A sum of money is divided in the ratio 3:5:9.calculate the smallest share given the largest share is 108

Answer:

C

Step-by-step explanation:

36:60

= 18:30

= 9:15

= 3:5

Answer:  roughly 151.81788 square meters of metal

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

Explanation:

The base is a square with side lengths x, so its area is x*x = x^2

Let h be the height of the tank. We have four identical wall panels that have area of xh square meters. The four walls lead to a lateral surface area of 4xh. Overall, the entire tank requires x^2+4xh square meters of metal. We're ignoring the top since the tank is open.

-----------

Let's set up a volume equation and then isolate h.

volume = length*width*height

108 = x*x*h

108 = x^2*h

x^2*h = 108

h = 108/(x^2)

-----------

Plug that into the expression we found at the end of the first section.

x^2+4xh

x^2+4x(180/(x^2))

x^2+(720/x)

------------

Depending on what class you're in, the next step here will vary. If you are in calculus, then use the derivative to determine that the local min happens at approximately (7.11379, 151.81788)

If you're not in calculus, then use your graphing calculator's "min" feature to locate the lowest point on the f(x) = x^2+(720/x) curve.

This lowest point tells us what x must be to make x^2+(720/x) to be as small as possible, where x > 0.

In this context, it means that if the square base has sides approximately 7.11379 meters, then you'll need roughly 151.81788 square meters of metal to form the open tank. This is the least amount of metal required to build such a tank, and that will have a volume of 108 cubic meters.

Answer: (c)

Step-by-step explanation:

Given

The function is [tex]y=-x^2+6x-4[/tex]

Range of a function describes the values y can take

from the graph it is clear that the maximum value of y is 5

[tex]\therefore y\leq5[/tex]

Hence. option (c) is correct.

Answer:

The PERIMETER P is the distance around the rectangle.

Let's call the width of the rectangle W and the length of the rectangle L.

As you go around the edge there two equal lengths and two equal widths.

The formula for the perimeter of a rectangle is P=2*L+2*W.

P=2L%2B2W

Substitute 290 for P and 62 for the width.

290=2L%2B2%2862%29

Solve for L.

290=2L%2B2%2862%29

290=2L%2B124

290-124=2L

2L=166

L=83

The equation L=83 means that the length is 83 cm.

CHECK your work.

2(62)+2(83) = 124+166 = 290cm.

The length of the rectangle is 83cm.

Answer:

Step-by-step explanation:

3mn (m+y)

= 3[tex]m^{2}[/tex]n + 3mny

Answer: See explanation

Step-by-step explanation:

1. 5x-7+3x and 3x-7+5x

5x - 7 + 3x

Collect like terms

5x + 3x - 7 = 8x - 7

3x-7+5x

Collect like terms

3x + 5x - 7 = 8x - 7

They're equivalent

2. 4y+9+3y and 3y+9+4y

4y + 9 + 3y

Collect like terms

4y + 3y + 9 = 7y + 9

3y + 9 + 4y

Collect like terms

3y + 4y + 9 = 7y + 9

They're equivalent

3. 6z-2z+4 and 4+2z-6z

6z - 2z + 4 = 4z + 4

4 + 2z - 6z = 4 - 4z

They're not equivalent

Answer:

8038.65

Step-by-step explanation:

[tex]4000(1+\frac{.07}{12})^{12*10}=8038.65[/tex]

Answer:

a) 2.5 pounds of candy

b) 2.5 pounds of candy

    [tex]\frac{0.5}{1} :\frac{y}{5}[/tex]

    y × 1 = 0.5 × 5

    y = 2.5

Step-by-step explanation:

1 = 5

1/2 = y or 0.5 = y

[tex]\frac{0.5}{1} :\frac{y}{5}[/tex]

y × 1 = 0.5 × 5

y = 2.5

Answer:

Sin(E) = 7/25

Sin(D) = 24/25

Tan(D)= 24/7

Step-by-step explanation:

Sin=opp/hyp

Tan=opp/adj

Cos=adj/hyp

The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7

The given parameters are:

EF = 24

DF = 7

Start by calculating the length DE using:

DE²= EF² + DF²

So, we have:

DE²= 24² + 7²

Take the square root of both sides

DE= 25

The sine of the angles is calculated using:

sin(Ф) = opp/hyp

So, we have:

sin(E) = 7/25

sin(D) = 24/25

The tangent of the angles is calculated using:

tan(Ф) = opp/adj

So, we have:

tan(D)= 24/7

Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7

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Step-by-step explanation:

the total mass of each empty carton

1284×2568kg

the total mass of books alone

30816×10=12840kg

Answer:

it is not considered a major earthquake, for it to be considered a major earthquake it has to have a rating of 8.0 or higher

Answer:

x could be 0 or it could be 5/2

Step-by-step explanation:

Answer:

x= 5/2

Step-by-step explanation:

4x^2 + 4x - 14x = 0

subtract 4x from 14x because they are like terms

4x^2 - 10x=0

4x^2 = 0 + 10x

4x^2 = 10x

x^2/x = 10/4

x=10/4

x=5/2

straightAnswer:

Step-by-step explanation:

The strategy would be to look for the equations of  lines that passes for the points. it can be done but it's a hard work. I prefer to use a calc sheet . You can se that house 2 has a perfect fit to data because it has a [tex]R^2=1[/tex], however house 1 does not have a perfect fit, [tex]r^2=0.99..[/tex] altough it is a very good fit, in the image you can see the corresponding equations

Answer:

Scale of the drawing would be 20/12 inch and 0.6 (6/12) inch

Step-by-step explanation:

For most of the residential buildings an scale of 1 inch = 12 feet can be used to draw the residential units.

