A manufacturer has an order from flower shop to make gift boxes. A gift box is to be constructed from a piece of cardboard 60x60 cm by cutting out squares from the corners and folding up the sides. What is the size of cut out that will provide a gift box of maximum volume?

Answer:

Step-by-step explanation:

Interest per annum - 4.5

Interest per 1/3 of an annum - 4.5 x 1/3 = 1.5%

Use the S.I formula,

2400 x (100 + interest)/100

= 2400 x (100 + 1.5)/100

= 24 x 101.5

= 12 x 203

= 2436.

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Answer:

b.

Step-by-step explanation:

the result is created :

first result row first result element =

= first A row × first B column

first result row second result element =

= first A row × second B column

...

third result row second result element =

= third A row × second B column

third result row third result element =

= third A row × third B column

the multiplication of a row and a column is done by :

left row element × top column element +

middle row element × middle column element +

right row element × bottom column element

AB =

-4×3 + -3×-5 + 5×-1 -4×-4 + -3×-5 + 5×-3 -4×-1 + -3×1 + 5×2

-5×3 + -4×-5 + -2×-1 -5×-4 + -4×-5 + -2×-3 -5×-1 + -4×1 + -2×2

-1×3 + -2×-5 + -4×-1 -1×-4 + -2×-5 + -4×-3 -1×-1 + -2×1 + -4×2

=

-2 16 11

7 46 -3

11 26 -9

so, b is correct.

Answer: To find the perimeter of a triangle, we need to add the length of all three sides of the triangle.

To find the length of each side, we can use the distance formula which is the square root of (x2-x1)^2 + (y2-y1)^2.

The distance between point A (9,-2) and point B (5,1) is: √((9-5)^2 + (-2-1)^2) = √16 + 9 = √25 = 5.

The distance between point B (5,1) and point C (9,-3) is: √((9-5)^2 + (-3-1)^2) = √16 + 16 = √32 = 5.66.

The distance between point C (9,-3) and point A (9,-2) is: √((9-9)^2 + (-3- -2)^2) = √1 + 1 = √2 = 1.41

The perimeter is the sum of the length of all three sides:

Perimeter = 5 + 5.66 + 1.41 = 12.07

Round the answer to two decimal places, the perimeter of the triangle is 12.07.

Step-by-step explanation:

Answer:

t = I/(Pr)

Step-by-step explanation:

We divide P*r on both sides to isolate t and we get t=I/(P*r)

The following equations which are equivalent are:

2 + x = 5

collect like terms

x = 5 - 2

x = 3

x + 1 = 4

Subtract 1 from both sides

x = 4 - 1

x = 3

9 + x = 6

Subtract 9 from both sides

x = 6 - 9

x = -3

x + (negative 4) = 7

x +(-4) = 7

Open parenthesis

x - 4 = 7

x = 7 + 4

x = 11

Negative 5 + x = negative 2

-5 + x = - 2

x = -2 + 5

x = 3

Therefore, 2 + x = 5; x + 1 = 4; Negative 5 + x = negative 2 are equivalent to each other.

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So, The line is a horizontal one, and the equation is y = -2 of a line in slope-intercept form if the slope is 0 and the point is (-3, -2).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

Positive slope lines lean to the right, and they become steeper as the slope increases. A line with a negative slope slopes left, and the slope's magnitude determines how steep the line is. Since there is no slope on a horizontal line, it has a slope of zero.

The slope of the line is 0, which means the line is horizontal.

The point-slope form of the equation of a line is: y - y1 = m(x - x1)

With the point (-3, -2) and the slope of 0, we have:

y - (-2) = 0(x - (-3))

y = -2

The slope-intercept form of the equation of a line is: y = mx + b

The y-intercept of the line is -2, so the equation of the line in slope-intercept form is: y = 0x + (-2)

The line is a horizontal one and it's equation is y = -2

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The equation of the line in slope intercept form is  y = - 1 / 2 x - 8.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Let's find the slope of the line before we can find the equation of the line.

The slope is the change in the dependent variable with respect to the change in the independent variable.

Hence,

m = y₂ - y₁ / x₂ - x₁

Therefore,

(0, -8)(-2, -7)

Hence,

slope = m = -7  + 8 / -2 - 0

m = 1  / -2

m = - 1 / 2

The y-intercept is -8.

Therefore, the equation of the line is y = - 1 / 2 x - 8.

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Answer:30

Step-by-step explanation:2*5 + 2*4 + 2*2 + 2*4

=10+8+8+4

=30

Answer:

5 hours and 40 minutes late

Step-by-step explanation:

I am assuming by 1435 hours you meant 14:35 -- 2:35 pm.

