Find the measurement of each numbered angle.

There are 10% of the 60 students which is 6 students who are 18 years old or younger.

To get number of students who are 18 years old or younger, we have to determine percentage of students who fall into this category.

The percentage of students who are 18 years old or younger will be derived by subtracting the sum of the percentages of students who are 19 years old, 30 years old and over 20 years old from 100%.

The percentage of students who are 18 years old or younger is:

= 100% - (20% + 30% + 40%)

= 100% - 90%

= 10%.

Translated question:

A university course has 60 students. If 20% are 19 years old, 30% 30 and 40% over 20 years old, how many students can there be 18 years old or younger?

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The expression 13√22b - 10√22b is equivalent to 3√22b.

We have,

To simplify the expression 13√22b - 10√22b, we can combine the terms with the same radical.

Since both terms have √22b, we can factor it out:

13√22b - 10√22b = √22b(13 - 10)

Simplifying further, we have:

√22b(3) = 3√22b

Therefore,

The expression 13√22b - 10√22b is equivalent to 3√22b.

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The expression (tan x + 1) / (1 - tan x) can be written as tan (x - π/4)

Option D is the correct answer.

We have,

To explain why the expression (tan x + 1) / (1 - tan x) can be written as - tan (x - π/4), we can simplify the expression step by step:

- Start with the given expression: (tan x + 1) / (1 - tan x).

-We can rewrite tan x as sin x / cos x.

- Substitute sin x / cos x in the numerator and denominator:

[(sin x / cos x) + 1] / [1 - (sin x / cos x)].

- Combine the fractions in the numerator:

[(sin x + cos x) / cos x] / [1 - (sin x / cos x)].

- Simplify the denominator by multiplying by the conjugate:

[(sin x + cos x) / cos x] / [(cos x - sin x) / cos x].

- Invert and multiply to divide by a fraction:

[(sin x + cos x) / cos x] * [cos x / (cos x - sin x)].

- Cancel out the common factor of cos x in the numerator and denominator:

(sin x + cos x) / (cos x - sin x).

- Use the identity tan (x - π/4) = (sin x + cos x) / (cos x - sin x).

Therefore,

The expression (tan x + 1) / (1 - tan x) can be written as - tan (x - π/4).

By simplifying the expression, we can see that it is equivalent to:

tan (x - π/4).

Thus,

The expression (tan x + 1) / (1 - tan x) can be written as tan (x - π/4)

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There are 40 cubes in the bag.

Using algebra to represent the number of black and white cubes in the original bag.

We know that the ratio of black to white cubes = 3:7,

So we can represent the number of black cubes as 3x

And the number of white cubes as 7x.

After adding 8 black cubes,

The ratio becomes =  5:7.

This means that the new number of black cubes is 5x,

And the new number of white cubes is 7x.

To solve for x,

Use the information that we have about the number of black cubes.

We know that we added 8 black cubes to the original bag,

So we can set up the equation:

⇒ 3x + 8 = 5x

Solving for x, we get:

⇒ 2x = 8

⇒   x = 4

Now that we know that x = 4,

We can find the total number of cubes in the bag,

original number of black cubes + 8 = 3x + 8

= 3(4) + 8

= 20

Total number of cubes = original number of black cubes + original number of white cubes

= 3x + 7x

= 10x

= 10(4)

= 40

Therefore,

The required number of cubes = 40.

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The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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The two functions intersect at x = 0 and x = π/2, which are values in the interval [0, 2π). Therefore, the correct answer is option A.

The given functions are f(x)=cos(2x)-5 and g(x)=sin(2x)-5 intersect.

To find the intersections of the two functions, we will set the two equations equal to each other and solve for x.

Set f(x) = g(x):

cos(2x) - 5 = sin(2x) - 5

Subtract 5 from both sides

cos(2x) = sin(2x)

cos(2x) - sin(2x) = 0

2×sin(x)×cos(x) = 0

We can now factor this equation and break it into two equations:

sin(x) = 0 or cos(x) = 0

To solve for x, we plug in the two equations into the given interval.

For sin(x) = 0, x = 0

For cos(x) = 0, x = π/2

The two functions intersect at x = 0 and x = π/2, which are values in the interval [0, 2π).

Therefore, the correct answer is option A.

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The zeros of g(x) = (x + 2)(x − 1)(x − 2) are x = -2, 1 and 2

From the question, we have the following parameters that can be used in our computation:

The 5 functions of g(x)

To determine the key features of the function g(x), we make use of the first

g(x) = (x + 2)(x − 1)(x − 2)

So, we have

Zeros

This is when the function equals 0

(x + 2)(x − 1)(x − 2) = 0

Evaluate

x = -2, 1 and 2

The y-intercept

This is when the value of x in the function equals 0

g(0) = (0 + 2)(0 − 1)(0 − 2)

Evaluate

g(0) = 4

End behaviour

This is the behavior of the graph of the function as it approaches the ends of the x-axis

So, we have

[tex]\mathrm{as}\:x\to \:+\infty \:,\:g\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:g\left(x\right)\to \:-\infty \:[/tex]

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Answer:

0.3x - 8 = 0.5x + 10

0.3x - 0.5x = 10 + 8

-0.2x = 18

x = 18 / (-0.2)

x = -90

Step-by-step explanation:

Answer:

-90

Step-by-step explanation:

0.3x-8=0.5x+10

collecting like terms

0.3x-0.5x=10+8

-0.2x/-0.2=18/-0.2

x=-90

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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The area of the triangle is 33 square centimeters.

Remember that for a triangle of base B and height H, the area is given by the formula:

A = B*H/2

So base times the height over two.

Here we can see that the base is B = 6cm, and the height of the triangle is 11cm, so we can replace these values in the formula above so we get:

A = 6cm*11cm/2 = 3cm*11cm = 33cm²

That is the area of the green triangle.

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After simplification the value of expression is,

⇒ (2x - 4) / (x + 5)

We have to given that,

An expression to simplify is,

⇒ 12 (x - 2)² / 6(x - 2) (x + 5)

Now, We can simplify as,

⇒ 12 (x - 2)² / 6(x - 2) (x + 5)

⇒ 12 (x - 2) (x - 2) / 6(x - 2) (x + 5)

⇒ 2 (x - 2) / (x + 5)

⇒ (2x - 4) / (x + 5)

Therefore, After simplification the value of expression is,

⇒ (2x - 4) / (x + 5)

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The function f(x) = x² - 2x - 6 written in vertex form is

f(x) = (x - 1)^2 - 7.

To write the function f(x) = x² - 2x - 6 in vertex form, we need to complete the square.

the vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

complete the square for the given function

f(x) = x² - 2x - 6

f(x) = (x² - 2x) - 6

take half of the coefficient of x (-2) and square it:

(-2/2)² = 1

add and subtract the value inside the parentheses:

f(x) = (x² - 2x + 1 - 1) - 6

rearrange the terms:

f(x) = (x² - 2x + 1) - 1 - 6

factor the perfect square trinomial inside the parentheses:

f(x) = (x - 1)² - 7

Therefore, the function f(x) = x^2 - 2x - 6 written in vertex form is f(x) = (x - 1)^2 - 7.

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The angle LKN in the rhombus is 62 degrees.

A rhombus is a quadrilateral that has 4 sides equal to each other. The sum of angles in a rhombus is 360 degrees.

Opposite angles are equal in a rhombus. The diagonals bisect each other at 90 degrees. Adjacent angles add up to 180 degrees.

Therefore, let's find ∠LKN as follows:

m∠JMN = (-x + 69)

m∠LMJ = (-6x + 166)

Therefore,

1 / 2 (-6x + 166) = -x + 69

-3x + 83 = -x + 69

-3x + x = 69 - 83

-2x = -14

x = -14 / -2

x = 7

Therefore,

∠LKN = 1 / 2 (-6x + 166)

∠LKN = 1 / 2 (-6(7) + 166)

∠LKN = 1 / 2 (-42 + 166)

∠LKN = 62 degrees

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Answer: Made it hard but here you go

Step-by-step explanation:

To find an equation for the curve of best fit, we need to perform a regression analysis on the data. This requires specialized software or tools that I do not have access to. However, based on the data provided, it appears that the value of Ashleigh’s investment is increasing linearly over time. If this trend continues, we can estimate the value of her investment in 2018 by finding the slope of the line and using it to extrapolate the value for 2018.

