One polygon has a side of length 3 feet. A similar polygon has a corresponding side of length 9 feet. The ratio of the perimeter of the smaller polygon to the larger is (3)/(1) (1)/(6) (1)/(3)

Answer:

13.33 hours

Step-by-step explanation:

\(\frac{12}{360} =\frac{x}{400} \\\\360x=4800\\x= 13.33\)

Answer:

shoqwwkalakidsb II oakqijq8ww mulero 288

Answer:

D

Step-by-step explanation:

\( \sin(60) = \frac{6 \sqrt{3} }{x} \\ x = \frac{6 \sqrt{3} }{ \sin(60) } = 12 \\ \cos(60) = \frac{y}{12} \\ y = 6\)

Answer:

Radius = 4.95 cm

Step-by-step explanation:

I am assuming you need the radius of the base of the cylinder.

Volume = 1.54 * 1000 = 1540 cm^3

Volume = πr^2h so:

1540 =  π*r^2*20

r^2 = 1540/20 π = 24.510

r = 4.95 cm.

The given statement "spearman's rho describes a linear relationship between two quantitative variables." is False, because it is a correlation coefficient that measures the strength of a monotonic relationship.

In particular, Spearman's rho is used to measure the degree of association between two variables when the relationship between them is not linear. It works by ranking the values of the two variables and then computing the correlation between the ranks.

If the variables have a monotonic relationship, the Spearman's rho will be close to 1 or -1, depending on the direction of the relationship. If there is no relationship, the Spearman's rho will be close to 0.

For example, consider a dataset where the number of hours studied and the grade obtained in an exam are recorded for a group of students.

If the relationship between the two variables is non-linear, such as a U-shaped or inverted U-shaped curve, then the Spearman's rho would be more appropriate than the Pearson correlation coefficient, which measures the strength of a linear relationship.

In summary, Spearman's rho is used to measure the strength of a monotonic relationship between two variables, which can be non-linear.

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Answer:

b!!!!!

Step-by-step explanation:

Answer:

-(x+8)(3x-1)

Step-by-step explanation:

Take out the - sign, then factor as if it is positive.

Answer:

$59.60

Step-by-step explanation:

Charge per check = $0.20

Monthly maintenance fee = $12.50

Total fees that will be paid in. 4 months :

Check written per month = 12

Charge per month :

Check fee + maintenance fee

(12 * 0.20) + 12.50

= $14.90 per month

In 4 months ;

$14.90 * 4 = $59.60

The opposite side with the A is the reference angle ,the answer is the opposite side of angle A is AC.

A triangle is  closed two-dimensional geometric figure that formed by three straight line segments called sides. The sides of  triangle meet at the three points called vertices. A triangle has three angles, and  sum of  angles is = 180 degrees.

Triangles are classified based on  lengths of their sides and sizes of their angles.

In the given diagram, if A is the reference angle, then:

a) AB is the adjacent side of angle A.

b) BC is the hypotenuse of the right triangle.

c) AC is the opposite side of angle A.

Therefore, the opposite side of angle A is AC.

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Answer:

It has given that the area of the rectangular floor in Tamara's room is 95 ⅚ square feet. the width of the room is 8 ⅓ feet.

we can solve for x:

x = ln[(0.5 - 0.004c) / (-0.004c)] / -0.004

The resulting value of x represents the median benefit for this insurance policy.

What is the median?

the median is defined as the middle value of a sorted list of numbers. The middle number is found by ordering the numbers. The numbers are ordered in ascending order. Once the numbers are ordered, the middle number is called the median of the given data set.

To find the median benefit for the insurance policy, we need to determine the value of x for which the cumulative distribution function (CDF) reaches 0.5.

The cumulative distribution function (CDF) is the integral of the probability density function (PDF) up to a certain value. In this case, the CDF can be calculated as follows:

CDF(x) = ∫[0 to x] f(t) dt

Since the PDF is given as \(f(x) = ce^{(-0.004x)}\) for x > 0, the CDF can be calculated as follows:

CDF(x) = ∫[0 to x] \(ce^{(-0.004t)}\)dt

To find the median, we need to solve the equation CDF(x) = 0.5. Therefore, we have:

0.5 = ∫[0 to x]  \(ce^{(-0.004t)}\) dt

Integrating the PDF and setting it equal to 0.5, we can solve for x:

0.5 = [-0.004c *  \(ce^{(-0.004t)}\)] evaluated from 0 to x

0.5 = [-0.004c *  \(ce^{(-0.004t)}\)] - [-0.004c * e⁰]

Simplifying further, we have:

0.5 = [-0.004c *  \(ce^{(-0.004t)}\)] + 0.004c

Now, we can solve this equation for x:

[-0.004c *  \(ce^{(-0.004t)}\)] = 0.5 - 0.004c

\(ce^{(-0.004t)}\) = (0.5 - 0.004c) / (-0.004c)

Taking the natural logarithm of both sides:

-0.004x = ln[(0.5 - 0.004c) / (-0.004c)]

Hence, we can solve for x:

x = ln[(0.5 - 0.004c) / (-0.004c)] / -0.004

The resulting value of x represents the median benefit for this insurance policy.

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The magnitude of the vector 2ū - 3v is 34m and its direction is approximately -61.93° with respect to the positive x-axis.

To find a unit vector parallel to the sum of vectors a = 2m[E] and b = 3m[N], we need to find the sum of these vectors and then normalize it.

The sum of vectors a and b is given by:

a + b = 2m[E] + 3m[N]

To find the unit vector parallel to this sum, we divide the sum vector by its magnitude. The magnitude of the sum vector can be calculated using the Pythagorean theorem:

|a + b| = sqrt((2m)^2 + (3m)^2)

|a + b| = sqrt(4m^2 + 9m^2)

|a + b| = sqrt(13m^2)

|a + b| = sqrt(13) * m

Now, to find the unit vector parallel to the sum vector, we divide the sum vector by its magnitude:

u = (a + b) / |a + b|

u = (2m[E] + 3m[N]) / (sqrt(13) * m)

Simplifying, we get:

u = (2/sqrt(13))[E] + (3/sqrt(13))[N]

Therefore, a unit vector parallel to the sum of vectors a and b is (2/sqrt(13))[E] + (3/sqrt(13))[N].

Given u = 8m[W] and v = 10m[S30°W], we need to determine the magnitude and direction of the vector 2ū - 3v.

To find the magnitude of the vector 2ū - 3v, we can calculate its length using the Pythagorean theorem:

|2ū - 3v| = sqrt((2u)^2 + (-3v)^2)

|2ū - 3v| = sqrt((2 * 8m)^2 + (-3 * 10m)^2)

|2ū - 3v| = sqrt(256m^2 + 900m^2)

|2ū - 3v| = sqrt(1156m^2)

|2ū - 3v| = sqrt(1156) * m

|2ū - 3v| = 34m

The magnitude of the vector 2ū - 3v is 34m.

To find the direction of the vector 2ū - 3v, we can calculate its angle with respect to the positive x-axis using the arctan function:

θ = arctan((-3v)/(2u))

θ = arctan((-3 * 10m)/((2 * 8m)))

θ = arctan((-30m)/(16m))

θ = arctan(-30/16)

Using a calculator or reference table, we find θ ≈ -61.93°.

Therefore, the magnitude of the vector 2ū - 3v is 34m and its direction is approximately -61.93° with respect to the positive x-axis.

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An expression to model the number of movies in Ann's collection is A = 2B - 3.

In order to write a linear equations that could be used to model the situation, we would assign variables to the number of movies in Ann's collections and the number of movies in Bob's collections respectively as follows:

Next, we would translate the word problem into linear equation as follows:

A = 2B - 3

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The formula given is a logistic function, which is used to map a set of input variables (x1, x2, x3, x4, x5, x6) to a single output value.

The formula takes the maximum of x1 and x2, multiplies it by x3 and x4, and then takes the product of (x5 x6) and 1/2. This product is then passed through a probability , which is a non-linear transformation that outputs a value between 0 and 1. Finally, this output value is taken to the power of 5 to produce the final output of the function. This logistic function is used to map the input values to a single output value, which can then be used to make predictions, such as determining a probability of an event occurring.

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\(A = B^-1 * BC\)

Since B is invertible, it can be used to solve the equation.

1. Calculate the inverse of B, \(B^-1\).

2. Multiply\(B^-1\) with BC, to obtain A.

Assuming that AB and C are square matrices and B is invertible, the equation AB=BC can be solved for A. To do this, we first need to calculate the inverse of B, \(B^-1\). The inverse of a matrix is defined as the matrix which when multiplied to the original matrix, yields the identity matrix. Once we have the inverse of B, we can use it to solve the equation by multiplying \(B^-1\) with BC, which will give us A. This works because when we multiply a matrix by its inverse, the result is always the identity matrix. Hence, by multiplying the inverse of B with BC, we can obtain A.

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If sofia has a collection of 200 coins, 40 coins represent 20% of Sofia's collection.

To find out how many coins represent 20% of Sofia's collection, we need to first calculate what 1% of her collection is.

To do this, we can divide the total number of coins by 100:

1% of Sofia's collection = 200 coins ÷ 100 = 2 coins

Now that we know that 1% of her collection is 2 coins, we can find 20% by multiplying 2 by 20:

20% of Sofia's collection = 2 coins × 20 = 40 coins

Therefore, 40 coins represent 20% of Sofia's collection.

To find out what percentage a different number of coins represents, we can use the same method. For example, if we want to know what percentage 30 coins represent, we can divide 30 by 2 (since 2 coins represent 1%), which gives us 15%.

So, 30 coins represent 15% of Sofia's collection.

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Step-by-step explanation:

Hope this helps, happy learning!!!

The diagram of translatation FGH 3 units down and 2 units left followed by a rotation counterclockwise 90° is attached below.

Dilation is the process of increasing the size of an item without affecting its form.

Depending on the scale factor, the object's size can be raised or lowered.

The translate FGH 3 units down and 2 units left followed by a rotation counterclockwise 90°.Then followed by a dilation by a scale factor of 2.

F ( -1, 0)

G (1, 0)

H ( -1, 1)

Thus, counterclockwise 90°

F' ( 0, 1)

G' (0, -1)

H' ( -1, -1)

Scale factor = 2

Then

F'' ( 0, 2)

G'' (0, -2)

H'' ( -2, -2)

The diagram of translatation FGH 3 units down and 2 units left followed by a rotation counterclockwise 90° is attached below.

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9514 1404 393

Answer:

  a) no

  b) yes

  c) maybe (no)

Step-by-step explanation:

There are two versions of the triangle inequality. One requires ...

  a + b > c

for any triple of side measures a, b, c.

The other allows ...

  a + b ≥ c

which admits "triangles" that have zero height and look like line segments.

Most questions asking "do these lengths form a triangle" are concerned with the "greater than" case, and disallow the "or equal to" case.

__

a)

  \(16+21=37\ngtr39\qquad\text{not a triangle}\)

b)

  \(27+34=61>58\qquad\text{could be a triangle}\)

c)

  \(9+29=38\ge38\qquad\text{could be a triangle if "equal to" is allowed}\)

Answer:3.28 yards

Step-by-step explanation:

Given

length of fence \(L=3\ m\)

width \(w=2\ cm\ or\ 0.02\ m\)

We know, \(1\ m=1.093\ yard\)

\(\therefore 3\ m=3\times 1.093=3.28\ yards\)

he requires 3.28 yards to build the fence

Answer:

r = -4

Step-by-step explanation:

Subtract 4 from both sides, so r = -4

Answer:

1. 45

2. 105

3. 95

4. 85

Step-by-step explanation:

For problems 1 and 4:

Consecutive angles are supplementary in a parallelogram, which means they equal 180.

