The time when h(t) = 169 is 4.13am.
For (a), one possible formula for h(t) is the sinusoidal function, h(t) = Asin(Bt + C) + D, where A is the amplitude (maximum height - minimum height), B is the angular frequency (2 pi/period), C is the phase (starting point), and D is the minimum height. In this case, A = 3, B = 2pi/24, C = 0, and D = 170. Therefore, the formula for h(t) is h(t) = 3sin(2pit/24) + 170.
For (b), we need to solve for t when h(t) = 169. We can rearrange the equation to 3sin(2pit/24) = -1 and solve for t. Using a calculator, we can find that t = 8.21 hours. As 8.21 hours after midnight is 4.13am, the time when h(t) = 169 is 4.13am.
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Solve for question 1. Linear or exponential
2. Additively or multiplicatively
3. Common difference/ slope or common ratio/ multiplier/ base
Linear function would better model the data because as x increases, the y values change additively. The common difference of this function is approximately 159.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
For this problem, the function is classified as linear, as the difference between consecutive terms is of approximately 159, while the ratios are different.
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a p-value is .1151. what is the test-statistic (z-score)? explain how you know this. (explain how you calculated the answer.)
The test-statistic (z-score) is 1.19984.
To find the test statistic (z-score) using the p-value, you will need to use the inverse of the standard normal cumulative distribution function (CDF), also known as the inverse normal function or the "normal inverse function." This function can be found using a calculator or a spreadsheet program with built-in functions, or you can use a table of standard normal probabilities to find the corresponding z-score for a given p-value.
For example, if the p-value is 0.05, you would look up the corresponding z-score in a table of standard normal probabilities and find that it is approximately 1.645. This means that the test statistic (z-score) for a p-value of 0.05 is 1.645.
It's important to note that this method only works for a one-tailed test, for a two-tailed test you need to divide your p-value by 2 and then use the inverse normal function.
so, the p-value is 0.1151, you would look up the corresponding z-score in a table of standard normal probabilities and find that it is approximately 1.19984.
Therefore, the test-statistic (z-score) is 1.19984.
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7) Complete the blanks in this bank statement.
Date
25/03/20
28/03/20
29/03/20
Income Outgoings Balance
£453
£1200
£957
Using the arithmetic operations the balance amount for 28/03/20 and incoming amount for 29/03/20 is obtained as £ 747 and £ 210 respectively.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The statement of bank account is given.
On 25/03/20 the balance amount left in bank was £ 1200.
On 28/03/20 the outgoing amount from the bank was £ 453.
To find the balance amount for 28/03/20, use the arithmetic operation of subtraction -
Balance amount = Previous Balance - Outgoing Amount
Substitute the values in the equation -
Balance amount = 1200 - 453
Balance amount = 747
Therefore, the balance amount for 28/03/20 was £ 747.
Now, On 29/03/20 the balance amount left in bank was £ 957.
To find the incoming amount for 29/03/20, use the arithmetic operation of subtraction -
Incoming Amount = New Balance - Previous Balance
Incoming Amount = 957 - 747
Incoming Amount = 210
Therefore, the incoming amount for 29/03/20 was £ 210.
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The table represents a proportional relationship. Write an equation to represent the relationship.
For the table of values gives, the equation of line is obtained as y = 1/3x.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The coordinate points for cups of flour, x and loaves of bread y is given in the table.
The slope-intercept form of an equation is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
(3 - 2)/(9 - 6)
1/3
So, the slope point is obtained as m = 1/3.
The equation becomes - y =1/3 x + b
To find the value of b substitute the values of x and y in the equation -
2 = 1/3(6) + b
2 = 2 + b
b = 2 - 2
b = 0
So, the value for b is 0.
Now, the equation becomes -
y = 1/3x + 0
y = 1/3x
The graph is plotted for the equation.
Therefore, the equation is y = 1/3x.
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the wage for 35 people in a factory for one day i 7175. if on another day the factory paid 9225, how many people worked on that day, if the wage per day i the ame for everyone?
The total wage can only be an integer multiple of the wage per person.
