The diameter C of the top of a randomly selected large drink cup at a fast-food restaurant follows a Normal distribution with a mean of 3.96 inches and a standard deviation of 0.01 inch.
The diameter Lof a randomly selected large lid at this restaurant follows a Normal distribution with mean 3.98 inches and standard deviation 0.02 inch.
Assume that Land Care independent random variables. Let the random
variable D = L - C be the difference between the lid's diameter and the
cup's diameter.
For a lid to fit on a cup, the value of L has to be bigger than the value of C, but not by more than 0.06 inch. Find the probability that a randomly selected lid will fit on a randomly selected cup.
Interpret this value. Justify your answer.

The maximum is 12 diagonals or a length of 12 × 2√2 =24√2 centimeters.

Note that the ball moves only on the diagonals of the 15 non-overlapping squares. Thus we must find the path that traverses the most diagonals.

From point 1, the path traverses 6 diagonals before ending up at D.

From point 2, the path traverses 12 diagonals before ending up at A (incidentally, it passes through point 5 in the specified direction so we do not need to check point 5).

From point 3, the path traverses 3 diagonals before ending up at B.

From point 4, the path traverses 9 diagonals before ending up at C.

From point 6, the path traverses 10 diagonals before ending up at D.

Thus the maximum is 12 diagonals, or a length of 12 × 2√2 =24√2 centimeters.

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To convert 0.1667 to a fraction, we write it as 1667/10000, and simplify it to 1/6. Hence, the fraction of .1667 is 1/6.

To convert the decimal number 0.1667 to a fraction, we can write it as 1667/10000. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 167.

1667 ÷ 167 = 10

10000 ÷ 167 = 60 + 40/167

So, the fraction equivalent to 0.1667 is 1667/10000, which can be simplified to 10/60 + 40/167.

10/60 can be simplified to 1/6, so the final simplified fraction is:

0.1667 = 1/6 + 40/167

Therefore, the fraction equivalent to 0.1667 is 1/6.

Converting a decimal to a fraction involves expressing a decimal number as a ratio of two integers. To convert a decimal to a fraction, the decimal is written in the form of a fraction, with the decimal value as the numerator and a power of 10 as the denominator. The resulting fraction can be simplified by finding the greatest common factor between the numerator and denominator, and then dividing both by that factor. For example, to convert 0.1667 to a fraction, we write it as 1667/10000, and simplify it to 1/6.

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The sorting algorithms that are not comparison based are counting sort, bucket sort, and radix sort.

Counting sort works by counting the number of occurrences of each element in an array and then using this information to determine the position of each element in the sorted array.

Bucket sort works by dividing the array into a number of smaller arrays, called buckets, and then sorting each of these smaller arrays separately.

Radix sort works by sorting the elements of an array based on the individual digits of each element, starting with the least significant digit and working up to the most significant digit.

These algorithms do not rely on comparisons between elements, which is why they are not considered comparison based.

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Answer:

m = -5/3

Y-intercept: (0, 64/3)

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (14, -2) and (5,13)​

We see the y increase by 15 and the x decrease by 9, so the slope is

m = -15/9 = -5/3
The y-intercept is located at ( 0, 64/3)

Answer:is this real

Step-by-step explanation:

1 =727

Answer:

Step-by-step explanation:20

Answer:

Step-by-step explanation:

The answer is 120.3676. i assume you are converting between grams MgSO4 and mole. You can view more details on each measurement unit: molecular weight of MgSO4

The initial value (initial fee) for the picnic is $40. Then the correct options are A, B, and D.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

Let 'x' be the number of people and 'y' be the total cost.

From the table, the two points are (6, 52) and (9, 58). Then the equation of the line is given as,

(y - 52) = [(58 - 52) / (9 - 6)](x - 6)

y - 52 = 2x - 12

y = 2x + 40

The initial value (initial fee) for the picnic is $40. Then the correct options are A, B, and D.

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Answer:

ky - c

Step-by-step explanation:

K(Y) - C

(K*Y) - C

The distance is 295 feet from the surfers from his eyes.

Geometry is the description of figures in a space with a specific number of dimensions and types. Plane geometry is the most prevalent sort of geometry (dealing with objects like the point, lines, circles, triangles, and polygons),

According to the given question, we have attached a figure which represents the given situation.

Let the distance would be x from the surfers from his eyes

As per the figure, using the sine ratio to find x:

sin 29° = perpendicular/hypotenuse

Substitute the known values and solve for x:

sin 29° = 143/x

0.4848 = 143/x

x = 294.96

x ≈ 295 feet

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The circles with the specified angle of internal sectors, indicates that we get the following arc and radial lengths;

2. m∠ADC = 160°

m∠BDC = 160°

3. Length of [tex]\widehat{CB}[/tex] ≈ 11.17 inches

4. Length of [tex]\widehat{ABC}[/tex] ≈ 13.96 inches

5. a. The radius of ⊙ Q ≈ 14.324 inches

The radius is the straight line extending from the circle center to the circumference. The radius is the shortest distance from the circle center to the circumference of the circle.

Angle ∠ADC is congruent to ∠BDC in the circle with center D

∠ADC ≅ ∠BDC

2. ∠ADC ≅ ∠BDC, therefore;

m∠ADC = m∠BDC

The angle sum property of the angle at the center of a circle, indicates that we get;

40° + m∠ADC + m∠BDC = 360°

Therefore by plugging in m∠ADC = m∠BDC, we get;

40° + m∠ADC + m∠ADC = 360° (substitution property)

40° + 2 × m∠ADC = 360°

2 × m∠ADC = 360° - 40° = 320°

m∠ADC = 320° ÷ 2 = 160°

m∠ADC = 160° = m∠BDC

m∠BDC = 160°

3. The length of the arc [tex]\widehat{CB}[/tex], can be obtained from the proportion of the circumference of the circle D represented by the sector BDC as follows;

Length of the arc [tex]\widehat{CB}[/tex] = ((m∠BDC)/360°) × 2·π·r

Where;

r = The radius of the circle

The radius of the circle, r = 4 inches

Therefore; Length of the arc [tex]\widehat{CB}[/tex] = (160°/360°) × 2 × π × 4 ≈ 11.17

4. The length of the arc [tex]\widehat{ABC}[/tex] can be found as follows;

The angle at the center of the arc [tex]\widehat{ABC}[/tex] = 40° + m∠BDC

Therefore; The angle at the center of the arc [tex]\widehat{ABC}[/tex] = 40° + 160° = 200°

5. The length of the arc [tex]\widehat{AB}[/tex] = 15 inches

The angle formed by the sides AQ and BQ of the sector AQB = 60°

Therefore, we get;

length of the arc [tex]\widehat{AB}[/tex] = (60°/360°) × 2 × π × r = 15 inches

r = 15/((60°/360°) × 2 × π) ≈ 14.324

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The Venn diagram shows that the number of students who offer accounting is 30 and offer Accounting and Economics are only 5.

It should be noted that a Venn diagram is an illustration which uses circles to show the relationship between the objects.

We are given that class of 50 students, the number of students who offer accounting is twice as the number who offer Economics 10 students offer neither of the two subjects and 5 students offer both subjects

The number of students who offer Economics are;

= 10 + 5

= 15

Since accounting is twice as the number who offer Economics.

The number of students who offer accounting are;

= 25 + 5

= 30

The number of students who offer only one subject will be as follows;

= 25 + 10

= 35

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Answer:

-3

Step-by-step explanation:

Answer:

28 lawns

Step-by-step explanation

If there is 7 lawns for 4 hours there will be 14 lawns in 8 hours. and 28 lawns in 16 hours

The value of y is -2.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2 (y + 6) = 8

Using the distributive operation of multiplication over addition.

2y + 12 = 8

2y = 8 - 12

2y = -4

y = -2

Thus,

y = -2.

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The correct answer is a) No you cannot, because the lower boundary of the confidence interval is .131, which is less than .30, and so the true correlation could be less than .30.

