What is the quotient of (x3 6x2 11x 6) ÷ (x2 4x 3)?

Answer: volume of the cylinder = 1583.36 ft3

Step-by-step explanation: where volume of a cylinder = π h

where h = 14 ft

diameter 12 ft, so radius = 12 / 2 = 6 ft

therefore volume = π * * 14 = 1583.362697 to the nearest tenths place will be 1583.36

The probability that this person has an IQ greater than 95 =62.93%

The area of mathematics known as probability is concerned with the outcomes of random events. Probability refers to a chance or potential for something to happen. It explains the likelihood that a specific event will take place.

We frequently say things like, "It will probably rain today," "He will probably pass the test, "There is very little chance of getting a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for all of the words chance, doubt, maybe, likely, etc. in these sentences.

In essence, probability is the ability to forecast an outcome based on the variety and quantity of potential outcomes or the analysis of historical data.

Let X be the IQ

IQ is normally distributed with a mean of 100 and a standard deviation of 15.

a) the probability that this person has an IQ greater than 95

=62.93%

b) the probability that this person has an IQ less than 125

=4.75%

c) Sample size =500

No of people = 0.2486(500) =124.3

d)

No of persons = 0.0047(500) = 2.35

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Answer:

(5,1)

Step-by-step explanation:

The growth rate of bacteria in a culture is not specified, so assuming it is exponential, the number of bacteria present after 2 hours will be approximately 1.8 x 10^8.

To solve this problem, we can use the exponential growth formula: N(t) = N0 * e^(rt), where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, r is the growth rate, and e is the base of the natural logarithm. First, we need to find the growth rate, r. We can use the initial and final number of bacteria and the time interval to do this.

N(t) = N0 * e^(rt)

171 = 38 * e^(49r)

ln(171/38) = 49r

r = ln(171/38)/49

r ≈ 0.069 Now we can use the formula to find N(120) (i.e., the number of bacteria after 2 hours, or 120 minutes):

N(120) = 38 * e^(0.069 * 120)

N(120) ≈ 1.8 x 10^8 Therefore, approximately 1.8 x 10^8 bacteria will be present in the culture after 2 hours.

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Answer:

79/96

Step-by-step explanation:

Answer:

Step-by-step explanation:

b is an inscribed angle. The rule for this is that the measure of an inscribed angle is half the measure of the arc it intercepts. The arc it intercepts is 56 degrees, so the measure of angle b is half of that at 28

Answer: 36, 64, 225

Step-by-step explanation:

6^2 is 6 multiplied by 6. Same goes for any number. 467^2 is 467x467.

I hope you found my answer helpful! If you have any other questions you can ask me :) If you ended up finding it helpful give it a thanks! Maybe even a brainliest if you feel like it ;D

Answer:

150

Step-by-step explanation:

Answer:

first one is 11,150

second one is 8,995

Third one is 21,213

The fourth one is 10.29

The last one is 4158

Step-by-step explanation:

Step-by-step explanation:

mass(m)= 3kg

height(h)= 2m

gravity(g)= 9.8 m/s^2

P.E.= mgh

=3*2*9.8

=58.8 Joule

Answer:

58.84 Joules

Step-by-step explanation:

3(Mass)*2(Height)*9.8=58.84J

Answer:

3 x 4 x 5 is 60

so the answe would be 60 cm^3

Step-by-step explanation:

The ultimate change in the price of rice is a decrease of Rs 3 per kilogram.

To determine the ultimate change in the price of rice, we need to calculate the net change over the two weeks.

In the first week, the price of rice rose by Rs 10 per kilogram.

In the next week, the price fell by Rs 13 per kilogram.

To find the net change, we subtract the decrease from the increase:

Net change = Increase - Decrease

Net change = Rs 10 - Rs 13

Net change = -Rs 3

Therefore, the ultimate change in the price of rice is a decrease of Rs 3 per kilogram.

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Answer:

x = 6

Step-by-step explanation:

sin 30° = 3/x

0.5 = 3/x

.5x = 3

x = 3/.5

x = 6

The indicated side of the right-angled triangle is 6.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

Given:

The triangle is a right-angled triangle.

So, we know,

SinФ = perpendicular / hypotenuse.

And here, perpendicular = 3 unit

And hypotenuse = x unit

Substituting the values,

Sin30° = 3/x

1/2 = 3/x

x = 6

Therefore, the value of x is 6.

