Linear or nonlinear:
why?

The inequality that represents the condition based on the number of wooden sticks is 2K + 12L ≥ 87    .

In the question ,

it is given that ,

to make a kite , 2 wooden sticks and 1.5 square feet of paper is required ,

and ,

to make a lamp 12 wooden sticks and 8 square feet of paper is needed .

let the number of kites that Min-Young make = "K"

and the number of Lamps that Min-Young make = "L"

given that number of wooden sticks used should be at least 87

Which  is represented as

2K + 12L ≥ 87   and

the paper used should be more than 63 square feet, that is represented as

1.5K + 8L > 63  .

Therefore , The inequality that represents the condition based on the number of wooden sticks is 2K + 12L ≥ 87    .

The given question is incomplete , the complete question is

It takes 2 wooden sticks and 1.5 square feet of paper to make a kite, and it takes 12 wooden sticks and 8 square feet of paper to make a lamp.

Min-Young wants to make kites and lamps using at least 87 wooden sticks and more than 63 square feet of paper.

Let K denote the number of kites she makes and L the number of lamps she makes. Write an inequality that represents the condition based on the number of wooden sticks .

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The Fourier series of one period a(x) on \(-\pi\) to \(\pi\) is 23.096.

What is Fourier series ?

A fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier Series makes use of the orthogonality relationships of the sine and cosine functions. Expand the function f(x) = ex in the interval [ – π , π ] using Fourier series formula.

Have given,

a(x) on domain (\(-\pi ,\pi\))

Let ,

I = ∫\(\pi\) \(e^{x}\) dx

on integration

I = \([e^{x}]^{\pi }_{-\pi }\)

I = \(e^{\pi } - e^{-\pi }\)

I = 23.14 - 0.043

Thus, I = 23.096

The Fourier series of one period a(x) on \(-\pi\) to \(\pi\) is 23.096.

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Answer:

the shapes below are similar because,

Step-by-step explanation:

36 divided by 4 is 9.

9 is also the length on shape 2.

(9x2) + (4x2) = 36

36 is also the area of shape 2

Answer:

I think it is the area and perimeter are the same

Step-by-step explanation: Shape 1: If the perimeter is 26. one side is 9. 26-18= 8. You divide that to get the measure of the other side which is 4. 9*4=36.          Shape 2: area is equal to 36, one side is for so the other side has to be 9. So the perimeter of shape 2 is 26 too.

For regular shapes, add the lengths of the sides, and for irregular shapes, measure each side individually and sum them up. Finally, round the perimeter to the desired level of precision.

To compute the perimeter of a window, here is a different sequence of steps:

1. Identify the shape of the window: Determine if the window has a regular shape, such as a rectangle, square, or circle, or if it has an irregular shape.

2. Measure the sides: If the window is a regular shape, measure the lengths of its sides. For a rectangle or square window, measure the lengths of two adjacent sides. If it's a circular window, measure the radius or diameter.

3. Calculate the perimeter based on the shape:

  - For a rectangle or square window: Add the lengths of all four sides together to obtain the perimeter. If the lengths of the adjacent sides are different, ensure you measure each side accurately.

  - For a circular window: Calculate the circumference using the formula C = 2πr or C = πd, where r is the radius and d is the diameter of the window. If you have the diameter, divide it by 2 to get the radius.

4. If the window has an irregular shape: In this case, measure each side or segment of the window individually. Then, add up the lengths of all the sides to obtain the total perimeter. Make sure to measure each side accurately, taking into account any angles or curves.

5. Round the perimeter: Once you have calculated the total perimeter of the window, round the value to the desired level of precision or decimal places, depending on your requirements.

It's important to note that accurate measurements are crucial for obtaining an accurate perimeter. Ensure that you use appropriate measuring tools and techniques to obtain precise measurements of the window's sides or segments.

In summary, to compute the perimeter of a window, identify its shape, measure the appropriate sides or segments, and calculate the perimeter based on the shape. For regular shapes, add the lengths of the sides, and for irregular shapes, measure each side individually and sum them up. Finally, round the perimeter to the desired level of precision.

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Answer: 0

Step-by-step explanation:

slope = Δy/Δx

slope = (17-17)/(3-8) = 0

The probability that the child will catch 10 or more balls is approximately 0.4757 or 47.57%

In this scenario, we can model the number of successful catches by the child using a binomial distribution. Let's identify the values of N, P, and X, and calculate the probability.

N: N represents the number of trials or attempts. In this case, the ball is thrown 15 times, so N = 15.

P: P represents the probability of success in a single trial. Here, the chance of the child catching a ball is given as 0.4, so P = 0.4.

X: X represents the number of successful outcomes we are interested in. In this case, we want to find the probability that the child will catch 10 or more balls, so X = 10, 11, 12, 13, 14, 15.

