The indicated function values for f(x) = 8x + 4 if x is:
(a) f(-4) = -13, (b) f(2) = 22
(c) f(0) = 8, (d) f (-100) + f(100) = 215
What is meant by function ?
A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).
We must look at the value of x to determine which equation to take into account. In the first equation, we will substitute x if it is negative; in the second equation, we will substitute x if it is positive or null.
(a) x = -4 so x is negative.
We use the first equation f(x) = 5x + 7 and we have f(-4) = 5 × (-4) + 7 = -13
(b) x = 2 and is positive.
We use the second equation f(x) = 7x + 8.
The result is f(2) =7 × (2) + 8 = 22
(c) x = 0 In this case the function is defined by the second equation f(x) = 7x + 8. So f(0) =7 × (0) + 8 = 8
(d) We need to calculate the function values of each one and then make the sum.
With f(-100), x = -100 and is negative
We use the first equation f(x) = 5x + 7 and
we have f(-100) = 5 × (-100) + 7 = -493.
With f(00), x = 100 is positive so we use the second equation f(x) = 7x + 8 and get f(100) = 7 × 100 + 8 = 708
We add them to get the result: f(-100) + f(100) = -493 + 708 = 215
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The complete question is:
The function below is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for non-negative numbers in the domain. Find the indicated function values.
f (x) = { 5x+7 if x < 0
{ 7x+8 if x ≥ 0
(a) f (- 4)
(b) f (2)
(c) f (0)
(d) f (-100) + f(100)
Find the difference in the given lengths of the polygons. (7x + 2) units (6x - 5) units
By solving a subtraction, we can write the difference between the lengths as:
|x + 7|
How to find the difference between the lengths?Here we want to find the difference between the two lenghts below:
L₁ = (7x + 2)
L₂ = (6x - 5)
The difference between these can be written as the absolute value of the subtraction, then we will get:
| L₁ - L₂|
We use the absolute value because we don't know which one is the larger value.
Replacing the expressions we will get:
| (7x + 2) - (6x - 5)|
|7x + 2 - 6x + 5|
| x + 7|
That is the difference.
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based on the information in the table, what quantity of reserves would the federal reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?
The public increased the amount of currency it held and that banks increased the reserve-deposit ratio is $0.66 million.
Now, According to the question:
December 1921
-Currency held by public: $4.59
-Reserve Deposit ratio: 0.095
-Bank reserves: $3.11
-Money supply: $37.3
December 1932
-Currency held by public: $4.82
-Reserve Deposit ratio: 0.109
-Bank reserves: $3.18
-Money supply: $34.0
We know that:
Bank deposits = (Bank reserves)/(Desired reserve-deposit ratio).
The Fed injected $0.30 billion (the public held $0.23 billion as currency and reserves increased by $0.07 billion was held as reserves). However, the money supply still fell by $3.3 billion.
It would have taken an additional 0.109 × $3.3 billion = $0.36 billion in reserves to support $3.3 in additional deposits.
So the answer is $0.30 billion + $0.36 billion = $0.66 billion.
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The given question is incomplete, complete question is :
Based on the information in the table, what quantity of reserves would the Federal Reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?
December 1921
-Currency held by public: $4.59
-Reserve Deposit ratio: 0.095
-Bank reserves: $3.11
-Money supply: $37.3
December 1932
-Currency held by public: $4.82
-Reserve Deposit ratio: 0.109
-Bank reserves: $3.18
-Money supply: $34.0
What fraction is not greater than 1/2? 7/8 4/6 3/5 2/5
Answer:this is so ez
Step-by-step explanation: 2/5
A blood test indicates the presence of a particular disease 96% of the time when the disease is actually present. The same test indicates the presence of the disease 0.8% of the time when the disease is not present. Two percent of the population actually has the disease. Calculate the probability that a person has the disease, given that the test indicates the presence of the disease.
The probability of a person that has the disease and indication of the test also shows the presence of the disease is given by 0.92.
Let us consider 'A' represents the test indicate the presence of disease when it was actually present
A = 96%
= 0.96
And 'B' represents the population percent actually has the disease
B = 2%
= 0.02
A' represents the population who represents the disease when actually disease is not present.
A' = 0.08
Probability of a person that has the disease when test also indicates its presence is given by :
P ( A/ B) = P( A∩B) / [ P(A∩B) + P(A'∩B) ]
= ( 0.02 × 0.96 ) / [ ( 0.02 × 0.96 ) + ( 0.02 × 0.08 ) ]
= 0.0192 / 0.0208
= 0.92
Therefore, the required probability of a person having disease when test also indicates it is equal to 0.92.
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Express the answers to the following operations with the
proper number of significant figures.
(a) (1.600 × 10-¹)(2.1 × 10³)
(b) (1.33)³
(c) 1.93.x 2.651
(d) 4.4/2.200
I don’t understand what it is asking for, help please!
Expressed the answers to the given operations with the proper number of significant figures:
(a) (1.600 × 10-¹)(2.1 × 10³) = 336
(b) (1.33)³ = 2.352637
(c) 1.93.x 2.651 = 5.11643
(d) 4.4/2.200 = 2
What's meant by integers?In calculation, single integers called integers are used to represent values. To represent all fine values, the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in colorful combinations and reiterations.
A number is a symbol that can be used to represent any of the ten integers ranging from 0 to 9. an illustration of a two- number.
When a number has two integers, it's called a 2- number . 2- number figures have two integers and range from 10 to 99.
They're unfit to begin with zero since it'll also be regarded as a single- number .
Any number between 1 and 9 can be used as the number in the knockouts place. For case, the figures 45, 78, and 12 have two integers.
a) (1.600 × 10-¹)(2.1 × 10³)
= 1.6 × 2.1 × 10⁻¹⁺³
= 3.36 × 10²
= 336
b) (1.33)³
= 2.352637
c) 1.93 × 2.651
= 5.11643
d) 4.4/2.200
= 2.0
= 2
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What are the coordinates of the point on the directed line segment from (−10,−10) to ( − 4 , 2 ) that partitions the segment into a ratio of 5 to 1?
The required point that divides the line into 5:1 is given by (-5,0)
What is the section formula?Let M(x, y) be the point which divides line segment PQ internally in the ratio m : n. PA, MN and QR are drawn perpendicular to x- axis. PS and MB are drawn parallel to x – axis. This is known as section formula.
Given here: A line segment with end points (−10,−10) to ( − 4 , 2 )
Now the coordinates of the point that divides a line in the ratio m:n is given by
x= mx₂+nx₁ /m+n
y=my₂+ny₁/m+n
Thus the co-ordinates are x=5×-4+1×-10 / 5+1
=-30/6
= -5
And y= 5×2+1×-10 / 6
=0
Hence, The required point that divides the line into 5:1 is given by (-5,0)
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When an economy produces a good where the marginal benefit equals the marginal cost it is
At that level of output and price, profit is maximized when marginal revenue and the marginal cost of production are equal:
MR = *TR/*Q
MC = *C/*Q
Eq. = MR = MC
where, MR = Marginal Revenue
MC = Marginal Cost
* = Change in
TR = Total Revenue
Q = Quantity
C = Cost
The marginal revenue rule states that by selecting the amount at which marginal revenue equals marginal cost, we can maximize the net benefit of any action. The activity's net benefit is maximum at this amount.
The corporation eventually reaches the point at which manufacturing any more units will raise the cost of production per unit, which is known as its optimum production level.
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How to solve this problem
Answer:
656 cm sq
Step-by-step explanation:
2 x 10 x 2 x 10 = 400
8 x 2 x 8 x 2 =256
256+400 = 656
if interest is compounded monthly, then the actual amount you would owe in the situation of part (b)is given by $7000 ✕ 1.01612. What is the actual amount you would owe at the end of the year? (Round your answer to the nearest cent.
