Solve the systems of equations by substituting
10) x-y=4
-2X+2y=-8

Standard form of ellipse has equation \(\frac{y^2}{a^2} +\frac{x^2}{b^2} =1\) where, a and b are the halves of the length of major and minor axis respectively.

Given that,

Length of major axis(2a)=6.

So

a=6/2

 =3

Length of minor axis(2b)=4.

So

b=4/2

 =2

Putting in equation of standard ellipse. We get

\(\frac{y^2}{3^2} +\frac{x^2}{2^2} =1\)

After simplifying

4y² + 9x² = 36

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Answer: x =5

Step-by-step explanation:

subtract 7 on both sides than divide by 2

Answer:

x = 5

Step-by-step explanation:

Given: 2x + 7 = 17

1. Subtract 7 from both sides

2x + 7 - 7 = 17 - 7

2x = 10

2. Divide both sides by 2

2x ÷ 2 = 10 ÷ 2

x = 5

Final answer: x = 5

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Answer:

Hiking

Step-by-step explanation:

Given: Kayaking burns 4.5 calories per minute

The slope of the graph is 5

You can use rise over run to figure out the slope. Or you may have noticed the order pair (1,5)

This means hiking burns 5 calories per minute, which is greater than 4.5

The percentage change of the first quantity with reference to the second quantity: 480 units, 560 units is: -14.29%.

First step is to find the difference between the two numbers

Difference = New Number - Original Number

Difference =  480 -560

Decrease  = -80

Now let find the percentage change

Percentage change = Decrease  / Original Number × 100

Percentage change = -80 /560 × 100

Percentage change = -14.29%

Therefore we can conclude that the percentage change is -14.29%.

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Answer: There would be 2224 kilograms left in the truck

Answer:

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. .The range is the resulting y-values we get after substituting all the possible x-values.

Step-by-step explanation:

Answer:

Mass of coffee A beans = 9 kg

Step-by-step explanation:

Coffee A = 3

Coffee B = 5

Coffee C = 7

A : B : C = 3 : 5 : 7

Total ratio = 15

Total mass of the bag = 45 kg

find the mass coffee beans A in the mixture?

Mass of coffee A beans = ratio of coffee A / total ratio × total mass of the bag

= 3/15 × 45

= 1/5 × 45

= (1 * 45)/5

= 45/5

= 9 kg

Mass of coffee A beans = 9 kg

Mass of coffee B beans = ratio of coffee B / total ratio × total mass of the bag

= 5/15 × 45

= 1/3 × 45

= 45/3

= 15 kg

Mass of coffee C beans = ratio of coffee C / total ratio × total mass of the bag

= 7/15 × 45

= (7*45)/15

= 315/15

= 21 kg

Answer:
16.01 gallons of fuel.

Step-by-step explanation:

So we already know that there were initially 1.9 gallons. We have to add 14.11 gallons of fuel to the starting amount.

14.11 + 1.9 = 16.01 gallons

I hope this was able to help you :D

To find out how much fuel is in Leila's car now, we need to add the amount of fuel she just put in to the amount that was already in the car.

Leila put 14.11 gallons of fuel in the car and there were 1.9 gallons in the car to begin with.

So, 14.11 gallons + 1.9 gallons = 16.01 gallons

This is the correct answer because 14.11 gallons is the fuel Leila put into her car and 1.9 gallons is the fuel that was already in the car. Adding these two values together gives the total amount of fuel in the car now, which is 16.01 gallons.

The following distributions has a mean that varies

II. The distribution of sample data

III. The sampling distribution of the sample mean

The correct answer is option v) II and III."

Here, we have,

In the context of statistical distributions:

I. The population distribution refers to the distribution of a specific variable within the entire population. The mean of the population distribution which is fixed and does not vary.

II. The distribution of sample data refers to the distribution of a variable within a specific sample. The mean of the sample data can vary from one sample to another.

III. The sampling distribution of the sample mean refers to the distribution of sample means taken from multiple samples of the same size from a population. The mean of the sampling distribution of the sample mean is equal to the population mean, but the individual sample means can vary from sample to sample.

Therefore, the mean varies in both the distribution of sample data (II) and the sampling distribution of the sample mean (III), but not in the population distribution (I).

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In Milgram's first study of obedience, the majority of teachers initially complied but refused to deliver more than slight levels of shock.

In Milgram's first study of obedience, participants were assigned the role of 'teacher' and were instructed to administer electric shocks to a 'learner' whenever they answered a question incorrectly. The shocks ranged from mild to severe, with the highest level labeled as 'XXX.' The learner was actually an actor, and no real shocks were administered.

The study found that the majority of teachers initially complied with the experimenter's orders and delivered shocks, but they refused to deliver more than slight levels of shock. This suggests that while they were willing to follow the instructions to some extent, they had moral reservations about causing significant harm to another person.

It is important to note that the study has been criticized for ethical concerns and the potential psychological harm it may have caused to participants. However, it remains a significant contribution to our understanding of obedience and the power of authority figures.

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If a random sample of 29 time intervals between eruptions has a mean greater than 106, it may be concluded that the average time between eruptions is longer than 106 units of time. However, it is important to note that the sample size of 29 may not be representative of the entire population of time intervals between eruptions, and therefore the conclusion drawn may not be entirely accurate.
Additionally, it is important to consider the variability of the data. If the standard deviation of the sample is high, it may indicate that there is a wide range of time intervals between eruptions, making it difficult to draw a definitive conclusion. On the other hand, if the standard deviation is low, it may indicate that the time intervals are more consistent, and the conclusion drawn may be more reliable.

Overall, it is important to consider both the mean and variability of the sample when drawing conclusions about the population of time intervals between eruptions. Further research and analysis may be necessary to validate the findings and provide a more accurate answer.

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Answer:

When x is 12, \(5-(\frac{x}{3})=1\)

Step-by-step explanation:

\(5-(\frac{x}{3} )\)

Insert the given value of x:

\(5-(\frac{12}{3} )\)

Simplify the expression. Divide 12 by 3:

\(5-4\)

Simplify subtraction:

\(1\)

:Done

Answer:1

Step-by-step explanation:

Using Z-table ,

the required probability that their mean total body protein is between 12.2 and 12.4 kg is 0.691..

We have given that,

The sample is Normal distribution,

the mean of sample(X-bar,) = 12.3 kg

standard deviations of sample(sigma) = 0.4 kg

sample size(n) = 4

confidence interval= (12.2, 12.4)

we have to find the probability that mean body protein is between 12.2 and 12.4 kg

Using the confidence interval formula, for finding the value of Z-value ,

C.I = X-bar +- Z(s/√n)

put all avaliabile values we get,

12.2 = 12.3 + Z(0.4/√4) = 12.3 + Z(0.2)

=> Z = - 0.5

or 12.4 = 12.3 + Z(0.2)

=> Z = 0.1/0.2 = 1/2 = 0.5

so, -0.5 < Z< 0.5

now , using the z-value we can easily calculate the value of p i.e. probability

Use the Z-table , we get p -value is 0.691

Hence , probability that their mean total body protein is between 12.2 and 12.4 kg is 0.691

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The scale factor was applied to the first diamond is 2.5

From the question, we have the following parameters that can be used in our computation:

The diamonds

The scale factor is calclated as

scale factor = Diamond 2/Diamond 1

Substitute the known values in the above equation, so, we have the following representation

scale factor = 1.5/0.6

Evaluate

scale factor = 2.5

Hnce, the scale factor is 2.5

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The angle XBC is 55° due to Corresponding relationship while BXC is 70°

XBC = 55° (Corresponding angles are equal)

To obtain BXC:

XBC = XCB = 55° (2 sides of an isosceles triangle )

BXC + XBC + XCB = 180° (Sum of angles in a triangle)

BXC + 55 + 55 = 180

BXC + 110 = 180

BXC = 180 - 110

BXC = 70°

Therefore, the value of angle BXC is 70°

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When constructing a frequency distribution for a numerical variable, it is important to remember that the size of the class intervals must be appropriate.

It is not a good idea to use small class intervals, as it may result in too many classes and low frequencies. However, it is also not a good idea to use large class intervals, as it may result in too few classes and high frequencies.Furthermore, it is important to ensure that the lower limit of each class interval is included in that class, but the upper limit is not.

Additionally, the class intervals should be mutually exclusive and should not overlap. Finally, the data should be properly categorized before constructing the frequency distribution.The purpose of constructing a frequency distribution is to organize data into groups or categories, known as classes or intervals, to facilitate data analysis and interpretation.

