In an arithmetic sequence, the first term is 6 and the fifth term is 22. Find the third term.

Answer:

I'm not exactly sure what you were doing in class but this is what I would do.

I really hope it helps!! :)))

Step-by-step explanation:

for A I would connect the D point of the top angle to the D point of the bottom angle and draw the line across line t. For B the points all share the same angle because the figure is being reflected over line t the position of the figure changes but the size and angles stay the same. use a protractor in B to verify all the angles are the same. For C the only thing that would make sense is that all the lines are parallel because the figure was flipped. and for D just trace one on top of the other

That is, if \(y_1(x), y_2(x), ..., y_n(x)\)are all solutions of the ODE, then any linear combination of the form \(c_1y_1(x) + c_2y_2(x) + ... + c_n*y_n(x)\) is also a solution of the ODE, where \(c_1, c_2, ..., c_n\) are constants.

True.

This property is known as the superposition principle for linear ODEs, and it arises from the linearity of the differential equation. A linear ODE is an ODE of the form:

\(a_n(x)y^(n) + a_(n-1)(x)y^(n-1) + ... + a_1(x)y' + a_0(x)y = f(x)\)

where y^(k) denotes the k-th derivative of y(x) with respect to x, and \(a_n(x), a_(n-1)(x), ..., a_1(x), a_0(x)\)and f(x) are given functions of x.

Suppose that y1(x) and y2(x) are both solutions of this ODE, so that when we substitute them into the differential equation, we get:

\(a_n(x)y1^(n) + a_(n-1)(x)y1^(n-1) + ... + a_1(x)y1' + a_0(x)y1 = f(x)\)

and

\(a_n(x)y2^(n) + a_(n-1)(x)y2^(n-1) + ... + a_1(x)y2' + a_0(x)y2 = f(x)\)

We want to show that any linear combination of y1(x) and y2(x), such as c1y1(x) + c2y2(x) where c1 and c2 are constants, is also a solution of the ODE.

To do this, we substitute the linear combination into the differential equation:

\(a_n(x)(c1y1(x) + c2y2(x))^(n) + a_(n-1)(x)(c1y1(x) + c2y2(x))^(n-1) + ... + a_1(x)(c1y1'(x) + c2y2'(x)) + a_0(x)(c1y1(x) + c2y2(x)) = f(x)\)

Using the linearity of differentiation and the distributive property of multiplication, we can simplify this expression:

\(c1(a_n(x)y1^(n) + a_(n-1)(x)y1^(n-1) + ... + a_1(x)y1' + a_0(x)y1) + c2(a_n(x)y2^(n) + a_(n-1)(x)y2^(n-1) + ... + a_1(x)y2' + a_0(x)y2) = f(x)\)

Since y1(x) and y2(x) satisfy the differential equation individually, the expressions in parentheses on the left-hand side are equal to f(x). Therefore, we have shown that the linear combination c1y1(x) + c2y2(x) also satisfies the differential equation, and is therefore a solution of the ODE.

In general, this result extends to any finite linear combination of solutions of the ODE. That is, if y1(x), y2(x), ..., yn(x) are all solutions of the ODE, then any linear combination of the form c1y1(x) + c2y2(x) + ... + cn*yn(x) is also a solution of the ODE, where c1, c2, ..., cn are constants.

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Answer:

\(y=-0.4x+8\)

Step-by-step explanation:

Let the Linear Function to represent the drip of water out of the water tank be:

\(y=mx+c\)

Where \(x\) is the time

\(y\) is the number of gallons at that time

\(m\) is the rate at which water drips

\(c\) is the initial number of gallons of water in the tank

Putting the given values in the above equation:

\(6.8 = m\times 3+c ..... (1)\)

\(4.4 =m\times 9+c..... (2)\)

Subtracting (1) from (2):

\(6m=-2.4\\\Rightarrow m =-0.4\)

Putting in equation (1):

\(6.8=-0.4\times 3+c\\\Rightarrow c = 8\)

Therefore, the linear function equation to represent in the situation is:

\(y=-0.4x+8\)

The equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is: (x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.

To find the equation of the sphere passing through the point (4, 3, -1) with a center at (3, 8, 1), we can use the general equation of a sphere:

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2

where (h, k, l) represents the center of the sphere and r represents the radius.

First, we need to find the radius. The distance between the center and the given point can be calculated using the distance formula:

√[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]

Substituting the coordinates of the center (3, 8, 1) and the given point (4, 3, -1), we have:

√[(4 - 3)^2 + (3 - 8)^2 + (-1 - 1)^2]

Simplifying, we get:

√[1 + 25 + 4] = √30

Therefore, the radius of the sphere is √30.

Now we can substitute the center (3, 8, 1) and the radius √30 into the general equation:

(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30

So, the equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is:

(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.

This equation represents all the points on the sphere's surface.

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The flow rate of 5 MGD is equivalent to 7.73615 cfs

To convert million gallons per day (MGD) to cubic feet per second (cfs), we need to use the conversion factor between the two units. The conversion factor is 1 MGD = 1.54723 cfs.

Therefore, to convert MGD to cfs, we can multiply the given value of MGD by the conversion factor. For example, if we have a flow rate of 5 MGD, we can convert it to cfs as follows:

5 MGD x 1.54723 cfs/MGD = 7.73615 cfs

So, the flow rate of 5 MGD is equivalent to 7.73615 cfs. Similarly, we can convert any given flow rate in MGD to cfs by using the same conversion factor.

It is important to note that these units are commonly used in the context of water supply and distribution systems, where flow rates are a crucial factor in the design and operation of such systems. Therefore, knowing how to convert between different flow rate units is essential for engineers and technicians working in this field.

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To find the larger consecutive integers, x, given that the sum of the smaller integer and four times the larger integer is -11, we can set up an equation and solve it. The larger integer, in this case, is -3.

Let's assume the smaller consecutive integer is x, and the larger consecutive integer is x + 1 (since they are consecutive). According to the problem, the sum of the smaller integer (x) and four times the larger integer (4(x + 1)) is -11.
Setting up the equation: x + 4(x + 1) = -11
Simplifying the equation, we get: x + 4x + 4 = -11
Combining like terms: 5x + 4 = -11
Subtracting 4 from both sides: 5x = -15
Dividing both sides by 5: x = -3
Therefore, the larger consecutive integer (x + 1) is -3 + 1 = -2. Thus, the larger consecutive integers are -2 and -3.

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Answer:

Step-by-step explanation:

C the probability that a customer buys a hat given that the customer has bought a sweater.

Answer:

12'x2+2x-4

Step-by-step explanation:

=(3x+2)(4x+−2)

=(3x)(4x)+(3x)(−2)+(2)(4x)+(2)(−2)

=12'x2−6x+8x−4

=12'x2+2x−4

Step-by-step explanation:

(3x + 2) (4x - 2) = (3x)(4x) + (3x)(-2) + (2)(4x) + (2)(-2)  [multiply through brackets]

                        =  12x² - 6x + 8x - 4  [add the middle terms]

                        =  12x² + 2x - 4

Answer:

The circle x^2+y^2-2x-8y+17=0 has translated 5 units to the leftand 2units down.

Step-by-step explanation:

If we translate this circle to the left 5 units, and 2 units down,

we will subtract 5 from the center x coordinate and 2 for the center y coordinate

The center is (1,-4)

So the new center prime is (-4,-6)

Since a translation keep angles and measures,

Our radius will remain untouched so our new equation is

\((x + 4) {}^{2} + (y + 6) {}^{2} = 16\)

The scale Denise used is as follows:

3 centimetres: 2 metres

Denise measured a community college and made a scale drawing. In real life, at the college is 122 meters long. it is 183 centimetres long in the drawing.

The scale of Denise use can be calculated as follows:

Using the proportional relationship,

3 / x = 183 / 122

cross multiply

122(3) = 183x

366 = 183x

divide both sides by 183

x = 366 / 183

x  = 2 metres.

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Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

Answer:

a=8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

7 * 8 = 56

56 + 5 = 61

Answer:

where's the question?

Step-by-step explanation:

I don't see a question.

In long division, 63.92/9.4 results with quotient of 6.8.

Long division is a method of dividing two numbers by repeatedly subtracting the divisor from the dividend and keeping track of the resulting quotient and remainder. This method is often used when dividing two numbers with several digits. The process of long division involves several steps that are repeated until there is no remainder left or until a desired level of precision is achieved.

In long division, the dividend is the number being divided, and the divisor is the number by which the dividend is being divided. The quotient is the result of the division, and the remainder is the amount left over after the division is complete.

         006.800

94   |  639.200

 −0                  

 63        

 −0                

   639      

 −564            

           752    

    −752      

   0  

Thus, In long division, 63.92/9.4 results with quotient of 6.8.

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Answer:

I think 26. pls give me brainliest.

First to Answer:

18m/5h = 3.6mph

3.6mp * 4h = 14.4mph

Amanda can go 14.4 miles in 4 hours

Answer:

domain ( 0-5) minutes

Range ( 0-300) miles

Step-by-step explanation:

Here, we are interested in writing the domain and range for the journey to the prospective colleges.

The range simply deaths with the distances in miles while the domain is the time in seconds.

The range is simply the smallest value on the y-axis to the largest value on the y-axis

The domain refers to the smallest value on the x-axis to the largest value of the x-axis

Kindly note that the domain and range does not refer to the labelings of the highest and lowest value on the axes but the highest and lowest value involved in plotting of the line in the graph.

From the graph, we can see that we have a range of; (0-300) miles while the domain is from (0-5) minutes

ansewer:

25+.33h=34.95 solving for h gives h=(34.95-25)/.33 =30.15 hours. So if you are going to use more than 30 hours it better to go with the flat rate company.

Step-by-step explanation:

You want to find, h, the number of hours of usage that will make the costs for the two equal so

There are 15 ways to select four door prizes from six different ones and distribute them among four people.

To find the number of ways to select four door prizes from six different ones, we can use the combination formula:
C(n,r) = n! / (r! * (n-r)!)

In this case, n = 6 (the number of different door prizes) and r = 4 (the number of door prizes we want to select). Plugging these values into the formula, we get:
C(6,4) = 6! / (4! * (6-4)!)
C(6,4) = 720 / (24 * 2!)
C(6,4) = 720 / (24 * 2)
C(6,4) = 720 / 48
C(6,4) = 15

So there are 15 ways to select four door prizes from six different ones.
Once we have selected the four door prizes, we need to distribute them among four people. There are 4! (or 24) ways to do this. However, since we have already accounted for the different ways to select the door prizes in the combination formula, we do not need to multiply by 4! again.

Therefore, the total number of ways to select four door prizes from six different ones and distribute them among four people is 15.

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Answer:

x = 129

Step-by-step explanation:

86/48 = x/72

6192 = 48x

x = 129

2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probability that both randomly chosen people own a dog can be calculated using the concept of independent events. If 18% of people own dogs, it means that the probability of a person owning a dog is 0.18.

When picking the first person, there is a 0.18 probability that they own a dog. Now, assuming replacement (putting the person back before picking the second person), the probability that the second person also owns a dog is also 0.18.

To find the probability of both events occurring, we multiply the individual probabilities together: 0.18 * 0.18 = 0.0324.

Therefore, the probability that both randomly chosen people own a dog is 0.0324, which is equivalent to 3.24%. This means that if we were to repeat this random selection process many times, we would expect approximately 3.24% of the time to end up with two dog owners.

It's important to note that this calculation assumes independence between the events and replacement, meaning the probability of one person owning a dog does not affect the probability of the other person owning a dog.

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If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

Based on the given information, it can be concluded that the average age of all the students at City College is likely around 20. However, it's important to note that this conclusion is only valid if the sample of 90 students is representative of the entire student population at City College. If the sample is not truly representative, the conclusion may not accurately reflect the actual average age of all the students at the college.

The average age in a sample of 90 students at City College is 20. However, based on this sample alone, it cannot be conclusively determined that the average age of all the students at City College is also 20. This is because the sample may not be fully representative of the entire student population. More information or a larger sample would be needed to make a more accurate conclusion about the average age of all students at City College.

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If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

Based on the given information, the average age in a sample of 90 students at City College is 20.

To determine if this sample can be used to conclude the average age of all students at City College, we need to consider these terms:
Sample:

A subset of a population, which in this case is the group of 90 students at City College.
Population:

The entire group of students at City College that we want to make a conclusion about.
Average (Mean) Age:

The sum of ages divided by the total number of students, in this case, 20 years.
Representativeness:

How well the sample reflects the characteristics of the entire population.
If the sample of 90 students is representative of the entire student population at City College, then we can conclude that the average age of all students is approximately 20 years old.

However, if the sample is not representative, the conclusion may not be accurate.

To make a more accurate conclusion, it is important to ensure that the sample is representative by using a larger sample size or random sampling methods.

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Answer:

Rate and speed are similar since they both represent some distance per unit time like miles per hour or kilometers per hour.... To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

Answer:

In my opinion solving for speed is similar to solving for time because when trying to do both of those you want to have a certain amount of time left for instance solving for speed I could Say "oh I want to solve this math question fast!"

Solving it fast will mean I have time left to do something else same with solving for time

"I want to solve this math question for time!" Meaning I want to solve it fast enough to have time left Hopefully this is what you want in an answer! I'm sorry if this isn't what you want

The most people are fed up with celebrities who get on their soapbox and air their political opinions. When people on the street have been asked by TV reporters how they feel about this issue, they almost always say that they wish celebrities would keep their opinions to themselves.

This issue has always been a topic of debate where famous people voice their political opinions, and the public seems to get tired of it. There are various reasons why people feel this way, some of which include the following:

One reason is that people feel like celebrities should stick to what they know, which is their profession and not involve themselves in politics. People believe that their opinions may not be genuine or well-informed because they have not experienced what regular citizens go through.

Another reason is that many people feel like celebrities are not well-versed in politics and may not have a good understanding of the situation, which is why their opinion may not matter. Moreover, some people feel that their opinions are irrelevant, especially when it comes to politics and policies that affect the general public.

Some celebrities do not have a formal education on political matters that would support their opinion.Having said that, there are still people who feel the opposite and believe that celebrities have every right to voice their opinions as long as they are responsible and well-informed.

However, the people are divided on this issue, but most feel that celebrities should not have the right to speak up when it comes to political matters.

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The given statement "the central limit theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small." is true because it use sample statistics to make inferences about a population

The central limit theorem states that, regardless of the underlying distribution of a population, if we take a sufficiently large sample size and calculate the mean of the sample, the distribution of those sample means will be approximately normal.

More specifically, the central limit theorem says that the mean of a large sample from any population with a finite mean and variance will follow a normal distribution.

However, it is important to note that the central limit theorem applies to sufficiently large sample sizes. The larger the sample size, the more closely the sample means will approximate a normal distribution.

Moreover, if the population is skewed, the sample mean may not be a perfect normal distribution but it still will be an approximation of normal distribution

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This reflection transformation ensures that corresponding angles and side lengths of the original triangle are preserved in the reflected triangle

After a reflection in the line y = 1, the graph △RST undergoes a transformation. The line y = 1 acts as a mirror, flipping the points across it. The resulting graph will be a new triangle △R'S'T' where each vertex R', S', and T' is the reflection of the corresponding vertex R, S, and T.

If a point lies on the line of reflection, its image remains the same. In this case, the point S lies on the line y = 1, so S' coincides with S. The remaining two vertices, R and T, will be reflected across the line y = 1.

To perform the reflection, we consider the vertical distance between each original vertex and the line y = 1. The image vertices will be at the same vertical distance but in the opposite direction. For example, if the distance from R to the line y = 1 is 2 units above the line, then the distance from R' to the line will be 2 units below the line.

The resulting triangle △R'S'T' will have the same shape and size as △RST, but will be flipped vertically with respect to the line y = 1.

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