Ben makes orange paint by mixing red, yellow and white paint in the ratio 20 : 16 : 1. 5. How much of each colour does he need to make 1. 5 litres of orange paint?​

The required number of children and adults for sitting in the theater are 300 and 50 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.

Let be consider number of children be x and that of adults is y.

We have,

x + y = 350-------(1)

y = 350 - x

And 5x + 10y = 2000------------------(2)

Put value of y in equation (2)

5x + 10( 350 - x) = 2000

5x + 3500 - 10x = 2000

-5x = -1500

x = 300

Then

y = 350 - x = 350 - 300 = 50

Thus, There will be 300 children and 50 adults in the  theater .

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The height of the tree to the nearest hundredth of a meter = 7.54 m

What are similar triangles?

If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.

From the figure,

AB= 21.15 meters

AE = AB - BE = 21.15 - 16.8 = 4.35 meters

BC= height, h

The triangles ABC and ADE are similar triangles

So,

AE/DE  = AB/BC

4.35 / 1.55 = 21.15/  h

h = ( 21.15 * 1.55 ) / 4.35

  = 32.78/4.35 = 7.54 m

So, the height of the tree to the nearest hundredth of a meter = 7.54 m

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The fraction of the occupied apartments is 9/10.

In mathematics, a fraction is a symbol for a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

Given that,

Total apartments in the building = 200.

Also,

The number of apartments leased by realtor = 180

The fraction of the apartments which is occupied by realtor

= number of apartments leased /Total apartments

= 180 / 200

= 18 / 20

= 9 / 10

The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.

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The option that matches to the given equation is as follows:

a.) Option A

b.) Neither A nor B

C.) Option A

d.) Neither A nor B

e.) Option B

f.) Option B

g.) Option B

h.) Neither A nor B

Option A = 4+3 = 7 can also be written as 7-4 = 3

Option B = 3+3+3+3 =12

= 4(3) = 12

= 12/4 = 3

For question a.)

7 = 3+4 . This represents the diagram of option A.

For question b.)

4-3 = 7 . This doesn't have any representation.

For question C.)

7-4 = 3 . This represents the diagram of option A.

For question d.)

4-3 = 7. This doesn't have any representation.

For question e.)

3+3+3+3 = 12. This represents the diagram of option B.

For question f.)

12= 4÷3. This doesn't have any representation.

For question g.)

12÷4 = 3. This represents the diagram of option B.

For question h.)

3÷3÷3÷3 = 12. This doesn't have any representation.

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Answer:

The answer would be six for the first one. Second one would be 18. Third one would be 24. Fourth one would be 45.

Now the reason I got these as the answer is because I thought about it in a multiplication/division problem because for me it makes it easier.

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Answer:

\(x = \frac{16}{3} \)

Step-by-step explanation:

Solve the equations:

\(4x \: 2 - 5x = 16\)

Multiply the monomals:

\(8x - 5x = 16\)

Combine like terms:

\(3x = 16\)

Divide both sides of the equation by the coefficient of variable:

\(x = 16 \div 3\)

Calculate:

\(x = \frac{16}{3} \)

hi buddy i can help you with this

Answer:

C or d

Step-by-step explanation:

Not sure but i think it's 6.3.

Pythagoras theorem

a²+b²=c²

6.9 is the hypotenuse (c)

2.9 is the base (b)

a is the altitude of the wall or the height of the wall (a)

a²+2.9²=6.9²

a= 6.3

Answer:

Question 3: 582 ft²

Question 4: 348 in²

Step-by-step Explanation:

Question 3:

Consider the solid shape given as being consisting of two rectangular prism. With careful examination, you'd observe that the offer one beneath has dimensions, \( l, w, h, as 15, 4, 9 \)

The second one has \( l, w, h, as 6, 4, 6 \)

Surface area of the bigger rectangular prism = total surface area - area of the surface that is joined to the smaller rectangular prism.

Area of the face joined to the smaller rectangular prism = 4*6 = 24 ft²

Surface area of the bigger rectangular prism = \( 2(wl + hl + hw) - 24 \)

\( 2(4*15 + 9*15 + 9*4) - 24 \)

\( 462 - 24 \)

Surface area of the bigger rectangular prism = 438 ft²

Surface area of the smaller rectangular prism = total surface area of rectangular prism - area of the surface that is joined to the bigger rectangular prism.

= \( 2(wl + hl + hw) - 24 \)

\( = 2(4*6 + 6*6 + 6*4) - 24 \)

\( = 168 - 24 = 144 ft^2 \)

Surface area of the solid = 438 + 144 = 582 ft²

Question 4:

Surface area of the triangular prism is given as: 2(B.A) + P*L

Where,

B.A = area of 1 triangular base = ½*height of the triangle*base of the traingle

B.A = ½*6*16 = 3*16 = 48 in²

P = perimeter of 1 triangular base = sum of all sides of the triangle.

P = 16+10+10 = 36 in

L = length or height of prism =

Plug in the values to find surface area of the prism

Surface area = 2(B.A) + P*L

= 2(48) + 36*7 = 96 + 252 = 348 in²

Surface area of prism = 348 in²

Bill is most likely using a power tool cord or an extension cord designed for power tools.