To calculate the probability, we need to sum the probabilities of each individual outcome. We can use the binomial probability formula:

P(X=k) = (N choose k) * P^k * (1-P)^(N-k)

Let's calculate the probability using the formula for each value of X and sum the probabilities for X ≥ 10:

P(X ≥ 10) = P(X=10) + P(X=11) + P(X=12) + P(X=13) + P(X=14) + P(X=15)

P(X ≥ 10) = [ (15 choose 10) * (0.4^10) * (0.6^5) ] + [ (15 choose 11) * (0.4^11) * (0.6^4) ] + [ (15 choose 12) * (0.4^12) * (0.6^3) ] + [ (15 choose 13) * (0.4^13) * (0.6^2) ] + [ (15 choose 14) * (0.4^14) * (0.6^1) ] + [ (15 choose 15) * (0.4^15) * (0.6^0) ]

Now, we can calculate the probability:

P(X ≥ 10) ≈ 0.0032 + 0.0172 + 0.0524 + 0.1083 + 0.1651 + 0.1295

P(X ≥ 10) ≈ 0.4757

Therefore, the probability that the child will catch 10 or more balls is approximately 0.4757 or 47.57%

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Answer:

5 and 6

Step-by-step explanation:

The number √28 comes between the two integers number will be 5 and 6.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The number is given as √28.

The two integers number will be

√25 and √36

5 and 6

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The average rate of change between the years 2002 and 2007 was  2,.939.8 (option B).

In demographics, the average rate of change refers to how much the population of a city, country, etc. changes over a year period usually by increasing or decreasing. Due to this, the rate of change can be calculated by using the following formula change in the population/ number of years.

239,839 (population in 2002) - 254,538 (population in 2007)

2007 - 2002 = 5 years (number of years)

14699 / 5 years = 2,.939.8 (option B)

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Answer:

1.5 m/s

Step-by-step explanation:

Distance = 6.8×1609.344 = 10943.5392

time=2×60×60 = 7200

velocity= distance/time = 10943.5392/7200= 1.51 m/s

We are required to divide the fraction 4 and 2 over 3 divided by 3 and 1 over 2?

The answer is 14 over 3 times 2 over 7

Given:

4 and 2 over 3 divided by 3 and 1 over 2?

= 4 2/3 ÷ 3 1/2

= 14/3 ÷ 7/2

= 14/3 × 2/7

= (14 × 2) / (3 × 7)

= 28 / 21

= 4/3

A. 4 and 2 over 3 times 3 and 2 over 1 = 4 2/3 × 3 2/1

B. 14 over 3 times 2 over 7

= 14 / 3 × 2 / 7

C.b14 over 3 times 7 over 2

= 14 / 3 × 7 /2

D. 42 over 3 times 2 over 31

= 42 / 3 × 2 / 31

Therefore,

4 2/3 ÷ 3 1/2 = 4/3

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Answer:

\(\displaystyle{P(x)=x^3-x^2}\)

Step-by-step explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

\(\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}\)

Hence:

\(\displaystyle{P(x)=(x-0)(x-0)(x-1)}\)

Which can be simplified to:

\(\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}\)

Convert to the standard form by distributing x²:

\(\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}\)

The cost of each drink purchased at the AMC theaters is $6.09

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the cost of one drink. After using the coupon, their total cost before tax was $29.18. Hence:

2(11) + 2(x) - 5 = 29.18

x = 6.09

The cost of each drink purchased at the AMC theaters is $6.09

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Answer:

0.035 litros

Step-by-step explanation:

V = (pi)*(r^2)*(h)

V = pi * 2.25 * 5

= 35 cm^3

1 cm^3 = 0.001

(35)*(0.001)

= 0.035 litros

The expression of the number 0.133333 as a fraction would give us 133333/1000000.

Let us recall that the term fraction is used to show that there is a top and a bottom part in the expression. The top part of the fraction is called the numerator while the bottom part of the fraction is called the denominator.

If we want to convert the fraction as we have it back to the decimal then we just have to divide the numerator by the denominator and we are back to the decimal. The decimal is marked by the presence of a decimal point.

To convert 0.133333 to fraction, we would take the decimal point as 1 and all other digits after it as zero thus we have;

133333/1000000.

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The abelian groups (up to isomorphism) of order 360 are:

1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.

First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.

In this case, we can form the following abelian groups of order 360:

C360: This is the cyclic group of order 360 itself.

C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.

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Answer:

The initial price of the store item would be the price before any price adjustments were made, which corresponds to when x=0.

Plugging x=0 into the given function, we get:

f(0) = 320(0.90)^0 = 320(1) = 320

Therefore, the initial price of the store item was $320.