The number of people working in the factory on a particular day can be calculated by dividing the total wage by the wage per person. This can be expressed mathematically as:
Number of People = Total Wage ÷ Wage per Person
For the given scenario, the number of people working on the day when the factory paid 9225 can be calculated as:
Number of People = 9225 ÷ 7175
Number of People = 1.287
Since the number of people has to be a whole number, this means that there were 1 people working in the factory on the day when the factory paid 9225. This is because when the wage per person is the same for everyone, the total wage can only be an integer multiple of the wage per person.
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W is inversely proportional tof
When f = 12, w = 40
(a) Find a formula connecting w and f
(b) Find the value of w when f = 60
3
B is inversely proportional to y
When B = 0. 8, y = 13
(a) Find an equation for B in terms of y.
(b) Work out the value of B when y = 5
Equation with inversely proportional relation gives answer of the following questions :
1. a. w = k₁ / f b. f =60 ⇒ w = 8
2. a. B = k₂/ y b. y = 5 ⇒ B = 2.08
1. Representation of the formula connecting :
w is inversely proportional to the variable f
a . w ∝ ( 1 / f )
⇒ w = k₁ / f
where k₁ is the constant of proportionality.
When w = 40 , f = 12
40 = k₁ / 12
⇒ k₁ = (40)(12)
⇒ k₁ = 480
b . f = 60
Value of 'w' is equal to :
⇒ w= 480 / 60
⇒ w = 8
2. B is inversely proportional to the variable y
a . B ∝ ( 1 / y )
⇒B = k₂ / y
where k₂ is the constant of proportionality.
When B = 0.8 , y = 13
0.8 = k₂ / 13
⇒ k₂ = (0.8)(13)
⇒ k₂ = 10.4
b . y = 5
⇒ B= 10.4 / 5
⇒ B = 2.08
Therefore, the required values and formula to represents the inversely proportional relation are:
The above question is incomplete, the complete question is :
1. W is inversely proportional to f , When f = 12, w = 40
(a) Find a formula connecting w and f .
(b) Find the value of w when f = 60.
2. B is inversely proportional to y , When B = 0. 8, y = 13
(a) Find an equation for B in terms of y.
(b) Work out the value of B when y = 5
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3/4x-5=3/8 without fractions or decimals
Answer:
X= 7 1/6
Step-by-step explanation:
-3/4x-5=3/8
-Add 5 on both sides
-3/4x=43/8
-Divide 3/4 on both sides
-X= 7 1/6 (there is no way for this not to be a fraction or decimal.)
Simply the expression & explain
Answer:
780
Step-by-step explanation: The answer is 780!
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
Range provides a precise measurement of variability for both sets of data because it compares the greatest and lowest values in a dataset.
It is a helpful measure of variability for comparing the constancy of temperature between Desert Landing and Flower Town because it is unaffected by skewness or symmetry.
The histogram is what?A histogram is a graph that shows how a dataset is distributed. In a dataset, it is a way to show the frequency of various values or ranges of values.
In a histogram, the y-axis normally indicates the frequency or count of the values, and the x-axis typically shows the values or ranges of values.
Each bin in the data is represented by a bar whose height is equal to the number of observations in that bin. The data is divided into bins. The distribution of data is visualized using histograms, which are also used to spot anomalies and spot patterns or trends in the data.
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The sum of two numbers is 30. One exceeds the other by 15. What are the two numbers?
let the number be x and y
x + y = 30 -----(1)
x = y + 15 -----(2)
y + y + 15 = 30
2y = 15
y = 7.5
x = 7.5 + 15 = 22.5
x= 22.5 , y = 7.5
Drag each object to show whether cost is proportional to area in the situation represented.
The image has been dragged to show where cost is proportional to area and attached
When is a linear function proportional?Equation y = kx can be used to define proportional functions, which are linear functions that include the origin.
While all proportional functions are linear, not all linear functions are proportional functions.
From the table the equation s calculated to be y = kx
where k = 1.25
for x = 400, y = 1.25 * 400 = 500
for x = 500, y = 1.25 * 500 = 750 and so on
this is a proportional function
For asphalt sealant the labor fee added made the function not to be a proportional function
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Solve the simultaneous equation
3x + 4y = 67
5x + 6y = 106
Answer:
Step-by-step explanation:
if it takes 8 seconds for a ball to roll 24 meters downhill, what is the average speed of the ball?
The average speed of the ball which travelled 24 meters in 8 seconds is 3m/s.
What is the average speed of the ball?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Distance travelled by the ball = 24 metersElapsed time = 8 secondsSpeed of the ball = ?To determine the average speed of the ball, plug the given values into the above equation and simplify.
Speed = Distance / time
Speed = 24 meters / 8 seconds
Speed = 3m/s
Therefore, the speed is 3 meters per seconds.
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The ratio of side lengths of a quadrilateral is 3 : 5 : 6 : 9, and its perimeter is 9.6cm. What is the length of the longest side?
The length of the longest side is solved to be 3.76 cm
How to determine the length of the longest sideAn ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
The perimeter o the quadrilateral have a formula that add all the sides together, assuming the factor of the original length is x, the perimeter is solved by
9.6 = 3x + 5x + 6x + 9x
9.6 = 23x
x = 9.6 / 23
x = 0.4174
The length of the longest side
= 9x
= 9 * 0.4174
= 3.76 cm
3.76 cm is the length of the longest side
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Two neon signs are turned on at the same time. Both signs blink as they are turned on. One sign blinks every 9 seconds. The other sign blinks every 15 seconds. In how many seconds will they blink together again? please use prime factorization tree
After 45 seconds they blink together again.
What is Least Common Multiple?Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20.
Given:
One sign blinks every 9 seconds. The other sign blinks every 15 seconds.
Now, to find they blink together again we have to find the LCM of 9 and 15.
For 9 the lights will blink at seconds: 0, 9, 18, 27, 36, 45, 54, 63,
and, For 15 the lights will blink at seconds: 0, 15, 30, 45, 60, 75
Hence, they blink together at 45 seconds.
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Distributive property > Remove the parenthesis
-3(-3v^3+3-4w^2)
The expression -3(-3v^3+3-4w^2) after using the distributive property is 9v³ - 9 + 12w²
What is a distributive property?The distributive property of multiplication over addition is a mathematical method of expanding bracket mostly applied when you need to multiply a value by a sum.
This property of multiplication explains how to solve expressions that are in the form of a(b + c).
From the information given, we have the expression;
-3(-3v^3+3-4w^2)
To carry out the distributive multiplication , we need to remove the parentheses of the expression by taking the following steps, we have;
expand the bracket and take note of the mathematical signs, we get
-3(-3v³ + 3 - 4w²)
9v³ - 9 + 12w²
Note that we can no longer add the terms because they are not like terms.
Hence, the expression is 9v³ - 9 + 12w²
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assume we are playing a game. you will roll an unfair dice with the following probability p = {1 : 0.1, 2 : 0.3, 3 : 0.1, 4 : 0.2, 5 : 0.1, 6 : 0.2}. (i.e. p(x = 2) = 0.3). the reward depends on whether the rolled dice shows an even number or an odd number. if you roll an even number you will win 100$ and if you roll an odd number you will lose 200$ (i.e. you win -200$). what is the expected reward amount (the expected value may be negative)?
The expected reward amount is -10$.
Expected Reward Amount
The product of the likelihood of each occurrence and the related reward results in the anticipated reward amount, which is equal to the expected reward value.
According to the question
We must multiply the odds of rolling an even number by the payout for rolling an even number, the odds of rolling an odd number by the payout for rolling an odd number, and then sum the results to determine the expected payoff.
P(odd) = P(1) + P(3) + P(5) = 0.1 + 0.1 + 0.1 = 0.3
P(Even) = P(2) + P(4) + P(6) = 0.3 + 0.2 + 0.2
The expected reward is calculated as follows:
(p(even) * 100 + (p(odd) * 200)) = (0.7 * 100 + (0.3 * 200)) = 70 - 60 = -10
As a result, the predicted reward is -10$.
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Neely has $1. 73 in coins. He gives his friend 1 quarter and 3 nickel
What is the value of the coins he has left?
If Neely has $1.73 in coins and he gives his friend 1 quarter and 3 nickel , then the value of coins he has left is $1.65 .
the value of number of coins Neely has is = $1.73 ;
he gives his friend "1 quarter" , and the value of 1 quarter in dollar is = $0.25
the amount left with Neely is = $1.73 - $0.25 = $1.48 ;
next he gave his friend "3 nickels" , and value of 3 nickels in dollars in $0.15 ;
So , the amount left with Neely is - $1.48 - $0.15 = $1.65 .
Therefore , the Neely is left with $1.65 value of coins .
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An artist draws a stained glass window to scale. The actual window will have a length of 5ft and a width of 2ft. The scale from the drawing to the window is 2in to 1 ft. What is the width of the drawing?
Answer: 4 in
Step-by-step explanation:
michael has a drawer with 8 pairs of black socks and 12 pairs of white socks. without looking he takes a white pair of socks out of the drawer. what is the probability that the next pair he takes out is white?
The Probability that the next pair Michael takes out is black = 8 / 19
What is Probability?
Probability is deals with "occurrence of Random event. The value is expressed from 0 to 1".
According to the question,
Total number of pairs of socks = 8 + 12 =20
Probability of taking pairs of black socks, P(B )= 8 / 20
Probability of taking pairs of white socks, P(W) = 12 / 20
But after taking Black pair socks the total number socks = 19.
Hence, the Probability of taking Black pair socks from drawer is 8 / 19 .
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Witch is cheaper 50 head of cattle for $24,500 or 37 head of cattle for $18,870
What is 2/3 x 9/16?
Answer:
.375 as a decimal
Step-by-step explanation:
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The length of the room are y2 – 5y = 750 , y(y – 5) + 750 = 0 and (y + 25)(y – 30) = 0
How to determine the expressionit is important to note that the formula for calculating the area of a rectangle is expressed as;
A = lw
Such that;
A is the area of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
Length = y
Width = y - 5
Area = 750 square feet
Substitute the values into the formula
750 =y(y - 5)
expand the bracket
750 = y² - 5y
y² - 5y- 750 = 0
This is factorized to give;
(y + 250 (y - 30)
Hence, the expression is y² - 5y- 750 = 0
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8. A cylindrical basket has a volume of 15 cubic feet. If the height of the basket is 1.5 feet, what is the area of the base of the basket?
The Area of the base of the basket is 10 ft².
What is volume and area of the cylinder? Volume and area are two different measures of a cylinder. Volume measures the amount of space an object occupies, while area measures the two-dimensional surface of an object. The volume of a cylinder is equal to the area of its base multiplied by its height. The area of a cylinder is equal to the circumference of its base multiplied by its height.To find the volume of a cylinder, multiply the area of its base by its height. The area of the base can be calculated by multiplying pi (3.14) by the radius of the base squared. The circumference of the base can be calculated by multiplying pi (3.14) by the diameter of the base. The height of the cylinder is simply the distance between the two bases. Once the area of the base and the height of the cylinder are known, the volume of the cylinder can be calculated by multiplying the area of the base by the height.The area of the cylinder can be calculated by multiplying the circumference of the base by the height.Given,
Volume of basket = 15 cubic feet
h = 1.5 ft
V = πr²h
15 = πr² (1.5)
πr² = 15/1.5
πr² = 10 ft²
Area of base of the basket = 10 ft²
(or)
15 = πr² (1.5)
r = √15/π(1.5)
Simplifying the values, we can get radius of basket = 1.78
Then, area of base of basket = πr²
Substituting the values of π = 3.14 and r = 1.78 in above formula, we get,
Area of base of the basket ≈ 9.95 ft²
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A cylinder can be measured in two separate ways: volume and area. As area gauges an object's two-dimensional surface, volume gauges how much space an object takes up.
What area of the base of the basket?If the cylinder's height and base area are known, the cylinder's volume may be determined by multiplying the base area by the cylinder's height. By dividing the base's circumference by its height, one may get the cylinder's area.
Given,
Volume of basket = 15 cubic feet
h = 1.5 ft
V = πr²h
15 = πr² (1.5)
πr² = 15/1.5
πr² = 10 ft²
Area of base of the basket = 10 ft²
(or)
15 = πr² (1.5)
r = √15/π(1.5)
We may obtain radius of basket = 1.78 by simplifying the numbers.
Then, area of base of basket = πr²
By replacing the values of 3.14 and 1.78 in the formula above, we obtain,
Area of base of the basket ≈ 9.95 ft²
Therefore, The Area of the base of the basket is 10 ft².
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Logan spent $275 for a tree for the front yard. He was charges 7% sales tax. How much money did he spend on the sales tax? How much did he spend in total?
Answer:294,25$
Step-by-step explanation:
you make 7% of 100 multiply by $275 and the price that gives you you make more $275 and that gives you your results
I need 2 and example 3 please help I am desperate
the measure of ∠ABE is 47°.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
ΔABE and ΔCEB both are congrurent trinalge.
∠ABE =∠ CEB
The ∠ CEB+ ∠CBE = 90
∠ CEB = 90-43 = 47
As ∠ABE =∠ CEB =47°
So the measure of ∠ABE is 47°.
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assuming the company's claim is true, what is the probability that the mean loss from fire is greater than 300
The probability that the mean loss from f-i-re is larger than $300 for an S-R-S of 1000 home owners is 0.3085.
This problem can be solved using the Central Limit Theorem, which states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal if the sample size is large enough (typically if n > 30).
Since the population is strongly right-skewed and the sample size is large (n = 1000), we can assume that the sampling distribution of the mean loss from fi-re will be approximately normal.
The mean of the sampling distribution is equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, we have:
Populatio mean (μ) = $250
Population standard deviation (σ) = $5000
Sample size (n) = 1000
Sample mean = $300
Probability of sample mean > $300 = ?
Now, standard deviation of sample mean = σ / sqrt(n) = $5000 / sqrt(1000) = $158.11
Now, we need to standardize the sample mean using the z-score formula:
z = (sample mean- population mean) / (σ / sqrt(n)) = (300 - 250) / 158.11 = 0.316
Using a standard normal distribution table or calculator, we can find the probability of a z-score greater than 0.316 to be approximately 0.3765 or about 37.65%.
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take away 7 from 4 times x
Answer:
4x-7
thats your answer
Step-by-step explanation:
:))))
Determine the values of m in the equation m2 = 36.
m = 18
m = 6
m = ±18
m = ±6
the values of m in the equation m^2 = 36 , is m= ±6.
What is Square root?A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.
here, we have,
given that,
the equation m^2 = 36.
taking root on both side, we get,
m= ±6.
Hence, the values of m in the equation m^2 = 36 , is m= ±6.
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Adam buys a bag of dog food with a weight of 7/8 pound and a bag of cat food with a weight of 1 whole 3/4 pounds. Estimate the total weight of the pet food he buys with benchmark fractions
Answer:
To estimate the total weight of the pet food Adam buys, we can use benchmark fractions to compare the weight of the dog food (7/8 pound) and the weight of the cat food (1 3/4 pounds) to a benchmark fraction that we are familiar with.
We know that 1 whole pound is equal to 16 ounces. So, we can use this as a benchmark to estimate the weight of the dog food and cat food.
First, we'll convert 7/8 pound to ounces. 7/8 pound is equal to 7/8 * 16 = 14 ounces
Next, we'll convert 1 3/4 pound to ounces. 1 3/4 pound is equal to 1 * 16 + 3/4 * 16 = 16 + 12 = 28 ounces.
Now we can add the weight of the dog food and the cat food to get the total weight of the pet food Adam buys.
14 ounces + 28 ounces = 42 ounces
So, the total weight of the pet food Adam buys is approximately 42 ounces, which is roughly 2.6 pounds.
The estimate was made with benchmark fractions, which allows us to make a rough estimation of the weight of the pet food, but it's not as precise as the exact weight in pound or ounces.