THEORY
1a. In a class of 58 students, 35 offer Biology, 28 offer Economics and 15 offer Physics. Each
students offers at least one of the three subjects. If 12 students offer both Biology and
Economics, 7 students offer both Biology and Physics and 5 students offer both Economics and
Physics, how many students offer all three subjects?
b. A regular polygon with (2m+1) sides has each interior angle equal to 1440. Find the value of
m.

The equations x² + 4x + 3 = 0 and x² -6x + 13 = 0 are equivalent to (x + 2)² = 1 and (x - 3)² = -4

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The standard equation of a quadratic function is:

y = ax² + bx + c

1) Given that:

x² + 4x + 3 = 0

subtract 3 from both sides:

x² + 4x = -3

add to both sides the square of half the coefficient of x:

x² + 4x + 4 = -3 + 4

(x + 2)² = 1

2) Given that:

x² - 6x + 13 = 0

subtract 13 from both sides:

x² - 6x = -13

add to both sides the square of half the coefficient of x:

x² - 6x + 9 = -13 + 9

(x - 3)² = -4

The equations are (x + 2)² = 1 and (x - 3)² = -4

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The price is £12,880.

First, do 14000  x 0.08 = 1,120.

Next do 14,000 - 1,120 = 12,880.

So, the price is £12,880.

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On solving the provided question, we can say that  The area of the arrow is equal to A = A1 + A2 = 68+12 = 80 cm sq.

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

The area of rectangle is equal to

A1 = LW

L = 17cm

W = 4cm

A1 = 68 cm sq.

The area of triangle is equal to

A2 = 1/2*b*h

A2 = 1/2*8*3

A2 = 12 cm sq.

The area of the arrow is equal to

A = A1 + A2 = 68+12 = 80 cm sq.

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The correct question is -

In the figure, the dashed line divides the arrow in half. What is the total area of the arrow? 60 square centimeters 68 square centimeters 80 square centimeters 82 square centimeters

Answer:

89 Bills of 10$ and 1 of 5$

Step-by-step explanation:

Pretty simple division which gets you 89.5 and that decimal is just the one 5$

The sales tax on telephone is 1 percent.

Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.

Given that, after sales tax, a $27 telephone costs $27.27.

Here, sales tax =27.27-27

= 0.27

Now, tax rate is 0.27/27 ×100

= 1%

Therefore, the sales tax on telephone is 1 percent.

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Answer:

no. 2/8 is equivalent to 1/4 and not equal to 1/6

The coordinates of the image is A'(3, 4), B'(1, 1), C'(-2, 2) and D'(-3, 4).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

A(-3, -4), B(-1, -1), C(2, -2) and D(3, -4).

In case the quadrilateral ABCD is rotated 180° counterclockwise about the origin, then according to the rule for the rotation of point (x, y) by 180° (x, y) changes into (-x, -y).

Then, the coordinates of the image is

A'(3, 4), B'(1, 1), C'(-2, 2) and D'(-3, 4).

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The simplified expression for this problem is given as follows:

6x + 16z.

The expression for this problem is defined as follows:

2x-3z*4/(-2)+1x+10z+3x

The quotient has the higher precedence, hence it is given as follows:

3z * 4/(-2) = 12z/(-2) = -6z.

Then the expression is given as follows:

2x + 6z + x + 10z + 3z.

The like terms are given as follows:

Hence the simplified expression is given as follows:

6x + 16z.

The problem asks to simplify the expression 2x-3z*4/2z+1x+10z+3x.

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The algebraic expression for the area is:

A = (2H - 8)*H/2

Here we want to write the expression:

"the area of a triangle that has a base 8 inches less than 2 times wider than the height."

Remember that for a triangle of base B and height H, the area is:

A = B*H/2

So if the base is 8 inches less than 2 times the height, we can write:

B = 2*H - 8

Replacing that in the area equation we get:

A = (2H - 8)*H/2

That is the equation for the area.

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Answer:

Step-by-step explanation:

The mean depression level  for the first group is μ₁ = 16.

The mean depression level for the second group is μ₂ = 12

The weighted mean is closer to 12 than to 16.

The calculated weighted mean  for  CES-D is 13.5

The calculated weighted mean  for  MAST is 17.25 ≈ 17.0 rounded to 17.

Calculating the weighted mean μ

μ=         {where x1 =μ₁ and x2= μ₂ }

μ= 16×6 + 10×12/ 6+10

μ= 216/16

μ= 13.5

The first group has a mean score of μ₁= 18.

The second group has a mean score of μ₂ = 14

Calculating the weighted mean μ

{where x1 =μ₁ and x2= μ₂ ; w1= number of women in the first   group and w2= number of women in the second group}

μ=        

μ= 18×6 + 14×12/ 6+10

μ= 276/16

μ= 17.25≈ 17

The value of the function at g = 1 and g = 4 will be 55 and 105, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

C(g) = 55          if 0 < g < 2

C(g) = 25g + 5  if g ≥ 2

The value of the function at g = 1 is given as,

C(1) = 55

The value of the function at g = 4 is given as,

C(4) = 25(4) + 5

C(4) = 100 + 5

C(4) = 105

The value of the function at g = 1 and g = 4 will be 55 and 105, respectively.

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Answer:

158

Step-by-step explanation:

So the sample size said 15 out of 50. Using the sample size to relate to the total number of students, we get this ratio

[tex] \frac{15}{50} = \frac{x}{526} [/tex]

Let's cross multiply

[tex]50x = (15)(526)[/tex]

[tex]50x = 7890[/tex]

Last, divide by 50 to get X alone

[tex]x = 157.8[/tex]

Which rounds up to 158

The grid reference number is 623313.

None of the given option is correct.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

The grid is given in the attached image.

From the given graph:

The grid number is,

623313.

Therefore, the grid number is 623313.

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The given function is continuous at  x = 5,  RHL = LHL = F(5)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  [x² - 49]/[x² + 6x -7][x² + 14x + 49]

To check whether it is continuous at x = 3

First taking LHL,

[tex]\lim_{h \to \00 } F(x)[/tex]  

[tex]\lim_{h \to \00 }[/tex]   [(5-h)² - 49]/[(5-h)² + 6(5-h) -7][(5-h)² + 14(5-h) + 49]

⇒  -24/(48x144)

⇒   -1/288

Now, taking RHL

[tex]\lim_{h \to \00 }[/tex]   [(5+h)² - 49]/[(5+h)² + 6(5+h) -7][(5+h)² + 14(5+h) + 49]

⇒  -24/(48x144)

⇒   -1/288

The value at x = 3

F(3)  =  [(5)² - 49]/[(5)² + 6(5) -7][(5)² + 14(5) + 49]

⇒  -24/(48x144)

⇒   -1/288

Hence Proved,   RHL = LHL = F(5)

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Answer:

∠ A = 23.6°

Step-by-step explanation:

complementary angles sum to 90°

sum the 2 angles and equate to 90

2x - 20 + 3x + 1 = 90

5x - 19 = 90 ( add 19 to both sides )

5x = 109 ( divide both sides by 5 )

x = 21.8

Then

∠ A = 2x - 20 = 2(21.8) - 20 = 43.6 - 20 = 23.6°

The expression which represents the amount he spent at the mall and the estimate of how much Gabe spent if he bought 7 items are:

For the first part of the question, you put the unknown variable multiplied by 16.62.

Next, what you have to do is to then add 26 which equals an unknown variable.

For the second part, since we want to find an estimate of how much Gabe spent if he bought 7 items, we would have to multiply 16.62 by 7 and add 26.

This would be $152.34

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The series given in number 9 is a convergent series

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

Tthe summation of 1/(n^(1/5)) from n=1 to infinity

To determine the convergence or divergence of the summation notation, we can use the comparison test.

The series 1/n^(1/5), which is a convergent p-series with p = 1/5.

Since 1/(n^(1/5)) <= 1/n^(1/5) for all n

It implies that the given series converges by the comparison test.

Therefore, the summation notation converges.

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The period of the sinusoidal function is given as follows:

5 units.

