from 6 positive and 8 negative numbers, 4 numbers are chosen at random (without replacement) and multiplied together. what is the probability that the product is a positive number?

The volume enclosed by the torus rho=4sin(φ) for cylindrical or spherical coordinates is V = 32\(\pi^{2/3}\).

We can use cylindrical coordinates to find the volume enclosed by the torus.

The torus can be defined in cylindrical coordinates as:

ρ = 4sin(φ)

where ρ is the distance from the origin to a point in the torus, and φ is the angle between the positive z-axis and the line connecting the origin to the point.

To find the volume enclosed by the torus, we integrate over ρ, φ, and z. The limits of integration for ρ and φ are 0 to 4 and 0 to 2π, respectively, since the torus extends from the origin to a maximum distance of 4 and wraps around the z-axis.

For z, we integrate from -√(16-ρ²) to √(16-ρ²), which represents the range of z values that lie on the surface of the torus at a given value of ρ and φ.

The integral for the volume of the torus is:

V = ∫∫∫ ρ dz dφ dρ

where the limits of integration are:

0 ≤ ρ ≤ 4

0 ≤ φ ≤ 2π

-√(16-ρ²) ≤ z ≤ √(16-ρ²)

Evaluating this integral gives the volume of the torus as:

V = 32\(\pi^{2/3}\)

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The value of x and y in the algebra (3x - y, 2) = (2, x + y) ​ are 1 and 1 respectively.

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Given the algebra:

(3x - y, 2) = (2, x + y) ​

Therefore, equation:

3x - y = 2        (1)

Also:

x + y = 2        (2)

From both equations, solving simultaneously:

x = 1, y = 1

The value of x and y are 1 and 1 respectively.

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Yes, the tangent constraint can be applied between a line and an arc in many CAD (Computer-Aided Design) software programs.

In CAD, a tangent constraint is a geometric constraint that forces two entities (lines, arcs, circles, etc.) to share a common tangent at their point of contact. When you apply a tangent constraint between a line and an arc, the software will ensure that the line and the arc are always tangent to each other at their point of intersection.

This constraint is useful for designing mechanical components, such as gears or cams, where you need to ensure that the contact between two parts is smooth and continuous. It is also commonly used in architecture, where a building's curved surfaces may need to be tangent to adjacent straight lines or walls.

In short, the tangent constraint can be applied between a line and an arc, and it is a useful tool in many different fields of design.

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Draw the circle with the center at the intersection of the perpendicular bisectors and the radius equal to the distance found in step 4.

When constructing a circle circumscribed about a triangle, the following step is needed:

Identify the three vertices of the triangle.

Let's say the triangle has vertices A, B, and C.

Find the perpendicular bisectors of the triangle's sides.

For each side of the triangle, construct a line that is perpendicular to the side and passes through its midpoint.

Locate the point of intersection of the perpendicular bisectors.

The point where all three perpendicular bisectors intersect is the center of the circumscribed circle.

Measure the distance from the center to any of the triangle's vertices.

This distance is the radius of the circumscribed circle.

By following these steps, you can construct a circle that passes through all three vertices of the triangle. This circle is known as the circumscribed circle or circumcircle of the triangle. It is unique to each triangle and provides a useful geometric property that can be applied in various mathematical and geometric contexts.

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In ABCD a square with four congruent sides and four congruent angles, ΔBAD is congruent to ΔBCD by the ASA rule.

In mathematics, the term "congruent" refers to figures and forms that may be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.

A triangle is a closed polygon with three line segments that intersect at each of its three angles. When the sides and angles of two triangles match, the triangles are said to be congruent. Hence, two triangles may be placed side by side and angle by angle on top of one another.

According to the ASA rule, two triangles are said to be congruent if any two angles and sides included between the angles of one triangle are comparable to the corresponding two angles and sides included between the angles of the second triangle.

In the given figure ABCD is a square.

In ΔBAD and ΔBCD

∠B ≅ ∠B ----Common Angle

∠A ≅ ∠A  ------Each of 90° angle

Side BD ≅ Side BD ----Common Side

So we can say that ΔBAD ≅ ΔBCD -----(ASA rule)

Hence, ΔBAD is congruent to ΔBCD by the ASA rule.

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Answer:

Step-by-step explanation:

from table , we can see that ,

quadratic equation gives same solution for positive and negative numbers .

According to this we can se that option 1 is a quadratic equation

Answer:

23

Step-by-step explanation:

We Know

The sequence (1,3,5,7)

Each time it increases by 2

What is the 12th term in the sequence (1,3,5,7)?

Let's list it out

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,....

So, the 12th term in the sequence is 23.

A proportional (P) controller is used to regulate the position of the carriage x(t) when f(t) = 0, provided that a position sensor with a transfer function H(s) = S + 1 is available.

The transfer function of the plant is given by:

`V(s)/X(s) = 53s^2 + 10.592s + 555`We must first determine the closed-loop transfer function T(s).T(s) = H(s) G(s) / [1 + H(s) G(s)]

where G(s) = KP is the transfer function of the proportional controller.Hence, T(s) = KP (S + 1) / [KP (S + 1) + 53 S^2 + 10.592 S + 555]At s = jω (where j = sqrt(-1)), the magnitude of T(s) is given by:

|T(jω)| = K / √[(ω^4 + 107.184ω^2 + 2915.025) + (KPω^3 + 53ω^2 + 10.592ω + KP) ^2]Let's choose KP such that the system is marginally stable, that is, the closed-loop transfer function T(s) has a unit gain margin, i.e.|T(jω)| = 1, or|T(jω)|^2 = 1

From the above equation, we can calculate the value of KP that produces the unit gain margin for the given system. Substituting the above equation, we get:

KP^2 ω^6 + KPω^3 (53 - 1) + ω^4 + 107.184ω^2 + 2915.025 = 0

We are interested in finding the value of KP such that the root of the above polynomial has a multiplicity of two at s = jω, i.e. it is a double root or pole of the closed-loop system. By setting Δ = b^2 - 4ac = 0, we obtain the quadratic equation in KPω^3,0 = (52)^2 - 4 (1) (ω^4 + 107.184ω^2 + 2915.025)

Therefore, ω = 8.201 rad/sKP = 1.93

From the transfer function of the closed-loop system, we can now find the value of the pole(s).The characteristic polynomial of the closed-loop system is:

P(s) = KP (S + 1) + 53 S^2 + 10.592 S + 555By substituting KP = 1.93 in P(s), we obtain:

P(s) = 1.93 (S + 1) + 53 S^2 + 10.592 S + 555

This can be factored to obtain the poles of the system:

P(s) = (S + 11.18) (S + 0.132)

The poles of the system are -11.18 and -0.132.

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Answer:

X> 3/17

Step-by-step explanation:

6x+ 6/6 > 1/3x + 2

Answer:

B. Since \(\triangle ABC \cong \triangle DEF\) by SSS and \(\triangle DEF \cong \triangle GHJ\) by SAS, \(\triangle ABC \cong \triangle GHJ\) by the Transitive Property of Congruence.

The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS

From the question, we have the following parameters that can be used in our computation:

Triangles = ABC, DEF and GHJ

There are several theorems that make any two triangles to be congruent

One of these theorems is the SSS congruent theorem

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark

AC and GJ

CB and JH

This implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following angles must also be congruent

AB must be congruent to GH

Hence, the congruent statement on the congruency of the triangles is (d)

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The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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Answer:divideing by the whole number

Step-by-step explanation:

Answer:

We set up 2 equations

A) C + A = 100

B) 5C + 12A = 780

We multiply A by -5

A) -5C -5A = -500   then we add B

B) 5C + 12A = 780

7A = 280

Number of Adults = 40

5C = 780 - 40*12

5C = 780 -480

5C = 300

Number of Children = 60

Step-by-step explanation:

The statement about the fraction 4/7 is false because: B. False, because in a fraction, the top number is the numerator and the bottom is the denominator

There are different types of fractions such as:

Mixed Fractions

Proper Fractions

Improper Fractions

Now, we know that when we have a fraction x/y that:

x is the top term and the numerator

y is the bottom term and the denominator

Thus, in the given fraction 4/7, 7 is not the numerator because it is the bottom term which is the denominator.

