On Saturday, The Toy Box offered customers a free gift with each puzzle they bought. The store sold 29 puzzles for $17 each. In all, they paid $319 for the puzzles and $60.76 for the free gifts. How much profit did The Toy Box make?
$

Answer:

120 seconds

Step-by-step explanation:

1) The time it takes for each light to complete its cycle is 6 seconds, 8 seconds, and 10 seconds respectively. The three lights will all be off at the same time when they are all at the beginning of their cycles at the same time. The smallest number that is divisible by 6, 8, and 10 is 120. Therefore, all three lights will be off at the same time after 120 seconds.

2) The next time all three lights come on together at the same moment will be when they are all at the beginning of their cycles at the same time. The smallest number that is divisible by 3, 4, and 5 is 60. Therefore, all three lights will come on together at the same moment after 60 seconds.

The number of possible elections of the officers having at least 1 of the past officers is 4242, using combinations.

The combination is the process of counting the number of ways of selecting a smaller set from a larger set, where the order of selection is invariable.

If we select r articles from n articles with the order of selection invariable, we use the combination to find the number of ways of selecting as:

nCr = n!/{ r!(n - r)! }.

If we select 5 officers from 16 officers, the total possible outcomes, using combinations are 16C5 = 16!/{ 5!(16 - 5)! } = 16!/{5! * 11!} = 4368.

We are asked of all possible elections of the officers, how many will have at least 1 of the officers.

We calculate the number of possible election officers, where we have 0 past officers, using combinations = 7C0 * 9C5 = 7!/{ 0!(7 - 0)! } * 9!/{ 5!(9 - 5)! } = 1 * 126 = 126.

Thus, the number of possible election officers, where we have at least 1 past officers = 4368 - 126 = 4242.

Thus, the number of possible elections of the officers having at least 1 of the past officers is 4242, using combinations.

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Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,

and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.

They need to think about how their technology could be used, and whether it could be used to harm people or the environment.

They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,

and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.

If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.

It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.

For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.

In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.

This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.

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Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.

If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:

Volume (V) = length × breadth × height

where;

the base = length × breadth = 16ft²

∴ the volume of the rectangular bathtub = 16h ---  (1)

Using differentiation to differentiate 16h with respect to t implicitly, then:

dV/ dT = 16 dH /dT

When the rate of rising of the volume is 0.5 ft³/min

Then:

0.5 = 16 dH /dT

dH /dT = 1 / 16 * 0.5

dH /dT = 0.3125.

Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.

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Answer: 96

Step-by-step explanation:

8 boxes of crackers

They cost 9$

8•9 is 72

4 bags of cookies

They cost

4•6 is 24

72+24 is 96

"The speed of a randomly selected car on a highway" and "the percent change in the price of a share of IBM stock in a month" are examples of continuous random variables. Options A and C are the correct answers.

Continuous random variables are those that can take on any value within a given range, as opposed to discrete random variables, which can only take on certain values.The speed of a randomly selected car on a highway and the percent change in the price of a share of IBM stock in a month are examples of continuous random variables.

These variables have a range of values and can take on any value within that range.The number of claims on a medical insurance policy on a given year, the number of customers that enter a particular store on a randomly selected day, and the time that elapses between two customer service calls are examples of discrete random variables. These variables can only take on certain values, such as whole numbers or specific times.

Thus option A and option C are the correct answers.

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The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m

where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925

And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075

Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.

This is option D.

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Answer:

The third picture

Step-by-step explanation:

Solve for x in both equations

2x<6

Divide both sides by 2:

x<3

3x+2>-4

Subtract 2 from both sides:

3x>-6

Divide both sides by 3:

x>-2

There is this trick you can use when x is on the left side of the equation to find out which way to shade in you graph. Keep in mind this is only for the left side, it will not work if your variable is on the right.

When the symbol is facing left < then shade left, imagine it is pointing which way to shade. x<3 is represented by the 3 picture on the left. When the symbol is facing right > then shade right, again it is pointing which way to shade. x>-2 is represented by the 3 picture on the right.

