there are 7 people from the computer science (cs) department and 5 people from the math (m) department that could serve on a 4-person committee. a. find the number of different combinations if there are no restrictions on whom could serve on the committee. b. find the probability that the only people serving on the committee are from the cs department.

The Volume of Each Shape is Shown below.

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m³, cm³, in³ etc.

Given:

1. r = 6 inch, height = 6 inch

So, Volume of Cone = 1/3 πr²h

                                  = 1/3 x 3.14 x 6 x 6 x 6

                                   = 226.08 inch³

2. diameter = 6cm

r = 3 cm,

so, volume of each piece

= 4/3 πr³

= 4/3 x 3.14 x 3 x 3 x 3

= 113 cm³

now, volume of 20 candies

= 20 x 113

=  2260 cm³ of chocolate.

3. The height of the cone shape, h = 84 inches

radius = 8 inches

The cost per cubic inch is $2.25.

The cost of nickel for the sculpture is given by

= 2.25 x 1/3πr²h

= 2.25 x 1/3 x 3.14 x 8 x 8 x 84

= $12660.48.

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S = {(t, 1, 1), (1, 0, 1), (1, 1, 3t)} is linearly independent of t.

Therefore the answer is b) S = {(t, 1, 1), (1, 0, 1), (1, 1, 3t)}.

(a) S is linearly independent for all values of t if the following equation has a non-trivial solution:

a(t, 1, 1) + b(1, t, 1) + c(1, 1, t) = (0, 0, 0).

Expanding this equation, we get:

at + b + c = 0

a + bt + c = 0

a + b + ct = 0.

Solving this system of linear equations, we find that a = b = c = 0. This implies that any linear combination of the vectors in S results in the zero vector, so S is linearly dependent for all values of t.

(b) S is linearly independent if the following equation has a non-trivial solution:

a(t, 1, 1) + b(1, 0, 1) + c(1, 1, 3t) = (0, 0, 0).

Expanding this equation, we get:

at + b + 3ct = 0

b = 0

a + c = 0.

Since a and c cannot both be zero, this system has no trivial solution, which means that S is linearly independent for all values of t.

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One square mile contains 640 acres. 640 acres in a square mile.

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The surface area of square pyramid is 207.04 square inches.

Surface area is the area of all outer facing surfaces on an object. The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object.

The formula to find the surface area of square pyramid is A=a²+2a√(a²/4+h²)

Here, a=8 inches and h=8 inches

Now, A= a²+2a√(a²/4+h²)

A= a²+2a√(a²/4+h²)

A= 8²+2×8√(8²/4+8²)

A= 64+16√(16+64)

A= 64+16√80

A= 64+16×8.94

A= 207.04 square inches

Therefore, the surface area of square pyramid is 207.04 square inches.

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A. The circular base of the bucket is larger.

B. The bale has a larger volume.

A. The circular base of the bucket has a larger area than the rectangular base of the bale.

The formula for the area of a circle is π * r^2, where r is the radius. The diameter of the bucket is 3 feet, so the radius is 3/2 feet. The area of the circular base is therefore π * (3/2)^2 = 7.07 square feet.

The rectangular base of the bale has length 2 feet and width 3 feet, so its area is 2 * 3 = 6 square feet.

Since 7.07 > 6, the circular base of the bucket is larger.

B. The bale has a larger volume than the bucket.

The formula for the volume of a rectangular prism is l * w * h, where l is the length, w is the width, and h is the height. The bale has length 2 feet, width 3 feet, and height 5 feet, so its volume is 2 * 3 * 5 = 30 cubic feet.

The formula for the volume of a cylinder is π * r^2 * h, where r is the radius and h is the height. The radius of the bucket is 3/2 feet and the height is 5 feet, so the volume of the bucket is π * (3/2)^2 * 5 = 22.36 cubic feet.

Since 30 > 22.36, the bale has a larger volume.