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Answer:

23.11

Step-by-step explanation:

0.1

The 1 is in the tenths

0.01

The one is in the hundredths

Rounding the 0.109 to the nearest hundredth gives 0.11, from which the 9 is above 5, from which you then round up

The total weight is 18.5 kilograms

Answer:

225 patches

Step-by-step explanation:

Leia cuts congruent triangular patches with an area of 45 square centimeters from a rectangular piece of fabric that is 27 centimeters long and 15 centimeters wide.

Step 1

Find the Area of the rectangular piece of fabric

= Length × Width

= 27 cm × 15 cm

= 405 cm²

Leia cuts congruent triangular patches with an area of 45 square centimeters from a rectangular piece of fabric.

The number of Triangular patches cut =

45 cm² = 1 triangular patch

405 cm² = x triangular patch

Cross Multiply

45 × x = 405

x = 405/45

x = 9 triangular patches

Hence, she can cut 9 triangular patches from 1 rectangular piece of fabric.

Step 2

How many of the patches can Leia cut from 25 pieces of the fabric?

If:

1 piece of fabric = 9 triangular patches

25 pieces of fabric = x

Cross Multiply

x = 25 × 9 triangular patches

x = 225 patches(triangular).

If the Height of Eiffel Tower in Paris is 1063 feet tall and we took an elevator 3/4 up the tower then we would be 797.25 feet from the ground.

Given The height of the Eiffel Tower is 1063 feet tall. We have taken an elevator that is 3/4 up the tower.

Height is the measurement of someone  from head to foot or from base to top. It is the distance upward.

Height of The Eiffel tower is 1063 feet.

We have taken 3/4 up the elevator.

Then the height from ground to us can be calculated by multiplying 1063 by 3/4 which will be as under:

=1063*3/4

=729.25 feet

Hence if the height of the Eiffel Tower is 1063 feet then we would be 729.25 up from the ground if we have taken elevator 3/4 up the tower.

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Answer:

Therefore, the answer to 421 divided by 27 calculated using Long Division is:

15

16 Remainder

Step-by-step explanation:

421 = dividend

27 = divisor

Step 1:

Start by setting it up with the divisor 27 on the left side and the dividend 421 on the right side like this:

 2 7 ⟌ 4 2 1

Step 2:

The divisor (27) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:

       0    

 2 7 ⟌ 4 2 1

Step 3:

Multiply the divisor by the result in the previous step (27 x 0 = 0) and write that answer below the dividend.

       0    

 2 7 ⟌ 4 2 1

      0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.

       0    

 2 7 ⟌ 4 2 1

     - 0    

       4    

Step 5:

Move down the 2nd digit of the dividend (2) like this:

       0    

 2 7 ⟌ 4 2 1

     - 0    

       4 2  

Step 6:

The divisor (27) goes into the bottom number (42), 1 time(s). Therefore, put 1 on top:

       0 1  

 2 7 ⟌ 4 2 1

     - 0    

       4 2  

Step 7:

Multiply the divisor by the result in the previous step (27 x 1 = 27) and write that answer at the bottom:

       0 1  

 2 7 ⟌ 4 2 1

     - 0    

       4 2  

       2 7  

Step 8:

Subtract the result in the previous step from the number written above it. (42 - 27 = 15) and write the answer at the bottom.

       0 1  

 2 7 ⟌ 4 2 1

     - 0    

       4 2  

     - 2 7  

       1 5  

Step 9:

Move down the last digit of the dividend (1) like this:

       0 1  

 2 7 ⟌ 4 2 1

     - 0    

       4 2  

     - 2 7  

       1 5 1

Step 10:

The divisor (27) goes into the bottom number (151), 5 time(s). Therefore put 5 on top:

       0 1 5

 2 7 ⟌ 4 2 1

     - 0    

       4 2  

     - 2 7  

       1 5 1

Step 11:

Multiply the divisor by the result in the previous step (27 x 5 = 135) and write the answer at the bottom:

       0 1 5

 2 7 ⟌ 4 2 1

     - 0    

       4 2  

     - 2 7  

       1 5 1

       1 3 5

Step 12:

Subtract the result in the previous step from the number written above it. (151 - 135 = 16) and write the answer at the bottom.

       0 1 5

 2 7 ⟌ 4 2 1

     - 0    

       4 2  

     - 2 7  

       1 5 1

     - 1 3 5

         1 6

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 421 divided by 27 calculated using Long Division is:

15

16 Remainder

More Information

If you enter 421 divided by 27 into a calculator, you will get:

15.5926

Answer:

1. 1/2

2. 1/5

Step-by-step explanation:

I used a calculator!

Answer:

1.3/6 or 1/2

2.1/5

Step-by-step explanation:

Just write that out, thats all the steps there is, 3/6 simplifies to 1/2 because they're equivalent

Answer:2301

Step-by-step explanation:

do 64 x 36 then subtract by 3

To find the measure of angle R in triangle PQR, subtract the measure of angle P from 180 degrees, giving an approximate measure of 127 degrees, which is closest to 42 degrees.

To find the measure of angle R in triangle PQR, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Given that angle P (m P) is 53 degrees, we can use the angle sum property to find angle R.

First, let's find the measure of angle Q:

m Q = 180 - m P - m R

m Q = 180 - 53 - m R

m Q = 127 - m R

Since PQ and PR are sides of the triangle, we can apply the Law of Cosines to find the measure of angle Q:

PQ² = QR² + PR² - 2(QR)(PR)cos Q

(7.4)² = QR² + (9.6)² - 2(QR)(9.6)cos Q

54.76 = QR² + 92.16 - 19.2QRcos Q

Now, we can substitute m Q with 127 - m R:

54.76 = QR² + 92.16 - 19.2QRcos (127 - m R)

Next, we can solve for QR using the given side lengths and simplify the equation:

QR² - 19.2QRcos (127 - m R) + 37.4 = 0

To find the measure of angle R, we need to solve this quadratic equation.

However, it seems that there may be an error or omission in the given information or calculations, as the provided side lengths and angle measures do not appear to be consistent.

Therefore, without additional information or clarification, it is not possible to determine the exact measure of angle R.

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9514 1404 393

Answer:

  p = 20

Step-by-step explanation:

Collecting terms gives ...

  (4/5 -3/5)p - 4 = 0

  1/5p - 4 = 0

Multiplying by 5, we get ...

  p - 20 = 0

Then, adding 20 gives the solution:

  p = 20

Answer:

a(n) = 10+5(n - 1)

Step-by-step explanation:

This is an arithmetic sequence with first term 10 and common difference 5.  The general formula for a(n) is:

a(n) = 10+5(n - 1)

Answer:

43

Step-by-step explanation:

Substitute x = 3 into the expression, that is

5(3)² - 2 = 5(9) - 2 = 45 - 2 = 43

Answer:

It's B

Step-by-step explanation:

Given that we have the graph of f(x), we want to see which one is the graph of its inverse. i just had that question and i got a 100 on it

Answer: 32 + 18 + 4 + 30 = 8432+30=6262+18=8080+4=84

Step-by-step explanation: i did this question before so i dont know if you can understand it but i got it correct last week