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The length of a room is

3

4

times its breadth. The total area of the four walls of this room is

15

28

times the area of the floor of the room. What is the ratio of the height of the room to the length of the room?

Medium

Solution

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Correct option is D)

Let breadth =x units

Then length =

3

4

x units

⇒ Area of floor = x×

3

4

x=

3

4

x

2

square units

Let the height of the room =y units. Then

Area of four walls = 2[xy+

3

4

xy]=

3

14

xy

Now,

3

14

xy=

15

28

(

3

4

x

2

)⇒xy=

15

2

×4x

2

y=

15

8

x ⇒

x

y

=

15

8

⇒ y:x=8:15

Answer:

[tex]5\frac{1}{3} or \frac{16}{3}[/tex]

Step-by-step explanation:

endless 3’s are always 1/3

So now we just add 5 in front of it

5 1/3

Hopes this helps please mark brainliest

[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

5.333333

= [tex]\frac{16}{3}[/tex]

We see that,

3 ) 16 ( 5.333333

    15

      10

       9

        10

         9

           1

and so on...

Thus,

[tex]\frac{16}{3}[/tex] is the fraction of 5.3333333.

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It is worthwhile to enter the race if it costs $1000.

Total cost is an economic measure that includes not only the initial cash outlay but also the opportunity cost of their choices when producing a product, purchasing an investment, or acquiring a piece of equipment. TVC + TFC = TC

The sum of fixed and variable costs is the total cost. For example, if a company has a fixed cost of $30 per unit and a variable cost of $5 per unit as output increases, the total cost is $35.

In this case, first place pays $4800 to the winner, second place $3300 and third place $1300. It is therefore worthwhile since the amounts are more than $1000.

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Step-by-step explanation:

given

f(x)=6x+9

solve

6(6x+9)+9=0

36x+54+9=0

36x+63=0

36x=_63

36x/36 = _63/36

x=_63/36

[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \begin{array}{llll} \textit{\small "z" varies directly with }x^2\\ \textit{\small and inversely with }y^2 \end{array}}{ z=\cfrac{kx^2}{y^2}}\qquad \textit{we know that} \begin{cases} z=76\\ x=5\\ y=2 \end{cases} \implies 76=\cfrac{k(5)^2}{(2)^2} \\\\\\ 76=\cfrac{25k}{4}\implies \cfrac{4}{25}\cdot 76=k\implies \cfrac{304}{25}=k~\hfill \boxed{z=\cfrac{304x^2}{25y^2}} \\\\\\ when \begin{cases} x=9\\ y=9 \end{cases}\implies z=\cfrac{304(9)^2}{25(9)^2}\implies z=\cfrac{304}{25}\implies z= 12.16[/tex]

Answer:

10%

Step-by-step explanation:

3/30

1/10

10/100

10%

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The domain of the given graph is x≤ 2, option A is correct.

A relation is a function if it has only One y-value for each x-value.

We have to find the domain of the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.

As we observe the graph the value of x are less than 2

Hence, the domain of the given graph is x≤ 2

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Area of rectangle is 86 square inches.

What is area of triangle?

What is area of rectangle ?

Area of triangle = 1/2 * b* h

43 = 1/2 *b * h

86 = b * h

Area of rectangle = Length * Breadth

We know that base of triangle = Breadth of the rectangle and

Height of triangle = length of triangle

So, Area of rectangle is 86 square inches.

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For given transformation of ΔABC to ΔA'B'C' the line of reflection is x = y

Triangle A'B'C' is the image of ΔABC under a reflection.

Given A(-2, 5), B(0, 9), C(3, 7),

A'(5,-2), B'(9, 0), and C'(7,3)

We need to find the line of reflection.

We can observe that the coordinates (x, y) of preimage are transformed to (y, x) in image.

This means, the line of reflection is x = y

Therefore, for given transformation of  ΔABC to ΔA'B'C' the line of reflection is x = y

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Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

According to question,

slope = (-1/2-3/4)/(5/6-(-2/3))

slope = (-5/4)/(9/6)

slope = -30/36

slope = -5/6

Answer:

Step-by-step explanation:

We know that corresponding parts of congruent figures are congruent.

It means:

|-2.65| can be found between numbers 2.6 and 2.7

Absolute value means to remove any negative sign in front of a number and to think of the number as positive.  This is what the vertical lines |  | surrounding -2.65 means.

Thus,   |-2.65| = 2.65

If we examine the options, then we can say 2.65 is between 2.6 and 2.7 i.e. 2.6, 2.65, 2.7

Therefore,  |-2.65| can be found between the numbers 2.6 and 2.7. So option D is the answer

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The first number is 8  and the second number is 20

let the first number =  X

the second number = 4 + 2X

sum = 28

X + (4 + 2X) = 28

3X + 4 = 28

3X = 24  

X = 8                                                                  

The first number is 8

and the second number is 4 + 2X = 4 + 2(8) = 20

Addition:

When we say "the addition," we mean adding two or more numbers together. The plus sign (+) denotes addition of two numbers, therefore three is written as three plus three. You also have control over how often the plus sign (+) is used. such as 3 + 3 + 3 + 3. Mathematical addition is an essential part of children's education. Students learn basic addition sums in primary school, including one-digit facts, math addition sums, and double-digit math addition sums. Sums in addition are one of the most fundamental and fascinating Math concepts for elementary school students. Children first learn fundamental mathematical ideas like adding numbers in their early years because math is an enthralling subject.

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Answer: 46 ft

Step-by-step explanation:

You didn't specify what those numbers mean, so I'm going to assume they're the length of the sides of the shape.

The perimeter equals the sum of all sides' lengths of the shape.

So, it equals 8 + 8 + 15 + 15 = 46 ft

You can ask where you don't understand.

Answer: 493/16

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 493 and 16 is 1

Divide both the numerator and denominator by the GCD

493 ÷ 1

16 ÷ 1

Reduced fraction:

493

16

Therefore, 493/16 simplified to lowest terms is 493/16. or 30.8125

The depth of the bottom of the hole after the second day is 425 feet using addition operation.

What is addition?

In math, addition is the process of adding two or more integers together. The terms addends and sum describe the input and output of the addition operation, respectively.

Given the depth on the first day is 232 feet.

Depth on the second day = 193 feet more than on the first day i.e. 193 feet + depth on the first day

This implies, depth on the second day = 193+232

=  425 feet

The hole's bottom will therefore be 425 feet deep after the second day.

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Answer:

option A - 2

Step-by-step explanation:

event A { 2 4 6 8 10 12 }

event B { 3 6 9 12 }

The set AnB means A intercept B, which simply means all the elements that are common in event A and event B

So we just have to look at all the elements in A and B, we can see that the common elements are 6 and 12 so therefore:

set AnB = { 6 12 }

and the number of elements in set AnB is 2

a) The break-even quantity (in units) is 59 units.

b) If the company is selling no more than 34 units, A. The product should not be produced because it will lead to a loss of $625.

The break-even point is the production and sales point at which the total costs equal the total revenue.

At the break-even point, there is no profit or loss.

Total units produced = x

Let the cost of production = C

Let the revenue = R

C = 84x+1,475

R = 109x

At the break-even point, 109x = 84x + 1,475

109x - 84x = 1,475

25x = 1,475

x = 59 units

If x = 34 units:

Total cost = 84x+1,475

= 84(34) + 1,475

= 2,856 + 1,475

= $4,331

Total revenue = 109x

= 109(34)

= $3,706

Loss = $625 ($3,706 - $4,331)

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(a) Find the break-even quantity units (Simplify your answer.)

(b) Decide whether the product should be produced on the basis of whether it will earn a profit. (Profit = Revenue - Cost.)

Choose the correct answer below and, if necessary, in the answer box to complete your choice.

A. The product should not be produced because it will lead to a loss of  B. The product should be produced because it will lead to a profit of

The base of a cylinder is circular and it's area is given as B= πr^2

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

The base of a cylinder is circular . If the base area is B, then the area of the base is πr^2.

where r is the radius of the circle and π is 22/7

The volume of a cylinder is V = B × h

where B is the base area and h is the height or length of the cylinder.

Therefore the volume of a cylinder is V= πr^2h

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Answer:

x=25

Step-by-step explanation:

2x-14=36

2x=50

x=25

The Solution of the equation y = C₁e⁴ˣ + C₂e⁻ˣ

The derivative of a function is a function that indicates how quickly another function is changing. Differentiation is a term used to describe the process of finding a derivative. In an equation, it is shown as the dependent variable with respect to the independent variable. A value's derivative is a change in value relative to its input. The symbol for a derivative is f'(x).

Here we have

d²y/dx²-3(dy/dx) - 4y = 0

As we know (d/dx) = D

=> D²-3D - 4 = 0

=> D²- 4D + D - 4 = 0

=> D(D - 4) + (D - 4) = 0

=> (D - 4) (D + 1) = 0

=> (D - 4) = 0 and (D + 1) = 0  

=>  D = 4 and  D = -1  

Here, roots are real and distinct

Therefore,

Solution of the equation y = C₁e⁴ˣ + C₂e⁻ˣ

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Answer:

The slope is -1.

Step-by-step explanation:

When given two points, the formula for slope is [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

4 - 7 / -2 - (-5) = -3 / 3

-3 / 3 = -1, so the slope is -1.

According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

Given,

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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The value of the 10th term for the sequence 11,12,13,14 is 20.

It's important to note that this is an arithmetic sequence. The formula for an arithmetic sequence is:

= a + (n - 1)d

where a = first term = 11

d = common difference = 1

n = number of terms = 10

The 10th term will be:

= a + (n - 1)d

= 11 + (10 - 1)1

= 11 + (9 × 1)

= 11 + 9

= 20

The value is 20.

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Complete question

The first four terms of an arithmetic sequence are 11,12,13,14. Find the 10th term.

The expressions (4×2⁵) / (2³ × 1/16) written as the power of 2 is 2⁸

Given: (4×2⁵) / (2³ × 1/16)

In order to write this expression as the power of 2, we need to use some in indices law:

Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base":   5⁴ x 5³ = 5⁴⁺³ = 5⁷ and  P⁴ x P⁶ = P¹⁰

Division law: To divide two variables or numbers with the same base, we need to subtract their powers and raise them to that base":   5¹⁰ ÷ 5³ = 5¹⁰⁻³ = 5⁷ and  P⁸  ÷  P² = P⁸⁻² = P⁶

Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:

8⁻² = 1/8²   and b⁻⁶ = 1/b⁶  

Let's use the laws to create the given expressions as the power of 2:

(4×2⁵) / (2³ × 1/16) = (2²×2⁵) / (2³× 1/2⁴)       Note: 4 = 2² and 16 = 2⁴    

                            = (2²⁺⁵) /(2³⁺⁽⁻⁴⁾)               Note: 1/2⁴ = 2⁻⁴ (reciprocal law)

                            = 2⁷ / 2⁻¹

                            = 2⁷⁻⁽⁻¹⁾                            Division law

                            = 2⁸

Therefore, the expressions as the power of 2 is 2⁸

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The graph that shows how many of each type of drink she can buy is as shown below.

The correct answer is an option (D)

In this question, we have been given  Holly is getting a combination of soda and juice. The soda costs $2 each and the juice costs $5 each. Holly

needs to bring at most 10 drinks but doesn't want to spend more than $50.

Let x be the number of soda cans and y be the number of soda cans(or bottles)

Holly needs to bring at most 10 drinks

So, we get an inequality,

x + y ≤ 10

She doesn't want to spend more than $50.

So, we get an inequality,

2x + 5y ≤ 50

In following graph, an inequality x + y ≤ 10 is represented by blue shaded region and the inequality 2x + 5y ≤ 50 is represented by red shaded region.

The solution set for the given inequalities is represented by a purple region (common region for both the inequalities)

Therefore, the graph that shows how many of each type of drink she can buy is as shown below.

The correct answer is an option (D)

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The probability of rolling a number less than 12 is 91.6%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

each case in the set is mutually exclusive with the others in the set, the probability that any one of its components will occur is equal to the sum of its component probabilities.

We can have the number 12, the probality will be 1/12

So the probability of rolling a number less than 12 is = (1 -  probability of 12)

=1-1/12

=11/12

=0.916

Hence the probability of rolling a number less than 12 is 91.6%.

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Answer:

24:23

Step-by-step explanation: