Distance of the race is 500 feet.
Given that tortoise moves at 50 feets per hour and hare moves at 250 feets per hour.
So speed of tortoise = 50 feets per hour.
Speed of hare = 250 feets per hour.
Let hare takes T hours to complete the race
Than tortoise will take (T + 8) hours to complete the race.
Total distance traveled by hare = speed * time = 250T
Total distance traveled by tortoise = speed * time = 50(T + 8)
Total distance traveled by both is same.
250T = 50(T + 8)
250T = 50T + 400
250T – 50T = 400
200T = 400
T = 2 hours
So, total distance of the race = 250T = 250 * 2 = 500 feet.
Therefore, total distance of the race is 500 feet.
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the weight of football players is normally distributed with a mean of 220 pounds and a standard deviation of 15 pounds. what is the minimum weight of the middle 95% of the players?
The minimum weight of the middle 95% of the players are 151 pounds.
The question is asking for the lower bound of the 95% two tailed Confidence interval of the normally distributed population.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
95% of C.I. is given by 220 + or - 1.96(15)
= 200 + or - 29 = (191)
Two standard deviations is =2×15=30 pounds
Minimum Weight =220−29 = 191 pounds
Therefore, the minimum weight of the middle 95% of players is 191 pounds.
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a water system of 2 in. (inside diameter) pipe, having a length of 1 4 mile, is to be flushed with a volume of water equal to twice that contained in the system. how much water (gallons) must be flushed through the system?
To flush twice the volume of water contained in the system, you would need to flush 18.2 gallons x 2 = 36.4 gallons of water through the system.
Calculate the volume of waterTo calculate the volume of water contained in the system, you would use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the pipe (half the diameter), h is the length of the pipe, and π is approximately 3.14.
In this case, the radius of the pipe is 2 inches / 2 = 1 inch, and the length of the pipe is 1/4 mile = 1320 feet (since there are 5280 feet in a mile).So the volume of the pipe is: V = πr^2h = 3.14 x (1 inch)^2 x 1320 feet = 4201.6 cubic inches.Since there are 231 cubic inches in a gallon, the number of gallons of water in the pipe is: 4201.6 cubic inches / 231 cubic inches/gallon = 18.2 gallons.To flush twice the volume of water contained in the system, you would need to flush 18.2 gallons x 2 = 36.4 gallons of water through the system.Learn more about the volume of water here:
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bryce and alejandro hiked miles. In one day, dominic hiked times as far as bryce and alejandro hiked. How far did he hike?
We can write the expression as →
{z} = n{x + y}
What are algebraic expressions?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.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Bryce, Alejandro and Dominic went for hiking.
Assume that Bryce and Alejandro travelled {x} and {y} miles respectively.
Assume that Dominic hiked {z} miles and {n} times as far as Bryce and
Alejandro hiked.
We can write the expression as -
z = n{x + y}
Therefore, we can write the expression as →
{z} = n{x + y}
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Which lines are perpendicular to 3x – y = 10? Select all that apply.
A. y = 3x + 5
B. y = –1/3x + 17
C. x + 3y = 27
D. y – 2 = 1/3 (3x + 36)
The lines that are perpendicular to 3x – y = 10, are y = –1/3x + 17 and x + 3y = 27.
The correct option is B and C.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
We have a linear equation,
3x – y = 10.
Arranging to the slope-intercept form.
y = 3x - 10.
The slope of the lines that are perpendicular to line y = 3x - 10,
= negative reciprocal of 3
= -1/3
Therefore, the required lines are y = –1/3x + 17 and x + 3y = 27.
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Solve each inequality and graph the solution on a number line.
a. x² - 2x 15 < 0
b. |3x-2| ≥ 10
The solution of the given inequalities is given below:
a. x < 5 or x < -3
b. x ≥ 4
What is the solution of an inequality?The solution of an inequality is the value that will make the inequality true.
The solution of the given inequalities is determined as follows:
a. x² - 2x - 15 < 0
x² - 5x + 3x - 15 < 0
x(x - 5) + 3(x - 5) < 0
x - 5 < 0
x < 5
or
x + 3 < 0
x < -3
b. |3x-2| ≥ 10
3x - 2 ≥ 10
3x ≥ 10 + 2
3x ≥ 12
x ≥ 4
The solutions are shown in the number lines attached.