When replacing a worn-out cable for a power table saw, it is important to use a cable that is specifically designed for power tools. These cables, often called "extension cords" or "power tool cords," are built to handle the high electrical currents required by power tools such as table saws. They are constructed with durable insulation and conductors that can withstand the demands of power tools. These cords are also designed to be flexible, allowing for easy movement and maneuverability while operating the tool. They may also include grounding features to enhance safety. Therefore, it is reasonable to assume that Bill would choose a power tool cord or an extension cord suitable for powering his table saw.

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15(h) + 12

h = hours worked

//

15(2) + 12

The value of the fractions will be:

1. 4/10 + 2/10 = 6/10

2. 9 /12 + 3/12 = 1

3. 6/10 + 4/10 = 1

4. 2/8 + 3/8 = 5/8

5. 2/7 + 6/7 = 1 1/7

6. 11/9 + 8/9 = 2 1/9

7. 5/13 + 10/13 = 1 2/13

8. 3/5 + 7/10 = 1 3/10

9. 7/8 + 13/16 = 1 11/16

10. 9/30 + 3/5 = 9/10

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

It should be noted that in order to add the numbers it's essential to have a common denominator. For example, 7/8 + 13/16 will be:

= 7/8 + 13/16

= 14/16 + 13/16

= 27/16

= 1 11/16

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Answer:

The answer is 3

Step-by-step explanation:

Answer:

\(3\)

Step-by-step explanation:

7-4=3

7+(-4) means 7-4

Hope it helps! :)

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Additional Comment

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Cos(angle) = adjacent leg/ hypotenuse

Cos(61) = x/19

X = 19 * cos(61)

X = 9.2114

Rounded to the nearest tenth = 9.2

Yes.

It is true that if v1, v2, ..., vp are vectors in Rⁿ, then Span{v1, v2, ..., vp} is the same as the column space of the matrix [v1 v2 ... vp].

True, let A = [v1 v2 ... vp] be the matrix columns are the given vectors.

The column space of A is the set of all linear combinations of the columns of A, which is exactly the same as the span of the vectors v1, v2, ..., vp.

In other words, any vector that can be written as a linear combination of the columns of A is also in Span{v1, v2, ..., vp}, and vice versa.

The tools of linear algebra to study the span of a set of vectors, by considering the column space of the corresponding matrix.

Techniques like row reduction and rank to determine if a set of vectors is linearly independent or spans the whole space Rⁿ.

Yes, the given vectors should be used as the matrix columns in A = [v1 v2... vp].

The span of the vectors v1, v2,..., vp is exactly the same as the column space of A, which is the set of all linear combinations of the columns of A.

This means that any vector that can be expressed as a linear combination of columns from A is also a vector in Spanv1, v2,..., vp and vice versa.

By taking into account the column space of the associated matrix, the techniques of linear algebra may be used to examine the range of a collection of vectors.

To establish if a group of vectors spans the whole space Rn or is linearly independent, use methods like rank and row reduction.

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We are given the following dimensions of a concrete wall.

Height = 4 feet

Width = 18 inches

Length = 375 feet

We are asked to determine how many cubic yards of concrete will it take to pour the wall.

Recall that the volume of a rectangular prism is given by

Where l is the length, w is the width, and h is the height.

First, we need to convert all the given dimensions to yards.

There are 3 feet in 1 yard.

There are 36 inches in 1 yard.

Now, we have all the dimensions in yards, let us substitute them into the formula

Therefore, 83.33 cubic yards of concrete is required to pour the wall.

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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Answer:

96 cm³

Step-by-step explanation:

V=1/2×6×8×4=196/2=96cm³

Answer:

15

Step-by-step explanation:

Let's call the mystery number x.

\(14\cdot 15\cdot x=3150 \\\\210x=3150 \\\\x=3150/210=15\)

Hope this helps!

The equation that represents the third number is x × 15 × 14 = 3150. Then the third number is 15.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The product of three numbers is 3150. Two of the number are 14 and 15.

Let 'x' be the unknown number. Then the equation is given as,

x × 15 × 14 = 3150

Simplify the equation, then we have

x × 15 × 14 = 3150

210x = 3150

x = 3150 / 210

x = 15

The equation that represents the third number is x × 15 × 14 = 3150. Then the third number is 15.

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let's assume the temperature on 5th day be x

We know that :

\( \boxed{mean = \frac{sum \: \: of \: all \: \: observations}{number \: \: of \: \: observations} }\)

So,

\( \hookrightarrow \: 0 = \dfrac{ - 2 + ( - 2) + ( - 2) + ( - 2) + x}{5} \)

\( \hookrightarrow \: 0 \times 5= - 2 - 2 - 2 - 2 + x\)

\( \hookrightarrow \: 0 = - 8 + x\)

\( \hookrightarrow \: x = 8\)

Therefore, temperature on the fifth day was x = 8

Answer:

The point N lies inside the circle

Step-by-step explanation:

A circle is centered at the point T(-6,3) and has a radius of r=1.

To determine if the point N(3,-3) is inside or outside the circle, the distance between N and the point T must be lower than 11.

