Answer:
The area of the sign is 706.5 cm^2.
Step-by-step explanation:
We know,
The formula of area of a circle,
A = πr^26
Here A is area and r is radius.
Here we have radius is 15 cm, so we can put the values in the above equation and find the area,
A = π * 15^2
A = 3.14 * 225
A = 706.5
The area of the sign is 706.5 cm^2.
The number of candies sold can be determined by the equation: T = 0.3c,
where T is number of candies and c is the number of children. Find the
constant of proportionality.
The constant of proportionality in the equation is 0.3.
What is constant of proportionality?Firstly, there is proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called constant of proportionality.
WE are given that number of candies sold can be determined by the equation: T = 0.3c, where T is number of candies and c is the number of children.
0.3 = constant of proportionality
0.3 = p / n
which is the ratio of p to n
The constant of proportionality is the ratio between the two quantities that are directly proportional.
Therefore,
0.3 is the constant of proportionality in the equation.
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Question 1
Identify the function type represented by the graph. Explain your reasoning, and include at least one key feature to
support your choice.
The function type of the graph with asymptotes, x = 2, and y = 0 is a rational polynomial, where the degree of the numerator is less than the degree of the denominator, and (x - 2) is a factor of the denominator, which is a function of the form;
[tex]f(x) = \frac{1}{(x - 2)}[/tex]
What is an asymptote?An asymptote is a line to which the output value of a function approaches as the input value becomes very large approaches infinity.
The function type represented by the graph is a polynomial function that has an horizontal asymptote of y = 0, and a vertical asymptote of x = 2
A function has a vertical asymptote at the location at which the denominator approaches zero.
The vertical asymptote of x = 2 , indicates that the denominator approaches zero when x = 2, therefore, (x - 2) is a factor of the denominator
A function has an horizontal asymptote which is the value the function approaches as the input value approaches infinity.
Therefore, the horizontal asymptote of y = 0, indicates that the the degree of the numerator is less than the degree of the denominator
The function type in the question is therefore;
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A town has a population of 4.11 x 10^4 and shrinks at a rate of 9.6% every year. Which equation represents the town's population after 4 years?
Answer:
Step-by-step explanation:
The equation that represents the town's population after 4 years can be found using the formula:
P = P0 * (1 - r)^t
Where P is the population after t years, P0 is the initial population (4.11 x 10^4), r is the annual shrink rate as a decimal (9.6% as 0.096), and t is the number of years (4).
P = 4.11 x 10^4 * (1 - 0.096)^4
P = 4.11 x 10^4 * 0.6994^4
P = 4.11 x 10^4 * 0.4139
P = 1.70 x 10^4
So the town's population after 4 years is 1.70 x 10^4.
Answer:
Let P(t) be the population of the town after t years. We know that P(0) = 4.11 x 10^4. Then, the rate of change of the population is given by -0.096P(t), so we can write the differential equation:
dP/dt = -0.096P(t)
To find the population after 4 years, we need to solve this differential equation with the initial condition P(0) = 4.11 x 10^4. We can do this by separating variables and integrating both sides:
∫(dP/P) = -0.096 ∫dt
ln|P(t)| = -0.096t + C
where C is a constant of integration that can be found using the initial condition. Solving for P(t), we get:
P(t) = Ce^(-0.096t)
where C = e^(ln|P(0)|) = e^(ln|4.11 x 10^4|) = 4.11 x 10^4
Substituting in t = 4, we get:
P(4) = 4.11 x 10^4 e^(-0.096 × 4) = 4.11 x 10^4 e^(-0.384)
So, the equation representing the town's population after 4 years is:
P(t) = 4.11 x 10^4 e^(-0.096t)
16. Higher Order Thinking The box plots show the average daily high temperatures
of two cities from January to December. Which city should you live in if you want
a greater variability in temperature? Explain.
The city that you should live in if you want a greater variability in temperature is city Y.
Which city should you live in?In order to determine the city that has the greater variability in temperature, the interquartile range has to be determined. The interquartile range is used to measure the variation in a dataset.
The interquartile range is the difference between the third quartile and the first quartile.
interquartile range = third quartile - first quartile
Interquartile range for City X = 50 - 30 = 20
Interquartile range for City Y = 50 - 25 = 25
The interquartile range for city Y is greater than that of city X. This means that city Y has a greater variation in temperature.
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need help asap. pls somebody help.
Answer:
D
Step-by-step explanation:
why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.
x²
-x²
-x -x
x x x x (clearly that means 4x)
-1 -1 -1
1 1
so, we see it is D.
Examine the right triangle below, solve for x, round to two decimal places if
necessary.
The numerical value of x in the given right triangle is 20.14.
What is the value of x in the given right triangle?The figure in the image is right-triangle.
Angle A = 32°Opposite to angle A = xHypotenuse = 38Value of x = ?To find the value of x, we use trigonometric ratio.
Sine = Opposite / Hypotenuse
Plug in the values and solve for x.
sin( 32° ) = x / 38
x = sin( 32° ) × 38
x = 0.529919 × 38
x = 20.14
Therefore, the value of x is 20.14.
Option C) 20.14 is the correct answer.
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Assume you have interest in only two goods: food and environmental quality. That is, these
goods are the only ones that provide utility to you. Consider the following graph:
This curve symbolizes the curve of indifference. Those combinations of quantities that the customer considers to be of equal value are connected by a curve on a graph whose axes reflect amounts of two commodities.
Why is it called indifference curve?It dislikes all product combinations that offer the same level of enjoyment to the consumer. Because each combination provides the same level of enjoyment, the buyer Favours them all equally. The indifference curve therefore gets its name.
An indifference curve is a graphic representation of a collection of products that give consumers comparable levels of satisfaction, leading to their indifference. A consumer or person is indifferent between the two products at every point on the indifference curve because they provide the same kind of benefit.
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Rectangle A: 2 * 3 Rectangle B: 8 * 12 Rectangle C: 5 * 7 Rectangle D: 10 * 12 Which pair of rectangles is similar?
Answer: your mom
Step-by-step explanation:
Data for car production per shift at a car manufacturing facility are shown below: 688 711 625 701 688 667 694 630 547 703 688 697 703 656 677 700 702 688 691 664 688 679 708 699 667 703 i.
The mean of the data is given by the equation M = 679.3846 and the standard deviation σ = 34.1535
What is Standard Deviation?The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Standard Deviation is calculated by
Each number's deviation from the mean must be determined, and then squared.
Next, add up all of these values.
Divide the result by the quantity of numbers.
Then calculate its square root.
σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²
Given data ,
Let the data be represented as Set A
Now , the value of set A is
Set A = { 688 , 711 , 625 ,701 , 688 , 667 , 694, 630, 547, 703, 688, 697, 703, 656, 677, 700, 702, 688, 691, 664, 688, 679, 708, 699, 667, 703 }
The mean of the sample data = Sum of all the values / number of values
The mean M = 17664 / 26
The mean M = 679.3846
Now , the standard deviation is calculated by
σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²
Substituting the values in the equation , we get
The standard deviation σ = √ ( 30328.153846154 / 26 )
The standard deviation σ = √ ( 1166.4674556213 )
The standard deviation σ = 34.1535
Hence , the standard deviation is 34.1535
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A card is drawn from a standard deck of 52 cards and then placed back into the deck. Find the probability that a red card is drawn at least once by the third draw. Round your answer to two decimal places.
Given that there are 26 red cards in the deck of 52 cards, the probability of obtaining a red card on any given draw is 26/52 = 1/2.
What is probability?The probability of the complimentary event—the probability that no red cards are drawn in the first three draws—can be used to determine the likelihood that a red card will be pulled at least once by the third draw.
Particular that there are 26 non-red (black) cards in the 52-card deck, there is a 50% chance that no red cards will be drawn on any given draw.
As a result, the likelihood that none of the three draws will result in a red card is:
(1/2) x (1/2) x (1/2) = 1/8
The likelihood of drawing a red card at least once by the third draw is the counterpart of this probability.
1 - 1/8 = 7/8
Therefore, by the third draw, there is a 7/8 chance of drawing a red card at least once, or 0.88 rounded to two decimal places.
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RECAP DO NOT UNDERDSTAND PLEASE HELP
The required Length of the DC is 30.47 Units.
What is right angled triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
According to question:We have;
In ΔABD, ∠BAD = 54° and in ΔBDC, ∠BCD = 28°.
Then, In ΔABD
Sin∅ = BD/20
Sin(54°) = BD/20
BD = 0.809(20)
BD = 16.18
in ΔBDC
tan(28°) = BD/DC
DC = BD/tan(28°)
DC = 16.18/0.531
DC = 30.47 Units.
Thus, required Length of the DC is 30.47 Units.
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Solve for x.
3/4x + 3 = 27
Answer:
x = 32
Step-by-step explanation:
First we would move the x's to the left and the numbers to the right. When doing so they switch from being positive to negative or from negative to positive.
3/4x = 27-3
Now we would try to simplify it as much as we can. Here I would make 3/4 a decimal and subtract 37-3
0.75x = 24
Now we can divide 24 by 0.75 to find x
x = 32
x = 32.
Step-by-step explanation:1. Write the expression.[tex]\frac{3}{4} x+3=27[/tex]
2. Subtract "3" from both sides of the equation.[tex]\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x=24[/tex]
3. Divide by " [tex]\frac{3}{4}[/tex] " ob both sides of the equation.[tex]\frac{\frac{3}{4} x}{\frac{3}{4}} =\frac{24}{\frac{3}{4}}\\ \\x=24*\frac{4}{3}\\ \\x=\frac{24*4}{3} \\ \\x=\frac{96}{3} \\\\x=32[/tex]
4. Verify the answer.If "32" is our correct answer, then substituting it by variable "x" on the original equation should make the equation return the same number on both sides of the equal (=) symbol. Let's test it!
[tex]\frac{3}{4} (32)+3=27\\ \\\frac{3*32}{4}+3=27\\ \\\frac{96}{4}+3=27\\ \\24+3=27\\ \\27=27[/tex]
That's correct!
5. Conclude.x = 32.
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se the log tables in your book to find the following logarithms. You should use a calculator ONLY TO MULTIPLY and ONLY in parts c,d, andg. a.log(2^100)=b.log(100^2)=c.log(3.0862.062)=d.log(55^−3.1)=e.log(51)=f.log(1/51)=g.log(1/81^2)=
The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3
a. log(2^100) = 100 log(2) ≈ 30.103
b. log(100^2) = 2 log(100) = 2 log(10^2) = 2 × 2 = 4
c. log(3.0862.062) = log(3.086) + log(2.062) ≈ 0.488 + 0.316 = 0.804
(Note: The multiplication of 3.086 and 2.062 can be done using a calculator.)
d. log(55^(-3.1)) = -3.1 log(55) ≈ -3.1 × 1.740 = -5.394
e. log(5/1) = log(5) - log(1) ≈ 0.699 - 0 = 0.699
f. log(1/5) = log(1) - log(5) ≈ 0 - 0.699 = -0.699
g. log(1/81^2) = log(1) - 2 log(81) = -2 log(9^2) = -2 × 2 log(9) ≈ -2 × 0.954 = -1.908
(Note: We can use the property that log(a^b) = b log(a) to simplify the expression.)
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I’m setting up his latest wiring job an electrician out the following lengths of wire 272 946 662 28 23 and 856ft find the total length of wire used
Answer:
2787
Step-by-step explanation:
add them all together
factorise 1331x³y-11y³x pls i really need it!! thank you :) !!
Answer:
11xy(121x²-y²)
Step-by-step explanation:
When factorizing, you should always look for what each term has in common.
First, let's look at the coefficients (numbers) in each term: 1331 and 11. Both are divisible by 11, so let's factorize out 11:
1331x³y-11y³x
11(121x³y-y³x)
Looking at the terms in the bracket, we see they both have 'x's in common (121x³y has three x's multiplied in and y³x has one). Let's factorize out this x:
11(121x³y-y³x)
11x(121x²y-y³)
We can also see both terms in the brackets have 'y's in common (121x²y has one y and y³ has three multiplied in). Let's factorize out this y:
11x(121x²y-y³)
11xy(121x²-y²)
Since there is nothing in common left between the terms, we can say the expression is fully factorized!
Help !! I can’t find the answer for this question
Answer:
41 inches
Step-by-step explanation:
to find the perimeter of any shape, add the length of all the sides together
Let S be the universal set, where: S = { 1 , 2 , 3 , ... , 18 , 19 , 20 } Let sets A and B be subsets of S , where: Set A = { 1 , 2 , 4 , 10 , 12 , 14 , 16 } Set B = { 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 } Find the following: The number of elements in the set ( A ∪ B ): n ( A ∪ B ) = The number of elements in the set ( A ∩ B ): n ( A ∩ B ) is
The values for the sets are -
A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 } and n(A∪B) = 14.
A∩B = { 10 , 12 , 14 , 16 } and n(A∩B) = 4
What is sets?
A set is a precisely defined collection or aggregate of all feasible objects with predetermined qualities that are specified in accordance with a precisely defined rule. Elements of sets are the items used to compare sets.
The set S is - S = { 1 , 2 , 3 , ... , 18 , 19 , 20 }
The set A is - A = { 1 , 2 , 4 , 10 , 12 , 14 , 16 }
The set B is - B = { 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }
A∪B is the set of elements of S that are part of A or B, or both.
A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }
Count the number of elements present in set A∪B.
Therefore, n(A∪B) value is 14.
A∩B is the set of elements of S that are common to A and B.
A∩B = { 10 , 12 , 14 , 16 }
Count the number of elements present in set A∩B.
Therefore, n(A∩B) value is 4.
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In the spinner below, each sector is equal in size.
If you spin the spinner 7 times, what is the prediction for the number of times it will not land on blue?
B
4
5
6
7
The number of times it is not land on the blue color sector is 7-1 = 6
What is a probability?A probability is defined as the ratio to the number of required outcomes to the total number of outcomes of an event.
The spinner is divided into 7 sectors, in which each sector is equal in size.
Among 7 sectors two of of them are blue in color.
We have to calculate that how many times the spinner not landing on the blue color sector.
For that we have to calculate the possible outcome for the blue color sector for 1 spin.
For 1 spin , the number of possible outcomes = 7.
Number of required outcomes = 2.
Probability of number of spins on blue sector for 1 spin = 2/7.
Probability of number of spins on blue sector for 7 spin = 7*(2/7) = 2.
Standard deviation = [tex]\sqrt{\frac{2}{7} *\frac{5}{7} }[/tex]= 0.4518.≅0.452.
Standard error=root(7)*0.452= 1.19≅1.2
Expected value =2-1.2 = 0.8 ≅1
Therefore the expected value is 1.
Number of times it will land on the blue color sector is 1.
Hence, the number of times it is not land on the blue color sector is 7-1 = 6.
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PLS HELPPPPP!!!!!!!!! DUE TODAY!!!!!! 100 points and brainliest if correct!!!! pls answer all of them!
Answer and solve the proportions then the percent equation.
what is the percent equation for the following:
6.5% of $400 is
what number?
12.5% of $100 is
what number?
130 is what percent
of 650?
$5.40 is what
percent of $4.50?
$8.40 is what
percent of $28?
56% of what
number is $21.84?
$495 is 55% of
what number?
144 is what percent
of 240?
Answer:The first question requires the calculation of the 6.5% of $400, which is equal to $26.
The second question requires the calculation of 12.5% of $100, which is equal to $12.50.
For the third question, 130 is 20% of 650.
For the fourth question, $5.40 is 120% of $4.50.
For the fifth question, $8.40 is 30% of $28.
For the sixth question, 56% of 39 is $21.84
For the seventh question, $495 is 55% of $900.
For the last question, 144 is 60% of 240.
Step-by-step explanation:
Answer:
Step-by-step explanation:
26
12.5
20%
120%
30%
12.23
900
60%
Examine the right triangle below, solve for x, round to two decimal places if
necessary.
The solution for x in the triangle is x = 51.98 units
How to solve for x in the triangle?
Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Using trigonometric ratio:
sin 38° = 32/x (Sine = opposite/hypotenuse)
x = 32/sin 38°
x = 51.98 units
Therefore, the solution is x = 51.98 units
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The median monthly rent in 1990 was $447 and $658 in 2002. What was the percent increase in the median monthly rent prices from 1990 to 2002? Round to the nearest tenth of a percent.
Answer:
Step-by-step explanation:
Step 1: Define each variable
Let's define some variables to make the calculations easier:
t1 = the median monthly rent in 1990, which is $447
t2 = the median monthly rent in 2002, which is $658
Δ = the change in median monthly rent, which is t2 - t1
Step 2: Calculate the change in median monthly rent
Δ = t2 - t1 = $658 - $447 = $211
This means that the median monthly rent increased by $211 from 1990 to 2002.
Step 3: Divide the change by the original amount
To find the percentage increase, we need to divide the change by the original amount and multiply by 100:
Δ / t1 * 100 = ($211 / $447) * 100 = 47.2%
This means that the median monthly rent increased by 47.2% from 1990 to 2002.
Step 4: Round to the nearest tenth of a percent
The final answer is 47.2%, rounded to the nearest tenth of a percent.
The percent increase in the median monthly rent prices from 1990 to 2002 was 47.2%.
(SAT Prep) Find the value of x.
X
Answer: 70˚
Step-by-step explanation:
Goal: find the other angles in the triangle and subtract them from 180 to find x:
180 - 105 = 75˚
the other angle is 35˚, (alternate interior angles).
.: x = 180 - 75 - 35 = 70˚
Mrs. Becker is walking down the hallway and suddenly spots the world's largest ladybug. If her eyes are 6 feet off the ground and the bug is 100 feet away, what angle is she looking down at?
