The given statement about Histogram that , " if median of a data set is larger than mean, then the histogram of data will likely have a longer right tail" is FALSE .
A histogram is a graph in which most of data falls to the right of graph's peak and is known as a right-skewed histogram. This type of histogram is also known as a positively skewed histogram.
The relation between the mean , median and mode in a right-skewed histogram is denoted as : mean > median > mode .
A distribution is called skewed Right if, in histogram , the right tail (smaller values) is much longer than the left tail (larger values).
Therefore , For histogram to have longer right tail , the median should be less than the mean .
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George is building a fence. He builds his fence at a constant rate of 1/3 section of fence every 1/2 hour. At his ate, what fraction represents the section of fence George can build per hour?
someone help me please > .
The fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.
How is division of fractions performed?Divide implies to distribute anything evenly. After learning about whole number division, let's move on to fraction division. The numerator and the denominator are the two components of a fraction. Fractional division is roughly the same as fractional multiplication. When dividing fractions, we multiply the smaller of the two fractions by their reciprocals.
Given that George builds the fence at a rate of 1/3 section per 1/2 hour.
The fraction of fence that George build per hour can be obtained as:
1/3 = 1/2 hour
x = 1 hour
Using the butterfly method for multiplication we have:
x = (1/3) ÷ (1/2)
x = (1/3) × (2)
x = 2/3
Hence, the fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.
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A scatterplot is used to display data where x is the amount of time, in minutes, one member can tolerate the heat in a sauna, and y is the temperature, in degrees Fahrenheit, of the sauna.
Which interpretation describes a line of best fit of y = –1.5x + 173 for the data?
The member can tolerate a temperature of 173° Fahrenheit for 0 minutes.
What is Equation of a straight line ?
The equation of a straight line as follows : y = mx+c where m is slope of a straight line and c is y-intercept.
Given that the equation of the line of best fit is given by
Let x represents the amount of time in minutes.
Let y represents the temperature in degrees Fahrenheit.
From the equation of line of best fit, it is obvious that the temperature that a person can tolerate is 173 degrees Fahrenheit at 0 minutes.
Because the y - intercept represents the temperature when the x - value is zero.
So, the member can tolerate a temperature of 173° Fahrenheit for 0 minutes.
Therefore, The member can tolerate a temperature of 173° Fahrenheit for 0 minutes
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A train left Vicky's town and traveled for 4 hours and 50 minutes to Wildgrove. Then it traveled 2 hours and arrived in Westminster at 12:28 P.M. What time did the train leave Vicky's town?
Answer:
5:38 am
Step-by-step explanation:
Since the train arrived at it's final destination at 12:28 pm and it took two hours to get there. Subtract two hours from the final destination time and it's 10:28 am. Then it took 4 hours and 50 minutes to arrive to Wildgrove, so subtract four hours of the time when the train arrived. It is now 6:28 am. Subtract fifty minutes from that and you would get 5:38 am.
p.s. There are time calculators online if you need an answer if this is kinda hard to understand
question 6
Match each number that is in scientific notation to its calculator shorthand representation
The calculator short hand notations are;
a) -4E3
b) -3E4
c) 3E4
d) 4E3
What is the calculator short hand notation?We have to note that the calculator short hand notation has to do with the manner in which the calculator would show an exponential function when we are solving the mathematical problem using the calculator.
It is common to see that the calculator would display the letter E to stand in for the mathematical figure * 10^n. The letter that is depicted by n would then be written at the right hand side of the letter E.
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What happens when X is replaced with (x-3)
In a scenario when X is replaced with (x-3) then it means that the value of x will be reduced by 3 units.
What is Substitution?This is referred to as the process which involves the replacement of a word , number or phrase with another when performing different types of operations.
During an arithmetic operation and X is replaced with (x-3), then it means that the value of X will be reduced by 3 units and an example is given below:
Let's assume X is 5 and we substitute it with (x-3) will therefore become (5-3) = 2. This depicts that there has been a reduction by 3 units thereby making it the correct choice.
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What is the length of every median in an equilateral triangle whose side length is 5?
The length of every median in an equilateral triangle whose side length is 5 is; 4.33
What is the length of the triangle median?In geometry, a median of a triangle is defined as a line segment joining a vertex to the midpoint of the opposite side which therefore bisects that side.
This tells us that every single triangle has exactly three medians, with one from each vertex, and as a result they all intersect each other at the centroid of the triangle.
The median joins a vertex and the opposite side's midpoint. Thus;
side = 5
half side = 5/2 = 2.5
Using Pythagoras theorem;
a² + b² = c²
Thus;
2.5² + b² = 5²
b² = 18.75
b = √18.75
b ≈ 4.33
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Please help me with this geometry question
a. The length of x is 4 cm.
b. The area of the shaded face in the triangle prism is 36 cm².
How to Calculate the Area of a Face of a Triangular Prism?The net of the triangular prism shows that the shaded face is a rectangle.
The side labelled x is the same as the side of the triangular face with a side of 4 cm, when the net of the triangular prism is folded.
Therefore:
a. Length of x = 4 cm
b. Area of shaded face = area of rectangle = length × width
= 9 × 4
= 36 cm²
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The circle graph below represents the number of students at a middle school who buy lunch. If 624 students go to the school, about how many students do not buy lunch? Students who do not buy lunch Students who buy lunch 255⁰
The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.
Approximately what percentage of pupils skip lunch at school?In comparison to only 4% of children aged 6 to 13 years old, nearly one in ten adolescents (aged 14 to 17) admitted to skipping lunch.The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022. Comparatively, the cost of the national school lunch program in the prior year was about 7.9 billion dollars.The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.Comparatively, the cost of the national school lunch program in the prior year was about 7.9 billion dollars.To learn more about percentage refer to:
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The number of students who do not buy lunch is 624 students - 420 students = 204 students.
Approximately how many pupils skip lunch at school?The circle graph represents the proportion of students who buy lunch and those who don't. To find the number of students who don't buy lunch, we need to subtract the number of students who buy lunch from the total number of students.
Since 255° represents the proportion of students who buy lunch, we can use this to find the number of students who buy lunch. To do this, we divide the number of degrees by 360° and multiply by the total number of students, 624:
(255° / 360°) x 624 students = 420 students
Therefore, the number of students who do not buy lunch is 624 students - 420 students = 204 students.
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How do I solve for x for similarities in triangles
Answer: you can solve for x using the Pythagorean theorem:
Step-by-step explanation. let's say your questing in sides are 12 and 40 what is x. you have side x, y, and h. y=12 h=40. now you solve using the Pythagorean theorem x2 + y2 = h2. (The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent).)
Simplify rational expressi
Simplify the following rational expression.
11k
55k^2+ 22k
The simplify of given equation 11k/ (55k^2+ 22k) is 1/(5k+2).
Given,
[tex]\frac{11x}{55^{2}+22k }[/tex] We have to simplify in rational expression
The common factor is 11. So, we have to pick the common factor from the equation.
= [tex]\frac{11x}{55^{2}+22k }[/tex]
= [tex]\frac{1}{5x + 2}[/tex]
Therefore the simplification of given equation is 1/(5k+2).
Reasonable expressions resemble fractions with variable denominators (and often numerators too). An example of a rational expression is x 2 x + 3 dfracx2x+3 x+3x2 start fraction, x, squared, divided by, x, plus, 3, end fraction.
Removing parenthesis and brackets requires factor multiplication.If the words have exponents, use the exponent rule to eliminate grouping.By adding or subtracting coefficients, combine similar phrases.Add the constants together.For such more question on simplify:
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C The triangles in this picture are similar. Find the height of the tree.
Answer:
30 ft
Step-by-step explanation:
h/(40 + 8) = 5/8
h = 30
Elizabeth rode her bike 6 1/2 miles from her house to the library And then another 2 2/5 miles to his friend Milo's house, how far would she travel from her house to Carsons house?
Elizabeth would travel a distance of [tex]11\frac{2}{5}[/tex] miles.
The distance between Elizabeth's house and Carson's house = Sum of (the distance between Elizabeth's house and the Library + the distance between the library and Millo's house + the distance between Millo's House and Carson's House). That is:
Total Miles = [tex]6\frac{1}{2}[/tex] + [tex]2\frac{2}{5}[/tex] + [tex]2\frac{1}{2}[/tex]
To calculate the total miles, we need to transform the mixed numbers into fractions. We can do that as:
[tex]6\frac{1}{2}[/tex] = [(6 × 2) + (1)]/2 = 13/2
[tex]2\frac{2}{5}[/tex] = [(2 × 5) + (2)]/5 = 12/5
[tex]2\frac{1}{2}[/tex] = [(2 × 2) + (1)]/2 = 5/2
So, the distance from Elizabeth's house to Carson's House has 57/5 miles, and it is calculated as:
13/2 + 12/5 + 5/2 = 57/5
Then, convert 57/5 into a mixed number, and we get:
57/5 = [tex]11\frac{2}{5}[/tex]
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2. Write these measures in ascending order
(1 Point)
0. 845kg 80g 12254 1. 2kg
The ascending order of the given data is-
80g < 12254g < 0. 845kg < 1. 2kg.
From smallest value to largest value, numbers are arranged in ascending order. From left to right, comes the order. Additionally known as increasing order, ascending order is a common terminology. Taking a set of natural numbers as an example, they are arranged in ascending order as follows: 1, 2, 3, 4, 5, 6, 7, 8, and so on. To indicate the increasing order, use the symbol less than (). Decreasing order of values is used to arrange the numbers in descending order, which is the opposite of increasing order. Ascending numbers from -6 to 6 are listed in the number lines above. According to this statement, numbers on the left side of a number are smaller than those on the right side of a number.To know more about ascending order here
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NGC 5866
is about 44 million light years, or 13.5 megaparsecs, from
the Milky Way. How fast is NGC 5866 receding?
It has a diameter of about 60,000 light-years (18,400 parsecs).
Size of NGC 5866?A distance of 44 million light-years separates NGC 5866 from Earth in the Northern constellation Draco (13.5 Megaparsecs). Even though it has a diameter only around two-thirds that of the Milky Way and a mass similar to our galaxy, it has a diameter of about 60,000 light-years (18,400 parsecs).NGC 5866, a lenticular galaxy, contains many intricate dust lanes that appear black and red, but its disk is largely composed of brilliant stars, giving it a more subtly blue undertone.Numerous globular clusters—gravitational groups of nearly a million stars—that are gravitationally bound are scattered throughout the outer halo. Through the halo, it is also possible to detect background galaxies that are millions to billions of light-years away from NGC 5866.To learn more about diameter refer to:
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In ΔQRS, r = 83 cm, mm∠R=161° and mm∠S=5°. Find the length of q, to the nearest centimeter.
The required value of side q is 117. 05 cm for the triangle ΔQRS.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
In triangle ΔQRS, r = 83 cm, mm∠R=161° and mm∠S=5°
To find the length of the side q,
The third angle can be calculated using the angle sum property as;
angle Q + angle R + angle S = 180 degrees
angle Q + 161 degrees + 5 = 180 degrees
angle Q = 180 - (166) degrees
angle Q = 14 degrees
To find the length of q we shall apply the Sine rule.
q / Sin Q = r / Sin R
q / Sin 14 = 83 / Sin 161
Now cross multiplication we will get;
q = (83 x Sin 14 ) / Sin 161
q = 117. 05 cm (approximately)
So, the length of q is 117. 05 cm.
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Ë Solve & Share
|) Rose bought a length of copper pipe. She used
1
1
2
yard to repair a water line in her house. How much
pipe does she have left? Solve this problem any way
you choose.
7/8 yard
She left the 1/6 yards pipes.
Now, According to the question:
Rose bought a length of 4/6 copper pipe.
She used 1/2 yard to repair a water line in her house.
To find how much pipe does she have left?
Pipes available = 4/6 yards
Pipes used = 1/2 yards
Pipes left = total pipes bought - she doesn't suit that way
Pipes left = Total pipes available - pipes used
= 4/6 yards - 1/2 Yards
= 4-3/6
= 1/6 yards
Pipes left = 1/6 yards
Hence, She left the 1/6 yards pipes.
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The given question is incomplete, complete question is:
Rose bought a length of 4/6 copper pipe. She used 1/2 yard to repair a water line in her house. How much pipe does she have left? Solve this problem any way.
A metal oxide reacts chemically with water to form a base in the reaction shown below.
If the temperature of the metal oxide and water solution is increased, this will most likely
A.
reverse the chemical reaction.
B.
increase the rate of chemical change.
C.
produce an acid.
D.
decrease the rate of chemical change.
Determine the value of x in the figure.
The value of x in the figure is 20
What is the ratio?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or [tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
Given;
Ratio of first line segment = 4.4/6.3
Ratio of other line segment= 14.08/x
Now, to find the value of x
4.4/6.3 = 14.08/x
4.4x= 14.08x6.3
x=14.08x6.3/4.4
x=20.16
Therefore, according to ratio x will be equal to 20
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Need ASAP pls
Solve
x-y=2
y=2x-4
which of the following are true about large commercial vehicles? select one: a. more than 3,000 people are killed yearly in crashes involving large trucks or buses. b. large trucks and buses have smaller blind spots than cars. c. large trucks and buses take less space to make a right turn. d. large trucks and buses have a shorter stopping distance.
a. More than 3,000 people are killed yearly in crashes involving large trucks or buses.
The stopping distance of a large truck or bus is determined by calculating the kinetic energy (K) of the vehicle, the coefficient of friction (μ) between the road and the tires, and the weight (W) of the vehicle. The formula for calculating the stopping distance is K = (μ * W2) / 2g, where g is the acceleration due to gravity. This means that the heavier the vehicle and the lower the coefficient of friction, the longer the stopping distance. Since large trucks and buses are heavier than cars, they have a longer stopping distance and are more likely to be involved in fatal crashes.
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Find the length of GH.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
G(-9, -4)
OA. About 3 units
OB. 53 units
O C. 9 units
12345678910
D. About 7.3 units
-2
-3
-4
-5
H(-2,-6) 7
-6
-8
-9
The length of GH is about 7.3 units. The solution has been obtained by using the formula of distance between two points.
What is distance between two points?
The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation
[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex] is used to calculate the distance between two points. One can use this formula to get the separation between any two points on an x-y plane or coordinate plane.
We are given two points as G(-9,-4) and H(-2,-6)
Using the distance formula,
[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]
[tex]d=\sqrt{(-2 +9)^{2} + (-6 +4)^{2} }[/tex]
[tex]d=\sqrt{(7)^{2} + (-2)^{2} }[/tex]
[tex]d=\sqrt{49 + 4 }[/tex]
[tex]d=\sqrt{53 }[/tex]
d = 7.3 units
Hence, the length of GH is about 7.3 units.
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2. MODELING REAL LIFE A dumpster rental fee is $350 for
the first week and $10 for each additional day or any portion
of a day. Write and graph a step function that represents the
cost y (in dollars) to rent the dumpster for x days.
The required function that represent the given situation is y = 10x + 350.
What is equation of line?In order to write the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Find two locations on the line and create a sloping triangle connecting the two places.
According to question:Rental fee is $350 for the first week and $10 for each additional day or any portion of a day.
So, The equation that represent this problem is;
Let cost y (in dollars) to rent the dumpster for x days.
y = 350 + 10x (y in dollar)
y = 10x + 350
Here, slope of function is 10 and y- intersect is 350.
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Where there is a jump at x = 7 from y = 350 to y = 350 + 10 * (x - 7). Before x = 7, the cost would remain constant at $350. After x = 7, the cost would increase by $10 for each additional day.
What is equation of line?In order to write the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Find two locations on the line and create a sloping triangle connecting the two places.The step function representing the cost to rent the dumpster for x days can be defined as follows:y(x) = 350, if 0 < x <= 7y(x) = 350 + 10 * (x - 7), if x > 7The graph of this step function would look like a piecewise function, where there is a jump at x = 7 from y = 350 to y = 350 + 10 * (x - 7). Before x = 7, the cost would remain constant at $350. After x = 7, the cost would increase by $10 for each additional day.To learn more about Equation of line refer::
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two hot air balloons, one purple and one gold, took off at the same time. the purple balloon started from sea level and the gold balloon started from a hill 15 1515 meters above sea level. the gold balloon began climbing at a constant rate of 2 22 meters per second. the purple balloon began climbing at 2.5 2.52, point, 5 meters per second. after how many seconds were the balloons at the same altitude?
The balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.
Let t be the number of seconds since the balloons took off, and Hp(t) and Hg(t) be the altitude of the purple and gold balloons respectively at time t.
We know that:
Hp(t) = 0 + 2.5t (the purple balloon starts at sea level and climbs at a rate of 2.5 m/s)
Hg(t) = 1515 + 222t (the gold balloon starts 1515 m above sea level and climbs at a rate of 2*22 m/s)
We want to find the time t when the balloons are at the same altitude, so we can set Hp(t) = Hg(t) and solve for t:
0 + 2.5t = 1515 + 222t
2.5t = 1515 + 222t
2.5t - 222t = 1515
0.5t = 1515 - 1515
t = 0
So the balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.
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it rained on a hot summer afternoon and a puddle formed. after several hours, the puddle was gone. identify and describe the two processes made the puddle form and then disappear?
The two processes that caused the puddle to form and then disappear were evaporation and infiltration.
Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.
Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.
The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.
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Marlene works as a cashier at a grocery store. At the end of the day, she has a total of 125 five-dollar bills and ten-dollar bills. The total value of these bills is $990
A) The system of equations that you can use to find the number of five-dollar bills and ten-dollar bills are;
x + y = 125
5x + 10y = 990
B) The number of five-dollar bills are 52 and ten-dollar bills are 73.
How to solve simultaneous linear equations?The parameters are that the total number of five and ten-dollar bills equals 125 dollars.
Let x denote the number of five dollar bills and let y denote the number of ten dollars bills. Thus;
Total number of bills is;
x + y = 125 --- (1)
The total value of all bills is $990
Thus, we have;
5x + 10y = 990
Divided by 5 into both sides to get;
x + 2y = 198 ----- (2)
Now solve (1) and (2) for x and y values
Subtract eq (1) from eq (2) to get;
x + 2y - x - y = 198 - 125
y = 73
Substitute y = 73 in (1)
x + 73 = 125
x = 52
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3x - 9x^2 factorised
Answer:
3x (1 - 3)
Explanation in detail:
= 3x - 9x²
= 3x (1 - 3x) (1 - 3x)
A square-shaped painting has a length and a width of 1 foot. A line painted
diagonally on the painting has a length of V2 feet. About how long is the length of
the diagonal line, to the nearest tenth of a foot?
The diagonal V2 of the square will be √2 feet.
What are squares?
A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°.All four sides of the square are congruent or equal to each other.The opposite sides of the square are parallel to each other.The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other.The square has 4 vertices and 4 sides.The diagonal of the square divides into two similar isosceles triangles.The length of diagonals is greater than the sides of the square.Area of square=(side)²
Perimeter of square=4*side
Now,
as side=1 foot
By applying Pythagorean theorem,
Diagonal²=side²+side²
therefore,
V2²=1²+1²
=2
V2= √2 feet
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Show that the following recurring decimal are rational. (1) 0,4 (2) 0,21 (5) 0,124 (6) 0,124 (3) 0,14 (7) -1,124 (4) (8) 19,45 -2,35
The given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.
(1) 0.4 is a rational number because it can be written as 4/10 which is a fraction with a denominator that is not zero.
(2) 0.21 is a rational number because it can be written as 21/100 which is a fraction with a denominator that is not zero.
(3) 0.14 is a rational number because it can be written as 14/100 which is a fraction with a denominator that is not zero.
(4) 0.124 is a rational number because it can be written as 124/1000 which is a fraction with a denominator that is not zero.
(5) -1.124 is a rational number because it can be written as -1124/1000 which is a fraction with a denominator that is not zero.
(6) 19.45 is a rational number because it can be written as 1945/100 which is a fraction with a denominator that is not zero.
(7) -2.35 is a rational number because it can be written as -235/100 which is a fraction with a denominator that is not zero.
In conclusion, all the given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.
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Select the correct answer from the drop-down menu. Find the missing term. 7-147 × 798 = 718 × 7-38 ×
Using exponents rule the missing term in the equation 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____ is found to be 7^(-29).
What is an exponent?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
The given expression is - 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____
Let the missing term be x.
Then the equation is -
7^(-147) × 7^(98) = 7^(18) × 7^(-38) × x
Since, the base of the exponents is same, so apply the operations on the powers of the base.
The exponent rule is - a^(b) × a^(c) = a^(b + c)
Write the equation according to the rule -
7^(-147 + 98) = 7^(18 - 38) × x
Now perform the arithmetic operation of addition and subtraction -
7^(-147 + 98) = 7^(18 - 38) × x
7^(-49) = 7^(-20) × x
The exponent rule is - a^(b) / a^(c) = a^(b - c)
Write the equation according to the rule -
x = [7^(-49)] / [7^(-20)]
x = 7^[-49 - (-20)]
x = 7^(-49 + 20)
x = 7^(-29)
Therefore, the missing term is x = 7^(-29).
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Select the correct answer from the drop-down menu. Find the missing term. 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____
an airline runs a commuter flight between two cities that are 720 miles apart. if the average speed of the plane is increased by 40 mph, the travek time is decraesed by 12 minutes. what speed is required to obtain this decrease in travel time?
The speed required to obtain this decrease in travel time is 360 mph.
Formula between speed, distance, and travel time
v = d/t
The formula to calculate distance is
d = v × t
v = the speed (mph)In the first condition
d₁ = v₁ × t₁
720 = v × t₁
t₁ = 720/v
In the second condition
d₂ = v₂ × t₂
720 = (v + 40) (t₁ - 0.2)
720 = (v + 40) (720/v - 0.2)
720 = v (720/v - 0.2) + 40 (720/v - 0.2)
720 = 720 - 0.2v + 28,800/v - 8
0.2v + 8 - 28,800/v + 720 - 720 = 0
0.2v + 8 - 28,800/v = 0
0.2v² + 8v - 28,800 = 0
v² + 40v - 144,000 = 0
Factorize quadratic equations
v² + 40v - 144,000 = 0
v² + 400v - 360v - 144,000 = 0
v (v + 400) - 360 (v + 400) = 0
(v + 400) (v - 360) = 0
v + 400 = 0 or v - 360 = 0
v = - 400 v = 360 mph
(negative speed is impossible)
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