For numbers 3, 4, and 5, find the value of the indicated length(s) in ⨀C. A and B are points of tangency. Simplify all radicals.

I just need help with these three problems!

Perimeter, area, and circumference are important mathematical concepts that have numerous real-world applications.

How to apply?

For example, in construction and architecture, these concepts are used to measure and design buildings, rooms, and other structures. Knowledge of perimeter is important when determining how much material is needed for a fence or wall, while understanding area is crucial for calculating how much paint or flooring material is needed for a room.

Circumference is important for designing circular objects such as wheels, pipes, and round tables. In addition to construction and design, these concepts are also used in various fields such as engineering, science, and finance.

For instance, understanding area and circumference is important in calculating the surface area and volume of 3D objects in science, while in finance, perimeter and area can be used to calculate the cost of goods or real estate. Overall, the applications of perimeter, area, and circumference are numerous and essential in many aspects of our daily lives.

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Therefore, it will cost $350 to carpet Carli's rectangular bedroom with carpet that costs $2.50 per square foot.

Area is a measure of the size of a two-dimensional surface or region. It is usually expressed in square units, such as square meters (m²) or square feet (ft²). To calculate the area of a shape, you need to multiply its length by its width or use an appropriate formula for the specific shape. The concept of area is important in many fields, including mathematics, geometry, physics, engineering, architecture, and more. It is used to quantify the space occupied by objects or regions, to determine the amount of material needed to cover a surface, or to calculate the amount of paint or wallpaper required to decorate a room, among other applications.

Given by the question.

The area of Carli's rectangular bedroom can be calculated by multiplying its length by its width:

Area = Length × Width

Area = 14 ft × 10 ft

Area = 140 sq ft

The cost of carpeting her room can be found by multiplying the area of the room by the cost per square foot of carpet:

Cost = Area × Cost per square foot

Cost = 140 sq ft × $2.50/sq ft

Cost = $350

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Answer:

£22

Step-by-step explanation:

50% of 88=88/100 ×50=44

44÷2=25%=22

75% of £88 is deducted, so that 88-66=£22

Answer:

The claim that healthcare laptop replacement costs are higher than in other industries.

Answer:

30% of the number is 102.

Answer:

Bus vs Highway: Houston

Let's start by finding out how many people took the bus.

If the number of people who took the highway is x, then the number of people who took the bus is 1.5x (since it's one and a half times the number of people who took the highway).

We know that the total number of people who traveled to Houston is 31,426, so we can write an equation:

x + 1.5x = 31,426

Simplifying the equation:

2.5x = 31,426

Dividing both sides by 2.5:

x = 12,570.4

Since we can't have a fraction of a person, we can round this down to 12,570.

Now we can find the number of people who took the bus:

1.5x = 1.5(12,570) = 18,855

To find out how many more people took the bus, we can subtract the number of people who took the highway from the number of people who took the bus:

18,855 - 12,570 = 6,285

Therefore, 6,285 more people took the bus.

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√5 /x²y is equivalent  expression to the given question . Then the correct option is C.

What is Expression?

A mathematical expression is a phrase with at least two variables or integers and one arithmetic operation.

a)Constant It has a set numerical value and is a constant.

For instance: 7,45,413,18,5.

b) Variables don't accept any predetermined values. Value is depend on Equation

Like a, p, and z

Constants, variables, or constants multiplied by variables are all acceptable terms (s). The "+" or "" symbol or both separates each term in an expression.

Instance: 5a+12b.

d) Operators: Addition (+), subtraction (-), multiplication (-), and division (-) are the four operations that are used to combine the terms in an expression.

Therfore, √5 /x²y is equivalent  expression to the given question . Then the correct option is C.

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The value of the probability is 0.3125 and this is proved by the calulations below

The probability of getting exactly 3 heads in 5 coin tosses can be calculated by multiplying the probability of one specific combination of 3 heads and 2 tails by the number of possible combinations.

The probability of one specific combination, for example HHTTT, is (1/2)^5 = 1/32, because each toss has a 1/2 chance of being a head or a tail.

There are 5C3 = 10 possible combinations of 3 heads and 2 tails in 5 tosses.

For example: HHTTT, HTHTT, HTTHT, HTHHT, TTHHH, etc.

Therefore, the probability of getting exactly 3 heads is:

Probability = 10 * (1/32)

Probability = 10/32

Probability = 0.3125.

Hence, the value of the probability is 0.3125.

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Answer:

To find g(f(2)), we first need to find f(2) and then use that result as the input for g.

We are given that f(2) = -3, so we substitute that value into g(x) to get:

g(f(2)) = g(-3)

We are also given that g(-3) = 10, so we substitute that value in:

g(f(2)) = g(-3) = 10

Therefore, g(f(2)) = 10.

Answer:

12 dollars

Step-by-step explanation:

480 / 40 = 12

12 dollars

Answer:

Step-by-step explanation:

If they had $11: Fred gets $3, George gets $8.

So the ratio is:  3:8

The equation 32 - 3x + 13 = 0 can be rewritten as 3x = 19. Therefore, x = 19/3. Because x is a real number, the solution to the equation is x = 19/3.

Real numbers are any number that can be expressed as a decimal number or a fraction. This includes the natural numbers (1,2,3,4, etc.), the negative numbers (-1,-2,-3, etc.), the rational numbers (fractions, such as 1/2, 3/4, etc.), and the irrational numbers (numbers that cannot be expressed as a fraction, such as pi, square root of 2, etc.). Real numbers can be manipulated with basic arithmetic operations such as addition, subtraction, multiplication, and division. Real numbers have an infinite number of decimal places, making them useful for measuring physical quantities such as time, distance, and temperature.

Expressing this answer in the form a + bi, where a and b are real numbers, gives the solution a = 19/3 and b = 0. Therefore, the answer is 19/3 + 0i = 19/3.

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The value of x in the equation that is given as 2/3x + 4/5x = 6 will be 4.

Based on the information given, one should note that an equation has to do with the statement in a question which depicts the variables given. In this case, one should note in an equation, one will need to consider two or more components are to be able to illustrate the scenario.

In this case, it is important to note that an equation simply depicts the mathematical statement which can be made up of two expressions which are simply connected by an equal sign.

The equation is explained thus:

2/3x + 4/5x = 6

10/15x + 12/15x = 6

22/15x = 6

1.467x = 6

x = 6 / 1.467

x = 4

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Solve the equation

2/3x + 4/5x = 6

The first limit,  [tex]\lim_{x\to \→-2^- } -3(x+2)/x²+4x+4[/tex]  , evaluates to negative infinity, while the second limit, [tex]\lim_{ x\to \-2^+}-3(x+2)/x²+4x+4[/tex] , evaluates to positive infinity.

Function in maths is a relation between two sets of values. It is a type of mathematical equation in which each input value has a unique output value. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.

This indicates that the function has a vertical asymptote at x=-2.

In order to understand why this is the case, we can first rewrite the function as follows:

f(x) = -3(x+2)/(x+2)(x+2)

The denominator of the function is (x+2)(x+2), which has a double root at x=-2. This means that the denominator is equal to zero when x=-2. As a result, the function f(x) will have a vertical asymptote at x=-2, since the denominator will be equal to zero and the function will approach negative or positive infinity. This is why the two limits mentioned above both evaluate to either negative or positive infinity.

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The limit of the given functions are:

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = positive infinity

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = negative infinity

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined

Function is a relation between two sets of values. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4

= -3(-2+2)/(-2)²+4(-2)+4

= -3/0 + 8 + 4

= +∞  (infinity)

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4

= -3(-2+2)/(-2+2)²+4(-2+2)+4

= -3/4 + 0 + 4

= -∞

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4

= -3(-2+2)/(-2+2)²+4(-2+2)+4

= -3/0 + 0 + 4

= Undefined

Therefore, the limit of the functions given are:

[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = +∞

[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = -∞

[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined

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a) The domain and the range of the function are given as follows:

The graph of the function is given by the image presented at the end of the answer.

b) The trip was 5.1875 hours long.

The function for this problem is defined as follows:

g(t) = 23 - 3.2t.

The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the volume is given as follows:

23 - 3.2t = 0

3.2t = 23

t = 23/3.2

t = 7.1875 hours.

The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].

The graph is a linear function between points (0, 23) and (7.1875, 0).

At the end of the trip there were 6.4 gallons left, hence the length of the trip is given as follows:

23 - 3.2t = 6.4

t = (23 - 6.4)/3.2

t = 5.1875 hours.

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Answer:

The correct answer is B.

[tex]f(x) = \frac{1}{(x - 1)(x + 1)} [/tex]

The vertical asymptotes are at x = -1 and at x = 1.

Step-by-step explanation:

So first of all u have to convert the metres into centimetres. After the conversation draw the map of both in centimetres and your map is done. The question is answered

Answer:

Determine the dimensions of the room: Measure the length and width of the room you want to draw a floor plan for using a tape measure. Record these measurements in meters.

Choose a scale: Since you want to use a scale of 1cm to 0.5m, you need to convert your measurements from meters to centimeters. For example, if your room measures 6 meters by 4 meters, you need to multiply each measurement by 100 to get 600cm by 400cm. Then, divide each measurement by 2 to get your scale measurement. In this case, your floor plan will be 300cm by 200cm.

Draw a rough sketch: Using a pencil and graph paper, draw a rough sketch of the room's shape based on the dimensions you have recorded.

Add doors and windows: Using the same scale, add doors and windows to your floor plan. Doors are typically represented by a straight line with an arc on top, while windows are represented by a straight line with a horizontal line through the middle.

Add fixtures and appliances: Add any fixtures and appliances that are permanent to the room, such as sinks, cabinets, and appliances. You can use symbols to represent these items, such as a rectangle for a refrigerator or a triangle for a sink.

Label everything: Finally, label everything on your floor plan using a legible font. This includes the dimensions of the room, the location of doors and windows, and the names of fixtures and appliances.

Step-by-step explanation:

A fraction of the variation in y that can be explained by the variation in the values of x is equal to 0.25189186354.

In Mathematics, the standard form of the equation of a regression line is represented or modeled by the following mathematical expression;

y = bx + c

Where:

In Mathematics and Statistics, the value of slope can be calculated by using the following mathematical expression;

[tex]b=r(\frac{S_y}{S_x})[/tex]

where:

By rearranging, we have:

[tex]r=b(\frac{S_x}{S_y})[/tex]

r = 1.13(1.67/3.76)

r = 0.50188829787

By taking the square of both sides, we have:

r² = 0.25189186354.

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Answer:

45,000 is standard form.

4.5 is the coefficient.

4 of 10⁴ is the exponent.

7.6 × 10⁻⁴ is scientific notation.

10 of 10⁻⁴ is the base.

Step-by-step explanation:

Scientific notation is a way of writing very large or very small numbers in a compact and convenient form. It consists of two parts:

The base of scientific notation is always 10, which means that the number is written in terms of powers of 10.

For example, the number 4,000,000 can be written in scientific notation as 4 x 10⁶. In this case, the coefficient is 4, and the exponent is 6.

The standard form of a number is simply the usual way of writing it, without using scientific notation. For example, the standard form of 4 x 10⁶ is just 4,000,000.

Therefore, for the given problem:

The value of R500 decrease to ratio 9:8 is x = 400.

By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.

Given that, decrease R450 in the ratio 9:8.

Let 9 = 450

Then 8 will have the value = x.

That is,

9 = 450

8 = x

Using cross multiplication we have:

9x = 450(8)

x = 50(8)

x = 400

Hence, the value of R500 decrease to ratio 9:8 is x = 400.

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Answer:

1

Step-by-step explanation:

We must solve the absolute values first

An absolute value is the numbers distance from zero

So a simplified version of your problem would be

2-1

So your answer is 1

The absolute value of a number is its distance from 0, so |-2| is 2 and |-1| is 1. Substituting these back in, the expression 2 - 1 equals 1.

To evaluate the expression |-2| – |-1|, you first need to understand what the absolute value symbol does. The absolute value of a number is its distance from 0 on the number line, regardless of direction. So, both |-2| and |-1| become positive numbers, as distance is always positive.

Therefore, |-2| equals 2 and |-1| equals 1. If we substitute these values back into the original expression, 2 - 1, the result is 1.

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Step-by-step explanation:

Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:

P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.

Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.

Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).

However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.

An exponential function can model California's population growth from 1950 to 1980. The predicted population in 2020 is around 43.3 million (43,301,300), assuming exponential growth.

To find an exponential function that models the population, we can use the formula:

P(t) = P0 * e^(rt)

where P0 is the initial population, r is the growth rate, and t is the time in years. We can use the information given to find P0, r, and then plug in t = 0 to find the exponential function.

P0 = 10,586,223 (initial population in 1950)

P(30) = 23,668,562 (population in 1980, 30 years later)

t = 30

P(0) = P0 * e^(0*r) = P0 (population in 1950)

So we have:

23,668,562 = 10,586,223 * e^(30r)

Dividing both sides by 10,586,223:

e^(30r) = 2.234

Taking the natural logarithm of both sides:

30r = ln(2.234)

r = ln(2.234)/30

Now we can use this value of r to find the exponential function:

P(t) = 10,586,223 * e^(t*ln(2.234)/30)

To predict the population in 2020, we can plug in t = 70 (since 2020 is 70 years after 1950) into the function we just found:

P(70) = 10,586,223 * e^(70*ln(2.234)/30) ≈ 43,301,300

Therefore, the predicted population of California in 2020 is approximately 43,301,300.

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The congruence x + 13 ≡ 55 (mod 34) simplifies to x ≡ 12 (mod 34). There are three solutions for x less than 100 that satisfy this congruence.

The given congruence is x + 13 ≡ 55 (mod 34). Simplifying this, we get x ≡ 12 (mod 34).

We need to find the number of solutions for x that are less than 100 and satisfy this congruence.

The general solution for the congruence x ≡ 12 (mod 34) is x = 12 + 34k, where k is an integer.

The solutions that are less than 100 are obtained when k = 0, 1, or 2.

Thus, the number of solutions is 3.

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The balance of the account after the seventh deposit can be calculated using the formula below:

A = P (1 + r/n)ⁿ

where:

A = the balance of the account

P = The initial deposit of $800

r = the interest rate of 5%

n = the number of times the interest is compounded annually

n = 1

Therefore, the balance of the account after the seventh deposit is:

A = 800 (1 + 0.05/1)⁷

A = 800 (1.05)⁷

A = 800 (1.4176875)

A = 1128.54

Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.

Using the functions, we can predict that the population in the town will grow 't' times as t is directly proportional to the function.

A function in mathematics is a connection between two x and y values that come from different sets. These four types of correspondence are all possible. Yet not every correspondence serves a purpose.

The following are the results of a survey conducted by the National Institute of Standards and Technology (NIST) on the effectiveness of the standardised testing process. So, we state that a function can only have one input and one output. If we are given any x, the only y that can be coupled with that x is the one and only y. Two outputs cannot be connected to the same function.

Here in the given question,

The functions a(t) = 8.75 × (1+0.01) t and

b(t) = 8.75 × e × (0.01t) here are dependent on the variable t, where t is the time in years after 2010.

So, as t will increase after 2010, the value of a(t) and b(t) will increase with t.

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Answer: 77/6 or 12 5/6

Step-by-step explanation:

To solve this subtraction problem, we need to first convert the mixed numbers to improper fractions.

20 1/3 can be written as:

20 + 1/3 = 60/3 + 1/3 = 61/3

7 1/2 can be written as:

7 + 1/2 = 14/2 + 1/2 = 15/2

So, the problem becomes:

61/3 - 15/2

To subtract two fractions, we need to have a common denominator. The smallest number that both 3 and 2 divide into is 6. So we will convert both fractions to have a denominator of 6.

61/3 = (61/3) * (2/2) = 122/6

15/2 = (15/2) * (3/3) = 45/6

Now we can subtract the two fractions:

122/6 - 45/6 = 77/6

So, the final answer is:

20 1/3 - 7 1/2 = 77/6 or 12 5/6 (as a mixed number)

Check the picture below.

btw, we could have used the f(4) for both subfunctions just the same.

1. Graph is attached below. 2. 0.51 3. the percent of tiles with an area between 15.975 and 16.01 square inches is 82.78%. 4. 0.08% 5. 304 tiles 6.  0.4938x tiles.

A uniform density function is a type of probability distribution that assigns equal probability to all values within a specified range. It is also known as a rectangular distribution because the graph of the probability density function appears as a rectangle with a constant height over the interval of possible values.

The probability density function of a uniform distribution is defined by two parameters: a minimum value (a) and a maximum value (b). The function assigns a probability of 1/(b-a) to each value within the range [a, b], and a probability of 0 to any value outside this range.

1. The graph of the uniform density function that takes on values from -2 to 3 is mentioned below

2. To find P(-1.25 < X < 1.3), we need to find the area under the uniform density function between -1.25 and 1.3. Since the density function is uniform, the area is simply the rectangle with base (1.3 - (-1.25)) = 2.55 and height 1/5 (since the range of values is 5). Therefore,

P(-1.25 < X < 1.3) = (2.55 * 1/5) = 0.51

3. To find the percent of tiles that have an area between 15.975 and 16.01 square inches, we need to standardize the values using the z-score formula and then find the area under the normal curve between those two values:

z1 = (15.975 - 16) / 0.008 = -3.125

z2 = (16.01 - 16) / 0.008 = 1.25

Using a standard normal table or calculator, we find the area between these two z-scores to be approximately 0.8278.

Therefore, the percent of tiles with an area between 15.975 and 16.01 square inches is 82.78%.

4. To find the probability that a tile will have an area that is more than 16.025 square inches, we again need to standardize the value using the z-score formula and then find the area under the normal curve to the right of that value:

z = (16.025 - 16) / 0.008 = 3.125

Using a standard normal table or calculator, we find the area to the right of this z-score to be approximately 0.0008.

Therefore, the probability that a tile will have an area that is more than 16.025 square inches is 0.08%.

i. Yes, this is unusual because the probability is very low, indicating that it is highly unlikely for a tile to have an area greater than 16.025 square inches.

5. To find the number of tiles that can be expected to have a surface area less than 15.985 square inches, we first need to standardize the value using the z-score formula:

z = (15.985 - 16) / 0.008 = -1.875

Using a standard normal table or calculator, we find the probability to the left of this z-score to be approximately 0.0304.

Therefore, out of 10,000 tiles, we can expect approximately 0.0304 * 10,000 = 304 tiles to have a surface area less than 15.985 square inches.

6. To find the number of tiles that must be produced to ensure that the manufacturer has 70,000 tiles that are between 15.98 and 16.02 square inches, we need to find the z-scores for the lower and upper bounds of this range:

z1 = (15.98 - 16) / 0.008 = -2.5

z2 = (16.02 - 16) / 0.008 = 2.5

Using a standard normal table or calculator, we find the probability between these two z-scores to be approximately 0.4938.

Therefore, out of x tiles, we can expect approximately 0.4938x tiles to have a surface area between 15.

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1. The graph of the uniform density function that takes on values from -2 to 3 is attached below.

2. P(-1.25 < X < 1.3) = (2.55 * 1/5) = 0.51

3. The percent of tiles with an area between 15.975 and 16.01 square inches is 82.78%.

4. The probability that a tile will have an area that is more than 16.025 square inches 0.08%.

5. Number of tiles that can be expected to have a surface area less than 15.985 square inches

6.   To find the number of tiles that must be produced to ensure that the manufacturer has 70,000 tiles that are between 15.98 and 16.02 square inches, 0.4938x tiles.

A uniform density function is a type of probability distribution that assigns equal probability to all values within a specified range. It is also known as a rectangular distribution because the graph of the probability density function appears as a rectangle with a constant height over the interval of possible values.

1. The graph of the uniform density function that takes on values from -2 to 3 is mentioned below:

2. To find P(-1.25 < X < 1.3), we need to find the area under the uniform density function between -1.25 and 1.3. Since the density function is uniform, the area is simply the rectangle with base (1.3 - (-1.25)) = 2.55 and height 1/5 (since the range of values is 5). Therefore,

P(-1.25 < X < 1.3) = (2.55 * 1/5) = 0.51

3. To find the percent of tiles that have an area between 15.975 and 16.01 square inches, we need to standardize the values using the z-score formula and then find the area under the normal curve between those two values:

z1 = (15.975 - 16) / 0.008 = -3.125

z2 = (16.01 - 16) / 0.008 = 1.25

Using a standard normal table or calculator, we find the area between these two z-scores to be approximately 0.8278.

Therefore, the percent of tiles with an area between 15.975 and 16.01 square inches is 82.78%.

4. To find the probability that a tile will have an area that is more than 16.025 square inches, we again need to standardize the value using the z-score formula and then find the area under the normal curve to the right of that value: z = (16.025 - 16) / 0.008 = 3.125

Using a standard normal table or calculator, we find the area to the right of this z-score to be approximately 0.0008.

Therefore, the probability that a tile will have an area that is more than 16.025 square inches is 0.08%. Yes, this is unusual because the probability is very low, indicating that it is highly unlikely for a tile to have an area greater than 16.025 square inches.

5. To find the number of tiles that can be expected to have a surface area less than 15.985 square inches, we first need to standardize the value using the z-score formula:

z = (15.985 - 16) / 0.008 = -1.875

Using a standard normal table or calculator, we find the probability to the left of this z-score to be approximately 0.0304.

Therefore, out of 10,000 tiles, we can expect approximately 0.0304 * 10,000 = 304 tiles to have a surface area less than 15.985 square inches.

6. To find the number of tiles that must be produced to ensure that the manufacturer has 70,000 tiles that are between 15.98 and 16.02 square inches, we need to find the z-scores for the lower and upper bounds of this range:

z1 = (15.98 - 16) / 0.008 = -2.5

z2 = (16.02 - 16) / 0.008 = 2.5

Using a standard normal table or calculator, we find the probability between these two z-scores to be approximately 0.4938.

Therefore, out of x tiles, we can expect approximately 0.4938x tiles to have a surface area between 15.

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