How do I solve this challenging math problem?

The linear equation in standard form is 19x - 14y = -182.

What is Linear equation?

A linear equation is a mathematical equation that describes a straight line on a graph. In other words, it is an equation that relates a variable or variables to a constant through a linear function, where the highest power of the variable is one. A general form of a linear equation is:

y = mx + b

To write the linear equation in standard form Ax + By = C, where A, B, and C are integers and A is positive, we need to get rid of the fraction in the equation.

To do this, we can multiply both sides of the equation by the denominator of the fraction, which is 14. This gives:

14y = 19x + 182

Next, we can rearrange this equation by subtracting 19x from both sides:

-19x + 14y = 182

Finally, we can multiply both sides of the equation by -1 to make the coefficient of x positive:

19x - 14y = -182

So, the linear equation in standard form is 19x - 14y = -182.

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Answer:

16

Step-by-step explanation:

When we divide the entire equation by 1/-2 to get rid of the coefficient of n we get n = 16.

Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.

A mathematical concept known as proportionality describes the relationship between two quantities that have different sizes but keep the same ratio or proportion. In other words, to preserve the same ratio, if one item changes, the other quantity must also change in proportion. For instance, if an automobile's speed and distance are proportionate, doubling the distance it travels will cause the car to go twice as quickly while retaining the same speed-to-distance ratio. Equations or ratios in mathematics are frequently used to express proportionality.

given

We can use the following formula to determine the lower and upper bounds of the 95% confidence interval for the population proportion:

Lower limit: sqrt((p * q) / n) * p - z

Upper limit: sqrt((p * q) / n) = p + z

With q = 1 - p, z is the z-score corresponding to the level of confidence, and p is the sample proportion.

Here, p = 130/520 = 0.25, q = 1 - p = 0.75, n = 520, and the z-score is 1.96 at a 95% confidence level (from the standard normal distribution).

Lower limit: 0.210 (0.25" * 0.75") - 1.96 * sqrt(0.25" * 0.75")

The maximum is equal to 0.25 + 1.96 * sqrt((0.25 * 0.75) / 520) = 0.290.

Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.

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Yes, the value of 0.75 to 0.83 for a 95% confidence interval is plausible.

A confidence interval is a range of values that has a 95% chance of containing the true population parameter, which in this case is the population proportion (p).

A 95% confidence interval has a margin of error of 5%. Thus, a range of 0.75 to 0.83 has a 95% chance of containing the true population proportion p.

The 95% confidence interval is an estimated range of values which is calculated from sample data, with a 95% chance of containing the true population parameter, p. To calculate the confidence interval, the confidence level and the margin of error must be known.

The confidence level is the probability that the confidence interval will contain the true population parameter, and the margin of error is the amount that the sample statistic can differ from the true population parameter.

A 95% confidence level has a margin of error of 5%, meaning that the sample statistic can be up to 5% away from the true population parameter.

In this case, the 95% confidence interval for the population proportion is 0.75 to 0.83. This means that the range of 0.75 to 0.83 has a 95% chance of containing the true population proportion p, and is thus a plausible value for the population proportion.

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Answer:

let angle GJK be x

GJK=GHK (Base angle of isosceles triangle)

Step-by-step explanation:

x=5x+8

5x-x=8

4x=8

x=8/4

x=2 ans.

Hence,

5x+8

5*2+8

10+8

18.ans

Answer: they all include a variable, an "x" in parentheses, and they all have the number 2 in it.

Step-by-step explanation:

The probability of drawing at least one spade when drawing two cards with replacement from a standard deck of cards is approximately 0.26%.

When drawing two cards at random with replacement from a standard 52-card deck, there are 4 possible outcomes for the first card being a spade and 4 possible outcomes for the second card being a spade.

However, there is also 1 possible outcome where both cards are spades, which would be counted twice if we add the outcomes for the first and second cards separately. Therefore, the total number of outcomes where at least one card is a spade is 4 + 4 - 1 = 7.

The total number of possible outcomes when drawing two cards with replacement is 52 x 52 = 2,704.

Therefore, the probability that at least one card is a spade when drawing two cards with replacement is:

P(at least one spade) = 7 / 2,704 ≈ 0.0026

So, the probability that at least one card is a spade is approximately 0.0026 or 0.26%.

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Answer:

£21

Step-by-step explanation:

We know

kai and David share £84 in the ratio 1:3. Meaning for every £4, Kai receive £1 & David received £3.

Calculate the amount of money kai gets​?

To get from 4 to 84, we time 21.

We take

1 x 21 = £21

So, Kai gets £21

Answer: The speed of light is approximately 89,100 times faster than the speed of sound.

Step-by-step explanation: To find out how many times faster the speed of light is than the speed of sound, we need to divide the speed of light by the speed of sound:

Speed of light / Speed of sound = (6.710610^7) / (7.5410^2)

Simplifying this calculation gives us:

Speed of light / Speed of sound = 8.91*10^4

This means that the speed of light is approximately 89,100 times faster than the speed of sound.

Hope this helps, and have a great day!

The shorter side of the rectangle is approximately 237.25 millimeters, and the diagonal makes angles of approximately 41 degrees and 49 degrees with the longer and shorter sides, respectively.

Let us denote the shorter side of the rectangle as x. We can use the Pythagorean theorem to relate the length of the diagonal to the two sides of the rectangle:

diagonal^2 = longer side^2 + shorter side^2

Substituting in the given values, we get:

450^2 = 393^2 + x^2

Solving for x, we get:

x = √(450^2 - 393^2) ≈ 237.25 mm

To find the angles that the diagonal makes with each side of the rectangle, we can use trigonometry. Let θ be the angle between the diagonal and the longer side, and let φ be the angle between the diagonal and the shorter side. Then we have:

sin(θ) = shorter side / diagonal

sin(φ) = longer side / diagonal

Substituting in the given values and solving for θ and φ, we get:

θ ≈ 41 degrees

φ ≈ 49 degrees

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Answer: 7

Step-by-step explanation:

The required day if yesterday is the day before yesterday of Saturday is Thursday and day after tomorrow is Sunday.

If yesterday was the day before yesterday of Saturday,

Yesterday was Saturday

Day before yesterday is Friday,

then yesterday was Thursday.

Now,

If yesterday was Thursday, then today is Friday.

Day representing tomorrow is Saturday.

And day after Saturday is definitely Sunday.

This implies,

The day after tomorrow would be Sunday.

Therefore, day after tomorrow is Sunday as per given situation.

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Answer:

To find how many refrigerator magnets can be made with 9 3/8 inches of magnetic tape, we need to divide the total length of magnetic tape by the length of magnetic tape used for each magnet.

First, we need to convert the mixed number 9 3/8 to an improper fraction:

9 3/8 = (9 x 8 + 3)/8 = 75/8

Next, we divide 75/8 by 5/8 to find how many magnets can be made:

(75/8) ÷ (5/8) = (75/8) x (8/5) = 15

Therefore, 15 refrigerator magnets can be made with 9 3/8 inches of magnetic tape.

The bookshop will receive a total amount of Rs. 23,200 by selling all the books.

WHAT IS SELLING PRICE ?

The selling price is the price at which a product or service is sold to a customer. It is the amount of money that a seller charges to a buyer for a particular product or service. The selling price may include various factors such as the cost of production, overhead costs, profit margin, taxes, and other charges. It is an important concept in business and commerce, as it determines the revenue generated by a company and its profitability.

We can represent the given information using matrices as follows:

Let A be the matrix of the number of books in dozens, where each row represents a subject and each column represents the number of dozens of books:

A =

| 10 8 10 |

|____________|

Let B be the matrix of the selling prices of each book, where each row represents a subject and each column represents the selling price of each book:

B =

| 80 |

| 60 |

| 40 |

To calculate the total amount the bookshop will receive, we need to multiply the matrices A and B using matrix algebra:

C = A * B

C =

| 10 8 10 | | 80 | | 12000 |

| 60 | = | 7200 |

| 40 | | 4000 |

Therefore, the bookshop will receive a total amount of Rs. 23,200 by selling all the books.

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Answer:

1=26°

2=154°

3=26°

4=26°

5=154°

6=154°

7=26°

Answer:

C. A limited government protects individual freedoms.

Step-by-step explanation:

There are more individual freedoms as opposed to the lifestyle of those who are under a monarchy

Answer:

3

8

Step-by-step explanation:

probability= no. of blue marbles

total no. of marbles

= 3

8

They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.

The null hypothesis is a claim made in statistical hypothesis testing that presupposes there is no correlation between groups or any meaningful difference between a set of variables. It is commonly denoted by "H0," and the alternative hypothesis is compared with it ("H1"). The null hypothesis is typically assumed to be true, and in order to determine whether it can be rejected or not, it must be statistically tested. The alternative hypothesis is accepted if there is enough data to refute the null hypothesis. In contrast, the null hypothesis is maintained if there is not sufficient evidence to support it.

given

The group of 50 males who are chosen to take part in the study serves as the sample for the experiment.

They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.

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Answer:

Let's use "x" to represent the total number of students in the class.

According to the problem, the number of boys is 7/10 of the total number of students, and the number of girls is 3/10 of the total number of students. We can set up the following equation based on this information:

Number of Boys = 7/10 x

Number of Girls = 3/10 x

The problem also tells us that there are 16 more boys than girls in the class. We can set up another equation based on this information:

Number of Boys = Number of Girls + 16

Now we can use these two equations to solve for the total number of students:

7/10 x = 3/10 x + 16

Subtracting 3/10 x from both sides, we get:

4/10 x = 16

Multiplying both sides by 10/4, we get:

x = 40

Therefore, there are 40 students in the class. To find the number of boys and girls, we can use the equations we set up earlier:

Number of Boys = 7/10 x = 7/10 * 40 = 28

Number of Girls = 3/10 x = 3/10 * 40 = 12

So there are 28 boys and 12 girls in the class.

Answer:

119% of 550

Step-by-step explanation:

add the percentages

The correct basis step for proving the statement P(n) using strong induction is to show that P(8) is true

Strong induction is a method of proving that a statement is true for all values of n by demonstrating that it is true for a base case and that if it is true for all values up to n, then it must also be true for n+1. It can be used to prove the statement P(n) that a postage of n cents can be formed using only 3-cent stamps and 5-cent stamps.

To demonstrate that P(8) is true is to do the proper basis step for strong induction. This is so that we may create an 8 cent postage using a 3-cent and a 5-cent stamp.

The following argument can be used to demonstrate that the basic step is P(8) being true:

A postage of 8 cents can be made with one 3-cent stamp and one 5-cent stamp.

Thus, P(8) must be true.

We don't need to check any other values for the base step because P(n) only depends on the values of P(k), where k n.

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Answer:

Step-by-step explanation:

The inequality statement that describes the two numbers on a number line "2 and a number 9 units to the left of 2" would be:

x < 2

where x represents the number that is 9 units to the left of 2.

The T-shirt takes 2.25 seconds to reach its maximum height and the maximum height is approximately 90.125 feet above the court.

The equation for the height of the T-shirt at time t is given as h(t) = -16t² + 72t + 5, where h(t) is the height in feet and t is the time in seconds.

To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function. The vertex of a parabola in the form y = ax² + bx + c is given by (-b/2a, c - b²/4a). In this case, a = -16, b = 72, and c = 5. So, the time it takes for the T-shirt to reach its maximum height is:

t = -b/2a = -72/(2(-16)) = 2.25 seconds

To find the maximum height, we need to substitute the value of t we just found into the equation for h(t):

h(2.25) = -16(2.25)² + 72(2.25) + 5 ≈ 90.125 feet

Therefore, the T-shirt takes 2.25 seconds to reach its maximum height and the maximum height is approximately 90.125 feet above the court.

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to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.

To determine the amount of fencing required to enclose a circular garden with a radius of 26 meters, we need to calculate the circumference of the circle. The circumference is the distance around the perimeter of the circle, which can be calculated using the formula:

Circumference = 2 x π x radius

where π is the mathematical constant approximately equal to 3.14, and the radius is the distance from the center of the circle to any point on its perimeter.

So, in this case, the circumference of the circular garden can be calculated as follows:

Circumference = 2 x 3.14 x 26 m

= 163.64 m

Therefore, to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.

It's worth noting that the formula for calculating the circumference of a circle can be used to find the amount of fencing required for any circular enclosure, such as a circular pond or a circular pool.

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Answers: 36

Step-by-step explanation:

However, it is important to note that without additional information about the function and the windmill itself, further conclusions about its design and performance cannot be made.

Hi! I'd be happy to help you describe the windmill based on the provided graph.The graph of the function represents the relationship between the height (y) of the tip of a windmill blade and the angle of rotation (Θ) made by the blade. This function is periodic, indicating that the windmill blade follows a repetitive motion as it rotates.

The height of the blade tip varies sinusoidally with respect to the angle of rotation, suggesting that the windmill has a circular or rotational motion. The amplitude of the function gives the length of the windmill blade, while the period of the function represents a full rotation (360 degrees) of the windmill blade.

In summary, the windmill has a rotational motion, with the height of the blade tip following a sinusoidal pattern. The length of the windmill blade and the time it takes to complete a full rotation can be determined by analyzing the amplitude and period of the function.

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The vertices of the image triangle N′M′O′: N′(-1, 2), M′(-4, 1), O′(-3, 3).

What are vertices?

Vertices (singular: vertex) are the points where two or more straight lines or edges meet in a geometric shape such as a polygon, polyhedron, or graph. In two-dimensional shapes like polygons, a vertex is a corner where two sides intersect.

We can do this by finding the difference between the x-coordinate of the preimage vertex and -3, doubling this difference, and then subtracting this result from the x-coordinate of the preimage vertex. This will give us the x-coordinate of the image vertex.

For example, to find the x-coordinate of the image of vertex N, we have:

x-coordinate of N = -5

Difference between x-coordinate of N and -3 = -5 - (-3) = -2

Double the difference = -2 x 2 = -4

Subtract this result from the x-coordinate of N = -5 - (-4) = -1

Therefore, the x-coordinate of the image of vertex N is -1.

Using the same method, we can find the x-coordinates of the image vertices:

x-coordinate of N′ = -1

x-coordinate of M′ = -4

x-coordinate of O′ = -3

To find the y-coordinates of the image vertices, we don't need to do any calculations since the reflection is over a vertical line and does not affect the y-coordinates. Therefore, the y-coordinates of the image vertices are the same as the y-coordinates of the preimage vertices:

y-coordinate of N′ = 2

y-coordinate of M′ = 1

y-coordinate of O′ = 3

Putting it all together, we get the vertices of the image triangle N′M′O′:

N′(-1, 2), M′(-4, 1), O′(-3, 3)

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The doctor goes home at 5 pm if all patients are finished before 5 pm.

The possible values of t are from 0 to 300.

Let t be the time exceeding 5 pm in minutes.

Therefore, we have to find the expected time for the doctor to go home after the last patient has been served, or at 5 pm if all patients are finished before 5 pm.

We will determine its pmf as well.

Expected time that the doctor will go home

The doctor goes home at 5 pm if all patients are finished before 5 pm.

Let the doctor takes x amount of time to see the patients in hours.

Then the total time taken to see n patients will be xn.

If the doctor sees n patients in the first x hours and leaves the remaining patients, then the time will be (n-x) hours.

The total time that the doctor will go home will be given as:

{(n-x)x} + (n-x) if (n-x) > 0

Otherwise, the doctor will go home at 5 pm.

The pmf of t

To find the possible values of t, we need to find the minimum and maximum value of x.

{(n-x)x} + (n-x) if (n-x) > 0 will be greater than 0 when x is less than n/2.

Therefore, the possible values of t are from 0 to 300.

We know that t is defined as the time exceeding 5 pm in minutes.

pmf of t is given as :

P(t = 0) = P(all patients are done before 5 pm) = 1/32

P(t = i) = P(last patient finishes at 5pm + i minutes) = 31/32 × (1/300) for i = 1, 2, 3, ..., 299.

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According to the given information, the sale price is 160% of the purchase price and she would need to buy at least 4 jackets to make at least $250 in total sales.

What is the percentage?

The percentage is a way of expressing a fraction or proportion out of 100. It is commonly used in many different areas such as finance, math, science, and everyday life.

a. To find the percent of the purchase price that the sale price represents, we can use the formula:

percent = (sale price/purchase price) x 100

Plugging in the given values, we get:

percent = (96 / 60) x 100 = 160%

Therefore, the sale price is 160% of the purchase price.

b. If the owner increases the sale price by 160% when buying jackets for $45, then the new sale price for each jacket will be:

new sale price = 1.6 x $45 = $72

To find the number of jackets the owner must buy to make at least $250 in total sales, we can set up an equation:

number of jackets x $72 = $250

Solving for the number of jackets, we get:

number of jackets = $250 / $72 ≈ 3.47

Since the owner can only sell a whole number of jackets, she would need to buy at least 4 jackets to make at least $250 in total sales.

This is because selling 3 jackets would only bring in $216 in total sales, which is less than $250.

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