If you look at this rationally I believe it will be 7.0 with the odd number.
Which expression is equivalent to -63y² + 27y?
O-9y(7y-3)
O9y(7y-3)
O-9y(7y + 3)
O9y(7y + 3)
HELP ASAP
Answer:
[tex]9y\left(-7y+3\right)[/tex]Step-by-step explanation:
[tex]-63y^2+27y[/tex]
[tex]-63yy+27y[/tex]
[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]
[tex]9y\left(-7y+3\right)[/tex]
Find the measure of a single exterior angle of the regular polygon shown below. If necessary, round to the nearest tenth.
The measure of an exterior angle of the regular polygon shown in the figure is 60°.
What are exterior angle?The angle between a side of a polygon and an extended adjacent side is called its exterior angle.
Given is a polygon, since, it has six vertices, so we can say it is a regular hexagon,
We know that, the sum of interior angles of regular hexagon is 720°
Therefore, one interior angle = 720 / 6 = 120°
If we extend a side of the hexagon, (refer to figure attached in solution)
Then, the interior angle and an exterior angle "A" will make a linear pair,
Therefore,
120° + A = 180°
A = 60°
Hence, the measure of an exterior angle of the regular polygon shown in the figure is 60°.
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4/7 x 3/8 then simplify
Answer:
0.2142857143
Step-by-step explanation:
4/7 × 3/8
=12/56
=0.2142857143.
Translate these statements into English, where the domain for each variable consists of all real numbers.
a) ∀x∃y(x < y)
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))
c) ∀x∀y∃z(xy = z)
a) ∀x∃y(x < y): For all values of x there exist number y such that all x are less than y.
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0)) : For any numbers x and y if x is greater tha or equal to 0 and y is greater than or equal to 0 then their product is greater than or equal to 0.
c) ∀x∀y∃z(xy = z) : For any numbers x and y there exist number z such that the product of x and y is equal to z.
We know that a mathematical statement is nothing but a sentence which is either true or false.
We need to translate these statements into English.
The meaning of some mathematical symbols:
∀ : for all
∃ : there exists exactly one
∧ : and
Here, x, y, z are real numbers.
Consider given mathematical statements.
a) ∀x∃y(x < y)
For all values of x there exist number y such that all x are less than y.
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))
For any numbers x and y if x is greater tha or equal to 0 and y is greater tha or equal to 0 then their product is greater than or equal to 0.
c) ∀x∀y∃z(xy = z)
For any numbers x and y there exist number z such that the product of x and y is equal to z.
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Type the correct answer in each box. Lmk!
There were 0-5 Listeners when the song was released.
The approximate number of listeners who had heard the song after the hour 5 was 15- below 50
The number of listeners was about 29,458 after hour 5842.62/
How can I explain?Alternative forms
Y= 4,637(1.26)ˣ
292131/50,5842,31/50,5.84262 =10³
5842.62
Including polynomial components, such as squared or cubed predictors, is the most popular technique to fit curves to data using linear regression. Typically, the model order is determined by the number of bends required in your line. Each exponent increment causes one additional bend in the curved fitting line.
Curve of Best Fit: a scatter plot curve that best approximates the trend. If the data looks to be quadratic, we use quadratic regression to get the equation for the best-fit curve. We do a cubic regression if it looks to be cubic.
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The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin Ït + 4 cos Ït, where t is measured in seconds. (Round your answers to two decimal places.)(a) Find the average velocity during each time period.i. [1,2]ii. [1,1.1]iii. [1.1.01]iv. [1.1.001]
The average speed throughout the given time was [1,2] = -2.00 cm/sii. -0.26 cm/siii for [1,1.1]. [1.1,1.01] = 0.17 cm/siv. [1.1,1.001] = 0.02 cm/s
The particle's displacement divided by the passage of time represents its average velocity at each time interval. The displacement of the particle for the above motion equation is given by s = 2 sint + 4 cost. By subtracting the displacement at the beginning and end of the period and dividing it by the change in time, we can determine the average velocity for each time period. As an illustration, the displacement for the time period [1,2] is 2 sin + 4 cos at the beginning of the period and 2 sin + 4 cos at the end of the period. These two figures differ by -4, and one second has passed between them.
