a student committee has 6 membersâ€""4 undergraduate and 2 graduate students. a subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. what is the probability that there will be no graduate students on the subcommittee?

1a. The interest that Thato will pay equals to R3,840.

1b. The final amount he will pay for the bicycle will be R 11 840.

a) To calculate the interest that Thato will pay, you can use the following formula:

Interest = Principal * Rate * Time

Interest = R 8,000 * 0.14 * 3

Interest = R3 840

Final amount = Principal + Interest

Final amount = R 8,000 + R 3,840

Final amount = R 11,840

Cost price per rose = Total cost of roses / Number of roses

Cost price per rose = R 900 / 200

Cost price per rose = R 4.50

Selling price per rose = Price of bouquet of 5 roses / Number of roses in the bouquet

Selling price per rose = R 35 / 5

Selling price per rose = R 7.00

Profit per rose = Selling price per rose - Cost price per rose

Profit per rose = R 7.00 - R 4.50

Profit per rose = R 2.50

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4. The value of b is 180+2a (option C)

11. the distance between A and B is 4√2 (option A)

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °.

The total angle at a point is 360°

therefore the third angle in the triangle = 180-(a+a) = 180-2a

therefore b = 360-( 180-2a)

b = 360-180+2a

b = 180+2a

If the volume of the cube is 64, then AB = √4²+4²

= √16+16 = √32

AB = √32

AB = √ 16×2

AB = 4√2

Therefore the distance between A and B is 4√2

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The surface area of a right cylinder with a radius of 6 units and a height of 14 units is equal to 753.6 square units.

Mathematically, the surface area (SA) of a right cylinder can be calculated by using this formula:

SA = 2πrh + 2πr²

Where:

By substituting the given parameters into the surface area of a right cylinder formula, we have;

Surface area (SA) of cylinder = (2 × 3.14 × 6 × 14) + 2 × 3.14 × 6²

Surface area (SA) of cylinder = 527.52 + 226.08

Surface area (SA) of cylinder = 753.6 square units.

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Answer:

DE = 6 cm

Step-by-step explanation:

The concept behind this question is the Chord-Chord Power Theorem. This product states that "if two chords intersect in a circle, then the products of the lengths of the chords segments are equal". In this case:

CE × DE = AE × BE

4 × DE = 8 × 3

4 × DE = 24
DE = 6 cm

Hope this helps!

The value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2

We shall evaluate for the value of x to know what makes the algebraic equation true as follows;

3(2x - 5 + 8x) = 5(2x + 5)

3(10x - 5) = 5(2x + 5)

30x - 15 = 10x + 25 {expand bracket}

30x - 10x = 25 + 15 {collect like terms}

20x = 40

x = 40/20 {divide through by 20}

x = 2

Therefore, the value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2.

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The complete tables for the given equations is:-

For y = 3x

X   Y

1     3

2    6

3    9

For y = -2x + 5

X   Y

1    3

2   1

3   -1

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The given two equations are;-

y = 3x

y = -2x +5

The different points passing through the line y =3x are:-

X   Y

1     3

2    6

3    9

The different points passing through the line y =-2x + 5 are:-

X   Y

1    3

2   1

3   -1

The graph of the points and the line as is attached with the answer below.

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The value of the equation is 35 = 15 + 2y , where y is the number of years and the y = 10 years

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the initial height of the weeping willow be = 15 feet

Let the final height of the weeping willow be = 35 feet

The height in feet the weeping willow grows each year = 24 inches = 2 feet

Let the number of years be = y

On simplifying the equation , we get

35 = 15 + 2y

Subtracting 15 on both sides of the equation , we get

2y = 20

Divide by 2 on both sides of the equation , we get

y = 10 years

Hence , the equation is y = 10 years

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The total cost of an order is $900 if 50 invitations cost is $298.50

To calculate the cost of an order of personalized invitations, you would need to know the cost of each invitation and the one-time design fee.

Let calculate the cost of each invitation and the one-time design fee as follows:

50 Invitations: $298.50 / 50 = $5.97 per invitation

500 Invitations: $2049 / 500 = $4.098 per invitation

Design Fee: ($2049 - ($5.97 × 50)) / 500

= $3.90 one-time design fee

If you wanted to order 150 personalized invitations, the cost would be:

150 Invitations x $5.97 per invitation = $896.50

Plus one-time design fee of $3.90 = $890.40

Total cost = $896.50 + $3.90 = $900.

Hence, the total cost of an order is $900 if 50 invitations cost $298.50

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The amount of wrapping paper used by Gavin to wrap a triangular prism box is 647.75 m².

What is a prism?

A prism is a polyhedron in geometry made up of an n-sided polygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.

The formula for area of rectangle is -

Area = length × breadth

The area of rectangle ABFG is -

Area = AB × BF

The value for line segment AB = 15 m

The value for line segment BF is -

BF = BC + CE + EF

BF = 14 + 7 + 15.65

BF = 36.65 m

So, the area of rectangle ABFG is -

Area = 15 × 36.65

Area = 549.75 m²

Now, the triangular prism has triangle part left.

The formula for area of triangle is -

Area = 1/2 × base × height

So, the area of triangle IJH is -

Area = 1/2 × IJ × JH

The value for line segment IJ = 14 m

The value for line segment JH = 7 m

So, the area of triangle IJH is -

Area = 1/2 × 14 × 7

Area = 49 m²

Since, there are two triangles (Δ IJH = Δ CDE ) so the area of total shape is -

Total area = Area of ABFG + 2(Area of Δ IJH)

Total area = 549.75 + 2(49)

Total area = 647.75 m²

Therefore, the area of triangular prism box is 647.75 m².

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a) The missing frequency is 20

b) The modal number of people in a car is 1

c) The median is 3

d) The mean is 0.95

The sum of the frequencies must be 60.

The missing frequency by subtracting the sum of the other frequencies from 60

60 - (28 + 3 + 7 + 1 + 1) = 20

To find the median, we need to arrange the data in order from smallest to largest:

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6

There are 60 numbers in total, so the median is the average of the 30th and 31st numbers:

median = (3 + 3)/2 = 3

The mode is the value with the highest frequency, which is 1.

mean = (1 x 28 + 2 x 20 + 3 x 3 + 4 x 7 + 5 x 1 + 6 x 1) / 60

= (28 + 40 + 9 + 28 + 5 + 6) / 60

= 0.95

Therefore, the missing frequency, mode, median and mean has been found

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The given question is incomplete, the complete question is

Hassan recorded the number of people in 60 passing cars

people 1 2 3 4 5 6

frequency 28 ? 3 7 1 1

a)find the missing frequency

b)median

c)modal

d)mean

Solution of given inequality is x < -12.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

Given inequality

- (1/2)x > 6
Multiplying with 2 on both sides

- (2/2)x > 6×2

- x > 12

Multiplying with -1 on both sides

x < -12

Hence, x < -12 is the solution of given inequality.

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The angle to the nearest tenth of a degree, we round the result to 50.7 degrees.

In trigonometry, cosine is a function that takes an angle as an input and produces a numeric value between -1 and 1 as an output. The cosine of an angle A is represented by cos A. In this problem, cos A is given to be 0.8945. To find the angle, we can use the inverse cosine function (or arccosine) which returns the angle in radians. To obtain the angle in degrees, we can multiply by 180/π (which is equal to 57.2958). The angle A is then equal to 50.6 degrees.  To find the angle to the nearest tenth of a degree, we round the result to 50.7 degrees.

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The equation of the linear function is y = x - 5

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

The ordered pairs (0,-5) and (-2,-3)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

y = mx - 5

Using the other point (-2, -3), we have

-2m - 5 = -3

Evaluate the like terms

-2m = 2

Divide by 2

m = 1

Substitute the known values in the above equation, so, we have the following representation

y = x - 5

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Complete question

Find the equation of the linear function represented by the line that goes through: (0,-5) and (-2,-3) in slope-intercept form.

y = ___?___

The ordered pairs from the graph of quadratic and linear equations are (-2, 7) and (2, -1)

A graph of a quadratic equation is a parabolic curve that opens up or down, depending on the sign of the coefficient of the squared term. A general form of a quadratic equation is given by:

y = ax^2 + bx + c,

where a, b, and c are constants. The graph of this equation can be plotted by choosing a range of values for x and calculating the corresponding values of y.

A graph of a linear equation is a straight line. A general form of a linear equation is given by:

y = mx + b,

where m is the slope of the line and b is the y-intercept.

In this problem, the ordered-pairs will be the point in which they intersect with each other.

Looking carefully at the graph, the ordered pair will be at points

A = (-2, 7)

B = (2, -1)

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The right response is, "5 hexagons are made up of 15 pattern block trapezoids."

Geometric shapes known as pattern block trapezoids are frequently utilized in arithmetic instruction. On a flat surface, they are one of a number of forms that can be used to make tessellations, or repeating patterns. Different colored plastic or foam pattern block trapezoids are available in a variety of sizes, with each color denoting a distinct size and form. Pattern block trapezoids are frequently used to teach geometry principles like area, perimeter, and angles in addition to their application in making tessellations. They can also aid in the development of kids' spatial reasoning and problem-solving skills.  

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The expression for the given model will be 3÷2/5.

What exactly are expressions?

Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.

Now,

as shown in figure the model is shaded uptil 3

and in 1 unit there are 5 total boxes which are divided in 2 parts

Therefore, it will be represented by 3÷2/5.

Hence,

         The expression for the given model will be 3÷2/5.

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Un-simplified rate of dollars-gallons = 22.5/9  $ and and gallons to dollars 9/22.5 $ .  and simplified rate of dollars-gallons = 22.5/9  $ = 2.5 and and gallons to dollars 9/22.5  = 0.4 .

Here first we have to calculate the rate of gallons of gas as per gallons so for that we will find the rate of 1 gallons for that we will divide the  22.4$ to 9 gallons so ans is 22.5$/9 is the rate for 1 gallons

and 2nd we have to calculate the amount of gas as per $ like we have to calculate the the amount if we spend 1 $  so for that we will divide 9 gallons / 22.5$ = 9/22.5

And here in 1st part we  are not calculate the ans in decimal as we have to calculate this on un-simplified  ans .

and in 2nd part we calculate it .

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Answer:

  G  descends about 8 ft per second

Step-by-step explanation:

You want to know the descent rate of an airplane whose altitude is shown on a graph as being 1500 ft at 0 seconds and 0 ft at 180 seconds.

The airplane descended 1500 feet over a period of 180 seconds. That rate of change is ...

  (-1500 ft)/(180 s) ≈ -8.333 ft/s

The plane descends about 8 feet per second.

__

Additional comment

The slope of the line segment is the change in y divided by the change in x. For computing these changes, it is useful to consider points whose coordinates are obvious. Here, the y-intercept (1500 ft) and the x-intercept (180 seconds) are good choices.

The change in y from 1500 to 0 is a change of -1500. The change in x from 0 to 180 is a change of +180. The ratio of these changes is the slope, which is often designated by the letter m:

  m = -1500/+180 = -25/3 = -8 1/3 . . . . . . about -8

The units of the slope are the ratio of the y-axis units to the x-axis units: feet/second.

The slope of -8 feet/second tells you the plane is descending about 8 feet per second.

Answer: 2 *(3+4)= (2x3)+ (2x4)

Step-by-step explanation:

Yes, the product of (x - 3)^2 is a perfect square trinomial because it can be written as the square of the binomial (x - 3).

A perfect square trinomial is a trinomial of the form a^2 + 2ab + b^2, where a and b are terms that can be squared. When we expand the square of a binomial, we get a perfect square trinomial.

In this case, the binomial is (x - 3), and its square is (x - 3)^2. When we expand this expression, we get:

(x - 3)^2 = (x - 3)(x - 3) = x^2 - 6x + 9

This is a perfect square trinomial, because it can be written as the square of the binomial (x - 3). Specifically, we can write:

(x - 3)^2 = (x - 3)(x - 3) = (x - 3)^2

Therefore, the product of (x - 3)^2 is a perfect square trinomial.

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The greatest common factor of the 24x³ + 36x² is 12x².

It is the greatest factor common to all the numbers given such that there are no greater factors common other than that.

Example:

4 is the gcd of 12, 8, 16.

We have,

24x³ + 36x²

Taking out the common factor.

= 12x² (2x + 3)

Thus,

GCF of the expression is 12x².

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The roots of the polynomial equation are x = −1, 1/3, and 3.

A polynomial equation is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.

Finding the value(s) of 'x' that satisfy the polynomial equation p(x) = 0 is all that is required to solve the problem. A number "a" is a polynomial p(x) "zero" if and only when p(a) = 0. 

Given that:

3x³- 7x² - 7x + 3 = 0

Factor the left side of the equation.

(x + 1) (3x − 1)(x − 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x + 1 = 0

3x − 1 = 0

x − 3 = 0

Set x + 1 equal to 0 and solve for x; x = - 1

Set 3 x − 1 equal to 0 and solve for x; x = 1/3

Set x − 3 equal to 0 and solve for x;  x = 3

The final solution is all the values that make (x + 1)(3 x − 1)( x − 3) = 0 true is x = −1, 1/3, 3.

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