Intersecting lines l, m, and n form a triangle.

What is the value of x?​

Answer: x = 1, y = 4

Step-by-step explanation:

First, you would need to set the equations equal to each other.

y = 3x + 1 and y = -2x + 6

They can be set equal to each other because they are equal to the same y.

So, you would get the equation:

3x + 1 = -2x + 6

From there, solve for x.

3x + 2x = 6 - 1

5x = 5

x = 1

Now, plug that x-value into the original equations to get y.

y = 3(1) +1

= 3 + 1

= 4

Plug the x-value into the other equation and if you get the same answer, you're correct!

y = -2(1) + 6

= -2 + 6

= 4

So, as an ordered pair (in the form [x, y]), the answer would be (1, 4).

Answer:

this system of equations does not have the same solution

Step-by-step explanation:

x+2y=5              2x + y=4

x+2y/2=5/2       2x/2 +y=4/2

x+y=2.5               x+y=2

The solution to the given compound inequality include the following:

x ≥ 4.5

x > -35/4

Based on the information provided above, you are required to solve the following compound inequality;

2x ≥ 9

By dividing both sides of the inequality by 2, we have the following:

x ≥ 9/2

x ≥ 4.5

-4/5(x) - 6 > 1

By adding 6 to both sides of the inequality, we have the following:

-4/5(x) - 6 + 6 > 1 + 6

-4/5(x) > 7

By multiplying both sides of the given inequality by -5/4, we have the following ;

-4/5(x) × -5/4 > 7 × -5/4

x > -35/4

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The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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The number of parts is 10 and the value of the expression is 4/10

Given that

7/10 - 3/10

The above expressions are fractions and the denominator is 10

This means that the number of parts between 0 and 1 is 10

Recall that

7/10 - 3/10

When evaluated, we have

7/10 - 3/10 = 4/10

Hence, the solution si 4/10

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a. X1 - X2 is an unbiased estimator of µ1 - µ2.

b. The standard error of X1 - X2 is √(S1²/n1 + S2²/n2).

A) To show that X1 − X2 is an unbiased estimator of µ1 − µ2, we need to show that the expected value of X1 − X2 equals µ1 − µ2.

E[X1 − X2] = E[X1] − E[X2] (since expectation is linear)

= µ1 − µ2 (since X1 and X2 are unbiased estimators of µ1 and µ2, respectively)

Therefore, X1 − X2 is an unbiased estimator of µ1 − µ2.

B) The variance of X1 − X2 can be calculated as:

Var[X1 − X2] = Var[X1] + Var[X2] (since X1 and X2 are independent)

= σ1²/n1 + σ2²/n2

The standard error of X1 − X2 is the square root of the variance:

SE(X1 − X2) = √(σ1²/n1 + σ2²/n2)

To estimate the standard error, we can use the sample standard deviations S1 and S2 as estimators of the population standard deviations σ1 and σ2, respectively. Therefore, the estimated standard error of X1 − X2 is:

SE(X1 − X2) ≈ √(S1²/n1 + S2²/n2)

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The factors of the expression are 2t and (15 - 8t).

We have,

To find the factors of the expression 30t - 16t², we need to factor out the greatest common factor, which is 2t. We can then rewrite the expression as:

30t - 16t² = 2t (15 - 8t)

This is the factored form of the expression, with the factors being 2t, 15, and 8t.

Factor 2t accounts for the common factor of the two terms, while (15 - 8t) represents the remaining difference between the two terms.

Thus,

The factors of the expression are 2t and (15 - 8t).

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Thus, the probability that a randomly selected card has a consonant is 62.5%. This means that if you were to randomly select a card from the pile of cards, there is a 62.5% chance that the card would be a consonant.

The number of consonants in the word "probable" and the total number of cards. There are 5 consonants in "probable" (p, r, b, l, and b) and a total of 8 cards.

In the word "probable," there are 5 consonants (p, r, b, b, and l) and 3 vowels (o, a, and e). To calculate the probability of choosing a consonant, divide the number of consonants by the total number of letters:

Probability = (Number of consonants) / (Total number of letters)

The probability of selecting a consonant can be calculated by dividing the number of consonants by the total number of cards:

5 consonants / 8 cards = 0.625 or 62.5%

Therefore, the probability that a randomly selected card has a consonant is 62.5%. This means that if you were to randomly select a card from the pile of cards, there is a 62.5% chance that the card would be a consonant.

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The calculated height of the​ patio, h will be 22 ft

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

Blueprint with base 8 in and height 11

This means that

Ratio = 8 in : 11 in

So, we have

16 ft : height = 8 in : 11 in

Multiply by 2

So, we have the following representation

16 ft : height = 16 in : 22 in

By comparison, we have

height = 22 ft

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The probability that Elsie gets heads and red on the spinner is 1/8

Given data ,

Elsie is going to flip a coin and spin a spinner

The coin has a heads and a tails

The spinner has four equal parts that are yellow, blue, red, and green

Now , The chance of getting heads on the coin is 1/2, and the chance of getting red on the spinner is 1/4, since there are four equal parts.

To find the probability of getting both events together, we need to multiply the probabilities:

P(heads and red) = P(heads) × P(red) = (1/2) × (1/4) = 1/8

Hence , the probability of Elsie getting heads and red on the spinner are 1/8

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Option A is correct, the length of side A is 12 cm and length of side B is 42 cm  in triangle ABC.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The blue triangle is similar to the red triangle.

The sides are proportional.

30/5=A/2=B/7

Now compare two of the equation

30/5=A/2

60/5=A

12=A

Length of A is 12 cm

and Now B/7=6

B=42

Hence, option A is correct, the length of side A is 12 cm and length of side B is 42 cm.

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Answer: D. 1/10

Step-by-step explanation:

With there being 5 sections on the spinner and only one number wanted to be spun, the probability of that would be 1/5.

On a dice, 3 of the numbers on a cube are prime (1, 3 and 5). So the probability would be 3/6 or 1/2.

1/5 x 1/2 = 1/10, so the probability of spinning a 4 and rolling a prime number would be 1/10, or 10%

Answer:

42 Hope this is what you were looking for :)

Step-by-step explanation:

180=46+92+x

add

180=138+x

Subtract from both sides

180-138=138-138+x

  Answer

     42

Part A:

Let's start by setting up the equation. We know that the service station charges an installation fee of $84 and a set price for each new tire. If t represents the price of one tire, then the total cost of four tires and installation can be expressed as:

4t + 84 = 791

Part B:

Now we can solve for t to find the price of one tire:

4t + 84 = 791

4t = 707

t = 176.75

Therefore, the price of one tire is $176.75.

For the given circle, OC ⊥ AB and OC pass through the center O because it is the radius of the circle.

Consider two triangles OAC and OBC.

OC = OC = 4 units (Common side)

OA = OB = 5 units (Radii)

AC = BC (As C is the midpoint of AB)

As per the RHS rule, the ΔOAC is congruent to ΔOBC.

So, ∆OAC ≅ ∆OBC

Now, as per the RHS rule,

∠OMA = ∠OMB = 90°

Thus, conclude that OC ⊥ AB.

Since OC is the radius of the circle, and AB is a chord of the circle passing through the center, we can conclude that OC passes through the center O.

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The complete question is as follows:

AB is a chord of the circle. AC = CB and the length of the radius is 5 units. AC = 3 units and OC = 4 units. Show that OC ⊥ AB and explain why OC passes through the center O.

By reducing the denominator each time, the given real-number's [tex]1-\frac{1}{1-\frac{1}{1-\frac{1}{2}}}[/tex]simplification yields the answer of 2, which is 2.

They display the value of something actual, which is why they are not referred to as "Real". All numbers are part of the real number system, which is a collection of all numbers. Every number you have ever used, ever since you were old enough to count, is a component of the real number system. The real number system divides the numbers into two fundamental groups. Both sets of numbers fall into two categories: rational and irrational. Natural numbers, whole numbers, integers, ratios of two integers, decimal numbers that terminate, and decimal numbers with recurrent digit patterns all fall within the category of rational numbers.

Given expression is:  [tex]1-\frac{1}{1-\frac{1}{1-\frac{1}{2}}}[/tex]

[tex]1-\frac{1}{1-\frac{1}{\frac{1}{2}-\frac{1}{2}}}[/tex] Equivalent rational number of 1 with denominator 2 = 2/2

[tex]1-\frac{1}{1-\frac{1}{\frac{1}{2}}}[/tex]  subtraction 2/2 - 1/2 = 1/2

[tex]1-\frac{1}{1-2}[/tex]  reciprocal of 1/2 = 2

[tex]1-\frac{1}{-1}[/tex]  subtraction of 1-2=-1

1 - (-1)   Writing -1/1 = -1

1+1

2

The value of given expression is [tex]1-\frac{1}{1-\frac{1}{1-\frac{1}{2}}}=2[/tex]

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Answer:

3π

Step-by-step explanation:

We Know

The arc of the circle is the same thing as the circumference.

Circumference of circle = 2 · r · π

r = 12 units

Let's solve

2 · 12 · π = 24π

It is divided into 8 congruent slices - what is the arc of each slide?

24π ÷ 8 = 3π

So, the arc of each slice is 3π

The age of the basalt (unit m) is approximately 1.14 x 10⁹ years years, if 0.5 half-lives of 40K/40Ar have elapsed and the half-life of 40K/40Ar is 1.3 billion years.

The age of the basalt can be calculated using the formula

age = (t₁/2 x loge(1 + (D/P)))/1.21 x 10⁻¹¹

where t₁/2 is the half-life of the radioactive isotope (in seconds), D is the ratio of the daughter isotope (in this case 40Ar) to the parent isotope (in this case 40K), and P is the initial ratio of the daughter isotope to the parent isotope.

In this case, we are given that

t₁/2 = 1.3 billion years = 4.1 x 10¹⁶ seconds (since 1 billion = 10⁹ and there are 31,536,000 seconds in a year)

0.5 half-lives of 40K/40Ar have elapsed, which means that D/P = 0.5 (i.e., half of the initial amount of 40K has decayed to 40Ar)

Plugging in these values, we get:

age = (4.1 x 10¹⁶ seconds x loge(1 + 0.5))/1.21 x 10⁻¹¹

= (4.1 x 10¹⁶ seconds x loge(1.5))/1.21 x 10⁻¹¹

= 1.14 x 10⁹ years

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The given statement F(x + 2) - F(x) = 4x + 8 is proved where the function is F(x) = x² + 2x + 1.

Given the function is,

F(x) = x² + 2x + 1

And the given statement which we have to prove is: F(x + 2) - F(x) = 4x + 8.

Now, to find F(x + 2) we have to replace x with (x + 2).

F(x + 2) = (x + 2)² + 2(x + 2) +1

F(x + 2) = x² + 2² + 2*2*x + 2x + 2*2 + 1 [Since, (a +b)² = a² + b² + 2ab]

F(x + 2) = x² + 4 + 4x + 2x + 4 + 1

F(x + 2) = x² + 6x + 9

So now calculating left hand side of expression which have to be proved,

F(x + 2) - F(x)

= x² + 6x + 9 - (x² + 2x + 1)

= x² + 6x + 9 - x² - 2x - 1

= (x² - x²) + (6 - 2)x +(9 - 1)

= 0 + 4x + 8

= 4x + 8

Hence the given statement is proved.

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Answer:

Mean= 22.666666666667

Median= 17

Model= No mode from what I have figured out

Step-by-step explanation:

The statement "secondary data should be gathered first because this type of information is less expensive to obtain" is actually false because it has already been collected, there are some important factors to consider.

Primary data is data that is collected specifically for the purpose of the research project at hand. This type of data can include surveys, interviews, experiments, and observations. On the other hand, secondary data is data that has already been collected by someone else for a different purpose.

Firstly, it's important to consider the quality of the data. Secondary data may not always be reliable or up-to-date, which could impact the accuracy of your research findings. In some cases, you may need to spend time and resources verifying the accuracy of the secondary data, which could end up being more expensive in the long run.

Additionally, it's important to consider the specific needs of your research project. Depending on your research question, primary data may be necessary to obtain the specific information you need. In other cases, secondary data may be sufficient.

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Answer:

15.2 (rounded)

Step-by-step explanation:

To solve we need to use the pythagrom theorem. This theory states that [tex]a^{2} + b^2 = c^2[/tex]. In which a and b are the legs of the triangle and c is the hypotenuse.

Because we have these numbers we can plug them into our equation:

[tex]5^2 + b^2 = 16^2[/tex]. [tex]5^2 = 25[/tex] and [tex]16^2 = 256[/tex] so our final equation is [tex]25 + b^2 = 256[/tex]. To find b (our missing leg) we need to subtract 25 from both sides. This leaves us with the problem [tex]b^2=231[/tex]. The final step would be to square root both sides and we get our answer of about 15.2

The value of n in the geometric sequence is 10.

The first term of the sequence is 7, the common ratio is 2 and the nth term is 3584. Therefore, the value of n can be found as follows:

using geometric progression formula,

aₙ = arⁿ⁻¹

where

Therefore,

3584 = 7 × 2ⁿ⁻¹

divide both sides by 7

2ⁿ⁻¹ = 3584 / 7

2ⁿ⁻¹ = 512

2ⁿ⁻¹  = 2⁹

n - 1 = 9

n = 9 + 1

Therefore,

n = 10

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Standard Deviation: Is a measure of how spread out values are in a data set compared to the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.

Mean: The average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the result by the total number of numbers in the set.

Distribution Curve: is a bell shaped curve that displays the mean with a line down the center of the curve and standards deviations within standard deviations.

See attached file for model of curve, from: https://commons.wikimedia.org/wiki/File:Standard_deviation_diagram.svg

Given the mean and standard deviation we can use a general rule to determine the population between the given lengths.

Generally in a normal distribution:

176 cm is 1 standard deviation less than the mean and 184 cm is 1 standard deviation greater than the mean. Using the general rules above, 68% of data falls between -1σ and +1σ. Therefore, the answer to this question would be B. 68%

If "Robo-advisors" have lower account minimums than "traditional-advisors", then the impact that investing accessible is that people will have more opportunity to invest.

Making investing more accessible by lowering account minimums through "Robo-advisors" can have a significant impact on individuals who previously could not afford "traditional-financial-advisors".

By removing this barrier, more people will have the opportunity to invest and grow their wealth, potentially leading to a more financially secure future.

The increased accessibility to investing lead to greater financial literacy and education, as more people are exposed to investing concepts and strategies.

So, the impact of making investing more accessible could be a positive one, by empowering more individuals to take control of their financial futures.

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The wavelength of a particle in a finite well can be very large, allowing it to extend into the classically forbidden region outside the barriers. This means even a small potential barrier can hold the particle, resulting in at least one bound state.

A finite well always has at least one bound state, meaning that even a small potential barrier can hold a particle. This is because the wavelength of the wave extends into the classically forbidden region outside the barriers on both sides of the well, leading to a very large wavelength.

According to the formula λ = hp, a larger wavelength corresponds to a smaller momentum. As kinetic energy is directly proportional to momentum, a smaller momentum means a larger kinetic energy. Thus, even a small potential barrier can hold the particle. The argument of fails in the case of a finite well because of the wave's extended wavelength.

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--The given question is incomplete, the complete question is given

" A finite well always has at least one bound state. Why does the argument of fail in the case of a finite well?

In the case of the finite well, the wave extends into the classically forbidden region on the outside of the barriers on both sides of the well, so its wavelength can be very large."--

Answer: for number 1 it is 4 and 5

For number 2 it is 7.6 and 7.7

Number 3 is c

Step-by-step explanation: (I don’t know the last one)

The solution is : 95% of the data lies between $54 and $86

Use the Empirical Rule.

The mean monthly utility bill for a sample of households in a city is $70, with a standard deviation of $8. Between what two values do about 95% of the data lie? (Assume the data set has a bell-shaped distribution.)

Given;

Mean x = $70

Standard deviation r = $8

Confidence level = 95%

To determine the range of the data, we will solve using the confidence level of 95%

Using the formula

x +/- zr/√n

Where r = standard deviation and n is the number of samples tested.

But since n is not given, and since the distribution is bell shaped and thus normal.

The emprical rule states it about 95% of the data is within 2 standard deviations from the mean.

x+/-2r

Substituting x and r

$70 +/-2(8)

$70 +/- $16

Which gives,

$54,$86

Therefore, 95% of the data lies between $54 and $86

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complete question:

The mean monthly utility bill for a sample of households in a city is $70, with a standard deviation of $8. Between what two values do about 95% of the data lie?

After set s1.addAll(s2), s1 is [1, 2, 5, 2, 3, 6].

After performing the operation s1.addAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become[1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].

2. Apply the addAll operation with set s2: [2, 3, 6]

3. Add each element from set s2 to set s1, while avoiding duplicates (since sets cannot have duplicate elements).

4. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.addAll(s2), the set s1 becomes [1, 2, 5, 2, 3, 6].

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