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The complete question goes thus:

At a farm, animals are fed bales of hay and buckets of gain.Each bale of hay is in the shape of a rectangular prism.The base side lengths 2 feet and 3 feet,and the height is 5 feet. Each bucket of grain is a cylinder with diameter of 3 feet. The height of the bucket is 5 feet as the height of bale. A. Which is larger in area, the rectangular base of the bale or the circular base of the bucket? Explain how you know B. Which is larger in volume, the bale or the bucket? Explain how you know

Probability determines the likelihood of an event occurring: P(A) = f / N

P(A) = f / N indicates the likelihood of an event occuring. Odds and probability are connected, but odds are affected by probability. Before calculating the chances of an event occurring, you must first calculate probability.

Finding the chance of a simple event occurring is simple: add the probabilities together. For instance, if you have a 10% chance of winning $10 and a 25% chance of winning $20, your total chances of winning are 10% + 25% = 35%. According to probability, heads have a 12 chance, thus we may expect 50 heads. But when we attempt it, we could get 48 heads, or 55 heads, or anything else, but in most circumstances, we’ll get something close to 50.

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To find the width of Wyoming, we need to find the area of the state and divide by the width.

Area = population density x total population

Area = 2.16 x 564,000 people

Area = 1,222,624 square kilometers

Width = Area / Length

We don't have the length, so we'll have to rearrange the formula to solve for it:

Width = Area / Length

Length = Area / Width

Length = 1,222,624 square kilometers / Width

We'll solve for width:

Width = 1,222,624 square kilometers / Length

Since we don't know the length, we cannot solve for width.

The limit as h→0 of f(x+h) − f(x) / h is 0. the denominator of the fraction is 0, the limit is undefined.

To evaluate this limit, we need to plug in the given value for x and the function f(x). We are given that f(x) = x2 and x = 3.

Therefore, we have:

limh→0 f(3+h)−f(3) h

Since f(3) = 3^2 = 9, we can rewrite the limit as:

limh→0 f(3+h)−9

We can now plug in the value of h=0 to get the value of the limit:

limh→0 f(3+0)−9 0

Since the denominator of the fraction is 0, the limit is undefined.

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The ratio of their volumes is 3: 1

If two solids are identical, their volume ratio is equal to the cube of their corresponding side ratio. (It should be noted that volume is a 3-D measurement, not a “length” measurement. When the base and height of a pyramid and a prism are the same, their volumes are always in the ratio of 1:3Volume of prism.

A triangular prism and a triangular pyramid with identical bases and heights with the volume of the prism being three times that of the pyramid. Students should use manipulatives such as water, rice, or beans to physically represent this connection.

The volume of a prism =Base Area× Height and Volume of Pyramid = 1/3 × base area × Height

Given:

Height of both pyramid and a prism is 8.2 cm.

Area of base is 22.3 cm cube.

Volume of Prism = 22.3 × 8.2

Volume of Pyramid = 1/3 × 22.3 × 8.2

Ratio of volume of prism and volume of pyramid = (22.3 × 8.2) : 1/3 × (22.3 × 8.2)

Ratio of volume of prism and volume of pyramid = 1: 1/3

Ratio of volume of prism and volume of pyramid = 3: 1

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Step-by-step explanation:

3/4*7.5

5.625

7.5-5.625

1.875

of blue pints

The pair of variables with an inverse relationship is y = 1/x. This relationship can be seen by graphing the two variables on a coordinate plane and observing the shape of the graph.

As x increases, y decreases and as x decreases, y increases. This is because the equation y = 1/x can be written as y = c/x, where c is a constant. Since c is a constant, as the value of x increases, the value of y decreases, and vice versa.

For example, if x = 4, then y = 1/4, or 0.25. If x increases to 8, then y decreases to 1/8, or 0.125. On the other hand, if x decreases to 2, then y increases to 1/2, or 0.5. As can be seen, as x increases, y decreases, and as x decreases, y increases, which shows the inverse relationship between the two variables.

