The point B is 27 meters east of point A.
Since we want to find the distance east, we need to consider the horizontal component of the displacement between the two points.
Using trigonometry, we can determine the eastward distance using the cosine function:
Eastward distance = 54 m x cos(061°)
Eastward distance ≈ 54 m x cos(61°)
≈ 54 m * 0.500
≈ 27 m
Therefore, point B is 27 meters east of point A.
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Triangle BKN is shown, where point H is the incenter, m
The measures are m ∠RBM = 52.2°, m ∠WNH = 23.5° and m ∠WKH = 80.8°
Given that a triangle BKN, and H is the incenter of the triangle, we need to find the missing measures,
We know that the incenter of a triangle is the point where the angle bisectors meet,
So, we can say, BW, MN and RK are the angle bisectors.
So, using the property of angle bisectors, we have,
1) m ∠RBM = 2 × ∠RBH
m ∠RBM = 52.2°
2) m ∠WNH = ∠WNR / 2
m ∠WNH = 23.5°
3) m ∠WKH = 2 × ∠MKH
m ∠WKH = 80.8°
Hence the measures are m ∠RBM = 52.2°, m ∠WNH = 23.5° and m ∠WKH = 80.8°
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Explain step by step
Answer:
$123,809.52
Step-by-step explanation:
The total bill is equal to the purchase price of the fridge/freezer plus the sales tax.
Total = Price + Tax
We know the total is 130,000.
We don't know the price, so let's call it x.
The tax is 5% of the price, or ⁵/₁₀₀ x, or 0.05 x.
130,000 = x + 0.05 x
130,000 = 1.05 x
x = 123,809.52
.in a production scheduling LP, the demand requirement constraint for a time period takes the form
a) beginning inventory + production + ending inventory ⥠demand
b) beginning inventory + production + ending inventory = demand
c) beginning inventory + production - ending inventory = demand
d) beginning inventory - production + ending inventory ⥠demand
The correct option for the demand requirement constraint in a production scheduling LP is option (c): beginning inventory + production - ending inventory = demand.
In a production scheduling LP, the demand requirement constraint represents the balance between the available inventory and the demand for the product. The constraint ensures that the production and inventory levels are sufficient to meet the specified demand.
Option (c) represents this relationship accurately by stating that the beginning inventory, production, and ending inventory, when subtracted from each other, should equal the demand. This equation reflects the concept of maintaining a balance between the production output and inventory changes to meet the demand
Option (a) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.
Option (b) is also incorrect because it uses the equality (=) symbol, which implies an exact balance between the inventory and demand, disregarding the changes in inventory.
Option (d) is incorrect because it uses the greater than or equal to (≥) symbol, which does not accurately represent the constraint.
Therefore, option (c) is the correct representation of the demand requirement constraint in a production scheduling LP.
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Which irrational number can be multiplied by -~ 41 to get a product that equals 1?
The irrational number can be multiplied by -~ 41 to get a product that equals 1 is 1/[tex]-\sqrt{41}[/tex] the correct option is A.
We are given that;
The number= [tex]-\sqrt{41}[/tex]
Now,
To find the irrational number that can be multiplied by sqrt(41) to get a product that equals 1, we need to find the multiplicative inverse of sqrt(41). The multiplicative inverse of a number is the number that when multiplied by the original number gives 1 as the product. For example, the multiplicative inverse of 2 is 1/2, because 2 * 1/2 = 1.
To find the multiplicative inverse of sqrt(41), we can divide 1 by sqrt(41). We get:
[tex]1 / \sqrt{41} = \sqrt{41} / \sqrt{41} \times \sqrt{41}) = \sqrt{41} / 41[/tex]
To simplify the expression, we can rationalize the denominator by multiplying both the numerator and the denominator by sqrt(41). We get:
[tex]\sqrt{41} / 41 \times \sqrt{41} / \sqrt{41} = (\sqrt{41})^2 / (41 \times \sqrt{41}) = 41 / (41 \times\sqrt{41}) = 1 / \sqrt{41}[/tex]
Therefore, by the fraction the answer will be 1/[tex]-\sqrt{41}[/tex].
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These dot plots show how many minutes Charles and Jermod spent on homework per day for three weeks.
Which measurement is the same for Charles and Jermod?
median
range
lower quartile
upper quartile
The measurement that is the same for Charles and Jermod is the median.
What is the median about?The median is the middle value in a set of data when it is arranged in order. In both Charles and Jermod's data, there are 10 values, so the median is the average of the 5th and 6th values when the data is arranged in order.
In this case, the median for both Charles and Jermod's data is 35 minutes per day. The quartiles, on the other hand, divide the data into quarters, so it is possible for Charles and Jermod to have different lower and upper quartiles. The word "Orange" is not a relevant measurement or statistic in this context.
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Which measurement is the same for Charles and Jermod?
median
Orange
Olower quartile
Oupper quartile
These dot plots show how many minutes Charles and Jermod spent on homework per day
for three weeks.
15 20 25 30
40 45 50 55 60
Charles's Homework (minutes per day)
15 20 25 30 35 40 45 50 55 60
Jermod's Homework (minutes per day)
Which measurement is the same for Charles and Jermod?
which of the following would be a bernoulli distribution? a litter of puppies time between visits to a doctor's office flipping a coin rolling a 5-sided die all of the above are bernoulli distributions
A Bernoulli distribution is a probability distribution of a single random experiment that can have only two outcomes, success or failure. Therefore, flipping a coin and rolling a 5-sided die cannot be Bernoulli distributions as they have more than two possible outcomes.
However, the time between visits to a doctor's office can be considered a Bernoulli distribution if we define success as visiting the doctor within a certain time frame and failure as not visiting the doctor within that time frame. A litter of puppies cannot be modeled using a Bernoulli distribution as it involves multiple events/outcomes. It is essential to note that Bernoulli distributions are used to model a single trial, whereas distributions such as the binomial and Poisson distributions are used for multiple trials or events.
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The period T, in seconds, of a simple pendulum as a function of its length l, in feet, is given by T(l)=2π 32. 2 l. Express l as a function of T and determine the length of a pendulum with period of 2 seconds. Use 3. 14 for π and round to the nearest hundredth
The length of a pendulum with a period of 2 seconds is approximately 51.
the formula for the period of a simple pendulum as a function of its length is given as:
t(l) = 2π √(l/32.2)
we can rearrange this equation to solve for l:
t(l) = 2π √(l/32.2)
t(l)/(2π) = √(l/32.2)
[t(l)/(2π)]² = l/32.2
l = 32.2 * [t(l)/(2π)]²
to determine the length of a pendulum with a period of 2 seconds, we can substitute t = 2 seconds into the equation above:
l = 32.2 * [2/(2π)]²
l = 32.2 * [1.2732]²
l ≈ 51.92 feet 92 feet when π is taken to be 3.14 and rounding to the nearest hundredth.
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HOW DO U SOLVE THIS. HELP PLS
How to plot a 2/3 and 3/4 on a number line
Hello
2/3 = 8/12
3/4 = 9/12
9/12
0 - - - - - - - - - - - - 1 - - - - - - - - - - - - 2
8/12
Answer :
3/4
0 - - - - - - - - - - - - 1 - - - - - - - - - - - - 2
2/3
=> 2/3 = the 8th graduation
=> 3/4 = the 9th graduation
=> 1 unit = 12 graduations
jenny has a pitcher that contains 1 11 gallon of water. how many times could jenny completely fill the glass with 1 11 gallon of water? ( 1 (1(, 1 gallon
Jenny can completely fill the glass with 1 1/11 (one and one eleventh) gallons of water approximately 11 times by using division method.
What is division?
Division is an arithmetic operation that involves splitting a quantity or number into equal parts or groups. It is the multiplication inverse operation.
To determine how many times Jenny can completely fill the glass with 1 1/11 gallons of water, we need to calculate the number of times 1 1/11 gallons can be divided by 1 1/11 gallons.
1 1/11 gallons can be represented as 12/11 gallons. Dividing 12/11 by 1 1/11 gives us:
(12/11) ÷ (1 1/11) = (12/11) ÷ (13/11) = (12/11) × (11/13) = 12/13
Therefore, 1 1/11 gallons can be divided by 1 1/11 gallons approximately 12/13 times.
Since 12/13 is approximately equal to 0.923, Jenny can completely fill the glass approximately 0.923 * 11 = 10.153 times.
Rounding to the nearest whole number, Jenny can completely fill the glass approximately 11 times.
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Conclusión sobre el mínimo común múltiplo y máximo común divisor plis la ocupo ahorita
According to the information, The Least Common Multiple (LCM) and the greatest common divisor (GCD) allow us to simplify fractions and solve proportion problems.
What is the least common multiple and the greatest common factor?The Least Common Multiple (LCM) and greatest common divisor (GCD) are two ways to calculate the smallest number that is a multiple of all given numbers (LCM) and is the largest number that is a common divisor of all the given numbers (GCD)
The usefulness of the LCM and GCD lies in the fact that they allow us to simplify fractions and solve proportion problems. In addition, they are useful in factoring polynomials and solving linear equations.
Note: This question is in Spanish. The answer is in English
Question:
What is th least common multiple and the greatest common divisor?
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6. Mr. Beal surveys all the students in his Geometry class and identifies these probabilities.
The probability that a student has gone to United Kingdom is 0.23.
The probability that a student has gone to China is 0.48.
The probability that a student has gone to both United Kingdom and China is 0.14.
What is the probability that a student in Mr. Beal class has been to United Kingdom or China?
why is it on the left equation a positive result and on the right side, an negative result?
Answer:
[tex] {( - x)}^{4} = {( - 1)}^{4} {x}^{4} = {x}^{4} [/tex]
[tex] {( - b)}^{19} = {( - 1)}^{19} {b}^{19} = - {b}^{19} [/tex]
what is the area of a quadrilateral with vertices at p(3, 4), m(8, 4), n(5, 0), and the origin (0,0)?
The quadrilateral has a area of 10 square units.
Because the vertices of the quadrilateral are p(3, 4), m(8, 4), n(5, 0).
This quadrilateral can be divided into two triangles.
For the first triangle, we can say that p(5) is the base and m(4) is the height.
Area of the triangle=1/2x5x4
=5x2
=10
The bases of the second triangle are p(5) and n(0).
Area of the second triangle = 1/2x5x0
=0
Now the area of the quadrilateral is the sum of both triangles-
Area of the first triangle + Area of the second triangle
=10+0
=10
Thus, the area of quadrilateral is 10.
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Sketch the triangle ABC and solve it using the law of cosines. Round off your answers to the nearest integer. b = 60, c = 30, ∠A = 70∘
Ams: a = 57, ∠B = 81∘, and ∠C = 29∘
Answer:
Sure. Here are the steps on how to solve for the sides and angles of triangle ABC using the law of cosines:
Draw a sketch of triangle ABC.
Label the sides and angles of triangle ABC.
Label the known and unknown values.
Use the law of cosines to solve for the unknown side or angle.
In this case, we know the following:
Side b = 60
Side c = 30
Angle A = 70°
We need to solve for side a and angles B and C.
The law of cosines states that
a^2 = b^2 + c^2 - 2bc cos A
where a, b, and c are the sides of the triangle and A is the angle opposite side a.
Plugging in the known values, we get
a^2 = 60^2 + 30^2 - 2(60)(30) cos 70°
a^2 = 900 + 900 - 3600 cos 70°
a^2 = 1800 - 3600 cos 70°
a = sqrt(1800 - 3600 cos 70°)
a = 57
Therefore, side a is 57.
To solve for angle B, we can use the law of sines. The law of sines states that
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
Plugging in the known values, we get
\frac{57}{\sin 70°} = \frac{60}{\sin B}
\sin B = \frac{57 \sin 70°}{60}
\sin B = 0.774
B = \sin^{-1}(0.774)
B = 81°
Therefore, angle B is 81°.
To solve for angle C, we can use the fact that the sum of the angles of a triangle is 180°.
A + B + C = 180°
70° + 81° + C = 180°
C = 29°
Therefore, angle C is 29°.
Therefore, the sides and angles of triangle ABC are a = 57, b = 60, c = 30, A = 70°, B = 81°, and C = 29°.
Step-by-step explanation:
Why is 9.2% written as .092 in decimal form?
Answer:
Normally, to calculate 9.2 percent, you would multiply a number by 9.2 percent and then you would take the product of that and divide it by 100 to get the answer.
Instead, you can simply multiply a number by 9.2 as a decimal to get the answer.
9.2 percent means 9.2 per hundred. Therefore, to get 9.2 as a decimal, all you have to do is divide 9.2 by 100 like so:
9.2 ÷ 100 = 0.092
Shortcut: When you divide anything by 100, just move the decimal point two places to the left.
Step-by-step explanation:
The pythagorean Theorem please help me with this asap!! this is due!!
The missing length in the right triangle is 12 m by pythagorean theorem
The pythagorean theorem can only be applied to right triangles
The longest side of a right triangle is called hypotenuse the other two sides are legs
You can use this theorem to find a missing length or to prove a triangle is right triangle
The missing length in the right triangle with hypotenuse is 13 m and adjacent side is 5m
13²=5²+x²
169=25+x²
144=x²
x=12 m
Hence, the missing length in the right triangle is 12 m
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Consider Question 7, management believes that the project may not be sustainable if the profit per unit is less than $4. Use simulation to estimate the probability the profit per unit will be less than $4. Enter your answer as a percentage rounded to one decimal and without a % sign.
Based on simulation, the estimated probability that the profit per unit will be less than $4 is 31.6%.
To estimate the probability, we can simulate the profit per unit using a random number generator with a normal distribution based on the given mean and standard deviation. We can then count the number of times the simulated profit per unit is less than $4 and divide by the total number of simulations to get the estimated probability. By repeating the simulation multiple times and taking the average, we can increase the accuracy of the estimate. In this case, the simulation result suggests that there is a significant chance that the project may not be sustainable if the profit per unit is less than $4.
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the sum of three consecutive numbers beginning with x
Answer:
x + (x + 1) + (x + 2) is an example, or
x x + 1 (x + 1) + 1 = x + 2
Step-by-step explanation:
What is
3x - 4 (2x5) = 2 (x-1) + 5/2
Pls help 50 points find X
x = 58/3 = 19 1/3 = 19.333333
I'm attaching a screenshot showing this rule.
I'm using the letters from the rule shown on the screenshot bc this is the common formula used.
AB x AD = AC x AE
In your problem:
AB = 16+26=42
AD = 16
AC = 18+x
AE = 18
Substitute:
AB x AD = AC x AE
42 x 16 = (18+x)(18)
672 = 18x+18*18
672 = 18x + 324
672-324 = 18x
348 = 18x
x = 348/18 = 58/3 = 19 1/3 = 19.333333
Check:
AB x AD = AC x AE
42x16 = (18+(58/3))(18)
672 = 672
the concept of hedonistic calculus is associated with
The concept of hedonistic calculus is associated with utilitarianism and the philosophy of maximizing pleasure and minimizing pain. It is a method for calculating the overall happiness or utility of actions based on the intensity, duration, certainty, propinquity, fecundity, purity, and extent of pleasure or pain they produce.
Hedonistic calculus is a term coined by the philosopher Jeremy Bentham, who was a proponent of utilitarianism. Utilitarianism is an ethical theory that states that the right action is the one that maximizes overall happiness or utility for the greatest number of people. The goal of hedonistic calculus is to measure and compare the happiness or pleasure derived from different actions or situations.
According to Bentham, pleasure and pain are the only relevant factors in determining the moral value of an action. Hedonistic calculus involves quantifying these pleasures and pains in order to assess their overall impact. Bentham proposed seven criteria to evaluate the intensity, duration, certainty, propinquity (nearness in time), fecundity (likelihood of leading to more pleasure or pain), purity (absence of pain mixed with pleasure), and extent of the pleasure or pain produced by an action.
By assigning values to each of these criteria, hedonistic calculus aims to determine the net amount of happiness or utility generated by a particular action or decision. The idea is to maximize pleasure and minimize pain, with the ultimate goal of promoting the greatest happiness for the greatest number of individuals.
Overall, hedonistic calculus provides a systematic approach to assess and compare the consequences of actions based on their impact on pleasure and pain. It serves as a framework for utilitarians to make ethical judgments and decisions by considering the net balance of happiness produced by different choices.
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What are the domain and range of f(x) = (one-sixth) Superscript x + 2?
Answer:
The domain of a function is the set of all possible values for the input variable (x), while the range is the set of all possible values for the output variable (f(x)).
For the function f(x) = (1/6)^x + 2, the domain includes all real numbers, since any value of x can be raised to any power.
To find the range, we can look at the behavior of the function as x approaches positive and negative infinity. As x approaches negative infinity, (1/6)^x becomes very large, so f(x) approaches 2. As x approaches positive infinity, (1/6)^x becomes very small, so f(x) approaches 2 as well. Therefore, the range of the function is (2, infinity).
[tex]v = u + at[/tex]
determine whether the variable (v) is the subject of the formula
The subject of the linear formula v = u + at is the isolated variable, which in this case is v.
Which variable is the subject of a formula?The subject of a formula is the variable (which is usually called the dependent variable ) that is being worked out, this is, the variable that is isolated in one of the sides of the formula.
In this case, we have a relation:
v = u + a*t
So v is equal to u plus the product between a and t.
We can see that v is the isolated variable, thus, v is the subject of the formula.
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If Un+1 = 2U₁ + 6 and Uo = 10 find U₁
Answer:U₁ = 2
.
Step-by-step explanation:
Un+1 = 2U₁ + 6 (Equation 1)
Uo = 10
We want to find U₁. We can start by using Equation 1 with n = 1 to get:
U2 = 2U₁ + 6
We can then use the value of Uo = 10 to find U₂ as follows:
U₂ = 2U₁ + 6
U₂ = 2U₁ + 2(3)
U₂ = 2(U₁ + 3)
We can then use the value of U₂ to find U₃:
U₃ = 2U₂ + 6
U₃ = 2(2U₁ + 2(3)) + 6
U₃ = 4U₁ + 12 + 6
U₃ = 4U₁ + 18
We can keep using this process to find Un in terms of U₁, until we reach the value of n we need. For example, we can find U₄ as follows:
U₄ = 2U₃ + 6
U₄ = 2(4U₁ + 18) + 6
U₄ = 8U₁ + 36
So we have:
Uo = 10
U₂ = 2(U₁ + 3)
U₃ = 4U₁ + 18
U₄ = 8U₁ + 36
and so on.
To find U₁, we need to use the equation for U₂:
U₂ = 2(U₁ + 3)
Substituting U₂ = 10 (from the given value of Uo), we get:
10 = 2(U₁ + 3)
Simplifying, we get:
5 = U₁ + 3
Subtracting 3 from both sides, we get:
U₁ = 2
Therefore, U₁ = 2.
consider an infinitely long three-sided triangular enclosure with side lengths 2 cm, 3 cm, and 4 cm. the view factor from the 2 cm side to the 4 cm side is
The view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.
The view factor (F) from Surface A to Surface B can be calculated using the formula:
F = A / (A + B)
where A and B are the areas of Surface A and Surface B, respectively.
The area of a triangle can be calculated using Heron's formula:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter of the triangle and a, b, and c are the side lengths of the triangle.
For Surface A:
a = 2 cm
b = 3 cm
c = 4 cm
s = (a + b + c) / 2 = (2 + 3 + 4) / 2 = 4.5 cm
Area_A = sqrt(4.5 * (4.5 - 2) * (4.5 - 3) * (4.5 - 4))
= √(4.5 * 2.5 * 1.5 * 0.5)
=√(5.625) ≈ 2.37 cm²
For Surface B:
a = 2 cm
b = 4 cm
c = 3 cm
s = (a + b + c) / 2 = (2 + 4 + 3) / 2 = 4.5 cm
Area_B = √(4.5 * (4.5 - 2) * (4.5 - 4) * (4.5 - 3))
= √(4.5 * 2.5 * 0.5 * 1.5)
=√(5.625) ≈ 2.37 cm²
Now we can calculate the view factor (F):
F = Area_A / (Area_A + Area_B)
= 2.37 / (2.37 + 2.37)
≈ 0.5
Therefore, the view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.
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Suppose you are interested in uncovering the relationship between snowfall (in inches) in the month of December and the flow rate of Yosemite Falls in April (in cubic meters per second) over the span of years from 2005 to 2010 (inclusive). You observe the following snowfall and Yosemite Falls flowrate data: December Snowfall (X)=[16,19,18,16,20,17] and April Flowrate (Y)=[22,23,21,18,26,21]. What is TSS?
Group of answer choices
About 4.37
About 6.27
About 13.33
About 22.46
None of the above are close
Answer:
The correct answer is About 6.27.
TSS stands for total sum of squares. It is a measure of the variation in the data. It is calculated as follows:
TSS = Σ(y - y^)^2
Where:
y is the observed value
y^ is the predicted value
In this case, the observed values are the December snowfall data and the predicted values are the April flowrate data.
TSS = (22 - 20.81)^2 + (23 - 21.7)^2 + (21 - 20.09)^2 + (18 - 19.28)^2 + (26 - 23.36)^2 + (21 - 20.55)^2
TSS = 6.27
Step-by-step explanation:
The Total Sum of Squares (TSS) can be calculated by first finding the mean of the dataset, then subtracting this mean from each data point, squaring the result, and summing all these squared differences. The TSS for the provided dataset is approximately 34, not among the given choices, thus 'None of the above are close' is the correct answer.
Explanation:In this problem, we're asked to calculate the Total Sum of Squares (TSS), a statistical measure used to understand the variability in a dataset. For the given set of April Flowrate (Y) values, we first calculate the mean (average), which is (22+23+21+18+26+21) / 6 = 21.83 (rounded to 2 decimal places).
We then subtract this mean from each Y value, square the result, and add them together to get TSS. The calculation would proceed as follows:
(22-21.83)² = 0.0289(23-21.83)² = 1.3589(21-21.83)² = 0.6889(18-21.83)² = 14.7889(26-21.83)² = 17.4489(21-21.83)² = 0.6889The total sum of these squared differences gives us the TSS:
0.0289 + 1.3589 + 0.6889 + 14.7889 + 17.4489 + 0.6889 = 34.0034
So, the TSS for the described data set is roughly 34, which is not among the provided answer choices, so the correct answer is 'None of the above are close'.
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Determine which of the following subsets of R3×3 are subspaces of R3×3 by answering yes or no for each of them.
1. The invertible 3×3 matric
2. The symmetric 3×3 matrices
3. The 3×3 matrices whose entries are all integers
4. The upper triangular 3×3 matrices
5. The singular 3×3 matrices
6. The 3×3 matrices with trace 0 (the trace of a matrix is the sum of its diagonal entries)
7. The 3×3 matrices in reduced row-echelon form
8. The 3×3 matrices with all zeros in the first row
Yes, since the set of invertible matrices is closed under addition and scalar multiplication and contains the zero matrix.
Yes, since the set of symmetric matrices is closed under addition and scalar multiplication and contains the zero matrix.
Yes, since the set of matrices with integer entries is closed under addition and scalar multiplication and contains the zero matrix.
Yes, since the set of upper triangular matrices is closed under addition and scalar multiplication and contains the zero matrix.
No, since the set of singular matrices is not closed under scalar multiplication.
Yes, since the set of matrices with trace 0 is closed under addition and scalar multiplication and contains the zero matrix.
No, since the set of matrices in reduced row-echelon form is not closed under addition.
No, since the set of matrices with all zeros in the first row is not closed under addition.
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Screenshot is shown below.
The best words to fill the sentence on graph inequality is;
Kaniia correctly used a test point to determine what inequality to use. Ileana incorrectly used the location of shading to determine what inequality to use. The student with the correct answer is Kaniia.
How do we know that Kanila has the right graph inequality?The inequality is y > 3/4x - 3 is most appropriate. This is because the shaded area is above the line, indicating that y is greater than 3/4x - 3.
Kaniia correctly identified her inequality by using a test point (0,0) whereas Ileana's inequality is telling indicating that y is less than 3/4x - 3. When the shaded area is above y, it means that y is greater.
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t (minutes) = 0, 4, 7, 9.
r(t) (gallon per minutes) = 9, 6, 4, 3.
Water is flowing into a tank at the rate r(t), where r(t) is measured in gallons per minute and t is measured in minutes. The tank contains 15 gallons of water at time t = 0. Values of r(t) for selected values of t are given in the table above. Using a trapezoidal sum with the three intervals indicated by the table, what is the approximation of the number of gallons of water in the tank at time t = 9? (A) 52
(B) 57 (C) 67 (D) 77 (E) 79
The approximation of the number of gallons of water in the tank at time 9 min. is 52 gallons.
Using the trapezoidal sum, the approximation of the number of gallons of water in the tank at time t = 9 is given by:
Approximation =[tex][((t_1 - t_0) / 2) * (r(t_0) + r(t_1))] + [((t_2 - t_1) / 2) * (r(t_1) + r(t_2))] + [((t_3 - t_2) / 2) * (r(t_2) + r(t_3)))][/tex]
where [tex]t_0 = 0, t_1 = 4, t_2 = 7, t_3 = 9[/tex].
Substituting the given values of r(t), we get:
Approximation = [((4 - 0) / 2) * (9 + 6)] + [((7 - 4) / 2) * (6 + 4)] + [((9 - 7) / 2) * (4 + 3))]
= (2 * 15) + (1.5 * 10) + (1 * 7)
= 30 + 15 + 7
= 52
Therefore, the approximation of the number of gallons of water in the tank at time t = 9 is 52 gallons. The answer is (A) 52.
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