Hence you subtract 8:15 by 2:35 as the two times you're subtracting should always be the same time format (12 or 24-hour) which is 12 hours in this case.

 08:15

- 02:35

Since the minutes of the time above (:15) is higher than 35, we need to add 60 to 15 minutes and at the same time, reduce 8 hours by 1 hour to 7 hours since we are adding 60 minutes (1 hour) to :15:

 07:75 (15+60)

- 02:35

and answer will be 5 hours and 40 minutes

The second function 100(.1593)^t decays faster than the first function 100(.2661)^t.

To find which function decays the fastest, we need to compare the decay rates of the two functions.

The decay rate of a function is determined by the exponent in the function. In this case, the exponent is t.

The smaller the exponent, the faster the decay rate.

So, in the first function 100(.2661)^t, the exponent is t.

In the second function 100(.1593)^t, the exponent is also t.

We can compare the decay rates of the two functions by comparing the values of the bases, .2661 and .1593.

The base of a function represents the rate of decay, the smaller the base the faster the decay rate.

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Answer:

Rs. 7.50

or a gain of 10%

Step-by-step explanation:

Let x be the price of the stool

10% = 10/100 = 0.10

Loss = 0.1x

Selling price at 10% loss = x - 0.1x = 0.x

We are given this sale price is 67.50

So

0.9x = 67.50

x = 67.50/0.9 = 75

If he sells it at 82.50, the profit would be 82.50 - 75 = 7.5

This would represent a gain of 7.5/75 x 100 percent

= 10%

Answer:

The carpenter would gain 10% profit.

Step-by-step explanation:

67.5 is 90% of 75.

82.50 is 110% of 75.

Answer: 8.8 hours

Step-by-step explanation:

To start off, we’ll make an equation that “connects” both companies:

10 + 4.75h = 21 + 3.5h (we put h to represent the number of hours)

Move all similar terms to one side:

4.75h - 3.5h = 21 - 10

Simplify:

1.25h = 11

h = 8.8

I hope this helps!

The area of this circle is 12.5 yd²

The incircle is defined as the largest circle that can be made in a triangle and is tangent to each side of the triangle.

The area of the circle is the product of the pie and the square of the radius.

The area of the circle = πr²

We are given that floor of a round hut has a diameter of 4 yards.

r = 2 d

Then we know that

Area = πr²

Substitute the values r = 2

π = 3.14

Area = 3.14(2)²

Area = 3.14 × 4

Area = 12.5663706 yd²

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Answer:

[tex]\frac{y-7}{y+8}[/tex]

y cannot equal -8

Step-by-step explanation:

[tex]\frac{(y-7)(y-5)}{(y+8)(y-5)}[/tex]           y-5 cancel out

[tex]\frac{y-7}{y+8}[/tex]

Volume of earth in shape of a sphere is 1 Trillion km^3 i.e. D.

What is a sphere?

A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.

The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere. Examples of spheres are a ball, a globe, the planets, etc.

Volume of sphere=4/3πr^3. where r=radius.

Surface area=4πr^2.

Now,

Given radius for earth=6371 km

so, Volume of earth=4/3*3.14*6371^3≈1Trillion km^3.

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Measure of ∠CEA = 91°

The arc of a circle is defined as the part or segment of the circumference of a circle.  A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle.

Given,

In figure

chord AB and chord CD intersect at E

m(arc CA) = 140°

m(arc DB) = 42°

∠CEA intercepts arc CA and has it vertex inside the circle

Thus,

∠CEA = (m(arc CA) + m(arc DB))/2

∠CEA = (140° + 42°)/2

∠CEA = 182°/2

∠CEA = 91°

∠CEA measures 91°

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Part (a)

Line p can be named as "line RV" or "line AV" since these points are on line p. The order of the lettering doesn't matter.

==============================================

Part (b)

Pick any three non-collinear points in plane W. In other words, we pick three points in the plane that do not fall on the same line.  

The following points are located in this plane: S, R, Q, T, Z

Here are some possible names:

Something like "Plane SRQ" isn't valid since those three points are on the same line. Infinitely many planes pass through these three points.

The ordering of the letters doesn't matter. For instance, "plane STR" is the same as "plane RTS".

==============================================

Part (c)

As mentioned in part (b) earlier, these points fall on the same straight line. Hence they are considered collinear.

==============================================

Part (d)

Pick any four points that reside in plane W.

You have this list to choose from: S, R, Q, T, Z

Let's say we pick the first four to write S, R, Q, T as the answer

These points are coplanar because they reside in the same plane. The non-coplanar points are A and V since they are outside the plane W.

==============================================

Part (e)

Technically there aren't any line segments shown. Instead the diagram shows lines. But we can focus on a subset of a particular line to form a segment.

For instance, line p has points A and V on it. Therefore we can form segment AV

The symbolic notation for this would be to write [tex]\overline{\text{AV}}[/tex]

==============================================

Part (f)

Reason:

A line is composed of opposite rays. For instance, a vertical line consists of a ray pointing north and a ray pointing south. The two rays are glued together at the endpoints.

For line p, we can glue together ray RA and ray RV to form this line. Unlike the other naming conventions, the order does matter. Something like "ray RV" is not the same as "ray VR". The first letter tells us the endpoint that doesn't go on forever.

Answer:

Yeah, [tex] \sf b = 12 [/tex]

Step-by-step explanation:

Given equation,

→ b - 7 = 5

Now the value of b will be,

→ b - 7 = 5

→ b = 7 + 5

→ [ b = 12 ]

Hence, the value of b is 12.

Answer: Yes

Step-by-step explanation: If you plug 12 into b, you will get the equation 12 - 7 = 5.

Try solving 12-7. It is 5.

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The plotted graph is shown below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

s (h) = √64h

now, when h=0

s(0) = √64h = 0

and, when h= 5

s(5) = √64h

        = √64 x 5

       = 8 x 2.25

       = 17.88

and, when h= 10

s(25) = √64h

        = √64 x 10

       = 8 x 3.162

       = 25.29

and, when h= 15

s(25) = √64h

        = √64 x 15

       = 30.98

and, when h= 20

s(25) = √64h

        = √64 x 20

       = 35.77

and, when h= 25

s(25) = √64h

        = √64 x 25

       = 8 x 5

       = 40

The plotted graph is shown below.

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Answer:

in 3 days Tom made $149.25

Step-by-step explanation:

If Tom made 298.50 in 6 days, you can find the amount made in 3 days by dividing that number in half.

298.5 / 2 = 149.25

9.6 KB kilobytes is equal to 0.0096 MB

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

1kB=1000 bytes

1MB=1000 KB

1kB=1/1000MB=0.001 MB

9.6 KB is nothing but 9600 bytes

9.6 KB in MB we have to convert

Now multiply 9.6 with 0.001

9.6×0.001

0.0096 MB

Hence,  9.6 KB kilobytes is equal to 0.0096 MB

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The area of the Triangle is 24.11 inch².

The area of any triangle can be calculated using the lengths of two of its sides and the sine of their included angle.

The trigonometric formula for the area of triangles is

area sin C= 1/2  , where and are the lengths of two sides and is the measure of the included angle.

Given:

a= 14 inch

b= 6.5 inch

and, angle = 32 degree

Now, The area of Triangle

= ab sin [tex]\theta[/tex] /2

= 14 x 6.5 x sin 32 /2

= 7x 6.5 x sin 32

= 7 x 6.5 x 0.5299

= 24.11 inch²

hence, the area is 24.11 inch²

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Answer:

C) -24

Step-by-step explanation:

We have two functions here:

[tex]f(x) = x^{2} + 4[/tex]

and

[tex]g(x) = 2x + 1[/tex]

Now, both of these functions will be multiplied together after they are figured out (since they are next to each other), and they will have -2 replace x. For function f, we get:

[tex]-2^{2} + 4[/tex]

For function g, we get:

[tex]2 * -2 + 1[/tex]

Simplifying these two gives us:

[tex](4 + 4) * (1 - 4)[/tex]

Simplifying further gives us:

[tex]8 * -3 = -24[/tex]

So, the value of f(-2)g(-2) is C) -24.

Hope this helped!

Answer:

B)  -24

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x^2+4\\g(x)=2x+1\end{cases}[/tex]

To find f(-2)g(-2), substitute x = -2 into both functions and multiply them:

[tex]\begin{aligned}\implies f(-2)g(-2)&=\left((-2)^2+4\right)\left(2(-2)+1\right)\\&=\left(4+4\right)\left(-4+1\right)\\&=8 \cdot -3\\&=-24\end{aligned}[/tex]

The number of tiles in figure 70 and figure 93 are 142 and 188.

Figure 2 = 6

Figure 3 = 8

The common difference = 8 - 6

= 2

figure 2 = a + (n - 1)d

Where,

a = first term

figure 2 = a + (n - 1)d

6 = a + (2 - 1)2

6 = a + (1)2

6 = a + 2

6 - 2 = a

a = 4

Figure 70 = a + (n -1)d

= 4 + (70-1)2

= 4 + (69)2

= 4 + 138

Figure 70 = 142

Figure 93 = a + (n -1)d

= 4 + (93 - 1)2

= 4 + (92)2

= 4 + 184

Figure 93 = 188

Therefore, figure 70 and 93 have 142 and 188 tiles respectively.