The slope of the line can be estimated by taking two points from the data and calculating the change in value divided by the change in time. For example, using the data for 2004 and 2009, we get a slope of (457 - 375) / (2009 - 2004) = 82 / 5 = 16.4. This means that the value of Ashleigh’s investment is increasing by approximately $16.4 per year.

Using this slope and the data for 2009, we can estimate the value of her investment in 2018 as follows: 457 + (16.4 * (2018 - 2009)) = 457 + (16.4 * 9) = 457 + 147.6 = $604.6. Therefore, I estimate that the value of Ashleigh’s investment in 2018 is approximately $604.6.

Please note that this is only an estimate and may not be accurate.

Answer:

a = -6

Step-by-step explanation:

[tex]64^{-a} =16^{-2a-3} \\4^{3(-a)} = 4^{2(-2a-3)} \\4^{-3a} = 4^{-4a-6} \\-3a = -4a-6\\3a=4a+6\\Hence, a=-6.[/tex]

If triangle ABC is rotated 180 degrees, reflected over the y-axis, and reflected over the x-axis, point A' would lie at: D. (−5, 4).

In Mathematics and Geometry, the rotation of a point 180 degrees about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure 180 degrees about the origin is given by this mathematical expression:

(x, y)                       →            (-x, -y)

Point A (-5, 4)        →     Point A = (5, -4)

Next, we would apply a reflection over the y-axis to the new coordinate A as follows:

(x, y)                       →            (-x, y)

Point A (5, -4)        →     Point A = (-5, -4)

Lastly, we would apply a reflection over the x-axis to the new coordinate A as follows:

(x, y)                       →            (x, -y)

Point A (-5, -4)        →     Point A' = (-5, 4)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The Fourier series representation of X(t) is:

X(t) = -1 for 0 ≤ t ≤ T/2

= 1 for T/2 < t < T

To solve the Fourier series equation for the given periodic function X(t), we can follow these steps:

Step 1: Determine the fundamental frequency (ω0) and period (T) of the function X(t).

The period of X(t) is given as T.

The fundamental frequency (ω0) can be calculated as ω0 = 2π / T.

Step 2: Express X(t) as a Fourier series using complex exponential form.

The Fourier series representation of X(t) can be written as:

X(t) = A0 + Σ[Ak × cos(kω0t) + Bk × sin(kω0t)]

Since X(t) is an even function, all the sine terms will be zero. So, the series simplifies to:

X(t) = A0 + Σ[Ak × cos(kω0t)]

Step 3: Calculate the Fourier coefficients (Ak) for k = 0, 1, 2, ...

The Fourier coefficients can be calculated using the following formulas:

A0 = (1/T) × ∫[X(t)]dt

Ak = (2/T) × ∫[X(t) × cos(kω0t)]dt, for k > 0

Step 4: Calculate the Fourier coefficients A0 and Ak for the given function X(t).

Since X(t) is a piecewise function, we need to evaluate the integrals separately for each interval.

For 0 ≤ t ≤ T/2:

A0 = (1/T) × ∫[-2]dt = (1/T) × [-2t] (integrating from 0 to T/2)

= -2/T × (T/2 - 0) = -1

Ak = (2/T) × ∫[-2 × cos(kω0t)]dt = (2/T) × [-2/kω0 × sin(kω0t)] (integrating from 0 to T/2)

= -4/(kπ) × [sin(kπ) - sin(0)]

= -4/(kπ) × [0 - 0]

= 0

For T/2 < t < T:

A0 = (1/T) × ∫[2]dt = (1/T) × [2t] (integrating from T/2 to T)

= 2/T × (T - T/2) = 1

Ak = (2/T) × ∫[2 × cos(kω0t)]dt = (2/T) × [2/kω0 × sin(kω0t)] (integrating from T/2 to T)

= 4/(kπ) × [sin(kπ) - sin(kπ/2)]

= 4/(kπ) × [0 - (-1)^k]

= (-1)^(k+1) × (4/(kπ))

Step 5: Write the final Fourier series representation of X(t) using the calculated coefficients.

Since Ak = 0 for all k, except when k = 0, the series simplifies to:

X(t) = A0

= -1 for 0 ≤ t ≤ T/2

= 1 for T/2 < t < T

Therefore, the Fourier series representation of X(t) is:

X(t) = -1 for 0 ≤ t ≤ T/2

= 1 for T/2 < t < T

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The correct statement regarding the quadratic function f(x) = (x - 4)(x + 1) is given by:

It is increasing for x < -1 and x > 4.

We have,

Considering a concave up quadratic function, with positive leading coefficient, we have that:

It is increasing to the left of the lower root and to the right of the upper root.

It is decreasing between the roots.

In this problem, the function is given by:

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

The roots are:

x - 4 = 0 -> x = 4.

x + 1 = 0 -> x = -1.

Hence the correct statement is:

It is increasing for x < -1 and x > 4.

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question:

The graph of the function f(x) = (x – 4)(x + 1) is shown below. Which statement about the function is true?

As a forecaster in the northeast, based on the storm's path over the last 48 hours, I would inform the Northeast coast audience of the potential trajectory and impact of the storm. I would likely use inductive reasoning in this scenario.

Inductive reasoning involves drawing general conclusions based on specific observations or patterns. By analyzing the storm's previous path and observing the direction and speed of its movement, I can make a reasonable prediction about its future path and likely impact on the Northeast coast.

b. Write an if-then statement to describe your conjecture.

If the storm has followed a consistent eastward trajectory over the last 48 hours, then it is likely to continue moving in that general direction and potentially affect the Northeast coast in the coming hours or days.

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Answer:

x=10.5

Step-by-step explanation:

Pythagorean Theorem:

x²+17²=20²

x²+289=400

x²=400-289

x²=111

x=√111

x=10.5356

The answers are a) 1730.485 cm³, b) 1157.33 cm³ and c) 201%

To solve this problem, we need to calculate the volumes of the cylinder and the three balls.

Let's break it down step by step.

a. Volume of the cylinder:

The cylinder's volume can be calculated using the formula V = πr²h, where r is the radius and h is the height.

Since the balls just touch the top, bottom, and sides of the cylinder, we can consider the height of the cylinder to be equal to the diameter of the balls, which is 13 cm.

The radius of each ball is half of the diameter, so the radius of each ball is 13 cm / 2 = 6.5 cm.

Substituting the values into the formula, we get:

V_cylinder = π × (6.5 cm)² × 13 cm

≈ 3.14 × 42.25 cm² × 13 cm

≈ 1730.485 cm³

Rounded to the nearest cubed centimeter, the volume of the cylinder is approximately 1730 cm³.

b. Volume of three balls:

The volume of a sphere can be calculated using the formula

V = (4/3) × πr³.

Since the diameter of each ball is 13 cm, the radius of each ball is 13 cm / 2 = 6.5 cm.

Substituting the values into the formula, we get:

V_ball = (4/3) × π × (6.5 cm)³

≈ 4/3 × 3.14 × 274.625 cm³

≈ 1157.33 cm³

The volume of each ball is approximately 1157 cm³.

Since there are three balls, the total volume of the three balls is:

V_total_balls = 3 × V_ball

≈ 3 × 1157 cm³

≈ 3471 cm³

Rounded to the nearest cubed centimeter, the total volume of the three balls is approximately 3471 cm³.

c. Percentage of the volume occupied by the three balls:

The percentage can be calculated using the formula:

Percentage = (V_total_balls / V_cylinder) × 100

Substituting the values, we get:

Percentage = (3471 / 1730) × 100

≈ 200.69%

Rounded to the nearest whole percent, the three balls occupy approximately 201% of the volume of the container.

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The correct question =

Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.

a. What is the volume of the cylinder rounded to the nearest cubed centimeter?

b. What is the total volume of the three balls rounded to the nearest cubed centimeter ?

c. What percent of the volume of the container is occupied by the three balls?

Personification is indeed a strategy that can be used to connect mathematical ideas, particularly for Grade 4 learners.

By attributing human qualities or characteristics to mathematical concepts or objects, students can develop a deeper understanding and create meaningful connections.

In Figure 1, we can personify geometric shapes to enhance students' understanding. For instance, the triangular patterns in Ndebele beadwork can be represented as "Triangular Tina" or "Triangle Tom." By giving the geometric shape a human name and personality, students can relate to it more easily.

Ndebele beadwork patterns often exhibit symmetry and repetition. To illustrate personification, we can introduce the concept of "Symmetrical Sarah" or "Patterned Paul." Students can examine the patterns in Figure 1 and discuss how these patterns can be personified.

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Here, since all the given distances are in yards, you can use 1 yard as 1 unit on the number line. The number line will need to be long enough to include -4.1, -3.5, and 3.5.

Zero on this number line represents the level of the boat. All positive numbers represent points above the boat and all negative numbers represent points below the boat.

The absolute value of a number is its distance from zero on the number line. In this case:

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Being respected is generally considered better than being forced.

We have,

Whether it is better to be forced or respected depends on the context and the specific situation.

In general, being respected is considered more favorable and desirable than being forced.

Respect is earned through positive qualities such as integrity, competence, empathy, and treating others with dignity.

When people respect you, they value your opinions, trust your judgment, and are more likely to cooperate and work together effectively.

On the other hand, being forced implies the use of power, authority, or coercion to make others comply with your demands or actions.

It often leads to negative feelings, and resistance, and can damage relationships.

While there may be situations where force is necessary to maintain order or safety, it is generally preferred to find solutions that are based on mutual understanding, consent, and respect.

Ultimately, fostering an environment of mutual respect and collaboration tends to lead to healthier and more positive outcomes in personal relationships, work settings, and society as a whole.

Thus,

Being respected is generally considered better than being forced.

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Changing the value of 'a' changes the shape, position, and concavity of the graph of the function.

We have,

In mathematics, a function is a rule that assigns to each element in a set (called the domain) a unique element in another set (called the range or codomain).

Stretching or compressing the graph: If 'a' is greater than 1, the graph of the function will be stretched vertically, making it thinner and taller. If 'a' is between 0 and 1, the graph will be compressed vertically, making it wider and shorter. If 'a' is negative, the graph will be upside down.

Shifting the graph: If 'a' is positive, the graph will be shifted up or down depending on the value of 'a'. If 'a' is negative, the graph will be shifted down or up.

Changing the concavity of the graph: The graph of the parent function G(x) is an upward-facing parabola, which means it has a positive concavity. If 'a' is positive, the graph of the function will also have a positive concavity. If 'a' is negative, the graph of the function will have a negative concavity, which means it will be a downward-facing parabola.

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Sequence 1,2,4,8,16 represents the ordered pairs that are plotted in the coordinate plane.

To determine the table that represents the ordered pairs plotted in the coordinate plane, we need to analyze the patterns in the sequences given.

Looking at the first sequence in each option:

The sequence is a geometric sequence with a common ratio of 2 (1, 2, 4, 8, 16).

The sequence does not follow a clear pattern (1, 3, 6, 9, 18).

The sequence is a geometric sequence with a common ratio of 2 (1, 2, 4, 8, 16).

The sequence does not follow a clear pattern (1, 3, 6, 9, 18).

Now, let's examine the second sequence in each remaining option:

The second sequence is an arithmetic sequence with a common difference of 4 (4, 8, 12, 16, 20).

Since only option C provides a pattern for the second sequence and matches the geometric pattern for the first sequence, we can conclude that option C represents the ordered pairs plotted in the coordinate plane.

Hence, sequence 1 1,2,4,8,16 sequence 2 4,8,12,16,20  represents the ordered pairs that are plotted in the coordinate plane.

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The domain of the function represented by the graph is,

x ≥ - 5

The graph of function is shown.

By the definition of the domain, the domain of a function is the set of all possible inputs or values for which the function is defined.

Therefore, the value of the domain of the function represented by the graph is determined by considering the set of all inputs or values that correspond to the points on the graph.

So, The value of domain of the function represented by the graph is,

x ≥ - 5

Thus, the domain of the function represented by the graph is,

x ≥ - 5

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Let (x₁,y₁) denote the given point, and m denote the given slope.

y - y₁ = m(x - x₁)

y - 2 = 6(x + 9)

y = 6x + 4

Answer:

Point-slope form: y - 2= 6(x + 9)

Slope-intercept form: y = 6x + 56

Use the formula:

point slope form formula