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The area bounded by the given curve is =4.44.

There are several ways to calculate the area under the curve, but the antiderivative approach is the most widely used. Knowing the curve's equation, its bounds, and its enclosing axis will allow you to determine the area under the curve. In general, there are formulas for calculating the areas of standard shapes like squares, rectangles, quadrilaterals, polygons, and circles, but there isn't one specifically designated for calculating the area beneath curves. The integration method aids in equation solution and area determination.

The antiderivative methods are highly useful for locating the regions of irregular plane surfaces. In this lesson, we'll learn how to calculate the curve's area under the axis.

the area of the region that is bounded above by the curve f(x)=(x- 9)2 and the line g(x)=x−7.

The area enclosed by the curves is-

[tex]A=\int_a^b[{f(x)-g(x)]dx[/tex]

[tex](x-9)^2=x-7\\\\x^2-19x+88=0\\(x-8)(x-11)=0\\x=8 , x=11\\\\\int_8^{11}[(x-9)^2-(x-7)]dx\\\\=\int_8^{11}[x^2-19x+88]dx\\\\\\=[x^3/3-19x^2/2+88x]_8^{11}\\\\=4.44[/tex]

The area bounded by the given curve is =4.44.

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The measure of angle D is ∠D = 65°.

Two triangles are said to be similar if there corresponding sides are proportional and their corresponding angles are equal.

Given is that triangle ΔABC is similar to triangle ΔDEF.

We can write -

∠D + x + 90° = 180°

∠D = 90° - x

Since both the triangles are similar, we can write -

∠D = ∠A

{90° - x} = {2x + 15}°

3x = 75°

x = 25°

∠D = 90 - x = 65°

∠D = 65°

Therefore, the measure of angle D is ∠D = 65°.

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The value of c for the given function at x = 0 to be continuous is c = 8/15.

The following three requirements must all be met for a function to be regarded as continuous at a point:

In other words, a function is continuous at a place if you can draw it without moving your hand and the function's graph doesn't have any gaps or leaps at that location. Calculus' central idea of continuity is crucial for defining derivatives and integrals.

According to the question

Given function =  f(x)= 12x−4sin(3x)/5x3

We require f(0) = c, where c is the value given to the function at x = 0, in order to make the function continuous at that point. We may assess the limit of f(x) as x gets closer to zero to determine c.

The limit of f(x) as x approaches 0 may be determined using L'Hopital's rule as follows:

lim x→0 f(x) = lim x→0 (12x - 4 * sin(3x)) / (5x^3)

= lim x→0 (12 - 4 * 3 * cos(3x)) / (15x^2)

= 8 / 15.

So, c = 8 / 15. Therefore, the function f(x) = (12x - 4 * sin(3x)) / (5x^3), x ≠ 0 and c, x = 0 is continuous at x = 0 with c = 8 / 15.

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The required equation is C = 8 + 0.25m, where m represents the number of mats used per month and C represents the total cost in dollars.

Let's use "m" to represent the number of center floor mats used per month, and "C" to represent the total cost in dollars. The total cost can be expressed as the sum of a fixed monthly fee of $8 and an additional fee of $0.25 per center floor mat used:

C = 8 + 0.25m

This equation expresses the relationship between the number of center floor mats used (m) and the total cost (C) in dollars.

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The value of t for which the linear functions are parallel is given as follows:

t = 5.

Linear functions are parallel when they have the same slope.

Given two points, the slope is calculated as the change in y divided by the change in x.

Considering points (-4, -7) and (2,-3), the slope is given as follows:

m = (-3 - (-7))/(2 - (-4)) = 4/6.

Considering points (-4,1) and (2,t), the slope is given as follows:

m = (t - 1)/(2 - (-4)) = (t - 1)/6.

The two lines will be parallel when:

4/6 = (t - 1)/6.

Hence the value of x is obtained as follows:

t - 1 = 4.

t = 5.

