The equation y = 10x + 15 models the amount of money y, in dollars, that Jack earns shoveling snow for x hours. How many hours does Jack need to work to earn $55?

Answer:

2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.

Step-by-step explanation:

To divide 2 1/4 by 1 1/2, we first need to convert both mixed numbers to improper fractions:

2 1/4 = (2 × 4 + 1) / 4 = 9 / 4

1 1/2 = (1 × 2 + 1) / 2 = 3 / 2

Now we can divide by multiplying by the reciprocal of the second fraction:

(9/4) / (3/2) = (9/4) * (2/3)

We can simplify this multiplication by canceling the common factor of 3 in the numerator of the second fraction and the denominator of the first fraction:

(9/4) * (2/3) = (33/4) * (2/13) = 9/2

So 2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.

[tex]\boxed{\sf \dfrac{3}{2}}.[/tex]

[tex]\sf \dfrac{2\dfrac{1}{4} }{1\frac{1}{2} }[/tex]

[tex]\sf 2\dfrac{1}{4}\Longrightarrow\dfrac{4}{4} +\dfrac{4}{4} +\dfrac{1}{4} =\dfrac{4+4+1}{4} =\dfrac{9}{4}[/tex]

[tex]1\dfrac{1}{2} =\dfrac{2}{2} +\dfrac{1}{2} =\dfrac{2+1}{2} =\dfrac{3}{2}[/tex]

[tex]\sf \dfrac{\dfrac{9}{4} }{\dfrac{3}{2} }[/tex]

• Check the attached image.

[tex]\dfrac{9}{4} *\dfrac{2}{3}[/tex]

[tex]\dfrac{9*2}{4*3} =\dfrac{18}{12} \\ \\\dfrac{18/2}{12/2} =\dfrac{9/3}{6/3}=\boxed{\sf \dfrac{3}{2}} .[/tex]

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The probability of hitting the shaded region is 0.755 or 75.5%.

To find the probability of hitting the shaded region, we need to find the area of the shaded region and divide it by the area of the entire square.

Let's label the side length of the small square as x.

Then, we know that the diagonal of the small square is 7, so we can use the Pythagorean theorem to solve for x:

x^2 + x^2 = 7^2

2x^2 = 49

x^2 = 24.5

So the area of each white square is x^2 = 24.5 square units.

Let's label the side length of the large square as y.

Then, we know that the diagonal of the large square is 20, so we can use the Pythagorean theorem to solve for y:

y^2 + y^2 = 20^2

2y^2 = 400

y^2 = 200

So the area of the large square is y^2 = 200 square units.

Now, we can find the area of the shaded region by subtracting the area of the two white squares from the area of the large square:

Area of shaded region = Area of large square - 2 * Area of white square

= 200 - 2(24.5)

= 151

Therefore, the probability of hitting the shaded region is:

Probability = Area of shaded region / Area of entire square

Probability = 151 / 200

Probability = 0.755 or 75.5% (rounded to one decimal place)

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If a candle having diameter as 9 cm, height as 12 cm is placed in a cylindrical box, then the height of the cylindrical box will be 13cm.

The "cylindrical-candle" diameter is given as = 9 cm;

The "cylindrical-candle" height is given as = 12 cm;

The candle is placed in a box which has a space of 0.5 cm between the candle and the box for packaging material;

which means that, there will an additional 0.5 cm in the top and bottom of the candle,

So, the height of the "cylindrical-box" is written as : 0.5 + 12 + 0.5;

Therefore, the "cylindrical-box" has a height of 13 cm.

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Answer:

(x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25

Step-by-step explanation:

The equation of a circle can be written in the form (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Since the lines are tangent to the circle at points (0,5) and (6,5), we can use these points to find the center and radius of the circle.

First, let’s find the slope of each line. The slope of the line y = 3/4x+5 is 3/4. The slope of the line 3x + 4y = 38 can be found by rearranging it into slope-intercept form: y = (-3/4)x + 19/2. So the slope of this line is -3/4.

Since the lines are tangent to the circle, they are perpendicular to the radius at their point of tangency. This means that the center of the circle lies on the line that passes through (0,5) and has a slope of -4/3, and also on the line that passes through (6,5) and has a slope of 4/3.

Let’s find the equation of these two lines. The line passing through (0,5) with a slope of -4/3 has an equation y - 5 = (-4/3)(x - 0), or y = (-4/3)x + 5. The line passing through (6,5) with a slope of 4/3 has an equation y - 5 = (4/3)(x - 6), or y = (4/3)x - 3.

The center of the circle is at the intersection of these two lines. To find it, we can set their right-hand sides equal to each other and solve for x: (-4/3)x + 5 = (4/3)x - 3. Solving this equation gives us x = 24/5. Substituting this value into either equation for y gives us y = (4/3)(24/5) - 3 = 21/5.

So the center of the circle is at (24/5, 21/5). To find its radius, we can use either point of tangency. Let’s use (0,5). The distance between this point and the center is given by sqrt((0-24/5)^2 + (5-21/5)^2), which simplifies to sqrt(481)/5.

Therefore, the equation of the circle is (x-24/5)^2 + (y-21/5)^2 = (sqrt(481)/5)^2, or (x-24/5)^2 + (y-21/5)^2 = 481/25.

Answer:

19/20--no

32/4--yes (32/4 = 8)

74--yes

23--yes

5.95--no

The correct statement regarding the end behavior of the function is given as follows:

The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.

The function in this problem is given as follows:

f(x) = 2(x - 4)² + 3.

We have the square of a number, which is always positive, hence the function goes to positive infinity when the input goes to negative infinity/positive infinity.

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The table for the function y = f(x) - 5 is

x    f(x) - 5

5   -33

-3    -5

-2     2

0    21

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

x    f(x)

5   -28

-3    0

-2     7

0    26

To create a table for the function y = f(x) - 5, we subtract 5 from the values of f(x)

using the above as a guide, we have the following:

x    f(x) - 5

5   -28 - 5

-3    0 - 5

-2     7 - 5

0    26 - 5

Evaluate

x    f(x) - 5

5   -33

-3    -5

-2     2

0    21

This represents the table for the function y = f(x) - 5

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The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine.

Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time?

The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine with the x-axis labeled time in seconds going from 0 to 28 and the y-axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16.

A scatter plot is a useful way to show the relationship between two variables, in this case, the amount of hot chocolate and time. Each point on the scatter plot represents a pair of values for time and hot chocolate amount. A line graph with line segments connecting each point to the next would not be appropriate because the data is not continuous, and there is no reason to assume that the relationship between time and hot chocolate amount is linear.

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Answer: We can start by simplifying the cube root of 8:

³√8 = 2

Next, we can rewrite 5^-2 as 1/5^2:

1/5^2 x 2 = 1/25 x 2 = 2/25

So the answer, as a decimal, is 0.08 (or 0.08 rounded to two decimal places).

The expression for the number of cookies Anna has left is [tex]3c - 8[/tex].

An expression refers to statement that have minimum of two numbers or variables or both and an operator connecting them.

The total number of cookies Anna baked is:

= 3 batches * c cookies/batch

= 3c cookies

After eating 8 cookies, Anna has left:

= 3c cookies - 8 cookies

So, the expression for the number of cookies Anna has left is [tex]3c - 8[/tex].

Full question "Anna baked 3 batches of cookies with c cookies in each batch she then ate 8 cookies. How many cookies does anna have left write your answer as an expression.

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The equation of the circle is x² + y² - 2x - 10y + 22 = 0

Any locations on a plane that are a certain distance from a fixed point (referred to as the radius) are considered to be parts of a circle, which is a two-dimensional geometric shape (is called the center). Each point on the circle may be found at the same distance from the circle's centre.

The following is the equation for a circle with centre (h,k) and radius r:

r²=(x - h)² + (y - k)²

In this case, the center of the circle is (1,5) and the radius is 2. So, we may change these values in the equation:

(x - 1)² + (y - 5)² = 2²

Simplifying and expanding the equation, we get:

(x - 1)×(x - 1) + (y - 5)(y - 5) = 4

x² - 2x + 1 + y² - 10y + 25 = 4

x² + y² - 2x - 10y + 22 = 0

Therefore, the equation of the circle is:

x² + y² - 2x - 10y + 22 = 0

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Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.

Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).

Here,

When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).

Let x represent the desired shadow's length. Next, we have

=> tan 35° = 15/x

When we multiply both sides by x, we obtain:

=> x tan 35° = 15

By dividing both sides by 35° of tan, we obtain:

=> x = 15 / tan 35°

We may calculate the value of the tangent of 35 degrees using a calculator:

=> tan 35° ≈ 0.7002

Next, we have

=> 15x/0.702x=21.424 metres

Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.

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Answer:

1,3,5,7,9

Step-by-step explanation:

0 can't be, let's take 10 or 20 or 30 for example, not a prime number.

1 can be because let's take 11, 31 as example, they're prime numbers.

2, 4, 6, 8 can't be the answer because they have factors

The rest of off numbers, namely 3,5,7,9 can be. Let's take for example 23, 05, 67, 59

Answer:

A) circle.

When a sphere is cut by a horizontal plane, the resulting cross section is a circle. This is because a sphere is a three-dimensional object that is perfectly symmetrical in all directions, so any plane that intersects it will create a circular cross section.

Answer:

The age of the radioactive element of half-life 5750 years is 11047.8  years.

Radioactive elements are atoms that are unstable in normal conditions and are converted in another different atoms.

To calculate how old is the bone at the time it was discovered, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for t

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part a.

The equation that has the variable in the correct place to match the given situation is: Sunday's mile

part b

the Mansour family drove 210 miles on Sunday.

An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign =..

We have that the equation that has the variable in the correct place to match the given situation is: Sunday's mile

Sunday's miles = Total miles - Friday's miles - Saturday's miles

Sunday's miles = 687 - 313 - 164

Sunday's miles = 210

In conclusion, the Mansour family drove 210 miles on Sunday.

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The given function, f(x) = x⁴ - 2x², is even function.

The nature of the function, whether it is even or odd can be determined by applying the following rules.

Even function, f(x) = f(-x)

Odd function; f(x) = -f(-x)

The given function, f(x) = x⁴ - 2x²

Test of for even function;

f(-x) = (-x)⁴ - 2(-x)²

f(-x) = x⁴ - 2x²

so f(x) = f(-x), the function is even.

Test for odd function;

-f(-x) = - [(-x)⁴ - 2(-x)²]

-f(-x) = -x⁴ + 2x²

so, f(x) ≠ -f(-x), the function is not odd.

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Answer:

C

x1=2

-2(2)+1=3

which is the answer for y1

Answer:

That number is 230 × 1.08 = 248.4.

To find this number, we calculated 8% of 230, which is 18.4 , and then added it to 230, Hence The number that is 8% larger than 230 is 248.4.

To find a number that is 8% larger than 230, we can calculate the 8% increase of 230 and add it to the original number.

Step 1: Calculate the 8% increase of 230:

8% of 230 = (8/100) * 230 = 0.08 * 230 = 18.4

Step 2: Add the 8% increase to 230:

230 + 18.4 = 248.4

Therefore, a number that is 8% larger than 230 is 248.4.

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The given line AB is having endpoints A(-3,5) & B(1,-1).

To find the equation of line AB it can be written as[tex]y-y_1=(x-x_1){(y_2-y_1)/(x_2-x_1)}\\[/tex]

Substituting the given points

[tex]y-(-1)=(x-1){(5-(-1))/(-3-1)}\\[/tex]

y=-(3/2)x+1/2

For two perpendicular lines [tex]m_1*m_2=-1[/tex]

Therefore, (-3/2)*[tex]m_2[/tex]=-1

or [tex]m_2[/tex] = 2/3

Also, the midpoint of AB will be [tex]{1-(-3)}/2, {5-(-1)}/2[/tex] = (2,3).

The line passing through (2,3) & perpendicular to y=-3/2x+1/2 will be given as follows

(y-3)=(2/3)(x-2)

3y-9=2x-4

3y=2x+5 is the required equation of the line.

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The volume of vase A is given as follows:

504 cm³.

The volume of vase A is obtained applying the proportions in the context of the problem.

Vase A has height 10 cm. Vase B has height 15 cm, hence the ratio between the heights is given as follows:

[tex]\frac{h_B}{h_A}[/tex] = 15/10

[tex]\frac{h_B}{h_A}[/tex] = 1.5.

The heights are given in units, while the volumes are given in cubic units, hence the rate between the volumes is given as follows:

[tex]\frac{vB}{vA}[/tex] = 1.5³

[tex]\frac{vB}{vA}[/tex]= 3.375

[tex]v_B = 3.375v_A[/tex].

The difference between the volume of vase A and the volume of vase B is 1197 cm³, hence:

[tex]v_B - v_A = 1197[/tex]

[tex]3.375v_A - v_A = 1197[/tex]

[tex]v_A = 1197/2.375[/tex]

[tex]v_A[/tex] = 504 cm³.

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Answer:

m<H = 62.7°

Step-by-step explanation:

If we use an inverse sin, then that would be sin^-1(8/9) Because Sin equals opposite over adjacent.

Answer:

H = 62.7 degrees

Step-by-step explanation:

Because this is a right triangle, we can use one of the trigonometric functions to find angle H:

Notice that sides HJ and IJ are given. If we are trying to find angle H, then HJ is the hypotenuse (longest side) and IJ is the opposite (side opposite to the angle we are trying to find). Since the opposite and hypotenuse are both given, we can use a sine function to find the angle of H (keep in mind that sin(<) = opp/hyp):

sin(H) = 8/9

We have to use the inverse of sine (sin^-1 or arcsin) to find angle H and use a calculator to solve:

arcsin(8/9) = H = 62.7 degrees

The correct sequence to model the given scenario is (b) f(n) = 1.12f(n-1)(1- f(n-1/6000)), and we can use this formula to calculate the oxygen released by the tree in each year, option (b) is correct.

The amount of oxygen released by the tree increases at a rate of 12% per year, which is represented by the factor 1.12f(n-1).

However, the tree cannot generate more than 6000 pounds of oxygen per year, which is represented by the limiting factor:

(1- f(n-1/6000)).

To understand this better, let's calculate the oxygen released by the tree in the second year using the formula

f(n) = 1.12f(n-1)(1- f(n-1/6000)).

f(2) = 1.12f(1)(1- f(1)/6000)

= 1.12(250)(1- 250/6000)

= 295.67 pounds of oxygen

Hence, option (b) is correct.

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The correct question is:

Which sequence below would best model the following description? A newly planted tree releases 250 pounds of oxygen over the period of its first year. The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year.

a. f(n) = 1.12f(n-1)(1+ f(n-1/6000)

b. f(n) = 1.12f(n-1)(1- f(n-1/6000)

c. f(n) = 1.12f(n-1) {6000/f(n-1)}

d. f(n) = 1.12f(n-1)(f(n-1) -6000)

The largest number of people for whom she can buy tickets, is 4 people.

:: Available money = $6000

:: Cost per person = $1300

So,

No. of maximum tickets = 6000/1300 = 4.6

That is,

Only 4.6 persons can have the tickets, and since, number of persons can only be a positive integer, so we have to only take the integer part of the number and eliminate the decimal part.

Therefore, the largest number of people for whom she can buy tickets, is 4 people.

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Answer

Construction Model Stats

User

Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

ChatGPT

To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

User

The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.

ChatGPT

We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:

tan(18 degrees) = h / d

Solving for h, we get:

h = d * tan(18 degrees)

Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:

h = 510 feet * tan(18 degrees)

h ≈ 157.3 feet

Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.

User

The following regular polygon has 15 sides. This distance from its center to any given vertex is 12 inches.

