PLS ANSWER....
Lcm of 12,24 and 36

The linearization l(x,y) of the function at each point.

L(x, y) = 2xy - 2x + 2y + 1 at the point (1, 1)

L(x, y) = -8y - 15 + x²y² at the point (0, -2)

L(x, y) = 8x(y - 3) + 6y(x - 2) + x²y² - 41 at the point (2, 3).

The given function is f(x,y) = x²y² + 1

To find the linearization L(x, y) of the function f(x, y) at each point, first,

we need to find the partial derivative of the function w.r.t. x and y as follows:

\(f_x\)(x, y) = 2xy²\(f_y\)(x, y) = 2yx²

Now, we can write the equation of the tangent plane as follows:

L(x, y) = f(a, b) + \(f_x\) (a, b)(x - a) + \(f_y\)(a, b)(y - b)where (a, b) is the point at which the linearization is required.

Substituting the values in the above equation, we get,

L(x, y) = f(x, y) + \(f_x\) (a, b)(x - a) + \(f_y\)(a, b)(y - b)

Now, let's find the linearization at each point.

(1) At the point (1,1), we have,

L(x, y) = f(x, y) + \(f_x\)(1, 1)(x - 1) + \(f_y\)(1, 1)(y - 1)L(x, y)

= x²y² + 1 + 2y(x - 1) + 2x(y - 1)L(x, y)

= 2xy - 2x + 2y + 1

(2) At the point (0, -2), we have,

L(x, y) = f(x, y) + \(f_x\)(0, -2)(x - 0) + \(f_y\)(0, -2)(y + 2)L(x, y)

= x²y² + 1 + 0(x - 0) + (-8)(y + 2)L(x, y)

= -8y - 15 + x²y²

(3) At the point (2, 3), we have,

L(x, y) = f(x, y) + \(f_x\)(2, 3)(x - 2) + \(f_y\)(2, 3)(y - 3)L(x, y)

= x²y² + 1 + 6y(x - 2) + 8x(y - 3)L(x, y)

= 8x(y - 3) + 6y(x - 2) + x²y² - 41

Hence, the linearizations of the given function f(x, y) at each point are:

L(x, y) = 2xy - 2x + 2y + 1 at the point (1, 1)

L(x, y) = -8y - 15 + x²y² at the point (0, -2)

L(x, y) = 8x(y - 3) + 6y(x - 2) + x²y² - 41 at the point (2, 3).

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it is 0.375

happy learning

Answer:

\(\boxed{\quad x= \dfrac{65}{12}\quad }\)

\(\boxed{\quad y = \dfrac{91}{12} \quad }\)

Step-by-step explanation:

The smaller and larger triangles you see in the image are similar because

By the AAA t(Angle-Angle-Angle) theorem the two triangles are similar

AAA Theorem
If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.

The smaller triangle has sides 5 and x

The larger triangle has corresponding sides 5 + 7 = 12  and x + y

By the similarity theorem

\(\dfrac{5}{12} = \dfrac{x}{x+y}\\\\\)      Equation [1]

Consider the larger triangle which is a right triangle with legs 12 and 5

The hypotenuse of this triangle = x + y

By the Pythagorean theorem,

hypotenuse² = sum of squares of the other two sides

=>  (x + y)² = 12² + 5² = 144 + 25 = 169

Therefore
x + y = √169 = 13

So we have x + y = 13

Plugging this value of x + y = 13 into equation [1] we get

\(\dfrac{5}{12} = \dfrac{x}{13}\\\\\)

Switching sides we get
\(\dfrac{x}{13} =\dfrac{5}{12}\\\\\rightarrow x = 13 \times \dfrac{5}{12}\\\rightarrow x= \dfrac{65}{12}\\\\\)

Since x + y = 13, we can plug the value of x into this equation to get
\(\dfrac{65}{12} + y = 13\\\\\\y = 13 - \dfrac{65}{12}\\\\y = 13 \times \dfrac{12}{12} - \dfrac{65}{12}\\\\y = \dfrac{156}{12} - \dfrac{65}{12}\\\\\\y = \dfrac{156-65}{12}\\\\y = \dfrac{91}{12}\\\\\)

Answer:

\(\boxed{\quad x= \dfrac{65}{12}\quad }\)

\(\boxed{\quad y = \dfrac{91}{12} \quad }\)

Just an additional note
Because of similarity, the ratio x/y must be equal to 5/7** but this would not be directly using the similarity ratios of triangles but it can be proved:

we have
\(\dfrac{x}{x+y} = \dfrac{5}{12}\)

Flipping both sides we get
\(\dfrac{x+y}{x} = \dfrac{12}{5}\\\\\dfrac{x}{x} + \dfrac{y}{x} = \dfrac{12}{5}\\\\1 + \dfrac{y}{x} = \dfrac{12}{5}\\\\\\\dfrac{y}{x} = \dfrac{12}{5} - 1\\\\\dfrac{y}{x} = \dfrac{7}{5}\\\\Or,\\\\\dfrac{x}{y} = \dfrac{5}{7}\)

and we can use this also to solve for x and y individually

**Incidentally, there is a theorem which directly provides this information. It is called the Side Splitter Theorem but not sure if you had heard about it so didn't want to go there

Using PEDMAS to simplify the expression, the result is -830t² + 164t + 5798.4

To solve this problem, we have to simplify the expression. This is a process of breaking it down from a complex form to the least possible form. In doing this, we often apply mathematical operations such as multiplication, addition, subtraction etc.

In the expression 362.4 * 16 - 2t + 83t * (2 - 10t)

Let's apply PEDMAS here

362.4 * 16 = 5798.4

83t (2 - 10t) = 166t - 830t²

We can bring them together now;

5798.4 - 2t + 166t - 830t²

Collecting like terms

-830t² + 164t + 5798.4

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Answer:

y = 5/4 (x) + 7

Explanation:

Slope of a line (m): (y₂ - y₁) ÷ (x₂ - x₁)

       Slope: (2 - -3) ÷ (-4 - -8) = 5 ÷ 4 = 5/4

Point slope form: y - y₁ = m (x - x₁)

       Equation: y - 2 = 5/4 (x - -4)

                        distribute the 5/4

                        y - 2 = 5/4 (x) + 5

                        add 2 to both sides

                        y = 5/4 (x) + 7

I hope this helps!

To complete a pairwise ranking matrix of 7 events, we need to make a total of 21 pairwise comparisons.What is a pairwise ranking matrix?

A pairwise ranking matrix is a matrix that lists the results of pairwise comparisons. In this type of matrix, each row and column represents a participant, team, or event, and the cell at the intersection of the row and column represents the outcome of a comparison between the two.

A comparison is made between every pair of events, and the result of the comparison is recorded in the matrix. The entries on the main diagonal of the matrix are all zero since an event cannot be compared to itself

.How to calculate the number of pairwise comparisons for 7 events?

To calculate the number of pairwise comparisons for 7 events, we use the formula n(n - 1)/2, where n is the number of events.

So, for 7 events, we have:n(n - 1)/2 = 7(7 - 1)/2= 7(6)/2= 21Therefore, we need to make 21 pairwise comparisons to complete a pairwise ranking matrix of 7 events.

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When choosing between two exponential smoothing models with different values of the smoothing constant, the decision should be based on the specific characteristics and requirements of the data and forecasting task.

Exponential smoothing is a time series forecasting technique that assigns weights to historical data points, with the weights decreasing exponentially as the data points get older. The smoothing constant (alpha) determines the rate at which the weights decrease and controls the level of responsiveness to recent observations.

Here are some considerations to guide your decision-making process:

Level of responsiveness: A higher smoothing constant (closer to 1) gives more weight to recent observations, making the forecast more responsive to short-term fluctuations. If your data exhibits high volatility and you want the model to quickly adapt to changes, a higher smoothing constant may be appropriate.

