C = 0

4A + 16B + 6C = 0

20A + 8B + 12C + 2D = 20

Therefore, A = -1, B = 1, C = -1 and D = 11

Thus, y_p = -1 + x - x² + 11x³

= x³ - x² + x - 1

Putting the value of y_p in equation (1), we get y(x) = C₁e^(-4x) + C₂xe^(-4x) + x³ - x² + x - 1

Where, C₁ and C₂ are constants.

Given differential equation is y'' + y' + y = x² - 3x

To solve the given differential equation by undetermined coefficients, assume that

y_p = A + Bx+ Cx² + Dx³ + Ex⁴ + Fx⁵ … (1)

Differentiating equation (1) with respect to x, we get

y_p' = B + 2Cx + 3Dx² + 4Ex³ + 5Fx⁴ + … (2)

Again differentiating equation (1) with respect to x, we get

y_p'' = 2C + 6Dx + 12Ex² + 20Fx³ + … (3)

Putting equation (1), (2) and (3) in the given differential equation, we get

2C + 6Dx + 12Ex² + 20Fx³ + 2B + 6Cx + 12Dx² + 20Ex³ + 30Fx⁴ + A + Bx + Cx² + Dx³ + Ex⁴ + Fx⁵ = x² - 3x

Simplifying, we get

Ex⁴ + (D + E)x³ + (C + 2E + F)x² + (B + 2C + 3E)x + (A + B + C + D + E + F) = x² - 3x

Comparing coefficients, we get

E = 0, D = 0, C = 1, B = -3 and A = 0

Thus, y_p = x - 3x²

Putting the value of y_p in the given differential equation, we get y(x) = C₁e^(-x) + C₂e^(-x) + x - 3x²

Where, C₁ and C₂ are constants.

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Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

Below are some authorial techniques that can be used to create mystery, tension, or surprise in literature.

Order of events: The order in which events are presented can create a sense of mystery or suspense.

Pacing: The pace of a story can also be used to create suspense. A slow-paced story can build tension by allowing the reader to dwell on the details of a situation, while a fast-paced story can create excitement and surprise by keeping the reader guessing what will happen next.

Structure: The structure of a story can also be used to create mystery, tension, or surprise. For example, a story that is told in flashback can create a sense of mystery by revealing information about the past that is relevant to the present.

Time manipulation: The manipulation of time can also be used to create suspense.

Language: The language that an author uses can also be used to create mystery, tension, or surprise. For example, an author might use vague or ambiguous language to create a sense of mystery, or use strong language to create a sense of tension or surprise.

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The diameter of the pizza to the nearest inch is 11 inches.

Let's call the diameter of the pizza "d". The circumference of the pizza can be calculated using the formula:

C = πd

And since the outer edge of the crust from one piece measures 5.5 inches, that length is equal to 1/8 of the circumference of the pizza:

5.5 = (1/8)C

So we can substitute the formula for the circumference into this equation:

5.5 = (1/8)(πd)

Solving for d, we can multiply both sides by 8/π:

d = (5.5)(8/π)

Calculating the approximate value of π as 3.14, we get:

d ≈ (5.5)(8/3.14) = 11 inches

So the diameter of the pizza is approximately 11 inches, rounded to the nearest inch.

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Answer:1.24

2.7 27/56

3.3/4

4.1 2/3

Step-by-step explanation:

You're looking for "parabola" like shapes in which the lowest point has a y coordinate of y = 0. In this case, it would be the "parabola" portion on the right that has its lowest point at (3,0). The only interval that fits is \(2 \le x \le 4\) which in interval notation is written as [2,4]. So this fits with choice D.

Answer:

3855

Step-by-step explanation:

Answer:

3,855

3955 - 100 = 3855

'Less than' implies subtraction.

The position of the particle at time t is given by s = f(t) = t^3 - 15t^2 + 72t, So, at t = 3 seconds, the particle's position is 108 feet.

Let's proceed with the calculation.

The law of motion for the particle is given by the function f(t) = t^3 - 15t^2 + 72t, where t represents time in seconds and s represents the displacement of the particle in feet.

To calculate the position of the particle at a specific time t, we substitute the value of t into the function f(t).

For example, let's calculate the position of the particle at t = 3 seconds:

f(3) = (3)^3 - 15(3)^2 + 72(3)
     = 27 - 135 + 216
     = 108 feet

So, at t = 3 seconds, the particle's position is 108 feet.

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To solve triangle ABC, we are given:

Angle A = 35.8°

Side a = 3.3 units

Side c = 13.7 units

To determine the triangle, we need to find the remaining angles and sides.

