(-3, -1) is a point given in rectangular coordinates. Find the 2 corresponding primary representations of the point in polar coordinates. Approximate the values to 4 significant figures.

To show that the projection maps π₁: X × Y → X and π₂: X × Y → Y are open maps, we need to demonstrate that for every open set U in X × Y, the sets π₁(U) and π₂(U) are open in X and Y, respectively.

Let U be an open set in X × Y. We can write U as the union of open sets U = U₁ × U₂, where U₁ is an open set in X and U₂ is an open set in Y. Since U is open, every point (x, y) in U has an open neighborhood contained within U.

Now, consider the image of U under the projection map π₁: X × Y → X. The set π₁(U) is the collection of all x-coordinates of the points in U. For any point x' in π₁(U), there exists a point (x', y') in U. Since U is open, there exists an open neighborhood N = N₁ × N₂ of (x', y') contained within U. The projection of N onto the x-coordinate, N₁, is an open neighborhood of x' contained within π₁(U). Therefore, π₁(U) is open in X.

Similarly, for the projection map π₂: X × Y → Y, we can show that π₂(U) is open in Y. For any point y' in π₂(U), there exists a point (x', y') in U. By a similar argument as above, there exists an open neighborhood N = N₁ × N₂ of (x', y') contained within U. The projection of N onto the y-coordinate, N₂, is an open neighborhood of y' contained within π₂(U). Therefore, π₂(U) is open in Y.

Since this holds for an arbitrary open set U in X × Y, we have shown that the projection maps π₁: X × Y → X and π₂: X × Y → Y are open maps.

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Answer:

13 inches

Step-by-step explanation:

diameter is the radius times 2

so

6.5x2=13

The diameter of the plate is 13 inches

Hope this helps :-)

\(-noorati\)

Answer:

624,600

Step-by-step explanation:

624,612

612 rounds to 600

624,600

Answer:

624,600

Step by step explanatiom:

cause math

First, let us calculate the forecast for week 7. The naïve method (most recent value) is used to make the forecast. The most recent value is 15, so the forecast for the next week, which is week 7, is 15.

Using the naïve method as the forecast for the next week, the following measures of forecast accuracy are calculated.The given data is as follows:

Week 1 2 3 4 5 6Value 19 13 16 10 18 15.

Now we will calculate the Mean absolute error:

Mae = (19-13)+(13-16)+(16-10)+(10-18)+(18-15) / 5=6+3+6+8+3 / 5=6.4.

Therefore, the Mean absolute error is 6.4.

Mean squared error can be calculated as follows:

Mse = [(19-13)²+(13-16)²+(16-10)²+(10-18)²+(18-15)²] / 5=196 / 5=39.2.

Therefore, the Mean squared error is 39.2.

Now let us calculate Mean absolute percentage error:

Map = [ (6/19) + (3/13) + (6/16) + (8/10) + (3/18) ] / 5= 0.962.

Therefore, the Mean absolute percentage error is 0.96.

The forecast for week 7 is 15. Mean absolute error is 6.4. Mean squared error is 39.2. Mean absolute percentage error is 0.96.

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Answer:

Your answer will be Sixty Six Fifty Fourths

Step-by-step explanation:

Make it the same denominator so you can add them (18.)

Multiply 5/9 by 2 and multiply 4/6 by 3.

10/18 + 12/18 = 22/18.

Since there is not 22/18 listed, you can use this fraction as a proportion. The only proportion that can be evident is answer A, as when you multiply 22/18 by 3, you get 66/54.

Hope this helps! ;)

Answer:

Answer:

Step-by-step explanation:

A function can only have one output for an input.  That is, for any value of x, there must be a unique value of y.

{(-6,-1), (13,8), (1,6), (1,-10)}   Not a  Function:  (1,6) and (1,-10)

{(10,5), (10,-5), (5,10), (5,-10)}  Not a  Function:  (10,5) and (10,-5)

{(3,5), (-17,-5), (3,-5), (-17,5)}   Not a Function:  (3,5) and (3,-5)

{(10,5), (-10,-5), (5,10), (-5,-10)}  Function:  No duplicate values of y for a value of x.

It is untrue to say that the exponential function f(x) has a base of 3.

A mathematical function termed an exponential function has the formula f (x) = axe, where x is a variable and a constant called the base of the function, which must be greater than 0. The most often used exponential function basis is the transcendental number e, or approximately 2.71828.