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An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 11 more than four times the length of the bottom of the triangle. The last side is 11 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle. Help please i'm not smart-
The expression for the perimeter of the triangle will be 6x + 22.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
A workmanship class is making a painting for their school which has a triangle attracted the center. The length of the lower part of the triangle is x. Another side is 11 a larger number of than 4 times the length of the lower part of the triangle. The last side is 11 a greater number of than the lower part of the triangle.
Then the dimension of the triangle will be x, 4x + 11, and x + 11. Then the perimeter isgiven as,
P = x + 4x + 11 + x + 11
P = 6x + 22
The expression for the perimeter of the triangle will be 6x + 22.
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1
2
2
y=1/30
y=3(4)
d
(3) *
LO
Which function is graphed below?
5
6
6
.CO...
8
X
7
8
9
10
TIME REMAIN
45:49
In a connection that is represented by an exponential function, the independent variable's proportional change is unchanged with a constant change in the independent variable.
Explain about the exponential function?Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.
When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.
After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The fundamental exponential function generally has the shape,
y = nakx-------
(0,3) is the function's y intercept.
This location has to satisfy the equation (1). So let's substitute in order to get,
3 = na k(0)
⇒ 3 = n x a 0
⇒ 3 = n x 1
⇒ n = 3
Our equation 1 now changes.
y = nakx-------
Noting that the graph crosses through,(1 ,1) it must also satisfy its equation because it does so. Equation (2) can be solved by substituting this point, giving us
1 = 3ak (1)
⇒ 1/3 = ak
Now let's enter the value of ak = 1/3 into equation (3) to get,
y = 3(1/3)x
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12. Estimate the average rate of change of p between peak, p(8), and closing, p(14). What is
the meaning of the rate of change in the context of this problem? Show all work.
The rate of change in this context refers to the change in the value of p, specifically between the peak and closing.This allows us to understand how much p changes on average between these two points in time.
What is the meaning of the rate of change in the context of this problem?It is a measure of how quickly or slowly the value of p is changing over time.
By calculating the average rate of change, we can understand the overall trend of the value of p and whether it is increasing or decreasing at a steady rate or if there are fluctuations.
This information can be useful for understanding the performance of a stock or investment, as well as predicting future trends.
Additionally, the rate of change can also help to identify any potential issues or opportunities within the market.
Overall, the rate of change provides a clear picture of the stock's performance over a certain period of time.
To calculate the average rate of change of p between peak and closing, we need to find the difference in p values (p(14) - p(8)) and divide that by the difference in time (14 - 8).
p(14) - p(8) = ? - ? = ?
(14 - 8) = ?
The average rate of change of p is ?/6.
The meaning of the rate of change in the context of this problem is the average change in the value of p per unit of time.
In this case, we are looking at the average change in p between the peak and closing, and expressing that change as a ratio of p(14) - p(8) to (14 - 8). This allows us to understand how much p changes on average between these two points in time.
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Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
i think it is 326.7 but i really not sure
For every mile of highway on land, the city needs two truckloads of asphalt and one gallon of paint. For every mile of highway on bridges, the city needs one truckload of asphalt and three gallons of paint. The city has 50 truckloads of asphalt and 80 gallons of paint.
(a)What is the largest total number of miles of highway the city can build?
(b)Suppose the city is on an island and must build at least 25 miles of highway on bridges to reach other islands. Now what is the largest total number of miles of highway the city can build?
A Are they are limited to the amount of paint they have? 80g / 1 g/mile = 80 miles using all of the paint
50 trucks /2 trucks/mile = 25 miles using all of the trucks of asphalt
B 25 miles of bridge = = 25 trucks leaving 25 trucks of asphalt 25 trucks/2 trucks/mile = 12.5 miles of land highway possible
25 miles of bridge = 25 miles x 3 gal/mile = 75 gallons of paint leaving only 5 gallons of paint for 5 add'l land miles
25 miles of bridge + 5 land miles = 30 miles total highway .
