A hat company wants to create a cylindrical travel case to protect its beach sun hats using the following pattern.

net drawing of a cylinder is shown as two circles with diameters labeled 15 inches and a rectangle with a height labeled 5 inches

How many square inches of leather will be necessary to create the travel case? Approximate using π = 3.14.

412.13 square inches
588.75 square inches
1,648.5 square inches
1,884 square inches

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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The correct answer from the drop-down menu is 3.5.

The mean is the average of the numbers. It is easy to calculate add up all the numbers, then divide by how many numbers in the data set.

Therefore the population mean is the sum of the 12 data set values divided by 12

4 + 6 + 7 + 11 + 12 + 18 + 26 + 23 + 14 + 31 + 22 + 12 = 186.

Therefore the population mean

= 186/12

= 15.5.

The sample mean is given by the sum of the 4 sample values divided by 4

11 + 31 + 22 + 12

Sum = 76.

Therefore the sample mean

= 76/4

= 19.

The sample mean is more than the population mean by

= 19 - 15.5

= 3.5.

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We want to find a number that is multiple of all the denominators of the fractions we have. For example, in the cases:

we have two denominators: 5 and 3

And for

we have 3 and 12

2/5 + 1/3:

We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be

5 x 3 = 15

then,

and

then we have that

1/3 + 3/12:

We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be

3 x 12 = 36

then

1/3 + 3/12:

We can find the denominator by finding the multiples of both denominators:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...

multiples of 12: 12, 24, 36, 48, ...

We find some the numbers that both multiples share:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...

multiples of 12: 12, 24, 36, 48, ...

We choose the first common multiple, and this is the common denominator. In this case it is 12. Since

3 x 4 = 12, then

The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.

This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.

Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.

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Answer:

25; 15^2+20^2=625. 25^2=625, therefore the answer is 25.

To change to spherical coordinates, we can use the following formula:

x = ρ sin φ cos θ

y = ρ sin φ sin θ

z = ρ cos φ

We also note that the region of integration is a hemisphere with radius 3, and that the integrand contains x^2z+y^2z+z^3. Since we are integrating over a hemisphere, the bounds of ρ can be from 0 to 3, φ can be from 0 to π/2, and θ can be from 0 to 2π.

Next, we need to express the integrand in terms of ρ, φ, and θ. Substituting x, y, and z, we get:

x^2z + y^2z + z^3 = ρ^4 sin^2 φ cos^2 θ (ρ cos φ) + ρ^4 sin^2 φ sin^2 θ (ρ cos φ) + (ρ cos φ)^3

Simplifying, we get:

x^2z + y^2z + z^3 = ρ^5 cos^2 φ + ρ^3 cos^3 φ

Thus, the new integral is:

∫0^(2π) ∫0^(π/2) ∫0^3 (ρ^5 cos^2 φ + ρ^3 cos^3 φ) ρ^2 sin φ dρ dφ dθ

Integrating with respect to ρ, we get:

∫0^(2π) ∫0^(π/2) [ 1/6 ρ^6 cos^2 φ + 1/4 ρ^4 cos^3 φ ]_|ρ=0^3 sin φ dφ dθ

Simplifying and integrating with respect to φ, we get:

∫0^(2π) [ 9/5 sin^5 φ - 27/14 sin^7 φ ]_|φ=0^(π/2) dθ

Evaluating the limits, we get:

∫0^(2π) [ 9/5 - 27/14 ] dθ

Finally, evaluating the integral, we get:

∫0^(2π) [ 33/35 ] dθ = 66π/35

Therefore, the value of the integral after changing to spherical coordinates is 66π/35.

Answer:

Step-by-step explanation:

-2/5

The binary numbers are:

a) (16.55)₁₀ = (10000.100011)₂

b) (26.24)₁₀ = (11010.001111)₂

c)  (0.5625)₁₀ = (0.1001)₂

a) (16.55)₁₀

⇒ 16 ÷ 2 = 8, Remainder = 0

    8 ÷ 2 = 4, Remainder = 0

    4 ÷ 2 = 2, Remainder = 0

    2 ÷ 2 = 1, Remainder = 0

    1 ÷ 2 = 0, Remainder = 1

So, (16)₁₀ = 10000₂

Now, for the fractional part

0.55 × 2 = 1 + 0.1

0.1  × 2 = 0 + 0.2

0.2  × 2 = 0 + 0.4

0.4 × 2 =  0 + 0.8

0.8 × 2 =  1 + 0.6

0.6 × 2 = 1 + 0.2

0.55 is equivalent to the binary number 0.100011.

Hence, (16.55)₁₀ = (10000.100011)₂

b) (26.24)₁₀

⇒ 26 ÷ 2 = 13, Remainder = 0

    13 ÷ 2 = 6, Remainder = 1

    6 ÷ 2 = 3, Remainder = 0

    3 ÷ 2 = 1, Remainder = 1

    1 ÷ 2 = 0, Remainder = 1

So, (26)₁₀ = 11010₂

Now, for the fractional part

0.24 × 2 = 0 + 0.48

0.48  × 2 = 0 + 0.96

0.96  × 2 = 1 + 0.92

0.92 × 2 =  1 + 0.84

0.84 × 2 =  1 + 0.68

0.68 × 2 =  1 + 0.36

Hence, (26.24)₁₀ = (11010.001111)₂

b) (0.5625)₁₀

⇒ Here, we only have the fractional part

0.5625 × 2 = 1 + 0.125

0.125  × 2 = 0 + 0.25

0.25  × 2 = 0 + 0.50

0.50 × 2 =  1 + 0

Hence, (0.5625)₁₀ = (0.1001)₂

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Answer:

1/4

Step-by-step explanation:

simple

Answer:

7² = 49 ans

Step-by-step explanation:

7² == 49 ans .....

Answer:

49

Step-by-step explanation:

7² = 7 x 7 = 49

\(\huge\text{Hey there!}\)

\(\mathsf{-12x < 36}\)

\(\huge\textbf{DIVIDE \boxed{\rm{\bf -12}} to both sides:}\)

\(\mathsf{\dfrac{-12}{-12}x < \dfrac{36}{-12}}\)

\(\huge\textbf{SIMPLIFY it:}\)

\(\mathsf{x < \dfrac{36}{-12}}\)

\(\mathsf{x > -3}\)

\(\large\text{It is a(n) \boxed{\rm{o p e n e d}} circle SHADED to the RIGHT of your number line}}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{x > -3}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

22+b = t

Step-by-step explanation:

22+b= t, where t is the total number of books in the past two months.

If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.

An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.

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Answer:

i think option d is the correct answer of this question.

Answer:

Each pair of shoes cost 26$

Step-by-step explanation:

find the total cost for shirts

2 shirts * 12$ each

2 * 12 = 24

they spent 24$ on shirts

create an equation

24$ shirts + x$ shoes = 76$

24 + x = 76

subtract 24 from both sides of the equation

24 + x - 24 = 76 - 24

x = 76 - 24

x = 52

they bought 2 pairs of shoes that cost the same amount

52 = x + x

52 = 2x

divide both sides of the equation

52/2 = 2x/2

52/2 = x

26 = x

each pair of shoes cost 26$

Answer:

4

Step-by-step explanation:

Step 1:

13 = 2f + 5         Equation

Step 2:

8 = 2f      Subtract 5 on both sides

Step 3:

f = 8 ÷ 2     Divide

Answer:

f = 4

Hope This Helps :)

Answer:

I did this before! heres what i did: 13=2f+5

We simplify the equation to the form, which is simple to understand  

13=2f+5

We move all terms containing f to the left and all other terms to the right.  

-2f=+5-13

We simplify left and right side of the equation.  

-2f=-8

We divide both sides of the equation by -02 to get f.  

f=4

Answer:

P=23.4

Step-by-step explanation:

so using the pytogoren theroum

c2-b2= a2

so a= 6.9

so P= 6.9+6.8+9.7=23.4

if my answer helped please mark as brainliest.

Answer:

The Pythagorean Theorem can be used to find the length of the legs and hypotenuse of a triangle. While the distance of a vertical or horizontal line can be counted easily, a diagonal line cannot be determined the same way. A diagonal line, such as the line between the two points shown on the graph, is the hypotenuse of an imaginary right triangle. If you draw the legs of the triangle by drawing straight lines through the points on the graph until the lines meet at a point, you can count the distance of the legs and plug those values into the Pythagorean Theorem.

Step-by-step explanation:

In this case, the meeting point of straight lines drawn through the points is

(-3, -4)

and the distances of the legs of the right triangle are 8 and 6. The theorem is

a² + b² = c²

so 8² + 6² = c²    to 64 + 36 = c²    to 100 = c²    and \(\sqrt 100 = \sqrt c^{2}\)

so 10 = c

The distance of the line (hypotenuse) is 10.

