Using the distance formula √(x₂ - x₁)² + (y₂ - y₁)² , find the distance from the center of your habitat to the point (x, y). Write this equation. Your answer will contain x- and y-terms. (1 point)

The HCF is 10, and the LCM is 2100

The equation of a polar curve r^2 = a cos 2θ describes a limaçon, which is a type of polar curve with a loop. When a is positive, the limaçon has an outer loop and an inner loop. When a is negative, the limaçon has a dimple instead of an inner loop.

In this case, a = 81, which is positive, so the limaçon will have an outer loop and an inner loop.

To graph the limaçon, we can start by considering the behavior of the curve at θ = 0, π/4, π/2, 3π/4, and π.

At θ = 0, r^2 = 81cos(2θ) = 81cos(0) = 81, so r = ±9. This means that there are two points on the curve at θ = 0, one at (9, 0) and one at (-9, 0).

At θ = π/4 and 3π/4, cos(2θ) = cos(π/2) = 0, so r^2 = 0 and r = 0. This means that there are two points on the curve at θ = π/4 and two points at θ = 3π/4, all located at the origin.

At θ = π/2, r^2 = 81cos(2θ) = 81cos(π) = -81, which is negative. Since r is always non-negative, there are no points on the curve at θ = π/2.

At θ = π, r^2 = 81cos(2θ) = 81cos(2π) = 81, so r = ±9. This means that there are two points on the curve at θ = π, one at (9, π) and one at (-9, π).

Based on this information, we can sketch the graph of the limaçon as follows:

There are two points on the x-axis, one at (9, 0) and one at (-9, 0).

There are four points at the origin.

There are two points on the line θ = π, one at (9, π) and one at (-9, π).

The curve passes through the origin at θ = π/4, π/2, and 3π/4, and has a loop that encloses the origin.

Overall, the limaçon has a symmetric, flower-like shape with a loop that encloses the origin.

Answer:

an infinity sign

Step-by-step explanation:

A 95% confidence interval on the difference in the towels' mean absorbency produced by the two processes is between -295.36 and -104.64

We can use the two-sample t-test formula to find the confidence interval for the difference in means:

t = (x1 - x2 - d) / √(s1²/n1 + s2²/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, d is the hypothesized difference in means (usually 0 in a two-sided test), and t follows a t-distribution with degrees of freedom given by:

df = (s1^2/n1 + s2^2/n2)^2 / (s1^4/n1^2(n1-1) + s2^4/n2^2(n2-1))

Plugging in the given values, we have:

x1 = 130, s1 = 15, n1 = 10

x2 = 310, s2 = 50, n2 = 4

d = 0 (since we are testing for a difference of means)

t(0.025, df) = 2.306 (using a t-table or calculator)

Substituting these values into the formula, we get:

t = (130 - 310 - 0) / sqrt(15^2/10 + 50^2/4) = -4.156

df = (15^2/10 + 50^2/4)^2 / (15^4/10^2(10-1) + 50^4/4^2(4-1)) = 7.38 (rounded to 2 decimal places)

The 95% confidence interval for the difference in means is given by:

(x1 - x2) ± t(0.025, df) * sqrt(s1^2/n1 + s2^2/n2)

= (130 - 310) ± 2.306 * sqrt(15^2/10 + 50^2/4)

= (-200 ± 95.36)

= (-295.36, -104.64)

Therefore, we can be 95% confident that the true difference in mean absorbency between the two processes is between -295.36 and -104.64. Since the interval does not contain 0, we can conclude that the means are significantly different at the 5% level.

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Clara is earning money at a faster rate than Tiffany, with a difference of $4 per hour.

A graph in x-y axis plot is a visual representation of mathematical functions or data points on a Cartesian coordinate system.

To determine who is earning money at a faster rate, we need to calculate the hourly earnings for each person.

For Tiffany, the hourly earnings can be calculated as follows:

Hourly earnings = Earnings / Time

Hourly earnings = 40 / 5 = 8

Hourly earnings = 80 / 10 = 8

Hourly earnings = 120 / 15 = 8

So, Tiffany's hourly earnings are a constant $8 per hour.