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The bearing of point X from point Z is 280°

To find the bearing of point X from point Z, we need to use the principle of alternate angles in each point and sum of angles of a triangle

The triangle formed is as follows

angle x = 100 - 65 = 35

angle y = (180 - 140) + 65 = 105

angle z = 180 - angle y + angle x = 180 - 35 + 105 = 40

The bearing of point X from point Z,

= 360 - angle z - alternate angle from y

= 360 - 40 - 40

= 280

Bearing of X from Z =  280

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Answer:

104976

Step-by-step explanation:

First multiply 6 by 2 and you get 12. Now add 6 to it and you get 18. Now power 18 to 4

18 times 18 times 18 times 18

and you get 104976

The linear regression equation that best fits the data is given as follows:

y = 1.2x - 21.3.

Hence the projected test score for an student with a homework score of 45 is given as follows:

32.7.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

The points for this problem are given as follows:

(78, 66), (89, 76), (54, 42), (86, 90), (74, 68), (73, 73), (86, 84), (63, 54), (64, 54)

Inserting these points into the calculator, the line of best fit is given as follows:

y = 1.2x - 21.3.

The projected test score for an student with a homework score of 45 is found replacing x by 45, hence:

y = 1.2(45) - 21.3

y = 32.7.

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Therefore , the solution of the given problem of ratio comes out to be

x has length of 5.2 .

The simple formula "a / b" can be used to create a pair of similar variables "a" and "b," where "b" may also be greater than zero. One ratio is created by combining two ratios. If there were only one man and three women, the ratio would be 1:1. There are 1/4 boys and 3/4 girls in the group. A separation between a or more objects, a numeral, or a piece of a component's volume are all examples of parts.

Here,

Given :

A figure of star shape

having diameter of 3.6 and length x

and other star having same shape but

having diameter 5.76 and length 8.32

Since , both the figures are same ,

Thus , there length ratio will also be same.

=> 8.32/5.76 =  x / 3.6

=> 832/576 =  10x/36

=>  832/576 * 36 /10 = x

=> x = 1.44 * 3.6 =5.2

Therefore , the solution of the given problem of ratio  comes out to be

x has length of 5.2 .

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92% is the percent of decrease.

A relation is a function if it has only One y-value for each x-value.

The function [tex]M(t)=975.(0.92)^{t}[/tex]

Function represents the number of milligrams of a medication in a patients body as a function of time.

t represents the time.

0.92×100=92%

975 is the initial value and 0.92 is the percent of decrease.

Hence, 92% is the percent of decrease.

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The value of the variable x for the function f(x) = x² + 4x for which

f(f(x) ) = f(x) is equal to x = -1 or x = -3.

The function f(x) = x² + 4x

Substitute the value in the required function we get,

Right hand side

= f ( f(x))

= f ( x² + 4x )

= ( x² + 4x )² + 4 ( x² + 4x )

= x⁴ + 8x³ + 16x² + 4x² + 16x

= x⁴ + 8x³ + 20x² + 16x

Left hand side

f(x)

= x² + 4x

Equate left hand side is equal to right hand side we get,

x⁴ + 8x³ + 20x² + 16x = x² + 4x

⇒x⁴ + 4x³ + 4x³ + 16x² + 4x² + 16x =  x² + 4x

⇒x² ( x² +4x ) + 4x ( x² + 4x )+ 4 ( x² + 4x ) = x² + 4x

⇒( x² + 4x ) ( x² + 4x + 4 ) = x² + 4x

⇒ x² + 4x + 4 = 1

⇒ ( x + 2 )²  - 1² =0

⇒ ( x + 2 -1 ) ( x+ 2 + 1) = 0

⇒ ( x+ 1 ) ( x+ 3 ) = 0

⇒ x = -1  or x = -3

Therefore, the value of x = -1 or x = -3 for the condition f(f(x)) = f(x).

The above question is incomplete , the complete question is:

Let function f(x) = x² + 4x for what value of x is f(f(x)) = f(x).