Correlation analysis allows us to examine the strength, direction, and nature of the relationship between two variables, and to determine whether or not there is a statistically significant association between them.

Based on the information given, there appears to be a positive correlation between time spent exercising and test scores. This means that as the time spent exercising increases, the test scores also tend to increase. However, we cannot determine the strength or causality of this correlation without additional information or analysis. It is possible that other factors could be influencing both variables or that there could be confounding variables affecting the relationship.

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Correct question:

Assume a researcher found that the correlation between a test she had developed and exam performance was .5 in a study of 25 students. She had previously been informed that correlations under .30 are considered unacceptable. The 95% confidence interval was [0.131, 0.747]. Can you be confident that the true correlation is at least 0.30?

Analyzing a distribution's form and the placements of its mean, median, and mode in relation to one another can reveal its symmetry.

Therefore by analyzing a distribution's form and the placements of its mean, median, and mode in relation to one another can reveal its symmetry. The following techniques can be used to determine a distribution's symmetry: Examining a distribution's histogram, box plot, or probability density function visually is one technique to identify a distribution's symmetry. If the distribution's shape appears to be symmetrical, it probably is. The subjective nature of this approach means that it might not give an accurate indication of symmetry.

Skewness is a measurement of a distribution's asymmetry. It may be calculated manually or with the aid of statistical tools. Examining a distribution's histogram, box plot, or probability density function visually is one technique to identify a distribution's symmetry. If the distribution's shape appears to be symmetrical, it probably is. Skewness is zero for a symmetric distribution. When the skewness is positive, the distribution is skewed to.

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The total amount that Jimmy has saved is $420.

Ratio shows the relationship between two or more numbers. It is the  number of times that one value is contained within other value.

Total amount saved = (sum of ratios x total value of R5 saved) / ratio that represents R5 saved

Sum of ratios = 2 + 5 + 7 = 14

Total value of R5 saved = 12 x 5 = R60

= (14 x 60) / 2 = $420

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The side length QR = 34 derived using the Pythagoras rule, and the following are the values of the trigonometric ratio:

sin Q = 30/34, cos Q = 16/34 , tan Q = 30/16, sin Q = 30/34, cos Q = 16/34, and tan Q = 30/16

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

QR² = 16² + 30²

QR = √(256 + 900) {take square root of both sides}

QR = √1156

QR = 34

since we have QR = 34, RS = 30, and SQ = 16, then:

Considering the angle Q for the right triangle;

sin Q = 30/34 {opposite/hypotenuse}

cos Q = 16/34 {adjacent/hypotenuse}

tan Q = 30/16 {opposite/adjacent}

Considering the angle R for the right triangle;

sin R = 16/34 {opposite/hypotenuse}

cos R = 30/34 {adjacent/hypotenuse}

tan R = 16/30 {opposite/adjacent}

Therefore, the side length QR = 34 derived using the Pythagoras rule, and the following are the values of the trigonometric ratio:

sin Q = 30/34, cos Q = 16/34 , tan Q = 30/16, sin Q = 30/34, cos Q = 16/34, and tan Q = 30/16.

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Answer:

B isa the answer for me it might be wrong for you or switch them

Step-by-step explanation:

factorials with algebraic expressions still be correct if you substitute the letter with a number.

Factorial is a mathematical operation denoted by the exclamation mark (!). It is used to find the product of all positive integers from 1 to a given number. For example, the factorial of 4 (written as 4!) is:

4! = 4 × 3 × 2 × 1 = 24

Given by the question.

if you substitute a numerical value for the algebraic expression, the resulting factorial can be computed and evaluated as a numerical expression.

For example, consider the factorial expression n! where n is an algebraic expression such as n = x + 2. Substituting a numerical value for x, say x = 3, we get n = 3 + 2 = 5, and hence we can compute 5! = 5 x 4 x 3 x 2 x 1 = 120.

Similarly, if we have an expression like (n+1)! /(n-1)! where n is an algebraic expression, we can substitute a numerical value for n and compute the resulting value. For example, if we substitute n = 4, we get (4+1)!/(4-1)! = 5!/3! = (5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 60.

It's important to note that substituting numerical values for algebraic expressions only works if the resulting expression is well-defined and doesn't lead to any undefined or indeterminate forms (such as division by zero).

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Answer: Jacinda has 4 cookies left over.

Step-by-step explanation:

If Jacinda divides 19 cookies into 5 equal piles using as many cookies as possible, but has some left over, we can use integer division to determine how many cookies are in each pile. Integer division divides two numbers and rounds down to the nearest integer. In this case, the number of cookies in each pile is:

19 cookies ÷ 5 piles = 3 with a remainder of 4

Answer: 4

Step-by-step explanation:

Based on the given conditions, formulate: 19-5

Calculate the sum or difference: 14

If a < b, we can say that b is to the right of a on the number line. In other words, a is to the left of b.

A number line is a horizontal line with evenly spaced number increments. The numbers on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, such as plotting a point.

If a b, then b is to the right of a on the number line. To put it another way, an is to the left of b.

This is because the number line depicts the order of real numbers, with smaller numbers to the left and larger numbers to the right. Because an is less than b, it is a smaller number and must be to the left of b on the number line.

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The approximate area of the remaining part of the fabric is given as 17.415 square feet

To get the solution, we have to solve for the area of the square shape and the area of the circle

The area of a square is given as A = a²

The area of a circle is given as πr²

We would have area of remaining fabric as

a² -  πr²

The square has its sides as a = 9 cm

the circle has π = 3.14

we  are to find the radius. But first we have to determine the diameter

The circle runs from one end of the square to the other end. This should be the diameter, because it is the length of the square as well

Diameter = 9 cm

radius = diameter / 2

= 9 / 2

= 4.5

When we put the values in the formula a² -  πr² we would have

9² - 3.14 * 4.5²

81 - 3.14 * 20.25

81 - 63.585

= 17.415

The area of the remaining part after the circle is cut is 17.415 square feet

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Answer:W+6

Step-by-step explanation:

The measure of the angle m∠C = m∠H is equal to 35°.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, Triangle ABC is similar to triangle FGH.

Therefore, m∠A = m∠F = 63° and m∠B = m∠G = 82°.

We know the sum of the measure of all the interior angles in a triangle is 180°.

Therefore, m∠C = m∠H = 180° - 63° - 82° = 35°.

Congruency can be applied to any two dimensional figure, For example,

Two circles are congruent if they have the same radius length.

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The value of DAC in the figure would be 47 degrees.

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

The angles EAD, DAC and CAB are all on a straight line which means they add up to 180 degrees.

Angle CAB is in a triangle which means all the angles add up to 180 degrees and the value of this angle is:

= 180 - 80 - 57 = 43 degrees

The value of DAC would then be;

= 180 - EAD - CAB

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

= 180 - 90 - 43

= 90 - 43  = 47 degrees

Hence, the angle is 47 degrees

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Multistage sampling is a probability sampling technique that involves sampling in stages or multiple steps. In this technique, a large population is divided into smaller subgroups, and then a random sample is selected from each subgroup.

Here is an example of multistage sampling:

Suppose we want to conduct a study on the prevalence of a certain disease among high school students in a particular country. The population of high school students in the country is very large, so it is not feasible to sample all of them. Instead, we can use multistage sampling to select a representative sample.

In the first stage, we randomly select a certain number of schools from different regions of the country. Let's say we select 20 schools.

In the second stage, we randomly select a certain number of classes from each of the selected schools. Let's say we select 2 classes from each of the 20 schools, resulting in a total of 40 classes.

In the third stage, we randomly select a certain number of students from each of the selected classes. Let's say we select 10 students from each of the 40 classes, resulting in a total of 400 students.

This process of selecting a sample in stages is an example of multistage sampling. By selecting schools, classes, and students in a random and systematic way, we can obtain a representative sample of high school students in the country, which can be used to estimate the prevalence of the disease.

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