A stone outbuilding is 4.3 metres high, 3.5 metres wide and 2.2 metres deep. The slope of its roof is 2.6 m long, whilst its side walls are 2.5 metres high.


Calculate its volume to 2 decimal places.
m3
Calculate the total area of its slate roof to 2 decimal places.
m2
‌

Answer:

8.407

Step-by-step explanation:

8.767−0.36

= 8.767−0.36

=8.767+(−0.36)

= 8.407

As the total of Rita and Shova's current ages is 20, they are both 20 years old.

A mathematical strategy for resolving proportional and ratio issues is called the unitary method. Finding the value of one unit of an amount and using that value to calculate the value of additional units is what this process entails. The foundation of the unitary approach is the idea that if two quantities are equal, then their ratios must also be equal. For instance, if five apples cost $10, then the expense-to-apple ratio is 10/5 = 2. This ratio can be used to calculate the price of a varied quantity of apples.

given

According to the issue statement, Rita was three times as old as Shova when her age and Shova's current age were equal.

R - (S - R) Equals 3(S - R) (S - R)

When we simplify this solution, we obtain:

2R = 4S - 2S

2R = 2S

R = S

As a result, we are aware that Rita and Shova are both currently the same age.

Additionally, we are aware that their combined current ages are 40 years.

R + S = 40

R = S, so we can change S in the second equation to R:

R + R = 40

2R = 40

R = 20

Rita is currently twenty years old. Since R = S, Shova is 20 years old at the moment.

As the total of Rita and Shova's current ages is 20, they are both 20 years old.

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Answer: the length is 6

Step-by-step explanation:

3+3+6+6=18

3x6=18

Answer:

C) 36.

Step-by-step explanation:

Since there are 9 game pieces in each tic-tac-toe board and the class has 4 tic-tac-toe boards, the total number of game pieces the class has is:

9 pieces/board x 4 boards = 36 pieces

Therefore, the answer is C) 36.

The slope of the lines are given as

a) m₁ = -2

b) m₂ = 4/3

c) m₃ = 5/2

d) The equation of line is y = ( 1/2 )x + 9/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

a)

Let the first point be P ( 3 , 5 )

Let the second point be Q ( 7 , -3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = ( -3 - 5 ) / ( 7 - 3 )

Slope m₁ = -8/4

Slope m₁ = -2

b)

Let the first point be P ( 4 , 2 )

Let the second point be Q ( 10 , 10 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₂ = ( 10 - 2 ) / ( 10 - 4 )

Slope m₂ = 8/6

Slope m₂ = 4/3

c)

Let the first point be P ( -1 , -2 )

Let the second point be Q ( -3 , -7 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₃ = ( -7 - ( -2 ) ) / ( -3 - ( -1 ) )

Slope m₃ = -5/-2

Slope m₃ = 5/2

d)

Let the first point be P ( 5 , 7 )

The slope of the line is y = 1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying , we get

y - 7 = ( 1/2 ) ( x - 5 )

y - 7 = ( 1/2 )x - 5/2

Adding 7 on both sides , we get

y = ( 1/2 )x + 9/2

e)

The slope of the line is y = 5/2 and the points are linear

Hence , the equation of line is y = ( 1/2 )x + 9/2

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The complete question is :

Determine the slopes between the points in lowest terms

a) ( 3 , 5 ) and ( 7 , -3 )

b) ( 4 , 2 ) and ( 10 , 10 )

c) ( -1 , -2 ) and ( -3 , -7 )

d) Draw and accurate graph of the line with the slope of ( 1/2 ) that passes through the point ( 5 , 7 )

Answer:

Step-by-step explanation:

a. 4x + 8

b. 14x

c. 8x + 12

d. 6x + 6y + 6z

Answer:

Step-by-step explanation:

1]4(x+2)

using distributive property ,

Multiply 4 to x and 2

4x + 8

2]4(2x+3)

using distributive property ,

Multiply 4 to 2x and 3

= 4 x 2x + 4 x 3

= 8x +12

3](6 + 8).x

= (14).x

14x

4] 6(x + y + z)

using distributive property ,

multiply 6 to x and y and z

6.x + 6.y + 6.z

6x + 6y +6z

Answer:

[tex]\frac{1}{256}[/tex]

Step-by-step explanation:

Given

[tex]\left(4^4\right)^{-1}[/tex]

We can use the power rule to multiply the exponents.

