In a class of 52 students, 13 excel in Science and Mathematics, 16 excel in Science and Arts, 12 excel in Mathematics and Arts, 24 excel in Arts and 2 excel in none. Twice as many students excel in science only as do in mathematics only. The number of students who excel in mathematics only is six times the number of students who excel in Arts only. Determine the number of students who excelled in: (a) All the three subjects (b) Two subjects

Answer: the answer to be smart is to learn

Step-by-step explanation:

if you learn then you can understand the u are not smart

The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below

Given the following equation

(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)

We start by simplifying the left-hand side of the equation:

(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]

Next, we have the following steps to simplify the expression

= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]

= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]

= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]

= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]

= -4(2p² + 1)/(p²-4) (p² - 1)

Hence, the given identity is proven.

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Using the table feature of a graphing utility  the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds would be 2.16 x 10¹⁴ joules/second/meter².

First, note that the   intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds can be calculated using the formula..

I = (1/2)ρv²

Here I   Intensity

ρ = density of the medium - this is a constatnt

v = velocity of the S-waves

If we used a graphing tool

a coumun ffor v will be created

a column for the formula for velocity will also be created.

The formula for velocity is

V = A/ T

A = amplitude

T = time or period in seconds


Since A = 200,000 micrometers; and

T = 0.05 secons

v = 200,000 / 0.5

v = 400,000 micrometer/sec

Back o the table, we ahve to add another oclumn for V²

then enter the values for V²

V² = 400,000²
v² = 160,000,000,000 micrometer²/sec²


Nowe we add another column which is

I = 1/2(pv²)

I = 2.16 x 10¹⁴ joules/second/meter².


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The composition of functions is solved and the expressions are

a) ( g o f ) ( -1 ) = 1

b) ( g o f ) ( 0 ) = 4

c) ( f o g ) ( -1 ) = -2

d) ( f o g ) ( 4 ) = -1

Given data ,

Let the composition of function be represented as A

Now , the value of A is

a)

( g o f ) ( -1 ) = g ( f ( -1 ) )

On simplifying the function , we get

when x = -1 , f ( -1 ) = 2

g ( 2 ) = 1

So , ( g o f ) ( -1 ) = 1

b)

( g o f ) ( 0 ) = g ( f ( 0 ) )

On simplifying the function , we get

when x = 0 , f ( 0 ) = 0

g ( 0 ) = 4

So , ( g o f ) ( 0 ) = 4

c)

( f o g ) ( -1 ) = f ( g ( -1 ) )

On simplifying the function , we get

when x = -1 , g ( -1 ) = 2

f ( 2 ) = -2

So , ( f o g ) ( -1 ) = -2

d)

( f o g ) ( 4 ) = f ( g ( 4 ) )

On simplifying the function , we get

when x = 4 , g ( 4 ) = 1

f ( 1 ) = -1

So , ( f o g ) ( 4 ) = -1

Hence , the composition of function is solved

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Answer:  36600 = E

Step-by-step explanation:

Given:

T=.2 (E - 10600)      

T=5200  

Find:  E

Solution:  

>substitute into thequation.  You know T=5200

5200 = .2(E-10600)     > Divide both sides by .2

26000 = E- 10600       > add 10600 to both sides

36600 = E                    

Using two column proof we have been able to show that AB ║ EC

by definition of alternate interior angles

A two-column proof is defined as a two-column table labeled with statements on the left-hand side and reasons on the right-hand side.

The two column proof of the given diagram is as follows:

Statement 1: ΔADE is an Isosceles Triangle

Reason 1: Given

Statement 2: ∠DEA ≅ ∠DAE

Reason 2: Properties of Isosceles Triangles

Statement 3: ∠ADE = 20°

Reason 3: Sum of angles in a triangle

Statement 4: ∠BAD ≅ ∠EDA

Reason 4: Congruent Angles

Statement 5: ∠BAD and ∠EDA are alternate angles

Reason 5: Alternate angles are congruent

Statement 6: AB ║ EC

Reason 6: Definition of alternate interior angles

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All real numbers greater than 5 can be expressed in interval notation as:

(5, ∞)

Interval notation is a way of representing an interval on a number line. Simply, it is a method of writing subsets of the real number line.

