The required probability for the given rate of calls per hour using Poisson distribution is ,
Probability of calls rate are 20 per hour is 0.734
Probability of calls rate are 30 per hour is 0.654..
Probability of 20 per hour is higher in comparison of 30 per hour.
Yes . Manager should consider second operator.
Actual rate of calls = 20 per hour,
Expected number of calls in a 15-minute period is,
= (20/60) × 15
= 5
The probability of getting 9 or more calls in a 15-minute period is,
P(X ≥ 9) = 1 - P(X ≤ 8)
Using the Poisson distribution with λ = 5, we have,
P(X ≤ 8)
= e^(-5) × (5^0/0!) + e^(-5) ×(5^1/1!) + ... + e^(-5) × (5^8/8!)
= 0.266
Probability of getting 9 or more calls in a 15-minute period is,
P(X ≥ 9)
= 1 - P(X ≤ 8)
= 1 - 0.266
= 0.734
If the rate of calls is really 30 per hour.
Expected number of calls in a 15-minute period is,
= (30/60) × 15
= 7.5
Probability of getting 9 or more calls in a 15-minute period is,
P(X ≥ 9) = 1 - P(X ≤ 8)
Using the Poisson distribution with λ = 7.5, we have,
P(X ≤ 8)
= e^(-7.5) * (7.5^0/0!) + e^(-7.5) * (7.5^1/1!) + ... + e^(-7.5) * (7.5^8/8!)
= 0.346
Probability of getting 9 or more calls in a 15-minute period is,
P(X ≥ 9)
= 1 - P(X ≤ 8)
= 1 - 0.346
= 0.654
Based on the calculations in parts a and b,
Probability of getting 9 or more calls in a 15-minute period is higher .
If the rate of incoming calls is 20 per hour (0.734) compared to if the rate is 30 per hour (0.654).
Based on the calculations,
Current operator can handle the call volume with a high probability if the call rate is 20 per hour.
However, if the call rate is 30 per hour, there is a relatively high probability of needing a second operator.
Manager should consider hiring a second operator if the rate of incoming calls is expected to be 30 per hour or higher.
Therefore, the probability of the given situation are,
For the rate of calls 20 per hour is 0.734.
For the rate of calls 30 per hour is 0.654.
Probability of 20 per hour is higher than 30 per hour.
Yes , manager should consider second operator is call rate are 30 per hour or higher.
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3 c ≈ mL? Round to the nearest hundredth if necessary.
By using conversion factor the solution for 3 c ≈ 709.78mL.
What is conversion factor?
A conversion factor is a ratio that is used to convert one unit of measurement to another. It is a mathematical expression that relates two different units of measure for the same quantity. By using conversion factors, we can easily convert between different units and make calculations and comparisons more convenient and meaningful.
The conversion factor between 3 c (cups) and mL (milliliters) is approximately 709.76, which means that 3 cups is approximately equal to 709.76 milliliters.
To convert from cups to milliliters, you can multiply the number of cups by the conversion factor:
3 cups x 236.59 mL/cup ≈ 709.76 mL
Rounding to the nearest hundredth, we get:
3 cups x 236.59 mL/cup ≈ 709.78 mL
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malik's new game, marble zoom, came with a big bag of 200 assorted marbles. he wants to see what the marbles look like, so he randomly picks one from the bag, records its appearance, and then puts it back in. he does this 25 times and gets 6 ribbon swirl, 9 solid, 4 frosted, and 6 clear marbles. based on the data, what is the probability of choosing a frosted marble?
The probability of choosing a frosted marble based on the given data is 0.16
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event (i.e., an event that will never occur) and 1 represents a certain event (i.e., an event that will always occur)
The probability of choosing a frosted marble can be calculated by dividing the number of frosted marbles by the total number of marbles
P(frosted) = number of frosted marbles / total number of marbles
In this case, Malik randomly chose 25 marbles from the bag, so the total number of marbles is 25. He recorded 4 frosted marbles, so
P(frosted) = 4 / 25
Simplifying, we get
P(frosted) = 0.16
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a television channel conducts a study on the number of tvs per household in their service area. out of 1000 households surveyed, 350 have one tv, 500 have two tvs, 120 have three tvs and 30 have four tvs. how many tvs does each household have on average?
Answer:
Step-by-step explanation: The answer is to be calculated with help of taking out averages of the households' Tvs.
In order to calculate the expected value we multiply each value of the random variable by its probability and then add the results.
(1 TV times 350/1000) + (2 TV times 500/1000) + (3 TV times 120/1000) + (4 TV times 30/1000) = 1.83.
on average, each household has 1.83 TVs.
As per the data given, a television channel conducted a study on the number of TVs per household in their service area. Out of 1000 households surveyed, 350 have one TV, 500 have two TVs, 120 have three TVs and 30 have four TVs. We need to determine the number of TVs each household has on average.To calculate the average number of TVs, we need to calculate the total number of TVs and divide that by the number of households.
Totals TVs = (Number of households with 1 TV × 1) + (Number of households with 2 TVs × 2) + (Number of households with 3 TVs × 3) + (Number of households with 4 TVs × 4)Total TVs
= (350 × 1) + (500 × 2) + (120 × 3) + (30 × 4)Total TVs = 350 + 1000 + 360 + 120
Total TVs = 1830
Average number of TVs per household = Total TVs / Number of households
Average number of TVs per household = 1830 / 1000
Average number of TVs per household = 1.83
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what is the probability that an international flight leaving the united states is delayed in departing given that the flight is transpacific flight
The probability that an international flight leaving the US is delayed in departing given that the flight is a transpacific flight is approximately 0.1964.
We can use Bayes' theorem to calculate the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight. Bayes' theorem states that:
P(D|P) = P(P|D) * P(D) / P(P)
where P(D|P) is the probability that a flight is delayed given that it is transpacific, P(P|D) is the probability that a flight is transpacific given that it is delayed, P(D) is the probability of a flight being delayed, and P(P) is the probability of a flight being transpacific.
Using the given values, we can calculate:
P(P and D) = 0.11 (the probability that a flight is both transpacific and delayed)
P(P) = 0.56 (the probability that a flight is transpacific)
P(D) = 0.28 (the probability that a flight is delayed)
To find P(D|P), we need to calculate P(P and D) / P(P):
P(D|P) = P(P and D) / P(P) = 0.11 / 0.56 = 0.1964
Therefore, the probability that an international flight is delayed in departing is approximately 0.1964 (rounded to 4 decimal places).
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--The given question is incomplete, the complete question is given
"The probability that an international flight leaving the United States is delayed in departing (event D) is .28. The probability that an international flight leaving the United States is a transpacific flight (event P) is .56. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .11. (a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight? (Round your answer to 4 decimal places.)"--
what are the answers to these questions??
in european roulette, the wheel is divided into 37 compartments numbered 1 through 36 and 0. (in american roulette there are 38 compartments numbered 1 through 36, 0, and 00.) one-half of the numbers 1 through 36 are red, the other half are black, and the number 0 is green. find the expected value of the winnings on a $6 bet placed on red in european roulette.
The expected value of the winnings on a $6 bet placed on red in European roulette is -$0.81.
In European roulette, the probability of winning a bet on red is 18/37, and the probability of losing is 19/37. If the bet wins, the payout is even money, which means the player receives $6 in addition to getting their original $6 bet back. If the bet loses, the player loses their $6 bet. Therefore, the expected value of the winnings can be calculated as:
Expected value = (probability of winning * payout if win) - (probability of losing * amount bet)
Expected value = (18/37 * $12) - (19/37 * $6)
Expected value = -$0.81
This means that on average, the player can expect to lose $0.81 for every $6 bet placed on red in European roulette.
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Find the value of $x$ that makes $\triangle DEF\sim\triangle XYZ$ .
Two triangles D E F and X Y Z. In triangle D E F, the length of sides D E, E F, and D F are labeled 10 units, 8 units, and 3 left parenthesis x minus 1 right parenthesis. In triangle X Y Z, the base side Z Y is labeled 4. The sides Z X and X Y are labeled 7.5 and x minus 1.
Their corresponding side's ratio will not change. Then, x has a value of 4.
What is a Triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
ABC refers to a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object.
A polygon also includes a triangle.
Triangle ABC is shown in the image above.
So, it is made up of two triangles: DEF and XYZ.
The similarity between the DEF and XYZ is assumed.
When it happens, the ratio of their corresponding side will not change. Which is:
5/10 = 2x-1/14 = 11/5x+2
The first two are what we have.
5/10 = 2x-1/14
Then, we have:
x = 4
Therefore, their corresponding side's ratio will not change. Then, x has a value of 4.
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Correct question:
Find the value of x that makes Triangle DEF~ triangle XYZ.
why is a scatter the most appropriate visualization of this bivariate relationship? group of answer choices the data is collected on two different populations of people: those that use the internet, and those that don't. one variable is quantitative, and one variable is categorical. the data was collected over a 10 year time period. both variables are numeric, we know both their age and how often they use the internet each week.
The data is collected on two different populations of people: those that use the internet, and those that don't, and the data was collected over a 10-year time period. Therefore, the correct option is A.
A scatter plot is a graphical representation of data in which two variables are plotted on the x-axis and y-axis,
respectively.
It is used to visualize the relationship between two quantitative variables. In the scatter plot, each point represents a
value for each variable.
A scatter plot is the most appropriate visualization of this bivariate relationship because one variable is quantitative,
and one variable is categorical.
Both variables are numeric, and we know both their age and how often they use the internet each week.
This explains why scatter plot is the most appropriate visualization of this bivariate relationship.
Therefore, the correct option is A. The data is collected on two different populations of people: those that use the
internet, and those that don't, and the data was collected over a 10-year time period.
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What else would need to be congruent to show that ABC=XYZ by ASA?
On solving the provided question we can say that angle A is congruent to angle X, angle B is congruent to angle Y, and side AB is congruent to side XY.
What is triangle?A triangle is a geometric shape that consists of three straight sides and three angles. It is a polygon with three sides. Triangles are one of the most fundamental shapes in geometry, and they are used extensively in mathematics, science, engineering, and other fields. The sum of the internal angles of a triangle is always equal to 180 degrees, and there are various types of triangles, such as equilateral, isosceles, and scalene, depending on the lengths of their sides and the sizes of their angles.
To demonstrate that two triangles are congruent using the ASA (Angle-Side-Angle) postulate, show that two angles and one included side of one triangle are congruent to two angles and one included side of the second triangle. To demonstrate that the triangles are congruent using ASA, you must also demonstrate that the second pair of corresponding sides is congruent.
To properly prove that triangles ABC and XYZ are congruent by ASA, you would need to show that side AC is congruent to side XZ in addition to the given knowledge that angle A is congruent to angle X, angle B is congruent to angle Y, and side AB is congruent to side XY.
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got this rates of change equation. please list the 3 variables involved in the question
The area of the circle is decreasing at a rate of 0.2 cm³/s. We simply multiply dA/dr by dr/dt, giving us dA/dt.
What is radius?A line segment connecting the center of the circle to a point on the circle, and is equal in length to all other line segments connecting the center to points on the circle.
The three variables involved in the question are the area of a circle (A), the radius of a circle (r), and the rate of change of the radius (dr/dt). Using the chain rule, we can link all of these rates together with the equation dr/dt = dA/dr x dA/dt.
We know that the area of a circle is equal to r², so we can rewrite the equation as
dr/dt = 2r x dA/dt.
We are given the value of dr/dt, which = 0.4 cm/s, and so we can use this to calculate the value of dA/dr.
To do this, we first divide both sides of the equation by 2r, giving us dA/dr = dr/dt/2r.
Plugging in the values for dr/dt and r (which is 8 cm) gives us a value of dA/dr = 0.05 cm²/cm.
We can use this to calculate the rate at which the area of a circle is decreasing when its radius= 8 cm and decreasing at 0.4 cm/s.
To do this, we simply multiply dA/dr by dr/dt, giving us dA/dt = 0.2 cm³/s. This means that the area of the circle is decreasing at a rate of 0.2 cm³/s.
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Pls help me with this question
Answer: It's the third rectangle
Step-by-step explanation: If you cut from the vertex vertically it would be a triangle but if you cut a pyramid horizontally its either a square or rectangle.
30 points to whoever solves
The relative frequency of business majors in the given table survey is: 0.24
How to calculate relative frequency?Relative frequency is defined as the number of times an event occurs divided by the total number of events occurring in a given scenario
To calculate the relative frequency the following must be known:
- Number of total events/trials
- Frequency count for a category/subgroup
We want to find the relative frequency of business majors in the given table.
Total number of business majors = 37 + 38 = 75
Total number of students in the survey = 318
Thus:
Relative Frequency = 75/318 = 0.2358 ≈ 0.24
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Michael is making a scale drawing of a rectangular room using a scale of 1 inch equals 1.5 feet. He wants to use paper that has a width of 8.5 inches and length of 11 inches.
Will a room that is 12 feet by 15 feet fit on a single sheet of the paper?
HINT: Write and solve a proportion comparing the scale of 1 inch to 1.5 feet equal to how many inches to 12 feet. Then solve for how many inches. Do the same step for the other dimension of 15 feet.
REMEMBER: Your paper is 8.5 inches by 11 inches. Each dimension of the room must be less than both 8.5 inches and 11 inches.
A
Yes
B
No
PLEASE ANSWER ASAP. I REALLY NEED HELP LIKE FR FR
From the statements, the expression is 1 inch/2.2 ft = x/16 ft
How to determine the expression?
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We can use ratios to solve
Changing 11/5 into a decimal
1 inch x
-------------- = -----------
2.2 ft 16 ft
Using cross products
16 = 2.2 x
Divide each side by 2.2
16/2.2 = x
7.2727 =x Since this is less than 8.5 inches Yes
1 inch x
-------------- = -----------
2.2 ft 15 ft
Using cross products
15 = 2.2x
Dividing each side by 2.2
6.8 =x
Yes
1 inch x
-------------- = -----------
2.2 ft 20 ft
Using cross products
20 = 2.2x
9.09 =x
If this is the 11.5 inch side (15 ft is 6.8 inches which is less than 8.5 inches)
yes
1 inch x
-------------- = -----------
2.2 ft 12 ft
12 = 2.2x
5.4 inches yes since 16 is 6.8 inches
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it is impossible to construct a frame for a(n) . a. sampled population b. finite population c. target population
It is not impossible to construct a frame for a finite population or a target population, but it is impossible to construct a frame for a sampled population.
A frame is a list or map of all the units in a population, which is used to select a sample for a survey or study. If a population is finite, it is possible to list all the units in the population and create a frame. Similarly, if the target population is well-defined and can be identified, a frame can be constructed.
However, if the population is sampled, the frame cannot be constructed because the population is unknown and constantly changing. Therefore, it is impossible to construct a frame for a sampled population.
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The complete question is :
Is it impossible to construct a frame for a sampled population, a finite population, or a target population?
What is 2 1/2+1 1/3x<6? Please hellllppppp!!!!
There are 46,000 adults living in Grand City. In examining attitudes toward the news, a research group asked a random sample of Grand City adults "What Is your main source of news?" The results are shown below.
Based on the sample, predict the number of adults in Grand City whose main source of news is television. Round your answer to the nearest whole number. Do not round any intermediate calculations.
Therefore, we predict that there are approximately 18,078 adults in Grand City whose main source of news is television.
Prediction number?I predict that in the near future, there will be significant advancements in renewable energy technology, particularly in the areas of solar and wind power. This will lead to a shift away from fossil fuels and towards more sustainable energy sources, ultimately reducing carbon emissions and mitigating the effects of climate change. Additionally, I predict that artificial intelligence and machine learning will continue to play an increasingly important role in many aspects of our lives, from healthcare and education to transportation and entertainment. However, there may also be concerns about the ethical implications of AI and the need to ensure that these technologies are developed and used in a responsible and transparent manner.
o predict the number of adults in Grand City whose main source of news is television, we use the sample proportion of adults who selected television as their main source of news and apply it to the total adult population of Grand City.
The sample proportion of adults who selected television as their main source of news is:
[tex]p = 135 / (65 + 90 + 135 + 22 + 49) = 0.393[/tex]
To predict the number of adults in Grand City whose main source of news is television, we multiply the sample proportion by the total adult population:
[tex]number of adults = p * 46,000 = 0.393 * 46,000 = 18,078[/tex]
Rounding this number to the nearest whole number gives:
number of adults whose main source of news is television ≈ 18,078.
Therefore, we predict that there are approximately 18,078 adults in Grand City whose main source of news is television.
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10 less than a number p is the same as 25 as an equation !
Answer:
35
Step-by-step explanation:
The equation can be written as:
p - 10 = 25
To solve for p, we can add 10 to both sides of the equation:
p - 10 + 10 = 25 + 10
Simplifying the left side by canceling out -10 and +10, we get:
p = 35
Therefore, the number we are looking for is 35.
please help!!!!!!!!!!!!!!!!!!!
Part 1. The employee who is [tex]32[/tex] years old could have [tex]2[/tex] doctor visits in one year, according to the given equation.
Part 2.The new employee is predicted to have [tex]3[/tex] more doctor visits per year than the previous employee, according to the given equation.
What is the equation?In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
For instance, [tex]3x+5 = 14[/tex] is an equation, in which [tex]3x+5[/tex] and [tex]14[/tex] are two expressions separated by an 'equal' sign.
Part 1: To predict how many doctors' visits an employee who is [tex]32[/tex]years old could have in one year, we need to substitute a = [tex]32[/tex] in the equation [tex]v = 1/4a - 6[/tex] and solve for v:
[tex]v = 1/4a - 6[/tex]
[tex]v = 1/4(32) - 6[/tex]
[tex]v = 8 - 6[/tex]
[tex]v = 2[/tex]
Part 2: The previous employee's age is not given, so we cannot directly compare their doctor visits with the new employee's visits. However, we can use the same equation to predict how many doctor visits the new employee might have based on their age.
Let's assume that the age of the new employee is [tex]a+12[/tex], where a is the age of the previous employee. Then, we can substitute [tex]a+12[/tex] for a in the equation [tex]v = 1/4a - 6[/tex] and solve for v:
[tex]v = 1/4(a + 12) - 6[/tex]
[tex]v = 1/4a + 3 - 6[/tex]
[tex]v = 1/4a - 3[/tex]
Therefore, the employee who is [tex]32[/tex] years old could have [tex]2[/tex] doctor visits in one year, according to the given equation.
Therefore, the new employee is predicted to have [tex]3[/tex] more doctor visits per year than the previous employee, according to the given equation.
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if PQRS is a rectangle with QS=5x+3 and PR=28,find the value of x
help asap assignment closes soon!
Answer:
Step-by-step explanation:
v = π · r² · h
v = π · 5² · 10
v = 25· 10π
v = 250π
v =785.39816339
v =785.4
Find the values of x and y
The value of x and y in the figure are
5. x = 29
6. y = 5 and x = 5
How to find the value of x and y5. The value of x is found knowing that angles in a straight line is supplementary hence we have that
6x + 4 + 10x = 180
16x = 180 - 4
6x = 174
x = 174 / 6 = 29
6. Applying vertical angle theorem and angles in a straight line is supplementary
155 + 5y = 180
5y = 180 - 155
5y = 25
y = 5
also
5y + 13x = 90
5(5) + 13x = 90
13x = 90 - 25
13x = 65
x = 65 / 13 = 5
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congruent figures, thanks for helping
Value of x is 9.
What is the congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes same, or if one is the mirror image of the other. Congruent involves comparing two numbers, .In, two line segments are congruent implies that the two lines have equal measurements.
What is the properties of congruent triangles?Triangle congruence; If all three corresponding sides and all three corresponding angles are equal . two triangles are said to be congruent If Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
if,ΔABC≅ΔDEC
than ∠B=∠E
So, 3 x = 6 x-39
⇒6 x = 3 x+39
⇒6 x -3 x=39
⇒3 x = 39
⇒x=13.
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Kyle runs 6 times as many laps as Chad. If represents the laps Chad runs, and represents the laps Kyle runs, which equation expresses the relationship between these two variables?
The equation that expresses the relationship between the two variables is 6x = y.
Let's assume that Chad runs 'x' laps, then Kyle runs 6 times as many laps as Chad, which means Kyle runs 6x laps. Therefore, the equation expressing the relationship between Chad's laps and Kyle's laps can be written as:
Kyle's laps = 6 times Chad's laps
or
6x = the number of laps Kyle runs
So, the equation is: 6x = y, where 'x' represents the number of laps Chad runs i.e. he ran six times more, and 'y' represents the number of laps Kyle runs i.e. he ran six times lesser than Chad.
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The surface of a cylinder is represented by [tex]A = 2\pi rx^{2} + 2\pi rh[/tex], where r is the radius of the cylinder and h is its height. Factor the right side of the formula.
factor the right side of the formula A = 2πrx² + 2πrh, we can factor out 2πr from both terms:A = 2πr(x² + h)
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.
To factor the right side of the formula A = 2πrx² + 2πrh, we can use the distributive property of multiplication. We can factor out the common factor of 2πr from both terms in the expression, leaving us with 2πr times the sum of x² and h. This gives us the factored form A = 2πr(x² + h). This expression represents the surface area of a cylinder in terms of its radius (r) and height (h).
Factoring the right side of the formula in this way can simplify calculations and help us better understand the relationship between the variables in the formula.
Therefore, to factor the right side of the formula A = 2πrx² + 2πrh, we can factor out 2πr from both terms:A = 2πr(x² + h)
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Find measure AD. Please hurry due at midnight
The measure of arc mAD is 119°.
Describe Arc?In geometry, an arc is a portion of a curve or a circle. It is defined as a connected portion of the circumference of a circle, which is characterized by its central angle, length, and location. The length of an arc is proportional to the measure of its central angle, and the measure of the arc is given in degrees or radians.
The circumference of a circle is the distance around the circle, and it is equal to 2πr, where r is the radius of the circle. An arc of a circle is a part of the circumference, and its length can be calculated using the formula:
Arc length = (central angle/360 degrees) * 2πr
where the central angle is measured in degrees, and r is the radius of the circle.
Since chord AB, BC, CD, and DA form a quadrilateral, we know that the opposite angles of the quadrilateral add up to 180°. Therefore, ∠ABC = 180 - ∠DAB = 180 - 75 = 105°, and ∠BCD = 180 - ∠ADC = 180 - 102 = 78°.
Next, we can use the inscribed angle theorem to find the measure of arc AD. We know that ∠ACD is half the measure of arc CD, so arc CD = 2 * ∠ACD = 62°. Therefore, ∠ACD = 31°.
Similarly, ∠ABD is half the measure of arc AB, so arc AB = 2 * ∠ABD. We can find angle ABD by subtracting angle DAB from ∠ABC: ∠ABD = ∠ABC - DAB = 105 - 75 = 30°. Therefore, arc AB = 2 * 30 = 60°
Since the sum of the measures of angles ABD, ACD, and the central angle arc AD is 180°, we have:
∠ ABD + ∠ ACD + arc AD = 180
Substituting the values we found, we get:
30 + 31 + arc AD = 180
Solving for arc AD, we get:
arc AD = 180 - 30 - 31 = 119°
Therefore, the measure of arc mAD is 119°.
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which type of error occurs when potential respondents are improperly excluded before the sample is taken?