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The expression in the mathematical form will be (1/4)( 2 - 3x ) / ( 2x ).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The word form of the expression is given as adding one-fourth of two subtracted from thrice a number to twice the same number.​

The expression can be written as,

E = (1/4)( 2 - 3x ) / ( 2x ).

Hence, the expression will be (1/4)( 2 - 3x ) / ( 2x ).

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The correct statement regarding the graph of the function f(x) = (x - 2)(x - 1)(x - 4) is given as follows:

The graph starts at the bottom left, continues up through the x axis at 1 to a maximum around y equals one half, goes back down through the x axis at 2 to a minimum at y equals negative 2, and goes back up through the x axis at 4.

The function is defined as follows:

f(x) = (x - 2)(x - 1)(x - 4).

Considering the linear factors of the function, the values of x through which the function intercepts the x-axis are given as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

As the function has three zeros with multiplicity one, it is a cube function, hence:

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Answer:

The probability that a given household has lost electricity is 10%, or 0.1. So the probability that a given household has not lost electricity is 1 - 0.1 = 0.9.

Since the loss of electricity is independent among the households of the management team, we can find the probability that none of them has lost electricity by multiplying the probability of no loss in any one household (0.9) by itself 6 times, since there are 6 members of the team:

0.9 * 0.9 * 0.9 * 0.9 * 0.9 * 0.9 = 0.54

So the probability that none of the management team members has lost electricity in his or her household is  54%.

The volume of the solid generated by revolving the regions bounded by the curves and lines about the​ y-axis is  8.90 unit³.

Since the region is the one for  then the intersection we are interested on is x=1 as it can also be seen in the graph.

Where h(x) is the height of the shell which here is the distance between the parabola and the line, so  (since the line is on the top we subtract from it the parabola

Notice the limits of the integral are the x-axis (x=0) and the intersection of the parabola and the line that we found before (x=1)

We want the volume generated when the area bounded by the curves :

v = x2 v = 8 —7x , and

x = 0 for x > 0 is revolved about the y axis using the cylindrical shell method .

The intersection of y = x2 and y = 8 —7x is :

y= x2 = 8 — 7x x2 + 7x —8 = 0

(x + 8)(x — 1) = 0 x = —8 or

x = 1 .

We thus have for x > 0 the two curves intersect at x = 1 and y = 12 = 1 .

The limits for integration are --- 0 <x < 1 .

The upper curve is --- y2 = 8 —7x ,

and the lower curve is --- yi = x2 .

The height of the shell is --- h = y2 -yi = 8 —7x — x2 •

The radius of the shell is --- R = x •

[tex]$$The surface area of the shell is :$$A=2 \pi \mathrm{Rh}=2 \pi x\left(8-7 x-x^2\right)=2 \pi\left(8 x-7 x^2-x^3\right) .$$The differential of volume which is the cylindrical shell is :$$\mathrm{dv}=\mathrm{Adx}=2 \pi\left(8 x-7 x^2-x^3\right) \mathrm{dx}$$[/tex]

[tex]$$We then have the volume of revolution is :$$\begin{aligned}v & =2 \pi \int_0^1\left(8 x-7 x^2-x^3\right) \mathrm{d} x \\& =2 \pi\left(4 x^2-\frac{7}{3} x^3-\frac{1}{4} x^4\right)_0^1 \\& =2 \pi\left[4\left(1^2-0^2\right)-\frac{7}{3}\left(1^3-0^3\right)-\frac{1}{4}\left(1^4-0^4\right)\right] \\& =2 \pi\left(4-\frac{7}{3}-\frac{1}{4}\right) \\& =2 \pi\left(\frac{48-28-3}{12}\right) \\& =2 \pi\left(\frac{17}{12}\right) ; \text { or, we have : } \\v & =\frac{17 \pi}{6} .\end{aligned}$$[/tex]

17π/6 = 8.90 unit³

Thus, The volume of the solid generated by revolving the regions bounded by the curves and lines about the​ y-axis is  8.90 unit³.

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Answer:1/30 is the correct answer

Step-by-step explanation:

first, calculate the total number of chips: 4+5+1=10

since we know that chips are not replaced.

probability of finding the first white chip: 4/10 (4 white chips,10 total)

after removing 1 white chip remaining white chips=3, total chips=9

probability of finding the second white chip:3/9 (3 white chips,9 total)

after removing 1 white chip remaining white chips=2, total chips=8

probability of finding the third white chip 2/8 (2 white chips,8 total)

after removing 1 white chip remaining white chips=1, total chips=7

Now the probability of finding 3 white chips is:

probability=(4/10) * (3/9) * (2/8)=1/30