Stability and trend: If your data has a stable pattern or a slowly changing trend, a lower smoothing constant (closer to 0) may be suitable. A lower constant places more emphasis on the long-term average and smooths out short-term fluctuations, resulting in a more stable forecast.

Forecast accuracy: It is advisable to assess the accuracy of both models using appropriate evaluation metrics, such as mean absolute error (MAE) or root mean squared error (RMSE). Compare the accuracy of the forecasts produced by each model to determine which one performs better for your specific data set.

Data availability: Consider the amount and availability of historical data. If you have a limited amount of data, a higher smoothing constant may be more appropriate as it relies more on recent observations. Conversely, if you have a longer time series, a lower smoothing constant can provide stability and better capture long-term trends.

Ultimately, the choice between the two exponential smoothing models with different smoothing constants should be driven by a careful consideration of these factors, the nature of your data, and the specific requirements of your forecasting task. It may also be helpful to experiment and compare the performance of the models on a validation set before making a final decision.

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

The value of a₃ is equal to 8.

To find a₃ using the given terms, aₓ = a₂x-1 and a₁ = 2, follow these steps:

Step 1: Identify the value of x when finding a₃.
Since you want to find a₃, the value of x will be 3.

Step 2: Use the given formula to find a₃.
The formula provided is aₓ = a₂x-1.

Plug in the value of x as 3:

a₃ = a₂(3)-1.

Step 3: Simplify the formula.
Simplify the formula as follows:

a₃ = a₁(4).

Step 4: Substitute the given value of a₁ into the formula.
You're given that a₁ = 2, so substitute it into the simplified formula:

a₃ = 2(4).

Step 5: Solve for a₃.
To find a₃, multiply the values:

a₃ = 8.

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We need to find the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45.

In order to find this probability, we need to find the number of doctors that are General Practitioner or under under the age of 45. Then, divide that number by he total of 17.

We know that 7 doctors are General Practitioners. And 2 of them are also under the age of 45.

Therefore, since ther are 4 doctors that are under the age of 45, there are 2 additional doctors, besided those 2 that follow in both categories, there are under the age of 45.

Summarizing, the number of doctors that are General Practitioner or a doctor under the age of 45 is:

Notice that this result can also be obtained by the formula:

where A is the set of General Practitioners, B is the set of doctors under the age of 45, and the symbol |...| represents the number of elements in that set:

Therefore, the required probability is:

Answer

Answer:

D.-11

Step-by-step explanation:

There are 35% sixth-graders at Kendrick's school who picked the museum.

Percentage is a part of the whole number.

When the denominator is 100, percentages are really just fractions. We place the percent symbol (%) beside a number to indicate that it is a percentage.

1 %= 1/100.

Given that,

Total number of sixth-graders at Kendrick's school = 56,

Also,

The number of s sixth-graders that picked the museum = 14.

The percentage of the sixth-graders that picked the museum

= (14/56) x 100

= (1/4) x 100

= 25 %

25 percent of the sixth-graders picked the museum.

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The value of A has been illustrated, computed and proven based in the triangle given.

It should be noted that that a triangle is a shape that has three sides and the value of the addition of all the angles are equal to 180°.

Based on the information that's given, it should be noted that the value of angle A, angle B, and angle C will be equal to 180°.

In this case, the following can be deduced:

A = 5x

B = 90°

C = x + 10°

Therefore, A + B + C = 180° (sum of angles in a triangle)

5x + 90 + x + 10 = 180°

6x = 180° - 90° - 10°

6x = 80°

x = 80/6

x = 13 1/3

Therefore, the value of A will be:

= 5x

= 5 × 13 1/3

= 66 2/3

Therefore, A is 66 2/3.

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On solving the provided question, we can say that we excluded example 2 above, a maximum of 3 triangles can be created with those rods.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear.

\(2-inch, 3 inch, 4-inch\)

triangle, because 2+3 > 4, 2+4 > 3, and 3+4 > 2

\(2-inch, 3 inch, 5-inch\)

This is doesn't make  a triangle as  \(2+5 > 3, and 3+5 > 2,\)

2+3 is not more  than 5,, they cannot make triangle.