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Answer: And the answer is b 6,7

Step-by-step explanation:

Did you meant “Please help me on this question if you would want brainliest!! Thank you!!”

Answer:

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Let the cost price of the camera be x.

When the selling price is 60000 there is a loss of 20%. Let's show this as equation and find the cost price:

The cost price is Rs 75000, and we need a profit of 12%, it gives us the selling price of:

The linear relationship represented by the table is proportional.

Proportional relationships are relationships between two variables where their ratios are equivalent.

In other words, proportional relationship is one in which two quantities vary directly with each other. Proportional relationship can be represented as follows:

y ∝ x

y = kx

where

Therefore, let's check if the relationship between the ounces and cost is proportional.

0.7 = 2k

k = 0.7 / 2

k  = 0.35

y = 0.35 × 4 = 1.4

y = 0.35 × 6 = 2.1

y = 0.35 × 8 = 2.80

Therefore, the relationship is proportional

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A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.

You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).

Given,

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.

Let s represent the truck's speed and (s+20) represent the car's speed.

to determine each vehicle's time

Time = Speed / Distance

truck time = 350/s

Time in an automobile is 350/(s+20)

Truck time - car time = 2 hours

So,

(350/s) - [350/(s+20)] = 2

LCM is s(s+20)

[350(s+20) - 350s]/s(s+20) = 2

Cross multiplying,

350(s+20) - 350s = 2s(s+20)

Simplifying the equation,

350s + 7000 - 350s = 2s² + 40s

Now, we have quadratic equation to simplify,

2s² + 40s - 7000 = 0

Dividing the equation by 2

s² + 20s - 3500 = 0

Factorizing,

s= 50

s= -70 (impossible because of the sign)

Hence the truck's speed is s = 50 km/h.

The speed of the car is s + 20 = 70 km/h.

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There are 1820 different groups of applicants for 4 management trainee positions, 126 different groups of trainees consisting entirely of women, and a 0.0692 probability that the trainee class will consist entirely of women.

The number of different groups of applicants that can be selected for the four management trainee positions can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of applicants (16 in this case) and r is the number of positions to be filled (4 in this case).

So the number of different groups of applicants that can be selected is:

16C4 = 1820

Therefore, there are 1820 different groups of applicants that can be selected for the four management trainee positions.

The number of different groups of trainees that would consist entirely of women can be calculated using the combination formula again, but this time we are selecting all 4 positions from the 9 female applicants:

9C4 = 126

Therefore, there are 126 different groups of trainees that would consist entirely of women.

Assuming that all groups of four are equally likely to be selected, the probability that the trainee class will consist entirely of women can be calculated by dividing the number of different groups of trainees that consist entirely of women (126) by the total number of different groups of applicants (1820):

Probability = 126 / 1820 = 0.0692

So the probability that the trainee class will consist entirely of women is 0.0692 (rounded to four decimal places).

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The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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The interior of a regular 6-sided polygon, that is a hexagon is 120 degrees. Therefore, the correct option is option (a) 120 degrees.

The sum of the interior angles of a polygon with n sides is given by the formula:

Sum of interior angles = (n-2) x 180 degrees

For a regular polygon, all the interior angles have the same measure.

So, for a regular 6-sided polygon (hexagon), we have:

Sum of interior angles = (6-2) x 180 degrees = 4 x 180 degrees = 720 degrees

To find the measure of each interior angle, we divide the sum of interior angles by the number of sides:

Measure of each interior angle = Sum of interior angles / Number of sides

Measure of each interior angle = 720 degrees / 6 = 120 degrees

Therefore, the interior angle of a hexagon is 120 degrees.

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For given number 100

the exponent form = 10²

the word form = One Hundred

For given question,

The area of a closet is 100 square feet.

We need to write the number in exponent form and word form.

First we write given number in exponent form

⇒ 100 = 10 × 10

⇒ 100 = 10²

So, the exponent form given number 100 is 10²

And the word form of given number is : One Hundred

Therefore, for given number 100

the exponent form = 10²

the word form = One Hundred

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Observe the diagram

So triangle is isosceles

So

We know that:

The triangle is an isosceles triangle because if we look at the triangle carefully, we can tell that OP and QP are equivalent.

This means that:

Now, let's substitute the measure of QP in the equation to find the measure of OP.

Substituting the measure of QP.

OP = QP ⇒ OP = 15 units

Note: OP is same as PO. It does not make a difference.

If the area and perimeter of a right triangle are 30 cm² and 30 cm, respectively, the length of the hypotenuse is 13 cm.

Given that, the area of the right-angled triangle is 30 cm² and the perimeter is 30 cm.

Let a, b, and c be the lengths of the sides and assume that c is the hypotenuse.

Area = 30 cm²

1/2×a×b = 30

ab = 60.

Perimeter = 30 cm

Perimeter is the sum of the sides of the triangle.

a + b + c = 30.

a + b = 30 - c

Squaring on both sides

a²+b²+2ab = 900+c²-60c

In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the adjacent side and the opposite side.

So, a²+b²=c²

c²+2ab = 900 + c²-60c

c²+120 = 900+c²-60c    [we know that ab=60]

Subtracting c² on both sides.

60c = 780

c = 13.

Therefore, the length of the hypotenuse is 13 cm.

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Answer:

0.57142857142

Step-by-step explanation:

Use a calculator.

Answer:

7. the slope of the line containing the points (3, 4) and (2, 6) is -2.

8. the slope of the line containing the points (-2, -1) and (2, -3) is -1/2.

Step-by-step explanation:

7. To find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6), we first need to find the slope of the line through those two points using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (3, 4) and (x2, y2) = (2, 6). Substituting these values into the formula, we get:

m = (6 - 4) / (2 - 3) = -2

So the slope of the line containing the points (3, 4) and (2, 6) is -2. Since we are looking for a line that is parallel to this line, the slope of the parallel line will also be -2. Therefore, the answer is m = -2.

8. To find the slope of a line that is perpendicular to the line containing the points (-2, -1) and (2, -3), we first need to find the slope of the line through those two points using the same formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-2, -1) and (x2, y2) = (2, -3). Substituting these values into the formula, we get:

m = (-3 - (-1)) / (2 - (-2)) = -2 / 4 = -1/2

So the slope of the line containing the points (-2, -1) and (2, -3) is -1/2. To find the slope of a line that is perpendicular to this line, we need to take the negative reciprocal of -1/2, which is 2/1 or simply 2. Therefore, the answer is m = 2.

The phase diagrams provide a visual representation of the system's behavior by plotting the vector field and trajectories in the x-y plane.

The given system of differential equations is described by:

\(˙x = a - x^2˙y = x - y\)

To find the equilibria, we set ˙x and ˙y equal to zero:

\(a - x^2 = 0 -- > x^2 = a -- > x = ±√ax - y = 0 -- > y = x\)

So, the equilibria are (±√a, ±√a).

Now let's analyze the behavior of the system for different values of 'a'.

For a > 0:

In this case, there are two real equilibria, (√a, √a) and (-√a, -√a). We can observe that (√a, √a) is a stable node, as the eigenvalues of the linearized system around this point have negative real parts. On the other hand, (-√a, -√a) is a saddle point, as the eigenvalues have opposite signs (one positive and one negative).

For a < 0:

In this case, there are no real equilibria since √a and -√a are imaginary. Therefore, the system has no equilibrium points.

To visualize the phase diagrams for a = 1 and a = -1:

For a = 1:

The system has two real equilibria, (1, 1) and (-1, -1). The point (1, 1) is a stable node, and (-1, -1) is a saddle point. The phase diagram would show trajectories converging towards (1, 1).

For a = -1:

Since a < 0, there are no equilibrium points, and thus the phase diagram would show no fixed points or trajectories.

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The conjecture "A square number is either measurable by 4 or will be after the removal of a unit" is true. If a number is a perfect square, it can be expressed as either 4k or 4k+1 for some integer k.

However, if 4 is replaced by 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3.

To prove the conjecture that a square number is either divisible by 4 or will be after subtracting 1, we can consider two cases:

Case 1: Let's assume the square number is of the form 4k. In this case, the number is divisible by 4.

Case 2: Let's assume the square number is of the form 4k+1. In this case, if we subtract 1, we get 4k, which is divisible by 4.

Therefore, in both cases, the conjecture holds true.

However, if we replace 4 with 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3. For example, consider the square of 5, which is 25. This number is not divisible by 3. Similarly, the square of 2 is 4, which is also not divisible by 3. Hence, the conjecture does not hold when 4 is replaced by 3.

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Answer: B

Step-by-step explanation: