Find an equation of the tangent line to the curve x2/3 + y2/3 = 10 (astroid)at the point(−27 ,1)

Answer:

12.8

Step-by-step explanation:

Quotient means the answer of two things divided.

62.72/4.9=12.8

Answer:

Words of the Devil, by Parau na te Varua ino, is a painting that was created in 1892 in French Polynesia. The painting depicts a scene from Tahitian mythology, in which the goddess Hina is visited by the devil, who is represented as a horned figure with a large, forked tongue. The painting is rich in detail and vivid color, with the figures depicted in bright, bold colors that stand out against the darker background.

The style of the painting is characteristic of the Tahitian art of the time, which was heavily influenced by the traditional Polynesian art forms of carving, tattooing, and tapa cloth decoration. The figures in the painting are depicted in a stylized, almost abstract way, with exaggerated features and bold, sweeping lines. The use of bright colors and bold brushstrokes gives the painting a dynamic, almost chaotic energy that reflects the intense emotions of the scene.

Overall, Words of the Devil is a powerful and striking work of art that captures the mythology and cultural traditions of French Polynesia in the late 19th century.

Answer: The least common multiple is (x−5) (x−5)

Step-by-step explanation:

The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

The wrestler's weight at the first match will be 152.1 pounds. The solution has been obtained by using the substitution method.

What is the substitution method?

The substitution method is a strategy used in algebra to solve simultaneous linear equations. In this process, as the name suggests, the value of one variable from one equation is swapped in the second equation.

We are given that the given situation can be modeled by the equation

y = −1.1x + 162.

Now, we need to find weight at the first match which is 9 weeks away.

So, we get that x = 9.

By substituting this value in the equation, we get

⇒ y = -1.1 (9) + 162

⇒ y = -9.9 + 162

⇒ y = 152.1

Hence, the wrestler's weight at the first match will be 152.1 pounds.

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Answer:

3 x 195 = 585 minutes

Step-by-step explanation:

In one week, Alejandro attends a 45-minute lesson and practices for (6 x 25) = 150 minutes (assuming a 7-day week). So, the total number of minutes that Alejandro spends on his guitar in one week is:

45 + 150 = 195 minutes

In 3 weeks, the total number of minutes that Alejandro spends on his guitar is:

3 x 195 = 585 minutes

Therefore, Alejandro spends 585 minutes on his guitar in 3 weeks, including attending a 45-minute lesson once a week and practicing for 25 minutes on the remaining days of the week.

Answer: The mean absolute deviation is approximately is 11.43.

The conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle

The summary statement from the question is given as

A plane parallel to the base of a circular cone that intersects the cone.

By definition, a circle is the cross-section that is parallel to the base of a cone

This means that when a cone is cut through the base, the resulting shape is a circle

So, the conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle

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The shortest path from vertex A to vertex L in the given diagram is ABDGJLKFI, with a total length of 89.

We can find the length of the shortest path from vertex A to vertex L by calculating the sum of the shortest paths from A to C to F to I to L.

Using Dijkstra's algorithm, we can find the shortest path from A to C, then from C to F, then from F to I, and finally from I to L.

The shortest path from A to C is AB + BC = 3 + 16 = 19. The shortest path from C to F is CF = 25. The shortest path from F to I is FI = 21. The shortest path from I to L is IL = 24.

Therefore, the length of the shortest path from A to L is 19 + 25 + 21 + 24 = 89.

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Looking at the information provided, we can guess the triangle is similar to the one attached.

Therefore the area of the joint triangle is 40.825 unit²

a = b = 3 is the side lengths of the equilateral triangle c = 5 is the side length shared by both triangles = 12 which is the base of the right triangled = 13 which is the hypotenuse of the right triangle

The height of the equilateral triangle is 4.33 units.

Looking at this information, we solve for the area of the  equilateral triangle;

Area = (base × height) / 2 (5 × 4.33) / 2= 10.825

Area = (base × height) / 2

Area of the right angle triangle = (12 × 5) / 2 = 30

The total area 10.825 + 30 = 40.825

The above answer is partly based on the figure provided in the image. The numbers used were the ones provided by you, except for the height of the equilateral triangle.

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Looking at the information provided, we can guess the triangle is similar to the one attached. Therefore the area of the joint triangle is 40.825 unit²

a = b = 3 is the side lengths of the equilateral triangle

c = 5 shared by both triangles

12 = the base of the right triangle

13 = the hypotenuse of the right triangle

4.33 = height of the equilateral triangle

To solve the total area, we say

Triangle 1

Area = (base × height) / 2

(5 × 4.33) / 2= 10.825

Triangle 2

Area = (base × height) / 2

Area of the right angle triangle = (12 × 5) / 2 = 30

The total area ∴ 10.825 + 30 = 40.825

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The surface area of the shape will be 46 yards².

Surface area refers to the total area that the surface of a three-dimensional object covers. It is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), etc.