180 - 135 = 45

180 - 95 = 85

For problems 2 and 3:

Opposite angles are congruent or equal each other in a parallelogram,

The sequence  aₙ = 2n is divergent.

To show that the sequence aₙ is divergent, we need to show that it does not converge to a finite limit.

Let's assume that the sequence aₙ converges to some finite limit L, i.e., lim(aₙ) = L. Then, for any ε > 0, there exists an integer N such that |aₙ - L| < ε for all n ≥ N.

Let's choose ε = 1. Then, there exists an integer N such that |aₙ - L| < 1 for all n ≥ N. In particular, this means that |2n - L| < 1 for all n ≥ N.

However, this is impossible because as n gets larger, 2n gets arbitrarily large and so it is not possible for |2n - L| to remain less than 1 for all n ≥ N. Therefore, our assumption that aₙ converges to a finite limit L is false, and hence aₙ is divergent.

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The given question is incomplete, the complete question is:

Show that each of the following sequences is divergent aₙ=2n

The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.

Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.

For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.

In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.

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The solution to the integral of f(t) = t^2 + sin(2t) + 2cos(2t) + e^(-t)sin(3t) is:

F(t) = (1/3)t^3 - (1/2)cos(2t) + (1/2)sin(2t) - 4e^(-t)cos(3t) + C

where F(t) represents the antiderivative or the indefinite integral of f(t).

To find the solution for the function f(t) = t^2 + sin(2t) + 2cos(2t) + e^(-t)sin(3t) manually, we need to analyze each term separately.

Term: t^2

The integral of t^2 with respect to t is (1/3)t^3.

Term: sin(2t)

The integral of sin(2t) with respect to t is -(1/2)cos(2t).

Term: 2cos(2t)

The integral of 2cos(2t) with respect to t is (1/2)sin(2t).

Term: e^(-t)sin(3t)

To integrate this term, we can use integration by parts. Let's define u = e^(-t) and dv = sin(3t) dt.

Taking the derivatives and integrals:

du = -e^(-t) dt

v = -(1/3)cos(3t)

Using the integration by parts formula:

∫ u dv = uv - ∫ v du

∫ e^(-t)sin(3t) dt = -e^(-t)(1/3)cos(3t) - ∫ -(1/3)cos(3t)(-e^(-t)) dt

= -e^(-t)(1/3)cos(3t) + (1/3)∫ cos(3t)e^(-t) dt

We can apply integration by parts again to the remaining integral:

Let u = cos(3t) and

dv = e^(-t) dt.

Taking the derivatives and integrals:

du = -3sin(3t) dt

v = -e^(-t)

Using the integration by parts formula again:

∫ cos(3t)e^(-t) dt = -e^(-t)cos(3t) - ∫ (-e^(-t))(-3sin(3t)) dt

= -e^(-t)cos(3t) + 3∫ e^(-t)sin(3t) dt

Substituting the value we found for the previous integral:

∫ e^(-t)sin(3t) dt = -e^(-t)(1/3)cos(3t) + (1/3)(-e^(-t)cos(3t) + 3∫ e^(-t)sin(3t) dt)

Now we can solve for the integral:

∫ e^(-t)sin(3t) dt = (-e^(-t)(1/3)cos(3t) - (1/3)e^(-t)cos(3t))/(1 - 1/3)

= -3e^(-t)(1/3)cos(3t) - 3e^(-t)cos(3t)

= -e^(-t)cos(3t) - 3e^(-t)cos(3t)

= -4e^(-t)cos(3t)

Now we can put all the terms together:

∫ f(t) dt = (1/3)t^3 - (1/2)cos(2t) + (1/2)sin(2t) - 4e^(-t)cos(3t)

Let's continue with the expression for the integral:

∫ f(t) dt = (1/3)t^3 - (1/2)cos(2t) + (1/2)sin(2t) - 4e^(-t)cos(3t) + C

where C is the constant of integration.

So, the solution to the integral of f(t) = t^2 + sin(2t) + 2cos(2t) + e^(-t)sin(3t) is:

F(t) = (1/3)t^3 - (1/2)cos(2t) + (1/2)sin(2t) - 4e^(-t)cos(3t) + C

where F(t) represents the antiderivative or the indefinite integral of f(t).

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\(x - 3 = x + 4 \\ x - x = 3 + 4 \\ 0 = 7\)

The equation is false, therefore there are no solutions.

Clark stayed up on water skis \(\bold{3\frac{1}{6}}\) minutes longer on his first attempt than he did on his second attempt.

To find out how much longer did Clark stay on the skis on his first attempt, we only need to find the difference between the number of minutes he stayed up on water skis for on his first attempt and the number of minutes he did on his second attempt. In other words, we need to subtract \(3\frac{3}{8}\) from \(\frac{5}{16}\). Here's how:

First, convert the mixed number to an improper fraction.

\(3\frac{3}{8}-\frac{5}{16}=\frac{27}{8}-\frac{5}{16}\)

Then, find the least common multiple (LCM) of the denominators and use it so that the denominators of both fractions are the same. Since 16 is a multiple of 8, just multiply the numerator 27 and the denominator 8 by 2.

\(\frac{27\times 2}{8\times 2}-\frac{5}{16}=\frac{54}{16}-\frac{5}{16}=\frac{49}{16}\)

That's it! Clark stayed on the skis on his first attempt 49/16 minutes longer. You can convert the number of minutes to \(3\frac{1}{16}\)  or 3.0625 if you will.

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To compare two numbers given in scientific notation, first compare the exponents. The one with the greater exponent will be greater. If the exponent is the same, compare the two numbers that are being multiplied by comparing their decimals.

The solution to the system of equations is (x, y) = ±(√(4/5), 24/5) or ± (√(4/5), 20/5).

What is the system of equations?

A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

The system of equations given is:

y = 6x²

y = x² + 4

To solve this system of equations, we need to find the values of x and y that satisfy both equations.

Setting the right-hand side of the two equations equal to each other, we get:

6x² = x² + 4

5x² = 4

x² = 4 / 5

x = ±√(4/5)

So, there are two possible values of x, which are positive and negative square roots of 4/5. For each of these values of x, we can use either equation to find the corresponding value of y:

y = 6x^2 = 6 * (4/5) = 24/5

y = x^2 + 4 = (4/5) + 4 = 16/5 + 4 = 20/5

So, the solution to the system of equations is:

(x, y) = ±(√(4/5), 24/5) or ± (√(4/5), 20/5)

This means that there are two points that satisfy both equations, one where x and y are positive, and one where x and y are negative.

Hence, the solution to the system of equations is:

(x, y) = ±(√(4/5), 24/5) or ± (√(4/5), 20/5).

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Answer:

The slope is -4

Step-by-step explanation:

rise over run

4 down, 1 right

The total amount of rainwater that flows into the pipe during the time interval of 0 to 8 hours is 880 cubic feet.

R(0) = 20sin(0/35) = 0 cubic feet per hour

R(8) = 20sin(\(8^2\)/35) = 19.48 cubic feet per hour

D(0) = -0.04(\(0^3\)) + 0.4(\(0^2\)) + 0.96(0) = 0 cubic feet per hour

Total amount of water that flowed into the pipe during the 8-hour time interval:

= (R(8) - R(0)) - (D(8) - D(0))

= (19.48 - 0) - (104.32 - 0)

= -84.84 cubic feet

We can also calculate the rate at which water is draining out of the pipe by using the function D(t) = -0.04t3 + 0.4t2 + 0.96t cubic feet per hour. Integrating this function over the same time period yields a total of 360 cubic feet of water draining out of the pipe. Therefore, the total amount of rainwater that flows into the pipe during the time interval of 0 to 8 hours is 880 cubic feet .Therefore, 84.84 cubic feet of rainwater flow into the pipe during the 8-hour time interval 0 ≤ t ≤ 8.

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