Solving a word problem using a system of linear equations of th.. One month Alan rented 5 movies and 2 video games for a total of $21. The next month he rented 3 movies and 8 video games for a total of $50. Find the

rental cost for each movie and each video game.

The function implies that a city with a population of 53.3 thousand people produces 5 tons of fast fashion waste during the autumn/winter season.

The city of Dunwoody, Georgia has a population of 53,300, which is equal to 53.3 thousand people. So, we can express this in terms of f as follows:

W = f(53.3) = 5

This means that the function f(x) gives the amount of fast fashion waste produced by a city with a population of x thousand people. In this case, f(53.3) = 5, which means that a city with a population of 53.3 thousand people produces 5 tons of fast fashion waste during the autumn/winter season.

This is a significant amount of waste, and it is important to be aware of the environmental impact of fast fashion. Fast fashion is a term used to describe the rapid production of cheap, trendy clothing.

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The largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.

To determine the largest and smallest possible number of people attending the football match, given that the figure is stated as 31,200 with 3 significant figures, we need to consider the range of values that can be represented within that significant figures constraint.

For a number to be stated with 3 significant figures, the last significant figure is uncertain and can be either rounded up or down.

To find the largest and smallest possible numbers, we'll consider the cases where the last significant figure is rounded up and rounded down.

Rounding up:

If we round up the last significant figure, the possible range of values is from 31,150 to 31,249.

So the largest possible number of people attending the match would be 31,249.

Rounding down:

If we round down the last significant figure, the possible range of values is from 31,100 to 31,199.

So the smallest possible number of people attending the match would be 31,100.

Therefore, the largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.

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Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

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The circumference of a circle = pi x diameter

Circumference = 3.14 x 32 = 100.48 meters (rounded to two decimal places)

The farmer needs to build a fence around the edge of the field, which has a circumference of 100.48 meters. So the total length of fence needed is 100.48 meters.

Each meter of fence cost £15.95, therefore the cost of building the entire fence can be calculated as:

Total Cost = Length of fence x Cost per meter of fence Total Cost = 100.48 x £15.95 Total Cost = £1601.08

Therefore, it would cost the farmer a total of £1601.08 to build a fence around the edge of the circular field.

Answer:

$1603.47

Step-by-step explanation:

KM, JK, PK, and MJ are shown on the diagram.

Then the correct options are B, C, D, and F.

Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A line segment in mathematics has two different points on it that define its boundaries.

All the line segments will be

JK, JM, KM, MP, PK, and KL

The triangle KPM.

And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.

Then the correct options are B, C, D, and F.

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The required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.

Given that number of water bottles purchased is 75 and cost price (C,P) of the 75 water bottles is $443.25. The increase %  on the purchase price is profit % = 25%.

To calculate the selling price when cost price and profit % is given by following steps:

Step 1 - Calculate the 25% of the cost price which gives profit.

Step 2 - Calculate SP, Selling price = Cost price + profit.

That implies, Profit = 25% of C.P.

Profit = 25/100 × 443.25.

Therefore, Profit = $110.81.

That implies, Selling price(S.P) = Cost price + profit.

S.P = 443.25 + 110.81.

Thus, S.P = $554.06.

Hence, the required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.

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Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

Answer:

14

Step-by-step explanation:

Assuming you meant to find MN.

Given that MN is parallel to the bases of the given trapezoid, and is connected to the midpoints of both sides, we can infer that MN is the midsegment of the given trapezoid.

The length of a midsegment is given by half the sum of the bases.
Therefore, MN = (18 + 10)/2 = 28/2 = 14

The Euclid math contest is the annual contest held by the University of Waterloo. The students from grade-11 to grade-12 can participate in the Euclid math contest.

Euclid contest is a Mathematics contest for senior-level high school students. This contest was participated by nearly 22000 students worldwide every year. This contest allows the students to demonstrate their knowledge of secondary school mathematics. This competition was held by the University of Waterloo.

The senior-grade students will participate in this contest and it takes 2 and a half hours to complete the contest. It has 10 questions and the total mark for the contest is 100. The University of Waterloo values the results from the Euclid math contest when it comes to admission and scholarship offers.

