#2: Solve the linear system below using the elimination method. Type your
answer as an ordered pair in the form (#,#). *
-3x + 5y = -32
7x – 4y = 67

The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.

This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.

Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.

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The rate of change of the area of a square is 12m^2/sec.

What do you mean by rate of change?

The term "rate of change" refers to the rate at which one quantity changes in respect to another. Consequently, if y value is the dependent variable and x value is the independent variable.

Rate of Change is equal to \(\frac{Change in y}{Change in x}\).

Change rates may be positive or negative. This reflects a change in the y-value between the two data points, either up or down. Zero rate of change is the state where a quantity does not change over time.

Solution Explained:

Given,

S = 2m and ds/dt = 3m/s

So, we use

Area = s^2

dA/dt = 2s ds/dt

         = 2 X 2 X 3

Therefore, the rate of change of the area is 12m^2/s.

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Answer: B. statistic

Step-by-step explanation: A characteristic, usually a numerical value, which describes a sample, is called a statistic.

This is a question related to permutation and combination.Let's Start off by distinguishing between those terms.

Permutation is all the possible arrangements of 'things' in which order matters. That means 'olives' and ' pepperoni' is different from 'pepperoni and olives'.Combination is all the possible arrangements of 'things' in which order does not matter. That means olives and pepperoni' is the same as 'pepperoni and olives'.

There are 9 ways to placing the first piece in the program

There are 8 ways to placing the second piece 

There are 7 ways to placing third piece

There are 6 ways to placing forth

There are 5 ways to placing fifth

There are 4 ways to placing sixth

There are 3 ways to placing seventh

There are 2 ways to placing eighth

There are 1 ways to placing ninth

This give the numbers of ways to arrange as 9×8×7×6×5×4×3×2×1=362,880

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(a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, (d) boxplot is attached, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

(a) The mean = sum of all values divided by the number of values

μ = (x1 + x2 + ..... + xn)/n

n = 20

μ = (0.0395 + 0.0443+ 0.0450 + ... + 0.0550 + 0.0571)/20

μ = 0.9878/20

μ = 0.0494

(b) Variance = sum of squared deviations from the mean divided by n-1

s² = {(x1-μ)² + (x2-μ)² + .... (xn - μ)²)/(n-1)

s² = {(0.0395-0.0494)² + (0.0443-0.0494)² + .... +(0.0571-0.0494)²}/19

s² = 0.000016

(b) The minimum is 0.0395 and the maximum is 0.0571.

since the number of data is even, the median will be the average of two middle values.

M = Q2 = (0.0496+0.0499)/2 = 0.04975

Now, the first quartile is the median of the data values below the median

so Q1 = (0.0470+0.0485)/2 = 0.04775

And third quartile will be the median of the data values above the median

Q3 = (0.0504+0.0516)/2 = 0.0510

(c) Since we know that the number of data values is even, the median will be the average of the two middle values of the data set

so M = (0.0496+0.0499)/2

or M = 0.04975

(d) The boxplot is at maximum and minimum values. It will start in Q1 and end in Q3 and has a vertical line at the median or Q2.

The boxplot is attached.

(e) The 5th percentile means 0.05(n+1)th data value

or = 0.05(20+1) = 1.05th data value

5th percentile = 0.0550 + 0.05(0.0443-0.0395) = 0.03974

similarly,

95th percentile = 0.0550 + 0.95(0.0571-0.0550) = 0.056995

Therefore, (a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

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Answer:

1. $15 x .3 = $4.50

2. $15 - $4.50 = $10.5

3. $15 x 1/4 = $3.75

4. $15 - $3.75 = $11.25

5. The better deal is 30% off because $4.50 is a greater savings than $3.75

Answer:

0.5m/s

Step-by-step explanation:

75m/150s(2min 30 sec)

?m/s

So,

75m÷150/150s÷150

0.5m/s

plzz mark brianliest if its correct

Answer:

The major field of anthroplogy and evolutionary and paleo anthropological perspectives on the origin of humankind

A)the density of |x| is f(|x|) = 1/(1-0) = 1. B) the density of p|x| is f(p|x|) = 1/(p-0) = 1/p. C) the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0. D) the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

(a) To find the density of |x|, we need to consider the range of values that |x| can take. Since x is uniformly distributed on the interval (-1, 1), the absolute value of x can take values between 0 and 1. The density function of |x| is given by f(|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = 1. Therefore, the density of |x| is f(|x|) = 1/(1-0) = 1.