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Which expressions are equivalent to -4(-25y + 4 + 50y - 8)? Select all
that apply.
A - 100y - 4
B -2(23y - 5 + 27y - 3)
C (100y + 32) - (200y + 16)
D -16 - 100y
E -(-100y + 16 + 200y - 32)
F
- 300y - 48
The two equivalent expressions to the given one are the ones in options C and E.
C (100y + 32) - (200y + 16)
E -(-100y + 16 + 200y - 32)
Which expressions are equivalent to the given one?We want to see which expressions are equivalent to:
-4*(-25y + 4 + 50y - 8)
Let's distribute that product so we will get:
-4*(-25)*y - 4*4 - 4*50y - 4*-8
100y - 16 - 200y + 32 = -(-100y + 16 + 200y - 32)
Then option E is a correct option
And also is C: (100y + 32) - (200y + 16)
If we keep simplifying this we wil get:
100y - 16 - 200y + 32 = -100y + 16
And here we end.
The only two equivalent expressions are E and C.
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Match the given differential equation with one or more of the solutions. (Select all that apply.) xy' = 4y y = 4x y = 0 y =4 Y = 4x4
The solutions that match the given differential equation are a)y=0 and b)y=2x.
The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.
In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.
Therefore, the general solution to this differential equation is y = c1 + c2x.
y=0 is a solution of the differential equation since it satisfies the equation when plugged in.
y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.
y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.
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6. Insert < >, or = to make the sentence true. (1 point)
3/4 ? 4/7
O>
O<
O=
Answer:
3/4 > 4/7
Step-by-step explanation:
1. Find the LCM of 4 and 7, which is 28
2. Take 3/4 and multiply the numerator and the denominator by 7 (because 7x4=28)
You will end up with 21/28
3. Take 4/7 and multiply the numerator and the denominator by 4 (because 4x7=28)
You will end up with 16/28
Now that the denominators are the same, the fraction with the bigger numerator is the greater fraction. Therefore, 3/4 is the greater than 4/7.
Jamie buys p bags of pears for $8 each and m melons for $6 each.
Write an expression to represent how much Jamie spends in all.
The expression to represent how much Jamie spends in all. we may state,0.40x + 0.40y is 8, 0.30x + 0.30y is 6
What is an expression to represent?Set variables to represent the amounts we wish to identify.
Let x = the quantity of p bagsLet y=the quantity of m melonsThen, using these variables, we create equations that fully capture the narrative.Since the overall cost is $8 and $6 the cost of each bags variety varies, we may state0.40x + 0.40y = 8.0.30x + 0.30y =6The total amount of bags purchased together will be represented by the other equation, as Mark said. Once you have those equations, you may solve the problem for the variables x and y by utilising substitution and elimination techniques.The expression to represent how much Jamie spends in all. we may state,0.40x + 0.40y = 8, 0.30x + 0.30yTo learn more about expression refer to:
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A recent study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. Forty- two hundred study? Florida residents were surveyed, Which of the following is the sample used in tho a) all Florida residents b) the 4200 Florida residents surveyed c) all Florida residents who lived along the beaches d) the Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters
The sample used in the study is b) the 4200 Florida residents surveyed. surveyed. To obtain the answer following steps are :
1. Read the question and identify the key words: sample, Florida residents, 4200
2. Consider the given options and eliminate those that don't match
3. Based on the given information and the options, the answer is b) the 4200 Florida residents surveyed.
This is because the sample used in the study was the 4200 Florida residents who were surveyed, and this sample was used to estimate the proportion of all Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters.
