From a cuboidal cardboard box of dimensions 80cm×40cm×15cm,6 circles of radius 7 cm were cut from the front face.Find the surface area of remaining box.​

Answer:

It is (x - 3)³ - 9x(3 - x)

Step-by-step explanation:

Express 27 in terms of cubes, 27 = 3³:

[tex] = {x}^{3} - {3}^{3} [/tex]

From trinomial expansion:

[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]

open first two brackets to get a quadratic equation:

[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]

expand further:

[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]

take y to be 3, then substitute:

[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]

Answer:

[tex]\frac{135}{15} =\frac{15(x+2)}{15}[/tex]

[tex]9=x+2[/tex]

[tex]x=7[/tex]

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Answer:

Option (a)

Step-by-step explanation:

[tex]\sqrt[6]{1000m^{3} n^{12} } = \sqrt[6]{10^{3} } \sqrt[6]{m^{3} } \sqrt[6]{n^{12} } =\\\sqrt{10} \sqrt{m} n^{2} = n^{2} \sqrt{10m}[/tex]

Answer:

c

Step-by-step explanation:

12/18 = 2/3

Answer:c

Step-y-step explanat:c

Answer:

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Step-by-step explanation:

There's a handy formula we can use to find the sum of a geometric sequence, and here it is

[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]

The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.

First lets visualize this sequence

[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]

Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.

[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]

Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.

[tex]S_n = \sum{a*r^{n-1}}[/tex]

To finish up lets plug these coefficients in and get our sum after 10 terms.

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Answer:

ok so you take m time h then like you count to h like a b c d e f g h and tgen with that you count 1 2 3 4 5 6 7 till h than you multiply that with 3

Answer:

x=13

Step-by-step explanation:

f(x) = sqrt(x-11)

The square root must be greater than or equal to zero

sqrt(x-11)≥0

Square each side

x-11≥0

x ≥11

The only answer that is greater than or equal to 11 is

x=13

Answer:

1. 1.66in

2. 6.66in

3. 3.33in

4. 1inch

Step-by-step explanation:

the area of a rectangle is found by multiplying the length times width or the two sides.

5 x 1/3 is about 1.66 inches

5 x 4/3 is about 6.66 inches

5/2 x 4/3 is about 3.33 inches

and 7/6 x 6/7 is 1 inch

Answer:

P = 24

Step-by-step explanation:

Since all the sides are the same length, the shape is a square.

Multiply all sides by 6.

6 cm x 4 sides = 24

Answer:

50

Step-by-step explanation:

Sum Even numbers

n = 50

d = 2

a1 = 2

The last number is

an = a1 + (n-1)d

an = 2 + (50 - 1)*2

an = 2 + 49 * 2

an = 2 + 98

an = 100

Sum of the even numbers

Sum = (a1 + a50)*n/ 2

Sum = (2 + 100)*50/2

sum = 102 * 25

sum = 2550

Sum of the first 50 odd numbers

a1 = 1

n = 50

d = 2

l = ?

Find l

l = a1 + (n - 1)*2

l = 1 + 49*2

l = 99

Sum

Sum = (1 + 99)*50/2

Sum = 2500

The difference and answer is 2550 - 2500  = 50

Step-by-step explanation:

Sequence is

4

,

7

,

10

,

13

,

16

,

.

.

.

a

1

=

4

,

a

2

=

7

,

a

3

=

10

,

.

.

.

If it is Arithmetic sequence,

a

2

−

a

1

=

a

3

−

a

2

=

a

4

−

a

3

& so on

In the given sum,

a

2

−

a

1

=

7

−

4

=

3

a

3

−

a

2

=

10

−

7

=

3

a

4

−

a

3

=

13

−

10

=

3

Since the difference between the successive terms is same and

hence

common difference

d

=

3

This is a question that asks about the advantages of a systematic random sampling. Thus, we first take a look at the types of sampling, and then we see the advantage of systematic random sampling.

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

Systematic:

One of the bigger advantages is that the systematic sampling eliminate clusters, which means that the last option is wrong.

Inadvertently missing patterns is a problem in systematic sampling, and not an advantage, thus the third option is also wrong.

It also does not reduce sampling variability, thus the first option is wrong.

From this, it can be concluded that the correct option is:

Systematic random sampling does not require a finite population size.

For another example of systematic random sampling, you can check https://brainly.com/question/21100042

Answer:

Bro what to do in this question I am not able to understand Hope you understand me

Your question is not complete but I guess you want to know the total price to be paid. This will be:

= $145 + (5.5% × $145)

= $145 + (0.055 × $145)

= $145 + $7.975

= $152.975

Answer:770

Step-by-step explanation:

There are a total of 6 faces, so we shall calculate the area of each face then add them

=(11×12) +(11×12) +(11×11)+(11×11)+(11×12)+(11+12)

=770cm^2

The total surface area of the given box will be 770 cm² hence correct option will be option (B).

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In another meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

Given that the box has 6 faces with sides

2 face has dimension = 11cm and 12 cm

2 face has dimension = 11cm and 11cm

2 face has dimension = 11cm and 12 cm

Total surface area = 2(11 × 12) + 2(11 × 11) + 2(11 × 12) = 770 cm²

Hence, the total surface area will be 770 cm².

To learn more about surface area,

https://brainly.com/question/2835293

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Answer:

The correct answer is - $720 or 20%.

Step-by-step explanation:

Given:

Total expense = 3600

Electric=30%

Heating and gas=50%

Water and sewer=X%

Solution:

For electric: 3600*30/100 = 1080

for heating and gas: 3600*50/100 = 1800

Left money for expense of water and shower = total - (electric and heating)

= 3600-1880

= 720

Percentage of water and shower = 720*100/3600

= 20%

Answer:

Correct!

Step-by-step explanation:

Thank you this is correct :) I took the test

Answer:

2.3

Step-by-step explanation:

.5 - .3 = .2

.8 - .5 = .3

1.2 - .8 = .4

1.7 - 1.2 = .5

We should add .6 next

1.7+.6 = 2.3

Answer:

5/8 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

A = 5/6 * 3/4

A = 3/6 * 5/4

A = 1/2 * 5/4

A = 5/8 ft^2

Answer:

don't know...........

Answer:

2 sin(2x)

Step-by-step explanation:

sin x stretched vertically by a factor 2 and compressed horizontally by a factor 2.

The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.

so, we get,

However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.

Hence, The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.

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brainly.com/question/21145944

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Answer:

15

Step-by-step explanation:

Answer:

0.0071164

Step-by-step explanation:

Answer:

yes it is. a polygon is any closed shape with at least 3 connected lines (eg. triangle, square, pentagon, hexagon, heptagon, octagon, etc)

Step-by-step explanation:

Answer:

655.35

Step-by-step explanation:

got it right on edmentum

Answer:

A

Step-by-step explanation:

Its not a linear function; there is no consistent rate of change between each of the points.

Answer:

C  -3 < x ≤ 4

Step-by-step explanation:

-9 < 4x + 3 ≤ 19.

Subtract 3 from all sides

-9-3 < 4x + 3-3 ≤ 19-3

-12 < 4x  ≤ 16

Divide by 4

-12/4 < 4x/4 ≤ 16/4

-3 < x ≤ 4

Answer:

x< - 8

Step-by-step explanation:

3x <-24

x < - 24

3

x< - 8

x < - 8

Step-by-step explanation:

3x < - 24

Divide 3 on both sides,

3x / 3 < - 24 / 3

x < - 8

Recall that

[tex]\dfrac{dv(t)}{dt} = a(t) \Rightarrow dv(t) = a(t)dt[/tex]

Integrating this expression, we get

[tex]\displaystyle v(t) = \int a(t)dt = \int(t^2 - 4t + 5)dt[/tex]

[tex]\:\:\:\:\:\:\:= \frac{1}{3}t^3 - 2t^2 + 5t + C_1[/tex]

Also, recall that

[tex]\dfrac{ds(t)}{dt} = v(t)[/tex] or

[tex]\displaystyle s(t) = \int v(t)dt = \int (\frac{1}{3}t^3 - 2t^2 + 5t + C_1)dt[/tex]

[tex]\:\:\:\:\:\:\:= \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + C_1t + C_2[/tex]

Next step is to find [tex]C_1\:\text{and}\:C_2[/tex]. We know that at t = 0, s = 0, which gives us [tex]C_2 = 0[/tex]. At t = 1, s = 20, which gives us

[tex]s(1) = \frac{1}{12}(1)^4 - \frac{2}{3}(1)^3 + \frac{5}{2}(1)^2 + C_1(1)[/tex]

[tex]= \frac{1}{12} - \frac{2}{3} + \frac{5}{2} + C_1 = \frac{23}{12} + C_1 = 20[/tex]

or

[tex]C_1 = \dfrac{217}{12}[/tex]

Therefore, s(t) can be written as

[tex]s(t) = \frac{1}{12}t^4 - \frac{2}{3}t^3 + \frac{5}{2}t^2 + \frac{217}{12}t[/tex]

Answer:

Table C

Step-by-step explanation:

r = j+3

In table A

j = 12 so r = 12+3 = 15  not true so it does not fit the equation

In table B

j = 3 so r = 3+3 = 6  not true so it does not fit the equation

In table C

j = 6 so r = 9+3 = 9 this could be the table

In table D

j = 27 so r = 27+3 = 30  not true so it does not fit the equation

Answer:

y = -6x -6

Step-by-step explanation:

The general form of the equation of a line in the slope-intercept form may be given as

y = mx + c where

m is the slope and c is the intercept

Hence given the equation

18x + 3y = -18

subtract 18x from both sides

3y = -18x - 18

Divide both sides of the equation by 3

y = -6x -6

This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept