Share £90 in the ratio 1:5

Answer:

4618.1 ft³

Step-by-step explanation:

Volume of the cone:

[tex]V_{cone} = \frac13 \pi r^2 h[/tex]

[tex]V_{cone} = \frac13 \cdot \pi \cdot 49 \cdot 12 = 196\pi[/tex]

Volume of the cilinder:

[tex]V_{cilinder} = \pi r^2 h[/tex]

[tex]V_{cilinder} = \pi \cdot 49 \cdot 22 = 1078\pi[/tex]

Total volume is 2*Vcone + Vcilinder = 1470π ≈ 4618.1 ft³

Answer negative 9 is the answer

Step-by-step explanation:

Answer:1/4

Step-by-step explanation:

The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.

Answer:

Step-by-step explanation:

 This problem is borers on elasticity of materials.

according to Hooke's law, "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."

[tex]F= ke[/tex]

where F is the applied force in N

          k is the spring constant N/m

          e is the extension in meters

Given data

mass m= 24kg

extensnion=15cm in meters= [tex]\frac{15}{100}[/tex]= [tex]0.15m[/tex]

we can solve for the spring constant k

we also know that the force F = mg

assuming [tex]g=9.81m/s^{2}[/tex]

therefore

[tex]24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\[/tex]

We can use this value of k to solve for the mass that will cause an extension of  [tex]10cm= 0.1m[/tex]

[tex]x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg[/tex]

Answer:

So you can divide by 2 for the picture. 4/2 = 2

So you can get 2 x 2 picture. The ratio would be 1

if you have a variable it would always be

x by x.

If you want to cover whole wall multiply by 4/3 on the 4 x 4 picture

The original needs to be scaled up by a factor of 75.

Given that, reproducing a 4 cm × 4 cm picture on a 3 m × 3 m wall.

We need to find what ratio we should use.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

We know that 1 m=100cm, then 3 m=300 cm.

The picture on the wall is (300 cm)/(4 cm) = 75 times as large in each dimension as the original.

Therefore, the original needs to be scaled up by a factor of 75.

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Answer:

T. S. A. =2πrh+2πr2

V=Bh

V = Base×h

V= (lw) × h

V= lwh

Answer:

Equation:  19^2 - 11^2 = width

Step-by-step explanation:

use Pythagorean theorem to find the width.

so, 19^2 - 11^2 = 361-121= 240.

so width = square root of 240

Answer:

19^2 - 11^2 = width

Step-by-step explanation:

Answer:

3 normal tickets were sold, 3 tickets were sold for the elderly, and 12 tickets were sold for children

Step-by-step explanation:

Let x = normal ticket number

Let y = child ticket number

Let z = elderly ticket number

The total amount spent is 480, so we can create this equation:

52 * x + 20 * y + 28 * z = 480

They also tell us that each adult took two children, so:

y = 2 * (x + z)

We have two equations and three unknowns, therefore we must simplify and do trial and error. First, let's substitute "y" in terms of "x" and "z" in the first equation, then simplify:

52 * x + 20 * y + 28 * z = 480

52 * x + 20 * 2 * (x + z) + 28 * z = 480

52 * x + 40 * (x + z) + 28 * z = 480

52 * x + 40 * x + 40 * z + 28 * z = 480

92 * x + 68 * z = 480

23 * x + 17 * z = 120

Let's solve for x in terms of e:

23 * x = 120-17 * z

x = (120-17 * z) / 23

We know that (120 - 17 * z) has to be a multiple of 23 for "x" to be an integer. So let's look at testing some values ​​of "z" to make valid values ​​for "x":

120-17 (0) = 120 (not multiple of 23)

120-17 (1) = 103 (not multiple of 23)

120-17 (2) = 86 (not multiple of 23)

120-17 (3) = 69 (multiple of 23)

120-17 (4) = 52 (not multiple of 23)

120-17 (5) = 35 (not multiple of 23)

120-17 (6) = 18 (not multiple of 23)

120-17 (7) = 1 (not multiple of 23)

After that, we get negative values ​​for "x", so here there is only one possible value for "x", so we know that z = 3:

Now we can solve for "x" and "y":

x = (120-17 * 3) / 23

x = (120-51) / 23

x = 69/23

x = 3

Now for and:

y = 2 * (x + y)

y = 2 (3 + 3)

y = 12

Therefore, 3 normal tickets were sold, 3 tickets were sold for the elderly, and 12 tickets were sold for children.

Answer:

Expected Payoff ⇒ $ 1.50 ; Type in 1.50

Step-by-step explanation:

Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;

[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]

Thus, Solution ; Expected Payoff ⇒ $ 1.50

Answer:

The correct graph should have x values that have no more than one y value.

Step-by-step explanation:

A the inputs (x values) of a function can have no more than one y value. This is a "fact" for functions. So you should click on the graph until you see a graph where every x value has exactly 0 or 1 y value.