A periodic function is a function that has the behavior repeating in intervals over the domain of the domain.

Then the period of the function is defined as the shortest difference between two points in which the function has the same behavior.

One of the examples of the shortest difference in this problem is between x = 1 and x = 6, hence the period is calculated as follows:

6 - 1 = 5 units.

Meaning that for the sinusoidal function, the following statement is true:

f(x + 5) = f(x) for all values of x.

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Kevin has $3840 invested in stocks in total.

Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principal refers to the borrowed or lent funds. The Amount is the total of the principal plus interest.

Given:

Annual interest in first investment - 11%

Annual interest in other investment - 14%

Total interest annually - $480

let the investment for each stock be x.

then total investment = 2x

We can write

0.11x + 0.14x=480

0.25x = 480

x= 480/ 0.25

x= $1920

Also, the total investment = 2x

= 2×(1920)

= 3840

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Answer:

Step-by-step explanation:

An equivalent method of approximating values of functions is called an approximation using differentials

The polygon is a regular 9 sided polygon with each exterior angles as 40° and the measure of the sum of the exterior angles of the polygon is 360°

The exterior angles of a polygon added together is equal to 360°. No matter what the size of the polygon is, the sum of the exterior angles will always add up to 360°. If the polygon is regular, then each exterior angle measures 360°/n.

the polygon is a 9 sided polygon and thus

each exterior angle derived as;

360°/9 = 40°

40° + 40° + 40° + 40° + 40° + 40° + 40° + 40° + 40° = 360°

Therefore, the 9 sided polygon with each exterior angles as 40° have the measure of the sum of the exterior angles to be 360°

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Answer:

120 mph

Step-by-step explanation:

t = 35 min = (35 min)/(60 min/hr) = 0.583 hr

d = 70 mi

speed = d/t = (70 mi) / (0.583 hr) = 120 mph

Janna will use 30 marshmallows and 45 graham crackers to make 15 s'mores.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Janna wants to make s'mores at the backyard campfire.

The table below shows the parts of marshmallows to graham crackers to make s'mores.

S'mores  Marshmallows  Graham Crackers

4                   8                           12

15

That means, the rate is,

8/4 = 2 Marshmallows for each S'mores,

And 12/4 = 3 Graham Crackers for each S'mores.

Therefore, 30 marshmallows and 45 graham crackers to make 15 s'mores.

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Answer:

30 marshmallows and 45 graham crackers

Step-by-step explanation:

Answer:

The monthly high temperature must be less than 25° Fahrenheit.

Answer:

y=1/2x-2

Step-by-step explanation:

Slope int. Form is y=mx+b.

Knowing this, we find the slope either using rise/run or or the slope formula. y2-y1/x2-x1

using rise/run, we rise up 1 unit and run over 2 units to the right.

So mx=1/2x.

Then finding the y-intercept we look at the y-axis and look for where the graph intersects the y-axis. In this case the y intercept is already plotted at (0,-2). So b=-2.

Put all of our information together and receive the equation y=1/2x-2.

-Hope this helped

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\textit{we'll use this one}}{log_a a^x = x}\qquad \qquad a^{log_a x}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(5)+\log_2(6.4)\implies \log_2( ~~(5)(6.4) ~~ )\implies \log_2(32) \\\\\\ \log_2(2^5)\implies \text{\LARGE 5}[/tex]

The solution is,

* The company’s degree of operating leverage: 1.38;

* The impact on net operating income of a 22% increase in sales: it will increase by 30.4%;

* New contribution format income statement:

                                              Engberg Company

                            Contribution format income statement

                                     Amount                        Percentage of sales

Sales                             $176,900                              100%

Variable expenses            70,760                               40%

Contribution margin         106,140                               60%

Fixed expenses                 24,000

Net operating income        82,140      

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

* The company’s degree of operating leverage = Contribution / profit = 87,000/63,000 = 1.38

* The impact on net operating income of a 22% increase in sales is calculated as: Degree of operating leverage x % changes in sales revenue = 1.38 x 22% = 30.4%.

* new contribution format income statement is shown in the answer part.

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