Which of the following is the best approximation for its perimeter?

(1) 68 inches

(3) 84 inches

(2) 75 inches

(4) 180 inches

ChatGPT

To find the perimeter of a regular polygon with n sides, we can use the formula:

Perimeter = n * s

where s is the length of each side. To find s, we can use trigonometry to find the length of one of the sides and then multiply by the number of sides.

In a regular polygon with n sides, the interior angle at each vertex is given by:

Interior angle = (n - 2) * 180 degrees / n

In a 15-sided polygon, the interior angle at each vertex is:

(15 - 2) * 180 degrees / 15 = 156 degrees

If we draw a line from the center of the polygon to a vertex, we form a right triangle with the side of the polygon as the hypotenuse, the distance from the center to the vertex as one leg, and half of the side length as the other leg. Using trigonometry, we can find the length of half of the side:

sin(78 degrees) = 12 / (1/2 * s)

s = 2 * 12 / sin(78 degrees)

s ≈ 2.17 inches

Finally, we can find the perimeter of the polygon:

Perimeter = 15 * s

Perimeter ≈ 32.55 inches

Rounding this to the nearest whole number, we get that the best approximation for the perimeter is 33 inches. Therefore, the closest option is (1) 68 inches.

Answer:

To find the percentage of Virginia's gross pay that she took home after deductions, we need to first calculate her gross pay and then subtract the total amount of deductions to find her net pay. Then, we can divide her net pay by her gross pay and multiply by 100 to find the percentage.

Virginia earns $69,500 per year, so her gross pay per paycheck (assuming she is paid every two weeks) is:

$69,500 / 26 = $2,673.08

Her total deductions from her most recent paycheck were:

$200.20 + $180.65 + $72.00 + $110.00 + $250.00 = $812.85

So her net pay was:

$2,673.08 - $812.85 = $1,860.23

To find the percentage of her gross pay that she took home, we can divide her net pay by her gross pay and multiply by 100:

($1,860.23 / $2,673.08) x 100 ≈ 69.59%

Therefore, the closest option is (3) 69.59%.

The value of side length c is 13.55 units.

The length of side c is calculated by applying sine rule as shown below;

The formula for sine rule is given as;

a/sinC = b/sinA

For the given question, we will have the following equation,

c/sin (34) = 11 / sin (27)

The value of c in the triangle is calculated as follows;

c = (sin 34 / sin 27 ) x 11

c = 13.55 units

Thus, the value of side length c is determined by applying sine rules.

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Answer:

----------------------

See attached graph to help with answer choices.

Given function:

Answer choices:

The loan will increase to $39599.29 in 5 years

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

Using the above as a guide, we have the following:

Amount = P * (1 + r)ᵗ

Where

P = Principal = 35000

r = Rate = 2.5%

t = time = 5

Substitute the known values in the above equation, so, we have the following representation

Amount = 35000 * (1 + 2.5%)⁵

Evaluate

Amount = 39599.29

Hence, the amount is 39599.29

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The amount it would cost to paint the wall, given the cost of paint and the area covered is $ 56 .

The surface area of the circular wall would be :

A = 2 x π x r x h

The area is therefore:

= 2 x π x r x h

= 2 x 3. 14 x 15 x 4

= 376. 8 square feet

The number of gallons needed is therefore:

= 376. 8 / 225

= 1. 674

= 2 gallons

The cost of two gallons is:

= 2 x 28

= $ 56

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The probability that a randomly decided piece of cake maybe chocolate is 1/2 or half of or 0.

The proportion of chocolate cakes to all other cakes can be used to calculate the probability that a person will pick a chocolate cake from the pattern tray.

In this case, there are 3 chocolate cakes out of a total of 6 cakes.

So the probability of selecting a chocolate cake is:

3/6 = 1/2 (Dividing the numerator and denominator by their greatest common factor, in this case, 3 will simplify the fraction 3/6.)

Therefore, the probability of selecting a chocolate cake is 1/2 or 0.5 when expressed as a decimal.

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