The power rule for exponents states

[tex]\left(a^b\right)^{c}=a^{bc}[/tex]

[tex]4^{4*-1}[/tex]

Multiply 4 by −1.

[tex]4^{-4}[/tex]

Rewrite the expression using the negative exponent rule.

The negative exponent rule states

[tex]a^{-b}=\frac{1}{a^b}[/tex]

[tex]\frac{1}{4^4}[/tex]

Raise 4 to the power of 4.

[tex]\frac{1}{256}[/tex]

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Mary can bake 8 cakes the with 7 cups of flour she possesses because we are unable to create a quarter of a cake.

Starch, a polymer, is one of the ingredients in all-purpose flour, which has the chemical formula (C6H5O10)n (C 6 H 5 O 10) n.

We need to divide Mary's total flour supply by the quantity of flour required for creating one cake in order to determine how many cakes she can produce.

First, we must divide 5 by 6 to get the fraction 5/6 in decimal form:

5 ÷ 6 = 0.8333...

Hence, 0.8333 cups of flour are required to produce one cake.

We're able to divide Mary's entire flour supply by the quantity of flour needed to produce one cake:

7 cups of flour ÷ 0.8333 cups of flour per cake = 8.4 cakes

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The one making the most money in one week is by sales manager which is an amount of $1006.25.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

Given that,

Hourly rate of a head mechanic = $37.52 per hour

Number of hours worked in a week = 25 hours

Money made = 25 × 37.52 = $938

Hourly rate of a assistant mechanic = $30.42 per hour

Number of hours worked in a week = 30 hours

Money made = 30 × 30.42 = $912.6

Hourly rate of a sales manager = $28.75 per hour

Number of hours worked in a week = 35 hours

Money made = 35 × 28.75 = $1006.25

Hourly rate of a front desk clerk = $15.09 per hour

Number of hours worked in a week = 40 hours

Money made = 40 × 15.09 = $603.6

Money most made is by sales manager.

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Your question is incomplete. The complete question is given as,

Who would make the most money in one week? a head mechanic working 25 hours with an hourly rate $37.52 per hour, an assistant mechanic working 30 hours with an hourly rate $30.42 per hour, a sales manager working 35 hours with an hourly rate $28.75 per hour, a front desk clerk working 40 hours with an hourly rate $15.09 per hour?

The solution to equation 1, 2, 3, 4, 5 and 6 are y = (-3/2) + 6, y = (-5/3) + 3,  y = (-1/5)x + 9/5, y = (1/4)x + 3/2, y = (-7/3)x + 3 and y = 6x + 3 respectively.

Given the linear equations in the question;

To make y the subject of the formula, we need to isolate y on one side of the equation by moving all other terms to the other side.

1) 3x + 2y = 12

Subtract 3x from both sides:

3x - 3x + 2y = -3x + 12

2y = -3x + 12

Divide each term by 2

2y/2 = -3x/2 + 12/2

y = (-3/2) + 6

2) 5x + 3y = 9

Subtract 5x from both sides:

5x - 5x + 3y = -5x + 9

3y = -5x + 9

Divide each term by 3

3y/3 = -5x/3 + 9/3

y = (-5/3) + 3

3) x + 5y = 9

Subtract x from both sides:

x - x + 5y = -x + 9

5y = -x + 9

y = (-1/5)x + 9/5

4) -2x + 8y = 12

8y = 2x + 12

y = (2/8)x + 12/8

y = (1/4)x + 3/2

5) -7x - 3y = -9

-3y = 7x - 9

y = (-7/3)x + 3

6) 6x - y = -3

-y = -6x - 3

y = 6x + 3

Therefore, the formula in terms of x is: y = 6x + 3.

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The number of ways that this can be done is given as follows:

272,160.

The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

The number of ways for each department is given as follows:

Hence the total number of ways is given as follows:

9 x 8 x 7 x 6 x 10 x 9 = 272,160.