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Answer: 17mm

Step-by-step explanation: 153/9 is 17

The elevation represents a distance from the sea level greater than 5 feet, because the original description specifies a distance greater than 5 feet below sea level.

Physical quantities like mass and electric charge are examples of scalar quantities because they only have magnitudes. In contrast, a vector quantity is a physical quantity like force or weight that has both magnitudes and directions.

The elevation is the height or distance above sea level and is expressed as a distance.

Given that it contains both magnitude (distance) and direction, elevation in the previous description is a vector (above sea level).

Distance is a scalar quantity with only one magnitude that describes the area travelled by a moving object.

A height of less than 5 feet denotes a location that is less than 5 feet above sea level, which is equivalent to a location that is more than 5 feet below sea level.

Greater than 5 feet below sea level = less than -5 feet above sea level, therefore;

A distance from (below) sea level of more than 5 feet is represented by an elevation of less than -5 feet.

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The value of h for which b in the plane spanned by a1 and a2 is 11.

A vector b is in the plane spanned by two vectors a1 and a2 if it can be written as a linear combination of a1 and a2. This means that there exist scalars x and y such that:

b = xa1 + ya2

[5, 4, h] = x[1, 4, -1] + y[-6, -20, 2]

Solving for x and y, we have:

5 = x - 6y

4 = 4x - 20y

h = -x + 2y

Using the first two equations, we can solve for x and y:

x = 5 + 6y

20y + 4 = 4x = 4(5 + 6y)

20y + 4 = 20 + 24y

4y = -16

y = -16/4 = -4

Substituting this value of y back into the first equation:

x = 5 + 6y

= 5 + 6 * -4

= 5 - 24

= -19

Finally, substituting x and y into the third equation:

h = -x + 2y

= -(-19) + 2 * (-4)

= 19 - 8

= 11

So for h = 11, the vector b is in the plane spanned by a1 and a2.

--The question is incomplete, answering to the question below--

"Let a1 = [1 4 -1], a2 = [-6 -20 2], and b = [5 4 h]. For what value(s) of h is b in the plane spanned by a1 and a2?"

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16 is the number which shows a proportional relationship between x and y.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

the ratio of x:y = 0.8 : 4

let, the number for y be a

so that, x: y is  proportional .

i.e. 3.2 : a = 0.8 : 4

or, a = 16

Hence, 16 is the solution.

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The value of k given sequence is =300 and the value of the term Sk=4875,

In mathematics, we may come across different types of numbers, and patterns. One of the number patterns includes sequences. The sequence is a specified collection of objects in which repetitions are allowed and order matters. Formally, a sequence is a function from natural numbers to the elements at each position. Similar to a set, it contains members, and they are called elements or terms. The number of elements is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and the order does matter.

value of k

U1 =1.3

U2= 1.4

Uk = 31.2

a = 1.3

d = 1.4 - 1.3 = 0.1

Uk = 1.3 + (k - 1)(0.1)

=> 1.3 + (k - 1)(0.1) = 31.2

=>  (k - 1)(0.1) = 29.9

=> k - 1 = 299

=> k = 300

Sk  = (300/2)(1.3 + 31.2)

= 150 * (32.5)

= 4875

F is the sum of the terms for which the term is not a multiple of 3

3rd term = 1.5

6th term = 1.8

300th term = 31.2

Total terms = 100

Sum = (100/2)(1.5 + 31.2)  =  1635

F = 4875 - 1635   = 3240

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The measure of angle B is m∠B = 71°

If ABCD is a kite, then ∠A and ∠C must be equal to each other.

∠A = ∠C, so ∠C = 87°.

ABCD is a quadrilateral, so all of its interior angles must add up to 360°. We know 3 of the 4 angles, so we'll add them up and subtract the answer from 360.

∠A + ∠C + ∠D ⇒ 87 + 87 + 115 = 289

360 - 289 = 71

m∠B = 71°

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