Translate the following statement to a symbolic representation. Papa Smurf is green or the Snorks use clams as money
The symbolic representation is pUq
Symbolic representation is defined as the representation of a principal, a nation for example, through a symbol, such as a flag, that evokes particular meanings and emotions about the nation
Papa Smurf is green or the Snorks use clams as money
let's suppose p = Papa Smurf is green
or q = Snorks use clams as money
here and logic is used in between Papa Smurf being green or the Snorks using clams as money
Or logic is represented by "U".
pUq will be the correct answer.
NOTE- a symbolic representation of Or is U.
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Let us assume that you started a job on 08/21/2019. You graduated on 05/20/2022. How many days have you been working at the job as a student?
Group of answer choices
a. 1215
b. 1287
c. 905
d. 1003
I have been working 1004 days at the job as a student
They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, and division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:Start = 08/21/2019Graduated = 05/20/2022Days =?Calculate the days from 08/21/2019 to 08/21/2022, we get:
Days 1 = (08/21/2022 - 08/21/2019) * (365 days/1 year)
Days 1 = 3 years * (365 days/1 year)
Days 1 = 1095 days
Calculate the days from 05/21/2019 to 08/21/2019, we get:
Days 2 = (08/21/2019 - 05/21/2019) * (30 days / 1 month)
Days 2 = 3 months * (30 days / 1 month)
Days 2 = 90 days
Calculating the days from 05/20/2019 to 05/21/2019, we get:
Days 3 = 05/21/2019 - 05/20/2019
Days 3 = 1 day
Calculate the total days from 08/21/2019 to 05/20/2022, we get:
Total days = Days 1 - days 2 - days 3
Total days = 1095 days - 90 days - 1 day
Total days = 1004 days
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Which answer choice correctly shows 6 x 6 in exponential notation?
The expression that correctly shows 6 x 6 in exponential notation is 6²
How to determine the expression in exponential notationFrom the question, we have the following parameters that can be used in our computation:
6 * 6
Next, we apply the law of indices/exponent
So, we have the following representation
6¹⁺¹
Evaluate the sum
6²
Hence, the correct expression of 6 * 6 is 6²
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in a sample of 2000 people, 430 people have their ears pierced. two unrelated people are selected at random without replacement, find the probability that at least one of the people selected have their ears pierced.
How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.There is a 50% chance that the outcome will be heads, thus 50 heads are to be expected. When we really attempt it, though, we might instead get 48 heads, 55 heads, or anything else at all, but in most situations, it will be a figure close to 50.How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.To learn more about probability refer to:
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Use the table, which shows the number of monthly users, in millions, for the 10
most used mobile gaming apps. Let the 10 mobile gaming apps be the universal
set. Use the list to determine the following set in roster form.
The set of mobile gaming apps in which the number of monthly users was greater
than 12 million.
Select the correct choice below and, if necessary, fill in the answer box within your
choice.
O A.
(Use a comma to separate answers as needed.)
OB. Ø
…
Mobile
Gaming App
A
B
CTIOπποο
D
Mobile
(in mill
23
5
6
6
13
9
12
11
11
10
The set of mobile gaming apps in which the number of monthly users was greater than 12 million is {A, B}
How to find the set of mobile gaming apps with monthly users greater than 12 million?A set is a collection of distinct objects, called elements or members, that are brought together by a common property or rule.
Sets can be represented using set notation, which uses curly brackets {} to enclose the elements of the set. For example, the set of natural numbers less than 5 can be represented as {1, 2, 3, 4}.
The set of mobile gaming apps in which the number of monthly users was greater than 12 million can be determined by checking given the table for mobile gaming apps with value greater than 12 million.
You will notice that only A and B have values greater than 12 million. That is 23 million and 13 million for A and B respectively.
Thus, the set will be {A, B}
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if thieves were to steal platinum from a bank using a small truck with a maximum payload capacity of 700 lb , how many 1 l bars of the metal could they take?
The thieves could take approximately 1555 bars of platinum.
Pt stands for platinum, an atomic number 78 chemical element. It is a thick, malleable, ductile, very inert, silvery-white-colored transition metal. Its name comes from the Spanish diminutive platina, meaning "silver"
One 1 lb bar of platinum has a volume of approximately 0.11 cubic feet. Assuming the density of platinum to be approximately 21 g/cm^3, the weight of 1 lb bar of platinum is approximately 0.45 kg. The maximum payload capacity of the small truck is approximately 317 kg. Hence, the thieves could take approximately 700 / 0.45 = 1555 bars of platinum.
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Given that B is between A and C,
find the value of x and the measure
of BC.
AB = 3x, BC = 5x, and AC = 8.
The numerical value of x and the measure of segment BC are 1 and 5 respectively.
What is the numerical value of and the measure of BC?Given that; B is a point between A and C.
Segment AB = 3xSegment BC = 5xSegment AC = 8Since B is between A and C
AC = AB + BC
8 = 3x + 5x
Solve for x
8 = 8x
8x = 8
x = 8/8
x = 1
Next, determine the measure of BC,
BC = 5x
Plug in x = 1
BC = 5( 1 )
BC = 5
Therefore, x equal 1 and the measure of BC is 5.
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whats the parallel equation and perpendicular?
The equations of the lines are
Parallel lines: y = 4/3x + 2 and y = 4/3x - 2Perpendicular line: y = -0.75x + 8.5How to determine the equationsThe parallel lines
We have the points to be
(3, 6) and (0, 2)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 2
Using the points, we have
6 = 3m + 2
So, we have
3m = 4
Divide
m = 4/3
So, the equation is
y = 4/3x + 2
For the other parallel line, we have
y = 4/3x - 2
Perpendicular line
The slopes of parallel and perpendicular lines are opposite reciprocals
So, we have
m = -3/4
This gives
y = -3/4x + c
We have the point to be (0, 8.5)
So, we have
y = -3/4x + 8.5
y = -0.75x + 8.5
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a bagel factory produced 90 bags of bagels. there were 10 bagels in each bag. how many bagels did the factory produce?
Answer:
900
Step-by-step explanation:
90 x 10
Part of the population of 6,000 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 7 of them are infected. How many elk are likely to be infected?
Answer: The number of elk that are likely to be infected can be estimated using the sample proportion of infected elk. The sample proportion is the ratio of the number of infected elk in the sample to the total number of elk in the sample.
In this case, the sample proportion is:
7/50 = 0.14
This proportion can be used to estimate the proportion of the entire population of elk that is infected. To do this, we can multiply the sample proportion by the total population of elk and round to the nearest whole number.
0.14 * 6,000 = 840
So, it's likely that 840 elk are infected.
Please note that this is an estimate and the actual number of infected elk could be different. Additionally, this estimation is based on a random sample, so it can have a margin of error.
Step-by-step explanation:
1. Cindy is doing a 30-day jumping jack challenge. On the first day she does 5 jumping jacks. On the second
day, she does 10 jumping jacks. On the third day, she does 15 jumping jacks. This pattern continues.
a. Let j(n) represent the number of jumping jacks Cindy does on the nth day of the challenge. Is j(n)
a linear function, a quadratic function, or neither? Explain.
Timear because w goes up by 5 each day.
b. Let t(n) represent the total number of jumping jacks Cindy has done by the nth day of the
challenge. Is t(n) a linear function, a quadratic function, or neither? Explain.
Answer:
a) linear function
b) quadratic function
Step-by-step explanation:
a) j(n) is a linear function since 5 is added everyday.
b) t(n) would be a quadratic function because the total amount of jumping jacks wouldn't have the same number that is beiung added.
day 1 = 5
day 2 = 15
day 3 = 30
day 4 = 50
day 5 = 75
This is showing that at first 10 jumping jacks are added but then for day 2 15 are added, for day 3 20 are added and so on.
simplify the expression 4^2(3-1/2)-121
Answer: its -81
hope this helps
Which is a correct solution for the following system of Inequalities
The correct solution for the following system of Inequalities is (-1, 1) because it is on the darker region.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Inequalities is used for the non equal comparison of these numbers and variables.
Let x represent the x axis and let y represent the y axis.
The solution to the system of linear equalities is the intersection of both inequalities which is the darker region.
The point that satisfies both inequalities as shown on the graph is (-1, 1) because it is on the darker region.
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A 5kg bag of peas cost $17.91 at the same rate what amount money would a 9kg bag of peas cost
The graph of a system of inequalities is shown.
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 6, negative 1) and (0, negative 4). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 2, negative 4) and (0, 0). Everything to the left of the line is shaded.
Which system is represented by the graph?
Answer:
graphing on a graph
Step-by-step explanation:
(Simple)......Classify the transformation pls
The transformation represented by the figure is (a) reflection
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we can
An arc and its mirrored image
When a shape is mirrored to form another, then the transformation is a reflection
Hence, the transformation is reflection
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The _____-coordinates of the endpoints are the same.?
The x-coordinates of the endpoints are the same.
What are the coordinates?
Coordinates are a set of numbers that are used to specify the position of a point on a graph or a coordinate plane. The most common type of coordinate system is the Cartesian coordinate system, which uses two perpendicular number lines called the x-axis and the y-axis to define the position of a point.
When talking about coordinates, there are two types of coordinates: x-coordinates and y-coordinates. The x-coordinate refers to the horizontal position of a point on a graph or a coordinate plane, while the y-coordinate refers to the vertical position of the point.
In the statement "The x-coordinates of the endpoints are the same," it means that the horizontal position of the two endpoints is the same. These endpoints could be the two points that define a line segment, a geometric figure, or a graph. The x-coordinates of both of these points are the same, while the y-coordinates could be different.
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a jet travels 2964 miles against the wind in 4 hours and 3564 miles with the wind in the same amount of time. what is the rate of the jet in still air and what is the rate of the wind?
The rate of the jet in still air is 741 mph, and the rate of the wind is 150 mph.
What is rate ?
A rate is a ratio of two quantities, typically a change in one quantity over a corresponding change in another quantity, often over a specific time period. For example, the interest rate on a loan is the ratio of the interest paid to the amount of the loan. A speed is a rate at which an object covers distance, velocity is a rate of change of position, etc.
To find the rate of the jet in still air:
Rate = Distance / Time
The distance is 2964 miles, and the time is 4 hours. So the rate of the jet in still air is:
Rate = 2964 / 4 = 741 mph
To find the rate of the wind, you can use the formula:
Wind Rate = (Distance with wind - Distance against wind) / Time
The distance with the wind is 3564 miles, the distance against the wind is 2964 miles, and the time is 4 hours. So the rate of the wind is:
Wind Rate = (3564 - 2964) / 4 = 600 / 4 = 150 mph
So the rate of the jet in still air is 741 mph, and the rate of the wind is 150 mph.
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in government data a household consists of all ocupants
American household size According to government statistics, a family is defined as two or more people who live together and are related by blood or marriage, whereas a household is defined as all the residents of a dwelling unit.
What do we mean by dwelling unit?A housing unit, also known as a dwelling unit or a housing unit, is a building, a portion of a building, or a space that is used as a home, a place to live, or a place to sleep by one or more people who maintain a common household.
Size of American households In contrast to a household, which is defined as all the occupants of a dwelling unit, a family is defined as two or more people who live together and are related by blood or marriage.
As a result, although all families are part of households, some households do not.
Therefore, American household size According to government statistics, a family is defined as two or more people who live together and are related by blood or marriage, whereas a household is defined as all the residents of a dwelling unit.
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which of the following is not true of a good hypothesis? a) it includes a null hypothesis b) it is experimentally testable c) it is phrased as an if, then statement d) it must contradict previous theories e) it could explain an unexpected observation.
False claims do not have to engage with previous theories in order to be effective. So it must contradict previous theories. So the option d is correct.
A tentative, verifiable explanation for a natural world phenomenon is what is known as a scientific hypothesis. The scientific method's foundational element is it.
It's sometimes referred to as a "informed guess" that was made using past knowledge and observation. Despite the fact that this is true, a hypothesis is a better guess.
Creating a hypothesis calls for active observation and background research, in contrast to making a "informed guess," which implies a random prediction based on one's expertise. A hypothesis is predicated on the fundamental tenet that no outcome is predetermined.
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