Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure. 3X1 + 6x2 = 18 4x1 +5X2 = 30 Find the solution to the system of equations. (Simplify your answer. Type an ordered pair.)

The information that is needed to write the equation of a line in point-slope form is the location of one ordered pair that lies on the line and the line's slope. The correct option is the first option

From the question, we are to determine the information that is needed to write the equation of a line in point-slope form.

The point-slope form of a line is given as

y - y₁ = m(x - x₁)

Where, (x₁, y₁) is a point on the line

and m is the slope of the line

Thus, in order to write the equation of a line in the point-slope form, the information that are needed are:

1. An ordered pair on the line

2. The slope of the line

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Answer:

d

Step-by-step explanationnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

The Pythagorean theorem is a fundamental concept in geometry that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as:

a² + b² = c²

where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.

The converse of the Pythagorean theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

The Pythagorean theorem is a powerful tool in solving problems involving right triangles. It allows us to calculate unknown side lengths or determine whether a triangle is a right triangle based on the lengths of its sides. It has numerous applications in various fields, including engineering, architecture, physics, and navigation.

Understanding the Pythagorean theorem and its converse is essential for working with right triangles and applying geometric principles. It provides a foundation for further exploration of trigonometry and advanced geometric concepts.

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Seating arrangement would best suit a family restaurant is c) a space with all booths.

This restaurant with a comfortable atmosphere usually serves food in large quantities by placing it in the middle of the table.

So, each family member can take food from the middle and enjoy it on their respective plates. This concept is exactly the same as how to eat at home with the family.

Apart from that, the characteristics of this restaurant are almost the same as a casual dining restaurant, the difference is the absence of alcoholic beverages in family restaurants.

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Answer:

\(15a^4b-12a^3b^2+6a^2b^3\)

Step-by-step explanation:

\((3a^{2}b)(5a^{2}-4ab+2b^{2})\\ =15a^4b-12a^3b^2+6a^2b^3\)

Answer:

b. To find the probability a customer who ordered pancakes came to thediner late, we need to look at the intersection of the "pancakes" row and the "late" column. This gives us a probability of 0.1, or 10%

c. To determine whether breakfast choice and meal time are independent, we need to see if the probability of one event changes based on the occurrence of the other event. In this case, it seems that breakfast choice and meal time are not independent, as the probability of being late seems to differ based on what breakfast item the customer chose. For example, the probability of being late is higher for customers who ordered pancakes compared to those who ordered cereal. Therefore, the choice of breakfast item appears to be related to the probability of being late, and so breakfast choice and meal time are not independent.

Step-by-step explanation:

Answer:

x > -2

Step-by-step explanation:

-6 (-2) + 30 > 36

12 + 30 > 36

42 > 36

Yes

Answer:

Step-by-step explanation:

x 5 and + 2 ( 5 x 5 ) + 2 = 25 + 2 = 27( 27 x 5 ) + 2 = 135 + 2 = 137( 137 x 5 ) + 2 = 685 + 2 = 687( 687 x 5 ) + 2 = 3435 + 2 = 3437So..( 3437 x 5 ...

Looking at the given diagram, line AB is parallel to line CD. Given that angle 1 = 110 degrees,

angle 5 = angle 1 = 110 degrees

The reason is because they are corresponding angles. The angles lie on the same side of the transversal and their positions correspond.

The first entry is 94 + 26 = 120 since there are 26 entries after the 27th entry.

A sequence is a list of items that is in order in mathematics (or events). It has elements, just like a set (also called elements or terms). The length of the sequence is the total number of ordered items (potentially infinity).

Between the 27th and 94th entries, there are 67-1 = 66 entries, or 94 - 27 = 67. Entry 93 is 28, entry 92 is 29, etc., since entries before to the 94th entry were likely one greater than ones after it. Given that E93's value is 28, which is the average of E92 and E94, this makes sense.

If entry number 27 is 94, entry number 26 must be 95, entry number 25 must be 96, etc. The first entry is 94 + 26 = 120 since there are 26 entries after the 27th entry.

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Answer:

120

Step-by-step explanation:

94 - 27 = 67, so between the 27th and 94th entries, there are 67-1 = 66 entries. The entries before the 94th entry were probably one greater than the entry after, so entry 93 is 28, entry 92 is 29, etc. This makes sense because the average of E92 and E94 is 28, which is the value in E93.

If the 27th entry is 94, then the 26th entry must be 95, the 25th entry must be 96, etc. From the 27th entry, there are 26 entries ahead of it, so the first entry is 94 + 26 = 120. The first entry is 120.

Answer:

C

and 10%

Step-by-step explanation:

the volume of the prism is 450 cubic units, obtained by multiplying the number of cubes along the length, width, and height.

The volume of a prism can be calculated by multiplying the length, width, and height of the prism.

In this case, the prism is packed with 15 cubes along the length, 6 cubes along the width, and 5 cubes along the height.

To find the volume, we multiply these three measurements together.

So, the volume of the prism is:

15 cubes * 6 cubes * 5 cubes = 450 cubes.

Therefore, the volume of the prism is 450 cubic units.

the volume of the prism is 450 cubic units, obtained by multiplying the number of cubes along the length, width, and height.

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The term that describes the number 92% in this scenario is (iii) sample parameter.

In this case, the poll conducted by the Associated Press is gathering information from a subset of individuals who were polled. This subset is the sample. The percentage of those polled who responded that their family financial situation would be as good as it is today or better, which is 92%, is a characteristic or parameter of the sample.

A statistic refers to a numerical value calculated from the data of a sample. However, in this scenario, we are given the actual percentage from the sample, so it is not a statistic itself.

A population parameter would be a characteristic or value that describes the entire population being studied, which is not the case here since the poll only represents a subset of the population.

Therefore, the term that best describes the number 92% is a sample parameter, as it represents a characteristic of the sample that was polled.

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Answer:

-33

Step-by-step explanation:

-11 + -11 + -11 = -33

-11 x 3 = -33

Hope this helps you :)

Hey there!

\(-11+-11+-11\)

If you want to solve, multiply -11 by 3 because it is being multiplied 3 times.

\(-11*3=-33\\-33(ANSWER)\)

Hope this helps!

\(\text {-TestedHyperr}\)

Answer:

c

Step-by-step explanation:

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(a) Kwan will drive approximately 1.276 miles in 2 hours at his constant speed. (b) The equation representing the distance Kwan has driven (D) in terms of time (t) is D = 0.638t. (c) Kwan will drive approximately 0.1595 miles in 15 minutes, and (d) Kwan's trip of 234 miles will take approximately 366.8 hours at his constant rate.

(a) To determine how far Kwan will drive in 2 hours at the same constant speed, we can use the concept of proportionality. We can set up a ratio between the distance and time:

Distance / Time = Constant Speed

Let's calculate the constant speed first:

Constant Speed = Distance / Time

                 = 90 miles / 141 hours

                 ≈ 0.638 miles per hour

Now we can use the constant speed to find the distance Kwan will drive in 2 hours:

Distance = Constant Speed × Time

            = 0.638 miles per hour × 2 hours

            ≈ 1.276 miles

Therefore, Kwan will drive approximately 1.276 miles in 2 hours at this rate.

(b) The equation for D (distance) in terms of t (time) can be written as follows:

D = Constant Speed × t

Using the constant speed calculated earlier (0.638 miles per hour), the equation becomes:

D = 0.638t

(c) To determine how far Kwan drives in 15 minutes (0.25 hours), we can substitute t = 0.25 into the equation from part (b):

D = 0.638 × 0.25

    = 0.1595 miles

Therefore, Kwan will drive approximately 0.1595 miles in 15 minutes at this rate.

(d) If Kwan is driving a total of 234 miles, we can rearrange the equation from part (b) to solve for t:

D = 0.638t

234 = 0.638t

Dividing both sides of the equation by 0.638:

t = 234 / 0.638

   ≈ 366.77 hours

Kwan's trip will take approximately 366.8 hours.

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Answer:

2.7m

Step-by-step explanation:

1.0m

0.5m

+1.2m

2.7m - answer

Hence the probability of two defective batteries is 0.59.