This distribution shows the number of occurrences of each value or group of values in a set of data. This information can be presented graphically using histograms or frequency polygons, which provide a visual representation of the distribution of the data.

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Creating a frequency distribution involves dividing the variable range into equal, non-overlapping class intervals and counting the number of scores that fall into each. These frequencies summarize the dataset and can be used for further analysis and visualization.

When constructing a frequency distribution for a numerical variable, it is important to remember that the variable range should be divided into equal interval groups (class intervals) but not overlapping. For example, for a set of exam scores ranging from 60 to 100, you might divide the range into class intervals of 60-70, 70-80, 80-90 and 90-100. Then, count the number of scores (frequency) that fall into each class interval. This distribution of frequencies gives a good summary of the data set and can be further utilized to create visual representations such as histograms or bar charts.

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Answer:

Step-by-step explanation:

4x^2+120x

4x^2+120x=0

4x^2=-120x

4x^2/x=-120

4x=-120

x=-120/4

x=-30

im pretty sure its 8.94

Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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This is because

tan(angle) = opposite/adjacent

For the reference angle 38, we have 10 as the opposite side and x as the adjacent side.

Therefore, tan(38) = opposite/adjacent = 10/x

Side note: if you solve for x, you should get roughly x = 12.799

The statistic p-hat and the parameter p indicate the proportion of successes in a sample and the population, respectively.

Two typical metrics are the population mean and standard deviation. Greek letters, such as (mu) for the mean and (sigma) for the standard deviation, are frequently used in statistics to denote population parameters.

P′ is equal to x / n, where x is the total number of successes and n is the sample size. As a point estimate for the genuine population percentage, the variable p′ represents the sample proportion. P is a parameter that describes a population-related percentage number. For instance, according to the 2010 United States Census, 83.7% of Americans were not classified as Hispanic or Latino.

\(p=xn_p = x_n\)

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Answer:

I think it's A ,Forgive me if its wrong its not a 100%.

Step-by-step explanation:

But if it is correct, im glad to be of service

The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

What is a normal distribution?

A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.

It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.

It is also known as probability distribution curve.

The normal distribution has two parameters:

What is the shape of the normal distribution?

The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.

Hence, the shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

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The simplified expression is: \(a^{(-14/3)} \times b^{(14/3)\)

Given is an expression, \((a^{(-1)} b^{(1/3)} \times a^{(-4/3)} b^2)^2\), we need to simplify the expression,

To simplify the expression, let's break it down step by step:

The given expression is:

\((a^{(-1)} b^{(1/3)} \times a^{(-4/3)} b^2)^2\)

First, let's simplify the exponents inside the parentheses:

\((a^{(-1)} b^{(1/3)} \times a^{(-4/3)} b^2)^2\) = \(a^{[(-1) + (-4/3)]} \times b^{[(1/3) + 2]}\)

= \(a^{(-7/3)} \times b^{(7/3)\)

Now, let's square this simplified expression:

\([a^{(-7/3)} \times b^{(7/3)]^2\) = \(a^{(-7/3)^2} \times b^{(7/3)^2\)

= \(a^{(-14/3)} \times b^{(14/3)\)

Therefore, the simplified expression is: \(a^{(-14/3)} \times b^{(14/3)\)

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Answer:

⇒  Draw a line segment AB=5.5cm

⇒  Take A as a center and draw an angle of 45

o

.

⇒  Cut off AD=5cm

⇒  Take D as a center with radius 4.5cm and draw an arc.

⇒  Take B as a center with radius 3.5cm and draw an arc, which meets previous arc at point C.

⇒  Join BC and CD.

∴  ABCD is a required quadrilateral.

Step-by-step explanation:

hope this helps!

Answer:

400 & 2

Step-by-step explanation:

Alright, so for the first question you do 14 + 6 which = 20 and if you do 20 × 20, it equals 400.

And for the second one 14 - 12= 2.

Answer:

70¢ per apple

Step-by-step explanation:

Because it's $3.50 per bag of 5 apples, you can divide $3.50 and 5 by 5 to get 70¢ per apple.

Answer:

70⊄

Step-by-step explanation:

$3.5 ÷ 5 = 70⊄