To calculate the distance between points T and N you use:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

where x1 and y1 are the coordinates of T, and x2 and y2 the coordinates of N.

\(d=\sqrt{(3-(-6))^2+(-3-3)^2}=\sqrt{9^2+6^2}=10.81\)

d < 11

The distance d is lower than the radius of the circle. Hence, the point N lies inside the circle

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(a) The supply when the price is $10 is 18 units. (b) The demand when the price is $10 is 21 units. (c) The equilibrium price is $7, and both the quantity supplied and demanded at this price are 9 units. (d) The supply curve crosses the horizontal axis at the point (4, 0), indicating that at a price of $4, there is no supply of CDs.

(a) To find the supply when the price is $10, substitute p = 10 into the supply equation:

q = 3p - 12

q = 3(10) - 12

q = 30 - 12

q = 18

Therefore, the supply when the price is $10 is 18 units.

(b) To find the demand when the price is $10, substitute p = 10 into the demand equation:

q = -2 + 23

q = 21

Therefore, the demand when the price is $10 is 21 units.

(c) To find the equilibrium price, set the supply equal to the demand and solve for p:

3p - 12 = -2 + 23

3p = 21

p = 7

The equilibrium price is $7. To find the corresponding quantity supplied and demanded, substitute p = 7 into either the supply or demand equation:

For supply:

q = 3p - 12

q = 3(7) - 12

q = 21 - 12

q = 9

For demand:

q = -2 + 23

q = 21

Therefore, at the equilibrium price of $7, both the quantity supplied and demanded are 9 units.

(d) To find where the two lines cross the horizontal axis, set q = 0 and solve for p in each equation:

For supply: q = 3p - 12

0 = 3p - 12

3p = 12

p = 4

For demand: q = -2 + 23

0 = -2 + 23

2 = 23 (not possible)

The economic interpretation of the point (4, 0) on the horizontal axis for the supply equation is that at a price of $4, there is no supply of CDs. This could indicate that the cost of production or other factors make it unprofitable to supply CDs at that price.

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Answer:

D

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × \(\frac{45}{360}\) ( r is the radius )

  = π × 1² × \(\frac{1}{8}\)

  = π × 1 × \(\frac{1}{8}\)

  = \(\frac{\pi }{8}\) cm²

1331.046

Step-by-step explanation:

The function y = 7|x + 1| - 5 can be written as a Piecewise Function as follows,

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

Given, a function y = 7|x + 1| - 5

Now, we have to write the given function as a piecewise function

|x + 1| = (x + 1) for x > -1 and

|x + 1| = - (x + 1) for x < -1

So, the given function can be written as a piecewise function

               7(x + 1) - 5                for x > -1

y   =

              -7(x + 1) - 5                for x < -1

On simplifying, we get

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

Hence, the given function y = 7|x + 1| - 5 can be written as a Piecewise Function as follows,

               7x + 2                for x > -1

y   =

              -7x - 12               for x < -1

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The formula to calculate the magic number in MLB is: Magic number = 163 - (number of wins by leading team) + (number of losses by trailing team) - 1.

The "magic number" in Major League Baseball (MLB) represents the combination of wins by the leading team and losses by the trailing team required for the leading team to clinch a playoff spot. To calculate the magic number, follow these steps:

1. Determine the total number of games in the season. In MLB, this is typically 162 games.

2. Subtract the number of games in the season from 163. For example, 163 - 162 = 1.

3. Subtract the number of wins by the leading team from 163. For example, if the leading team has 90 wins, 163 - 90 = 73.

4. Add the result from step 2 to the result from step 3. For example, 73 + 1 = 74.

5. Finally, subtract the number of losses by the trailing team from the result of step 4. For example, if the trailing team has 80 losses, 74 - 80 = -6. In this case, the magic number is zero, meaning that the leading team has already clinched a playoff spot.

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The exponential smoothing forecast for period 5, assuming an alpha (α) value of 0.4, is determined by applying the exponential smoothing formula.

The exponential smoothing formula is given by:

Forecast for period t = α * Actual value for period t + (1 - α) * Forecast for period t-1

In this case, we need the forecast for period 5, so we will use the formula to calculate it based on the available data.

To calculate the exponential smoothing forecast for period 5, we use the given alpha (α) value of 0.4 and the available data for previous periods. The formula considers the actual value for period t and the forecast for the previous period (t-1).

Since we are calculating the forecast for period 5, we need the actual value for period 5 and the forecast for period 4. However, these values are not provided in the given information. Without the actual value for period 5 or the forecast for period 4, it is not possible to provide a specific numerical answer for the exponential smoothing forecast for period 5.

The exponential smoothing technique is commonly used for forecasting, where the alpha (α) value determines the weight given to the most recent observations. A higher alpha value places more weight on recent data, while a lower alpha value gives more weight to historical data. By adjusting the alpha value, the forecast can be adjusted to respond more quickly or more slowly to changes in the data.

To calculate the exponential smoothing forecast for period 5, it is essential to have the necessary data points. With the provided alpha (α) value of 0.4, the formula can be applied once the required data is available.

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