1. Probability that in four tosses of a fair die, the number 2 appear:

a. At no time

We know that probability of not getting 2 on one throw is 5/6

Probability of not getting 2 on any of the four throws is (5/6) x (5/6) x (5/6) x (5/6)

= 625/1296

b. Once

The probability of getting 2 in one throw is 1/6 and not getting 2 in the other three throws is

(5/6) x (5/6) x (5/6)

Probability of getting 2 once in four throws
= 4C1 (1/6) (5/6)³

= 500/1296

c. Twice

Probability of getting 2 twice in four throws

= 4C2 (1/6)² (5/6)²

= 75/1296

d. Thrice

Probability of getting 2 thrice in four throws

= 4C3 (1/6)³ (5/6)

= 5/1296

e. Four times

Probability of getting 2 four times in four throws

= 4C4 (1/6)⁴

= 1/1296

So, the probability of getting 2 at no time is 625/1296; the probability of getting 2 once is 500/1296; the probability of getting 2 twice is 75/1296;

the probability of getting 2 thrice is 5/1296 and the probability of getting 2 four times is 1/1296.

2. Probability of different cases in a family of three children:

Let us assume that having a boy or a girl is equally likely, independent of other siblings

a. No boy

All children must be girls

Probability = (1/2)³ = 1/8b. 1 boy

This could happen in three ways: GBG, GGB or BGG. Each of these is equally likely, and the probability of each is (1/2)³ = 1/8Probability

= 3/8c. 2 boys

This could happen in three ways: GBB, BGB or BBG.

Each of these is equally likely, and the probability of each is (1/2)³

= 1/8

Probability = 3/8d. 3 boys

Only one way GGG, probability = (1/2)³

= 1/8e.

At least 1 boy

We can have no boy, 1 boy or 2 boys

Probability

= 1 – probability of no boy

= 1 – 1/8

= 7/8f.

At least 1 boy and 1 girl

Probability = 1 – probability of 3 boys

= 1 – 1/8

= 7/83.

Probability of getting at most two defective batteries out of 5 selected:

A defective battery has probability of 10/100 = 1/10

The probability of getting at most two defective batteries is sum of probability of getting 0, 1 and 2 defective batteries

P(getting 0 defective batteries) = (90/100)⁵P(getting 1 defective batteries)

= 5C1 (1/10) (9/10)⁴

P(getting 2 defective batteries)

= 5C2 (1/10)² (9/10)³

P(getting at most 2 defective batteries)

= (90/100)⁵ + 5C1 (1/10) (9/10)⁴ + 5C2 (1/10)² (9/10)³

= 0.59

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The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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To determine the appropriate significance level for performing a significance test based on the confidence level used to construct the confidence interval,

we need to consider the relationship between confidence level and significance level.

The confidence level represents the probability that the confidence interval will contain the true population parameter. In this case, the confidence level was not provided, so we cannot directly determine the significance level based on the given information.

Typically, a 95% confidence level is commonly used, which corresponds to an alpha (significance level) of 0.05. This means that there is a 5% chance of rejecting the null hypothesis when it is true.

However, it is important to note that the specific significance level to be used in a significance test should be determined in advance based on the requirements of the study, the consequences of Type I and Type II errors, and any relevant guidelines or standards in the field of study. The coach or researcher conducting the study should define the significance level based on these considerations.

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It is True that if the function f(x) is even, then the aₒ, aₙ are zero.

If the function f(x) is even, then it implies that for all x, f(x) = f(-x).

Properties of Even function f(-x) = f(x) - The graph of an even function is symmetric about the y-axis.

If the function is even, then a₀ will always be the average value of the function.-

The Fourier series of the even function will have only cosine terms, that is the series will be of the form f(x) = a₀/2 + Σ[an cos (nπx/L)] -

The sum of the product of an even function and an odd function is zero over a symmetric interval. -

If the function is even, then the series of Fourier will converge to the function f(x) at all points where f(x) is differentiable. - If the function is even, then all the odd coefficients in the Fourier series expansion will be zero.

