Answer as a mixed number = 1 1/8 mph
Answer as a decimal = 1.125 mph
Work Shown:
(3/4) of a mile : (2/3) of an hour
12*(3/4) of a mile : 12*(2/3) of an hour
9 miles : 8 hours
9/8 miles : 8/8 hours
1.125 miles : 1 hour
His speed is 1.125 miles per hour. This converts to the mixed number 1 1/8
a spherical balloon is being inflated at 3 cubic meters per second. how fast is the surface area changing in square meters per second when the volume is 36 cubic meters?
The surface area is changing at a rate of approximately 2.94 square meters per second when the volume is 36 cubic meters and the balloon is being inflated at 3 cubic meters per second.
Volume of a sphere in terms of its radius = V = (4/3)π[tex]r^3\\[/tex] .......(1)
Differentiating on both sides, [tex]\frac{dV}{dt}[/tex] = 4π[tex]r^{2}[/tex][tex]\frac{dr}{dt}[/tex] .......(2)
r = radius of the sphere.
Spherical balloon is being inflated at a rate of 3 cubic meters per second.
[tex]\frac{dV}{dt}[/tex] = 3 [tex]m^3/sec[/tex]
Volume is 36 cubic meters.
V = 36 [tex]m^3[/tex]
From equation (1), [tex]r^3[/tex] = [tex]\frac{3V}{4\pi }[/tex]
[tex]r^3[/tex] = [tex]\frac{3*36}{4*\pi }[/tex]
[tex]r^3\\[/tex] = [tex]8.59^1^/^3[/tex]
r = 2.04 meters
Substituting this in equation (2), [tex]\frac{dr}{dt}[/tex] = [tex]\frac{dV}{dt}[/tex] / 4π[tex]r^{2}[/tex]
[tex]\frac{dr}{dt}[/tex] = 3/(4π[tex]2.04^{2}[/tex])
[tex]\frac{dr}{dt}[/tex] = 0.05737 m/sec
Now, surface area of sphere = A = 4π[tex]r^{2}[/tex]
Differentiating on both sides,
Rate of change of surface area [tex]\frac{dA}{dt}[/tex] = [tex]8\pi r\frac{dr}{dt}[/tex]
= 8* 3.14* 2.04* 0.05737
= 2.94 [tex]m^2/sec\\[/tex]
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in how many ways can we arrange a standard deck of 52 cards so that all cards in a given suit appear contiguously (e.g., first all the spades appear, then all the diamonds, then all the hearts, and then all the clubs)?
There are 71,536,320 ways to arrange a standard deck of 52 cards so that all cards in a given suit appear contiguously.
There are 4 suits in a standard deck of 52 cards, and we need to arrange all the cards in a given suit contiguously. Once we choose a suit to be arranged in this way, we can treat it as a block of 13 cards that need to be arranged. Therefore, we have reduced the problem to arranging 4 blocks of 13 cards each, where each block represents a suit.
Within each suit, there are 13! ways to arrange the cards. However, once we arrange the cards in one suit, we fix the relative positions of the cards in the other suits. Therefore, we only need to consider the number of ways to arrange the suits themselves.
There are 4! = 24 ways to arrange the 4 suits. For each of these arrangements, there is only one way to arrange the cards within each suit contiguously. Therefore, the total number of ways to arrange the deck of cards so that all cards in a given suit appear contiguously is:
13! x 24 = 71,536,320
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There are 2.75 ounces of cream cheese in one slice of cheesecake. How
many ounces are there in a cake with 8 slices?
A. 22 ounces
B. 21.6 ounces
C. 16 ounces
D. 10.75 ounces
Answer:
Step-by-step explanation:
2.75 x 8 = 22
Which graph represents a linear function
Answer:
Any line except a vertical line represents a linear function.
Step-by-step explanation:
Any "diagonal" line is a linear function. Even a horizontal line represents a linear function. Only a vertical line does NOT represent a linear function.
The following is a WFF:
(S~T) V (~U.W)
Select one:
True or
False
The given statement about the disjunction is true.
What is Disjunction?A compound statement with two distinct statements (disjuncts) connected by the wedge symbol (v) is called Disjunction.
Given is the statement -
(S~T) v (~U.W)
The given statement about the disjunction is true.
Therefore, the given statement about the disjunction is true.
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a researcher records the change in weight (gain or lost) during the first semester of college for each individual in a sample of 25 freshmen, and calculates the average change in weight. this average is an example of a . group of answer choices
The average change in weight calculated by the researcher for the sample of 25 freshmen is an example of a statistic.
A statistic is a numerical summary of a sample that is used to make inferences about a population. In this case, the sample is the 25 freshmen, and the population could be all freshmen entering college.
The average change in weight is a statistic because it summarizes the data collected from the sample, and is used to make conclusions about the population.
It represents the typical or average amount of weight gained or lost by the freshmen in the sample during their first semester in college.
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What is the average rate of change of the function -4≤x≤-3
Check the picture below.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x) \qquad \begin{cases} x_1=-4\\ x_2=-3 \end{cases}\implies \cfrac{f(-3)-f(-4)}{-3 - (-4)}\implies \cfrac{[-6]~~ - ~~[-4]}{-3+4} \\\\\\ \cfrac{-6~~ + ~~4}{1}\implies \text{\LARGE -2}[/tex]
Answer:
-2
[tex]\hrulefill[/tex]
Step-by-step explanation:
The average rate of change of a function f(x) on the interval a ≤ x ≤ b can be calculated using the formula:
[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]
The given interval is -4 ≤ x ≤ -3, so:
[tex]a=-4[/tex][tex]b=-3[/tex]From observation of the given graph, the values of f(a) and f(b) are:
[tex]f(a)=f(-4)=-4[/tex]
[tex]f(b)=f(-3)=-6[/tex]
Substitute the values of a, b, f(a) and f(b) into the formula to calculate the average rate of change of the function f(x) on the interval -4 ≤ x ≤ -3:
[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(-3)-f(-4)}{-3-(-4)}\\\\&=\dfrac{-6-(-4)}{-3-(-4)}\\\\&=\dfrac{-6+4}{-3+4}\\\\&=\dfrac{-2}{1}\\\\&=-2\end{aligned}[/tex]
Therefore, the average rate of change of the function f(x) on the given interval is -2.
State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answer:
AAS
Step-by-step explanation:
[tex]\overline{PR} \cong \overline{PR}[/tex] by the reflexive property.
1 Aiden paints an unassembled gift box to use for
his sister's birthday gift.
The base of the box measures 2 inches by5 inches. When assembled the box measures7 inches tall. If Aiden only paints the outside of the unassembled box, how many square inches will he paint?
A 64 in.²
B 70 in.²
C 118 in.²
D 126 in.²
Suppose Q and R are independent events. Find P(Q and R).
P(Q) = 0.37, P(R) = 0.24
Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.
What is meant by probability?Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes.Statistics is the study of events subject to probability. The probability is typically expressed as a ratio between the number of positive outcomes and all of the outcomes in the sample space. It is written as follows: Probability of an Event P(E) = (Number of Favorable Outcomes) (Sample space).There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the discipline of mathematics that deals with the occurrence of a random event.Therefore,
Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.. In this instance, the likelihood of Q and R is equal to P(Q) × P(R), which is 0.1804. The solution to this issue is this.
The complete question is:
Suppose Q and R are independent events. Find the probability of Q and R when P(Q)=0.41 Ans P(R)=0.44.
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A water tower is 16 meters tall. Close by, there is a crane that is 24 meters tall. If the water tower's shadow is 30 meters long, how long is the crane's shadow?
The crane's shadow is 45 meters long when the crane is 24 meters tall.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"
Let the shadow cast by the crane be x.
The triangle formed by the tower and by the crane are similar.
Using the rule of similar triangles we have:
16/24 = 30/x
16x = (30)(24)
x = 45
Hence, the crane's shadow is 45 meters long.
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help pls! i don’t as much need the answer but to know how to do it?
Step-by-step explanation:
an inscribed angle has its vertex on the circle, and the sides of the angle are two chords of the circle.
the inscribed angle is half the size of the arc angle (the angle at the center of the circle) of the arc that the two sides cut out of the circle.
110° is the arc angle (at the center of the circle) of the arc GJ.
for the inscribed angle GFJ the vertex is F, and the angle there is half of the arc angle :
angle GFJ = 110/2 = 55°
the second problem is the opposite "direction".
we have the inscribed angle FJH = 36°.
and we want the arc angle FH.
now, since the inscribed angle is half of the arc angle, the arc angle is twice the inscribed angle :
arc angle FH = 36×2 = 72°
A local gym offers its members the opportunity to choose between two fitness classes: yoga and dance. Of the
400
400400 gym members,
300
300300 regularly attend yoga,
80
8080 regularly attend dance, and
50
5050 regularly attend yoga and dance. Using this information, answer each of the following questions. Let
Y
YY be the event that a randomly selected gym member regularly attends yoga and
D
DD be the event that a randomly selected gym member regularly attends dance
The probability of a gym member attending yoga is 0.625 or 62.5%.
Probability is the likelihood or chance of an event happening. In this scenario, we have information about the number of gym members attending yoga and dance, which can be used to calculate the probability of a gym member attending yoga.
Out of the 400 gym members, 300 regularly attend yoga, and 50 attend both yoga and dance. This means that the number of gym members attending only yoga is 300-50=250. The probability of a gym member attending yoga can be calculated by dividing the number of gym members attending yoga by the total number of gym members.
Probability of a gym member attending yoga= Number of gym members attending yoga/Total number of gym members
Probability of a gym member attending yoga= 250/400
Probability of a gym member attending yoga= 0.625 or 62.5%
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Complete Question:
400 gym members, 300 regularly attend yoga, 80 regularly attend dance, and 50 regularly attend yoga and dance. Using this information, answer each of the following questions.
What is the probability that a gym member attends yoga?
An equilateral triangle with side length 3 cm is shown in the diagram, work out the height of the triangle.
Give your answer rounded to 1 DP.
Answer:
The height of an equilateral triangle can be found using the Pythagorean theorem by treating it as a 30-60-90 triangle. In a 30-60-90 triangle, the ratio of the side lengths is 1:√3:2. In this case, the side length of 3 cm is the shorter leg, so the height (the longer leg) is 3√3 cm. Rounding to 1 decimal place, the height is approximately 5.1 cm.
What expression is equivalent to 24a+(-26b)-13a+12b?
The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.
What is algebraic expression ?
An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.
Examples of algebraic expressions include "3x + 4y", "2a^2 - 5b", and "(x + 3)(x - 2)".
Given expression ,
24a+(-26b)-13a+12b
= 24a - 13a +12 b - 26b
= 11a - 14b
Therefore, The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.
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shelly spent 40 minutes jogging and 22 minutes cycling and burned 620 calories. the next day, shelly swapped times, doing 22 minutes of jogging and 40 minutes of cycling and burned the same number of calories. how many calories were burned for each minute of jogging and how many for each minute of cycling?
Calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.
Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations.
When the equations are solved simultaneously, they are known as simultaneous equations.
Jogging be considered as x
Cycling be considered as y
Shelly spent 40 minutes jogging and 22 minutes cycling, and burned 620 calories to write this in equation we get,
40x + 22y = 620
Shelly swapped times,
22 minutes of jogging and 40 minutes of cycling and burned the same number of calories,
22x + 40y = 620
By multiplying two equation we get,
multiply equation 1 by 22 and equation 2 by 40 we get,
880x + 484y = 13640
880x + 1600y = 24800
Now subtracting equation 1 from 2 we get,
1116y = 11160
y = 11160/1116
y = 10
Therefore, putting value of y in equation 1 we get,
880x + 484(10) = 13640
880x = 13640 - 4840
x = 8800/880
x = 10
Therefore, calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.
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so what is 24 water bottles and 12 oz and 30 guest and 1 cup
There will be enough water for all the guests.
What are Measurements?Measurement is the method of comparing the properties of a quantity or object using a standard quantity.
Measurement is essential to determine the quantity of any object.
Total number of bottles = 24
Capacity of each bottle = 12 oz
Total capacity of the 24 water bottles = 12 × 24 = 288 oz
Now we have,
8 ounces = 1 cup
288 ounces = 288 / 8 = 36 cups
So there are 36 cups of water in total.
Number of guests = 30
If each guest drinks one cup of water, there will be 36 - 30 = 6 cups of water remaining.
Hence there will be enough water for the guests with 6 cups of water remaining.
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Your question is incomplete. Probably the correct question is as follows.
Before a party, Ashley bought a tray of 24 water bottles, each bottle has a capacity of 12 oz. There are 30 guests. If each guest drinks I cup of water, is there enough water for all the guests?
please heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp:
Determine whether each sequence is geometric. If so, find the common ratio
The sequence 3, 18, 108, 648, ..... is a geometric sequence.
The sequence 3.9, 19.5, 97.5, -487.5, ..... is a geometric sequence.
