Two-fifths of the students in the music class of twenty students were boys. How many boys are in the music class?

Answer:

B

Step-by-step explanation:

62x4=248

4x2=8

6x4=24 and carry the 0 and get 240

240+8=248 and you get B

The area of the complex figure is 132 square units

From the information given, we have that the composite shape is a combination of a:

The formula for area of a square is given as:

Area = a ²

Where 'a' is the length of it side

Area = 6²

Area of square = 36 square units

The formula for area of a rectangle is given as:

Area = width × length

Area = 8 × 12

Area of rectangle = 96 square units

Area of the complex figure = Area of square + area of rectangle

= 36 + 96

= 132 square units

Thus, the area of the complex figure is 132 square units

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Answer: x = - 10

Step-by-step explanation:

    We will use the equation given, substitute -1,000 in for y, and solve.

y = x³

(1,000) = x³

\(\sqrt[3]{ (1,000)} = \sqrt[3]{x^3}\)

- 10 = x

x = - 10

Step-by-step explanation:

area of square=length×length

=25ft²

area of rectangle=length × breath

=2×9

18ft²

area of the figure=25 +18

=43ft²

Answer:

x=16/5

Step-by-step explanation:

7-4=5x-13

3=5x-13

+13.  +13

16=5x

16/5 = x

Alexander is utilizing a scale of 1 inch : 300 feet for his map.

The Alexander's triangle has a height of 4 inches in inches.

When comparing the initial dimensions as used by alexander, the scale of the map may be determined.

The scale is 1 inch: 300 feet since he used 10 inches to symbolize 3000 feet, this is gotten by diving both sides by 10

Using the scale factor 1 inch: 300 feet, the height of 1200 feet would be.

300 feet per inch, then ? inch is 1200 feet

? * 300 = 1200 * 1

? = 1200 / 300

? = 4 inches

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Answer:

See below

Step-by-step explanation:

Remark

Base angles of Isosceles triangles are equal.

Equation

That means that 8x + 14 = 14x - 15

Solution

8x + 14 = 14x - 15              Add 15 to both sides

8x + 14+15 = 14x               Combine

8x + 29 = 14x                   Subtract 8x from both sides

8x - 8x + 29 = 14x - 8x    Combine

29 = 6x                            Divide by 6

x = 29/6

x = 4 5/6

Answer

x = 4 5/6 or 4.833

8x + 14 = 8 * (4 5/6)   +  14

8x + 14 = 38 2/3 + 14

8x + 14 = 52 2/3 or 52.6666

14x - 15 = 14 *(4 5/6) - 15

14x - 15 = 67 2/3   -15

14x - 15 = 52 2/3 or 52.666

Answer:

equal

alternate exterior angles

Step-by-step explanation:

The measure of given angles are equal to each other because they are alternate exterior angles,

Answer:

closing costs

Step-by-step explanation:

Answer:

You can use 48 and 24

Step-by-step explanation:

You can figure out 48 by simply multiplying 6 times 8. You can figure out the 24 by noticing that 24 is divisible by both 6 and 8. 6 x 4 =24, and 8 x 3=24. I hope this helps!

Answer:

The numbers we could use for the denominators is 48  and 24.

Answer:

45 minutes =34 hour. → Sasha mows 48=12 of an acre in 44=1 hour.

Step-by-step explanation:

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer:   10°

__________________________________________________________

We are given:

Sin(6θ)  = Cos(3θ)

Solving for θ:

Simplifying Cos(3θ):

We know that:  

Cos(θ) = Sin(90-θ)

So, we can say that:

Cos(3θ) = Sin(90 - 3θ)

Finding the value of θ:

Sin(6θ) = Cos(3θ)

Sin(6θ) = Sin(90 - 3θ)                             [Since Cos(3θ) = Sin(90 - 3θ)]

6θ = 90 - 3θ                                            [If Sin(θ) = Sin(A) ; θ = A]

9θ = 90                                                   [adding 3θ on both sides]