Answer:

C

Step-by-step explanation:

x4(x4-5)+5(x4-5)

=x8-5x4+5x4-25

x8-25

Answer:

= -9/2

Step-by-step explanation:

g(x) = -2x^2 -4

Let x = 1/2

g(1/2) = -2 (1/2)^2 -4

        = -2 ( 1/4) - 4

        -1/2 -4

      - 4 1/2

= -9/2

Answer:

The expression is: [tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}[/tex]

The thickness of the cookie is: [tex]\frac{123}{100}[/tex] cm

Step-by-step explanation:

The cookie is formed by two layers, the cookie and the frosting. So if we want to know the total thickness of the cookie and frosting we need to sum the thickness of each layer as shown below:

[tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}\\\text{total thickness} = \frac{9}{10} + \frac{33}{100}\\\\\text{total thickness} = \frac{10*9 + 33}{100}\\\\\text{total thickness} = \frac{123}{100} \text{ cm}[/tex]

The expression is: [tex]\text{total thickness} = \text{cookie thickness} + \text{frosting thickness}[/tex]

The thickness of the cookie is: [tex]\frac{123}{100}[/tex] cm

Answer:

$11.25 / hr

Step-by-step explanation:

36x+40x=855

76x=855

x=11.25

Answer:

[tex]\fbox{\begin{minipage}{3em}x = 6\end{minipage}}[/tex]

Step-by-step explanation:

Given:

Equation: [tex]3x - 3 = 27 - 2x[/tex]

Solve for:

[tex]x[/tex]

Solution:

Step 1: Select relevant approach:

Let's move all the components containing x to the left side and other components to the right side (notice the change of sign of each one from + to - or - to +), then calculate [tex]x[/tex]

Step 2: Perform the calculation:

      [tex]3x -3 = 27 - 2x[/tex]

Moving components:

<=> [tex]3x + 2x = 27 + 3[/tex]

Adding up components:

<=> [tex]5x = 30[/tex]

Dividing both sides by 5 (coefficient of component containing [tex]x[/tex]:

<=> [tex]\frac{5}{5} x = \frac{30}{5}[/tex]

Simplifying to work out [tex]x[/tex]:

<=>[tex]x = 6[/tex]

Hope this helps!

:)

Answer:

x = 6

Step-by-step explanation:

3x - 3= 27 - 2x

First we put all the x terms to on side, making it 3x + 2x - 3= 27.

Remeber that when we move a term to the other side of the equals sign (=), we change its sign to be the opposite of what it currently is.

Then, we move all the numberics to the other side, so we derieve 3x + 2x = 27 +3. Again, the sign changes when we move it across.

What is left to do is add up the quantities. So 3x + 2x = 5x and 27 +3 = 30.

We are left with 5x = 30. If 5 x's is 30, how much is one? Sinply divide it to get the answer of 30 / 5 which is six!

To make sure the answer is correct substituite 6 in the equation as x and see if its accurate: 3(6) -3 = 7 - 2 (6). And it is!

So x is equal to six.

Answer:

B, C, E

Step-by-step explanation:

The solution of the inequality is x ≤ -7

The graph would have a closed circle because it's less than or equal to

-7 is a part of the solution because it's less than or equal to -7

Answer:

Step-by-step explanation:

Subtract 22 from both sides to get [tex]x\leq -7[/tex]. So the 2nd one is correct

The sign is less than or equal to, so the graph does indeed have a closed circle. So the 3rd one is also correct

The answer is x is less than or EQUAL to -7, so -7 is included in the asnwer. So the 5th one is also correct

Answer:

Option (A). 363 units²

Step-by-step explanation:

Surface area of the rectangular pyramid = Area of the rectangular base + Area of the lateral sides of the pyramid

Area of the rectangular base = Length × Width

                                                = 11 × 11

                                                = 121 units²

Area of the lateral sides = 4(Area of one lateral side)

                                        = 4[[tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]]

                                        = 2(11)(11)

                                        = 242 square units

Area of the rectangular pyramid = 121 + 242

                                                      = 363 square units

Therefore, Option (A) will be the answer.

Answer:

a. [tex]8x^{2} -14x-15[/tex]

b. [tex](x+3)(x+2)[/tex]

Step-by-step explanation:

A. There are 3 methods (that I know of). The easiest method is the lattice multiplication, while the most commonly used is the FOIL method (First+Outer+Middle+Last)

For F, take the first terms of the 2 and multiply

[tex]4x*2x=8x^{2}[/tex]

For O, take the outer terms and multiply

[tex]4x*-5=-20x[/tex]

For I, take the inner terms and multiply

[tex]3*2x=6x[/tex]

For L, take the last terms and multiply

[tex]3*-5=-15[/tex]

After that, add all of them up

[tex]8x^{2} +(-20x)+6x+(-15)=8x^{2}-14x-15[/tex]

B. Since the equation is in the form x^2+bx+c,

[tex](x+?)(x+?)[/tex]

Now we need to find 2 numbers that will add up to 5 and multiply to 6.