For Clara, we can estimate her hourly earnings from the graph. The graph shows that Clara earns $60 for 5 hours of work, $120 for 10 hours of work, and $180 for 15 hours of work. Therefore, her hourly earnings can be calculated as follows:

Hourly earnings = Earnings / Time

Hourly earnings = 60 / 5 = 12

Hourly earnings = 120 / 10 = 12

Hourly earnings = 180 / 15 = 12

So, Clara's hourly earnings are a constant $12 per hour.

Thus, Clara is earning money at a faster rate than Tiffany, with a difference of $4 per hour.

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Using ratios, Carl will receive 24 oranges, while Dina will get 40 oranges, and Eva will receive 36 oranges.

A ratio shows the relative size of one quantity compared to another quantity or value.

Ratios are expressed in standard ratio forms using the colon (:), in decimals, fractions, or percentages.

The total number of oranges shared between Carl, Dina, and Eva = 100

The ratio Carl's oranges to Dina's oranges = 3:5

The ratio Carl's oranges to Eva's oranges = 2:3

Based on the above ratios, for every 2 oranges that Carl receives, Eva receives 3.

For Carl to receive 3 oranges, Eva will receive 4.5 oranges (3 x 3/2)

The ratios among the three friends are 3: 5: 4.5

The sum of ratios = 12.5 (3 + 5 + 4.5)

Carl's share = 24 (3/12.5 x 100)

Dina's share = 40 (5/12.5 x 100)

Eva's share = 36 (4.5/12.5 x 100)

Thus, based on the ratios, the number of oranges Carl receives is 24.

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The professional set of drawing pencils costs $18.51 more than the basic set. This is a significant difference in price and may be worth the additional cost depending on the user's needs.

First, we need to calculate the difference in price between the professional set and the basic set of drawing pencils. To do this, we will subtract the cost of the basic set ($8.98) from the cost of the professional set ($27.49).

We can write this difference as an equation:

Difference = Professional Set Cost - Basic Set Cost

Difference = 27.49 - 8.98

Next, we can solve for the difference in price by subtracting the two values.

Difference = 18.51

Therefore, the professional set of drawing pencils costs $18.51 more than the basic set. This is a significant difference in price and may be worth the additional cost depending on the user's needs.

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Answer:

1

Step-by-step explanation:

Answer: The answer is 1 tablespoon of vanilla.

Step-by-step explanation:

Based on the given conditions, formulate:

[tex]\frac{1}{6}[/tex]  ÷ [tex]\frac{2}{12}[/tex]

Simplify fraction(s): [tex]\frac{1}{1}[/tex]

Any fraction with a denominator of 1 is equal to its numerator, which is 1.

I hope this helped you! A brainilist is highly appreciated and helpful! <3

The correct order of presentation of sample distribution  should include the introduction, method, results, discussion, and conclusion.

The correct order of presentation for results of an independent samples t-test is as follows:Introduction: Introduction should include the aim of the research, the hypothesis, and the data collection method. Method: The method should include the sample size, the type of sample, the data collection method, and the statistical analysis techniques used. Results: The results should include descriptive statistics for each group, the t-test result, the degree of freedom, and the p-value. Discussion: The discussion should include the interpretation of the results, the significance of the findings, and the limitations of the study.Conclusion: The conclusion should summarize the findings and provide suggestions for future research.

Explanation In research, presenting the findings of an independent samples t-test involves comparing the means of two independent groups to determine if there is a significant difference between the two groups. The independent t-test is used when the data are independent, and it assumes that the samples have a normal distribution with equal variances.The results of the t-test can be presented using tables, graphs, or charts.

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The slope of the line is 2/5 and to represent the "rise" and "run" on the line, a vertical line and a horizontal line are drawn to show the change in y and x, respectively.

To find the slope of the line, we can choose two points on the line and use the formula:

slope = (change in y)/(change in x)

Let's choose the points (-2, 3) and (3, 5) on the line. The "rise" is the change in y and the "run" is the change in x between these two points:

Rise = change in y = 5 - 3 = 2

Run = change in x = 3 - (-2) = 5

So the slope of the line is:

slope = (change in y)/(change in x) = 2/5

Therefore, the slope of the line in simplest form is 2/5.

To represent the "rise and run" on the line, we can draw a vertical line going from the point (-2, 3) to the point (-2, 5) to represent the "rise" of 2 units, and a horizontal line going from the point (-2, 5) to the point (3, 5) to represent the "run" of 5 units.

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The values of a and b in the expression are a = 1 and b = 7

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

The expression

When the expression on the left hand side is simplified, we have

xy^7

So, we have

xy^7 = x^a * y^b

By comparison, we have

a = 1 and b = 7

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The statements that are true about the quadratic function and its graph include the following:

In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive i.e when the value of "a" is greater than zero.

Next, we would determine the statements about the quadratic function and its graph that are true:

At point (-10, 82), we have:

[tex]f(x) = \dfrac{1}{5} \ x^2 - 5x + 12[/tex]

[tex]f(x) = x^2/5 - 5x + 12[/tex]

[tex]f(-10) = -10^2/5 - 5(-10) + 12[/tex]

[tex]f(-10) = 82[/tex]

At point (20, -8), we have:

[tex]f(x) = \dfrac{1}{5} \ x^2 - 5x + 12[/tex]

[tex]f(x) = x^2/5 - 5x + 12[/tex]

[tex]f(20) = 20^2/5 - 5(20) + 12[/tex]

[tex]f(20) = -8[/tex]

In conclusion, the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.

Answer:21

Step-by-step explanation:

Therefore, the long dimension of the quilt is (26x + 60)/(x + 6) cm longer than the short dimension.

Area is the measure of the extent of a 2-dimensional surface or region, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²). It is the amount of space inside the boundary of a flat shape or the surface of an object.

Here,

The area of the original square is x^2 cm². Maria adds some fabric to one side of the square, which increases the length of the rectangle by a certain amount, and adds a different amount of fabric to the adjacent side, which increases the width of the rectangle by a certain amount. Let's say Maria adds y cm of fabric to one side and z cm of fabric to the other side. Then the length of the rectangle is x + y cm and the width is x + z cm. The area of the rectangle is given by:

(x + y)(x + z) = x^2 + xy + xz + yz

We know that the area of the rectangle is x² + 13x + 30 cm². So we can set these two expressions equal to each other:

x² + xy + xz + yz = x² + 13x + 30

Simplifying this equation, we get:

xy + xz + yz = 13x + 30

We want to find the difference between the length and the width of the rectangle, which is (x + y) - (x + z) = y - z. To solve for y - z, we need to express yz in terms of y - z. We can do this by factoring the left side of the equation above:

xy + xz + yz = y(x + z) + xz = (y - z)(x + y + z)

Substituting this expression for yz in the equation above, we get:

(y - z)(x + y + z) = 13x + 30

We want to solve for y - z, so let's focus on the left side of the equation:

(y - z)(x + y + z) = y(x + y + z) - z(x + y + z)

= xy + y² + yz - xz - z² - yz

= y² - z² + xy - xz

Substituting the expression we found earlier for xy - xz, we get:

(y - z)(x + y + z) = y² - z² + (y - z)(x + z)

(y - z)[x + y + z - (x + z)] = y² - z²

y - z = (y² - z²)/(y - z) = y + z

= (13x + 30)/(x + 6)

So the difference between the length and the width of the rectangle is:

y - z = (13x + 30)/(x + 6)

Therefore, the long dimension of the quilt is (x + y) = x + (13x + 30)/(x + 6) cm, and the short dimension is (x + z) = x + (30 - 13x)/(x + 6) cm. The difference between the long and short dimensions is:

[x + (13x + 30)/(x + 6)] - [x + (30 - 13x)/(x + 6)]

= (13x + 30)/(x + 6) - (30 - 13x)/(x + 6)

= (26x + 60)/(x + 6)

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After answering the provided question, we can conclude that Therefore, the simplified expression is [tex](y / x) * (1 / z^5)[/tex] and the value of the exponent for y is 1.

An expression in mathematics is a collection of manifestations, digits, and transnational corporations that resemble a significant correlation or regimen. A square root, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, pervasiveness, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To simplify the expression,

[tex]x^0xy^2z(^-3) = xy^2z(^-3)\\xy^2z(^-3) / x^2yz^2\\= (xy^2 / x^2y) * (1 / z^5)\\= (y / x) * (1 / z^5)[/tex]

Therefore, the simplified expression is [tex](y / x) * (1 / z^5)[/tex] and the value of the exponent for y is 1.

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The value of the ratio of baking soda to salt is 3/4 : 1.

A fraction is a number that represents a portion of a whole or a ratio of two quantities.  It consists of two integers arranged one above the other and divided by a horizontal line known as a vinculum or fraction bar.The ratio of baking soda to salt in the recipe can be written as:

Baking soda : Salt = 3/4 : 3

To simplify the ratio, we can first convert the fraction 3/4 to an equivalent fraction with a denominator of 12  

3/4 = 9/12

So the ratio becomes:

Baking soda : Salt = 9/12 : 3

We can simplify this ratio further by dividing both the numerator and denominator of the first fraction by 3:

Baking soda : Salt = 3/4 : 1

Therefore, the value of the ratio of baking soda to salt = 3/4 : 1.

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The ultralight airplane traveled a total of 1350 miles in September while tracking the monarch butterflies migrating to Mexico.

A mile is unit of distance on land in English-speaking countries equal to 5280 feet, or 1760 yards.

The ultralight airplane tracked monarch butterflies migrating to Mexico for 30 days in September, with a flight mile of 45 miles each day. To find the total miles traveled by the ultralight airplane in September, we can do the following:

Multiply flight mile per day by the number of days

= 45 miles/day x 30 days

= 1,350 miles.

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The caffeine is leaving Bree's body at a rate of approximately 11.96 mg per hour.

What is the rate?

Rate is a measurement of the speed of change or the amount of change that occurs per unit of time or per unit of some other quantity. It is a ratio between two different measurements, typically expressed in units of distance, time, weight, volume, or currency.

The caffeine in Bree's system is decreasing linearly over the course of 6 hours (from 8am to 2pm).

We can use the information given to find the hourly decreasing rate by calculating the slope of the line connecting the two data points.

The change in caffeine over 6 hours is:

100 mg - 28.24 mg = 71.76 mg

So the hourly decreasing rate can be calculated as:

Hourly decreasing rate = Change in caffeine / Time

Hourly decreasing rate = 71.76 mg / 6 hours

Hourly decreasing rate = 11.96 mg/hour (rounded to two decimal places)

Therefore, the caffeine is leaving Bree's body at a rate of approximately 11.96 mg per hour.

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Alexis can run at a rate οf 10 km/hr

Time: a measure οf the duratiοn between twο events.

Speed: the rate at which an οbject cοvers a distance.

Distance: the amοunt οf space between twο pοints οr οbjects.

We can use the fοrmula:

rate = distance / time

tο calculate the rate at which Alexis runs and rides his bicycle. Then, we can use the rate οf running tο find οut hοw many kilοmeters he can run in 1 hοur.

Fοr running, rate = distance / time = 5 km / 0.5 hr = 10 km/hr

Fοr riding his bicycle, rate = distance / time = 20 km / 0.8 hr = 25 km/hr

Therefοre, Alexis can run at a rate οf 10 km/hr

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Step-by-step explanation:

vertex             vertical angles

Answer wil be (4/14) .

.......

Answer:

Answer 4/14

Step-by-step explanation:

The point of intersection of the graph (2,9), means that at 2 minutes, the altitude was 9 thousand feet.

The y-axis in the presented graph denotes altitude in thousand feet, while the x-axis in the graph denotes time in minutes. The point of intersection, (2,9), indicates that the height was 9000 feet at 2 minutes.

The moment when the height was 9000 feet is indicated by the x-value, which in this instance is 2. It identifies the precise point in time when the height was displayed on the graph as 9000 feet.