θ = 10°                                                     [dividing both sides by 9]

Answer:

-7

Step-by-step explanation:

the full coordinate would be  3,-7. just line up the number directly above it and to the left/right and write it down x,y

Answer:

-225

Step-by-step explanation:

f(-5)= 3(-5)^2

f(-5)= -15^2

-225

Answer:

(1, -1, 3)

Step-by-step explanation:

Given system of linear equations is,

2x + 3y - 2z = -7 ---------- (1)

x - 2y + 4z = 15 ------- (2)

2y + z = 1 ------------ (3)

Equation (2) multiplied by 2 then subtracted from equation (1),

(2x + 3y - 2z) - 2(x - 2y + 4z) = -7 - 30

(2x - 2x) + (3y + 4y) + (-2z - 8z) = -37

7y - 10z = -37 ------ (4)

Equation (3) multiplied by 10 then added to equation (4),

(20y + 10z) + (7y - 10z) = 10 - 37

27y = -27

y = -1

From equation (3),

2(-1) + z = 1

-2 + z = 1

z = 3

From equation (2),

x - 2(-1) + 4(3) = 15

x + 2 + 12 = 15

x + 14 = 15

x = 1

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder with a radius of 5 inches and a height of 16 inches is 1256 in³.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.

Given the radius of the cylinder is 5 inches, while the height is 16 inches, therefore, the volume of the cylinder will be,

Volume of the cylinder = πr²h = π×(5)²×16 = 1,256.637 in³ ≈ 1,256 in³

Hence, the volume of the cylinder with a radius of 5 inches and a height of 16 inches is 1256 in³.

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Answer:

2/3

Step-by-step explanation:

\(2 \frac{1}{4} : \frac{1}{2}\) = \(\frac{9}{4} : \frac{1}{2}\)

\(\frac{\frac{9}{4} }{\frac{1}{2} }\) = \(\frac{3}{x}\)

3 * 1/2 = 9/4x

3/2 = 9/4 x

x = 3/2 ÷ 9/4 = 3/2 * 4/9 = 12/18 = 6/9 = 2/3

By using Percentage , Profit distributed to Charity A is £ 624 and Charity B is £ 336

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Total ticket sold = 800

Cost of each ticket is £ 2

Total fund raised (raw) = 2 * 800 = £1600

4% of the ticket won a prize of £20 each

so total number of tickets winning a prize = 4 % of 800 = 32

Total prize money distributed = 32 * 20 = £ 640

Total amount to distribute to charity = 1600 - 640 = £ 960

Total profit that goes to Charity A is = 65 % of 960 = £624

And rest to charity B is = £ 336

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Answer:

Step-by-step explanation:

12 NO WELCOME

:)

Step-by-step explanation:

I think the question is incomplete without an attachment of the diagram of the cone, but we can make do with the information provided.

Back to our question. the statements that apply are

Answer:

2 3 4 5

Step-by-step explanation:

Answer: -3.4

Step-by-step explanation:

\(-3\frac{2}{5} \\-\frac{3*5+2}{5} \\-\frac{15+2}{5} \\-\frac{17}{5} \\= -3.4\)

By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

What is the parallel lines?

Parallel lines are two lines in a plane that never intersect.

1. Orientation of Lines:

Parallel lines are lines that never intersect and remain equidistant from each other at all points.

When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.

On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.

2. Tools/Methods Used:

Constructing parallel lines and constructing perpendicular lines may require different tools or methods.

To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.

Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

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The factory will put 441 cans of soda in 7 cases.

If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.

Given:

Number of flavors = 9

Cans per flavor = 7

Number of cases = 7

To calculate the total number of cans, we can multiply these values:

Total cans = Number of flavors × Cans per flavor × Number of cases

Total cans = 9 × 7 × 7

Total cans = 441

To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).

Hence, the factory will put 441 cans of soda in 7 cases.

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Step-by-step explanation:

y = 4 ^(x+1)    by inspection

Answer:14+14=28

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

14+14=28

Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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