All real numbers greater than 5 can be expressed in interval notation as:

(5, ∞)

Where the round bracket "(" means 5 is not included in the interval, and the infinity symbol "∞" means the interval continues indefinitely to the right.

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Answer: X = 25

Step-by-step explanation: Since 36 divided by 2 equals 18, which would cancel out the two on the left side leaving us with. (x - 7) = 18 we can add 7 to both sides to get. X = 25

Edit: To whoever said my math is incorrect is wrong, I even double checked with multiple sources and people. It must’ve been a different equation or number. Sorry for not being able to help, however the math was correct.

The solution is: the area of the shaded base in square centimeters is:

B= 15 cm²

Here, we have,

The base of the triangular shaped wedge of cheese is a right-triangle.To find the area of a right-triangle you apply the formula for half base by height.

A=1/2*b*h

 = base area

 = B

In this case, assume the sides of the triangle given are;

a=5 cm and b=6 cm,

thus area will be 1/2*6*5 =15 cm²

Hence, the area of the shaded base in square centimeters is :

B= 15 cm²

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complete question:

Evelyn cut a wedge of cheese into the shape of a triangular prism-like the one shown below. The shaded part represents one of the bases of the prism.

A formula for the volume of a triangular prism is v=Bh . Which equation can be used to find B , the area of the shaded base in square centimeters?

The initial velocity of the car before the brake was pulled is 30m/s

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

A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds

This means that

Acceleration = -4.0m/s^2

Time = 7.5 seconds

Using the above as a guide, we have the following:

Initial velocity = -Acceleration  * Time

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

Initial velocity = 4  * 7.5

Evaluate

Initial velocity = 30

Hence, the initial velocity is 30

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The measure of the angle is 36.9^o. Option B.

A right triangle is a form or type of triangle in which the measure of one of its internal angles is 90^o. As such, either the trigonometric functions or Pythagorean theorem can be applied to determine any of its properties as the case may be.

From the details given in the question, we can deduced that;

Sin θ = 3/5

       = 0.6

So that,

θ = Sin^-1 0.6

  = 36.87

θ = 36.9^o

The measure of the angle is 36.9^o. Option B.

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Answer:

3rd choice:  when b>1

Step-by-step explanation:

For this function, a is the starting value (initial amount).  b is the decay or growth factor.  If b>1, then the function is a growth function.

FYI, if 0 < b < 1, then it is a decay function.

Answer:  

C is the answer

Given :   dilation with a scale factor of 3

To find :  Which statement is true

Step-by-step explanation:

Solution: A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

if Dilation factor  N then image Size is multiplied  by  N

if Scale factor  < 1 then image get reduced

if scale factor > 1  then image get enlarged

scale factor = 1 lead to Same size image

Here is given that Scale factor of 3

=> image will be enlarged to 3 times the original image

Hence correct option is :

C)Each side in the pre-image is multiplied by three to find the corresponding side length in the image

Answer: C

Step-by-step explanation: Edge Unit Test

The feasible region on the attached graph of the inequalities created with MS Excel indicates that the maximum value of g = 8·x + 12·y is 100

The feasible region is the region on the graph of the inequalities that satisfies the specified constraints.

The specified equations obtained from the constraints in slope intercept form are;

y = -0.5·x + 7; The region below the graph is shaded

y = -0.75·x + 9; The region below the graph is shaded

x = 0; The region to the right of the line x = 0 is shaded

y = 0; The region above the line y = 0 is shaded

The point of intersection of the graphs can be found from the equation; -0.5·x + 7 = -0.75·x + 9

Which indicates that at the intersection, x = 8, and y = -0.5×8 + 7 = 3

The corner points are; (0, 0), (0, 7), (8, 3), (12, 0)

The value of the function g for each of the feasible region are therefore;

g(0, 0) = 8 × 0 + 12 × 0 = 0

g(0, 7) = 8 × 0 + 12 × 7 = 84

g(8, 3) = 8 × 8 + 12 × 3 = 100

g(12, 0) = 8 × 12 + 12 × 0 = 96

Please find attached the graph of the inequalities showing the feasible region created with MS Excel

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The total units of length for the ice rink away from the origin is 14.42 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Note: Ice rink is located at point (12, 8).

