What is the common difference between the elements of the arithmetic sequence below?

–18, –22.5, –27, –31.5, –36

The segment of a triangle is the median of the triangle. This is the line that join a vertex of the triangle to the opposite side of the triangle.

The jogger is 3 km away from the starting point and is located at an angle of 45 degrees counter-clockwise from the east axis.

To calculate the distance from the starting point, we can use the Pythagorean theorem. The jogger first runs 5 km east, then 6 km northwest, and finally 3 km south.

The distance traveled east and west cancels out, as they are in opposite directions. So we only need to consider the north-south distance.

The north-south distance is the sum of the distances traveled north (0 km) and south (3 km), which gives us a total distance of 3 km.

Therefore, the jogger is 3 km away from the starting point.

To determine the direction from the starting point, we can use trigonometry. We can consider the east direction as 0 degrees, and measure angles counter-clockwise from the east axis.

Since the jogger traveled northwest, which is halfway between north and west, the angle from the east axis would be 45 degrees (45°).

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Slope-Intercept Form: The slope-intercept form of a linear equation is given by y = mx + b, where 'm' represents the slope of the line and 'b' represents the y-intercept (the point where the line intersects the y-axis).

This form is convenient for quickly identifying the slope and y-intercept of a line by inspecting the equation.

Point-Slope Form: The point-slope form of a linear equation is given by y - y₁ = m(x - x₁), where (x₁, y₁) represents a point on the line and 'm' represents the slope.

This form is useful when we have a specific point on the line and its slope, allowing us to write the equation directly without needing to determine the y-intercept.

Standard Form: The standard form of a linear equation is given by Ax + By = C, where 'A', 'B', and 'C' are constants, and 'A' and 'B' are not both zero.

This form represents a linear equation in a standard, generalized format.

It allows for easy comparison and manipulation of linear equations, and it is commonly used when solving systems of linear equations or when dealing with equations involving multiple variables.

These three forms provide different ways of representing a linear equation, each with its own advantages and applications. It is important to be familiar with all three forms to effectively work with linear equations in various contexts.

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The probable question may be:
Write the three forms of a linear equation for the following.

Slope-Intercept Form:

Point-Slope Form:

Standard Form:

The probability that the next bottle is underfilled is 0.8%.

Given that Machine A fills 60% of the bottles and underfills 1% of them, while Machine B fills the remaining 40% and underfills 0.5% of them, we can calculate the probability of the next bottle being underfilled.

To do this, we need to find the weighted average of the underfill probabilities for each machine, considering the proportion of bottles filled by each machine.

Probability of selecting Machine A: 60%

Probability of Machine A underfilling a bottle: 1%

Probability of selecting Machine B: 40%

Probability of Machine B underfilling a bottle: 0.5%

To calculate the overall probability, we multiply the probability of selecting each machine by the probability of it underfilling a bottle, and sum the results:

Probability of the next bottle being underfilled = (0.60 * 0.01) + (0.40 * 0.005)

= 0.006 + 0.002

= 0.008

Therefore, the probability that the next bottle is underfilled is 0.8%.

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Answer:

41.38%

Step-by-step explanation:

A= P(1+in)

7540 = 1749.28 + 13994.25i

5790.72= 13994.25i

i=0.41379×100

i=41. 38%

Answer:

- \(\frac{11}{3}\)

Step-by-step explanation:

Using the rules of exponents

\(\frac{1}{a^{m} }\) ⇔ \(a^{-m}\)

\((a^{m}) ^{n}\) = \(a^{mn}\)

Consider the right side

\((\frac{1}{27}) ^{a+3}\)

= \((\frac{1}{3^3}) ^{a+3}\)

= \((3^{-3}) ^{a+3}\)

= \(3^{(-3a-9)}\)

Now we have

9 = \(3^{(-3a-9)}\) , that is

3² = \(3^{(-3a-9)}\)

Since the bases on both sides are equal, equate the exponents

- 3a - 9 = 2 ( add 9 to both sides )

- 3a = 11 ( divide both sides by - 3 )

a = - \(\frac{11}{3}\)

Answer:

Your answer is - 11/3

Step-by-step explanation:

Hope this helps!

Answer:

g(x2+6x+7)=x2+6x+9

Step-by-step explanation:

Evaluate g(f(x)) by substituting in the value of f into g

g(2x)=6(2x)−7

Multiply 2 by 6

g(2x)=12x−7

Answer:

$4,255.557336768

Step-by-step explanation:

I think.

Answer:

dude my brain cells are perishing

-2/3 is your answer my guy

have fun

Step-by-step explanation:

Answer:

y = \(\frac{1}{5}\)x + 19

Step-by-step explanation:

Not sure what the stuff after "What is the equation of the line perpendicular to y = 5x +3 passing through the point (-3, 4)?" is, but I can create the equation from just that :D

So the equation will still be y = as it will be in slope intercept from (y=mx+b). The slope (m, or in this case currently it is 5) will change and be one-fifth as it is the opposite.

So far we have:

y = \(\frac{1}{5}\)x + b

We then plug in the point (-3, 4) to figure out our b

(given) y = 5x + b

(plugging-in) 4 = 5(-3) + b

(mutiply) 4 = -15 + b

(adding 15 to both sides) 19 = b

Our equation will then be:

y = \(\frac{1}{5}\)x + 19

Hopefully this is correct and helps, have a ncie day! :D

The solution set for each case are:

1) (-∞, ∞)

2) [-1, 1]

3)  (-∞, 0]

4)  {∅}

5)  {∅}

6) [0, ∞)

The first inequality is:

1) |x| > -1

Remember that the absolute value is always positive, so the solution set here is the set of all real numbers (-∞, ∞)

2) Here we have:

0 ≤ |x|≤ 1

The solution set will be the set of all values of x with an absolute value between 0 and 1, so the solution set is:

[-1, 1]

3) |x| = -x

Remember that |x| is equal to -x when the argument is 0 or negative, so the solution set is (-∞, 0]

4) |x| = -1

This equation has no solution, so we have an empty set {∅}

5) |x| ≤ 0

Again, no solutions here, so an empty set {∅}

6) Finally, |x| = x

This is true when x is zero or positive, so the solution set is:

[0, ∞)

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The lower bound for a 95% confidence interval for the proportion of defective iphones from this assembly line is 0.0524.

With the probability of a success of π , and a confidence level of 1-α, we have the following confidence interval of proportions:

π± z\(\sqrt{\frac{\pi (1-\pi }{n} }\)

z is the z-score having a p-value of 1-α/2.

we have η = 605 and ρ = 0.07

So, α = 0.1 and z is the value of Z that has a pvalue of:

1 - 0.1/2 = 0.95

Z= 1.645

Now the lower limit:

π - z\(\sqrt{\frac{\pi (1-\pi }{n} }\)

= 0.07-1.645\(\sqrt\frac{(0.07*0.93)}{605}\)

= 0.07 - 0.01706

= 0.0524

The lower bound for a 95% confidence interval for the proportion of defective Galaxy phones from this assembly line is 0.0524

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The probability that Rosa's mom chooses sausage and onion is: 1/8C₂.

Probability refers to the chance of an event occurring. It is given by the formula: number of favorable outcomes/number of total outcomes. The total number of groups from which Rosa's mom can make her choice is 1 and this is the number of favorable outcomes.

But, the total number of outcomes that Rosa can hope to expect are 2 two toppings(sausage or onions) out of 8. So, the selected answer is the representation of the probability.

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The Central Limit Theorem states that for a random sample of n observations drawn from any population with a finite mean μ and a finite standard deviation σ, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To apply the Central Limit Theorem, the following condition is necessary:

1. The random sample should be selected from a population that has a finite mean (μ) and a finite standard deviation (σ).

In this case, the population mean is given as $75 and the population standard deviation is given as $5. Since both the mean and standard deviation are finite, the condition for applying the Central Limit Theorem is satisfied.

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Jen's speed is 2.4 miles per hour, and Kamlee's speed is 2.88 miles per hour.

To find their speeds in miles per hour, we need to convert the distances they walked into miles and then divide by the time taken in hours.

Part A:

Jen has walked (4/5) mile in 20 minutes. To convert this to hours, we divide 20 minutes by 60 (since there are 60 minutes in an hour):

20 minutes / 60 = 1/3 hour

Now, we can calculate Jen's speed by dividing the distance she walked by the time taken:

Speed = Distance / Time = (4/5) mile / (1/3) hour = (4/5) * (3/1) = 12/5 = 2.4 miles per hour.

Similarly, for Kamlee:

Kamlee has walked (5/6) mile in 25 minutes. Converting this to hours:

25 minutes / 60 = 5/12 hour

Kamlee's speed:

Speed = Distance / Time = (5/6) mile / (5/12) hour = (5/6) * (12/5) = 2.88 miles per hour.

Therefore, Jen's speed is 2.4 miles per hour, and Kamlee's speed is 2.88 miles per hour.

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Answer: Yes

Step-by-step explanation:

6 can divide evenly into 12.

Answer:

yes 6 is a factor of 12

Step-by-step explanation:

Hope it helps I'm new :D

Answer:

angle pts is a 45 degree angle

Step-by-step explanation:

Answer:

57472

Step-by-step explanation:

The probability for a data point is less than is 0.8413.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

The mean(μ)=4

Standard deviation(σ)=1

(P<5)

From the figure, standard normal distribution curve probability which we have to find P<5

It is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

P(x=4)=x-μ/σ

=4-4/1=0

P(x=4)=50%

P(x<5)=P(x=4)+P(x=1)

=50%+34.13%

=0.8413

P(x<5)=0.8413

Therefore, the probability a data point is less than 5 is 0.8413.

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Answer:

the answer is altitudes in a triangle

Step-by-step explanation:

an altitude has a lines that will go up down left or right and it will be the intersection of everything

The orthocenter can be defined as the intersection of three: B. altitudes in a triangle.

Referring to the image attached below, note the following:

As you can see from the image attached, three altitudes intersect at a point to form an orthocenter.

Therefore, the orthocenter can be defined as the intersection of three: B. altitudes in a triangle.

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The number of tacos for $30 is 38.6

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

Michael bought 9 tacos and paid $7

This means that

Cost of 9 tacos = $7

Multiply both sides of the equation by 30/7

So, we have the following representation

Cost of 9  * 30/7 tacos = $7 * 30/7

Evaluate the products

Cost of 38.6 tacos = $30

Hence, the number of tacos is 38.6

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Answer:

The rate of decrement is given as: r = 4%. From the table, the initial population is. P (0) = 7900. So, the population in t years is. P (t) = P (0) * (1 - r)^t. This gives. P (t) = 7900 * (1 - 4%)^t. Evaluate the difference.

Population after 2 years = P (1 + 4/100)2 = 62500 X (104/100)2

= 62500 × 26/25 X 26/25 = 100 × 26 ×26 = 67600.

Hence, the population after two years will be 67,600.

Answer:

21 is the answer for 18x +3

Step-by-step explanation:

18x + 3

x=3+18

x=21

Each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Let's consider the number of ways to seat n couples around a circular table without any restrictions first.

Since there are 2 people in each couple, there are a total of 2n people. The number of ways to seat 2n people around a circular table is (2n-1)!/2n,

where we divide by 2n to account for rotations of the same seating arrangement.

Now, let's consider the restriction that no couple can sit together.

We can start by fixing one person in a couple, and then there are (2n-2) ways to seat the other person in that couple so that they don't sit together.

After that, we can fix another person and their partner, and there are (2n-4) ways to seat the remaining two people in their couple so that they don't sit together.

We can continue this process until all couples are seated.

Therefore, the total number of ways to seat n couples around a circular table so that no couple sits together is:

\((2n-2)(2n-4)(2n-6)...2 = 2^{n-1} * (n-1)!\)

We multiply by\(2^{n-1}\) to account for the fact that each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Note that reflected seatings are considered to be different, so we don't need to worry about dividing by 2 as we did in the unrestricted case.

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Answer:

CED = 117

Step-by-step explanation:

21x +21 = 7x +49

21x - 7x = 49 - 21

14x = 28

x = 28/14

x = 2

7x + 49

=7(2) + 49

=14 + 49

=63

180 -63 = 117

CED= 117

Answer:

7x+49=21x+21 ( vertically opposite side are equal )

49-21=21x-7x

28=14x

x=28÷14

x=2

hence, putting the value of x

7x+49=7×2+49

=63

21x+21=21×2+21

=63

The principal amount for account A is $200 and for account B is $700.

Account B earns more simple interest than account B in first month.

Given,

Account A

Simple interest, SI = $9.25

Time period, T = 15 months = 1 1/4 = 5/4 years

Rate of interest, R = 3.7%

Account B

Simple interest, SI = $25.20

Time period, T = 18 months = 1 1/2 = 3/2 years

Rate of interest, R = 2.4%

We have to find the principal amount for each account and also the account which earned the more simple interest;

Here,

Simple interest, SI = PRT/100

P is the principal amount

Now,

Account A.

SI = PRT/100

9.25 = (P × 3.7 × 5/4) / 100

9.25 × 100 = P × 4.625

P = 925/4.625

P = $200

SI = PRT/100

SI = (200 × 3.7 × 1/15) / 100

SI = 2 × 3.7 × 1/15

SI = $0.493

Next,

Account B

SI = PRT/100

25.20 = (P × 2.4 × 3/2) / 100

25.20 × 100 = P × 3.6

P = 2520/3.6

P = $700

SI = PRT/100

SI = (700 × 2.4 × 1/18) / 100

SI = 7 × 2.4 × 1/18

SI = $0.933

Here,

The principal amount for account A is $200

The principal amount for account B is $700

Simple interest for first month;

Account A = $0.493

Account B = $0.933

Therefore,

In first month account B earns more simple interest than account A.

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Answer:

false

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

Answer:

545

Step-by-step explanation:

Answer:

(D)$81

Step-by-step explanation:

Given that the number of purses a vendor sells daily has the probability distribution represented in the table.

Expected Value, \(E(x)=\sum_{i=1}^{n}x\cdot p(x)\)

Therefore:

\(E(x)=(0X0.35)+(1X0.15)+(2X0.2)+(3X0.2)+(4X0.03)+(5X0.07)\\=0+0.15+0.4+0.6+0.12+0.35\\E(x)=1.62\)

If each purse sells for $50.00, the number of expected daily total dollar amount taken in by the vendor from the sale of purses

=Expected Value X $50

=1.62 X $50

=$81

The correct option is D.