The sequence 1.1, -2.2, 4.4, -8.8, ..... is a geometric sequence.
The sequence 4, 20, 4, 20, ..... is not a geometric sequence.
How to calculate the nth term of a geometric sequence?In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Next, we would determine the common ratio as follows;
Common ratio, r = a₂/a₁ = a₃/a₂
Common ratio, r = 18/3 = 108/18
Common ratio, r = 6 = 6 (geometric sequence).
Common ratio, r = -19.5/3.9 = 97.5/-19.5
Common ratio, r = -5 = -5 (geometric sequence).
Common ratio, r = -2.2/1.1 = 4.4/-2.2
Common ratio, r = -2 = -2 (geometric sequence).
Common ratio, r = 20/4 = 4/20
Common ratio, r = 5 = 0.2 (not a geometric sequence).
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equation of the blue line?
Answer:
Step-by-step explanation:
y=kx+b
b=3
(1,5)
1*k+3=5
k=2
so, 2x+3=y
Mary is ( x -1 ) years old now. How old
i) was he 4 years ago?
ii) will he be 8 years from now?
iii) is he now, if his age in 8 years time will be three times his age 4 years ago
Mary age is ( x -1 ) years old now. 4 years ago= ( x -1 )-4 =0, x=4+1=5,
now he is x -1 =5-1=4, 4 years ago=5-4=1 year, iii) (3*8/3+8)=16 year old
Will he be 8 years from now .now she is 4 year old now.
if he is x year old . he will be 8 years from now=(3x+8)=0
x=- 8/3. now his age is (3x+8) =(3*8/3+8)=16
A time of human existence, defined in years starting at birth, that is typically characterized by a certain stage or degree of mental or physical development and involves the potential for legal responsibility. the discretionary age. the legal drinking age. The legal drinking age was increased by the state from 18 to 21. Age is a notion that describes a person's age at a specific period. It is described as the measurement of the amount of time that has passed between the date of the live birth to a particular point in time, typically the date the data was collected. Age range, according to the Longman Dictionary of Contemporary English, is the term for a group of people who fall between two certain ages.
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The length of a rectangle is shown below:
On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. The point A is on ordered pair 1, 2, and the point B is on ordered pair negative 2, 2. A straight line joins the points A and B.
If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (5 points)
C(−2, −1), D(1, −1)
C(−2, −4), D(1, −4)
C(−2, −2), D(1, −2)
C(−2, −5), D(1, −5
I NEEP HELP WITH THIS ONE LISTED BELOW:A solid is composed of squares and equilateral triangles. Its net is shown below:
A triangular prism and its net are shown. The net is three squares with side length 4 units. Attached above and below the middle square are equal sized triangles.
The area of each triangle is 7 square units. The surface area of the triangular prism is
square units. (Input whole number only.) (5 points)
PLEASE
The surface area of the triangular prism is 62 square units.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.
The side length of each of the three squares is 4 units.
The area of each would be:
4² = 16 sq. units.
For the three squares we have:
16(3) = 48 sq. units.
The area of each triangle is 7 sq. units.
This means together the area of the two triangles is 2(7) = 14 sq. units.
The surface area of the prism is:
14 + 48 = 62 sq. units.
Hence, the surface area of the triangular prism is 62 square units.
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Can anyone give me the answer ? will give brainliest
In given lines, y = -1/4 x + 7 represents a transversal line.
What is Transversal Line:A transversal is a line that, at two different locations, cuts through two lines in the same plane. Various types of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
Here we have
y = 1/6x - 3 ---- (1)
y = -1/4 x + 7 ---- (2)
y = 1/6x - 9 ---- (3)
Here given lines are in y = mx + c form
The slope of the line (1) is 1/6
The slope of the line (2) is -1/4
The slope of the line (3) is 1/6
As we can see that line (1) and line (3) have the same slope,
Hence, Lines (1) and (3) are two parallel lines
where Line (2) is transversal which cuts the given two parallel lines
Therefore,
In given lines, y = -1/4 x + 7 represents a transversal line.
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A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function?
Answer:
=3y - x =0
Step-by-step explanation:
[tex] \frac{y - y1}{x - x1} = m[/tex]
Therefore the gradient ( m ) is not given
from the question point =(-9,-3) and (-12,-4).
Gradient (m) =
[tex] \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 4 - ( - 3)}{ - 12 - ( - 9)} \\ = \frac{ - 4 + 3}{ - 12 + 9} \\ = \frac{ - 1}{ - 3} \\ = \frac{1}{3} [/tex]
therefore m = 1/3.