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The equation for the regression line from the data is y = -0.98x + 56.8

Given data ,

To find the equation of the regression line, we will use the method of least squares. The regression line is represented by the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

We need to calculate the values of m and b. Let's begin by finding the mean values of x and y:

Mean of x (x₁) = (6 + 13 + 14 + 10 + 13) / 5 = 12.2

Mean of y (y₁) = (25 + 44 + 46 + 52 + 57) / 5 = 44.8

Next, we calculate the deviations from the mean for both x and y:

Deviation from the mean of x (Δx) = x - x₁

Deviation from the mean of y (Δy) = y - y₁

Now, we calculate the sum of the products of the deviations from the mean:

Σ(Δx * Δy) = (6 - 12.2) * (25 - 44.8) + (13 - 12.2) * (44 - 44.8) + (14 - 12.2) * (46 - 44.8) + (10 - 12.2) * (52 - 44.8) + (13 - 12.2) * (57 - 44.8)

Σ(Δx * Δy) ≈ -51.6

Next, we calculate the sum of the squared deviations from the mean of x:

Σ(Δx²) = (6 - 12.2)² + (13 - 12.2)² + (14 - 12.2)² + (10 - 12.2)² + (13 - 12.2)²

Σ(Δx²) ≈ 52.8

Now, we can calculate the slope (m) using the formula:

m = Σ(Δx * Δy) / Σ(Δx²)

m ≈ -51.6 / 52.8 ≈ -0.98

Finally, we can calculate the y-intercept (b) using the formula:

b = y₁ - m * x₁

b ≈ 44.8 - (-0.98) * 12.2 ≈ 56.8

Hence , the equation of the regression line for the given data is:

y = -0.98x + 56.8

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Answer:

Step-by-step explanation:

To find the arithmetic means in the given sequence, we need to determine the missing numbers between 175 and 235.

Let's calculate the differences between consecutive terms:

1st difference: 235 - 175 = 60

2nd difference: (Next number) - (Previous number) = (Next number) - 235

Since the differences are constant, we can add the same value to each term to find the missing numbers.

Let's calculate the missing numbers using the 1st difference:

175 + 60 = 235

175 + 60 + 60 = 295

175 + 60 + 60 + 60 = 355

Now we have the complete sequence: 175, 235, 295, 355.

To find the arithmetic means, we take the average of consecutive terms:

1st arithmetic mean: (175 + 235) / 2 = 205

2nd arithmetic mean: (235 + 295) / 2 = 265

3rd arithmetic mean: (295 + 355) / 2 = 325

Among the given choices, the correct answer is:

c. 220, 205, 190

This answer represents the correct sequence of arithmetic means between 175 and 235.

[tex]\cfrac{x}{4}-\cfrac{x+10}{2}=3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{x}{4}-\cfrac{x+10}{2} \right)=4(3)}\implies x-(2x+20)=12 \\\\\\ x-2x-20=12-x-20=12\implies -20=12+x\implies \boxed{-32=x} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{2x+1}{5}-\cfrac{x-3}{7}=-2\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{2x+1}{5}-\cfrac{x-3}{7} \right)}=35(-2) \\\\\\ 14x+7-(5x-15)=-70\implies 14x+7-5x+15=-70 \\\\\\ 9x+22=-70\implies 9x=-92\implies \boxed{x=-\cfrac{92}{9}}[/tex]

Answer:

664

Step-by-step explanation:

6x17

6x17

10x6

10x6

10x17

10x17

add them all up and u get 664

The statement, yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

To determine if being a student and preferring logo A are independent events, we need to compare the probabilities of these events occurring.

The probability of being a student, denoted as P(student), is given as 0.8. This means that out of the total population (125), 80% are students.

The probability of a student preferring logo A, denoted as P(student | logo A), is given as 0.8.

This means that out of the students (100), 80% prefer logo A.

If the events of being a student and preferring logo A are independent, then the probability of a student preferring logo A (P(student | logo A)) should be the same as the probability of being a student (P(student)).

However, in the given options, both options A and D state that P(student | logo A) = 0.8, which is the same as P(student).

This suggests that being a student and preferring logo A are independent events.

Hence, Yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

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Answer:

1.5 is the correct answer

Answer:

Step-by-step explanation:how many grams of active dry yeast must be used for bread recipe

Answer:

w<13

Step-by-step explanation:

Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.

Answer:

w < 1`3

Step-by-step explanation:

Isolate the variable w on one side of the inequality sign.

w+7<20

w<20 - 7

w<13.

part a.

the expected value of playing the game is  found as -$0.50.

part b.)

Jim can expect to lose money in the long run if he plays the game many times because the expected value is negative.

The expected outcomes and their corresponding values are:

If we roll a 1 =  Jim wins $1.

If we roll a 2 =Jim wins $2.

If we roll  a 3 = Jim wins $3.

If we roll  a 4 = Jim wins $4.

If we roll  a 5 or 6 =  Jim loses $6.50.

We then calculate the value:

Expected value = (Probability of rolling a 1) × (Value of rolling a 1) + (Probability of rolling a 2) × (Value of rolling a 2) + (Probability of rolling a 3) × (Value of rolling a 3) + (Probability of rolling a 4) × (Value of rolling a 4) + (Probability of rolling a 5 or 6) × (Value of rolling a 5 or 6)

Expected value = (1/6) × $1 + (1/6) × $2 + (1/6) × $3 + (1/6) × $4 + (2/6) × (-$6.50)

EV = $1/6 + $2/6 + $3/6 + $4/6 - $13/6

EV = ($1 + $2 + $3 + $4 - $13)/6

EV = -$3/6

Expected value = -$0.50

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[tex]3a-2b=13\\4a+b=21|\cdot2\\\\3a-2b=13\\\underline{8a+2b=42}\\11a=55\\a=5\\\\3\cdot5-2b=13\\2b=2\\b=1[/tex]

Answer:

a = 5, b = 1

Step-by-step explanation:

We need to realize that in a parallelogram, opposite sides are congruent. Therfore, the length of NO and MP must be the same if we assume that Quadrilateral MNOP is a parallelogram.

Length of NO = 21

Length of MP = 4a + b

Therfore, we can get this equation: 4a + b = 21

We can do the same with the other 2 sides to get: 3a - 2b = 13

As you can see, this is a systems of equations! Lets solve it!

To find the values of "a" and "b" in the given system of equations:

Equation 1: 4a + b = 21

Equation 2: 3a - 2b = 13

We can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method:

Multiply Equation 1 by 2:

2(4a + b) = 2(21)

8a + 2b = 42

Now, we can add Equation 2 and the modified Equation 1 to eliminate the "b" term:

(3a - 2b) + (8a + 2b) = 13 + 42

3a + 8a - 2b + 2b = 55

11a = 55

Divide both sides of the equation by 11:

a = 55 / 11

a = 5

Substitute the value of "a" into Equation 1 to find "b":

4(5) + b = 21

20 + b = 21

b = 21 - 20

b = 1

Therefore, the solution to the system of equations is a = 5 and b = 1.