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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Answer:

5

Step-by-step explanation:

4x-8=12

4x=12+8

4x=20

x=20/4

=5

Step-by-step explanation:

4x-8=12

4x-8+8=12+8

4x=20

4x÷4=20÷4

x=5

Answer:

SAS

Step-by-step explanation:

They share a common side, equal angles, and the outside sides are the same.

SAS

Answer:

Specifically, if we want to think of multiplication as repeated addition, exponentiation as repeated multiplication, and ↑↑ as repeated exponentiation, three groups of five is the way to go. 53 means 5×5×5, not 3×3×3×3×3.

Step-by-step explanation:

Hey there!

a + b

= 2 + 3

= 5

Therefore, your answer is: 5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

2−12x+36

Step-by-step explanation:

Answer:

(x-6)² = (x-6)(x-6) = x² - 12x + 36

Step-by-step explanation:

The equation that represent the distance between Peach Court and x+4= 17.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation.

Given:

Distance of city center from main street is 4 miles.

Distance of Peach court from main street is 17 miles.

Now, we have to know distance difference between Peach Court and Main Street

x= 17 -4

So, the equation to represent the distance is

x + 4 = 17

Hence, equation that represent the distance between Peach Court and x+4= 17.

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Factorize the quadratic.

\(2x^2 + 5x + 3 = (2x + 3) (x + 1)\)

We have \(|ab| = |a||b|\), so

\(|2x^2 + 5x + 3| = |2x + 3| |x + 1| > 0\)

Now, both \(|2x+3|\ge0\) and \(|x+1|\ge0\) (since the absolute value of any number cannot be negative), so we just need to worry about when the left side is exactly zero. This happens for

\((2x + 3) (x + 1) = 0 \implies 2x+3 = 0\text{ or }x+1 = 0 \\\\ \implies x = -\dfrac32 \text{ or } x = -1\)

So the solution to the inequality is the set

\(\left\{x \in \Bbb R \mid x\neq-\dfrac32 \text{ and } x\neq-1\right\}\)

Answer:

5/18

Step-by-step explanation:

(5/6)/3

5/6 X 1/3

5/18

Option C : The volume of the redwood tree trunk using a right cylinder to model the trunk is approximately 8,100π cubic feet.

The circumference of the redwood tree trunk is given as 18π feet, which means the diameter of the trunk is 18 feet. Using a right cylinder to model the trunk, the radius of the cylinder is 9 feet (half of the diameter), and the height is given as 100 feet.

The formula for the volume of a right cylinder is V = π\(r^2\)h, where r is the radius of the base of the cylinder and h is the height of the cylinder. Substituting the given values, we get:

V = π(\(9^2\))(100)

V = 81π(100)

V = 8100π

Therefore, the approximate volume of the redwood tree trunk is 8100π cubic feet.

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Answer:

45

Step-by-step explanation:

The gradient ∇J(θ) based on your specific scenario and plug it into the update rule above to obtain the stochastic gradient update.

To determine the stochastic gradient update rule using the learning rate (α) for the current parameters (θ), we can express it as:

θ_new = θ_old - α * ∇J(θ)

Where:

θ_new represents the updated parameters after the gradient update.

θ_old represents the current parameters.

α (learning rate) controls the step size of the update.

∇J(θ) represents the gradient of the cost function J with respect to the parameters θ.

The specific form of the gradient ∇J(θ) depends on the particular cost function and the problem being solved. You would need to compute the gradient ∇J(θ) based on your specific scenario and plug it into the update rule above to obtain the stochastic gradient update.

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A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct. The correct option is A.

To compare the volumes of the rectangular pyramid and the rectangular prism, we need to find the base area (BA) of the pyramid. The volume (V) of a pyramid is given by the formula:

\(V = \dfrac{1}{3} \times BA \times h\)

where BA is the base area and h is the height.

Given that the volume of the pyramid is 40 units³ and the height is 6 units, we can find the base area:

40 = (1/3) x BA x 6

Now, solve for BA:

\(BA = \dfrac{(40 \times 3)} { 6}\\BA = 20\ units^2\)

Now, let's check the options:

A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units³; therefore, Shannon is incorrect.

The volume of the rectangular prism with BA = 20 and h = 6 is (20 x 6) = 120 units³, not 40 units³. So, this statement is incorrect.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units³; therefore, Shannon is incorrect.

We have already determined that the base area of the pyramid is 20 units², not 6.67 units². So, this statement is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

This statement matches our calculations. The volume of the rectangular prism with BA = 20 and h = 6 is (20 x 6) = 120 units³, which is three times the volume of the pyramid. So, this statement is correct.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

The base area of the pyramid is 20 units², not 6.67 units². So, this statement is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

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The complete question is attached below:

A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?

A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.