The type of error that occurs when potential respondents are improperly excluded before the sample is taken is called selection bias
The type of error that occurs when potential respondents are improperly excluded before the sample is taken is called "selection bias". Selection bias occurs when the sample is not representative of the population, leading to an overrepresentation or underrepresentation of certain groups. This can happen when certain individuals or groups are systematically excluded from the sample, either intentionally or unintentionally.
Selection bias can lead to inaccurate conclusions and invalid results, which can undermine the validity and reliability of the study. Therefore, it is essential to use appropriate sampling techniques and ensure that the sample is representative of the population of interest to avoid selection bias.
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0.25 recurring as a fraction
0.25 recurring can be expressed as the fraction 25/99.
What are Fractions?A fraction is a mathematical expression representing a part of a whole, or a ratio between two numbers. It consists of a numerator, which represents the part or ratio being considered, and a denominator, which represents the whole or total.
To express 0.25 recurring as a fraction, we can use the following method:
Let x = 0.25 recurring
Then 100x = 25.25 recurring (multiply both sides by 100 to move the decimal point)
Subtracting the first equation from the second equation, we get:
100x - x = 25.25 recurring - 0.25 recurring
99x = 25
x = 25/99
Therefore, 0.25 recurring can be expressed as the fraction 25/99.
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Answer:
Angle A: 49 degrees
Angle B: 139 degrees
Step-by-step explanation:
- Since Angles Y and A are vertical angles, they are congruent. Since Angle Y measures 49 degrees, Angle A also measures 49 degrees.
- Since Angle A, an unnamed angle, and the right angle in the triangle must sum up to 180 degrees, solve for the remaining angle that we don't know the measure of. We know the measure of the right angle is 90 degrees and Angle A measures 49 degrees, and 90 + 49 = 139, so the other angle measures 41 degrees because 180 - 139 = 41. That 41-degree unnamed angle is supplementary to Angle B because they are adjacent, so 180 - 41 = 139. Therefore, Angle B measures 139 degrees.
Wnte an equation in slope-intercept form of the line that passes through (-3, 2) and (-2, - 5).
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An equation in slope-intercept form of the line that passes through (-3, 2) and (-2, - 5) is: C. y = -7x - 19.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-5 - 2)/(-2 + 3)
Slope (m) = -7/1
Slope (m) = -7
At data point (-3, 2), a linear equation in slope-intercept form for this line can be calculated as follows:
y - y₁ = m(x - x₁)
y - 2 = -7(x + 3)
y = -7x - 21 + 2
y = -7x - 19
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Section 4.5-B Quadratics - Completing the Square
What is the formula?
Therefor , by solving these by using quadratic expression
A) 16n³-24n+9/16
B)169
C)361/4
D)361/4
what is a quadratic expression?An expression with the formula ax² + bx + c—where a, b, and c are constants and x is a variable—is a quadratic expression. The name "quadratic," which refers to the fact that the equation's variable x is squared, is derived from the Latin word "quadratus," which means "square." A quadratic equation is a "equation of degree 2," to put it another way.
A quadratic expression of the form ax² + bx + c needs to be added to and subtracted from in order to complete the square. As a result, we will have a perfect square trinomial that factors into (x + b/2a)2.
a) n³ - (3/2)n + 9/16
This expression can be rewritten as n³ - (3/2)n + 9/16 - 9/16
= 16n³-24n+9/16
b) x² + 26x + ?
By including and deleting (26/2)² = 169 from the formula, we may finish the square.
x²+ 26x + 169 - 169 + ? = (x + 13)² - 169
c) n² + 19n + ?
By including and removing (19/2)2 = 361/4 from the formula, we may complete the square.
n² + 19n + 361/4 - 361/4 + ? = (n + 19/2)² - 361/4
d) p² - 19p + ?
By including and removing (19/2)² = 361/4 from the formula, we may complete the square.
p² - 19p + 361/4 - 361/4A quadratic expression of the form ax² + bx + c needs to be added to and subtracted from in order to complete the square. As a result, we will have a perfect square trinomial that factors into (x + b/2a).
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