Since ABCD is an isosceles trapezoid, we know that AB = CD. Additionally, we know that AD = BC. Therefore, we can set up two equations:
AB = CD
AD = BC
Using the fact that B = x + 10 and C = 2x - 30, we can substitute those values into the equations:
AB = CD
x + 10 + AD = 2x - 30 + BC
Since AD = BC, we can simplify the second equation to:
x + 10 + AD = 2x - 30 + AD
x + 10 = 2x - 30
x = 40
Now that we know x, we can find the measures of angles B and C:
B = x + 10 = 50
C = 2x - 30 = 50
Since ABCD is an isosceles trapezoid, we know that angles B and C are congruent. Therefore, each of them measures 50 degrees. Since the sum of the angles in a quadrilateral is 360 degrees, we can set up the equation:
A + B + C + D = 360
Substituting in the values we have:
A + 50 + 50 + D = 360
Simplifying the equation:
A + D = 260
Since ABCD is an isosceles trapezoid, we know that angles A and D are congruent. Therefore, we can set up the equation:
A + D = 2D
Substituting in the value we have:
2D = 260
Simplifying the equation:
D = 130
Therefore, the measure of angle D is 130 degrees.
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12. eight people are to be seated around a table; the chairs don't matter, only who is next to whom, but right and left are different. two people, x and y, are seated next to each other. how many seating arrangements are possible?
There are 1440 possible seating arrangements for eight people with X and Y sitting next to each other around the table.
To find the number of possible seating arrangements for eight people with X and Y sitting next to each other, follow these steps:
1. Treat X and Y as a single unit since they are seated next to each other. This means we now have 7 "units" to arrange (6 individual people and 1 unit of X and Y together).
2. Determine the number of arrangements for these 7 units around the table. Since the chairs don't matter and right and left are different, we use the formula for circular permutations: (n-1)! = (7-1)! = 6! = 720 possible arrangements.
3. Within the X and Y unit, there are 2 possible arrangements: X can be on the left of Y or on the right. So, we need to multiply the number of arrangements by the arrangements within the X and Y unit: 720 * 2 = 1440.
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A baker has 3 eggs to use for making cakes. Each cake takes 5 eggs.
How many cakes will the baker be able to make?
The answer is simply 0 cakes. The baker has 3 eggs, and each cake takes 5 eggs, which means the baker cannot make a full cake with just 3 eggs.
Therefore, the baker cannot make any full cakes. However, if the baker is allowed to use fractions of eggs, then the baker can make partial cakes. For example, if the baker uses 2/5 of an egg per cake, then the baker can make 3/(2/5) = 7.5 cakes (where 2/5 of an egg is equal to 1 cake). However, since the baker cannot use fractions of eggs, the answer is simply 0 cakes.
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how many simple random samples of size 4 can be selected from a population of size 8? group of answer choices 32 4 1680 70
there are 70 simple random samples of size 4 that can be selected from a population of size 8. Your answer is 70.by using combination concept
There are 70 simple random samples of size 4 that can be selected from a population of size 8.
To determine how many simple random samples of size 4 can be selected from a population of size 8, we can use the combination formula, which is:
C(n, k) = n! / (k!(n-k)!)
where C(n, k) is the number of combinations, n is the total population size, and k is the sample size.
In this case, n = 8 and k = 4. Plugging the values into the formula:
By following function
C(8, 4) = 8! / (4!(8-4)!)
C(8, 4) = 8! / (4!4!)
C(8, 4) = (8×7×6×5) / (4×3×2×1)
C(8, 4) = 1680 / 24
C(8, 4) = 70
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a contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. the length of one side of the garden is represented by x, and the area of the garden is 108 square meters. determine the length of the garden, in meters.
Two values result in a perimeter of 48 and an area of 108, the rectangle must have two dimensions of 18 and 6. The garden's dimensions are 18 meters and 6 meters because we use meters.
We can use these two facts to set up our equations because perimeter is the sum of all four sides (X, X, Y, Y) and area is the product of length and width (X × Y).
Given : Perimeter = 2 X + 2 Y = 48
Area = X × Y = 108
We can determine the values of x and y by solving this system of equations because we have two equations and two unknown variables. To isolate x, let's reorder the area equation as follows:
X × Y = 108
X = 108/Y
The following expression should be used in place of X in the perimeter equation:
2 X + 2 Y = 48
2(108/Y) + 2 Y = 48
By multiplying everything by Y and solving the quadratic equation, we can now determine Y's value:
2(108/Y) + 2 Y = 48
216/Y + 2 Y = 48
216 + 2 Y² = 48 Y
2 Y² - 48 Y + 216 = 0
Y² - 24 Y + 108 = 0
(Y-18)(Y-6) = 0
So y can be 18 or 6. To determine the value of x, we plug these individually into the area equation and observe that x can also be 18 or 6:
X × Y = 108
X × 18 = 108
x = 6
X × Y = 108
X × 6 =108
X = 18
Since these two values result in a perimeter of 48 and an area of 108, the rectangle must have two dimensions of 18 and 6. The garden's dimensions are 18 meters and 6 meters because we use meters.
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a pair of standard, six-sided dice are to be rolled, with the result being the sum of the top-facing numbers. what is the probability of rolling a 9
The probability of rolling a 9 is 1/9, or approximately 0.111.
To find the probability of rolling a 9 with a pair of standard, six-sided dice, we need to count the number of ways we can get a sum of 9 and divide it by the total number of possible outcomes.
There are four ways to get a sum of 9:
rolling a 3 on the first die and a 6 on the second die
rolling a 4 on the first die and a 5 on the second die
rolling a 5 on the first die and a 4 on the second die
rolling a 6 on the first die and a 3 on the second die
Each die has six possible outcomes, so there are 6 x 6 = 36 possible outcomes in total.
Therefore, the probability of rolling a 9 is 4/36 = 1/9, or approximately 0.111.
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What is the THEORETICAL probability of choosing a vowel?
Based on the experiment, what is the probability of choosing a vowel?
The THEORETICAL probability of choosing a vowel is 3/8 and the experimental probability is 36/75
What is the probability of choosing a vowel?From the question, we have the following parameters that can be used in our computation:
Vowels = Letters A, I and EVowels = Letters of the word SAPPHIREIn the letters of the word, we have
Vowels = 3
Letters = 8
By calculation, the theoretical probability of choosing a vowel is
Theoretical probability = Vowels/Letters
So, we have
Theoretical probability = 3/8
Based on the experiment, we have
Vowels = 15+9+12 = 36
Letters = 8+15+7+5+20+20 = 75
So, we have
Experimental probability = 36/75
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for which of the following is frequency analysis not useful? group of answer choices locating outliers. determining the degree of item nonresponse. understanding the relationships among multiple variables. analyzing categorical and continuous variables.
Frequency analysis is not useful for understanding the relationships among multiple variables.
Frequency analysis is a statistical technique that involves counting the frequency of each value or category within a dataset. It is useful for analyzing categorical and continuous variables and determining the degree of item nonresponse. It can also help in locating outliers, as the frequencies of unusual values can be easily identified.
However, frequency analysis alone cannot provide insights into the relationships among multiple variables, as it only focuses on the distribution of individual variables. To understand the relationships among variables, more advanced statistical techniques such as correlation analysis or regression analysis need to be employed.
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Given ∫(−6x6−4x5 5x−3)dx, evaluate the indefinite integral. Do not include +C in your answer
The indefinite integral of ∫(−6x⁶−4x⁵ + 5x −3)dx is -6x⁷/7 - 2x⁶/3 + 5x²/2 + 3x.
What is the solution of the indefinite integral?The solution of the indefinite integral of ∫(−6x⁶−4x⁵ + 5x −3)dx, is calculated as follows;
Using the power rule, we can integrate each term of the given expression as follows:
∫(−6x⁶−4x⁵ + 5x −3)dx
= -6∫x⁶ dx - 4∫x⁵ dx + 5∫x¹ dx - 3∫dx
= -6(x⁷/7) - 4(x⁶/6) + 5(x²/2) - 3x
= -6x⁷/7 - 2x⁶/3 + 5x²/2 + 3x
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Your fishing bobber oscillates in simple harmonic motion from waves in the lake where you fish. Your bobber moves a total of 1.5 inches from its high point to its low point and returns to its high point every 3 seconds. a.) Write an equation modeling the motion of your bobber if it is at its high point at t = 0. b.) After how many seconds is the bobber at the midpoint between its high point and its low point for the first time?
a) The simple harmonic motion of the bobber can be modeled by the equation:
y(t) = A sin(ωt + φ)
where y is the displacement of the bobber from its equilibrium position at time t, A is the amplitude of the oscillation, ω is the angular frequency, and φ is the phase angle.
From the given information, we know that the amplitude A of the oscillation is 1.5 inches and the period T is 3 seconds. The angular frequency is related to the period by the formula:
ω = 2π/T
Substituting the values, we get:
ω = 2π/3
The phase angle φ can be determined from the initial condition that the bobber is at its high point at t = 0. At the high point, the displacement is maximum and positive, so we have:
y(0) = A sin(φ) = A
Substituting the values, we get:
1.5 = 1.5 sin(φ)
Solving for φ, we get:
φ = sin⁻¹(1) = π/2
Substituting the values of A, ω, and φ in the equation for simple harmonic motion, we get:
y(t) = 1.5 sin(2πt/3 + π/2)
b) The midpoint between the high point and the low point of the bobber corresponds to a displacement of 0.5*A = 0.75 inches.
The bobber reaches this point twice during each period, once while going up and once while going down. We need to find the time t when the bobber is going down and reaches the midpoint for the first time.
At the midpoint, the displacement of the bobber is given by:
y(t) = 0.75
Substituting the equation for y(t), we get:
1.5 sin(2πt/3 + π/2) = 0.75
Simplifying, we get:
sin(2πt/3 + π/2) = 0.5
Using the identity sin(π/6) = 0.5, we can rewrite the equation as:
sin(2πt/3 + π/2) = sin(π/6)
The general solution for this equation is:
2πt/3 + π/2 = π/6 + 2πk or 2πt/3 + π/2 = 5π/6 + 2πk
where k is an integer.
Solving for t in each case, we get:
t = (π/18 - π/2)/ (2π/3) + k or t = (5π/6 - π/2)/ (2π/3) + k
Simplifying, we get:
t = 1/4 + k/3 or t = 5/4 + k/3
The first solution corresponds to the time when the bobber is going down and reaches the midpoint for the first time, so we have: t = 1/4 seconds.
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Cereal boxes - A large box of corn flakes claims to contain 515 grams of cereal. Since cereal boxes must contain at least as much product as their packaging claims, the machine that fills the boxes is set to put 523 grams in each box. The machine has a known standard deviation of 3 grams and the distribution of fills is known to be normal. At random intervals throughout the day, workers sample 3 boxes and weigh the cereal in each box. If the average is less than 520 grams, the machine is shut down and adjusted. How often will the workers make a Type I error with this decision rule and the hypotheses
Probability of a type I error = ...
The probability of a Type I error is extremely small, which means that the workers are unlikely to make a mistake by shutting down the machine too often when the true mean weight of cereal in the boxes is equal to or greater than 520 grams.
What is probability?The probability is a metric for determining how likely an event is to occur. It assesses the event's certainty. P(E) = Number of Favorable Outcomes / Number of Total Outcomes is the probability formula.
To calculate the probability of a Type I error, we first need to specify the null and alternative hypotheses.
Null hypothesis: The true mean weight of cereal in the boxes is equal to or greater than 520 grams.
Alternative hypothesis: The true mean weight of cereal in the boxes is less than 520 grams.
Let's denote the true mean weight of cereal in the boxes as μ. Under the null hypothesis, we have μ ≥ 520.
We can use the fact that the distribution of fills is normal with a known standard deviation of 3 grams to find the sampling distribution of the sample mean weight of cereal in a sample of size 3. Since we are sampling without replacement, we need to use the formula for a finite population:
Standard error of the sample mean = standard deviation / sqrt(sample size) * sqrt(N-n/N-1)
where N is the population size (the total number of boxes filled), n is the sample size (3 in this case), and N-1 is the degrees of freedom.
We know that the population mean is μ and the population standard deviation is 3 grams. We also know that the machine is set to put 523 grams in each box, so N (the population size) is equal to 515 / 523 times the number of boxes filled. Let's assume that the machine fills 10,000 boxes per day, so N = 9,856.
Plugging in the values, we get:
Standard error of the sample mean = 3 / √(3) * √(9,856-3/9,855) = 1.539 grams
Next, we need to find the critical value of the sample mean weight that separates the rejection region (when we reject the null hypothesis) from the acceptance region (when we fail to reject the null hypothesis).
Since the alternative hypothesis is one-tailed (we are only interested in the left tail), we can use a one-tailed t-test with a significance level of 0.05. The degrees of freedom is n-1 = 2.
Using a t-table or a calculator, we find the critical value to be -2.353.
Finally, we can calculate the probability of a Type I error as follows:
Probability of Type I error = P(reject null | null is true)
= P(sample mean < critical value | μ ≥ 520)
= P(z < (critical value - μ) / standard error of the sample mean | μ ≥ 520)
= P(z < (-2.353 - 520) / 1.539 | μ ≥ 520)
= P(z < -9.747 | μ ≥ 520)
= extremely small (close to 0)
Therefore, the probability of a Type I error is extremely small, which means that the workers are unlikely to make a mistake by shutting down the machine too often when the true mean weight of cereal in the boxes is equal to or greater than 520 grams.
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An article reported on a school​ district's magnet school programs. Of the 1928 qualified​ applicants, 986 were​ accepted, 297 were​ waitlisted, and 645 were turned away for lack of space. Find the relative frequency for each decision made and write a sentence summarizing the results.
51.1% of the qualified applicants were accepted into the magnet school programs, 15.4% were waitlisted, and 33.5% were turned away due to a lack of space.
To find the relative frequency for each decision made by the school district's magnet school programs, we need to divide the number of applicants for each decision by the total number of qualified applicants.
Accepted applicants: 986 / 1928 = 0.511 or 51.1%
Waitlisted applicants: 297 / 1928 = 0.154 or 15.4%
Turned away applicants: 645 / 1928 = 0.335 or 33.5%
In summary, 51.1% of the qualified applicants were accepted into the magnet school programs, 15.4% were waitlisted, and 33.5% were turned away due to a lack of space.
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(L3) The orthocenter will lie at the vertex of the right angle in a(n) _____ triangle.
(L3) The orthocenter will lie at the vertex of the right angle in a(n) right triangle.
. In a right triangle, the orthocenter will not always lie at the vertex of the right angle. The location of the orthocenter depends on the type of right triangle. If the right triangle is also an isosceles triangle, then the orthocenter will lie at the vertex opposite the hypotenuse. If the right triangle is a scalene triangle, then the orthocenter will not lie at any vertex of the triangle. Instead, it will lie outside the triangle on the extension of one of the sides.
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Find x please help me
Answer:
x = 73°
Step-by-step explanation:
the inscribed angle x is half the measure of the central angle, that is
x = [tex]\frac{1}{2}[/tex] × 146° = 73°
A teacher wants to know how many students like to dance in his school. Which of the following samples would be most representative of the entire school?A teacher wants to know how many students like to dance in his school. Which of the following samples would be most representative of the entire school?
The sample that would be most representative of the entire school is 20 random students in the hall.
Selecting the sample that best represents the entire schoolFrom the question, we have the following parameters that can be used in our computation:
A teacher wants to know the number of students that like to dance in his school.
If they are coming out of a ball, the sample can be biased because they (more than likely) like to dance.
Also, the cheerleader are only a small population (cheerleading is dance oriented as well.)
Hence, the sample that would be most representative of the entire school is 20 random students in the hall.
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18
Solve for c.
с
43%
13
c = [?]
Round your final answer
to the nearest tenth.
Law of Cosines: c² = a² + b² - 2ab-cosC
Length of c
Enter
The length c of the triangle is 12.3 units.
How to solve for the length c of the triangle?The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given.
c² = a² + b² -2ab cosC
where a, b and c are the lengths and A, B and C are the angles
Using the formula:
c² = a² + b² -2ab cosC
c² = 18² + 13² - (2×18×13 × cos43)
c² = 150.73
c = √150.73
c = 12.3 units
Therefore, the length of c is 12.3 units.
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A number is rounded 2 decimal places the result is 3.87
Using inequality write error interval for n
The error interval for the number n as an inequality is 3.85 ≤ n ≤ 3.89
Writing the error interval for the number nFrom the question, we have the following parameters that can be used in our computation:
A number is rounded 2 decimal places the result is 3.87
Represent the number with n
So, we have
n = 3.87 i.e. 3.86 to 3.88
To write the error interval of n, we do the following:
Calculate the difference between the intervals
difference = 3.88 - 3.86
difference = 0.02
Divide by 2
difference/2 = 0.01
So, we have
Error interval: 3.86 - 0.01 ≤ n ≤ 3.88 = 0.01
Evaluate
3.85 ≤ n ≤ 3.89
Hence, the error interval for the number n is 3.85 ≤ n ≤ 3.89
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Could you please help me out? I have an exam this week and the topics are about this.
Answer:
Answer is :
x=45.5
y=129.5
Sorry for bad handwriting
Answer:
x + 2x + 4 + y = 270, so 3x + y = 266
x + y + 5 = 180, so x + y = 175
-----------------
2x = 91
x = 40.5, y = 134.5
Find the volume of the solid whose base is the region inside the circle x² + y² = 9 if cross sections taken perpendicular to the y‐axis are squares.
The volume of the solid is 12sqrt(3).
To find the volume of the solid whose base is the region inside the circle x² + y² = 9, we need to integrate the area of each square cross-section perpendicular to the y-axis.
Let's consider a cross-section of the solid taken at y = k, where k is a value between -3 and 3 (the range of y-values for the circle x² + y² = 9). The width of the cross-section is the distance between the x-coordinates of the intersection points of the circle with the line y = k. These intersection points are (sqrt(9 - k²), k) and (-sqrt(9 - k²), k). Since the cross-section is a square, its area is equal to the square of the width, which is sqrt(9 - k²) - (-sqrt(9 - k²)) = 2sqrt(9 - k²).
Therefore, the volume of the solid is given by the integral of the area of each cross-section as follows:
V = ∫(-3 to 3) 2sqrt(9 - y²) dy
To evaluate this integral, we can use the substitution u = 9 - y², du = -2y dy:
[tex]V = \int (9 to 0) \sqrt{u} du/(-2)\\= -1/2 \times [2/3 \times u^{(3/2)}](9, 0)\\= 2/3 \times (27\sqrt{3} - 9\sqrt{9} )\\= 2/3 \times 18\sqrt{3} \\= 12\sqrt{3}[/tex]
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*If a statistic is designed for nominal level of measurement, then it would be appropriate to use that statistic on data at all these levels of measurement EXCEPT:
a. ordinal.
b. interval.
c. ratio.
***d. all of the answers are levels of measurement upon which it would be appropriate to use a statistic designed for nominal level.
Statistical methods designed for nominal data are not appropriate for interval level data, which involves meaningful differences between values.
The correct answer is (b) interval.
Nominal level of measurement is the lowest level of measurement that involves categorizing data into distinct groups or classes. Examples of nominal data include gender, race, religion, and marital status.
Statistical methods designed for nominal data include mode and frequency distribution. These methods are appropriate for nominal, ordinal, and interval data. However, it would not be appropriate to use them for ratio data, which involves the presence of a true zero point.
Therefore, option (d) is incorrect. Option (b) is the correct answer, as statistical methods designed for nominal data are not appropriate for interval level data, which involves meaningful differences between values.
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Complete Quetion:
If a statistic is designed for nominal level of measurement, then it would be appropriate to use that statistic on data at all these levels of measurement
a. ordinal.
b. interval.
c. ratio.
d. all of the answers are levels of measurement upon which it would be appropriate to use a statistic designed for nominal level.
Find the approximate volume of the sphere. Use 3.14 for pi, Don't round.
The approximate volume of the sphere with a radius of 3 inches is 113.04 cubic inches.
What is the volume of the sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).
Given that: radius r = 3 in
Substituting r = 3 inches and π = 3.14
Volume = (4/3)πr³
Volume = (4/3) × 3.14 × (3 in)³
Volume = (4/3) × 3.14 × 27 in³
Volume = 113.04 in³
Therefore, the volume is 113.04 cubic inches.
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Lua is creating rectangular prism. The base of her prism is showen below. She plans to have a height of 7 cubes.What will the volume of the completed figure be ?
The volume of the completed rectangular prism that have a height of 7 cubes will be 63 cubic units.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism. In this case, the base of the prism has 3 x 3 cubes, which means the length and width are both 3 cubes.
Therefore, l = 3 and w = 3. The height of the prism is given as 7 cubes. Thus, h = 7.
Substituting the given values in the formula for volume, we get:
V = lwh
= 3 x 3 x 7
= 63
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PLS HELP ASAP!!!!!??????
√2+√2
-2√18+2√2
Answer:
Step-by-step explanation:
√2+√2= 2√2=√8
-2√18+2√2= -2√9*2 +2√2= -6√2+2√2=-4√2=-√32
the soup company wants to package its soup in a new can. the company has four choices for the cans. which can will provide the largest volume? soup can choices can radius height a 2 inches 6 inches b 2.5 inches 5 inches c 3 inches 4 inches d 3.2 inches 3 inches recall the formula v
The can that will provide the largest volume is Can C, with a volume of 36π cubic inches.
To determine which can will provide the largest volume, we need to use the formula for the volume of a cylinder, which is V = πr^2h (where V is volume, r is radius, and h is height).
Using the formula, we can calculate the volumes of each can as follows:
- Can A: V = π(2)^2(6) = 24π cubic inches
- Can B: V = π(2.5)^2(5) = 31.25π cubic inches
- Can C: V = π(3)^2(4) = 36π cubic inches
- Can D: V = π(3.2)^2(3) = 30.528π cubic inches
Therefore, the can that will provide the largest volume is Can C, with a volume of 36π cubic inches.
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can someone help mee w this one tooo:)
Answer:
the answer will be C have a great day
Is 1 an irrational number?
Answer:
The number 1 can be classified as: a natural number, a whole number, a perfect square, a perfect cube, an integer. This is only possible because 1 is a RATIONAL number.
Step-by-step explanation:
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The circle has a radius of 4cm.
The vertices of the rectangle lie on the circumference of the circle.
The rectangle has a width of 6 cm.
Calculate the height of the rectangle
If circle is having radius as 4 cm, then the length of the rectangle inscribed in circle is 5.29 cm.
The "Rectangle" is inscribed in the circle, So, its diagonal will be equal to the diameter of circle.
So, diagonal of rectangle has a length of = 2 × radius,
⇒ Diagonal = 2×4 = 8 cm.
We also know that width of rectangle is = 6 cm. To find length of rectangle, we use the property, which states that in "right-triangle", the sum of the squares of the "length" and "width" is equal to the square of "diagonal".
Let "h" denote "length" of rectangle which is inscribed in circle,
So, We have, h² + 6² = 8²,
⇒ h² + 36 = 64,
⇒ h² = 28,
⇒ h ≈ 5.29,
Therefore, the length of rectangle is approximately 5.29 cm.
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The given question is incomplete, the complete question is
The circle has a radius of 4cm. The vertices of the rectangle lie on the circumference of the circle. The rectangle has a width of 6 cm.
Calculate the length of the rectangle.
janet is planning to open a small two-bay car-wash operation, and she must decide how much space to provide for waiting cars. janet estimates that customers would arrive ran- domly (i.e., a poisson input process) with a mean rate of 1 every 5 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. the time that can be attributed to washing one car has an exponential distribution with a mean of 4 minutes. compare the expected fraction of potential customers that will be lost because of inadequate waiting space if (a) 2 spaces, and (b) 4 spaces were provided
If Janet provides 4 waiting spaces, the expected fraction of potential customers that will be lost due to inadequate waiting space is 0.0042, or about 0.42%.
What is the fraction?
A fraction is a mathematical representation of a part of a whole, where the whole is divided into equal parts. A fraction consists of two numbers, one written above the other and separated by a horizontal line, which is called the fraction bar or the vinculum.
To determine the expected fraction of potential customers that will be lost due to inadequate waiting space, we need to use queuing theory to model the car wash operation.
Let's consider the two scenarios:
(a) 2 waiting spaces:
In this case, we can model the system as an M/M/2 queue, where arrivals follow a Poisson process with a rate λ = 1/5 customers per minute and service times follow an exponential distribution with rate μ = 1/4 cars per minute.
The utilization factor of the system is ρ = λ/2μ = (1/5)/(2*(1/4)) = 0.4, which is less than 1, so the system is stable.
Using Little's Law, we can calculate the expected number of customers in the system:
L = λ * W
where L is the expected number of customers in the system, λ is the arrival rate, and W is the expected time a customer spends in the system (i.e., waiting time plus service time).
The expected waiting time in an M/M/2 queue can be calculated as:
Wq = (2ρ)/(2 - ρ) * (1/λ)
where Wq is the expected waiting time in the queue.
The expected time in the system can be calculated as:
W = Wq + (1/μ)
Substituting the values, we get:
Wq = (2*0.4)/(2-0.4) * (1/1/5) = 1 minute
W = 1 + 1/4 = 1.25 minutes
The expected fraction of potential customers that will be lost due to inadequate waiting space can be calculated as:
P(lost) = ρ² / (1 - ρ) * (1 - 2ρ⁽ⁿ⁻¹⁾ + ρⁿ)
where n is the number of waiting spaces. In this case, we have n = 2, so:
P(lost) = 0.4² / (1 - 0.4) * (1 - 2*0.4⁽²⁻¹⁾+ 0.4²) = 0.196
Therefore, if Janet provides 2 waiting spaces, the expected fraction of potential customers that will be lost due to inadequate waiting space is 0.196, or about 19.6%.
(b) 4 waiting spaces:
In this case, we can model the system as an M/M/4 queue, where arrivals follow a Poisson process with rate λ = 1/5 customers per minute and service times follow an exponential distribution with rate μ = 1/4 cars per minute.
The utilization factor of the system is ρ = λ/4μ = (1/5)/(4*(1/4)) = 0.25, which is less than 1, so the system is stable.
Using the same formulas as before, we can calculate:
Wq = (4*0.25)/(4-0.25) * (1/1/5) = 0.625 minute
W = 0.625 + 1/4 = 0.875 minutes
P(lost) = 0.25² / (1 - 0.25) * (1 - 2*0.25⁽⁴⁻¹⁾ 0.25⁴) = 0.0042
Therefore, if Janet provides 4 waiting spaces, the expected fraction of potential customers that will be lost due to inadequate waiting space is 0.0042, or about 0.42%.
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at travis' birthday party, `\frac{3}{4}` of his birthday cake was eaten. the next day, travis ate `\frac{1}{3}` of the remaining cake. what fraction of the whole cake did travis eat the next day
Travis ate 1/12 of the whole cake the next day
A fraction represents a part of a whole. In this case, the whole cake represents the whole, and the part that was eaten represents the fraction. When we say that 3/4 of the cake was eaten, it means that out of the whole cake, 3/4 or three-fourths of the cake was consumed.
Travis ate 1/3 of the remaining cake the next day.
This means that after 3/4 of the cake was eaten, there was 1/4 of the cake remaining. Travis ate 1/3 of that remaining 1/4 of the cake, which can be written as
=> 1/3 x 1/4.
To simplify this fraction, we multiply the numerators (1 x 1) and the denominators (3 x 4), giving us 1/12.
We can write this fraction as a percentage, which is 8.33%. To summarize, fractions are used to represent parts of a whole, and in this case, Travis ate 1/12 or 8.33% of the whole cake the next day.
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The middle of {1, 2, 3, 4, 5} is 3. The middle of {1, 2, 3, 4} is 2 and 3. Select the true statements (Select ALL that are true)
An even number of data values will always have one middle number.
An odd number of data values will always have one middle value
An odd number of data values will always have two middle numbers.
An even number of data values will always have two middle numbers.
In a case whereby the middle of {1, 2, 3, 4, 5} is 3 and the middle of 1, 2, 3, 4} is 2 and 3 the true statements are;
An odd number of data values will always have one middle valueAn even number of data values will always have two middle numbers.What are true statements?A statement can be considerd to be true ,in a case whereby if what it asserts is the case, in the same dimension it can be considered to be false if what it asserts is not the case.
Instance of this can be seen above whereby An odd number of data values will always have one middle value and An even number of data values will always have two middle numbers.
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Do I find the HCF for this or the LCM?? Please help quickly
Step-by-step explanation:
You are looking for the LCM of 15 and 42
