a computer programming team has 17 members. (a) how many ways can a group of nine be chosen to work on a project? as in example 9.5.4, since the set of people in a group is a subset of the set of people on the team, the answer is 24310 correct: your answer is correct. . (b) suppose nine team members are women and eight are men. (i) how many groups of nine can be chosen that contain five women and four men?

Answer:

I)3^4 x 3^7=3^4+7(b/c the base is similar)

3^4 x 3^7=3^11

Ii) first 3^4=3x3x3x3=81

3^7=2187

then 81 x 2187=177147

The dimensions of the rectangle will be 16 inches long and 7 inches wide,

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 112 square inches. Then the equations are given as,

LW = 112           ...1

L = 2W + 2       ...2

From equations 1 and 2, then we have

(2W + 2)W = 112

2W² + 2W - 112 = 0

W² + W - 56 = 0

W² + 8W - 7W - 56 = 0

W(W + 8) - 7(W + 7) = 0

(W + 8)(W - 7) = 0

W = 7, -8

Neglect - 8 because of negative signs. Then the length is given as,

L = 2 x 7 + 2

L = 14 + 2

L = 16

The dimensions of the rectangle will be 16 inches long and 7 inches wide,

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The truth value of proposition 2a, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], given that a and b are true and x and y are false, is TRUE.

In the provided scenario where a and b are true while x and y are false, proposition 2a, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], is evaluated to be true. Let's break it down to understand why.

The proposition is in the form of an implication (⊃), where the antecedent is [(x ⊃ a) • (b ⊃ ∼ y)] and the consequent is [(b ∨ y) • (a ⊃ x)]. To determine the true value, we need to examine both the antecedent and the consequent.

In the antecedent, we have two conditions connected by a conjunction (∧): (x ⊃ a) and (b ⊃ ∼ y). Since x and y are false, the condition (x ⊃ a) is vacuously true because false implies anything. Similarly, (b ⊃ ∼ y) is also true because b is true, and ∼ y (not y) is true since y is false. Therefore, the antecedent is true.

Moving on to the consequent, we have two conditions connected by a conjunction (∧): (b ∨ y) and (a ⊃ x). In this case, b is true, so (b ∨ y) is true regardless of the truth value of y. Additionally, a is true, and since x is false, (a ⊃ x) is false. Therefore, the consequence is false.

Now, when we evaluate the entire proposition, [(x ⊃ a) • (b ⊃ ∼ y)] ⊃ [(b ∨ y) • (a ⊃ x)], we find that a true antecedent implies a false consequent, which results in a true overall proposition. Hence, the truth value of proposition 2a is TRUE in the given scenario.

In conclusion, proposition 2a holds true when a and b are true, and x and y are false. Understanding the evaluation of logical propositions like these can help in reasoning and problem-solving tasks.

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The concept that a message gives different meanings to different objects is called option (b) polymorphism.

Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.

This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.

Therefore, the correct option is (b) polymorphism

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Answer:

\(\dfrac{3}{10}\)

Step-by-step explanation:

Length of an arc\(=\dfrac{\theta}{2\pi}X 2\pi r=\theta r\)

If the central angle of the arc is \(\dfrac{3\pi}{5}\)

Length of an arc\(=\dfrac{3\pi r}{5}\)

Therefore:

Ratio of the length of the arc to the circumference

\(=\dfrac{3\pi r}{5}:2\pi r\\=\dfrac{3\pi r}{5*2\pi r}\\=\dfrac{3}{10}\)

Therefore, the arc is \(\dfrac{3}{10}\) of the circumference is this arc.

Answer: 3 /10

Step-by-step explanation: Khan Academy

Answer:

x = 5

Step-by-step explanation:

Given

\(\frac{20}{16}\) = \(\frac{x}{4}\) ( cross- multiply )

16x = 80 ( divide both sides by 16 )

x = 5

Answer:

add

Step-by-step explanation:

because adddffffycy8gc

Answer:

refer pic

sorry for messy handwriting

hope it help u and i appreciate if you give brainliests, thanks

Answer:

question 2 answer. option. a. 55

Step-by-step explanation:

diameter of semi circular window is 35 inches

the radius is 17.5

perimeter of semicircular window =pie x radius

= 22 /7 ×17.5

=55 inches

Answer:

B)

Step-by-step explanation:

Answer:

My name jeff

Step-by-step explanation:

Hi mi nombre jeff

To find the 90% confidence interval of the mean, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error) First, we calculate the sample mean:

Sample Mean = (12.23 + 16.56 + 4.39 + ... + 12.24 + 2.76) / 30 Next, we calculate the standard deviation: Then, we calculate the standard error:

Standard Error = Standard Deviation / √n

where n is the sample size. Next, we find the critical value corresponding to a 90% confidence level. Since the sample size is small (n = 30), we use a t-distribution and degrees of freedom equal to (n - 1). Finally, we substitute the values into the confidence interval formula to find the lower and upper bounds of the interval. The specific numerical calculations are necessary to provide the exact confidence interval values.

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Answer:

y = -2/3x + 2

Step-by-step explanation:

Hey there!

Well since we already got the y-intercept to find slope we'll use the points,

(3,0) and (0,2).

Formula: \(\frac{y^2 - y^1}{x^2 - x^1}\)

Plug in the given points,

\(\frac{2 - 0}{0 - 3}\)

Slope = -2/3

Slope-intercept: y = -2/3x + 2

Hope this helps :)

Answer:

y = -2/3x + 2  or

2x + 3y  = 6   (standard form).

Step-by-step explanation:

I am assuming you want the equation of the straight line that passes through these 2 points.

The 2 points are (3, 0 ) and (0, 2).

The slope of the line =  (2 - 0) / (0 - 3)

= -2/3.

The equation is y = -2/3x + 2  ( as 2 is the y-intercept).

In standard form this is :

3y = -2x + 6

2x + 3y  = 6.

Answer:

A circle of radius = 7 or diameter = 14 or circumference = 43.98 kilometers has an area of: 153.9 square kilometers (km²) 1.539 × 10 8 square meters (m²)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

\( \frac{70 - 35.24}{8.69} \)

\( \frac{34.76}{8.69} \)

\( = 4\)

Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.

A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test  we can find the mean difference between pairs of measurements is zero or not. So  paired t-test is used, when data is in the form of matched pairs

Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

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Answer:

(2,0) is not a point on the graph of the function y=x+2

Step-by-step explanation:

Go to the TI-84 plus calculator and go to the y= button and then type in x+2 and then press the 2nd button and then the graph button and then you should get your answer.

Simplification of ( 11/24) - ( 1/4) is 5/24 after finding its lowest common multiple.

As given in the question,

Given expression is ( 11/24) - ( 1/4)

Find the lowest common multiple (L.C.M) of the denominators 24, and 4

L.C.M of ( 24 , 4 ) = 24

Equivalent fractions are:

( 11 /24 ) × ( 1 /1 )  =  11 / 24

( 1 / 4 ) × ( 6 / 6 ) = 6 / 24

Simplify by subtracting 6 / 24 from 11 / 24 we get,

( 11 / 24 ) - ( 6 / 24 )

= ( 11 - 6 ) / 24

= 5 / 24

Therefore, the simplified form of the expression ( 11/24) - ( 1/4) is equal to 5 /24.

The complete question is:

Find the lowest common denominator (multiple) of ( 11/24) - ( 1/4). Type the equivalent fractions. Then, add or subtract. Simplify your answer.

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Answer:

18.9 cm

Step-by-step explanation:

Pythagorean Theorem --> A² + B² = C²

2² + B² = 19²

4 + B² = 361

B² = 357

√357 --> 18.89 --> 18.9

The measure of the other leg to the nearest tenth will be 18.9 centimeters.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The hypotenuse of a right triangle measures 19 cm and one of its legs measures 2 cm.

Let the other leg be 'x'. Then the measure of the other leg will be given as,

19² = x² + 2²

361 = x² + 4

x² = 361 - 4

x² = 357

Take square root on both sides, then we have

x = √357

x = 18.8944

x ≈ 18.9 cm

The measure of the other leg to the nearest tenth will be 18.9 centimeters.

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The area of the region inside the cardioid and outside the circle is 3π/2 square units.

The area of the region inside the cardioid r=1+cosθ and outside the circle r=3cosθ using a double integral, follow these steps:

1. Determine the bounds of integration for θ: Find where the cardioid and circle intersect by setting r equal for both equations: (1+cosθ) = 3cosθ. Solve for θ, which results in θ = 0 and θ = π.

2. Set up the double integral: The area of the region can be found using the double integral of the difference between the two polar functions with respect to r and θ: Area = ∬(1+cosθ - 3cosθ) rdrdθ.

3. Determine the bounds of integration for r: The lower bound for r is the circle r=3cosθ, and the upper bound is the cardioid r=1+cosθ.

4. Integrate with respect to r: ∫[∫(1+cosθ - 3cosθ) rdr]dθ from r=3cosθ to r=1+cosθ. This results in: [1/2(r^2)] evaluated from r=3cosθ to r=1+cosθ.

5. Plug in the limits of integration for r: [(1/2)((1+cosθ)^2) - (1/2)(3cosθ)^2]dθ.

6. Integrate with respect to θ: ∫[(1/2)((1+cosθ)^2) - (1/2)(3cosθ)^2] dθ from θ=0 to θ=π.

7. Evaluate the integral: After integrating and evaluating the limits, you will find that the area of the region inside the cardioid and outside the circle is 3π/2 square units.

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Answer:

80

Step-by-step explanation:

area is length × width. 8 × 10 = 80

A circle is a curve sketched out by a point moving in a plane. The area of the circular paper is more than the area of the square.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The arc length of radius 6 inches is equal to,

Length of the Arc of a quarter = 2πr×(1/4) = 2×π×6×0.25 =0.9448 inches

The area of the circular paper = πr² = π×6×6 = 113.097²

The area of the square with a side of 6 inches = 36 in²

Therefore, the area of the circular paper is more than the area of the square.

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The equation for the asymptote of the graphed function is x = 7

The asymptote is a endlessly tendency to a given value. A vertical one is a tendency to infinity.

Here we can see that there is a vertical asymoptote, notice that in one end the function tends to positive infinity and in the other it tends to negative infinity.

The equation of the line where the asymptote is, is:

x = 7

So that is the answer.

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Answer:

See below

Step-by-step explanation:

3 (x^2 + 3x) = 4

3 ( x + 3/2)^2   = 4 + 27/4  

Answer:

I believe it is four dollars

The answer is , the given geometric series converges, and its sum is -1/2.

Let's consider the given geometric series: 2 +10+50 +250 + ...

To determine whether the given geometric series converges or diverges,

let's first identify the ratio between successive terms of the series.

So, we have:

a1 = 2r = (10/2) = 5a2 = 10r = (50/10) = 5a3 = 50r = (250/50) = 5...

Let's generalize the above sequence:

a1, a2, a3, ...ar, ar², ar³, ...

where a1 = 2 and r = 5.

On analyzing the above sequence, we can observe that the ratio between the successive terms is a constant, which is 5.

Therefore, the given series is a Geometric Series with a common ratio of 5, and the series can be expressed as:

S∞ = a1/(1 - r)

where S∞ represents the sum of an infinite geometric series.

Hence, the series converges, and its sum can be determined using the formula for the sum of an infinite geometric series.

So, substituting the values of a1 and r in the above formula:

S∞ = 2/(1 - 5) = -1/2

Therefore, the given geometric series converges, and its sum is -1/2.

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Determine if a geometric series converges or diverges given it in Section 10.2: Infinite Series. the geometric series below diverges.

In such case, calculate its total. 2 + 10 + 50 + 250 + ...

The formula S = a / (1 - r) may be used to get the sum of a geometric series with initial term "a" and common ratio "r" when |r| 1.above a = 2 and r = 10/2 = 5, the above geometric series diverges as |r| > 1. As a result, its amount is unknown. The geometric series below diverges as a result. If the series converged, we would need to use the formula S = a / (1 - r) t Given a geometric series, Infinite Series determine if it converges of diverges.

If it converges, then find its sum. 2 + 10 + 50 + 250 + ...The sum of a geometric series with first term 'a' and common ratio 'r' can be calculated by using the formula S = a / (1 - r) , when |r| < 1

In this case, a = 2 and r = 10/2 = 5As |r| > 1, the given geometric series diverges. Hence, its sum is undefined.

Therefore, the geometric series below diverges.

If the series converged, we would have to find its sum by using the formula S = a / (1 - r).

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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