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Therefore , the solution of the given problem of area  comes out to be potential dimensions are thus (19 m, 15 m) and (15 m, 19 m), or (8 m, 37 m), and (37 m, 8 m).

Its total size can be determined by how much space is required to completely cover the outside. The nearby surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. The sum of the boundaries for each of a cuboid's six rectangular edges represents its internal water capacity. To calculate the size of the box, use the following method:

Here,

Let's write L for the rectangular plot's length and W for its breadth. Consequently, the rectangle plot's perimeter can be written as:

=> 2L + W = 53

Additionally, since we are aware that the rectangle plot's area is 306, we can write:

=> LW = 306

By resolving the initial solution for W, we can obtain:

=> W = 53 - 2L

When we use this formula as W's substitute in the second equation, we obtain:

=> L(53 - 2L) = 306

Increasing the left edge gives us:

=> 53L - 2L² = 306

Rearranging and condensing results in:

=> 2L² - 53L + 306 = 0

To find L, we can use the cubic formula:

=> L = [53 + √53² - 4(2)(306))] / (2(2))

=> L = [53 ± 25] / 4

=> L = 19 or L = 8

The rectangular plot's two groups of potential dimensions are thus (19 m, 15 m) and (15 m, 19 m), or (8 m, 37 m), and (37 m, 8 m).

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The expression "eight more than the sum of a number and 7 is 90" can be written as: 8 + (x + 7) = 90

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

eight more than the sum of a number and 7 is 90

Express the numbers properly

So, we have

8 more than the sum of a number and 7 is 90

Express the operators properly

8 + (x + 7) = 90

hence, the expression is 8 + (x + 7) = 90

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Answer:

105 or 40500

Step-by-step explanation:

you have too add or mutilple

Answer:1.111

Step-by-step explanation:

Let's use the variable W to represent the percent of top earners who are women.

According to the problem statement, the percent of top earners who are men is more than four and a half times the percent of top earners who are women. Mathematically, we can write this as:

M > 4.5W

Additionally, the percent of top earners who are men is less than five times the percent of top earners who are women. This can be written as:

M < 5W

We can combine these two inequalities into a compound inequality:

4.5W < M < 5W

This means that the percent of top earners who are men is between 4.5 times and 5 times the percent of top earners who are women.

To solve for W, we can divide all three parts of the compound inequality by 4.5:

W < M/4.5 < W/0.9

Simplifying, we get:

W < 0.222M < 1.111W

Therefore, the percent of top earners who are women, W, must be less than 0.222 times the percent of top earners who are men, and also less than 1.111 times the percent of top earners who are women.

the hands do form a right angle during Mario's math class, at 2:35:17.5 p.m. (rounded to the nearest half-second).

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

During the class from 2:00 p.m. to 2:50 p.m.,

the hour hand will move from the 2 to the 3 and will be halfway between the 2 and 3 at 2:30 p.m. The minute hand will make one full revolution around the clock face, from the 12 to the 12, during this time.

Let's calculate the positions of the hour and minute hands at 2:30 p.m.:

The hour hand moves 1/12 of the way around the clock face for each hour or 30 degrees for each hour. At 2:30 p.m.,

it will have moved 2.5 hours, so it will be 2.5 * 30 = 75 degrees past the 2 o'clock mark.

The minute hand moves 360 degrees in 60 minutes or 6 degrees per minute. At 2:30 p.m.,

it will have moved 30 minutes, so it will be 30 * 6 = 180 degrees past the 12 o'clock mark.

To determine if the hands form a right angle, we need to calculate the angle between them. Let's call this angle "A".

The angle between the hour and minute hands is the absolute difference between their positions, which is 105 degrees in this case (180 degrees - 75 degrees).

If the minute hand is ahead of the hour hand by exactly a quarter of a revolution or 90 degrees, then the hands will form a right angle.

So, we need to check whether angle A is equal to 90 degrees. If A = 90 degrees, then the hands form a right angle, and we can calculate the time when this happens by finding the time at which the minute hand is exactly 90 degrees ahead of the hour hand.

Let's set up an equation to solve for the time t:

A = 90 = 180 - 75 - 6t

Solving for t, we get:

t = 17.5

Therefore, the hands do form a right angle during Mario's math class, at 2:35:17.5 p.m. (rounded to the nearest half-second).

