A group of 540 students are required to take a test. Of these,
495 actually take the test, and 45 are absent that day.
(i) Write down the ratio of the number of students who take the test
to the number of students who are absent. Simplify this ratio as far
as possible. [3]
(ii) Of the 495 students who take the test, the numbers of students
obtaining grades A, B, C and D are in the ratio 5 : 14 : 10 : 4,
respectively. Calculate the number of students obtaining each
grade. Explain how you could check that your answers are

Answer:

Below

Step-by-step explanation:

Arrange the given equation into y = mx + b form of a line

       'b' is the y-axis intercept

2x-5y+7 = 0

5y = 2x+7

y = 2/5 x + 7/5

Answer:

(0, 7/5)

Step-by-step explanation:

The correct stem-and-leaf plot for the data is:

i. Stem: 5,6,7,8,9 Leaf: 3, , 5 7 8 9, 1 2 4 9, 1

This plot shows the distribution of the data values, with the stems representing the tens place and the leaves representing the ones place. For example, the value 53 is represented by the stem 5 and the leaf 3, and the value 82 is represented by the stem 8 and the leaf 2.

The other three stem-and-leaf plots are incorrect because they do not accurately represent the distribution of the data.

A stem-and-leaf plot is a graphical representation of data that shows the distribution of values. The stems represent the tens place and the leaves represent the ones place. It is useful for identifying patterns and trends in the data.

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The triangles 1, 2, 4, 7 and 8 are right triangles by Pythagorean relationship.

Triangles are closed figures formed by three line segments, a right triangle is a triangle with one right angle. Right triangles have a long side known as hypotenuse (r) and two shorter sides known as legs (x, y), whose Pythagorean relationship is shown below:

r = √(x² + y²)

Now we proceed to check whether each triangle is a right triangle or not:

Case 1:

D = √(8² + 6²)

D = 10 (YES)

Case 2:

D = √(5² + 12²)

D = 13 (YES)

Case 3:

D = √(12² + 9²)

D = 15 (NO)

Case 4:

D = √(8² + 15²)

D = 17 (YES)

Case 5:

D = √(4² + 9²)

D ≈ 9.849 (NO)

Case 6:

D = √(14² + 5²)

D ≈ 14.866 (NO)

Case 7:

D = √(20² + 15²)

D = 25 (YES)

Case 8:

D = √(24² + 10²)

D = 26 (YES)

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The final velocity of the train is 30m/s.

The rate at which an object's velocity with respect to time changes is referred to as acceleration. When an object's velocity changes, it is said to have or be accelerating.

The rate of change in velocity over time is another name for acceleration. The magnitude of an acceleration vector indicates how much the velocity will change, while the vector's direction indicates how the velocity will change—whether the speed is rising or falling, the vector's direction is changing, or some combination of the three.

Given, initial velocity = 0 m/s (as the train starts from rest)

          time = 60 seconds

Acceleration = v - u / t = 30 - 0/ 60 =0.5 m/s square

We know,

v = u + at

v = 0 + (0.5 x 60)v = 30 m/s

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Step-by-step explanation:

I need the graph but it could be 216

The values of a and b in the given triangle are;

a = 59° and b = 6

From the given image, it is clear that in Triangle YVW that we have;

YV = WV

Now, a triangle that has two sides equal  is referred to as an Isosceles triangle which means that the two base angles are equal. Thus;

∠Y = ∠W = 31°

Now, the sum of angles in a triangle is 180° and as such;

∠YVW = 180 - 2(31)

∠YVW = 118°

Since VX is perpendicular to YW and so;

a = 180 - (90 + 31)

a = 59°

Thus; ∠WVX = 59°

This means that WX = YX = 6

Thus, b = 6

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To determine the regression equation, we need to fit a line to the data that best describes the relationship between the dependent variable and the independent variable. The equation of the line is typically expressed in the form:

where y is the dependent variable, x is the independent variable, a is the y-intercept (the point at which the line crosses the y-axis), and b is the slope of the line (the rate of change of y with respect to x).

If we determine that a = 10 and b = 0.5, the regression equation would be:

This equation describes the relationship between the dependent variable (days-on-the-market) and the independent variable (price). It tells us that for every unit increase in price, the number of days on the market is expected to increase by 0.5.

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The dy/dx at point (2,8) is 4/3

From the information illustrated, x + 3y^(1/3) = y and point (2,8)

Find the derivative of this equation with respect to x and solve for dy/dx:

x + 3y^(1/3) = y

1 + [3 × 1/3 × y^(-2/3)]dy/dx = dy/dx

1 + [y^(-2/3)]dy/dx = dy/dx

dy/dx -  [y^(-2/3)]dy/dx = 1

dy/dx [1-  y^(-2/3)] = 1

dy/dx = 1/ [1 - y^(-2/3)]

At point (2,8), x = 2 and y = 8.

Substitute into dy/dx:

dy/dx = 1/ [1 - y^(-2/3)]

dy/dx = 1/ [1 - 8^(-2/3)]

dy/dx  = 1/ [1 - 1/4)]

dy/dx = 4/3

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The expression for the height (h) in terms of radius r is h = 547/(∏r²).

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

Given that the volume of the cylinder is 547 cubic inches.

The volume of a cylinder is V = ∏r²h

Where r is the radius of the cylinder.

h is the height of the cylinder.

Putting V = 547, r = r and h = h in V = ∏r²h

547 = ∏r²h

∏r²h = 547

Divide both sides by ∏r²:

h = 547/∏r².

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Answer:

y = 18

Step-by-step explanation:

⭐Substitute the given x-value into the line of best fit

[tex]y = 9-3x[/tex]

[tex]y = 9-3(-3)[/tex]

[tex]y = 9 +9[/tex]

[tex]y = 18[/tex]

Answer:18

Step-by-step explanation:

9-3(-3)=18

Answer:

Step-by-step explanation:

Point A = (5, 6)  is reflected across the x axis which is y =0.

When the point is reflected across the x axis, the x coordinate

remains positive, but the y coordinate becomes negative.

The 6 becomes negative (-6).

So the coordinates of A' are (5, -6) which is the first answer.

The shadow price of a constraint, the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.

A constraint is a condition of an optimization problem that should be satisfied the condition.

We can formulate this problem as a linear programming model (LPM):

Suppose X1 be the number of belt A produced per day, X2 be the number of belt B produced per day and X3 be the number of belt C produced per day

The objective function is to maximize the profit;

3X1 + 5X2 + 4X3.

The constraints are as :

The time spent on machine M1 must be less than or equal to 8 hours per day so we get;

2X1 + 3X2 <= 8

The time spent on machine M2 must be less than or equal to 10 hours per day so we get;

3X1 + 2X2 + 5X3 <= 10

The time spent on machine M3 must be less than or equal to 15 hours per day so we get

2X1 + 2X2 + 4X3 <= 15

Thus number of belts produced must be positive:

X1, X2, X3 >= 0

To solve this LPM using the simplex algorithm,

Also the objective function is to minimize the cost, and all constraints are in the form of "less than or equal to" a certain value.

The pivot row is the row that corresponds to the smallest positive ratio between (RHS) value and the corresponding pivot column element the constraint 2X1 + 3X2 ≤ 8.

Now Interpret the shadow prices.

The shadow price of a constraint is the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.

Here the value of the constraints in the LPM and how they contribute to the optimal solution.

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Answer:

B

Step-by-step explanation:

Dont think you need this

The perimeter of the box has been obtained as 6a^3b^2 + 6ab^5.

We know that a box has the shape of a rectangle thus we would have to apply the formula for the area of a rectangle in this case and we would have;

P = 2(l + b)

P = perimeter

l =length

b = breadth

Then we have;

2[(-9a^3b^2 + 13ab^5) + (-10ab^5 + 12a^3b^2)]

Collect the like terms

2[(-9a^3b^2) + 12a^3b^2 + 13ab^5 +(-10ab^5)]

2[3a^3b^2 + 3 ab^5]

6a^3b^2 + 6ab^5

In  order of descending exponents of a, the perimeter is 6a^3b^2 + 6ab^5.

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Answer:

15

Step-by-step explanation:

When you see something like f (18), this means 18 needs to be plugged in for x

let's plug in 18

f (18) = [tex]\frac{2}{3} (18) + 3[/tex]

Let's solve

(18 × 2) ÷ 3 = 12

12 + 3 = 15

f (18) = 15

Answer:

Therefore, when the stadium is full, a total of 740 people can sit in the three sections.

Step-by-step explanation:

The red section seats 200 people.

The blue section seats 200 - 20 = <<200-20=180>>180 people.

The green section seats 180 * 2 = <<180*2=360>>360 people.

The total number of people who can sit in the stadium is 200 + 180 + 360 = <<200+180+360=740>>740 people.

Step-by-step explanation:

this is a college level question ?

and you don't know how to do this (because doing this yourself would have been much faster than posting the question and looking for the answer here) ?

oh my ...

red = 200

blue = red - 20 = 200 - 20 = 180

green = 2×blue = 2×180 = 360

total number = 200 + 180 + 360 = 740

Answer:

0.2 g/mL

Step-by-step explanation:

The calculation for density is density=mass/volume.
With a mass of 10g and a volume of 50mL, you divide them to get 0.2

Answer: 6.25%

Step-by-step explanation:

You can set up a proportion:

[tex]\frac{3}{48}=\frac{x}{100}[/tex]

100 x 3 = 300

300/48 = 6.25

It is assumed the statement is true for [tex]S_k[/tex]:

Show that [tex]S_{k+1}[/tex] is also divisible by 5:

The first part is divisible by 5 as we assumed in the beginning and the second part has a factor of 5 so the sum is divisible by 5.

Hence it makes [tex]S_{k+1}[/tex] true, so the proof is complete.

The Total Number of Hot Dogs sold were 240 and Cheese Burgers sold were 246

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of Hot Dogs Sold = x

Number of Cheese Burgers Sold = y

According to the Question:

x + y = 486 ----------(i)

2x + 3y = 1218 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 972 ----------(iii)

Substracting Equation (iii) from Equation (ii)

y = 246

x = 240

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The value of the differentiation dy / dx will be 13 / 5.

Calculus, also known as infinitesimal calculus or "the calculus of infinitesimals," is the mathematical study of continuous change, similar to how geometry studies shape and algebra studies generalizations of arithmetic operations.

Given that the expression is 5 - 2x²+y³ =-x³ -3y. The coordinate is (3,-2).

The value of dy / dx is calculated as,

5 - 2x²+y³ =-x³ -3y.

Differentiate the above equation with respect to x,

5 - 2x²+y³ =-x³ -3y

-4x + 3y² dy /dx = 3x² -3dy / dx

-4x - 3x² = (-3y² -3)dy/dx

dy /dx = [-4x - 3x²] / [ (-3y² -3) ]

Substitute the value of x and y in the above equation,

dy /dx = [-4x - 3x²] / [ (-3y² -3) ]

dy /dx = [-4 x 3- 3(3)²] / [ (-3(-2)² -3) ]

dy / dx = [ -12 - 27 ] / [ -15]

dy /dx = -39 /- 15 = 13 / 5

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The description and measure of the segments and angles of the triangular-shaped photo frame, found using the triangle inequality theorem are;

According to a triangle inequality theorem, the measure of the lengths of sides opposite angles of different measure, are also different and the the longest side of a triangle is opposite the largest angle of the triangle.

The interior angles of the photo frame are;'

∠B = 58°, ∠A = 82°

The angle sum property of a triangle indicates that we get the angle ∠C as follows;

The triangle inequality theorem indicates that the measure of the angles opposite sides that have different lengths are also different, such that the larger angle is opposite the larger side.

According to the triangle inequality theorem, we get;

The shortest side is opposite the smallest angle, which is the angle ∠C = 40°

The side opposite ∠C is AB,  therefore, the shortest side is AB

The longest side is opposite the largest angle, which is angle ∠A = 82°.

The side opposite the angle ∠A is BC, therefore, the longest side is BC

The smallest angle is the angle ∠C = 40°

The largest angle is the angle ∠A = 82°

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Since ABCD has four equal angles and four equal sides, then it is a square.

The formula for the distance between two coordinates (x₁, y₁) and (x₂, y₂) is;  Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

We are given the coordinates;

A(0, 6)

B(6, 6)

C(6, 0)

D(0, 0)

Thus;

AB = √[(6 - 0)² + (6 - 6)²]

AB = 6

BC = √[(6 - 6)² + (0 - 6)²]

BC = 6

CD = √[(0 - 0)² + (0 - 6)²]

CD = 6

AD = √[(0 - 0)² + (0 - 6)²]

AD = 6

Thus, we conclude that all the sides are equal and it is a square.

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The amount of sugar needed for the recipe to be tripled is 9 / 4 cups.

Caroline baked cookies from a recipe that called for 3/4 cups of sugar. she planned to triple the recipe. Therefore, the amount of sugar she needs is calculated as follows:

1 recipe = 3 / 4 cups of sugar

She wants to triple the recipe.

Hence,

1 recipe = 3 / 4 cups of sugar

3 recipe = ?

cross multiply

amount of sugar needed = 3 / 4 × 3

amount of sugar needed = 9 / 4

amount of sugar needed = 9 / 4 cups of sugars

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Number of People who knows the Code are 6401

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of People who kows the Code be x

Number of Peoplee who do not know the Code be y

According to the Question:

x + y = 7338 ----------(i)

2x + 5y = 17487 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 14676 ---------(iii)

Substracting Equation (iii) from Equation (ii)

3y = 2811

y = 937

This means x = 6401

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The equivalent expression of log(16 × 14) is log 16 + log 14.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Therefore, the equivalent expression of log(16 × 14) can be found as follows:

using logarithm law,

The log of a product is the sum of the logs.

logₐ xy = logₐ x + logₐ y

Therefore,

log(16 × 14) = log 16 + log 14

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Answer:

The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Step-by-step explanation:

hope this helped:)

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The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

Here, we have,

The factors of 54 are the numbers, that can divide 54 completely or evenly. When a pair of factors are multiplied together to produce the 54, then they are said to be pair factors. The factors divide the number completely. Hence, these factors cannot be a fraction.

Factors of 54: 1,2,3,6,9,18,27 and 54

Factor pairs of the number 54 are the whole numbers which are not a fraction or decimal number.

To find the factors of a number, 54, we will use the factorization method.

To find factors of 54, we have to divide 54 by all natural numbers from 1 to 54.

54 ÷ 1 = 54

54 ÷ 2 = 27

54 ÷ 3 = 18

54 ÷ 6 = 9

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