Answer:

1092 people attended the last basketball game.

Step-by-step explanation:

Given that:

Number of people who attended the first basketball game = 840

Percent increase for last game = 30%

Total people who attended last game = (100+30)% = 130% of first game

Number of people who attended last game = \(\frac{130}{100}*840\)

Number of people who attended last game = 1.30*840 = 1092

Hence,

1092 people attended the last basketball game.

Answer:

B

Step-by-step explanation:

+/- 7 is the sq root of 49

hope this helps

Answer:

Step-by-step explanation:

abc = 1

We have to prove that,

\(\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1\)

We take left hand side of the given equation and solve it,

\(\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}\)

Since, abc = 1,

\(\frac{1}{c}=ab\) and c = \(\frac{1}{ab}\)

By substituting these values in the expression,

\(\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}\)

                                       \(=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}\)

                                       \(=\frac{1+b+ab}{1+b+ab}\)

                                       \(=1\)

Which equal to the right hand side of the equation.

Hence, \(\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1\)

Solution

Step 1:

Write the function

Step 2:

SOLUTION

Since the house decreased by 15%, the value of this in dollars becomes

Which is

Hence the house value decreased by $39,150

The current value of the house becomes

Hence the current value is $221,850

Answer:

122.5

Step-by-step explanation:

0.034518 = 3.45% probability that the proportion of tickets sold in a sample of 691 tickets would be less than 9%.

In a set with mean µ and standard deviation σ , the z score of a measure X is given by:

Z = X - µ/σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For the sampling distribution of a sample proportion of size n, we have that

µ = √p(1-p)/n

p = 0.11, n = 691

so, µ= 0.11, σ= √0.11×0.89/691

σ = 0.011

What is the probability that the proportion of tickets sold in a sample of 691 tickets would be less than 9%?

This is the p value of Z when X = 0.09. So

Z = 0.09-0.11/0.011

Z = -1.8

Z = -1.8 has a p value of 0.034518

0.034518 = 3.45% probability that the proportion of tickets sold in a sample of 691 tickets would be less than 9%.

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Answer:

So heres what I think

C=2pie r

C=2*3.14*4

c=25.12

So basically half the circle is the radius and the whole is the circumference. So what you are doing is changing pie to 3.14 (since pie=3.14), since half the circle its radius so all you have to do is 2 times 3.14 times 4 to get 25.12 as your circumference.

Hope this helps!

Step-by-step explanation:

Answer: It is roughly 25.12 or 8π

Step-by-step explanation:

Well, it depends if you are using 3.14 as a subsitute for Pi, or you are just using the Pi symbol (π). Let me explain better:

The equation for solving the circumference of a circle is C=2πr

R is the radius, which is the 4 in the problem. If you were just using the Pi symbol, you would multiply 2*4 because you plugged 4 into the equation above. This would result in C=8π.

If you were using 3.14, you would subsitute both 3.14 and 4. So it would be C=2(3.14)(4) which would be 25.12

Hope this helped! (By the way, if it is wrong, I have not gotten this in my math class yet). ALSO remember to check whether the homework is using 3.14 for Pi or you just using the Pi symbol. And to put the squiggly equation symbol which means about.

Here, \(det(5B^T) = -2 * (5^n)\) and d\(et(SB^T) = (S^n) * (-2)\), where n is the dimension of B and S is the scaling factor of the scalar matrices S.

The determinant of the product of the scalar and matrices transpose is equal to the scalar multiplication of the matrix dimensions and the determinant of the original matrix. So \(det(5B^T)\)can be calculated as \((5^n) * det(B)\). where n is the dimension of B. In this case B is an n × n matrix, so \(det(5B^ T) = (5^n) * det(B) = (5^n) * (-2) = -2 * (5^ n )\).

Similarly, \(det(SB^T)\) can be calculated as \((det(S))^n * det(B)\). A scalar matrix S scales only the rows of B so its determinant det(S) is equal to the higher scale factor of B 's dimension. Therefore,\(det(SB^T) = (det(S))^n * det(B) = (S^n) * (-2)\). where\(S^n\) represents the n-th power scaling factor. 

The determinant of a matrix is ​​a scalar value derived from the elements of the matrix. It is a fundamental concept in linear algebra and has many applications in mathematics and science.

To compute the determinant of a square matrix, the matrix must have the same number of rows and columns. The determinant is usually represented as "det(A)" or "|"A"|". For matrix A 

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