Find the area of a circle with radius, r =
7.4m.
Give your answer rounded to 2 DP.
r
C
The diagram is not drawn to scale.

Answer:

27.2

Step-by-step explanation:

V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth

A, C, D are correct. In this question the options that are correct are

We have first with legs height to be =529 m and 229 m;

second with legs height =529 m and 347 m.

Then tan x = 529/229

tan y = 529/347

We can see that tanx > tany

Hence x> y

We have alternate angles in the question. This makes x=v, y=w

For D

x > y while x = v

This tells us that v>y

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Answer:

acd

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

C. 4^6 / 5^6

Step-by-step explanation:

(4/5)^6

= 4^6 / 5^6

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]

[tex]\mathbf{= \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}\times \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}}[/tex]

[tex]\mathbf{= \dfrac{4\times4\times4\times4\times4\times4}{5\times5\times5\times5\times5\times5}}[/tex]

[tex]\mathbf{= \dfrac{16\times16\times16}{25\times25\times25}}[/tex]

[tex]\mathbf{= \dfrac{256 \times 16}{625\times25}}[/tex]

[tex]\mathbf{= \dfrac{4,096}{15,625}}[/tex]

[tex]\mathbf{\approx \dfrac{4^6}{5^6}}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{Option\ C. \dfrac{4^6}{5^6}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

8/3 or 2(2/3) Textbooks to storybooks

Step-by-step explanation:

Textbooks:  (8 books)*(12 rupees/book) = 96 rupees

Storybooks:  (4 books)*(9 rupees/book) = 36 rupees

Total is 132 rupees

Ratio:  Textbook/Storybook = 96/36

96/36 = 8/3 or 2(2/3) Textbooks to storybooks

Answer:

45 numbers

Step-by-step explanation:

The 10-digit numbers are from 10-99. We can manually analyze each tenth digit and see if we can find a pattern from it. First, 10-19 ~ 10 is the only number in the sequence where the tenth digit is greater than the unit digit (because 1 > 0). In every other case, 1 is less than or equal to the unit digit.

Next, 20-29 ~ 20 and 21 are the two numbers where the tenth digit is greater than the unit digit

30-39 ~ 30, 31, 32 follow the property

40-49 ~ 40, 41, 42, 43 follow the property

We can keep going, but we can see that there is a pattern. The number of numbers that correspond with the property for each set of 10 numbers is equal to the value of the tenth digit. We see that for the 40s, there are 4 numbers. For the 20s, on the other hand, there are 2 numbers. This pattern carries through:

50-59 ~ 5 numbers, 60-69 ~ 6 numbers, 70-79 ~ 7 numbers, 80-89 ~ 8 numbers, 90-99 ~ 9 numbers

We need to find how many 2-digit numbers total follow the property. We can just add our results together to get our answer:

1+2+3+4+5+6+7+8+9=45

Answer:

f[g(x)] = 6x + 47

Step-by-step explanation:

The expression f[g(x)] represents a composite function. You need to plug the function g(x) into the "x" value of the f(x) function. Then, you can simplify.

f(x) = 6x + 11               g(x) = x + 6

f[g(x)]                                                    <----- Composition expression

f[g(x)] = 6(x + 6) + 11                             <----- Plug g(x) into x

f[g(x)] = 6x + 36 + 11                             <----- Multiply terms in parentheses by 6

f[g(x)] = 6x + 47                                  <----- Add 36 and 11

The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)

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Sample is the 3 selected customers; And population is all customers

According to the statement

we have given that a shopkeeper asks 3 customers to taste the chocolate icecream.

And we have to identify the sample and population.

So, A definition of sample is that a

A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.

And a Population is defines as the is a discrete group of people, animals or things that can be identified by at least one common characteristic for the purposes of data collection and analysis.

So, according to definition Sample is the 3 selected customers; And population is all customers.

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The percentage change in volume from cylinder A to cylinder B; D: 100%

Formula for Volume of a Cylinder is;

V = πr²h

Thus, volume of Cylinder A is;

V_a = π * 7² * 5

V_a = 245π

Thus, percentage change in volume is;

[245π/(490π - 490π)] * 100%

Percentage change in volume = 100%

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Answer:

100% increase

Step-by-step explanation:

I got it right on the test.

Answer:

5445

Step-by-step explanation:

We can use distributive property.  a*(b - c) = (a*b) - (a *c)

  99 = 100 - 1

55 * 99 = 55 * (100 - 1)

            = 55*100 - 55*1

            = 5500 - 55

            = 5445

Answer:

  (a)  (x, y) = (3, 2)

Step-by-step explanation:

The correct answer to the given system of equations can be found by trying the offered choices.

The equations are ...

The first equation tells you the sum of the x and y values is 5. Here's what we get for a sum from the different answer choices:

  A: 3 +2 = 5 . . . . a viable choice

  B: 4 +4 = 8 . . . . doesn't work

  C: 6 +1 = 7 . . . . doesn't work

  D: 3 +5 = 8 . . . . doesn't work

__

Checking (x, y) = (3, 2) in the other equation, we have ...

  7(3) +3(2) = 21 +6 = 27 . . . . as required

The solution is x = 3; y = 2.

__

Additional comment

Often, the easiest way to find the answer to a multiple-choice question is to see which answer works to solve the problem. It can sometimes be easier to check the answer than to develop it in the first place.

Substitution can work for this problem to find the correct y-value. (The answer choices differ by y-values, so knowing y tells the answer.)

  7(5 -y) +3y = 27 . . . . substitute x=5-y

  35 -4y = 27 . . . . . . simplify

  8 = 4y . . . . . . . . . add 4y-27

  2 = y . . . . . . . . . divide by 2. Matches the first answer choice.

Answer:

The slope is -3, in a y=mx+b equation the x coefficient is the slope

The correct answer is identity

the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

Angle of elevation can be defined as the angle formed between a horizontal line and the line of sight up to an object with the image of the object located above the horizontal line.

It is the height greater than the height of the observer.

The opposite of the angle of elevation is the angle of depression which is formed with an observer

Words associated with the angle of elevation are;

The angle of elevation is the angle between the line of sight and the horizontal line.

Hence, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

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Step-by-step explanation:

The equation of the line that is parallel to the given line and passes through the point (-2,2) is:

[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]

A linear function is modeled by:

y = mx + b

In which:

When two lines are parallel, they have the same slope. In this problem, the given line passes through (-5,-4) and (0,-3), hence the slope is:

m = (-3 - (-4))/(0 - (-5)) = 1/5.

Hence the equation is:

[tex]y = \frac{x}{5} + b[/tex]

When x = -2, y = 2, then:

[tex]y = \frac{x}{5} + b[/tex]

[tex]2 = \frac{-2}{5} + b[/tex]

[tex]b = \frac{12}{5}[/tex]

Hence:

[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]

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Answer:

20.1246118

Step-by-step explanation:

hypotenus^2 - (leg1)^2 = (leg2) ^2

27^2-18^2 = (leg2)^2

729-324 =  (leg2)^2

405 = (leg2)^2

20.1246118 = leg 2

The angle measurements of angle B as represented in the diagram shown is 150°

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠A = ∠B (alternate interior angles)

Hence:

8x - 10 = 3x + 90

x = 20

∠B = 3(20) + 90 = 150°

The angle measurements of angle B as represented in the diagram shown is 150°

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Answer:

60 ft^2

Step-by-step explanation:

The given statement is false. The option for the reason is the first option:

" The statement is false. A system of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."

A system of linear equations is a grouping of one or more linear equations with the same variables.

A linear system solution is the assignment of values to variables in such a way that all of the equations are concurrently fulfilled.

For a system of equations, three types of solutions exist:-

Thus, the given statement is false. The option for the reason is the first option:

" The statement is false. A system of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."

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The question is incomplete. For the complete question, check the attachment.

Answer:

9

Step-by-step explanation:

See the attached image.

25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path. This can be obtained by considering this as a right angled triangle.

Let x be the length between man and the pole, y be the distance between the tip of the shadow and the pole.

Then y - x will be the length between the man and the tip of the shadow.

Since two triangles are similar, we can write

[tex]\frac{y-x}{y} =\frac{6}{15}[/tex]

⇒15(y-x) = 6y

15 y - 15 x = 6y

9y = 15x

y = 15/9 x

y = 5/3 x

Differentiate both sides

dy/dt = 5/3 dx/dt

dy/dt is the speed of the tip of the shadow, dx/dt is the speed of the man.

Given that dx/dt = 5 ft/s

Thus dy/dt = (5/3)×5 ft/s

dy/dt = 25/3 ft/s

Hence 25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path.

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Si triplicamos la cantidad de cada artículo, el subtotal será de 2 940 soles, el impuesto al consumo será de 529,20 soles y el total será de 3 469,20 soles.

En esta pregunta tenemos un recibo con una lista de productos, cantidades, precios unitarios y precios de compra, además de un impuesto que se aplica al consumo por concepto de los productos comprados y el total, el cual refleja tanto el subtotal como el concepto por impuestos.

En cuanto a la compra de una determinada cantidad para un artículo, el coste total respectivo es igual a producto del número de artículos por el precio unitario.

El subtotal se determina mediante la suma de los costes totales asociados a cada artículo y luego se le recarga con el impuesto al consumo. Por último, el total de compra es la suma del subtotal y los pagos tributarios.

Si triplicamos el número de cada artículo comprado, tenemos los siguientes costes para cada artículo:

Chompas de dralom

12 / 4 × 280 = 840

Chompas de Orlon

6 / 2 × 100

300

Chompas de lana de alpaca

15 / 5 × 600

1 800

El subtotal es 2 940 soles y el impuesto al consumo es 18 / 100 × 2 940 = 529,20 soles. Por tanto, el total es 3 469,20 soles.

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Answer: 17 campers attended last year

Step-by-step explanation:

Let x be the number that attended last year.

The number of campers this year (23) is equal to 2 times the number of last year (x), minus 11.

23 = 2x – 11

23 + 11 = 2x

34 = 2x

34/2 = x

17 = x

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For this, multiply 150 × .20 = 30

Therefore, 20% of 150 is 30.

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Answer:

Step-by-step explanation:

Given : 10 seat in first row, and the seat will increase 1 by 1 as we go above.... (as we go to the next row) - total rows - 38

Solve ; 38 rows, 10 seat in first row, 1 seat increases each row....

Extra seats - 37,

So,

37 x 10 = 370

TOTAL SEATS = 370

Answer:

  1083 seats

Step-by-step explanation:

The number of seats is an arithmetic series with first term 10 and common difference 1. We want to find the sum of 38 terms of the series.

The sum of n terms of an arithmetic series with first term a1 and common difference d is given by the formula ...

  Sn = (2a1 +d(n -1))(n/2)

The sum of the series of interest is ...

  S38 = (2(10) +1(38 -1))(38/2)

The total number of seats in the theater can be found by evaluating the expression for S38:

  S38 = (20 +37)(19) = 57×19 = 1083

There are 1083 seats in the theater.

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

[tex]\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }[/tex]

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

[tex]\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}[/tex]

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

[tex]\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }[/tex]

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

[tex]\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}[/tex]

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

Permutations and combinations have many practical applications in various fields such as statistics, Probability theory, and computer science.

Permutations and combinations are two concepts in mathematics that deal with counting and arranging elements in a set.

Permutations refer to the number of ways in which a set of objects can be arranged or ordered. In other words, permutations involve counting the number of possible ways in which a group of objects can be arranged in a particular order. For example, if we have three objects A, B, and C, the possible permutations would be ABC, ACB, BAC, BCA, CAB, and CBA. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.

Combinations, on the other hand, refer to the number of ways in which a subset of objects can be selected from a larger set, without regard to the order in which they are selected. In other words, combinations involve counting the number of possible subsets that can be formed from a larger set. For example, if we have three objects A, B, and C, the possible combinations would be AB, AC, and BC. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects being selected.

The key difference between permutations and combinations is that permutations involve ordering objects, while combinations do not. Another important distinction is that in permutations, each arrangement is considered distinct, whereas in combinations, different arrangements that contain the same objects are considered identical.

Permutations and combinations have many practical applications in various fields such as statistics, probability theory, and computer science. For example, they are commonly used in solving problems related to probability, combinations of locks, and permutations of passwords. Understanding these concepts is essential in order to effectively analyze and solve problems in these fields.

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Answer: △JKL & △ MNP

Step-by-step explanation:

△JKL is similar because:

5 x 1.6 = 8

2.5 x 1.6 = 4

3.75 x 1.6 = 6

△MNP is also similar because:

4 x 2 = 8

2 x 2 = 4

3 x 2 = 6