Step-by-step explanation:
Area of parallelogram = base × height or say b×h
Given: h=8 inches
Area=120 sq.inches
⇒120=8×b
⇒120/8=b
⇒120/8=b = 15
Answer = 15 inches b
The following joint probability density function for the random variables Y1 and Y2, which represent the proportions of two components in a somaple from a mixture of insecticide.
f(y1,y2) = { 2, 0 <= y1 <= 1, 0 <= y2 <= 1, 0 <= y1+y2 <=1
{ 0, elsewhere
For the chemicals under considerationm an important quantity is the total proportion Y1 +Y2 found in any sample. Find E(Y1+Y2) and V(Y1+Y2).
The joint probability density function for the random variables Y1 and Y2 E(Y1+Y2) and V(Y1+Y2) is 41/144.
To find E(Y1+Y2), we need to integrate the sum of Y1 and Y2 over their joint probability density function:
E(Y1+Y2) = ∫∫ (y1 + y2) f(y1,y2) dy1 dy2
= ∫∫ (y1 + y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 <=1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex](y1 + y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (2y1 + 1) (1-y1)² dy1
= 5/12
To find V(Y1+Y2), we can use the formula V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]².
First, we need to find E[(Y1+Y2)^2]:
E[(Y1+Y2)²] = ∫∫ (y1+y2)² f(y1,y2) dy1 dy2
= ∫∫ (y1² + y2² + 2y1y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 = 1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex] (y1² + y2² + 2y1y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (1/3)y1³ + (1/2)y1² + (1/2)y1
(1/3)y1 + (1/4) dy1
= 7/12
Next, we need to find [E(Y1+Y2)]²:
[E(Y1+Y2)]² = (5/12)² = 25/144
Therefore, V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]² = (7/12) - (25/144) = 41/144.
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Construct triangle PQR in which angle Q = 30 deg , angle R=60^ and PQ + QR + RP = 10cm
We can see here that in order to construct a triangle PQR in which angle Q = 30°, angle R=60° and PQ + QR + RP = 10cm, here is a guide:
Draw a line segment AB = 10 cm.Construct angle 30° at point A and angle 60° at point B.Draw angle bisectors to angles A and B.Make sure these angle bisectors intersect at point P.Draw perpendicular bisector to line segment AP.Let this bisector meet AB at Q.Then draw perpendicular bisector to line segment BP.Let this bisector meet AB at R.Join PQ and PR.PQR is the required triangle.What is a triangle?A triangle is a geometric shape that is defined as a three-sided polygon, where each side is a line segment connecting two of the vertices, or corners, of the triangle. The interior angles of a triangle always add up to 180 degrees.
Triangles can be classified into different types based on their side lengths and angles, such as equilateral triangles with three equal sides and three equal angles, isosceles triangles with two equal sides and two equal angles, and scalene triangles with no equal sides or angles.
Triangles are used in many areas of mathematics and science, including geometry, trigonometry, and physics.
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Find the missing length indicated
The value of x is 5
Define the term Similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. To be more specific, two triangles are comparable if their respective sides are proportionate and their corresponding angles are congruent.
Two triangles are similar if corresponding angles are congruent and corresponding sides are proportional.
from the below figure, both the triangles are similar, ∆ABC ≈ ∆EFB
By using Thales's theorem, the ratio of the sides of triangles are;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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The ratio of triangle sides can be calculated using Thales' theory, and it is the value of x is 5
Define the term Similar triangles?Similar triangles are those with the same shape but varying sizes. To be more precise, two triangles are comparable if their matching angles and respective sides are congruent.
If matching sides are proportional and corresponding angles are congruent, two triangles are similar.
Both triangles in the following figure are comparable ∆ABC ≈ ∆EFB
The ratio of triangle sides can be calculated using Thales' theory, and it is;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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given natural numbers a and b not both equal to 0, we know that there exist integers k and l with ak bl
The equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l).
The equation ak + bl = 0 is a linear equation in two variables and is solved using the method of elimination. The equation can be written in the form ax + by = c, where a, b, c are constants. To solve this equation, both sides of the equation should be divided by the coefficient of one of the variables (a or b). This will result in a equation of the form x + qy = r, where q and r are constants. Then, the equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l). The two variables can then be calculated using the point of intersection by substituting the x and y values into the two equations. In this way, the two variables k and l can be found such that ak + bl = 0.
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What are the integers k and l such that ak + bl = 0?
On the day a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. Assume the
number of viewers continues to double each day.
1. On which day will 640 people see the video? Explain or show your reasoning.
2. What strategy would you use to find the first day when more than 20,000 people will see the video (if the trend continues)?
On the 7th day after the videο was pοsted, 640 peοple will see the videο.
What is Statistics?Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data.
1 Let's start by finding the pattern in the number οf viewers. We knοw that οn the first day, 5 peοple watched the videο. On the next day, the number οf viewers dοubled tο 5 x 2 = 10. On the third day, the number οf viewers dοubled again tο 10 x 2 = 20. We can see that the number οf viewers is dοubling each day, which means we can write the number οf viewers as:
[tex]V = 5 x 2^n[/tex]
where n is the number οf days after the videο was pοsted.
Nοw we want tο find οn which day the number οf viewers will be 640. Sο we can set V equal tο 640 and sοlve fοr n:
[tex]640 = 5 x 2^n[/tex]
[tex]2^n = 128[/tex]
n = lοg2(128) = 7
2. Tο find the first day when mοre than 20,000 peοple will see the videο, we can set V equal tο 20,000 and sοlve fοr n:
[tex]20,000 = 5 x 2^n[/tex]
2^n = 4,000
n = lοg2(4,000) ≈ 11.29
Since n represents the number οf days after the videο was pοsted, we can rοund up tο the next whοle number tο find the first day when mοre than 20,000 peοple will see the videο. Therefοre, οn the 12th day after the videο was pοsted, mοre than 20,000 peοple will see the videο if the trend cοntinues
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To the nearest hundredth, what is the volume of the sphere? (Use 3.14 for pie.)
Therefore, the volume of the sphere to the nearest hundredth is 724,775.70 cubic millimeters.
What is volume?Volume is a measurement of the amount of space occupied by a three-dimensional object. It is often expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal), depending on the context. The volume of a solid object can be calculated by multiplying its length, width, and height or using a specific formula depending on the shape of the object. For example, the volume of a rectangular box can be calculated as length x width x height, while the volume of a cylinder can be calculated as π x radius² x height. In general, volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. It is often used to describe the capacity of containers, the displacement of fluids, and the amount of material used in construction or manufacturing.
Here,
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is approximately 3.14.
Substituting the given value of the radius, we get:
V = (4/3) x 3.14 x 48³
V ≈ 724,775.68 cubic millimeters
Rounding this value to the nearest hundredth, we get:
V ≈ 724,775.68 ≈ 724,775.70 cubic millimeters (rounded to two decimal places)
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P, Q, R, S, T and U are different digits.
PQR + STU = 407
Step-by-step explanation:
There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:
P = 2
Q = 5
R = 1
S = 8
T = 9
U = 9
With these values, we have:
PQR = 251
STU = 156
And the sum of PQR and STU is indeed 407.
Increase £16470.45 by 3.5%
Give your answer rounded to 2 DP
Step-by-step explanation:
"increase" means to take the original 100% and put an additional 3.5% of these 100% on top of it.
so, we have to calculate
100% + 3.5% of £16470.45
100% of £16470.45 = £16470.45 × 100/100
3.5% of £16470.45 = £16470.45 × 3.5/100
the sum is therefore
£16470.45 × (100/100 + 3.5/100) =
= £16470.45 × (1 + 0.035) = £16470.45 × 1.035 =
= £17,046.91575 ≈ £17,046.92
Tell me which brand or which size is a better buy.
Answer:
The answer is brand B
Step-by-step explanation:
You divide $14.88 by 24 which equals 68 cents per item.
Then brand B is 60 cents per item which is the better buy!
What quadratic function is represented by the graph?
A. f(x) = −2x²+x+6
B. f(x) = 2x²x+6
C. f(x) = 2x²+x+6
D. f(x) = − 2x² - x - 6
Answer:
Answer: C. f(x) = 2x²+x+6
which statemnt is ture when the dimensions of a two-dimensional figures are dilated by a scale factor of 2
When a shape is dilated, the size of the shape changes. The true statement is (d) The scale factor is 2.5.
Dilation:
Dilation is the process of changing the size of an object or shape by reducing or increasing its size by a specific scale factor. For example, a circle with a radius of 10 units shrinks to a circle with a radius of 5 units. Applications of this method are in photography, arts and crafts, sign making and more.
According to the Question:
How to determine the scale factor
In figure A, we have:
Length = 0.6
In figure B, we have:
Length =1.5
The scale factor is then calculated as:
K = 1.5/0.6
Dividing the equation:
k = 2.5
Hence, the true statement is (d) The scale factor is 2.5.
Complete Question:
The first figure is dilated to form the second figure. Which statement is true?
The scale factor is 0.4.
The scale factor is 0.9.
The scale factor is 2.1.
The scale factor is 2.5.
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What was your recommended intake of carbohydrates (grams), and how far were you from it? Show the mathActual Intake Recommended Intake Percentage159.00 115-166 100%
The actual intake of carbohydrates is 138% as compare to recommended intake.
Recommended intake of carbohydrates or any other nutrient are,
Based on the information provided,
Consumed 159 grams of carbohydrates,
Recommended intake is between 115 and 166 grams.
Calculate the percentage of actual intake compared to the recommended intake, use the following formula,
Percentage = (Actual Intake / Recommended Intake) x 100%
Substituting the values in the formula we have,
⇒Percentage = (159 / 115) x 100%
⇒Percentage ≈ 138.3%
Therefore, the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.
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In a certain company, employees contribute to a welfare fund at the rate of 4% of the first $1000 earned, 3% of the next $1000, 2% of the next $1000 and 1% of any extra monies. How much will an employee who earned $20,000 contribute to the fund?
The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.
An employee who earned $20,000 will contribute $260 to the welfare fund.
To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.
The first $1000 will have a contribution rate of 4%.
Contribution for the first $1000 = 4% of $1000 = $40.
The next $1000 will have a contribution rate of 3%.
Contribution for the next $1000 = 3% of $1000 = $30.
The next $1000 will have a contribution rate of 2%.
Contribution for the next $1000 = 2% of $1000 = $20.
The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.
Contribution for the remaining amount = 1% of $17,000 = $170.
Now, let's sum up the contributions for each tier:
$40 + $30 + $20 + $170 = $260.
Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.
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Christine has a six-sided dice numbered from 1 to 6. She rolled it a total of 50 times. It landed on an odd number 21 times. a) Work out the relative frequency of the dice landing on an odd number. Give your answer as a decimal. b) If the dice were fair, what would the theoretical probablity of it landing on an odd number be? Give your answer as a decimal. c) Is the dice definitely biased or definetely not biased, or is it impossible to tell? Write a sentence to explain your answer.
A) Relative frequency is number of times an event happened over total number of events:
Answer is 21/50 = 0.42
B) On a 6 sides die, there are 3 even numbers and 3 odd numbers, so the theoretical probability of landing on odd would be 3/6 = 0.50
C) Because the die has an equal amount of chance landing on even or odd, both are 3/6, then the dice is not biased.
59, 60, 61, 62, 63, 64, 65, and 66 Find the values of x for which the series converges. Find the sum of the series for those values of x. 59. § (-5)".z" n=1 Answer + 00 60. Σ(α + 2)" n=1 61. (x - 2)" 3" n=0 Answer + 62. (-4)" (x - 5) n=0 00 63. 2" ch NO Answer
The values of x for which the series converges is x ∈ (-1/5, 1/5). The sum of the series for those values of x is (-5x)/(1 + 5x).
The series is [tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex].
We can write this series as [tex]\Sigma^{\infty}_{n=1}(-5x)^n[/tex].
This is a infinite geometric series with first term a = -5x and common ration r = -5x.
It is convergent when
|r| < 1
|-5x| < 1
|-5| |x| < 1
5|x| < 1
Divide by 5 on both side, we get
|x| < 1/5
The series is convergent when x ∈ (-1/5, 1/5).
Sum of the series is
Sₙ = a/1 - n
Sₙ = (-5x)/{1 - (-5x)}
Sₙ = (-5x)/(1 + 5x)
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The complete question is:
Find the values of x for which the series converges. Find the sum of the series for those values of x.
[tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex]
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.59°C and 0.88°C.
The probability of obtaining a reading between 0.59°C and 0.88°C is 0.7224 and 0.8106.
What is mean?The sum of all possible values, weighted by the chance of each value, is equal to the mean of a discrete probability distribution of the random variable X. Each possible number of X must be multiplied by its probability P(x) before being added as a whole to determine the mean. In statistics, the mean is one measure of central trend in addition to the mode and median. The mean is simply the average of the numbers in the specified collection. It suggests that values in a specific data gathering are evenly distributed. In order to find the mean, the total values given in a datasheet must be added, and the result must be divided by the total number of values.
In this question, using the formula,
z-score = (x – μ) / σ
where:
x: individual data value
μ: population mean
σ: population standard deviation
for x=0.59
μ= 0
σ= 1
z-score= 0.59
Probability=0.7224
for x=0.88
z-score= 0.88
Probability=0.8106
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.2 In the diagram below, given that XY = 3cm, XZY = 30° and YZ = x, is it possible to solve for x using the theorem of Pythagoras? Motivate your answer. Show Calculations
Sin 30 =3/x
1/2=3/x
x=6
Samir's statement shows a previous balance of $5,336.22, a payment of $607, and a
new transaction totaling $186. What is his new balance if his APR is 29.0%? Round
answer to hundredths place if answer does not have a hundredths place this use
zeros so it does. Do not include the units. Be sure to attach work for credit
Your Answer:
Samir's new balance is $5,044.17.
To calculate Samir's new balance, add the previous balance, subtract the payment, add the new transaction, and multiply by the interest rate for one period. The following formula can be used to calculate the interest for a single period:
balance * APR / 12 = interest
where APR stands for annual percentage rate and 12 represents the number of months in a year.
When we apply this formula to Samir's balance and APR, we get:
5336.22 * 0.29 / 12 = 128.95 in interest
As a result, the total new balance is:
5336.22 - 607 + 186 + 128.95 = 5044.17
We get the following when we round to the nearest hundredth:
$5,044.17
As a result, Samir now has a balance of $5,044.17.
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Will tracks the high and low tempters in his town for five days during a cold spell in January his results are shown in the table below
Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.
Define change in temperaturecalculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.
Change in temperature on Monday from High to low
=15-10=5°F
Change in temperature on Tuesday from High to low
=8-(-4)=12°F
Change in temperature on Wednesday from High to low
=-2-(-5)=3°F
Change in temperature on Thursday from High to low
=-3-(-7)=4°F
Change in temperature on Friday from High to low
=-1-(-12)=11° F
Days when change in temperature more than 10° F are Tuesday and Friday.
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The Complete question is attached below:
Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2
The function g(t) is defined as:
g(t) = 1/√(16-t^2)
The function is continuous for all values of t that satisfy the following conditions:
The denominator is non-zero:
The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].
There are no vertical asymptotes:
The function does not have any vertical asymptotes, because the denominator is always positive.
Thus, the function g(t) is continuous on the interval [-4,4].
For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).
Answer:
Find f(g(x)) f(x)=7x-8 , g(x)=3x-2. f(x)=7x−8 f ( x ) = 7 x - 8 , g(x)=3x−2 g ( x ) = 3 x - 2. Step 1. Set up the composite result function. f(g(x)) f ( g ...
please mark me as a brainalist
complete the table below.
4775 g968r648 747474874 483892874 23773259635y84b2375789325 7437594365825 4378574937587 49388959365n 98437858746587 32o4iy548569
Answer:
?
Step-by-step explanation:
2 bags of dog food. How many days will 3/4 last?
Answer:
3/4 of a bag of dog food will last 3 days.
The dot plots below show the number of students in attendance each day in Mr. Wilson's class and Mr. Watson's class in April. What is the difference of the medians as a multiple of the interquartile range? A. B. C. D.
The difference of the medians as a multiple of the interquartile range is 0.5,So the correct answer is option (A) 0.5.
What is median?The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in numerical order.
For example, consider the data set {3, 5, 2, 6, 1, 4}. When the values are ordered from smallest to largest, we get {1, 2, 3, 4, 5, 6}. The median in this case is the middle value, which is 3.
We can first find the medians and interquartile ranges of the two dot plots.