\(2-inch, 4 inch, 5-inch\)

triangle, because 2+4 > 5, 2+5 > 4, and 4+5 > 2

\(3-inch, 4 inch, 5-inch\)

a triangle, because 3+4 > 5, 3+5 > 4, and 4+5 > 3

Therefore, since we excluded example 2 above, a maximum of 3 triangles can be created with those rods.

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Answer:

x = 12

Step-by-step explanation:

2(x-4)=16

2 times x +2 times -4 = 16

2x -8 =16

2x -8 (+8) =16 (+8)

2x = 24

2x (divided by 2) = 24 (divided by 2)

x = 12

The translation from preimage P(9. 1.5) to image P'(12, 1)) in ordered pair is (3, -0.5)

Translation refers to a type of transformation that involve a straight line movement.

The type of movements related to translation includes

The up and down movements are on the vertical direction controlled by the y coordinate. In the question, the preimage moved form 1.5 to 1

hence we say

The left right movement is controlled by the x coordinate. The preimage moved from 9 to 12 ⇒ 9 + 3. Hence we say that

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The distance between the centers of the two wheels is approximately 11.86 feet.

The length of the conveyor belt is equal to the circumference of the circle formed by each wheel plus the distance between the centers of the two wheels.

Let's call the distance between the centers of the two wheels "d". The circumference of each wheel can be calculated using the formula

C = πd

Since each wheel has a diameter of 1 foot, its radius is 0.5 feet. Therefore, the circumference of each wheel is:

C = πd = π(0.5) = 1.57 feet (approx.)

The length of the conveyor belt is given as 15 feet. So we can write

2C + d = 15

Substituting the value of C, we get

2(1.57) + d = 15

3.14 + d = 15

d = 11.86 feet

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Step 1:

Write the equation of the line in the form of y = mx + c

m = slope

Step 2

Step 3

From the equation

Step 4:

Final answer

The measure of acute angle = 26.6

There are 8 feet³ of these sheets will Jill need to cover the floor.

We have to given that;

Plywood is sold in 1/4 inch thick sheets that have a length of 8 feet and a width of 4 feet.

Hence, The volume of for sheets are,

⇒ 1/4 × 8 × 4

⇒ 8 feet³

Therefore, There are 8 feet³ of these sheets will Jill need to cover the floor.

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Answer:

I am pretty sure that it is

heads 1

heads 2

heads 3

heads 4

heads 5

heads 6

Step-by-step explanation:

because in the question it says to roll a six sided die and a coin that lands on heads so there are all the numbers on die and heads only

Answer:

I think its all head

Step-by-step explanation:

Coin Number

cube Outcome

Heads  

1

Heads, 1

Heads  

2

Heads, 2

Heads  

3

Heads, 3

Heads  

4

Heads, 4

Heads  

5

Heads, 5

Heads  

6

Heads, 6

The function  in which the table is provided is an exponential function because it generates a growing curve.

The exponential function is a mathematical function of the form:

f(x) = \(a^{x}\),

where:

a is the base constant  

x is the variable.

In this function, the base, a, is a positive real number and is typically greater than 1, although it can also be between 0 and 1.

Properties

Exponential Growth: When the base, a, is greater than 1, the function exhibits exponential growth.

That is, as "x" increases, the function values increase at an increasingly rapid rate.

Exponential Decay: When the base, a, is between 0 and 1, the function exhibits exponential decay.

That is, as "x" increases, the function values decrease, approaching zero but never actually reaching it.

Constant Base: If the base "a" is equal to 1, the exponential function becomes f(x) = \(1^{x}\) = 1, resulting in a constant function.

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Answer:

n-2, n-1, n, n+1, n+2, n+3

Step-by-step explanation:

We have to,

→ find the numbers from n-3 to n+4.