Answer:
Step-by-step explanation:
To find the angle that Mrs. Becker is looking down at, we can use the tangent function. We know the height of her eyes (6 feet) and the distance from her eyes to the ladybug (100 feet), so we can use the formula:
tan(angle) = height/distance
First, we'll solve for the angle:
angle = tan^-1(height/distance)
angle = tan^-1(6/100)
Using a calculator, we can find that the angle is approximately 0.0349 radians, or approximately 2 degrees.
So, Mrs. Becker is looking down at an angle of approximately 2 degrees.
14,125 ÷ 18 = ? With a remainder
Answer:
784 R 13
Hope this helps!
Step-by-step explanation:
si en una division el dividendo es 872 el cociente es 62 y el residuo es 4 cual es el divisor
The divisor in the situation given is 14.
What is division algorithm?We can write the division algorithm as -
dividend = (divisor × quotient) + remainder
Given is that in a division the dividend is 872 the quotient is 62 and the remainder is 4
We can write -
dividend = (divisor × quotient) + remainder
872 = (d x 62) + 4
62d = 868
d = 868/62
d = 14
Therefore, the divisor in the situation given is 14.
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{Question in english -
if in a division the dividend is 872 the quotient is 62 and the remainder is 4 what is the divisor}
Find an angle α that is coterminal with an angle measuring 550∘, where 0∘≤α<360∘.
Answer:
190°
Step-by-step explanation:
Subtract 360° (this is one complete rotation)
"coterminal" is the exact same angle, but 360° bigger (or smaller)
550° - 360°
= 190°
Complete the sentence below.
325 is a hundred times bigger than
Answer:3.25
Step-by-step explanation:
Divide 325/100=3.25
put these decimals lease to greatest 2.16,2.1682,2.2,2.016?
Answer:
2.016, 2.16, 2.1682, 2.2
How to put anything from least to greatest?
The decimals that you have put are the following:
2.16
2.1682
2.2
2.016
How to do it:
If you look at the decimals the last one, 2.016 does not have a 1 or a 2 instead it has a 0 so that would be a our first decimal in the least to greatest form.
We can also include the third one 2.2 is the only one that has a 2 so now we know that 2.2 will go last.
Lets compare the first and second ones which are 2.16 and 2.1682 and I think we obviously know that the answer is 2.1682 because it is greater then 2.16.
So now here are the decimals from least to greatest:
2.016, 2.16, 2.1682, 2.2
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Point R is located at (1,1) on the coordinate plane. Point R is reflected over the y-axis to create point R ′ . Point R' is then reflected over the x-axis to create point R''. What ordered pair describes the location of R''?
Answer:
Step-by-step explanation:
Here's a step-by-step explanation of the reflections:
Point R is located at (1, 1) on the coordinate plane.
Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).
Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).
So the final location of R'' is at the ordered pair (-1, -1).
The diameters of bolts produced in a machine shop are normally distributed with a mean of 6.48 millimeters and a standard deviation of 0.06 millimeters. Find the two diameters that separate the top 3% and the bottom 3% . These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
To find the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop, we need to find the lower and upper bounds of the interval that contains the middle 94% of the data. This can be done using the standard normal distribution and the z-score.
First, we'll find the z-score that corresponds to the lower bound. To do this, we'll use the formula:
z = (x - μ) / σ
where x is the lower bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 3%:
z = (x - 6.48) / 0.06
z = -2.33
Next, we'll use the z-score to find the value of x (the lower bound). We'll use the standard normal distribution table to look up the value of -2.33 and find that it corresponds to a cumulative probability of 0.01. So, the lower bound is such that 1% of the data is less than or equal to this value. To find the value of x, we'll use the formula:
x = μ + zσ
x = 6.48 + (-2.33) * 0.06
x = 6.32
So, the lower bound of the interval that contains the middle 94% of the data is 6.32 millimeters. This is the diameter that separates the bottom 3% of the bolts from the rest.
Next, we'll find the upper bound in a similar way. To do this, we'll use the formula:
z = (x - μ) / σ
where x is the upper bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 97%:
z = (x - 6.48) / 0.06
z = 2.33
Using the standard normal distribution table, we find that the value of 2.33 corresponds to a cumulative probability of 0.99. So, the upper bound is such that 99% of the data is less than or equal to this value. To find the value of x, we'll use the formula:
x = μ + zσ
x = 6.48 + 2.33 * 0.06
x = 6.64
So, the upper bound of the interval that contains the middle 94% of the data is 6.64 millimeters. This is the diameter that separates the top 3% of the bolts from the rest.
Therefore, the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop are 6.32 millimeters and 6.64 millimeters, rounded to the nearest hundredth.
