A box contains 16 square chips, 12 triangular chips, and 4 circular chips. Identify the ratio of circular chips to square chips in all three forms.

The area of a segment of a circle is (12π-9√3) square inches.

We have to determine the area of a segment of a circle.

The formula for the area of the sector that:

Arc length = πr² (θ/360)

Where r = the radius of the circle,

θ = the angle (in degrees) subtended by an arc at the center of the circle.

As per the shown figure, it is given that:

Central angle θ = 120°

The radius of a circle r = 6 in.

The area of the sector A₁ = π(6)² (120/360)

The area of the sector A₁  = 12π in²

The area of the triangle within the sector:

A₂ = 1/2 × (6√3)(3) = 9√3 in²

Now, the area of the segment is:

A₁ - A₂ = (12π - 9√3) in²

Therefore, the area of a segment of a circle is (12π-9√3) square inches.

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Answer:

\(x^2 + 10x + 25\)

Step-by-step explanation:

Hello!

Formula: \((a +b)^2 = a^2 + 2ab + b^2\)

Plug it into the formula and simplify.

The answer is the first option: \(x^2 + 10x + 25\).

Answer:

x^2-10x+25

Step-by-step explanation:

This is the correct answer

Using a calculator, we find the quadratic regression equation, and find that the height at 5.1 seconds is of 879.57 feet.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are given as follows:

(0.4, 64), (0.8, 122), (1.2, 175), (1.6, 223), (2.3, 301).

Inserting these points into a calculator, the equation is:

y = 3.47231343x² + 157.1327045x - 12.12067446.

The height at 5.1 seconds is of:

y = 3.47231343(5.1)² + 157.1327045(5.1) - 12.12067446.

y = 879.57.

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Answer:

4y - 5x + 7 = 0

Step-by-step explanation:

To get to the equation of its perpendicular, firstly we'll need the slope of this line.

\( \boxed{ \mathfrak{slope = \red{ \mathsf{ \frac{y_{2} - y _{1}}{x_{2} - x _{1}} }}}}\)

(x1, y1) and (x2, y2) are any two points kn the given line.

I caught two points that lie on this graph, and they are :

\( \mathsf{ \implies \: slope = \frac{y_{2} - y _{1}}{x_{2} - x _{1}} }\)

\(\mathsf{ \implies \: slope = \frac{ - 6- 2}{8 - ( - 2)} }\)

\(\mathsf{ \implies \: slope = \frac{ -8}{8 + 2} }\)

(two minus make a plus)

\(\mathsf{ \implies \: slope = \frac{ -8}{10} }\)

\(\mathsf{ \implies \: slope = \frac{ \cancel{-8} {}^{ \: \: - 4} }{ \cancel{10} \: \: {}^{5} } }\)

slope = -4 /5

That's the slope of the given line.

Now, the slope of the line perpendicular to this one will be equal to its negative reciprocal.

slope (perpendicular) = 5/ 4

and they've given a point that lies in the perpendicular, it is = (3, 2)

For equation of a line thru a point, we have:

\( \boxed{ \mathsf{ \red {y} - {y}^{1} = slope \times (\red{x} - {x}^{1} }) }\)

the letters in red are the variables that won't be changed thruout.

and (x¹, y¹) are the points on the line.

\( \implies \mathsf{y - 2 = \frac{5}{4} \times (x - 3) }\)

\( \implies \mathsf{(y - 2)4 = 5x - 15}\)

\( \implies \mathsf{4y - 8 = 5x - 15}\)

\( \implies \mathsf{(4y - 5x) - 8 + 15 = 0}\)

\( \implies \mathsf{4y - 5x + 7 = 0}\)

and thats the required equation of the perpendicular.

The equations that have the same solution are:

2.3p – 10.1 = 6.49p – 4

230p – 1010 = 650p – 400 – p

23p – 101 = 65p – 40 – p

Options B, C, and D are the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

2.3p - 10.1 = 6.5p - 4 - 0.01p

2.3p - 6.5p + 0.01p = 10.1 - 4

2.31p - 6.5p = 6.1

-4.19p = 6.1

p = -6.1/4.19

p = -1.5

Now,

Solve for p.

2.3p – 10.1 = 6.4p – 4

2.3p - 6.4p = 10.1 - 4

-4.1p - 6.4

p = -6.4/4.1

p = -1.6

2.3p – 10.1 = 6.49p – 4

2.3p - 6.49p = 10.1 - 4

-4.19p = 6.1

p = -1.5

230p – 1010 = 650p – 400 – p

230p - 649p = 1010 - 400

-419p = 610

p = -1.5

23p – 101 = 65p – 40 – p

23p - 64p = 101 - 40

-41p = 61

p = -1.5

2.3p – 14.1 = 6.4p – 4

2.3p - 6.4p = 14.1 - 4

-4.1p = 10.1

p = 2.5

Thus,

Equations that have the same solution

2.3p – 10.1 = 6.49p – 4

230p – 1010 = 650p – 400 – p

23p – 101 = 65p – 40 – p

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Step-by-step explanation:

Let

c = 11.5 cm

a = 8.9 cm

b = ?

Since this is a right triangle, we can use Pythagorean theorem to find the length of side b:

\(c^2 = a^2 + b^2\)

\(\Rightarrow b^2 = c^2 - a^2\)

Taking the square root of the equation above, we get

\(b = \sqrt{c^2 - a^2} = \sqrt{(11.5\:\text{cm})^2 - (8.9\:\text{cm})^2}\)

\(\:\:\:\:=7.3\:\text{cm}\)

Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.

To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.

First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.

Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.

To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).

(1/3) * 69 ≈ 23

Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.

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The area of the Shaded region, when the frame is 1 unit wide, is 20 square units.

The area of the shaded region when one rectangle is framed within another and the frame has a width of 1 unit, we need to calculate the difference between the areas of the outer rectangle and the inner rectangle.

the dimensions of the outer rectangle as length and width, and the dimensions of the inner rectangle as length' and width'. Based on the information provided, the length and width of the outer rectangle are 5 and 7 units, respectively.

The dimensions of the inner rectangle can be found by subtracting twice the width of the frame (1 unit) from the dimensions of the outer rectangle:

Length' = length - 2 * frame width = 5 - 2 * 1 = 3 units

Width' = width - 2 * frame width = 7 - 2 * 1 = 5 units

Now we can calculate the areas of the outer and inner rectangles:

Area of the outer rectangle = length * width = 5 * 7 = 35 square units

Area of the inner rectangle = length' * width' = 3 * 5 = 15 square units

Finally, to find the area of the shaded region, we subtract the area of the inner rectangle from the area of the outer rectangle:

Area of shaded region = Area of outer rectangle - Area of inner rectangle = 35 - 15 = 20 square units

Therefore, the area of the shaded region, when the frame is 1 unit wide, is 20 square units.

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Answer:

Concrete Operational Stage or Perceptive thinking

The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

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An equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is \(7x > -22.\)

To find an equivalent inequality, we can start by simplifying the given inequality and then make adjustments to preserve its truth.

Let's simplify the given inequality step by step:

\(-4(x + 7) < 3(x - 2)\)

Expanding both sides:

\(-4x - 28 < 3x - 6\)

Grouping like terms:

\(-4x - 3x < -6 + 28\)

Simplifying:

\(-7x < 22\)

To maintain the direction of the inequality, we need to multiply both sides by -1.

However, when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality is reversed.

Therefore, we need to flip the inequality sign:

\(7x > -22\)

Hence, an equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is

\(7x > -22.\)

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Answer:

X=90

Step-by-step explanation:

The shape is a square and it has right angles which makes x=90

Answer:

90

Step-by-step explanation:

That middle part has to equal 360. Because its a square, we know that each on of those have to be 90

Answer: D

Step-by-step explanation: Cuz i just know

Answer:

165 minutes

Step-by-step explanation:

To solve for the number of minutes that Joaquin played for, we can use this expression:

(let 'a' represent how much time passed from the time Joaquin started playing basketball until the time he arrived at home)

Subtracting 1:10 from each side:

1:10 - 1:10 cancels out to 0, while 3:35 - 1:10 is equal to 2:25.

So, the expression is now:

So, 2 hours and 25 minutes passed.

If we know that 1 hour is equivalent to 60 minutes, we can use this expression to solve for however many minutes are in 2 hours:

Now we need to add on the number of minutes and the time it took him to get home:

Therefore, 165 minutes passed from the time Joaquin started playing basketball until the time he arrived at home.

Answer:

9 m²

Step-by-step explanation:

The perimeter of a square is 4x, where is the length of one side (because all the sides have the same length).

This means that 4x = 12, so x = 3, in other words the length of one side of the square is 3 m.

To work out the area of the square, multiply the length and the width together: 3 x 3 = 9 m²

Hope this helps!

Answer:

It's 366. 53*7=371 | 371-5 because the 0th term is -5

Three different expressions that simplify to x^6​ are

x¹²/x⁶

x¹⁸/x¹²

x¹. x¹⁰/x⁵

Index forms are defined as mathematical expressions used to write numbers too small or large in more convenient forms.

Other names for index forms are standard forms and scientific notations.

Note some rules of indices, they are;

Then, we have;

x¹²/x⁶

x¹⁸/x¹²

x¹. x¹⁰/x⁵

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Answer:

no ablo en inglés por q no soy loca

Answer:

Step-by-step explanation:

We need to find the value (f-g)(2), so we need first to substitute 2 into the given functions f(x) and g(x) and then subtract the result of g(2) from f(2).

Here, f(x) = 3x^2 + 1 and g(x) = 1 - x,

So, We will substitute 2 into these functions:

f(2) = 3(2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13

g(2) = 1 - 2 = -1

Now, we can subtract g(2) from f(2):

(f-g)(2) = f(2) - g(2) = 13 - (-1) = 13 + 1 = 14

Hence, the required value of (f-g)(2) is 14.

Answer:

The correct answer is 3. To solve for g(-2), we substitute -2 for x in the equation g(x) = 2x + 5. This gives us g(-2) = 2(-2) + 5, which simplifies to -4 + 5 = 1. Next, we substitute the value of g(-2) into the equation for f(g(x)) = 4 - x^2. Thus, f(g(-2)) = 4 - (1)^2, which equals 4 - 1 = 3.

The distance between point C  (-3, 3) and point D (0, -4) is equal to: √58 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(0 + 3)² + (-4 - 3)²]

Distance = √[(3)² + (-7)²]

Distance = √[9 + 49]

Distance = √58 units.

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The vertex of the graph is a maximum at (-2, 4)

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

The graph

The graph is a quadratic function

From the graph, we can see that the graph has a maximum value

This maximum value represents the vertex of the graph

And it is located at (-2, 4)

So, we have

Maximum = (-2, 4)

Hence, the maximum value of the function is (-2, 4)

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Step-by-step explanation:

\(\sf{ 2 |{\underline{84,102,100}}}\)

\(\sf{ 2|{\underline{42,51,50}}}\)

\(\sf {3|{\underline{21,17,25}}}\)

\(\sf {5|{\underline{7,17,25}}}\)

\(\sf {\:\:{7,17,5}}\)

Answer: The probability would be zero

Step-by-step explanation:

There are two children and one is a boy, so the probability of both being girls is a zero

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.

3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.

4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.

5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.

6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.

Answer:

\(\displaystyle \frac{4q^2-q+3}{q^2+6q+5}-\frac{3q^2-q-6}{q^2+6q+5}=\frac{q^2+9}{q^2+6q+5}\)

Step-by-step explanation:

Simplifying Rational Expressions

If two or more rational expressions have the same denominator, the add and subtract operations are done only with the numerator. The final denominator will be the common of both.

The expression is:

\(\displaystyle \frac{4q^2-q+3}{q^2+6q+5}-\frac{3q^2-q-6}{q^2+6q+5}\)

Operating on the numerators:

\(\displaystyle \frac{4q^2-q+3}{q^2+6q+5}-\frac{3q^2-q-6}{q^2+6q+5}=\frac{4q^2-q+3-(3q^2-q-6)}{q^2+6q+5}\)

Removing parentheses:

\(\displaystyle \frac{4q^2-q+3}{q^2+6q+5}-\frac{3q^2-q-6}{q^2+6q+5}=\frac{4q^2-q+3-3q^2+q+6}{q^2+6q+5}\)

Simplifying:

\(\boxed{\displaystyle \frac{4q^2-q+3}{q^2+6q+5}-\frac{3q^2-q-6}{q^2+6q+5}=\frac{q^2+9}{q^2+6q+5}}\)

The expression cannot be further simplified.

Answer:

0.002

Step-by-step explanation:

the digit "2" in this equation represents 0.02 or also 2/100

1/10 of 2/100 would be like multiplying 1/10 and 2/100 and that would get us 2/1000

2/1000 is also 0.002

0.002 is the value of the digit 2 in the number 1,947.5286​.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here we have,

the number 1,947.5286​.

the digit "2" in this equation represents 0.02 or also 2/100

1/10 of 2/100 would be like multiplying 1/10 and 2/100

and that would get us 2/1000

i.e.

2/1000 is also 0.002

Hence, 0.002 is the value of the digit 2 in the number 1,947.5286​.

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Answer:

is there a pic?

Step-by-step explanation:

The function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The coordinate points from the graph are (10, 550) and (30, 200).

Here, slope = (200-550)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 550) in y=mx+c, we get

550=-17.5(10)+c

c=550+175

c=725

So, the equation is y= -17.5x+725

Thus, f(n)= -17.5n+725

a) The fine at every speed should go up by $10.

So, the coordinates are (10, 560) and (30, 210)

New slope (m)= (210-560)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 560) in y=mx+c, we get

560=-17.5(10)+c

c=550+175

c=735

So, the equation is y= -17.5x+735

Thus, f(n)= -17.5n+735

b) The fine at every speed should be doubled in construction zones.

So, the coordinates are (20, 550) and (60, 200)

New slope (m)= (200-550)(60-20)

= -350/40

= -8.75

Substitute m= -8.75 and (x, y)=(20, 550) in y=mx+c, we get

550=-8.75(10)+c

c=550+87.5

c=637.5

So, the equation is y= -8.75x+637.5

Thus, f(n)= -8.75n+637.5

Therefore, the function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

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