Then the numbers are,

→ n-3, n-2, n-1, n, n+1, n+2, n+3, n+4

Hence, there are 6 numbers.

it is true that  0.5% of 200 is 10.

True.

To find 0.5% of a number, we need to multiply the number by 0.5/100, which can be simplified to 5/100 or 1/20. This is because "percent" means "per hundred", so 0.5% is equivalent to 0.5 per 100 or 0.5/100.

Multiplying the number by 5/100 is the same as multiplying it by 0.5/100, so it will give us the correct result.

For example, if we want to find 0.5% of 200, we can multiply 200 by 5/100 or 0.5/100:

\(0.5% of 200 = 200 \times 5/100 = 10\)

Therefore, it is true that  0.5% of 200 is 10.

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Answer:

158 degrees

Step-by-step explanation:

Step 1:

Let Angle CDE =y

Since Angle BCD = 2 X angle CDE

Angle BCD = 2y

Step 2

Consider Figure 2 attached, each of the figure forms an isosceles trapezoid ABCF and DEFC.

By these properties of Isosceles Trapezoids

Therefore:

\(\angle ABC+\angle BCF=180^\circ\\\angle FCD+\angle CDE=180^\circ\\Therefore:\\\angle ABC+\angle BCF+\angle FCD+\angle CDE=360^\circ\\$But \angle BCF+\angle FCD=\angle BCD\\So:\\\angle ABC+\angle BCD+\angle CDE=360^\circ\)

123+2y+y=360

3y=360-123

3y=237

y=79 degrees

Therefore:

\(\angle BCD=2 X 79^\circ=158^\circ\\\angle BCD=\angle AFE=158^\circ\\\angle AFE=158^\circ\)

Answer:

40x + 90y <2400

18x + 30y < 500

Step-by-step explanation:

Lee washes houses. It takes him 40 minutes to wash a one-story home, and he uses 18 gallons of water. Power washing a two-story home takes less than 90 minutes, and he uses 30 gallons of water. Lee works no more than 40 hours each week, and his truck holds 500 gallons of water. He charges $90 to wash a one-story home and $150 to wash a two-story home. Lee wants to maximize his income washing one- and two-story houses. Let x represent the number of one-story houses and y represent the number of two-story houses. What are the constraints for the problem

Let

x=one story houses

y=two story houses

The constraints are the following:

1. Lee works no more than 40 hours each week.

40 hours=40 × 60 minutes

=2400 minutes

2. Lee's truck holds 500 gallons of water.

it takes Lee 40 minutes and 18 gallons of water to wash a one-story house.

it takes Lee 90 minutes and 30 gallons of water to wash a two-story house.

First constraint:

40*x + 90*y < 2400

40x + 90y <2400

Second constraint:

18*x + 30*y < 500

18x + 30y < 500

Answer:

It’s D

Step-by-step explanation:

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Greetings! Hope this helps!

Answer

A = 157

Explanation

3.14 x 10^2

3.14 x 100

314

314/2

157

Have a good day!

_______________

A brainliest would help tons! :D

Let's solve

\(\\ \rm\Rrightarrow F=\dfrac{9}{5}C+32\)

\(\\ \rm\Rrightarrow 65=\dfrac{9}{5}C+32\)

\(\\ \rm\Rrightarrow \dfrac{9}{5}C=65-32=33\)

\(\\ \rm\Rrightarrow 9C=165\)

\(\\ \rm\Rrightarrow C=165/9\)

\(\\ \rm\Rrightarrow C\approx 18.34^{\circ}C\)

Answer:

A triangle must add up to 180° and be closed on all sides

Step-by-step explanation:

Answer:

Silurian, Triassic, Jurassic, Tertiary

Step-by-step explanation:

Convert 6.64 so that is is 10\(^8\)

So you'll have 0.664 × 10\(^8\)

Then you can just order them from largest to smallest :)

If it doesn't make sense you can also convert the index notation (the powers with 10) into whole numbers so

2.08 × 10\(^8\) = 2.08 × 100000000 = 208000000

and so on..