The circles are not filled in because the symbol is < and > rather than \(\leq and \geq\). When it is greater than or equal to or less than and equal to (represented by the line under the symbol), then the circle is shaded in.

The answer is x = 4

Step 1: Simplify both sides of the equation.

3 /2 (x−6)=−3

( 3 /2 )(x)+( 3 /2 )(−6)=−3(Distribute)

3 /2 x+−9=−3

3 /2 x−9=−3

Step 2: Add 9 to both sides.

3 /2 x−9+9=−3+9

3 /2 x=6

Step 3: Multiply both sides by 2/3.

( 2 /3 )*( 3 /2 x)=( 2 /3 )*(6)

x=4

Answer:

x=4

The remaining time of the trip is 3 5/6 hours.

If a trip from Boston to Washington takes 5 3/4 hours and you have traveled 1/3 of the way, the remaining time of the trip can be calculated by subtracting the time traveled from the total time of the trip.

First, we need to convert 5 3/4 hours to a fraction:
5 3/4 = (5 * 4 + 3)/4 = 23/4
Next, we need to calculate the time traveled so far:
23/4 * 1/3 = 23/12
Now we can subtract the time traveled from the total time of the trip:
23/4 - 23/12 = (23 * 3 - 23 * 1)/12 = 46/12 = 3 10/12 = 3 5/6
Therefore, the remaining time of the trip is 3 5/6 hours.
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Answer: 1/2

Step-by-step explanation: As the denominators (bottom numbers) of the fraction are the same, you don't need to change them. Therefore, you subtract the numerators (top numbers) so 7-3= 4/8 which you then divide by 2 on both sides leaving you with 1/2. You can't divide this answer anymore so your final result is 1/2.

The velocity, acceleration, and speed of the particle are:

velocity vector: v(t) = (-9 sin t) i + (8) j + (9 cos t) k

acceleration vector: a(t) = (-9 cos t) i + 0 j + (-9 sin t) k

speed: |v(t)| = sqrt((-9 sin t)^2 + (8)^2 + (9 cos t)^2)

To find the velocity, acceleration, and speed of the particle with the given position function, we need to differentiate the position function with respect to time.

r(t) = (9 cos t) i + (8t) j + (9 sin t) k

The velocity vector is the first derivative of the position vector with respect to time:

v(t) = r'(t) = (-9 sin t) i + (8) j + (9 cos t) k

The speed is the magnitude of the velocity vector:

|v(t)| = sqrt((-9 sin t)^2 + (8)^2 + (9 cos t)^2)

The acceleration vector is the second derivative of the position vector with respect to time:

a(t) = r''(t) = (-9 cos t) i + 0 j + (-9 sin t) k

Therefore, the velocity, acceleration, and speed of the particle are:

velocity vector: v(t) = (-9 sin t) i + (8) j + (9 cos t) k

acceleration vector: a(t) = (-9 cos t) i + 0 j + (-9 sin t) k

speed: |v(t)| = sqrt((-9 sin t)^2 + (8)^2 + (9 cos t)^2)

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Answer: Greater than 10.

Answer:

mark score is minus 14

7multiply minus 2

Answer:

14

Step-by-step explanation:

To calculate the present value of $51,270 payments to be made at the end of each period for 17 periods at a 9% interest rate, we need to find the discounted value of each payment and sum them up.

The present value (PV) is calculated by discounting each future payment back to its current value using the interest rate. The formula to calculate the present value of a series of payments is:

PV = Payment × [1 - (1 + interest rate)^(-number of periods)] / interest rate.

In this case, the payment is $51,270, the interest rate is 9% (or 0.09 as a decimal), and the number of periods is 17.

Using the provided formula and rounding the factor values to 5 decimal places, we can calculate the present value as follows:

PV = $51,270 × [1 - (1 + 0.09)^(-17)] / 0.09.

Evaluating this expression will give us the present value of the payments. It's important to round the final answer to 0 decimal places, as stated in the question.

By substituting the values and calculating the expression, we can determine the present value of the $51,270 payments made over 17 periods at a 9% interest rate.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

D) 29

Step-by-step explanation:

Step 1 solve for x

Complementary angles add up to 90 degrees.

This means that ∠A + ∠B = 90

If ∠A = 2x + 7 and ∠B = 6x - 5

Then 2x + 7 + 6x - 5 = 90

We now solve for x

2x + 7 + 6x - 5 = 90

==> combine like terms

8x + 2 = 90

==> subtract 2 from both sides

8x = 88

==> divide both sides by 8

x = 11

Step 2 , plug in x to find ∠A

Now to find ∠A we plug in the value of x into 2x + 7

∠A = 2x + 7

==> plug in x = 11

∠A = 2(11) + 7

==> multiply 2 and 11

∠A = 22 + 7

==> add 22 and 7

∠A = 29

The firm should produce 50 units in order to maximize profit by solving quadratic equations.

To determine the number of units, x, the firm should produce in order to maximize profit, we can start by finding the profit function. Profit is calculated by subtracting the total cost (C) from the total revenue (R).

Profit = Revenue - Cost

The total cost function is given as C = 700 + 1000x dollars, and the total revenue function is given as \(R = 1100x - x^2\) dollars.

Substitute the given functions into the profit equation:

Profit \(= (1100x - x^2) - (700 + 1000x)\)

\(= 1100x - x^2 - 700 - 1000x\\= -x^2 + 100x - 700\)

To find the maximum profit, we need to find the value of x that maximizes the profit function. This can be achieved by finding the vertex of the quadratic equation \(-x^2 + 100x - 700\).

The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in the form of \(ax^2 + bx + c\).

In this case, a = -1, b = 100, and c = -700.

Plugging these values into the formula, we get:

\(x = -100 / (2 * -1)\\x = 50\)

Therefore, the firm should produce 50 units in order to maximize profit by solving quadratic equations.

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Answer:

12

Step-by-step explanation:

2x - 6 = ?

x = 9

You substitute x for 9: the value of x.

2(9) - 6 = ?

2 * 9 = 18

18 - 6 = 12

So your answer is 12.

Hope it helps : )

Brainliest pleaseeee

Given that the production function of a firm is f(x1, x2) = x1^(1/3) * x2^(2/3), where price of x1 = 1 and price of x2 = 2. Let's derive the conditional demand for x1 and cost function c(y).

Conditional demand for x1 can be derived as:

∂f(x1, x2)/ ∂x1 = (∂/∂x1) (x1^(1/3) * x2^(2/3))= (1/3) * x1^(-2/3) * x2^(2/3)

Now, put the value of x2 = (y/ x1^(1/3))^3 in the above equation.

∂f(x1, x2)/ ∂x1 = (1/3) * x1^(-2/3) * (y/ x1^(1/3))^2 = (1/3) * y^2 * x1^(-4/3)

Since price of x1 = 1, the cost function can be written as c(y) = w1 * x1 + w2 * x2 = x1 + 2x2 = x1 + 4(y/ x1^(1/3))

The cost function of the firm is

c(y) = x1 + 4y^(1/3) * x1^(-1/3) = x1 + 4y^(1/3)/x1^(1/3)

In order to maximize the profit, we need to differentiate the cost function with respect to x1 and equate it to zero.

(c(y))/d(x1) = 1 - 4/3 * y^(1/3) * x1^(-4/3) = 0

x1 = (3/4) * y^(1/3)

On substituting the value of x1 in the cost function, we get:  

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The factor of its radius reduced is 3. The result is obtained by comparing the spherical volumes.

The volume of a spherical can be calculated by

V = 4/3 πr³

Where

A spherical balloon has volume v and radius r. Its volume is reduced by a factor of 27.0.

Find the factor of its radius reduced!

The factor of its volume is

V₁/V₂ = 27

We use the formula for spherical volume to find r₁/r₂.

V₁/V₂ = (4/3 πr₁³)/(4/3 πr₂³)

27 = (r₁/r₂)³

r₁/r₂ = ∛27

r₁/r₂ = 3

Hence, the radius is reduced by a factor of 3.

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Muslim scholars blended mathematical ideas from Greece, India, and Persia in the development of algebra and trigonometry.

There is solid proof of social mixing in how Muslims concentrated on arithmetic during the Islamic Brilliant Age, which endured from the eighth to the fourteenth century CE. During this time, researchers from different pieces of the Muslim world, as well as from Greece, India, and Persia, met up to share information and thoughts.

One illustration of this social mixing should be visible in the improvement of variable based math, which was vigorously affected by crafted by Indian mathematicians. Muslim researchers deciphered and developed Indian texts, integrating new ideas and images into their own numerical practices.

One more model is the improvement of geometry, which was impacted by crafted by Greek mathematicians. Muslim researchers deciphered and developed Greek texts, adding new applications and refinements to the discipline.

Generally, the social mixing of numerical thoughts and customs assumed a huge part in the improvement of Islamic science, and assisted with laying out a rich and various heritage that keeps on impacting the field today.

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The true statement about the function y = 40x is that it is a linear function

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

y = 40x

The given function is y = 40x, which represents the total number of dollars Mark earns depending on the number of lawns he mows.

Here are some properties of the function:

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To find the value of the expression we have to used crossed multiplication, then:

A segment that connects the vertex of a triangle with the opposite side so it makes a 90-degree angle is called Altitude.

In geometry, Altitude is used to describe the height of a polygon, triangle, or other two-dimensional shapes. The altitude of a figure is a line segment perpendicular to the base and passes through the vertex of the constitution. It is used to calculate the area of the figure and to determine the lengths of the sides and angles.

In three-dimensional figures, the altitude can also refer to the distance between the highest and lowest points of the constitution. The concept of altitude is widely used in mathematics, particularly in geometry, trigonometry, and related fields.

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Complete Question:

A line that connects the vertex of a triangle with the opposite side so it makes a 90 degree angle_____.

Answer:

\(3^{4}\)

Step-by-step explanation:

\(3^{4}\)

The equivalent expression will be;

⇒ 3⁴

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3 × 3 × 3 × 3

Now,

Since, The expression is,

⇒ 3 × 3 × 3 × 3

Hence, It can be written as;

⇒ 3 × 3 × 3 × 3 = 3 ⁴

Thus, The equivalent expression will be;

⇒ 3⁴

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It can be observed that there is a tangent, t, to the graphs of f and g. The tangent line to the graph of f at (a, f(a)) has a slope equal to 2a. Similarly, the tangent line to the graph of g at (b, g(b)) has a slope equal to 2(b - 3).