Therfore, the answer is B, which is what you got as well! Good job!

~~~Harsha~~~

Answer:  A   Polar is (6√2,  [tex]\frac{3\pi }{4}[/tex])

Step-by-step explanation:

Draw a line to point (see image).   You need to find the length of that line and then the angle.   Polar(length, angle)

Using pythagorean theorem

length²  = (6)² + (-6)²

length² = 36 +36

length =√72

length  = [tex]\sqrt{36 *2}[/tex]

length = 6√2

To find angle:

The triangle size is 6-6-6√2  Let's proportionally shrink so we can use unit circle numbers to figure angle.    Becomes: 1-1-√2

So when we do sin x =  opp/adj

sin x = [tex]\frac{1}{\sqrt{2} }[/tex]              >get rid of radical on bottom

sin x  = [tex]\frac{\sqrt{2} }{2}[/tex]             > when is sin = [tex]\frac{\sqrt{2} }{2}[/tex]     This happens at [tex]\frac{\pi }{4}[/tex]   but we are in the 2nd quadrant so the angle is [tex]\frac{3\pi }{4}[/tex]

Polar is (6√2,  [tex]\frac{3\pi }{4}[/tex])

The polar coordinates are (6([tex]\sqrt[]{2}[/tex], 3pi/4).

Rectangular coordinates are in the form of (x, y) and Polar coordinates are expressed in the form of (r, [tex]\theta[/tex]).  

x = r cos([tex]\theta[/tex]), y = r sin([tex]\theta[/tex]) and  x^2 +y^2 =r^2                                       ...(1)

So by using above formulas we can solve our question.

Here , x= -6 and y= 6

r^2 = (-6)^2 +(6)^2

       =72

=>r = 6([tex]\sqrt[]{2}[/tex])

Put the values of x and y in the mentioned formula in eq(1)

-6 =  6([tex]\sqrt[]{2}[/tex] )cos[tex]\theta[/tex]

 6 = 6([tex]\sqrt[]{2}[/tex] )sin([tex]\theta[/tex]),

=>-1/([tex]\sqrt[]{2}[/tex] = cos([tex]\theta[/tex]) , 1/[tex]\sqrt[]{2}[/tex]=  sin[tex]\theta[/tex]

Here cos is negative and sin is positive so it lies in 2nd quadrant

so here [tex]\theta[/tex] lies between [tex]\frac{\pi}{2} \leq\theta\leq\pi[/tex]

[tex]\theta[/tex]= π-π/4

 =3π/4

So,(r, [tex]\theta[/tex]) = ( 6√2, [tex]\frac{3\pi}{4}[/tex] )

Phi (Φ) can be determined for Cable 2 from:

[tex]tan^-1 (Fy/Fx).[/tex]

In trigonometry, [tex]tan^-1 (Fy/Fx)[/tex] represents the inverse tangent function, also known as arctan or atan.

This function is used to find the angle whose tangent is equal to the ratio of the y-component (Fy) to the x-component (Fx) of a vector.

By calculating the ratio Fy/Fx and applying the inverse tangent function, we can determine the angle phi (Φ) for Cable 2.

The value obtained from [tex]tan^-1 (Fy/Fx)[/tex] will represent the angle in radians.

It's important to note that the resulting angle phi (Φ) will provide information about the direction or inclination of Cable 2 based on the given vector components Fy and Fx.

In summary, to determine the angle phi (Φ) for Cable 2, we use the inverse tangent function, represented as[tex]tan^-1 (Fy/Fx),[/tex] which calculates the angle whose tangent is equal to the ratio of the y-component to the x-component of the vector.

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The given set is defined as the cartesian product of two sets X and Y.

In the given set,

We have to explain the meaning of {(x,y) : Ψ(x,y)}

Since we know,

The Cartesian product AxB of two sets A and B is the set of all feasible ordered pairs with A as the first element and B as the second element

Then,

 AxB ={ (p,q): p ∈ A and q ∈ B}

The typical Cartesian coordinates of the plane,

Where A is the set of points on the x -axis, B is the collection of points on the y -axis, and AxB is the xy -plane, are one example.

And we also know that,

A function of two variables is a function in the sense that each input has precisely one output.

The inputs are ordered pairs of letters (x,y). Real numbers (each output is a single real number) are the outputs.

A function's domain is the set of all possible inputs (ordered pairs), but its range is the set of all possible outputs (real numbers).

The function is expressed as z = f(x,y)

Hence,

The set {(x,y) : Ψ(x,y)} is defined as the set of cartesian product of X and Y in which the cartesian product is defined by the function  Ψ(x,y), which is a function of two variables.

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The value of x in the expression is 66/114.

Let's begin by addressing the issue in detail:

Emma runs 12 km, hence the time it takes her to complete that distance is 12/x hours.

Emma cycles 26 kilometers at a speed that is 10 kilometers per hour faster than she runs.

Her cycling pace is therefore (x + 10) km/hr. Her cycle distance is 26 kilometers, which can be calculated as 26/(x + 10) hours.

Emma's total time spent cycling and running is 22 hours and 48 minutes. By dividing 48 minutes by 60, we can translate it to hours: 48/60 = 0.8 hours.

We can now formulate an equation to express the entire amount of time spent:

12/x + 26/(x + 10) = 22.8

To get rid of the denominators and solve this equation, multiply both sides by x(x + 10).

12(x + 10) + 26x = 22.8x(x + 10)

To make the calculation easier:

12x + 120 + 26x = 22.8x² + 228x

Combining comparable phrases

38x + 120 = 22.8x² + 228x

Changing the equation's order:

22.8x² + 228x - 38x - 120 = 0

22.8x² + 190x - 120 = 0

By dividing the equation by 0.4, the coefficients are made simpler:

57x² + 475x - 300 = 0

Solving the equation by x = (-b ± √(b² - 4ac)) / (2a),

x = (-475 ± √(475² - 4 * 57 * -300)) / (2 * 57)

Simplifying further:

x = (-475 ± √(225625 + 68400)) / 114

x = (-475 ± √293025) / 114

x = (-475 ± 541) / 114

Now, we can calculate the two possible solutions:

x₁ = (-475 + 541) / 114

x₁ = 66 / 114

x₁ ≈ 0.579

x₂ = (-475 - 541) / 114

x₂ = -1016 / 114

x₂ ≈ -8.912

Take x = 66/114

Hence the value of x in the expression is 66/114.

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To find the probability that 15 or more instructors choose the book with the better format and illustrations, we can use the binomial distribution formula.

Let's denote the event of an instructor choosing the book with the better format and illustrations as "success" (S), and the event of an instructor choosing the other book as "failure" (F). The probability of success is p = 0.5, and the probability of failure is q = 1 - p = 0.5.

We want to find the probability of 15 or more successes in a sample of 25 instructors. We can calculate this probability by summing the probabilities of exactly 15, 16, 17, ..., 25 successes.

P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)

Using the binomial distribution formula, the probability of exactly k successes in a sample of n trials is:

P(X = k) = C(n, k) * p^k * q^(n-k)

where C(n, k) is the binomial coefficient "n choose k," given by:

C(n, k) = n! / (k! * (n-k)!)

Applying this to our problem, we can calculate the probability as follows:

P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)

= Σ[ k = 15 to 25 ] ( C(25, k) * p^k * q^(25-k) )

Let's calculate this probability using the binomial distribution formula:

P(X ≥ 15) = Σ[ k = 15 to 25 ] ( C(25, k) * (0.5)^k * (0.5)^(25-k) )

Calculating this sum gives us the probability that 15 or more instructors choose the book with the better format and illustrations.

The conical base of the silo provides stability and structural integrity, enabling the company to offer reliable storage solutions for grains. It optimizes space utilization and supports easy handling and retrieval of stored grains.

The silo manufactured by the company features a conical base, as depicted in the drawing. The given dimensions are as follows: the height is 8.5 feet, the length measures 4 feet, and the width is 13 feet.

The height of 8.5 feet refers to the vertical distance from the base of the silo to the top of the conical base. It represents the overall height of the silo structure.

The length of 4 feet represents the measurement from one side of the conical base to the other. This dimension determines the diameter of the circular base of the silo.

The width of 13 feet signifies the measurement from the front to the back of the conical base. It determines the circumference of the circular base of the silo.

With these dimensions, the silo exhibits a conical shape, where the circular base gradually tapers towards the top. This design is well-suited for storing grains, as it allows for efficient distribution of pressure and facilitates the flow of grains during loading and unloading processes.

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Answer:

[tex]u+v=4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]

Step-by-step explanation:

When adding two vectors, we add their horizontal components, and then their vertical components:

[tex]u=2\langle\cos325^\circ,\sin325^\circ\rangle=\langle2\cos325^\circ,2\sin325^\circ\rangle\\v=6\langle\cos155^\circ,\sin155^\circ\rangle=\langle6\cos155^\circ,6\sin155^\circ\rangle\\\\u+v=\langle2\cos325^\circ+6\cos155^\circ,2\sin325^\circ+6\sin155^\circ\rangle\\u+v\approx\langle-3.8,1.39\rangle[/tex]

We are not done however as we need to now calculate the magnitude and the direction of the resultant vector:

Magnitude:

[tex]||u+v||=\sqrt{(-3.8)^2+1.39^2}\approx4.1[/tex]

Direction:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{1.39}{-3.8}\biggr)\approx-20^\circ=180-20^\circ=160^\circ[/tex]

Therefore, the resultant vector is about [tex]4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]