1. Explain what Marc did in steps 4 and 5.
2. Why did he do this?
3. Create your own radical equation and explain how to solve it.
4. Is there an extraneous solution to your equation?
A radical equation is √(x + 2) = 4 - x and the extraneous solution is x = 7
Explaining step 4 and 5, and why it is doneFrom the question, we have the following parameters that can be used in our computation:
The solution to a radical equation
In step 4 and 5, we have
x = ∛5 * 5 * 5 * 5
x = 5∛5¬ * 5¬ * 5¬ * 5
The above steps are carried out because it would simplify the radical expression to its simplest form
The reason it is done is to have the value of x in its simplest form
Create a radical expression
Here's an example of a radical equation:
√(x + 2) = 4 - x
Square both sides
x + 2 = 16 - 8x + x^2
Evaluate the like terms
x^2 - 9x + 14 = 0
Factor the quadratic equation
(x - 2)(x - 7) = 0
Solve for x:
x = 2 or x = 7
Is there an extraneous solution to your equation?For x = 2:
√(2 + 2) = 4 - 2
√4 = 2
2 = 2
This is true, so x = 2 is a valid solution.
For x = 7:
√(7 + 2) = 4 - 7
√9 = -3
3 = -3
This is not true, so x = 7 is not a valid solution.
So, there is an extraneous solution
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Aiden estimates that the length of a piece of rope is 8. 5 inches. If it’s actual length is 7. 1 inches , what is the percent error of Aidens estimate ? Round to the nearest tenth if necessary
Aiden's estimated the length of a piece of rope as 8.5 inches, while its actual length is 7.1 inches. Therefore, the percent error of Aiden's estimate is 11.3%.
To calculate the percent error, you first need to find the difference between the actual length and the estimated length. Subtract 7.1 inches from 8.5 inches and you get 1.4 inches. This is the difference between the two lengths.
Next, divide the difference by the actual length and multiply by 100. The equation is: (difference/actual length) * 100. So, (1.4/7.1)*100 = 11.3%. Therefore, the percent error of Aiden's estimate is 11.3%.
It is important to be accurate when making measurements and estimates. A small difference in numbers can lead to a large error in the final result. Knowing the percent error can help you to improve your measurements and estimates and achieve greater accuracy.
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A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 16, negative 1, 2, negative 1, negative 4, negative 1.
Analyze the table of values for the continuous function, f(x), to complete the statements.
A local maximum occurs over the interval
A local minimum occurs over the interval
________
We can say that after answering the offered question Therefore, the equation constant of proportionality in this scenario is 11.25.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
As a result, the proportionality constant in this scenario is 11.25.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
Therefore, the constant of proportionality in this scenario is 11.25.
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One yoar consumars spent an avernge of $21 on a mead at a testurant. Assumo that the amount spent on a resturant meat is normally distributod and that the standard deviation is $4 . Complete parts (a) through (c) bolow a. What is the probability that a randomly selected person spent more than $24? P(X>$24)= (Round to four decimal places as needed.) b. What is the probability that a randomiy selected person spent between $10 and $19? P($10
a) The probability of finding a value greater than $24 is given by:P(X > $24) = P(Z > (24 - 21) / 4) = P(Z > 0.75)Using the standard normal distribution table, we can find that P(Z > 0.75) = 0.2266.Rounding this result to four decimal places, we have:P(X > $24) = 0.2266.
b) The probability of finding a value between $10 and $19 is given by:P($10 < X < $19) = P((10 - 21) / 4 < Z < (19 - 21) / 4) = P(-2.75 < Z < -0.5)Using the standard normal distribution table, we can find that P(-2.75 < Z < -0.5) = P(Z < -0.5) - P(Z < -2.75) = 0.3085 - 0.0030 = 0.3055.Rounding this result to four decimal places, we have:P($10 < X < $19) = 0.3055.
The probability that a randomly selected person spent more than $24One year consumers spend an average of $21 on a meal at a restaurant. The amount spent on a restaurant meat is normally distributed with a standard deviation of $4.The first step to solve this problem is to standardize the normal random variable using the z-score formula, which is:(1)z= (x-μ) / σwhere x is the random variable, μ is the mean, and σ is the standard deviation. The probability of finding a value greater than $24 is given by:P(X > $24) = P(Z > (24 - 21) / 4) = P(Z > 0.75)Using the standard normal distribution table, we can find that P(Z > 0.75) = 0.2266.Rounding this result to four decimal places, we have:P(X > $24) = 0.2266.
The probability that a randomly selected person spent between $10 and $19 The probability of finding a value between $10 and $19 is given by:P($10 < X < $19) = P((10 - 21) / 4 < Z < (19 - 21) / 4) = P(-2.75 < Z < -0.5)Using the standard normal distribution table, we can find that P(-2.75 < Z < -0.5) = P(Z < -0.5) - P(Z < -2.75) = 0.3085 - 0.0030 = 0.3055.Rounding this result to four decimal places, we have:P($10 < X < $19) = 0.3055.
The amount spent by the middle 50% of the customers The middle 50% of the customers is equivalent to the interval that goes from the 25th percentile to the 75th percentile. This interval is also known as the interquartile range (IQR).The 25th percentile can be found by using the standard normal distribution table, which gives us that:P(Z < -0.6745) = 0.25 Solving for Z, we have:Z = -0.6745 Using the z-score formula, we can find the corresponding value of X:$21 + (-0.6745)($4) = $17.30
Therefore, the lower limit of the IQR is $17.30.The 75th percentile can be found by using the standard normal distribution table, which gives us that:P(Z < 0.6745) = 0.75 Solving for Z, we have:Z = 0.6745Using the z-score formula, we can find the corresponding value of X:$21 + (0.6745)($4) = $24.70
Therefore, the upper limit of the IQR is $24.70.The amount spent by the middle 50% of the customers is between $17.30 and $24.70.
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A bridge is 440 metres long. There are four parts to the bridge. Assuming
each part is the same length, how long is each part of the bridge?
The height of a triangle is 3 inches less than twice the length of its base. If the total area of the triangle is 7 square inches, find the length of the base and height.
Answer:
Let x be the length of the base of the triangle, then the height h is given by h = 2x - 3 (since the height is 3 inches less than twice the length of the base).
The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. We are given that the total area of the triangle is 7 square inches, so we can write:
(1/2)(x)(2x - 3) = 7
Multiplying both sides by 2 to eliminate the fraction, we get:
x(2x - 3) = 14
Expanding the left side, we get:
2x^2 - 3x = 14
Subtracting 14 from both sides, we get:
2x^2 - 3x - 14 = 0
We can now use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac))/(2a)
where a = 2, b = -3, and c = -14. Plugging in these values, we get:
x = (-(-3) ± sqrt((-3)^2 - 4(2)(-14)))/(2(2))
= (3 ± sqrt(169))/4
= (3 ± 13)/4
Taking the positive value for x (since the length of the base must be positive), we get:
x = (3 + 13)/4
= 4
Therefore, the length of the base is 4 inches. To find the height h, we can use the formula h = 2x - 3:
h = 2(4) - 3
= 5
So the height of the triangle is 5 inches.
Please Help!! A Ferris wheel ride varies sinusoidally. When loading, people are 4 feet above the ground. The radius of the Ferris wheel is 60 feet. The ride takes 4 minutes to complete one revolution. if a person starts the ride 10 feet off the ground, give the cosine function of the ride.
f(x)=Acos(Bx-C)+D
I have found:
A=60
Period=4
B=π/2
I cannot find C and D.
Step-by-step explanation:
To find C and D, we can use the given information about the initial position of the person on the ride.