(b) To find the density of p|x|, we need to consider the range of values that p|x| can take. Since x is uniformly distributed on the interval (-1, 1), p|x| can take values between 0 and p. The density function of p|x| is given by f(p|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = 0 and b = p. Therefore, the density of p|x| is f(p|x|) = 1/(p-0) = 1/p.

(c) To find the density of -ln|x|, we need to consider the range of values that -ln|x| can take. Since x is uniformly distributed on the interval (-1, 1), -ln|x| can take values between 0 and ∞. The density function of -ln|x| is given by f(-ln|x|) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a  = 0 and b = ∞. Therefore, the density of -ln|x| is f(-ln|x|) = 1/(∞-0) = 0.

(d) To find the density of sin(x), we need to consider the range of values that sin(x) can take. Since x is uniformly distributed on the interval (-1, 1), sin(x) can take values between -sin(1) and sin(1). The density function of sin(x) is given by f(sin(x)) = 1/(b-a), where a and b are the lower and upper bounds of the interval. In this case, a = -sin(1) and b = sin(1). Therefore, the density of sin(x) is f(sin(x)) = 1/(sin(1)-(-sin(1))).

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Boyle's law, which relates the pressure and volume of an ideal gas, has various applications in science, engineering, and everyday life. Some of the applications of this measuring technique include:

Gas storage: Boyle's law is used in designing and managing gas storage systems, such as gas cylinders and tanks. It helps in determining the volume of gas that can be stored at a given pressure and vice versa.

HVAC systems: Heating, ventilation, and air conditioning (HVAC) systems use Boyle's law to control the pressure and volume of gases in order to regulate temperature and air flow.

Scuba diving: Boyle's law is applied in scuba diving to calculate the changes in volume of gases in diving cylinders at different depths, which affects the diver's breathing and decompression requirements.

Medical applications: In respiratory therapy, Boyle's law is utilized in devices like ventilators, which deliver oxygen or other gases to patients at specific pressures and volumes.

Industrial processes: Boyle's law is used in industrial processes where gases are compressed or expanded, such as in manufacturing, chemical processing, and power generation.

As for measuring surfaces that are not flat, Boyle's law is not directly applicable for such measurements. It is a gas law that relates the pressure and volume of a gas, assuming the gas behaves as an ideal gas.

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The cost of the event at Skate Fest can be represented as 200 + 3x. The cost of the event at Roller Rama can be represented as 5x.

The cost of the event at Skate Fest can be represented by the mathematical expression 200 + 3x, where x is the number of students attending the event. This represents the fixed fee of $200 plus an additional $3 for each skater.

The cost of the event at Roller Rama can be represented by the mathematical expression 5x, where x is the number of students attending the event. This represents $5 per skater.

By comparing these two expressions, the director can determine which skating rink is more cost-effective based on the number of students attending the event.

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Answer:

4. (2,1) 5. (-2,1) 6. (8, 80)

Step-by-step explanation:

2x + 4y - 2x + 2y = 8 - 2

6y = 6

y = 1

2x + 4 = 8

2x = 4

x = 2

(2,1)

3x + 4y + 6x - 4y = -2 - 14

8x = -16

x = -2

-6 + 4y = -2

4y = 4

y = 1

(-2,1)

multiply first equation by 4

4y = 40x

4y + 40x + 6y = 40x + 800

10y = 800

y = 80

80 = 10x

x = 8

(8, 80)

Therefore, 3m = 3 * 8.15484 = 24.46452 and b = -29.61936.

Given function is f(x) = x + 3e. We have to find f'(4) and use it to find the equation of the tangent line to the curve

y = x + 3e at the point (a, f(a))

when a = 4.