The equation
[tex] = \frac{y - y1}{x - x1} = m \\ \frac{y - ( - 3)}{x - ( - 9)} = \frac{1}{3} \\ \frac{y + 3}{x + 9} = \frac{1}{3} \\ 3(y + 3) = 1(x + 9) \\ 3y + 9 = x + 9 \\ 3y = x + 9 - 9 \\ 3y = x + 0 \\ 3y - x = 0[/tex]
therefore the equation of the line = 3y-x=0
4 less than the product of 7 and a number.
Answer:
7n - 4
Step-by-step explanation:
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 4
Blue 3
Green 2
Yellow 2
Purple 6
Based on these results, express the probability that the next spin will land on blue as a fraction in simplest form.
Answer: 3/17 or 17.64%
Step-by-step explanation:
Just add everything (adds up to 17), then you put the color frequency number as the numerator of the fraction, then have the added up number as the denominator.
what is 1/2 d =52 so what is the answer
Answer:104
Step-by-step explanation:
If 1/2 d=52,
d/2=52
Multiply both sides by 2.
Thus, d=52×2= 104.
Hope this helps! :)
How to write a congruence statement
Answer:
Step-by-step explanation: A congruence statement expresses that two figures have the same size and shape. Here's how you can write a congruence statement step by step:
Write the two figures you want to compare. For example, you could write "Triangle ABC" and "Triangle DEF".
Use the symbol "≅" to indicate congruence. Place the symbol between the two figures, like this: "Triangle ABC ≅ Triangle DEF".
Label the corresponding parts of the two figures to show that they are congruent. For example, you could write "AB = DE", "BC = EF", and "AC = DF".
The final congruence statement would look like this: "Triangle ABC ≅ Triangle DEF, with AB = DE, BC = EF, and AC = DF". This statement says that Triangle ABC is congruent to Triangle DEF, and that the lengths of their corresponding sides are equal.
The lengths of the three sides of a triangle (in inches) are consecutive integers. If the
perimeter is 27 inches, find the value of the shortest of the three side lengths.
The value of the shortest of the three side lengths is 3 inches.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The lengths of the three sides of a triangle (in inches) are consecutive integers.
The three sides are x, x+1 and x+2 which are consecutive.
We know that perimeter of a triangle is the sum of the three sides of a triangle.
Add the three Consecutive sides to find the perimeter.
Perimeter of triangle=x+x+1+x+2
The perimeter of triangle is 27 inhces.
27=3x+3
Substitute 3 from both sides
24=3x
Divide by 3 on both sides
8=x
Hence, the value of the shortest of the three side lengths is 3 inches.
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The best fit line is given by the equation y = 0.467x + 0.417 where y represents the distance in miles, and x represents the time for the trip in minutes. Use the best fit line to estimate the time for a trip that is 6 miles long. Show your reasoning.
Answer:
12 minutes
Step-by-step explanation:
To estimate the time for a trip that is 6 miles long, we need to solve for x in the equation y = 0.467x + 0.417, where y represents the distance in miles.
First, we substitute the value of y, which is 6:
6 = 0.467x + 0.417
Next, we subtract 0.417 from both sides:
5.583 = 0.467x
Finally, we divide both sides by 0.467:
x = 12
So, the estimated time for a trip that is 6 miles long is 12 minutes.
Is it always possible, no matter how the rabbit moves, and no matter what points are reported by the tracking device, for the hunter to choose her moves so that after $10^9$ rounds she can ensure that the distance between her and the rabbit is at most 100?
It is not always possible for the hunter to ensure that the distance between her and the rabbit is at most 100 after $10⁹$ rounds. The distance between the hunter and the rabbit can increase by a factor of 2 in each round, making it impossible for the hunter to catch the rabbit in some scenarios.
It is not always possible for the hunter to ensure that the distance between her and the rabbit is at most 100 after $10⁹$ rounds, regardless of how the rabbit moves or what points are reported by the tracking device. This is because the distance between the hunter and the rabbit can increase by a factor of 2 in each round, which means that after $10⁹$ rounds, the distance between them could be as much as $2⁽¹⁰⁾⁹$ times the initial distance. This value could be much larger than 100, making it impossible for the hunter to catch the rabbit. Therefore, there are scenarios in which the hunter cannot catch the rabbit within $10⁹$ rounds.
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