Using the Law of Sines, we can write:

sin(A) / a = sin(C) / c

Substituting the given values:

sin(35.8°) / 3.3 = sin(C) / 13.7

Now we can solve for sin(C):

sin(C) = (sin(35.8°) * 13.7) / 3.3 ≈ 0.7202

To find angle C, we can use the inverse sine function:

C = sin^(-1)(0.7202) ≈ 46.3°

Now that we have angle C, we can find angle B:

B = 180° - A - C

B = 180° - 35.8° - 46.3° ≈ 97.9°

To find side b, we can use the Law of Sines:

b / sin(B) = a / sin(A)

Substituting the given values:

b / sin(97.9°) = 3.3 / sin(35.8°)

Solving for b:

b = (3.3 * sin(97.9°)) / sin(35.8°) ≈ 6.68

Therefore, the possible solution for triangle ABC is:

A = 35.8°, B ≈ 97.9°, C ≈ 46.3°

a = 3.3 units, b ≈ 6.68 units, c = 13.7 units

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In the quadrilateral ABCD if AB ||CD and  AB=9 as well as are CD=9. Then, quadrilateral ABCD is both parallelogram and trapezium.

Parallelogram's characteristics

In the quadrilateral ABCD:

Thus, the quadrilateral ABCD is both parallelogram and trapezium.

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Given:

An organization reported that teenagers spent 3.75 hours per day on an average using their phones.

The claim is that the mean time teenagers spend using their phones is greater than 3.75 hours.

The null and alternative hypothesis respectively is,

In a rhombus, all sides are equal in length, so we can write:

AB = BC = CD = AD

Let's use n to represent the length of any of the sides, such as AB. Then, we can write:

AD = AB

Therefore, the expression in terms of n to represent AD in rhombus ABCD is simply:

AD = n

Step-by-step explanation:

Simply graph the two equations....the intersection of the two graphs is the solution

Answer:

please see details below

Step-by-step explanation:

11) area of square = length X width = 25 X 25 = 625 square feet.

we need to subtract the area of the semicircle.

area of full circle = π r ²,  where r is radius (radius here = 25/2 = 12.5).

so area of semicircle = 0.5 π r ² = 0.5 π (12.5) ² = (625/8) π.

area of shaded region = 625 -  (625/8) π = 379.6 square feet (to nearest tenth). area = 379.56 square feet (to nearest one-hundredth). area = 380 square feet (to nearest square foot).

12) length of diameter, D, (the line that splits the circle in 2 equal halves) is √(21² + 20²) = 29 (inches).

why 29? Pythagoras' Theorem states that in a right-angled triangle (in our question) D² = 21² + 20² = 841. so D = √841 = 29. for a visual description of this, please see attached document.

now we know that the diameter is 29, the radius must be 29/2 = 14.5.

area of triangle = 0.5 X 20 X 21 = 210 square inches.

area of full circle = π r ²,  where r is radius (radius here = 14.5)

= π (14.5) ² = (841/4) π square inches.

area of shaded region = area of circle - area of triangle

= (841/4) π - 210 = 450. 5 square inches (to nearest tenth), 450.52 square inches (to nearest one-hundredth), 451 square inches (to nearest inch).

Answer: Let's solve this problem step by step.

First, let's assume the salaries of An and B to be 5x and 3x, respectively, where x is a common multiplier.

According to the given information, they save Rs. 2600 and Rs. 1800, respectively. Since savings come from the remaining portion of their incomes after spending, we can calculate their expenditures as follows:

For An:

Income of An = Salary of An + Savings of An

Income of An = 5x + 2600

For B:

Income of B = Salary of B + Savings of B

Income of B = 3x + 1800

Now, let's consider the proportion of their expenditures. It is given that the proportion of their expenditures is 9:5. So, we can write the following equation:

(Expenditure of An)/(Expenditure of B) = 9/5

Since expenditure is the complement of savings, we have:

[(Income of An - Savings of An)] / [(Income of B - Savings of B)] = 9/5

Substituting the previously derived expressions for income, we get:

[(5x + 2600 - 2600)] / [(3x + 1800 - 1800)] = 9/5

Simplifying the equation, we have:

5x / 3x = 9/5

Cross-multiplying, we get:

5 * 3x = 9 * 3x

15x = 27x

Subtracting 27x from both sides, we have:

0 = 12x

This implies that x = 0, which is not a valid solution. Therefore, there seems to be an error or inconsistency in the given information or equations. Please recheck the problem statement or provide additional information to help resolve the issue.

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