Let's begin by computing the values of a and b. Since the tangent line to the graph of f at (a, f(a)) has a slope equal to 2a, we know that the equation of the tangent line is y - (a² - 3) = 2a(x - a).Furthermore, since this line passes through the point (3, 0), we can substitute x = 3 and y = 0 into this equation and solve for a:0 - (a² - 3) = 2a(3 - a)Simplifying this equation gives us:a³ - 6a² + 6a + 9 = 0Factoring this equation using the Rational Root Theorem yields:(a - 3)(a² - 3a - 3) = 0The only root in the interval (-∞, 3) is a = 3 - 2√2, since the quadratic factor has no real roots.The slope of the tangent line to the graph of g at (b, g(b)) is equal to 2(b - 3), so the equation of the tangent line is:y - (b² - 6b + 9) = 2(b - 3)(x - b)Since this line passes through the point (3, 0), we can substitute x = 3 and y = 0 into this equation and solve for b:0 - (b² - 6b + 9) = 2(b - 3)(3 - b)Simplifying this equation gives us:b³ - 12b² + 45b - 27 = 0Factoring this equation using the Rational Root Theorem yields:(b - 3)(b² - 9b + 9) = 0The only root in the interval (3, ∞) is b = 3 + 2√2, since the quadratic factor has no real roots.Now that we have computed the values of a and b, we can find the x-coordinate of the point of intersection of the graphs of f and g, which is the solution to the equation:x² - 3 = (x - 3)²Simplifying this equation gives us:x² - 3 = x² - 6x + 9Solving for x yields:x = -2We can now evaluate the areas of the two regions bounded by the graphs of f, g, and t. Using the point-slope form of the equation of the tangent lines, we can write the equations of the tangent lines as:y - (a² - 3) = 2a(x - a)y - (b² - 6b + 9) = 2(b - 3)(x - b)We can solve these equations for x and express the result in terms of y to get the equations of the graphs of the regions. For the region above the tangent lines, we have:x = y/2 + a - a²/2x = y/2 + b - (b² - 6b + 9)/2For the region below the tangent lines, we have:x = -y/2 + a - a²/2x = -y/2 + b - (b² - 6b + 9)/2We can use these equations to find the y-coordinates of the points of intersection of each pair of graphs. For the graphs of f and t, we have:y = x² - 3y = 2x - 6 + a² - 2aSolving for x yields:x = (y - a² + 2a + 3)/2Substituting this expression for x into the equation of the tangent line gives us:y - (a² - 3) = 2a((y - a² + 2a + 3)/2 - a)Simplifying this equation gives us:y = -2ay + a³ - 3a² + 6a + 3For the graphs of g and t, we have:y = (x - 3)²y = 2x - 6 + b² - 6b + 9Solving for x yields:x = (y - b² + 6b - 3)/2Substituting this expression for x into the equation of the tangent line gives us:y - (b² - 6b + 9) = 2(b - 3)((y - b² + 6b - 3)/2 - b).

Simplifying this equation gives us:y = 2by - b³ + 6b² - 9b + 3We can now find the y-coordinates of the points of intersection by solving the system:y = -2ay + a³ - 3a² + 6a + 3y = 2by - b³ + 6b² - 9b + 3Solving this system using a computer algebra system or by hand yields:y ≈ 4.184 or y ≈ -8.307The two regions are symmetric about the line x = -2, so we can compute the area of one region and multiply by two. For y between -8.307 and 4.184, the region above the tangent lines is:x = y/2 + a - a²/2x = y/2 + b - (b² - 6b + 9)/2The region below the tangent lines is given by the same equations with the sign of y reversed. Substituting the values of a and b and integrating gives us the area of one region:∫(-8.307, 4.184) [(y/2 + 3 - 2√2 - (8 - 12√2)/2) - ((y/2 + 3 + 2√2 - (8 + 12√2)/2)] dy = ∫(-8.307, 4.184) [(y/2 - 3√2 - 1) - (y/2 + 3√2 + 1)] dy = (-12.586 - (-15.988)) = 3.402Multiplying by two gives us the total area:6.804 square units.

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The simplification of the given expression 36-(12/2)2 will be 24.

Simplification involves proceeding with the pending operations in the expression. for ex; 6 + 2 is an expression whose simplified form can be obtained by doing the pending addition, that results in 8 as its simplified form. Simplification, involves making the expression simple and easy to use later.

We have been given an expression as;

36-(12/2)2

To simplify the above;

36-(12/2)2

36 - (6)2

Now multiply 6 by 2,

36 - 12

= 24

Therefore, the simplification of the given expression 36-(12/2)2 will be 24.

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Answer:

The answer is 24.

Step-by-step explanation:

(12/2)=6

36-(6)2

=36-12

=24

Answer:

BC = 50

Step-by-step explanation:

BC = AD in a parallelogram

4x-10 = 3x+5

Subtract 3x from each side

4x-3x-10 = 3x-3x+5

x-10 = 5

Add 10 to each side

x-10+10 = 5+10

x = 15

BC = 4x-10 = 4*15-10 = 60-10 = 50

Answer:

BC = 50

Step-by-step explanation:

BC = AD

4x - 10 = 3x + 5

4x - 3x = 5 + 10

x = 15

for BC

4x - 10

4*15 - 10

60 - 10

50

Answer:

Total area of Dartboard = 8×12 = 96

Area of blue squares = 3 × 2² = 12

Probability( hitting blue squares )= 12/96 = 1/8