Then, we have to find the values of m and b such that the equation of the tangent line can be written in the form

y = mx + b.

So, we will begin by finding f'(x).

We know that the derivative of x with respect to x is 1.

Also, the derivative of e^(kx) with respect to x is k * e^(kx).

Hence, the derivative of 3e with respect to x is 3e.

Now, we can find f'(x) as follows:

f'(x) = 1 + 3e.

Next, we will find f'(4).

Putting x = 4, we get:

f'(4) = 1 + 3e = 1 + 3 * 2.71828 = 8.15484 (rounded to five decimal places).

Now, we will find the equation of the tangent line to the curve y = x + 3e at the point (a, f(a)) when a = 4.

We know that the equation of a line passing through the point (a, f(a)) and having slope m is given by:

y - f(a) = m(x - a)

We need to find the values of m and b.

To find m, we will use the value of f'(4) that we just calculated.

We know that the slope of the tangent line is equal to f'(4) at x = 4.

Hence, we have: m = f'(4) = 8.15484 (rounded to five decimal places).

To find b, we will substitute the values of a, f(a), and m into the equation of the line.

We have:

a = 4f(a) = f(4) = 4 + 3e (putting x = 4 in the given function y = x + 3e)

m = 8.15484y - f(a)

= m(x - a)y - (4 + 3e)

= 8.15484(x - 4)

Expanding the right side, we get:

y - 4 - 3e = 8.15484x - 33.61936

Collecting like terms, we get:

y = 8.15484x - 29.61936

Hence, we have:

m = 8.15484

b = -29.61936

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Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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Answer:

To solve sin(pi/16), we can use the half-angle formula for sine, which states that:

sin(x/2) = ±√[(1 - cos(x))/2]

Let's use this formula with x = pi/8:

sin(pi/16) = sin(pi/8)/2 = ±√[(1 - cos(pi/8))/2]

To determine the sign, we need to know in which quadrant pi/16 lies. Since pi/2 < pi/16 < pi, pi/16 lies in the second quadrant where sine is positive. Hence,

sin(pi/16) = √[(1 - cos(pi/8))/2]

Now, we need to find cos(pi/8). We can use the half-angle formula for cosine, which states that:

cos(x/2) = ±√[(1 + cos(x))/2]

Again, let's use this formula with x = pi/4:

cos(pi/8) = cos(pi/4)/2 = ±√[(1 + cos(pi/4))/2]

To determine the sign, we need to know in which quadrant pi/8 lies. Since pi/2 > pi/8 > 0, pi/8 lies in the first quadrant where cosine is positive. Hence,

cos(pi/8) = √[(1 + cos(pi/4))/2] = √[(1 + √2/2)/2]

Finally, we can substitute this expression for cos(pi/8) into the expression we found for sin(pi/16):

sin(pi/16) = √[(1 - √[(1 + √2/2)/2])/2] ≈ 0.1951

Therefore, sin(pi/16) is approximately equal to 0.1951.

Answer:i dont know...

Step-by-step explanation:

Answer:

156

Step-by-step explanation

Divide 5,616 by 12 and then divide 5,616 by 18 and then subtract the quotient of dividing by 18 from the quotient of 12.

( PLEASE GIVE BRAINLIEST!!! )

Answer:

x = 4

Step-by-step explanation:

3x - 20 = -2x

Add 2x to both sides.

5x - 20 = 0

Add 20 to both sides.

5x = 20

Divide both sides by 5.

x = 4

Answer:

X = 4

Step-by-step explanation:

The Engel curve for good q2​, given Sally's utility function U=6(q1​)0.5+q2​, is Y= (6(q1​)0.5) / p2​.

To derive the Engel curve, we need to find the relationship between income (Y) and the quantity consumed of good q2​. In Sally's utility function, the first term represents the utility she receives from consuming q1​, and the second term represents the utility she receives from consuming q2​.

To find the Engel curve for q2​, we need to hold q1​ constant and vary Y. We can do this by solving the utility function for q1​ and substituting it into the income equation.

Rearranging the utility function, we have (q1​)0.5 = (U - q2​) / 6. Substituting this into the income equation Y = p1​q1​ + p2​q2​, we get Y = p1​(U - q2​) / 6 + p2​q2​.

Simplifying further, we have Y = (p1​U - p1​q2​) / 6 + p2​q2​.

Rearranging the terms, we get Y = (p1​U + 6p2​q2​ - p1​q2​) / 6. Finally, we can factor out q2​ from the numerator to obtain Y = (6(q1​)0.5) / p2​.

Therefore, the Engel curve for good q2​ is Y = (6(q1​)0.5) / p2​, where Y represents income, q1​ is the quantity consumed of good q1​, and p2​ is the price of good q2​.

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It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Hey! here is a trick for you

domain = all unique values of x

so, domain in the above relation is [0,1,4]

Answer:

you need to add number lines, but if you want the equation to be written and solved, then...

Step-by-step explanation:

5x - 25 > -15

     +25    +25

5x > 10

divide both sides by 5

x > 2

Hope this helps!!!

We can calculate the positions of both ships at that time and then find the angle between them. The course direction from ship T to ship V can be expressed as the inverse tangent of (-2/3)

Using trigonometry, we can express the course direction in terms of an inverse trigonometric function.

Let's first calculate the positions of ship T and ship V after 2 hours. Ship T travels at 12 mph on a bearing of S37°W, which means it is moving 37° west of south. In 2 hours, ship T would have traveled a distance of 12 mph * 2 hours = 24 miles in the given direction.

Next, ship V travels at 8 mph on a bearing of S53°E, which means it is moving 53° east of south. Similarly, ship V would have traveled a distance of 8 mph * 2 hours = 16 miles in the given direction.

Now, we can visualize the positions of ship T and ship V after 2 hours. Let's consider the starting point (the port) as the origin (0, 0) on a coordinate plane. Ship T would be at the point (-24, 0) (24 miles west) and ship V would be at the point (0, -16) (16 miles south).

To find the course direction from ship T to ship V, we can consider the line connecting these two points. This line represents the shortest path between the two ships. Using trigonometry, we can calculate the angle between this line and the south direction.

The tangent of the angle between the line and the south direction can be determined as the ratio of the vertical distance (change in y) to the horizontal distance (change in x) between the two points. In this case, the tangent of the angle is (-16)/(24) = -2/3.

Hence, the course direction from ship T to ship V can be expressed as the inverse tangent of (-2/3). Therefore, the course direction is given by the inverse trigonometric function: arctan(-2/3).

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The original price of the car before 4 years will be $23,032.

Consider the function:

y = P (1 ± r) ˣ

Where x is the number of times this growth/decay occurs, P = original amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

A Naomi's car exponentially depreciates at a rate of 8% per year.

If Nina bought the car when it was 4 years old for $16,500.

Then the original price will be

16500 = P(0.92)⁴

16500 = 0.716P

       P = $ 23,032

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Answer:

2x^2 + 3x+ 6

Step-by-step explanation: if u simplify the equation that should be the correct answer

Answer: per hour

Step-by-step explanation:

That is dependent. It is by itself

The floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be A. 2.3e^7.

It should be noted that scientific notation simply means. way that's used to express numbers that are either too large or too small to be written in decimal form.

Therefore, it should be noted that the floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be:

= 2.3 × 20^7

= 2.3 × e^7

= 2.3e7

The correct option is A.

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Which floating-point literal correctly represents the scientific notation value: 2.3 x 10^7?

a. 2.3e^7

b. 2.3 × 10e^7

c. 2.3e × 10^7

d. 2.3 × e^7

Answer:

Infinite amount of solutions

Step-by-step explanation:

Step 1: Write systems of equations

4x - y = 7

3y - 12x = -21

Step 2: Rewrite

-y = 7 - 4x

y = 4x - 7

Step 3: Solve for x

Here we see that we would have infinite amount of solutions.

Answer: infinite solutions. Just took the quiz

Step-by-step explanation: