Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched. What is the change in elevation?
The change in elevation will be 0.
What is the change in elevation?It should be noted that from the information, Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched.
Therefore, when it flew, the expression will be +168.
When it came down, the expression will be -168.
Therefore, the change in elevation will be:
= +168 - 168.
= 0
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Consider the queueing model of the bank in Conceptual Problem 6.9. Suppose the arrival rate is 18 per hour, the mean service time is 10 minutes, and the lobby can handle 15 customers at one time. How many tellers should be used if the aim is to keep the mean queueing time to less than 5 minutes
The number of tellers that should be used if the aim is to keep the mean queuing time to less than 5 minutes is 3.
To determine the number of tellers follow these steps:
1. Arrival rate (λ) = 18 customers per hour
2. Mean service time (μ) = 10 minutes per customer = 1/6 customer per minute
3. Lobby capacity = 15 customers
4. Target mean queuing time = 5 minutes
Now, calculate the service rate and find the number of tellers needed to achieve the target mean queueing time.
Step 1: Convert arrival rate to customers per minute: λ = 18/60 = 0.3 customers per minute
Step 2: Calculate the service rate per teller: 1/μ = 1/(1/6) = 6 customers per hour = 0.1 customers per minute
Step 3: Determine the number of tellers (n) needed to achieve the target queuing time:
Using the formula:
n > λ / (μ * (Wq_target + 1/μ))
Here, Wq_target is the target mean queuing time in minutes.
n > 0.3 / (0.1 * (5/60 + 1/(6/60)))
After solving the inequality, we get:
n > 2.4
Since the number of tellers must be a whole number, therefore, at least 3 tellers should be used in the queueing model of the bank to keep the mean queueing time to less than 5 minutes.
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what is the percent of change from 75 to 24?
A chocolate factory produces 19,56,870 chocolates in 2009. it produced 2,67,002 variety with coffee flavour; 6,54,512 with nuts; 3,21,785 with wafer and the rest were caramel flavour. how many chocolates were caramel flavoured
The number of chocolates that were caramel flavored is 7,13,571.
To find the number of chocolates that were caramel flavored, we can subtract the number of chocolates with the other three flavors from the total number of chocolates produced:
The total number of chocolates produced in 2009 was 19,56,870.
The number of chocolates produced with coffee flavour was 2,67,002, with nuts was 6,54,512, and with wafer was 3,21,785.
Therefore, the total number of chocolates produced with these three flavours is,
2,67,002 + 6,54,512 + 3,21,785 = 12,43,299.
To find out how many chocolates were caramel flavoured, we need to subtract this number from the total number of chocolates produced:
19,56,870 - 12,43,299
Total number of chocolates produced = 19,56,870
Number of chocolates with coffee flavor = 2,67,002
Number of chocolates with other flavors = Number of chocolates produced - (Number of chocolates with coffee flavor + Number of chocolates with nuts + Number of chocolates with wafer)
Number of chocolates with other flavors = 19,56,870 - (2,67,002 + 6,54,512 + 3,21,785)
Number of chocolates with other flavors = 19,56,870 - 12,43,299
Number of chocolates with other flavors = 7,13,571
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Question 31 and 32. 50 points for first correct person.
The equation of line is y = 20x and the number of months is x > 4
Given data ,
Let's represent the number of months as "x" and the amount of money in Rose's savings account after n months as S(x).
Since Rose deposits $20 every month, the amount of money in her savings account after n months can be expressed as:
S(x) = y = 20x
To determine when Rose will have more than $80 in her savings account, we can set up the following inequality:
y > 80
Substituting the expression for S(n):
20x > 80
Divide by 20 on both sides , we get
x > 4
Hence , the inequality that represents when Rose will have more than $80 in her savings account is: x > 4
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sketch the graph of
a,3y-2=5
The graph of the equation of line is explain below
Explain the concept of equation of line?The general equation of a straight line is y = mx + c, where m is the slope, and y = c is the worth where the line cuts the y-pivot. This number c is known as the block on the y-pivot. Central issue. The condition of a straight line with inclination m and block c on the y-hub is y = mx + c.
According to given data:We have, equation of line ,3y-2=5
⇒ y = 7/3
Its graph is shown below,
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a company has given you the task to research the salary of thirty-five-year-olds in new york city. would you be more interested in looking at the mean, median, or mode?
The correct answer is median.
The salary of 35 year olds would vary greatly, with significant variations. Undoubtedly, this type of data contains outliers. Because median is unaffected by outliers in the data set, it would be appropriate for the data that included outliers.
The observations are divided into two equal portions by the median. When observations are organised in order of magnitude, it reflects the middle value for the group of observations.
When data are input in ascending order, the median value is the middle value. In other words, the observation is in the middle.
If there are an even number of observations overall, the median is calculated as the average of the middle two observations.
The median is the middle observation in the arranged data if the total number of observations is an odd number.
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often a complicated expression in formal logic can be simplified. for example, consider the statement s
The statement for all possible combinations of truth values for its variables. This can help identify patterns and simplify the expression.
To simplify a complicated expression in formal logic, you can use various techniques such as logical equivalences, truth tables, and laws of logic. The goal is to reduce the expression to its simplest form, making it easier to analyze and understand.
Here are some steps you can follow to simplify the statement "s":
1. Identify the logical operators: Look for logical operators like AND (∧), OR (∨), and NOT (¬) in the expression. These operators help connect different parts of the statement.
2. Apply logical equivalences: Use logical equivalences to transform the expression into an equivalent, but simpler form. For example, you can use De Morgan's laws to convert negations of conjunctions or disjunctions.
3. Simplify using truth tables: Construct a truth table for the expression to determine the truth values of the statement for all possible combinations of truth values for its variables. This can help identify patterns and simplify the expression.
4. Use laws of logic: Apply laws of logic such as the distributive law, commutative law, or associative law to simplify the expression further. These laws allow you to rearrange the terms or combine similar terms.
5. Keep simplifying: Repeat the steps above until you cannot simplify the expression any further. This ensures that you have reached the simplest form of the expression.
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Helppppppppppppoppppppopopopoopop
thw correct answer is b
this is cuz she is running miles
ryan drove 260 miles using 12 gallons of gas. at this rate, how many gallons of gas would he need to drive 286 miles?
The gallons of gas required by Ryan to travel 286 miles is 13.2 gallons.
Define the term inversely proportional?When two parameters are related, an inverse connection exists, where the value about one parameter usually falls as the value of other parameter rises. It's frequently referred to as a bad relationship. When one quantity increases or declines, the other quantity also rises or falls in direct proportion. On the other hand, in indirect and inverse proportion, if such quantity rises, the other one falls, and vice versa.As the stated question;
Total gallon of gas used to drive the 260 miles = 12 gallons
Let 'x' be the gallon of gas used to drive the 286 miles.
Then, bu using the proportion
12 / 260 = x / 286
Thus,
x = 286 x 12 / 260
x = 13.2 gallons
Thus, the amount of gas required by Ryan to travel 286 miles is 13.2 gallons.
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(›)
Which is more, 1 tablespoon or 2 teaspoons?
Answer: 1 tablespoon
Step-by-step explanation:
Which expression is represented by the model below?
Answer:
-5+3....................
22. Find the measure of the indicated angle to the nearest degree.
Answer:
A
Step-by-step explanation:
using the cosine ratio in the right triangle
cos? = \(\frac{adjacent}{hypotenuse}\) = \(\frac{17}{27}\) , then
? = \(cos^{-1}\) ( \(\frac{17}{27}\) ) ≈ 51° ( to the nearest degree )
A 9-pack of candy bars costs $5.04. What is the unit price?
Answer:
unit price = $0.56
Step-by-step explanation:
9-pack of candy bars costs $5.04
so,
9 * c = $5.04 ...............where c is the unit price
c = $5.04 /9
c = $0.56
Answer:
0.56¢
Step-by-step explanation:
A 9 pack of candy bars costs $5.04.
So for a single unit (one candy bar), it would be:
$5.04÷9 = 0.56¢
The area between two negative scores can be found by
The area between two negative scores can be found by taking the absolute difference between the two scores.
The area between two negative scores can be found by taking the absolute difference between the two scores. This is because the absolute difference gives us the distance between the two scores without considering their signs.
To calculate the area between two negative scores, follow these steps:
1. Identify the two negative scores.
2. Subtract the smaller negative score from the larger negative score.
3. Take the absolute value of the result to remove the negative sign.
4. The absolute difference between the two negative scores represents the area between them.
For example, let's say we have two negative scores, -5 and -10. To find the area between them, we subtract -5 from -10, resulting in -10 - (-5) = -10 + 5 = -15. Since we are interested in the distance, we take the absolute value of -15, which gives us 15. Therefore, the area between -5 and -10 is 15.
The absolute difference between two negative scores gives us the area between them. This approach is applicable whenever we want to find the distance or area between any two numbers, not just negative scores.
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how do u do indices?
Answer:by make it in simple form
Step-by-step explanation:we firstly should start from 1st expression.Even by using algebra formula for ex:
=a/(a^2 -b^2) +(b/(a^2 -b^2)
=(a+b)/(a^2 -b^2)
=(a+b) / ((a+b)(a-b))
=1/(a-b)
tensile testing is not appropriate for hard brittle materials such as ceramics. what is the test commonly used to determine the strength properties of such materials? why there is scatter in the measured strength data for ceramics?
The tests commonly used to determine the strength properties of such materials are 3-point load test, direct tension test, cylinder split test.
What is Cylinder split test?In this method, a lone loading along length is applied at diametrically end points. Due to this loading cylinder splits into two parts.
Brittle ceramics are typically not subjected to tensile tests. These materials are challenging to mold into the right test structure, they are challenging to handle without breaking, and it is challenging to align the test samples to prevent bending stresses that could damage the samples.
A three-point bending apparatus is used to measure the stress-strain behavior of brittle ceramics, and from the results, an equivalent modulus of elasticity is calculated.
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PLZ HELPPP The statement below represents an equation.
Which equation is represented by this statemen
1. 1/n+6=1/4÷2
2. n/6=1/4+n/2
3. 1/n+6=1/4+n/2
4. n/6=1/4xn/2
/ is fractions
Answer: It number 4
Step-by-step explanation:
ses quoi le résultat s'il vous plaît
\(( \frac{3}{4} - \frac{1}{2} ) \times \frac{5}{6} \)
Répondre: \(\frac{5x5}{24}\)
Commentez si vous voulez l'explication :D
Write 1.7 as a mixed number and as a improper fraction do not try simplifying your answers
Answer:
17/10 as a fraction
1 7/10 as a mixed number
Step-by-step explanation:
1.7 means one and seven tenths or 1 7/10
When you want a fraction you look at denominator to see how many pieces are in the whole pieces which in this case would be 10 and add 7 pieces because you have one whole piece and 7 pieces of a different piece so 17/10 as a fraction
Hope this helps!
Answer:
1 7/10 and 17/10
Step-by-step explanation:
To get these you'll need to first convert 1.7 to a fraction, and then with the mixed number, you'll need to get a whole number and take what remains and make it a fraction. For the improper fraction, you do the same thing as making a mixed number, but this time you won't be making a whole number, you'll be making it into a single fraction
Simplify this expression.
6^7 ÷ 6^5
A.
30
B.
35
C.
36
D.
42
Answer:
C
Step-by-step explanation:
If you would recall one of the laws of exponents, when dividing powers of the same base you subtract their exponents. So for this expression:
6⁷ ÷ 6⁵ = 6^(7-5) = 6² =36
complete:
a 20% x ____ = $30
Answer:
20/100*x=$30
20x/100=$30
x/5=$30
x=$30*5
x=$150
Step-by-step explanation:
20 percent of 150 equals 30 so 150 times 20 percent would give you 30
Weight of gravel in a pile is 120 lb. is the value from a discrete or continuous data set?
The value illustrated by the weight of gravel in a pile is 120 lb. is a continuous data set.
What is a continuous data set?It should be noted that a continuous data set is the quantitative data set that represents a scale of measurement which can consist of numbers other than whole numbers, like decimals and fractions.
It should be noted that continuous data sets would consist of values like height, weight, length, temperature, etc.
Therefore, the value illustrated by the weight of gravel in a pile is 120 lb. is a continuous data set.
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What are geometric solids with circular cross sections? What are they used for? How are they created?
Geometric solids with circular cross-sections include cylinders, cones, and spheres. Geometric solids with circular cross-sections include cylinders, cones, and spheres. And Cylinders, cones, and spheres can be created by rotating a two-dimensional shape about an axis.
1. Cylinder: A cylinder is a 3-dimensional solid that has two parallel circular bases connected by a curved surface. Cylinders are commonly found in everyday objects like soda cans and water bottles.
2. Cone: A cone is a 3-dimensional solid that has a circular base and a curved surface that tapers to a point. Cones are often used in architecture, like on the top of a church steeple.
3. Sphere: A sphere is a 3-dimensional solid that has a circular shape in all directions. Spheres are found in many natural objects like planets and fruit, as well as in man-made objects like Christmas ornaments.
What are they used for?Geometric solids with circular cross-sections are used in various fields, including architecture, engineering, and science. They are used for creating objects such as cans, pipes, towers, and buildings. These shapes are also used for modeling the natural world, such as the earth, planets, and the stars.
How are they created?Cylinders, cones, and spheres can be created by rotating a two-dimensional shape about an axis. For instance, a circle that is rotated around its center axis forms a cylinder. Similarly, a triangle that is rotated around one of its sides forms a cone, while a circle that is rotated around its center axis forms a sphere.
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-3 7/9 + (-2 1/3)
awnser 1: -6 1/9
awnser 2: -8 1/9
which anwser please help
Answer:
the first one
Step-by-step explanation:
that the andser
When Cara drives to work, it takes her 30 minutes to drive 15 miles. On her days off, she likes to drive to her favorite donut shop. It takes Cara 6 minutes to drive to The Dreamy Donut Shop at the same rate. How many miles away is The Dreamy Donut Shop?
Answer:
3 miles
Step-by-step explanation:
First, we find the rate at which she drives, that is her speed.
Speed is given as:
speed = distance / time
When Cara drives to work, it takes her 30 minutes to drive 15 miles. Her speed is:
s = 15 / 30 = 0.5 miles per minute.
She drives at the same rate to The Dreamy Donut Shop and it takes her 6 minutes.
From the formula of speed, distance is given as:
distance = speed * time
Therefore, the distance of The Dreamy Donut Shop is:
distance = 0.5 * 6 = 3 miles
The Dreamy Donut Shop is 3 miles away.
Answer:
The answer is 3 miles
Step-by-step explanation:
6. Twenty 8th grade students were asked the same two questions: Do you like winter? Do you like fruit?
Which two way table correctly displays the data from the surveys
The two-way table which correctly records the information in the picture is Option C.
Two-way TablesTwo-way Tables are used to record the outcome of binary responses for two given variables. The variables here are Winter and Fruit. The response could either be Yes(Y) or No(N).
One way to correctly record data on a two-way table is the orientation of the variables in the table. Do you like winter? is oriented vertically while Do you like Fruits? is oriented horizontally.
The total number of responses for Do you like winter? would sum up vertically to give 20 while the total number of responses for Do you like Fruits would sum up horizontally to give 20.
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Which phrase describes the linear relationship between the values of x and y shown in the table? A. y is 4 more than x B. y is 6 more than x C. y is 3 times x D. x is 3 times y
The linear relationship on the table has a constant slope
The linear relationship is (c) y is 3 times x
How to determine the linear relationship?The table of values is given as:
x l y
3 l 9
0 l 0
For both x and y values on the table, we have:
y = 3x
i.e.
3 * 3 = 9 and 3 * 0 = 0
This means that the linear relationship is (c) y is 3 times x
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3/4x -9= 27 kinds need help
Answer:
X= 48
Step-by-step explanation:
math
Way
- It’s a calculator for algebra and stuff
For the series below calculate the sum of the first 3 terms, S3, and find a bound for the error. Make sure to include at least several decimals for accuracy when the problem is graded.∑
[infinity]
n
=
1
(
(
−
1
)
n
400
n
0.6
)
The sum of the first three terms in the series is -557.921 and a bound for the error is approximately 865.474.
What is series?
In mathematics, a series is the sum of the terms of a sequence. It is represented by the sigma notation (∑), which indicates that a sequence of terms is being added together.
To calculate the sum of the series and find the bounds for the error, let's break down the problem step by step.
The series can be represented as:
\(\sum_{n=1}^{\infty} [(-1)^n * 400*n^{0.6}]\)
To find the sum of the first three terms, S3, we need to calculate the values for n = 1, 2, and 3 and then sum them up.
For n = 1:
\((-1)^1 * 400 * 1^{0.6\) = -400
For n = 2:
\((-1)^2 * 400 * 2^{0.6\) = 564.189...
For n = 3:
\((-1)^3 * 400 * 3^{0.6\) = -721.110...
Now, let's calculate the sum of the first three terms, S3:
S3 = -400 + 564.189 + (-721.110) = -557.921
The sum of the first three terms, S3, is approximately -557.921.
To find a bound for the error, we can use the Alternating Series Estimation Theorem. The theorem states that the error in approximating an alternating series is less than or equal to the absolute value of the next term.
In this case, the next term of the series would be for n = 4:
\((-1)^4 * 400 * 4^{0.6\) = 865.474...
The bound for the error is given by the absolute value of this term:
|Next Term| = |865.474...| ≈ 865.474
Therefore, a bound for the error is approximately 865.474.
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