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series: 12, 11, 13, 12, 14, 13, … What number should come next? i believe its 12

12-11=1

13-11=2

So to get 11 you subtract 1 from 12 and to get 13 you add 2 to it

If you follow that procedure the next number should be 15 if you add 2 to 13

Answer:

21

Step-by-step explanation:

Answer:

25% of 84 is 21

Step-by-step explanation:

25% can be written as 0.25

0.25 times 84 = 21

Let's start by using "x" to represent the number of picture cards that Cevin has. We know that Tom has 3 times as many picture cards as Cevin, so:

Tom = 3x

We also know that Tom has 2304 picture cards, so:

3x = 2304

Solving for x, we get:

x = 768

So, Cevin has 768 picture cards.

We also know that Ron has 190 fewer picture cards than Kevin, so:

Ron = x - 190

Substituting x with 768, we get:

Ron = 768 - 190

Therefore, Ron has:

Ron = 578 picture cards.

Answer: 7 batches

Step-by-step explanation:

If Eduardo makes 4 batches, he will need 2/3 x 4 = 8/3 cups of flour.

To add 3 more batches, he will need 3 x 8/3 = 8 cups of flour.

In total, Eduardo will need 8/3 + 8 = 32/3 + 8 = 32/3 + 24/3 = 56/3 cups of flour for 7 batches. Therefore, Eduardo will need 8 cups of flour if he makes 3 more batches, and he will need 56/3 cups of flour in total if he makes 7 batches.

So, the simplified form of the given expression is cosxsinx(3cosx - sinx).

A statement, at least two parameters or integers, and one or more calculations make up a mathematical expression. It is possible to multiply, divide, add, or subtract quantities using this mathematical operation. The following is the expression's structure: An expression is (total count, numerical operator, number, or variable).

We can simplify the given expression using the product-to-sum identities:

sin2x × cosx + cos2x × sinx

= 2sinx × cosx × cosx + (cos²x - sin² x) × sinx [using the identity sin2x

= 2sinx × cosx and cos²x = cos² x - sin² x]

= 2sinx × cos² x + cos²x × sinx - sin² x × sinx [expanding the brackets]

= cosx × sinx(2cosx + cosx - sinx)

= cosx × sinx(3cosx - sinx)

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Answer:

Step-by-step explanation:

A.  h = -2(1)² + 7(1) + 4 = 9 ft

B.  use the quadratic formula to find the 2 solutions to t when

y = f(t) = -2t² + 7t + 4 = 0         a=-2, b=7, c=4

the 2 solutions for t are:  -1/2, 4

halfway between t=-1/2 and t=4 is:  (-1/2 + 4) /2 = 1.75   (vertex of the parabola)

so, at t = 1.75 s, the toy is at its max. height:

h = -2(1.75)² + 7(1.75) + 4 = 10.125 ft

C.  Toy is in the air for 4 sec

The answer is 4 s because f(4) = 0, meaning the toy hits the ground after 4 sec

Answer:

it 39 ×90 for sure it 3510

To find the area of the given circle we have to use the formula πr², where π=22/7 and r is radius of the circle. The area of the circle is 1519.76 square feet.

A circle is a closed two-dimensional figure in which all sets of points in the plane are equidistant from a specific point called the "center". A line passing through the circle forms a line of specular symmetry. It is also rotationally symmetrical about the center at any angle. 

Solution for the area of the circle:

Given, radius = 22 feet

∴Area of the circle = πr²

                               = (22/7)×22²

                               = 3.14 × 484

                               = 1519.76 square feet

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Answer:

a and b

Step-by-step ex

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &708000\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A = 708000(1 - 0.16)^{10} \implies A=708000(0.84)^{10}\implies A \approx 123830.07[/tex]

Check the picture below.

so we really have six 5.5x5.5 squares

[tex]\stackrel{ \textit{Area for 6 squares} }{(6)(5.5)(5.5)}\implies \text{\LARGE 181.5}[/tex]

Answer:

Step-by-step explanation:

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━

Hope it helps! :)

Answer: 9 and 3

Step-by-step explanation: Depends the signs +/- and the problem.