When the person starts the ride, they are 10 feet off the ground. This means that the cosine function has a vertical shift of 10 units, so we have:
f(x) = Acos(Bx - C) + D = 60cos(π/2x - C) + D
At the start of the ride, when x = 0, f(x) = 10. Substituting these values, we get:
10 = 60cos(-C) + D
Simplifying, we get:
D = 10 - 60cos(-C)
We can also use the fact that the minimum height of the ride is 4 feet above the ground. This means that the cosine function has a vertical shift of 4 units, so we have:
f(x) = Acos(Bx - C) + D = 60cos(π/2x - C) + D
At the lowest point of the ride, when x = 1/4, f(x) = 4. Substituting these values, we get:
4 = 60cos(π/8 - C) + D
Substituting D = 10 - 60cos(-C) from the first equation, we get:
4 = 60cos(π/8 - C) + 10 - 60cos(-C)
Simplifying, we get:
cos(-C) = (4 - 10 - 60cos(π/8 - C))/(-60)
cos(-C) = (3cos(π/8 - C) - 1)/2
Using the identity cos(-x) = cos(x), we can rewrite this as:
cos(C) = (3cos(π/8 - C) - 1)/2
Solving for C numerically, we get:
C ≈ 0.438
Substituting this value of C and D = 10 - 60cos(-C) into the equation for f(x), we get:
f(x) = 60cos(π/2x - 0.438) + 10 + 60cos(0.438)
Please help given mts & sqp find sp
The value of length SP for the two given similar triangles is 11.
What is similar triangle?
Similar triangles are triangles that have the same shape but are different in size. In other words, their corresponding angles are equal, and their corresponding sides are proportional.
This means that if you were to take one of the similar triangles and enlarge or shrink it, while keeping the angles the same, it would still be a similar triangle.
The value of length SP is calculated by applying the following method;
|SP| = |ST|
3x + 2 = 5x - 4
3x - 5x = -4 - 2
-2x = - 6
x = 3
Length SP = 3x + 2
= 3(3) + 2
= 11
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4. VPQRS is a rectangular pyramid where PQ = 10 cm and QR=6 cm. Given that the volume of the pyramid is 100 cm³, find its height VO. P S V 0 10 cm 0 R 6 cm
the height VO of the rectangular pyramid VPQRS is 5 cm.
WHAT IS RECTANGULAR PYRAMID?
A rectangular pyramid is a type of pyramid where the base is a rectangle and the lateral faces are triangles with a common vertex (apex) that is not in the plane of the base. It is a polyhedron with a rectangular base and triangular faces that meet at a single vertex. The height of the pyramid is the perpendicular distance from the apex to the base. The volume of a rectangular pyramid can be calculated using the formula:
V = (1/3) * base area * height
where base area is the area of the rectangular base and height is the perpendicular distance from the apex to the base.
To find the height VO of the rectangular pyramid VPQRS, we can use the formula for the volume of a pyramid:
V = (1/3) * base area * height
where base area is the area of the rectangle formed by the base of the pyramid, and height is the height of the pyramid.
We are given that the volume of the pyramid is 100 cm³. We can also find the base area by multiplying the length PQ by the width QR:
base area = PQ * QR = 10 cm * 6 cm = 60 cm²
Substituting these values into the formula for the volume of a pyramid, we get:
100 cm³ = (1/3) * 60 cm² * height
Simplifying, we get:
height = (100 cm³ * 3) / (60 cm²)
height = 5 cm
Therefore, the height VO of the rectangular pyramid VPQRS is 5 cm.
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PLEASE SHOW WORK!!!!!!!!!
By making linear equation for the given statement, The salesman sold 40 suits in that week.
What is a linear equation, exactly?
A linear equation is a mathematical equation in which the variables (usually represented by x and y) are raised to the first power and are related to each other by a straight line. In other words, a linear equation represents a straight line on a graph. The general form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
Now,
Let "x" the number of suits the salesman sells in that week.
We know that he sells discounted shirts with 10% of the suits sold, so he sells 0.1x discounted shirts.
The regular price of a suit is $200, so the total revenue from selling x suits is 200x.
The discounted price of a shirt is $20, so the revenue from selling 0.1x discounted shirts is 20(0.1x) = 2x.
Now we can set up an equation based on the total revenue:
200x + 2x = 8080
Simplifying this equation, we get:
202x = 8080
Dividing both sides by 202, we get:
x = 40
Therefore,
the salesman sold 40 suits in that week.
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please help me What is the circumference of a circular swimming pool with a diameter of 6 ½ feet? 0 20 -/-/ 099/ 0 6 1/1 0 71/1/2 .ft. (use 22/7 for pi)
The circumference of the circular swimming pool is approximately 245.04 inches.
What connection exists between a circle's diameter and circumference?The circumference of a circle is the distance around it, whereas the diameter is the distance across the circle that passes through its centre. The circumference is equal to (pi) times the diameter, according to the connection between the diameter and circumference. No of the size or proportions of the circle, this connection is true for all circles.
The circumference of the circle is given as:
C = 2πr
We know that, D = 2r = 6 1/2 feet.
6 ½ feet = 6.5 × 12 inches = 78 inches
Substituting the values we have:
C = π × 78 inches = 245.04 inches
Hence, the circumference of the circular swimming pool is approximately 245.04 inches.
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PLEASE HELP ASAP!!!
Question in photo
Answer:
Trinominal
Step-by-step explanation:
By definition, Trinominals are those expressions having 3 values, in this case, x^2, x, and the constant 6 are the values.
hope it helps.
why cant i just see the answers
Answer:
What do you mean?
Step-by-step explanation:
Some questions are new and have not been answered yet.
Which situation can be represented by 11+ 6.5p ≤ 89?
A Napoleon is buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at
least $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at
most $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $6.50 each. The cost to mail all the shirts is $11. He wants to spend at
least $89. What is p, the number of shirts Napoleon can buy?
Napoleon is buying shirts online for $6.50 each. The cost to mail all the shirts is $11. He wants to spend at
most $89. What is p, the number of shirts Napoleon can buy?
The answer of the given question based on the inequality equation the answer is given below,
What is Equation?An equation is mathematical statement that asserts equality of two expressions. It typically includes of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division
The situation that can be represented by 11+ 6.5p ≤ 89 is:
a) Napoleon is the buying shirts online for $11 each. The cost to mail all the shirts is $6.50. He wants to spend at most $89. What is p,
To solve for p, we can follow these steps:
11 + 6.5p ≤ 89 (subtract 11 from both sides)
6.5p ≤ 78 (divide both sides by 6.5)
p ≤ 12
Therefore, Napoleon can buy at most 12 shirts if he wants to spend at most $89.
b) None of the given situations can be represented by the inequality 11 + 6.5p ≤ 89 when p represents the number of shirts Napoleon can buy. This is because the inequality implies that the total cost of buying p shirts at $11 each and mailing them for $6.50 is no more than $89, which is not consistent with the given information about the cost of the shirts and mailing.
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A home has a replacement value of $324,000. What is the amount of the insurance if the
coverage is:
a. 100% of the replacement value?
b. 90% of the replacement value?
c. 80% of the replacement value?
Answer:
a) $324,000
b) $291,600
c) $259,200
Step-by-step explanation:
The percentage of the replacement value represents how much of the house will be insured.
a) 100% of 324000 = 1.00 * 324000 = $324,000
b) 90% of 324000 = 0.9 * 324000 = $291,600
c) 80% of 324000 = 0.8 * 324000 = $259,200
A person makes $1800 per month, but 1/3 of that amount goes to her rent. What two numbers can you multiply to find out how much she has after playing her rent?
The two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.
Explain about the fraction of number?Part of an entire unit is represented by a fraction. A fraction's numerator is the number at the top, and its denominator is the number at the bottom. Hence, the numerator of the fraction 3/5 is 3 and the denominator is 5.Total income of person: $1800 per month.
Rent amount = 1/3 * income
Remaining amount : 1 - 1/3 = 2/3 of income
So,
Remaining amount = 2/3*1800
Remaining amount = 1200
Thus, the two numbers that are multiplied to find out the amount she has after playing her rent is: 2/3 and 1800.