The Fourier series expansion of an even function f(x) can be represented as f(x) = a₀/2 + Σ[an cos (nπx/L)]

Here, all the odd coefficients, b n will be zero because f(x) is an even function.

Hence, if the function f(x) is even, then the a₀, aₙ are zero.

An even function can have Fourier series coefficients, but these coefficients should be zero if the function is entirely even.

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Answer:

Step-by-step explanation:

I don’t know why they bother teaching recursive formulas as the explicit is almost always used :)

For 2,9,16,23...

Recursive is a(n+1)=an+7

Explicit is an=2+7(n-1)

(or more neatly an=7n-5)

For 2,14,98,686...

Recursive is a(n+1)=7an

Explicit is an=2(7^(n-1))

(or (2/7)7^n )

Answer

Explanation

Given:

mm

A.

To determine the measure of \(\begin{gathered} m\angle TRQ+m\angle QRS=180 \\ 145+m\angle QRS=180 \\ \text{Simplify and rearrange} \\ m\angle QRS=180-145 \\ m\angle QRS=35\degree \end{gathered}\)

Therefore, m

B.

To determine the measure of \(\begin{gathered} m\angle QRS+\angle S+\angle Q=180 \\ 35+y+4y=180 \\ \text{Simplify and rearrange} \\ 35+5y=180 \\ 5y=180-35 \\ 5y=145 \\ y=\frac{145}{5} \\ y=29\degree \end{gathered}\)Now, we plug in y=29 into m\(\begin{gathered} m\angle Q=4y \\ m\angle Q=4(29) \\ m\angle Q=116\degree \end{gathered}\)Therefore, m

Answer:

\(\frac{59}{100}\)

Step-by-step explanation:

first divide 59 by 100

\(\frac{59}{100}\)

now simplify

as u can see we can not simplify and it is the last stage so the answer will be

\(\frac{59}{100}\)

Answer:

Not sure if this is what you meant by graph and table but heres what i got

Step-by-step explanation:

The relative frequency in the class interval with 15 observations is 0.20 or 20%.

The correct answers are: Measurements from a sample are called: statistics. The relative frequency in the class interval with 15 observations is: 0.20.

Statistics are measurements or data collected from a sample of a larger population. They are used to make inferences about the population.

To find the relative frequency of a class interval, you divide the frequency of that interval by the total number of observations. In this case, the relative frequency is:

relative frequency = frequency of interval / total number of observations

relative frequency = 15 / 75

relative frequency = 0.20

Therefore, the relative frequency in the class interval with 15 observations is 0.20 or 20%.

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Mikos has to pay back his loan on April 14, plus interest, for a total of $104,375. The amount of interest he paid was $4,375 ($104,375 - $100,000).

1. The loan was for $100,000, at 10.5% ordinary interest.

2. The loan's maturity value was $104,375, meaning Mikos has to pay back the loan plus interest on April 14.

3. The amount of interest paid is the difference between the loan's maturity value and the original loan amount, which is $4,375 ($104,375 - $100,000).

The complete question is :

On April 14, Mikos Souvakis borrowed $100,000 to remodel his restaurant kitchen with a single-payment loan at 10.5% ordinary interest. If his loan's maturity value was $104,375, when does Mikos have to pay it back, and how much interest did he pay?

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Answer: The dimensions are 7cm and 3cm.

Step-by-step explanation:

The following equation can be deduced from the question

L × W = 21 ....... i

2L + 2W = 20 .......... ii

Divide equation ii through by 2

(2L + 2W = 20) / 2

L + W = 10 ....... iii

From equation iii

L = 10 - W ......... iv

Put equation iv into I

L × W = 21

(10 - W) × W = 21

10W - W² = 21

W² - 10W + 21 = 0

W² - 7W - 3W + 21 = 0

W(W - 7) - 3(W - 7) = 0

W - 3 = 0

W = 0+3

W = 3 centimeter

Since,

Length × Width = 21

Length = 21/3

Length = 7 centimeters

The dimensions are 7cm and 3cm.

Answer:

This will be -8x^3y^9.