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Let y = πx + π. For what value of x is y = π^3?
The value of the variable x = π³ - π/π
What are algebraic expressions?Algebraic expressions are described as mathematical expressions that are comprised of variables, factors, constants, terms and coefficients.
These algebraic expressions are also comprised of arithmetic operations, such as;
DivisionMultiplicationSubtractionFloor divisionAdditionBracketParenthesesFrom the information, we have that;
y = π³
y = πx + π
Substitute the values, we get;
π³ = πx + π
collect like terms
π³ - π = πx
Divide both sides by the coefficient of x
x = π³ - π/π
Thus, the value is x = π³ - π/π
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is the linear relationship represented by the table a proportional relationship?
Tickets
Cost
0
$0
The linear relationship
the point (0, 0)
2
$14.50
Choose
4
$29
6
$43.50
a proportional relationship because the ratios between each pair of values are equivalent and the graph
Choose...
through
The linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).
What is proportional relationship?
Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".
We are given points as (2,14.5), (4,29), (6,43.5) and the origin (0,0).
We know that in a proportional relationship the ratios are equal i.e.
[tex]\frac{y_{1} }{x_{1}} = \frac{y_{2} }{x_{2} } = \frac{y_{n} }{x_{n} }[/tex]
So,
⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25
Since, the ratios are same, therefore the linear relationship is a proportional relationship.
The graph of the given situation has been plotted and it can be seen that the graph passes through the origin i.e. (0,0)
Hence, the linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).
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3xcube+x-200 divide by x-4
When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.
What is division?Division is the process of splitting a number or an amount into equal parts.
Given is an expression, 3x³+x-200 which is divided by x-4,
Therefore,
(3x³+x-200) / (x-4)
Step 1)Divide the leading term of the dividend by the leading term of the divisor:
3x³/x = 3x²
Multiply it by the divisor: 3x²(x−4)=3x³−12x²
Subtract the dividend from the obtained result:
(3x³+x−200)−(3x³−12x2) = 12x²+x−200
Step 2)Divide the leading term of the obtained remainder by the leading term of the divisor: 12x²/x = 12x
Multiply it by the divisor: 12x(x−4) = 12x²−48x
Subtract the remainder from the obtained result:
(12x²+x−200)−(12x²−48x) = 49x−200
Step 3)Divide the leading term of the obtained remainder by the leading term of the divisor: 49x / x = 49
Multiply it by the divisor: 49(x−4) = 49x−196
Subtract the remainder from the obtained result:
(49x−200)−(49x−196) = −4
Hence, When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.
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Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function:
y = (pie)x Power Function
y = xy Exponential Function
y = x2(2-x3) Polynomial (degree of 2)
y = tan t â cos t Trigonometric
y = s / 1+s Algebraic Function
y = sqrt(x3 â 1) / 1+ 3sqrt(x) Root Function
Not sure on these. Thanks!
A power function is a type of function with a variable in the form of an exponent. An exponential function is a type of function that contains a variable in the form of an exponent.
The most common example of this is y = xn, where n is the exponent and x is the independent variable. For example, y = (π)x is a power function with an exponent of x and an independent variable of π.
Exponential Function: An exponential function is a type of function that contains a variable in the form of an exponent. The most common example of this is y = bx, where b is the base and x is the independent variable. For example, y = xy is an exponential function with a base of x and an independent variable of y.
Polynomial: A polynomial is a type of function that has a degree, which is the highest exponent of its variables. For example, y = x2 (2-x3) is a polynomial with a degree of 2 since the highest exponent of its variables is 2.
Trigonometric: A trigonometric function is a type of function that involves trigonometric ratios. The most common example of this is y = tan t â cos t, which uses the trigonometric ratios of tangent and cosine.