It is crucial to understand the x-value of the point of contact because it enables precise computations and predictions about the height at various times.For example, if we want to know the altitude at 5 minutes, we can use the slope of the graph and the point of intersection to determine the altitude accurately.

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Answer: RM 86.40

Step-by-step explanation:

The profit can be calculated as follows:

Selling price = List price + Profit

Profit = (Percentage profit/100) x List price

Discount = (Discount percentage/100) x Selling price

Selling price after discount = Selling price - Discount

Let's plug in the given values into these formulas:

List price = RM 120

Percentage profit = 60%

Profit = (60/100) x 120 = RM 72

Discount percentage = 30%

Selling price = 120 + 72 = RM 192

Discount = (30/100) x 192 = RM 57.60

Selling price after discount = 192 - 57.60 = RM 134.40

To calculate the profit after discount, we need to subtract the cost price from the selling price after discount:

Profit after discount = Selling price after discount - Cost price

Cost price = List price - Profit = 120 - 72 = RM 48

Profit after discount = 134.40 - 48 = RM 86.40

Therefore, the profit after the discount is RM 86.40.

Answer:

4992/640

Step-by-step explanation:

As there are decimals in both, you can move the decimal point by 2!

49.92 will become 4992,

and 6.4 will become 640!

:)

The longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches.

The longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches. This can be calculated using the formula:

Maximum length - Current length = Amount of growth required

In this case, we substitute the values as follows:

23 inches - 19 inches = 4 inches

Therefore, the longest fish caught needs to grow an additional 4 inches in order to reach the maximum length.

To help visualize this, we can consider the scales of the fish. To reach the maximum length, the longest fish caught would need to add 4 scales, which is a relatively small amount. This is conceivable, as the fish can continue to grow as long as it has access to enough food and a suitable environment.

In summary, the longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches. This can be calculated using the formula: Maximum length - Current length = Amount of growth required. To help visualize this, the fish needs to add 4 scales which is a relatively small amount.

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Step-by-step explanation:

Take the derivative of this function using the power rule

[tex] \frac{d}{dx} ( {x}^{n} ) = nx {}^{n - 1} [/tex]

Since the terms are serpated using addition or subtraction we can take the derivative of this function separately

So our derivative end up becoming

[tex]6x - 7[/tex]

Plug in x=2

[tex]6(2) - 7 = 5[/tex]

So the gradient of the tangent line at 2,-7 is 5

Answer:

(-5, -7)

Step-by-step explanation:

To rotate a point (x,y) by 180 degrees about the origin, we can multiply its coordinates by the matrix:

-1  0

0 -1

So, to rotate the triangle JKL by 180 degrees about the origin, we can apply this transformation to each of its vertices. We have:

J(3,1)  ->  J^`(−3,−1)

K(7,−5) ->  K^`(−7,5)

L(5,7)  ->  L^`(−5,−7)

Therefore, the coordinates of the vertex L^(`) after the triangle is rotated by 180 degrees clockwise about the origin are (-5, -7).

Answer: 2(27+16)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The intersection points between the two lines y > (3x-4) and y > -(1/2)x+3, from the graph is (x, y) = (2, 2)

To graphically solve the system of inequalities, we will first graph the two boundary lines, which are the lines obtained by replacing the inequality symbols with equality symbols in each of the given inequalities:

y > 3x - 4 (red dotted line)

y > -(1/2)x + 3 (blue dotted line)

When we plug (0, 0) into y > 3x - 4, we get:

⇒ 0 > 3(0) - 4

⇒ 0 > -4

This inequality is true, so we shade the half-plane above the solid line,

y = 3x - 4

When we plug (0, 0) into y > -(1/2)x + 3, we get:

⇒ 0 > -(1/2)(0) + 3

⇒ 0 > 3

This inequality is not true, so we shade the half-plane below the dashed line, y = -(1/2)x + 3

The solution set is the region that is shaded in both half-planes, which is the triangular region above the solid line and below the dashed line.

Now, we have to determine the intersection points between the two lines y > (3x-4) and y > -(1/2)x+3, from the graph, we get; (x, y) = (2, 2)

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Graph of the solution-