By substituting the given end points into the distance formula, we have the following;

Distance = √[(12 - 0)² + (8 - 0)²]

Distance = √[(12)² + (8)²]

Distance = √[144 + 64]

Distance = √208

Distance = 14.42 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

7e+6

Step-by-step explanation:

biggest answer

The index forms are simplified to;

1. [tex]5^6^\sqrt{2}[/tex]

2.[tex]3^5\sqrt{3}[/tex]

3.  [tex]2^2^\sqrt{25}[/tex]

It is important to note the following about the rules of index forms;

From the information given, we have that;

[tex]5^\sqrt{2}[/tex] × [tex]5^\sqrt{50}[/tex]

Add the exponents, we have;

[tex]5^\sqrt{2} ^+ 5\sqrt{2}[/tex]

Then, we have;

[tex]5^6^\sqrt{2}[/tex]

2. [tex]3\sqrt{12}[/tex] × [tex]3^\sqrt{27}[/tex]

We have;

[tex]3^2^\sqrt{3} + 3\sqrt{3}[/tex]

Add the exponents

[tex]3^5\sqrt{3}[/tex]

3. [tex]2^2^\sqrt{25}[/tex]

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The left-handed students in the music program are option A 15 students.

A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.

From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.

Thus, he left-handed students in the music program are 15.

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The first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3

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

The sequence is generated by using gn = 2(gn-1)

Such that g1 = 1/3 and n is a whole number greater than 1.

Using the above as a guide, we have the following:

The sequence means that we multiply the current term by 2 to get the next term

So, we have the following representations

a(2) = 2 * 1/3 = 2/3

a(3) = 2 * 2/3 = 4/3

a(4) = 2 * 4/3 = 8/3

a(5) = 2 * 8/3 = 16/3

Hence, the first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3

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About 120 students have travel times within the quoted interquartile range.

The interquartile range (IQR) represents the range of the middle 50% of a set of data, which is the difference between the third quartile (Q3) and the first quartile (Q1).

Assuming that the travel times are normally distributed and that we have information on the quartiles, we can use the formula:

IQR = Q3 - Q1

To find the number of students whose travel times fall within the interquartile range, we need to know the values of Q1 and Q3.

Since the IQR is 32 minutes:

32 = Q3 - Q1

We also know that the total number of students in Year 12 is 240. Assuming that all students have reported their travel times, we can use the interquartile range to estimate the proportion of students whose travel times fall within this range.

If the interquartile range covers the middle 50% of the data, then each quartile should cover 25% of the data. Therefore, we can estimate that the number of students whose travel times fall within the interquartile range is:

Number of students = 240 x 0.50 = 120

Therefore, we estimate that 120 of the 240 Year 12 students have travel times within the interquartile range of 32 minutes.

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Answer:

60

Step-by-step explanation:

14 rounds to 10

23 rounds to 20

28 rounds to 30

10+20+30=60

Answer: 2.5

Step-by-step explanation:

the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5

hope it helped:)

a) is Right angle Triangles both of them

b) The scale factor is 1:2.

Given AFD = 90 degrees, So CFD = 90 degrees.

So it a Right Angle Triangle.

Again ABC = 90 degrees, It's also a Right Angle Triangle.

Here see both the Triangle are opposite to each other so according to the theorem sum of all three angles of a triangle is 180 degrees

so if any angle is 90 deg then the other two sum is also 90 deg.

Given the scale Factor, 1/6 inch = 1 foot,

So it is a Reducing Scale so let 'x' be in inches

So the Scale Factor = 1:2

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The conversion of 2,000 Swiss francs to United States dollars and from United States dollars into Dutch guilders (Holland) based on Wednesday's currency exchange rate is D. ƒ4,032.

The exchange rate represents the unit rate at which one currency is exchanged for or converted to another.

Exchange rate conversions rely on the mathematical operations of division or multiplication.

1 CHF = $1.12

2,000 CHF = $2,240 ($1.12 x 2,000 CHF)

On Wednesday April 26, 2023, $1.00 =  ƒ‎1.80

$2,240 = ƒ4,032 ($2,240 x ƒ1.80)

Thus, we can conclude that 2,000 CHF (Swiss francs) are worth 4,032 Dutch guilders.

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