For Mr. Wilson's class:
Median = 12
Q1 = 10
Q3 = 14
IQR = Q3 - Q1 = 14 - 10 = 4
For Mr. Watson's class:
Median = 10
Q1 = 8
Q3 = 12
IQR = Q3 - Q1 = 12 - 8 = 4
The difference of the medians is |12 - 10| = 2. Therefore, the difference of the medians as a multiple of the interquartile range is:
$$\frac{2}{4} = \boxed{0.5}$$
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Mrs. Cabana has 8 pets total. Three of the pets are chameleons and the rest are fish. Select all the answers that are a ratio relationship for Mrs. Cabana's pets.
Question 1 options:
Multi choice
3/5
3 to 11
3:8
5 to 8
8:1
Answer: numbers 1,3 and 4
Step-by-step explanation:
Kingsley knows that 1inch is about 2.45 centimeters. He wants to write an equation he can use to convert any given length in inches (i) to centimeters (c)
How should Kingsley write his equation?
A.) c/i = 2.54
B.) c = 2.54i
C.) i = c/2.54
Since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
What is equation ?
An equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). The expressions on either side of the equals sign may contain one or more variables, which are unknown values that can be determined by solving the equation.
Kingsley wants to convert a given length in inches to centimeters. He knows that 1 inch is about 2.45 centimeters.
Let's call the length in inches "i" and the length in centimeters "c".
We want to find an equation that relates i and c. We know that 1 inch is about 2.45 centimeters, so we can write:
1 inch = 2.45 centimeters
To convert from inches to centimeters, we can multiply the length in inches by 2.45. So:
c = 2.45i
This is the equation Kingsley can use to convert any given length in inches to centimeters.
Alternatively, we can rearrange this equation to solve for i:
c = 2.45i
Divide both sides by 2.45:
c/2.45 = i
So the equation for converting from centimeters to inches is:
i = c/2.45
Therefore, since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
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Question 11 (1 point)
(06.03 LC)
What is the product of the expression, 5x(x2)?
a
25x2
b
10x
c
5x3
d
5x2
The expressiοn 5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³). Thus, οptiοn (c) 5x3 is the cοrrect respοnse.
Hοw are prοducts οf expressiοn determined?The cοefficients (the numbers in frοnt οf the variables) οf the expressiοn 5x(x²) can be multiplied, and the expοnents οf the variables can be added, tο determine the prοduct.
The first cοefficient we have is 5 times 1, giving us 5. Sο, using the secοnd x², we have x tο the pοwer οf 2 multiplied by x tο the pοwer οf 1 (frοm the first x). Expοnents are added when variables with the same base are multiplied. Sο, x¹ multiplied by x² results in x³.
Cοmbining all οf the parts, the phrase becοmes:
5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³).
Thus, οptiοn (c) 5x³ is the cοrrect respοnse.
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4^(-x)=1/256
I believe it is x=4, but I need how to work it out pls thxxx
Answer:
x = 4
Step-by-step explanation:
using the rule of exponents
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then
[tex]4^{-x}[/tex] = [tex]\frac{1}{4^{x} }[/tex]
and 256 = [tex]4^{4}[/tex]
then
[tex]\frac{1}{4^{x} }[/tex] = [tex]\frac{1}{4^{4} }[/tex]
so
[tex]4^{x}[/tex] = [tex]4^{4}[/tex]
since bases on both sides are equal, bot 4 then equate exponents
x = 4
Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, compute the system's impulse response h[n] without using z-transforms.
Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, the impulse response of the system: h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
To compute the impulse response h[n] of a linear time-invariant (LTI) system given its input-output relationship, we can use the convolution sum:
y[n] = x[n] * h[n]
y[n] = (1/2)*(x[n] + 2x[n-1] + 3x[n-2])
y[n] = (1/2)*(δ[n] + 2δ[n-1] + 3δ[n-2])
y[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
Thus, the impulse response of the system is:
h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2],where δ[n] is the impulse signal.
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The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
a) The domain of the function is [0, 7.1875], while the range is [0,23]. Considering the domain and the range, the graph of the function is given by the image presented at the end of the answer.
b) The trip had a duration of 5.1875 hours.
How to obtain the domain and the range of the function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the domain is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is obtained as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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