An exponential function has the form f(x) = bx for b > 0 and b 1. Like in any exponential expression, the base is b and the exponent is x. Bacterial growth serves as an example of an exponential function. Some bacteria grow by two per hour.

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Answer:

50%

Step-by-step explanation:

175-110 to find percent increase

175-110 = 65.

65/110 to find percent of 110

65/110 = 50%, so 50% increase.

1. The solution for the equation is -16t² + 64t > 0

2. The interval notation for the equation is (0, 4)

Given,

The height of the building = 400 feet

A ball is thrown straight up from the top of the building.

The initial velocity of the ball = 64 feet/second

The height of the object is modeled by, s(t) = -16t² + 64t + 400

1. Solution for the equation:

s(t) > 400

So,

-16t² + 64t + 400 > 400

Add -400 to both sides

ie, -16t² + 64t + 400 - 400 > 400 - 400

We get,

-16t² + 64t > 0

2. Now find the interval notation for the equation:

-16t² + 64t > 0

Here, 64/16 = 4

So,

-16t (t - 4) > 0

Now,

t = 0 and t - 4 = 0  

The interval notation for the equation is (0, 4)

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Answer:

\(r^{3}=4050\)

r = ∛4050

Step-by-step explanation:

\(V=\frac{4}{3} \pi r^{3}\)

\(5400=\frac{4}{3} \pi r^{3}\)

\(r^{3}=3(\frac{5400}{4} )\)

\(r^{3}=3(1350 )\)

\(r^{3}=4050\)

Answer:

1

Step-by-step explanation:

Answer:

Your answer is literally 1

Step-by-step explanation:

(3−4+5−3)2

=1*1

=1

Hope this is what your looking for

Answer:

~63%

Step-by-step explanation:

67/106

=0.63207 × 100

= 63.207% or just 63%

The one function that satisfies f '(x) = 3x² + 6x + 5 is f(x) = x³ + 3x²÷2 + 5x + C. where C is the constant of integration.

The given function's derivative is f'(x) = 3x² + 6x + 5.

To find the original function f(x), we need to integrate the derivative.

We can integrate the given function f'(x) term by term, using the power rule of integration:

∫f'(x) dx = ∫(3x² + 6x + 5) dx

f(x) = x^3 + 3x²÷2 + 5x + C

Any constant value of C can be added to the above function, resulting in an infinite number of functions that satisfy

f '(x) = 3x² + 6x + 5.

f(x) = x^3 + 3x²÷2 + 5x + 2 and f(x) = x³ + 3x²÷2 + 5x - 7 are both valid solutions to f '(x) = 3x² + 6x + 5, with different constant values of C.

This is because the constant of integration represents an arbitrary constant, and when we take the derivative, the constant term becomes zero. Hence, any function that differs from the original function by a constant value will also have the same derivative.

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I would say that the answer is F, y= -2x+4

The correct answer is 85% confidence interval is (33.592, 53.050).

Confidence interval:

A confidence interval, in statistics, mention to the probability that a population parameter will fall between a set of values for afixedproportion of times

Margin of error:

Margin of error, also called confidence interval, tells you how much you can expect your survey results to reflect the views from the overall population.

Given:

Sample size (n)= 14 and dt= (n- 1) = 13

\(mean(\bar x)=\frac{\ xi}{n}\)

              = 606.5/14 = 43.32

\(\sigma=\sqrt{\frac{1}{N}(xi-\mu )^2 } \\\sigma^2=\frac{(20-43.32)^2+......+(40-43.32)^2}{14} \\\sigma=18.80\)

\(CI=\bar x \pm t(\frac{\sigma}{\sqrt{n} } )= 43.32\pm1.9354(\frac{18.808}{\sqrt{14} } )\\CI= 43.32\pm 9.72\)

Lower limit = 33.59.

Upper limit = 53.05.

85% confidence interval is (33.592, 53.050).

Therefore. 85% confidence interval is (33.592, 53.050).

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Answer: 22%

Step-by-step explanation:

Water will reach a depth of 12 meters after 3.1 hours approximately.

What is function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.

Main body:

Function representing the level of water by 'y' and number of hours by 'x' is,

y = 2.5 cos (2πx/12.5)+12

For y = 12 meters, (Substitute the value of y)

12 = 2.5 cos (2πx/12.5)+12

12 -12 = 2.5 cos (2πx/12.5)

cos (2πx/12.5) = 0

2πx/12.5 = π/2

πx/12.5 = π/4

x = 3.125

x ≈3.1 hours

Therefore, water will reach a depth of 12 meters after 3.1 hours approximately.

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Answer:

i would say probably 4/3? i.dk hope my answer is right

Step-by-step explanation:

brainliest please

The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m

where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925

And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075

Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.

This is option D.

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The four quantities in the given formula for the sum of an arithmetic series (Sn = n/2(a₁ + an)) are

1. Sn: The sum of the arithmetic series.

2. n: The number of terms in the series.

3. a₁: The first term of the series.

4. an: The nth term of the series, representing the last term in the series.

The formula provided is for the sum of an arithmetic series, and it involves four quantities. Let's describe each of these four quantities:

1. Sn: This represents the sum of the arithmetic series. It is the total of all the terms in the series up to the nth term. In other words, it represents the cumulative sum of the terms in the series.

2. n: This represents the number of terms in the arithmetic series. It indicates how many terms are included in the sum. The value of 'n' determines the extent of the series and influences the value of Sn.

3. a₁: This represents the first term of the arithmetic series. It is the initial value or the starting point of the series. The subsequent terms in the series are generated by adding the common difference (d) to this first term.

4. an: This represents the nth term of the arithmetic series. It is the last term or the final value in the series. The value of 'an' can be determined using the formula an = a₁ + (n-1)d, where 'd' is the common difference between consecutive terms in the series.

In summary, the four quantities in the given formula for the sum of an arithmetic series (Sn = n/2(a₁ + an)) are:

1. Sn: The sum of the arithmetic series.

2. n: The number of terms in the series.

3. a₁: The first term of the series.

4. an: The nth term of the series, representing the last term in the series.

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The probability that both marbles are blue is 1/4.

Since the marble is put back into the bag before the second draw, the probability of drawing a blue marble on the first draw is 3/6 or 1/2, and the probability of drawing a blue marble on the second draw is also 3/6 or 1/2.

The probability of both events happening together (drawing a blue marble on the first and second draws) is equal to the product of the probabilities of each event occurring separately, since the two events are independent of each other:

P(Blue on first draw AND Blue on second draw) = P(Blue on first draw) x P(Blue on second draw)

= 1/2 x 1/2

= 1/4

Therefore, the probability of drawing two blue marbles in a row with replacement is 1/4 or 25%.

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Answer:

Solve.

Step-by-step explanation:

make the 2 3 and 1 then turn them into 20 30 and 10 then you need to add them together to get the answer divide that by thirty and if its more than half yes, less than half no.

The costs of each treat are

To solve this, we use the followign representations

x = cookies

y = ice cream 1

z = ice cream 2

Treat 1

Using the columns to generate the system of equations, we have

x + y + z = 25.71

z + 2x = 23.21

3y = 26.94

So, we have

y = 8.98

The other equations become:

x + 8.98 + z = 25.71

z + 2x = 23.21

When solved, we have

x = 6.48

z = 10.25

Treat 2

Using the rows to generate the system of equations, we have

x + 2y = 7.17

y + 2x = 5.37

3z = 14.97

So, we have

z = 4.99

The other equations when solved, we have

x = 1.19

y = 2.99

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Answer:

16p+6

Step-by-step explanation:

Answer:

\(x\approx 24.0,\\y\approx 46.4\)

Step-by-step explanation:

Let the height of the largest triangle marked be \(h\). We can set up the following equation:

\(\sin 30^{\circ}=\frac{h}{34},\\h=34 \sin 30^{\circ}=17\) (if you're unfamiliar with trig, this is likely introduced to you as 30-60-90 triangle rules)

This height is also a leg of a 45-45-90 triangle, as marked in the diagram. From the isosceles-base-theorem, the other leg of this triangle must also be equal to \(h\). Therefore, we can use the Pythagorean theorem to solve for \(x\):

\(17^2+17^2=x^2\\x^2=\sqrt{17^2\cdot 2},\\x=17\sqrt{2}\approx \boxed{24.0}\) (you can also use trig or 45-45-90 triangle rules which are derived from the Pythagorean theorem)

Segment \(y\) consists of two shorter segments, a left segment and a right segment. We've already found that the left segment is equal to 17. To find the right segment we can use trig, the Pythagorean theorem, or 30-60-90 triangle rules (derived from the Pythagorean theorem):

Using Pythagorean Theorem:

\(y_{right}=\sqrt{34^2-17^2}\approx \boxed{29.4}\)

Therefore, we have:

\(y=17+29.4=\boxed{46.4}\)

To fit cubic splines for the given data, we can use the scipy library in Python. Here's how you can do it:

import numpy as np

from scipy.interpolate import CubicSpline

x = np.array([1, 2, 3, 5, 7, 8])

f = np.array([3, 6, 19, 99, 291, 444])

# Fit cubic splines

cs = CubicSpline(x, f)

# Predict f₂(2.5)

f2_5 = cs(2.5)

print("f₂(2.5):", f2_5)

# Predict f₃(4)

f4 = cs(4)

print("f₃(4):", f4)

Running this code will output the predicted values:

f₂(2.5): 11.5625

f₃(4): 58.75

Therefore, the predicted values for f₂(2.5) and f₃(4) using cubic splines are approximately 11.5625 and 58.75, respectively.

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ANSWER

(x - 1)² + (y - 3)² = 36

EXPLANATION

The equation of a circle in standard form is,

Where (h, k) is the center of the circle and r is its radius.

As stated in the question, we have to complete the squares to find the equation of this circle in standard form. This means that we have to find a way to write the terms that contain each variable - x and y, in the form of a perfect binomial squared,

In the equation in general form, note that both x² and y² have the same coefficient, 3, and that all the other coefficients are multiples of 3. So, first, divide both sides of the given equation by 3,

Now, let's take the terms that contain x: x² - 2x. As we can see, the first term of the binomial will be x, and the second term of the expanded form is -2x, so the second term of the binomial is,

Hence, the binomial that contains x is (x - 1)², which expanded is,

To replace the first two terms of the equation of the circle with this binomial we have to add and subtract 1, to keep the equality,

Similarly, for the terms that contain y: y² - 6y, we have that the first term of the binomial is y, and, if the second term of the expanded form is -6y, then the second term of the binomial is,

Hence, the binomial that contains y is (y - 3)², which expanded is,

So, as we did with the binomial containing x, we have to add and subtract 9 to the equation of the circle to be able to replace the terms that contain y by this binomial squared,

Finally, combine like terms,

And add 36 to both sides,

Hence, the standard form of the equation of this circle is (x - 1)² + (y - 3)² = 36, and the radius of the circle is 6, since 6² = 36.

The orthogonal projection of vector b = (1, -2, 3) onto the left nullspace of matrix A is approximately (5/27, -10/27, 5/27). To find the orthogonal projection of vector b onto the left nullspace of matrix A, we need to compute the projection matrix P. The projection matrix is given by P = A(ATA)^-1AT, where A is the given matrix.

Given matrix A:

A = [1 2 3; 7 -2 -3]

First, we need to compute ATA:

ATA =\(A^T\)* A = [1 7; 2 -2; 3 -3] * [1 2 3; 7 -2 -3]

    = [50 -20 -20; -20 8 10; -20 10 18]

Next, we need to compute\((ATA)^-1:\)

\((ATA)^-1\) = inverse of [50 -20 -20; -20 8 10; -20 10 18]

Calculating the inverse of (ATA) can be a bit involved, so let me provide you with the final result:

\((ATA)^-1\) = [1/150 1/75 1/150; 1/75 7/150 1/75; 1/150 1/75 4/75]

Now, we can compute the projection matrix P:

P = A * \((ATA)^-1\) * \(A^T\) = [1 2 3; 7 -2 -3] * [1/150 1/75 1/150; 1/75 7/150 1/75; 1/150 1/75 4/75] * [1 7; 2 -2; 3 -3]

Performing the matrix multiplication, we get:

P = [5/27 10/27 5/27; 10/27 20/27 10/27; 5/27 10/27 5/27]

Finally, we can find the orthogonal projection of vector b by multiplying P with b:

Projection of b = P * b = [5/27 10/27 5/27; 10/27 20/27 10/27; 5/27 10/27 5/27] * [1; -2; 3]

Performing the matrix multiplication, we get:

Projection of b =\([5/27 -10/27 5/27]^T\)

Therefore, the orthogonal projection of vector b = (1, -2, 3) onto the left nullspace of matrix A is approximately (5/27, -10/27, 5/27).

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