Here are some of the combinations of numbers that multiply to 6

3*2

1*6

-3*-2

-1*-6

3 and 2 add up to 5 so:

[tex](x+3)(x+2)[/tex]

Answer:

A

Step-by-step explanation:

If the equation of the line is written in slope-intercept form, y = mx + b then the value of b will be -21; the correct answer is option A.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. That is why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.

Formula for slope, thus, is;

Slope = (y₂ - y₁) / (x₂ - x₁)

Parameters;

J(-4, -5) and K(-6, 3)

= (3 - (-5)) / (-6 - (-4))

= (3 + 5) / (-6 + 4)

= 8 / -2

= -4

Substitute one of the coordinates into the formula to solve for b

y = mx + b

y = -4x + b

3 = -4(-6) + b

3 = 24 + b

3 - 24 = b

b = - 21

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Answer:

13

Step-by-step explanation:

1/3 of 6 1/2 multiply by 3/4 (56 divided by 7)  

1/3* 13/2 * 3/4 * 56/7= 1*13*3*56/3*2*4*7= 13*3*56/3*56= 13

Answer:

Exactly 26 cookies fit and there would be 0.75 of cookie space left over.

Step-by-step explanation:

In this case, we must calculate the area of a cookie and the total area of the cookie tray,

give us the diameter of the cookie, we need the radius, we know that the radius is half the diameter, so:

r = d / 2 = 1/2

the area would be:

A = pi * r ^ 2

replacing:

A = 3.14 * (1/2) ^ 2

A = 0.785

The area for each cookie is 0.785 in ^ 2

Now the area of the cookie tray would be:

A = 7 * 3

A = 21 in ^ 2

Therefore a total of:

 21 / 0.785 = 26.75

Which means that exactly 26 cookies fit and there would be 0.75 of cookie space left over.

Answer:

2/3

Step-by-step explanation:

There are 6 marbles in the jar

4 are not purple

P(not purple) = marbles that are not purple/ total marbles

                      = 4/6 = 2/3

Answer:

2/3

Step-by-step explanation:

since there are 6 total marbles and 4 of them are colors other than purple, there is a 4/6 chance of drawing a marble that is not purple which can be simplified to 2/3.

Answer:

The volume of the sphere is 32 π /3 cm^3

Step-by-step explanation:

Mathematically, the volume of a sphere can be calculated using the formula below;

V = 4/3 * pi * r^3

Now since we have the radius and diameter = 2 * radius

radius = diameter/2 = 4/2 = 2

Substituting this value into the volume equation;

V = 4/3 * pi * 2^3 = 32pi/3

Answer:

The correct answer is A

Step-by-step explanation:

Answer:

y = 1/2x+5

Step-by-step explanation:

You have two points so you can find the slope

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

m = (8-3)/(6 - -4)

   (8-3)/(6+4)

    5/10

 1/2

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 1/2 x+b

Substitute a point into the equation

8 = 1/2(6)+b

8 = 3+b

b=8-3 = 5

y = 1/2x+5

Answer:

3/5

Step-by-step explanation:

cos F = adjacent side/ hypotenuse

Cos F = 6/10

Cos F = 3/5

Answer:

6/10 which is 3/5

Step-by-step explanation:

Answer:

1 gram is 0.035274 in ounces

Answer:

It would be about 0.035274

Step-by-step explanation:

For an approximate result, divide the mass value by 28.35

Hope this helps

Answer:

a) 3

b) -4

c) -1/3

d) -2

e) -4/3

Step-by-step explanation:

a) 6w=2  ,   w=6/2    , ie. w= 3

b) 6+w=2   ,w=2-6   , ie. w= -4

c) 6w+2= 0,  6w=  0-2 , 6w= -2 , w= -2/6, ie. w= -1/3

d) 6w+2= -10, 6w= -10-2,  6w= -12, w= -12/6 , ie. w= -2

e) 6w+2= 12w+10, 6w-12w = 10-2 ( here we interchanged the digits to get the variables or you can say the terms having variables in this case 'w' to the same side. hereby changing the sign from '+' to '-')

so

6w-12w = 10-2 ,-6w=8, w= -8/6, ie. w= -4/3

You can check your answers by substituting with the answers in place of the variable and check if the equation is solved.

Tell me if this was helpful

Answer:

3/4

Step-by-step explanation:

The answer is The third angle measures 120 degrees

Step-by-step explanation:

I know this because a triangle has angle sum of 180 and so if you know two of the sides then you can add them together; 30+30 = 60 then substract it from 180; 180-60 and that would equal 120 degrees.