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Linda read 1/3 of her book on Friday. She reads 2/6 of the book on Saturday. On Sunday she reads the remaining 2/12 of the book. How much of the book did she read
As per the concept of unitary method, Linda read 5/6 of the book.
In this problem, the quantity we are dealing with is the book that Linda is reading. Let's call the total number of units in the book "x". Since Linda read 1/3 of the book on Friday, we can say that she read (1/3)x units of the book on Friday. Similarly, she read (2/6)x units of the book on Saturday, and (2/12)x units of the book on Sunday.
Now, we need to add up all of these quantities to find the total number of units of the book that Linda read. But before we do that, we need to make sure that all of the fractions have the same denominator. The smallest common multiple of 3, 6, and 12 is 12. So, we will convert all of the fractions to twelfths.
(1/3)x = (4/12)x
(2/6)x = (4/12)x
(2/12)x = (2/12)x
Now, we can add up all of these quantities:
(4/12)x + (4/12)x + (2/12)x = (10/12)x
So, Linda read (10/12)x units of the book in total. But we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
(10/12)x = (5/6)x
Therefore, the resulting value of x is 5/6
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Identify the radii of the given circle check all that apply
The radii of circle are AB, AC and AE.
The radius of a circle is the distance from the center of the circle to any point on its circumference. To find the radius of a circle, you can use the formula:
radius = diameter / 2
where the diameter is the distance across the circle, passing through its center.
Here, in this figure we need to identify the radii. It means we need to find those lines which starts from centre and touches it's circumference.
Let us first see the option AB, it follows the condition passes through centre and touches the circumference. So, it is radius of circle.
Now, let's look at CE in figure, it passes through centre and touch the two ends of circumference. So, it is diameter not radius.
Now, AC satisfies the condition of radius. So, AC is radius.
FD touches the two ends of circle at circumference not passes through centre. So, it is chord not radius.
AE starts from centre and it's other end touches the circumference of circle. So, it is radius.
So, the radii of circle in given figure are : AB, AC and AE.
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Baseball pitcher is employing a ballistic pendulum to determine the speed of his fastball. A 3. 3-kg lump of clay is suspended from a cord 2. 0 m long. When the pitcher throws his fastball aimed directly at the clay, the ball suddenly becomes embedded in the clay and the two swing up to a maximum height of 0. 080 m. If the mass f the baseball is 0. 21 kg, find the speed of the pitched ball
The solution to the given problem of speed comes out to be v=21.12m/s.
How quickly something is moving is measured by its speed at a distance. How far an object moves in one unit of time is determined by its speed. Speed is calculated as follows: speed = distance * time. The most widely used speed measurement units are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).
Here,
Given : A 2.0 m long cord is supporting a 3.3 kg lump of clay.
Two swing up to an absolute maximum of 0.080 meters
Ball and clay's subsequent impact velocity
=>√(2*10*0.08)=1.264m/s
To find the velocity of the ball before collision
0.21*v=(3.3+0.21)*1.264
v=21.12m/s
Therefore, the solution to the given problem of speed comes out to be v=21.12m/s.
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For the point P(19,10) and Q(26,13), find the distance d(P,Q) and the coordinates of the midpoint
M of the segment PQ.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{19}~,~\stackrel{y_1}{10})\qquad Q(\stackrel{x_2}{26}~,~\stackrel{y_2}{13})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~26 - 19~~)^2 + (~~13 - 10~~)^2} \implies PQ=\sqrt{( 7 )^2 + ( 3 )^2} \\\\\\ PQ=\sqrt{ 49 + 9 } \implies PQ=\sqrt{ 58 }\implies PQ\approx 7.62 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{19}~,~\stackrel{y_1}{10})\qquad Q(\stackrel{x_2}{26}~,~\stackrel{y_2}{13}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 26 +19}{2}~~~ ,~~~ \cfrac{ 13 +10}{2} \right) \implies \left(\cfrac{ 45 }{2}~~~ ,~~~ \cfrac{ 23 }{2} \right)\implies \stackrel{ \textit{\LARGE M} }{\left(22\frac{1}{2}~~,~~11\frac{1}{2} \right)}[/tex]
a catering service offers 7 appetizers, 5 main courses, and 12 desserts. a customer is to select 4 appetizers, main 3 courses, and 6 desserts for a banquet. in how many ways can this be done?
In 323,400 ways it can be done by using the Combination formula.
The number of ways in which the appetizers, main courses, and desserts can be selected is to be found when a catering service offers 7 appetizers, 5 main courses, and 12 desserts, and a customer is to select 4 appetizers, main 3 courses, and 6 desserts for a banquet.
Let's find the number of ways to choose 4 appetizers from the 7 available:
= ⁷C₄ ⇒ 35 ways (using combinations).
Let's find the number of ways to choose 3 main courses from the 5 available:
= ⁵C₃ ⇒ 10 ways (using combinations).
Let's find the number of ways to choose 6 desserts from the 12 available:
= ¹²C₆ ⇒ 924 ways. (using combinations).
Therefore, the total number of ways in which the customer can select 4 appetizers, 3 main courses, and 6 desserts is:
35 × 10 × 924 ⇒ 323,400 ways.
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A small hotel in a popular resort area has 20 rooms. The hotel manager estimates that 15% (1 −
???? = 0.15) of all confirmed reservations are "no-shows." Consequently, the hotel accepts
confirmed reservations for as many as 25 rooms (???? = 25). If more confirmed reservations arrive
than there are rooms, the overbooked guests are sent to another hotel and given a
complimentary dinner. If the hotel currently has 25 confirmed reservations, find
a. the probability that no customers will be sent to another hotel
b. the probability that exactly 2 guests will be sent to another hotel
c. the probability that 3 or more guests will be sent to another hotel.
Let ???? be number of customers who confirmed the reservations and showed up. Then ???? has a
binomial distribution with parameters ???? = 0.85 and ???? = 25. Recall the formula for P(???? = x).
For question (a). find P(???? ≤ 20). Why?
For question (b). find P(???? = 22). Why?
For question (c). find P(???? ≥ 23). Why?
In Excel, for binomial distribution with parameters of probability of success ???? and number of
trials ????, the formulas:
For PDF: P(???? = x) is binom.dist(x, n, ????, 0) and
For CDF: ????5(x) = P(???? ≤ x) is binom.dist(x, n, ????, 1).
Note that P(???? ≥ x) = 1− P(???? < x)
P(???? > x) = 1− P(???? ≤ x)
P(???? < x) = P(???? ≤ x −1) in discrete case
Problem 1:
a) The probability that no customers will be sent to another hotel is 0.039.
b) The probability that exactly 2 guests will be sent to another hotel is 0.228.
c) The probability that 3 or more guests will be sent to another hotel is 0.492.
Problem 2:
a) ( ≤ 20) - Probability of having 20 or fewer customers show up for the reservations.
b) ( = 22) - Probability of exactly 22 customers confirming and showing up for the reservations.
c) ( ≥ 23) - Probability of having 23 or more customers show up for the reservations.
Problem 1:
a. To find the probability that no customers will be sent to another hotel, we need to calculate the probability that all 25 confirmed reservations will show up. Since the hotel manager estimates that 15% of reservations are "no-shows",
Then the probability that a reservation will show up is 1 - 0.15 = 0.85. The probability that all 25 guests will show up is,
P(all 25 show up) = [tex](0.85)^{25}[/tex]
= 0.039
So the probability that no customers will be sent to another hotel is 0.039.
b. To find the probability that exactly 2 guests will be sent to another hotel, we have to use the binomial distribution.
The probability of a reservation being a no-show is 0.15, and the probability of a reservation showing up is 0.85. We have 25 confirmed reservations, so the probability of exactly 2 no-shows is,
P(exactly 2 no-shows) = (25 choose 2)[tex](0.15)^2 (0.85)^{23}[/tex]
= 0.228
So the probability that exactly 2 guests will be sent to another hotel is 0.228.
c. To find the probability that 3 or more guests will be sent to another hotel, we need to use the complement rule.
The probability of 0, 1, or 2 guests being sent to another hotel is,
⇒ P(0 guests sent) + P(1 guest sent) + P(2 guests sent)
= [tex](0.85)^{25}[/tex]+ (25 choose 1)[tex](0.15)^1 (0.85)^{24}[/tex] + (25 choose 2)[tex](0.15)^2 (0.85)^{23}[/tex]
= 0.039 + 0.168 + 0.301
= 0.508
The probability of 3 or more guests being sent to another hotel is,
P(3 or more guests sent) = 1 - P(0, 1, or 2 guests sent)
= 1 - 0.508
= 0.492
So the probability that 3 or more guests will be sent to another hotel is 0.492.
Problem 2:
a) To find ( ≤ 20),
We have to add up the probabilities of all the possible values of from 0 to 20. This is because we want to find the probability that 20 or fewer customers confirmed and showed up for the reservations.
We can use the binomial probability formula to calculate each individual probability, or we can use a binomial cumulative distribution table to look up the probability directly.
The reason we want to find this probability is to determine the likelihood of having fewer than 20 customers show up, which could impact staffing and resource allocation for the event.
b) To find ( = 22),
Use the binomial probability formula to calculate the probability of exactly 22 customers confirming and showing up for the reservations. This is because we are interested in a specific outcome, and want to know the likelihood of that outcome occurring. Knowing this probability can help us plan for specific scenarios, such as having to accommodate 22 customers if they all show up.
c) To find ( ≥ 23),
We have to add up the probabilities of all the possible values of from 23 to 25. This is because we want to find the probability that 23 or more customers confirmed and showed up for the reservations.
We can use the binomial probability formula or a binomial cumulative distribution table to find this probability.
The reason we want to find this probability is to assess the risk of having too few resources available if more customers show up than expected, which could lead to a poor customer experience.
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After heating up in a teapot, a cup of hot water is poured at a temperature of 207 F. The cup sits to cool in a room at a temperature of 71 F
The cup of water reaches the temperature of
182 F after 1.5 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes.
The cup of water reaches a temperature of 173 F after 5 minutes.
What is temperature?Temperature is a measure of the average kinetic energy of particles in a system. It is an important physical quantity used to describe the state of a system, and is widely used in science, engineering, and everyday life. Temperature is a thermodynamic property of a system that indicates how much energy is available to do work. In everyday terms, temperature is a measure of how hot or cold something is.
k = -0.2416
The equation for the cooling rate of the cup of water is:
T(t) = 207 - 0.2416t
After 5 minutes, the temperature of the cup of water can be found by substituting t = 5 into the equation:
T(5) = 207 - 0.2416(5) = 173.08 F
Therefore, the cup of water reaches a temperature of 173 F after 5 minutes.
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Write a linear equation to represent the line shown on the graph.
A linear equation to represent the line shown on the graph is given as:
y = 2x - 2.
Explain about the slope-intercept form?Given basic coordinates from two points on the line, use the slope equation to find the slope of the line. The slope formula, or the ratio of the change there in y values to the change in the x values, is m=(y2-y1)/(x2-x1).The initial point's coordinates are x1 and y1, respectively. The second points' coordinates are x2, y2.General point-slope form is:
y = mx + c
(x1, y1) = (3, 2)
y intercept = -2
m = (2 + 2)/(2 - 0)
m = 2
y = 2x + (-2)
y = 2x - 2
Thus, a linear equation to represent the line shown on the graph is given as: y = 2x - 2.
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The correct question is-
Write a linear equation to represent the line shown on the graphs shown by question 7.
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Find [g•f](x) for f(x) = 2x+5 and g(x) = x² - 3.
Show all work.