In that case the scale of the drawing would be 20/12 inch and 0.6 (6/12) inch

Dave should label the dimensions in inches

Answer:

4^4=4^3*4=64*4=256

4^6=4^5*4=1024*4=4096

Step-by-step explanation:

Answer:

4^4 = 256

4^6 = 4,096

9514 1404 393

Answer:

  no

Step-by-step explanation:

The first step is to understand that the question is asking about the future value of series of payments. An appropriate formula is ...

  P = A(n/r)((1 +r/n)^(nt) -1)

where P is the future value, A is the periodic payment made n times per year for t years. r is the annual interest rate.

The next step is to substitute the given values and do the arithmetic. Using the given values, we have ...

  P = 250(12/0.056)((1 +0.056/12)^(12×2.5) -1) ≈ 8030.32

Shen will have accumulated about $8,030.32, which is not enough to meet his goal.

Answer:

Step-by-step explanation:

The matched statement to its corresponding reason for the given alternate interior angles as:

Given: Let points A, B, and C form a triangle.

definition: Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.

Congruent angles: m∠1=m∠4, m∠3 = m∠5

Linear pair theorem: m∠4+m∠2+m∠5 = 180°

As per the shown figure,

Given:

Let points A, B, and C form a triangle.

Defining a parallel line and labeling angles:

Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.

Alternate Interior Angles Theorem:

∠1=∠4

∠3 = ∠5

Congruent angles have equal measures:

m∠1=m∠4

m∠3 = m∠5

Definition of a straight angle and angle addition:

m∠4+m∠2+m∠5 = 180°

Substitution:

m∠1 + m∠2 +m ∠3 = 180°

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Answer:

Step-by-step explanation:

perimeter of rectangle = 1100

let breadth be x

length = 300 + x

perimeter of rectangle = 2(l + b)

1100 = 2(300 + x + x)

1100 = 2(300 + 2x)

1100 = 600 + 4x

1100 - 600 = 4x

500 = 4x

500/4 = x

125 = x

therefore breadth is 125 feet

length = 300 + 125

=425 feet

Answer:

The rectangular field is 425 feet by 125 feet.

Step-by-step explanation:

Let w represent the width of the rectangular field.

Since the length is 300 feet more than the width, the length can be modeled by the expression (w + 300).

The perimeter of a rectangle is given by the formula:

[tex]P=2(w+\ell)[/tex]

Where P is the perimeter and w and l are the width and length, respectively.

We are given that the perimeter is 1,100 feet. Substitute:

[tex]1100=2(w+\ell)[/tex]

Divide both sides by two:

[tex]550=w+\ell[/tex]

We know that l = (w + 300). So:

[tex]550=w+(w+300)[/tex]

Simplify:

[tex]2w=250[/tex]

Divide both sides by two. So, the width is:

[tex]w=125\text{ feet}[/tex]

Since the length is 300 feet more than the width, that means the length is 425 feet.

The rectangular field is 425 feet by 125 feet.

The value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

We have:

y varies directly with x and inversely with z.

y ∝ x/z

Removing the proportional sign.

y = kx/z

k is the constant of proportionality.

Plug y = 27, x = 21, and z = 7 to get the value of k

27 = 21k/7

k = 9

y = 9x/z

Plug x = 25, and z = 5

y = 9(25)/5

y = 45

Thus, the value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z

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Answer:

yes I can help you but ???

Answer:

C 35:15

Step-by-step explanation:

because 35:15 =5:3 so it is not equal to a ratio of 5 is to 2

Answer:

C

Step-by-step explanation:

If you simplify all the ratios, then you get the following:

A. 25/5 : 10/5 = 5:2

B. 35/7 : 14/7 = 5:2

C. 35/5 : 15/5 = 7:3

D. 40/8 : 16/8 = 5:2

Answer:

|x - 4| ≤ 0.3

Step-by-step explanation:

The actual width = 4

Maximum variation, x = 0.3

Hence, the lowest width position based on actual width and possible variation is :

4 - 0.3 ≤ x ≤ 4 + 0.3

3.7 ≤ x ≤ 4.3

Answer:

C) 6

by-step explanation:

let x =the number

Step-by-step explanation:

81+x=3x-39

group like terms

81+39=3x-x

120=2x

120/2=2x/2

60=x

therefore x =60

Answer:

60

Step-by-step explanation:

number is represented as x.

81 is added to a number is

81 + x

39 less than three times the number

3x - 39

So

81 + x = 3x - 39

Solve for x.

81 + x = 3x - 39 Add 39 to each side so 39 cancels on the right.

81 + x + 39 = 3x - 39 + 39

81 + x + 39 = 3x

81 + 39 + x = 3x

120 + x = 3x Subtract x from each side.

120 + x - x = 3x - x

120 = 3x - x

120 = 2x    Divide each side by 2

120/2 = 2x/2

120/2 = x

60 = x

Answer:

-1  1/4 yards

Step-by-step explanation:

7 carries

-8.75 yards  total yardage

    -.8.75 / 7  =  -1.25 yards average per carry

In mixed number ?    -1  1/4 yards          

Answer:

Step-by-step explanation:

c