The numeric value of 1.6 multiplied by 0.125 is 0.2.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given we need to calculate the value of 1.6 multiplied by 0.125
Since Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.
Thus,
=> 1.6 multiplied by 0.125
=> 1.6 * 0.125
=> 0.2
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at what angle, in degrees south of east, is a line connecting your starting point to your final position?
The angle in degrees south of east, is a line connecting your starting point to your final position is 144.46°.
The displacement vector represents the displaced distance along with the direction of displacement. The initial point of the displacement is represented by a tail of a vector arrow whereas, the final point is represented by the arrowhead. Assume i walk 17.5 m straight west and then 24.0 m straight north. Let vectors A and B denotes the displacement. The total displacement, R is determined by adding both vector and direction is θ. So, [tex] \vec R = \vec A + \vec B[/tex]
[tex] \vec R = −17.5 \hat{i} + 24 \hat j[/tex]
The magnitude of the displacement vector is denoted by,
[tex]| \vec R |= \sqrt{{ (- 17.5)}^{2} + {24}^{2} } = \sqrt{882.25} = 29.70 \\ [/tex]
The angle of displacement is given by,
[tex]θ={tan}^{- 1} ( \frac{24}{ - 17.5}) [/tex]
From the above diagram, the displacement is at − 54.46° , which is in the west-north direction in the compass. Let the south of east angle be φ. Now, the angle south of east is φ = 180° - 90° - θ Hence required angle is 90° + 54.46° = 144.46°.
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Complete question:
Suppose you walk 17.5 m straight west and then 24.0 m straight north. At what angle, in degrees south of east, is a line connecting your starting point to your final.
question: 2.35 a contractor wishes to build 9 houses, each dif- ferent in design. in how many ways can he place these houses on a street if 6 lots are on
There is only 1 way to place the houses on the street.
If the contractor wishes to build 9 houses, each different in design, and there are 6 lots available on the street, there are 6 choose 9 (written as 6C9) ways to place these houses.
However, this number is not possible since 6C9 = 0,
which means there are no combinations of 6 elements taken 9 at a time.
A more appropriate calculation would be 6 choose 6 (written as 6C6), which represents the number of ways to place the 9 houses on the 6 available lots if each house must occupy a lot.
In this case, 6C6 = 1,
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Do the following lengths satisfy the Pythagorean Theorem? Lengths= 15 10 5
a hole of radius unit is bored through the center of a sphere of radius unit. find the exact value of the volume of the remaining portion of the sphere.
The volume of the remaining portion of the sphere is 2.096 cubic units.
Let's take the volume of the remaining portion of the sphere = V
The volume of the sphere = [tex]\frac{4}{3}[/tex] * π * [tex]r^3[/tex]
The volume of the sphere with radius 1 = 4/3 * π
The volume of the cylinder = π * [tex]r^2[/tex] * h
The volume of the cylinder with height 2 and radius 1 = π * [tex]r^2[/tex] * h = 2 * π.
The difference between the volume of the sphere and the cylinder is
V = 4/3 * π - 2 * π = 4/3 * π - 2 * π = 2/3 * π.
By taking π = 3.14
V = [tex]\frac{2}{3}[/tex] * 3.14
V= 2.096.
So, the volume of the remaining portion of the sphere is 2.096 cubic units.
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which of the following variables are categorical and which are numerical? if the variable is numerical, then specify whether the variable is discrete or continuous. a. colors of cars in a mall parking lot.
The variable "colors of cars in a mall parking lot" is a categorical variable because it is a qualitative variable.
Categorical variables are variables that describe the characteristics of a group of entities and are usually described by words or labels. They are used to classify data into categories or groups and do not have a numerical or quantifiable meaning.
Examples of categorical variables include gender, religion, nationality, etc. In contrast, numerical variables are quantitative variables that have numerical or quantifiable meaning. They can be either discrete or continuous.
Discrete variables are countable, meaning that they have a finite number of possible values. Examples of discrete variables include age, number of siblings, etc. Continuous variables are variables that can take on any value within a given range. Examples of continuous variables include height, weight, etc.
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so you have $9 and 12 candy bars what is your unit rate?
Answer: $0.75 per bar
Step-by-step explanation: To find the unit price for this, we need to either divide the bars by money or set up a proportion. So, 9 ÷ 12 = 0.75. The proportion would look like this:
[tex]\frac{9}{12} = \frac{x}{1}[/tex]
You'd cross multiply the 9 * 1 to get 9 then divde by 12. Either way, we should have gotten $0.75. To check if we are right, we multiply the unit price times the total amount of that item. So, 0.75 * 12 = 9, which makes this statement true. I hope this helped!
Graph the inequality.
The graph of the inequality y ≤ 5x - 3 is given below.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality:
y ≤ 5x - 3.
The intercepts are (0.6, 0) and (0, -3)
The graph of the inequality is given in the attached image.
Therefore, the graph is given.
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the amount of energy required to heat water for 10 mintues shower (50 gallons0 is 2.2125kj. how many calories is that?
The 2nd option 5.2880× [tex]10^{2}[/tex] calories is the correct answer.
There are different forms of energy on earth. The sun is considered the elemental form of energy on earth. In physics, energy is considered a quantitative property that can be transferred from an object to perform work. Hence, we can define energy as the strength to do any kind of physical activity.
According to the laws of conservation of energy, “energy can neither be created nor destroyed but can only be converted from one form to another”. The SI unit of energy is Joule.
Energy =2.2125 kJ
Energy =2212.5 J (1 kJ =1000 J)
using 1 calorie = 4.184 J
Energy =2212.5 J × (1 Cal / 4.184 J)
Energy =528.800 calories =5.2880× [tex]10^{2}[/tex] calories.
Out of the available options, 2nd and 3rd have the same value. But the given energy has 4 significant figures after the decimal then answer should also have 4 significant figures.
Therefore, 2nd option 5.2880× [tex]10^{2}[/tex] calories is the correct answer.
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Complete question: the amount of energy required to heat water for 10 minutes shower (50 gallons0 is 2.2125kj. how many calories is that? Report the answer in scientific notation.
(1) 5.2880
(2) 5.2880×[tex]10^2[/tex] calories
(3) 5.288×[tex]10^2[/tex] calories
(4) 9.2571×[tex]10^{3}[/tex]
cynthia jones recently surveyed 200 of her classmates to get a sense of the demand for a new software product she is working on. collecting data via a survey you administer yourself is referred to as research. question 6 options: a) secondary b) derivative c) primary d) initial e) direct
The survey conducted by Cynthia jones is an example of primary research
Primary research is a process used by researchers to acquire data directly rather than relying on data gathered from earlier study. They technically "own" the data. Primary research is conducted primarily to solve a specific problem that necessitates in-depth investigation.
There are two types of research:
Primary Research
Secondary Research
Businesses or organisations can do primary research themselves or hire a third party to do it on their behalf. One significant advantage of primary research is that it is "targeted," meaning that it is centered on a single topic or problem and all efforts are geared at obtaining relevant answers.
In Cynthia Jones's case, collecting data via a survey she administered herself is an example of primary research as she is collecting data directly from her classmates.
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A toy rocket is launched from a platform 39 feet above the ground at a speed of 83 feet per second. The height of the rocket in feet is given by the polynomial −16t2 + 83t + 39, where t is the time in seconds. How high will the rocket be after 3 seconds?
Answer:
144 ft
Step-by-step explanation:
Put in '3' where 't' is and compute
Height = -16(3^2) + 83(3) + 39 = 144 ft
The difference of a number b and seven is 10. Answer: ?
The product of a number t and eight is twelve. Answer: ?
Twice the sum of a number m and five is the difference of nine and n. Answer: ?
Twenty-one is the quotient of a number y and 4. Answer: ?
Thrice the difference of number b and one is the product of a number c and then. Answer: ?
Answer:The answer to the first question is b = 3.
The answer to the second question is t = 8.
The answer to the third question is m = 2 and n = 7.
The answer to the fourth question is y = 84.
The answer to the fifth question is b = 5 and c = 3.
Step-by-step explanation:
scrabble in the game of scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. th describe the sampling distribution
The sampling distribution of the A tile in this population is 0.04.
The sampling distribution is a probability distribution of an observed result from a sample that is used to draw inferences about a population. In the game of Scrabble, the sampling distribution is used to draw inferences about the population of 100 tiles. Specifically, the sampling distribution explains the likelihood of a certain tile being drawn. For example, if the population contains 4 A tiles and 96 other tiles, then the probability of drawing an A tile is 4/100 or 0.04. This probability is the sampling distribution of the A tile in the population of 100 tiles. The sampling distribution can also be represented by the formula P(X=x)=nx/n, where n is the total number of tiles and x is the number of tiles of a certain type. Therefore, in the example above, P(X=A)=4/100=0.04. Thus, the sampling distribution of the A tile in this population is 0.04.
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at 0 hours, clare and her cousin are 63 miles apart. how far apart are they after 1 hour? 2 hours? 3 hours? show or explain your thinking.
The required, after 1 hour, 2 hours, or 3 hours, would still be 63 miles apart.
What is inductive reasoning?Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.
If Clare and her cousin are 63 miles apart at 0 hours, their distance apart does not change with time, unless they are moving towards or away from each other. The distance between two static points cannot be affected by the passing of time.
So, after 1 hour, 2 hours, or 3 hours, they would still be 63 miles apart.
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9,37,39,13 Find the median and mean of the data set
Rearrange first
9,13,37,39
median=13+37÷2
=25
median is 25
mean=9+13+37+39÷4
=98÷4=24.5
Mean=24.5
high school students who take the sat math exam a second time generally score higher than on their first try. past data suggest that the score increase has a standard deviation of about 50 points. how large a sample of high school students would be needed to estimate the mean change in sat score to within 2 points with 95% confidence? show your work.
A sample size of 384 high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence.
To calculate the sample size needed to estimate the mean change in SAT score to within 2 points with 95% confidence, we need to use the formula for sample size calculation:
n = (z^2 * σ^2) / (E^2)
where n is the sample size, z is the confidence level, σ is the standard deviation, and E is the margin of error.
In this case, our confidence level is 95%, so z = 1.96. The standard deviation of the score increase is 50 points and the margin of error is 2 points. So, plugging these values into the equation, we get:
n = (1.96^2 * 50^2) / (2^2)
Solving, we get n = 384. Therefore, a sample size of 384 high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence.
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four students graphed the transformations below. Apply what you've learned to write a description of each transformation below as well as an algebraic rule.
The transformation rule descriptions are;
1) Reflection over the x-axis
(x, y) → (x, -y)
2) Reflection over the x-axis
(x, y) → (x, -y)
3) Reflection over the y-axis
(x, y) → (-x, y)
4) Reflection over the x-axis and then a reflection over the y-axis:
(x, y) → (-x, -y)
How to find the transformation rule?1) We clearly see that the transformed image is an exact mirror image of the original image which is a rhombus. Thus, the transformation is a reflection over the x-axis.
This is expressed as (x, y) → (x, -y)
2) We clearly see that the transformed image is an exact mirror image of the original image which is a triangle. Thus, the transformation is a reflection over the x-axis.
This is expressed as (x, y) → (x, -y)
3) We clearly see that the transformed image is an exact mirror image of the original image which is a rectangle. Thus, the transformation is a reflection over the y-axis.
This is expressed as (x, y) → (-x, y)
4) We clearly see that the transformed image is an exact mirror image of the original image which is a pentagon. Thus, the transformation is a reflection over the x-axis and then a reflection over the y-axis.
This is expressed as (x, y) → (-x, -y)
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if six numbers are chosen at random, with replacement, from the set of integers from 1 to 900, inclusive, what is the probability that the product of these six integers leaves a remainder of 4 when divided by 30? express your answer as a percent to the nearest thousandth.
Let's first find the total number of possible 6-number combinations from the set of integers 1 to 900, inclusive. This is simply 900^6.
Next, we need to find the number of 6-number combinations that leave a remainder of 4 when their product is divided by 30.
Since the remainder of a product of integers is equal to the product of the remainders of each integer when divided by the same number, we only need to focus on finding the number of combinations of integers from 1 to 900, inclusive, that leaves a remainder of 4 when divided by 30.
We can find this number by dividing 900 by 30 and rounding up to the nearest integer (since we're choosing with replacement, some numbers may be repeated), which gives us 30. So there are 30 possible integers that leave a remainder of 4 when divided by 30.
Since we're choosing 6 numbers from these 30 integers, the number of 6-number combinations that leave a remainder of 4 when their product is divided by 30 is simply 30^6.
Finally, to find the probability of this happening, we divide the number of favorable outcomes by the total number of possible outcomes, and express the answer as a percent:
(30^6) / (900^6) * 100 = 0.000008 * 100 = 0.0080 = 0.80% (rounded to the nearest thousandth)
So the answer is 0.80%
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juan starts walking at 4 miles per hour. an hour and a half later, cathy starts jogging along the same route at 5 miles per hour. how long will it take cathy to catch up with juan?juan starts walking at 4 miles per hour. an hour and a half later, cathy starts jogging along the same route at 5 miles per hour. how long will it take cathy to catch up with juan?
Answer:
6 hours
Step-by-step explanation:
They meet at distance d from their starting point.
Juan walks at 4 mph for time t.
Cathy jogs at 5 mph for time t - 1.5 since she starts 1.5 hour later.
speed = distance/time
distance = speed × time
Juan
d = 4t
Cathy
d = 5(t - 1.5)
4t = 5t - 7.5
t = 7.5
They meet 6.5 hours after Juan started walking.
Cathy jogged for 1.5 hours less than Juan walked.
7.5 hours - 1.5 hours = 6 hours
Answer: 6 hours
A student bought a pair of sunglasses in the USA. He paid $35.50 in the USA. In England, an identical pair of sunglasses costs £26.99 The exchange rate is £1 = $1.42. How much more did he pay for them in England compared to the USA?
Answer:all you do is multiply 26.99*1.42
this equals 38.33 dollars
35.50 is less than 38.33
thus, USA is cheaper than England.
Step-by-step explanation:
Which text structure does Scott Westerfeld use in this excerpt from Leviathan?
A descriptive
B problem solution
C cause and effect
D sequencing
The different text structures are discussed below.
What is text structure?Text structures refer to the way authors organize information in text.Recognizing the underlying structure of texts can help students focus attention on key concepts and relationships, anticipate what is to come, and monitor their comprehension as they read.Given is the excerpt from Leviathan by Scott Westerfeld.
Since the excerpt is not given, we will have a brief idea about the given text structures.
Description-Explanation
A description text structure shows mental images of the details of an event, person, place, or object. An explanation text structure shows a set of facts, which clarify the context, causes, and consequences of those facts.
Problem-Solution
A problem-solution text structure presents a problem, including why there is a problem, followed by one or more possible solutions.
Cause-Effect
A cause and effect text structure shows the connection between what has happened and its impact or result. Cause is what happened. Effect is the resulting action or consequence.
Sequence-Time
A sequence-time text structure describes or explains how things happen or work in chronological order.
Therefore, the different text structures are discussed above.
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What is 4.5pi minus pi/0.5?
Answer:
≈ 7.8598
Step-by-step explanation:
Let's round pi to 3.14159. First, we multiply 3.14159 by 4.5, which is around 14.13716. Then, we divide 3.14159 by 0.5, which is around 6.28318. So, 14.13716 - 6.28318 = 7.8598
models that are based on mathematic formula are called _____ models.
Symbolic models are those that are based on mathematical formulas.
By symbolic model, what do you mean?The goal of symbolic modelling is to help clients become more aware of their own "symbolic domain of experience," allowing them to create their own "metaphor landscape" and explore internal metaphors, which are believed by conceptual metaphor theory to influence behaviour.
What benefits do symbolic models offer?
One of the most significant and defining technologies of next-generation modelling methodologies is swiftly emerging as symbolic computation. It allows the freedom to easily create model equations, manage models more effectively, and reach the best outcomes more quickly.
Describe domain through an example.
the domain name example.com might be connected to the address 198.102. 434.8.
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if you find you are on a wait and have a party of 8 to accommodate, how many tables should you bring in and push together to fit the party of 8? (all your tables are 4 tops and square.)
If you are trying to accommodate a party of 8 and you have square tables that seat 4 people each, you would need to bring in 2 tables and push them together to fit the party of 8.
The reason for this is that 4 people can be seated at each table, and 2 tables together would provide enough seating for 8 people. Pushing the tables together will create a larger table that can accommodate the party of 8. It's important to ensure that the tables are pushed together securely so that they don't move or separate during the meal.
It's also important to consider the layout of the tables and how they will fit in the space where they will be used. It's a good idea to measure the space and the tables to ensure that they will fit comfortably and provide enough room for people to sit and move around. If the tables need to be rearranged or moved, it's important to do so carefully to avoid damaging the tables or injuring yourself or others.
When setting the tables, it's also important to consider the comfort of the diners. Make sure that there is enough room for people to sit comfortably and move their arms and legs, and that the tables are positioned so that everyone has a clear view of their surroundings and is not blocked by other diners or objects.
In conclusion, to accommodate a party of 8, you would need to bring in 2 square tables that seat 4 people each and push them together. It's important to consider the layout and comfort of the diners, as well as the safety of the tables and those who are setting them up.
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5200 is invested into an account that pay’s simple Interest annually after 8 years there is £6,240 in the account at what rate dose the account pay simple interest?
On solving the provided question, we can say that we have been provided with, by Simple Interest SI = PRT/100 =>rate = 15% per yr
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.
we have been provided with,
Interest = 6240
principal = 5200
time = 8 yrs
so, by SI = PRT/100
R = SI * 100/PT = 15%
rate = 15% per yr
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A 20-minute TV program consists of two commercials, each 13 over 4 minutes long, and three equal-length entertainment segments. How long is each entertainment segment? Enter your answer as a decimal.
Each single entertainment segment is 4.5 minutes.
How to find how long is each entertainment segmentOut of the 20 minute show there are two blocks of time that are ads. The ads are each 13/4 minutes long.
13/4 = 13 ÷ 4 = 3.25
minutes.
Let's take away the time used for ads from the 20 minute total.
20 - 3.25 - 3.25
= 13.5
Without ads the show's actual runtime is 13.5 minutes.
Now we'll divide that 13.5 into three equal parts.
13.5 ÷ 3 = 4.5
Each of the three equal entertainment segments is 4.5 minutes long.
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In the example, was more glass used to make the cone paperweight or the cylinder paperweight? How much more
There was more glass used to make the cylinder paperweight, and there was 16π cm³ more glass was used.
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Given that, Two solid glass paperweights in the shape of a solid cone having height 6 cm and radius 4 cm, and a solid cylinder with height 3 cm and diameter of 8 cm, we need to find the volume of glass used to make each paperweight,
Volume of cylinder = π×radius²×height
Volume of cone = π×radius²×height / 3
Therefore,
Volume of the cylinder =
π × 4² × 3
= 48π cm³
Volume of cone = π × 4² × 6 / 3
= 96π / 3
= 32π cm³
Therefore, the volume of glass used in the cone paperweight is 32π cm³, and the volume of glass used in the cylinder paperweight is 48π cm³
And, 48π-32π = 16π
Since, the volume of cylindrical paperweight is more than conical paperweight, therefore, there was more glass used to make the cylinder paperweight, and there was 16π cm³ more glass was used.
Hence, there was more glass used to make the cylinder paperweight, and there was 16π cm³ more glass was used.
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The question was incomplete, so I solved for,
"Two solid glass paperweights are shown at the right. What is the volume of glass used to make each paperweight? Write the volumes in terms of pi"
In the example, was more glass used to make the cone paperweight or the cylinder paperweight? How much more?
find the volume of the composite solid. round your answer to the nearest tenth
Answer:
2488.46 ft³
Step-by-step explanation:
the composite solid consists of;
cone and cylinder
volume of a cone=⅓πrh
volume of a cylinder=πr²h
then sum up the volume
⅓×3.142×8×9= 75.408 ft³
3.142×8×8×12=2413.056
2413.056+75.408=
2488.46 ft³
according to a 2018 survey, 74 percent of employed young adults expect to bring work on a vacation trip. a random sample of 20 employed young adults will be selected. what is the probability that 8 of the selected young adults will expect to bring work on a vacation trip? responses (208)(0.26)8(0.74)12 20 choose 8, times 0.26 to the eighth power, times 0.74 to the twelfth power (208)(0.74)8(0.26)12 20 choose 8, times 0.74 to the eighth power, times 0.26 to the twelfth power (128)(0.26)8(0.74)12 12 choose 8, times 0.26 to the eighth power, times 0.74 to the twelfth power (128)(0.74)8(0.26)12 12 choose 8, times 0.74 to the eighth power, times 0.26 to the twelfth power (288)(0.26)8(0.74)12
There is a 0.00108 probability of choosing 8 candidates the option b from given choices.
The discrete probability distribution known as the binomial distribution only offers Success or Failure as the only two possible outcomes for an experiment. In a binomial distribution, the two parameters n and p are employed. The variables "n" and "p" indicate how many times the experiment is conducted and the probability of each possible outcome, respectively. Let X be the interesting random variable; in this instance, we can suppose that it follows the following distribution: x- Binomial (n = 20; p = 0.74).
For the Binomial distribution, the probability mass function is given as
: p(x) = ( ⁿc ₋ₓ)ˣ (1 - p)ⁿ⁻ˣ.
where ( ⁿc ₋ₓ)ˣ refers to a combination. In this instance, we want this probability.
P ( x = 8 ) = (²⁰c₋₈) × (0.74)⁸ (1-0.74)²⁰⁻⁸ = 0.00108.
The probability of choosing 8 young adults is 0.00108.
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complete Question
according to a 2018 survey, 74 percent of employed young adults expect to bring work on a vacation trip. a random sample of 20 employed young adults will be selected. what is the probability that 8 of the selected young adults will expect to bring work on a vacation trip?
a) (²⁰c₈)(0.26)⁸(0.74)¹²⁻²⁰ choose 8, times 0.26 to the eighth power, times 0.74 to the twelfth power
b) (²⁰c₈)(0.74)⁸(1-0.74)²⁰⁻⁸ choose 8, times 0.74 to the eighth power, times 0.26 to the twelfth power
c) (¹²c₈)(0.26)⁸(0.74)¹²⁻¹² choose 8, times 0.26 to the eighth power, times 0.74 to the twelfth power
d) (¹²c₈)(0.74)⁸(0.26)¹²⁻¹² choose 8, times 0.74 to the eighth power, times 0.26 to the twelfth power (288)(0.26)8(0.74)12
a student bought a smartwatch that tracks the number of steps she walks throughout the day. the table shows the number of steps recorded t minutes after 3:00 p.m. on the first day she wore the watch. t (min) 0 10 20 30 40 steps 3,288 4,609 5,772 6,686 7,128 (a) find the slopes of the secant lines corresponding to the given intervals of t.
The slopes of the secant line corresponding to the given intervals of t is 132.1, 116.3, 91.4 and 44.2 steps per minute.
To find the slope of a secant line between two points, we need to divide the difference in the y-values (number of steps) by the difference in the x-values (time in minutes).
For the interval from t = 0 to t = 10 minutes:
y1 = 3,288 steps
y2 = 4,609 steps
x1 = 0 minutes
x2 = 10 minutes
The slope of the secant line is:
(y2 - y1) / (x2 - x1) = (4,609 - 3,288) / (10 - 0)
= 1,321 / 10
= 132.1 steps per minute
For the interval from t = 10 to t = 20 minutes:
y1 = 4,609 steps
y2 = 5,772 steps
x1 = 10 minutes
x2 = 20 minutes
The slope of the secant line is:
(y2 - y1) / (x2 - x1) = (5,772 - 4,609) / (20 - 10)
= 1,163 / 10
= 116.3 steps per minute
Similarly, for interval t = 20 to t = 30 minutes
Slope = (6,686 - 5,772)/ (30 - 20) = 91.4 steps per minute
for interval t = 30 to t = 40 minutes
Slope = (7,128 - 6,686)/ (40 - 30) = 44.2 steps per minute
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assuming that no one is born on feb. 29 (leap day), how many people should be selected to guarantee that at least 7 were born on the same day, not considering the year?
The number of people that should be selected to guarantee that at least 6 were born on the same day are, 2190
What are the Worst Case Scenarios?The worst case scenario is one of the many possible cases where the desired outcome comes after every other probable outcome has already occurred. This case can be used to determine the number of turns with would require to make sure the desired outcome is achieved.
The number of people that will ensure at least 7 people have their birthday one single day of a non-leap year (365 days) can be determined by considering that in the number of people picked in each trial, no two people have their birthday on the same day.
According to this process, if we pick 365 people, each one is born on a different day.
We repeat this selection 6 times, and the worst-case scenario is that on each day of the year, there are 6 people who are born on that day. The total number of people selected are
365×6 = 2190.
Now, as we select one more person, the number of people born on a day for one of the days in the year will increase to 7.
Hence, the number of people that should be selected to guarantee that at least 6 were born on the same day are, 2190
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