Answer: To find the composition g∘f, we first need to find g(f(x)), which means we need to substitute f(x) into g(x) everywhere we see x. So we have:
g(f(x)) = g(2x+5) = (2x+5)^2 - 3
Expanding the square, we get:
g(f(x)) = (4x^2 + 20x + 25) - 3
Simplifying, we get:
g(f(x)) = 4x^2 + 20x + 22
Therefore, the composition g∘f is equal to 4x^2 + 20x + 22.
Step-by-step explanation:
Calculate the Total amount that Theo has to pay back if she takes the loan
If Theo takes the loan R9000 that is payable over 48 months monthly installment =R 318,92, the total amount that Theo has to pay back for the loan is R15,307.16.
To calculate the total amount that Theo has to pay back if she takes a loan of R9000 payable over 48 months with a monthly installment of R318.92, we need to multiply the monthly installment by the number of months and add any applicable fees or interest charges.
First, let's calculate the total amount that Theo will pay for the loan over the 48-month period:
Total amount = Monthly installment x Number of months
Total amount = R318.92 x 48
Total amount = R15,307.16
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Complete question is:
Calculate the total amount that Theo has to payback if she takes the loan R9000 that is payable over 48 months monthly installment =R 318,92
what is 12/37 divided by 5/18
Answer: [tex]\frac{216}{185} \;\approx 1.1676[/tex]
Given:
[tex]\displaystyle \frac{\frac{12}{37}}{ \frac{5}{18} }[/tex]
Use the method of "keep, change, flip:"
* keep the first fraction, change to multiplication, flip the second
[tex]\displaystyle \frac{12}{37}* \frac{18}{5}[/tex]
Multiply across and divide:
[tex]\displaystyle \frac{216}{185} \;\approx 1.1676[/tex]
A manager must choose five employees from a pool of 17 people to
take a survey. How many different ways can the CEO choose these
people?
There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.
To determine how many ways the CEO can select five employees from a pool of 17 people to take a survey, you can use the combination formula. The combination formula is nCr = n!/r!(n-r)! where n is the total number of items to choose from, and r is the number of items to choose.
In this case, n = 17 and r = 5.Using the combination formula: n Cr = 17C5= 17!/5!(17-5)!= 6188 There are 6,188 different ways the CEO can choose five employees from a pool of 17 people to take a survey.
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The dimensions of a rectangular prism are 1.5 feet by 3.5 feet by 2 feet. What is the volume of the rectangular prism in cubic feet?
A. 7 ft³
B. 7.25 ft³
C. 8.5 ft³
D. 10.5 ft³
The volume of the rectangular prism in cubic feet is solved to be
D. 10.5 ft³.How to find the volume of the rectangular prism in cubic feetThe volume of a rectangular prism is given by the formula
V = l x w x h,
where
l, w, and h represent the length, width, and height of the prism, respectively.
in the problem, the dimensions are:
the length is 1.5 feet, the width is 3.5 feet, and the height is 2 feet.Therefore, the volume is:
= 1.5 feet * 3.5 feet * 2 feet
= 10.5 feet³
That is to say the volume of the prism is 10.5 feet³
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On Aurora Ave the distance between Thomas St to Denny Way is 0.2 miles.
What is the distance between these two streets on Broad St?
Show your work below and round your answer to the nearest tenth of a mile.
The distance between these two streets on Broad St 0.2 miles.
We must apply the idea of comparable triangles to this issue in order to find a solution. Assume that Thomas St. and Denny Way. are separated by x miles on Broad St. Then, we can establish the ratio shown below:
0.2 miles on Aurora Avenue equals x miles on Broad Street
By cross-multiplying and simplifying, we may find the value of x:
Distance on Aurora Ave / (x * 0.2 miles) on Broad St
Broad Street distance is equal to (x * 0.2 miles)/0.2 miles. (since the distance on Aurora Ave is given as 0.2 miles)
Broad Street: distance = x
As a result, Thomas St. and Denny Way are separated by x miles, or 0.2 miles, on Broad St. Thus, the response is:
Distance between Thomas St and Denny Way on Broad St = 0.2 miles (rounded to the nearest tenth of a mile)
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