The formula for the surface area of the 2 bases is just b*h

12*8=96 yd²

Finding the lateral area:

(10*10)+(10*10)+(12*10)=

100+100+120=

320 yd²

Add the lateral surface area and the surface area of the 2 bases for the total surface area:

320+96=416 yd²

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Using multiplication operation, the amount of pension that Edith will receive after 4 years of service and using the vesting percentage and the pension multiplier is $49,725.

The pension amount is the product of the multiplication of the average salary, the vesting percentage and the pension multiplier factor.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Edith's average salary = $65,000

The number of years of service = 4 years

Pension Multiplier = 2%

Pension multiplier factor = 1.02 (100% + 2%)

Vesting percentage = 75%

Pension to be received = $49,725 ($65,000 x 75% x 1.02)

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There are possible 4,782,969 different telephone numbers.

We will multiply the number of options for each digit to calculate the total number of possible telephone numbers,.

Using the multiplication principle to estimate the number of possible telephone numbers for each digit:  

n1 x n2 x n3 x ... x nk

Here:

the first three digits are fixed: 011

The 4th digit (the first digit of the local phone number) can be any digit from 1 - 9 (i.e. 9 options).

The remaining 6 digits (the second to seventh digit of the local phone number) can be any digit from 0 to 9, except 0 (9 options for each digit).

Therefore, the total number of possible telephone numbers:

9 x 9 x 9 x 9 x 9 x 9 x 9 = 4,782,969,

Therefore, 4,782,969 different telephone numbers are possible.

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Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.

The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.

The decay factor is used in exponential decay functions to determine the depreciated value of an asset.

Current price of stereo equipment = $2,500

Annual decreasing rate = 9%

Decrease factor = 0.91 (100% - 9%)

The number of years = 8 years

Value of the equipment after 8 years = ($2,500 x 0.91^8)

= $2,116.125 ($2,500 x 0.47025)

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The area of the shaded region is given as follows:

298.3 units².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The larger circle has a radius of 7 + 5 = 12 units, hence it's area is given as follows:

A = 3.14 x 12²

A = 452.16 units².

The smaller circle has a radius of 7 units, hence it's area is given as follows:

A = 3.14 x 7²

A = 153.86 units².

Hence the area of the shaded region is given as follows:

452.16 - 153.86 = 298.3 units².

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Answer: No, 2^7 is not equal to 2x7.

2^7 means 2 raised to the power of 7, which is 2 multiplied by itself 7 times:

2^7 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128

On the other hand, 2x7 means 2 multiplied by 7:

2x7 = 2 x 7 = 14

So 2^7 is not equal to 2x7.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

See, 2 ^ 7 is 2 TO THE POWER OF 7, which is repeated multiplication.

2 x 7 is 2 MULTIPLIED BY 7

2 ^ 7 written out completely is:

2 * 2 * 2 * 2 * 2 * 2 * 2 = 128

See the repeated multiplication above?

2 x 7 is just 14.

See the difference!

14 is NOT equal to 128

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The only expression that is not equivalent to the given fraction expression is: D (2 x 1/3) + (4 x 1/3)

The correct procedure that we will use to multiply fractions is:

- find a common denominator

- multiply the numerators

- multiply the denominators

- Simplify if necessary.

- Add the numerators and add the denominators

Looking at the options and comparing with the given fraction multiplication problem 2/3 * 4, we see that only option D is not equivalent to it because:

(2 x 1/3) + (4 x 1/3) = 6/3 = 2

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Complete question is:

Which expression is NOT equivalent to 2/3 x 4

A (2x4) /3

B 1/3 x (2x4)

C (4 x 1/3) x 2

D (2 x 1/3) + (4 x 1/3)

For the given right-angled triangle the measure of the angle is 11.30°.

Given adjacent base of the triangle =  10

given opposite side of the triangle = 2

To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.

So, we can use the above tan ∠ relation to find the angle.

Tan ∠ = opposite side / adjacent side

Tan ∠ = 2/10

Tan ∠ = 1/5

∠ = Tan⁻¹(1/5)

∠ = 11.30°.

From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.

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Answer:

2 (n - 3) (n - 6)

Step-by-step explanation:

[tex]-7n+5n^2+6-3n^2-11n+30[/tex]

Group like terms and combine...

[tex]2n^2-18n+36[/tex]

Observe that all terms contain a factor of 2.  Factor out a 2...

[tex]2(n^2-9n+18)[/tex]

The leading coefficient is 1.  The shortcut applies.  Find the factors of "c" (18)

Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").

Finish factoring the trinomial into two binomials:

[tex]2(n-3)(n-6)[/tex]

To verify that this is a valid factoring, distribute, and recombine terms:

[tex]2(n-3)(n-6)[/tex]

[tex]2(n^2-3n-6n+18)[/tex]

[tex]2(n^2-9n+18)[/tex]

The car will be worth half its original value after 4 years

A graph for straight-line depreciation for a car is given.

a

The number of years the car totally depreciates is 8 years as seen in the graph which is x -intercept.

Step 3/7

The model makes straight-line depreciation. In a straight line depreciation equation, the intercepts are

(0, maximum car value) and (maximum lifespan,0)

Let y represent the value of the car at any time during its lifetime. The minimum y -value is zero dollars and the maximum y -value is the purchase price of $25,600

The intercepts are (0, 25, 600) and (8,0)

Determine the slope of the equation.

Two points determine a line, so only two points are needed to determine the slope of a line.

Let the coordinates of the -intercept be the first point. That is, (xi,yi) = (0, 25, 600)

Let the coordinates of the -intercept be the second point. That is (x2, y2)= (8,0)

Use the slope ratio as shown below;

The slope of the depreciation equation is.

-3200

The general form for the equation of a straight line is:

y = mx + b

Where m represents the slope of the line and b represents the y-intercept.

The slope is -3,200 and the -intercept is 25,600 as obtained.

Therefore, the straight line depreciation equation is:

y = -3,200x + 25,600

Therefore, the value of the car after 4 years is $12,800

b.

Use the depreciation equation and substitute x=5 years to find the car worth after 5 years.

Therefore, the value of the car after 5 years is $9,600

c.

The half value of the car is half of $25,600 which is $12,800

The car will be worth half its original value after 4 years

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Carlos can expect the value of the computer to be $580 three years after purchase.

To model the value of the computer, we can use the formula:

y = abˣ

We know that the initial value of the computer is $1,350, so a = 1350.

We also know that one year after purchase, the value of the computer is $810, so we can use this to find the value of b:

810 = 1350b

b= 0.6

b = 0.6

So our exponential equation is:

y = 1350(0.6)ˣ

To find the value of the computer 3 years after purchase, we can substitute x = 3:

y = 1350(0.6)³

y = 583

Hence, Carlos can expect the value of the computer to be $580 three years after purchase.

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Answer:

The graph will be a circle with center (0, 2) and radius 6.

The volume of the rectangular prism is given as follows:

V = 0.9375 cubic inches.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

Hence the volume is given as follows:

V = 1 x 1.25 x 0.75

V = 0.9375 cubic inches.

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Answer:

[tex]\frac{10n}{1-30n}:\frac{m}{10(1+3m)}[/tex]

Step-by-step explanation:

Solve for 'm' and 'n':

'm' = [tex]\frac{10n}{1-30n}[/tex]

'n' = [tex]\frac{m}{10(1+3m)}[/tex]

Ratio: [tex]\frac{10n}{1-30n}:\frac{m}{10(1+3m)}[/tex]

Answer:

Set your calculator to degree mode.

Please sketch the figure to confirm my answer.

tan(18°) = h/510

h = 510tan(18°) = 165.7 feet

Answer:

Construction Model Stats

User

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

ChatGPT

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:

tan(18 degrees) = h / d

Solving for h, we get:

h = d * tan(18 degrees)

Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:

h = 510 feet * tan(18 degrees)

h ≈ 157.3 feet

Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.

(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.

(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population.

Range is a statistical measure that refers to the difference between the highest and lowest values in a set of data. In other words, it is the distance between the largest and smallest values in a dataset.

(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.

(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population. A biased estimator systematically overestimates or underestimates the population parameter of interest. The fact that the distribution of sample ranges is approximately symmetric and centered around the true population range suggests that the sample range is an unbiased estimator of the population range. However, the variability of the sample range is quite large, which means that a single sample range may not be a very precise estimate of the population range.

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The price of the bed after mark up is $475.00

Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.

The first discount given is 25% , therefore the price of the bed before mark up is

25/100 × 800

= 25×8

= 200

the price before mark up = 800-200 = $600

Another 25% is given after the first sale, there the price of the bed after mark up is

25/100 × 600

=$ 125

price after markup = 600-125

= $475.00

therefore the price of the bed after markup is $475.00

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If John pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

In order to arrive at a solution, it is necessary to commence by reducing the fraction 1/1.5 into a more basic form.

Thus, we do this below:

1 ÷ 1.5 = 1 ÷ (3/2) = 1 × (2/3) = 2/3

So, John has 29 full buckets and another bucket that is 2/3 full.

If he pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

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John has 29 full buckets of water and another bucket that is 1/1.5 full. How many full buckets of water would he have if he pours the partially filled bucket into an empty one?

The contradicting statement is

B. I and III

The contradictory statement is that of I and III since the sum of angles in a triangle is always 180 degrees.

Given that

I. triangle ABC is a right triangle. say angle C = 90 degrees and

angle B = 103 degrees,

So the sum of the angles in the triangle would be:

= angle B + m angle C

= 103 + 91

= 194

This is against the law of angles of a triangle

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Answer:  C, yes

Step-by-step explanation:

Again you have do the same thing to both sides

They added 1 to both sides

Answer is C , yes they are same

By looking at the y-values of the points, we can see that the first four terms are.

2, -2, -6, -10

We know that the x-value of each of the points is the index of the term, so:

x = 1 is the first term

x = 2 is the second term.

And so on.

The y-value will be the actual value of the term.

Here we can see 4 points graphed, these are:

(1, 2), (2, -2), (3, -6), (4, -10)

Then the values of the first four terms of the sequence are:

2, -2, -6, -10

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