Algebraic Function: An algebraic function is a type of function that can be expressed as a combination of polynomials. The most common example of this is y = s / 1+s, which is a combination of polynomials with a numerator of s and a denominator of 1+s.
Root Function: A root function is a type of function that involves a root of a polynomial. The most common example of this is y = sqrt(x3 â 1) / 1+ 3sqrt(x), which uses the root of the polynomial x3 â 1 in the numerator and 3sqrt(x) in the denominator.
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Solve the equation for N
The value of N would be N = q/(9 + 4uz).
What is algebraic manipulation?
Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.
Given:
q - 4Nuz = 9N
To find the value of N, we can use algebraic manipulation.
9N + 4Nuz = q
N(9 + 4uz) = q
N = q/(9 + 4uz)
Hence, the value of N would be N = q/(9 + 4uz).
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I dont understand this
What is the best name for this shape? Use the drop-down menus to explain your answer. 55° 125° 125° 55° Click the arrows to choose an answer from each menu. The shape has Choose... It has Choose.... It has Choose... The best name for this shape is Choose... angles that are acute and equal. angles that are obtuse and equal. angles that are right angles.
The best name for this shape is rectangle. There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle.
Four names for rectangles: what are they?Parallelograms, quadrilaterals, and polygons are some other names for rectangles that we use. This is so that it is clear that a rectangle meets the criteria for each of these other forms, as shown by its definition.There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle, hence the answer is that every rectangle is a parallelogram. Thus, it conforms to all of a parallelogram's characteristics.There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle, hence the answer is that every rectangle is a parallelogram.Parallelograms, quadrilaterals, and polygons are some other names for rectangles that we use.To learn more about rectangle refer to:
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The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?
Group of answer choices
68
33
47
40
Number of shingles in the 6th row is 110.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
Given;
Each row has 7 fewer shingles than the row below it
First row has 75 shingles
Now,
a=75
D=7
n=6
a_{n}=a_{1}+(n-1)d
a6=75+(6-1)7
a6=75+35
a6=110
Therefore, the answer of arithmetic sequence will be 110.
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Answer:
33
Step-by-step explanation:
it starts with 75 and decreases by 7 for each row. (75 -7) On the 6th row youll be at 33!
STARTS AT 75
row one: 68
row two: 61
row three:54
row four: 47
row five: 40
row six: 33
i need to know what it is written out
I think you want to know what written out means? If yes it means when someone writes something down on a book or paper.
There are 100 teachers in a school. 60 teach science, 25 teach humanities, 15 teach both science and humanities. 6Find the number of teachers who teach: (a) science but not humanities. (b) Humanities but not science. (c) Humanities or science.
The number of teachers who teach:
(a) science but not humanities = 45
(b) Humanities but not science = 10
(c) Humanities or science = 70
Finding the number of teachers:To find the number of teachers that teach only Science we can subtract the number of teachers who teach both subjects from the number of teachers that teach science.
Similarly, to find the number of teachers that teach only Humanities we can subtract the number of teachers who teach both subjects from the number of teachers that teach Humanities.
To find the number of teachers who teach Humanities or science we use the elementary set formula,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)Here we have
Total number of teachers = 100
No of teachers who teach Humanities, n(H)= 25
No of teachers who teach Science, n(S) = 60
No of teachers who teach both Science and Humanities, n(H ∩ S) = 15
The number of teachers who teach science but not humanities
= No of teachers who teach Science - No of teachers who teach both
= 60 - 15 = 45
The number of teachers who teach Humanities but not science
= No of teachers who teach Humanities - No of teachers who teach both
= 25 - 15 = 10
The number of teachers who teach Humanities or Science
As we know n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
The number of teachers who teach Humanities or Science
= n(S) + n(H) - n(S ∩ H)
= 60 + 25 - 15
= 70
Therefore,
The number of teachers who teach:
(a) science but not humanities = 45
(b) Humanities but not science = 10
(c) Humanities or science = 70
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