When released, a yo-yo falls towards the floor due to conservation of energy.
Conservation of energy:
As it falls, its potential energy is converted into kinetic energy. When the yo-yo reaches its lowest point, it begins to spin rapidly, storing some of this kinetic energy as rotational energy. As the string wraps around the yo-yo's axle, it exerts a force which starts pulling the yo-yo back up towards your hand. This force converts the rotational energy back into potential energy as the yo-yo rises. When the yo-yo reaches your hand, it has regained all its initial potential energy, enabling it to return to your hand.
When the yo-yo reaches the end of the string, the rotational kinetic energy it has stored is used to wind the string back around the axle. This winding motion causes the yo-yo to move back up toward your hand. As the yo-yo moves back up, its potential energy increases, while its rotational kinetic energy decreases. Eventually, the yo-yo reaches your hand and comes to a stop.
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Jessica went deep sea diving. She make the first stop on her descent at 25 meters below the surface of the water. From that point she dives down further, stopping every 5 meters. If she makes 4 additional stops, which number represents her position, relative to the surface of the water?
*
A 45
B 20
C -20
D -45
Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.Option(A) is correct.
What is sea diving?Divers who engage in scuba diving use breathing apparatus that is entirely independent of a surface air source. Christian J. Lambert-sen came up with the moniker "scuba," which stands for "Self-Contained Underwater Breathing Apparatus," in a 1952 trademark application.
According to question:Jessica's position relative to the surface of the water can be represented by the following arithmetic sequence:
[tex]$$25, 30, 35, 40, 45$$[/tex]
where the first term is 25 and the common difference is 5 (the distance between each stop).
To find the fifth term (her position after making 4 additional stops), we can use the formula for the nth term of an arithmetic sequence:
[tex]$$a_n = a_1 + (n-1)d$$[/tex]
where [tex]$a_1$[/tex] is the first term, d is the common difference, and n is the term number.
Plugging in the values we know, we get:
[tex]$$a_5 = 25 + (5-1)5 = 45$$[/tex]
Therefore, Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.
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Consider the expression (x2−9)(x+4). Select all the values of x for which (x2−9)(x+4)=0
Answer:
X= 567890
Step-by-step explanation:
Answer:
See below, please.
Step-by-step explanation:
Using the zero product property, we can set each factor equal to zero and solve for x:
(x² - 9)(x + 4) = 0
(x² - 9) = 0 or (x + 4) = 0
For the first factor, we can factor it further as the difference of squares:
(x + 3)(x - 3) = 0
So, either (x + 3) = 0 or (x - 3) = 0, giving us:
x = -3, x = 3, or x = -4
Therefore, the values of x for which (x² - 9)(x + 4) = 0 are -3, 3, and -4.
57% of people in state prisons for drug offenses in the us are african american. what percentage of illicit drug users in the us are african american?
The percentage of illicit drug users in the US are African American is a. 14%
According to data from the National Survey on Drug Use and Health, in 2019, 14.5% of African Americans reported using illicit drugs in the past month, compared to 12.4% of the overall population. While African Americans are overrepresented in state prisons for drug offenses, they do not use drugs at a significantly higher rate than other racial and ethnic groups.
It's important to note that drug use is a complex issue with many social and economic factors at play. It's crucial to approach drug use and addiction with a public health perspective that prioritizes prevention, treatment, and harm reduction over punitive criminal justice approaches.
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Your question is incomplete, but probably the complete question is :
57% of people in state prisons for drug offenses in the US are African American. What percentage of illicit drug users in the US are African American?
a. 14%
b. 28%
c. 42%
d. 56%
daisy has the following production possibilities frontier per week. her resource is 5 lbs of flour. note: you will use this ppf to answer the next several questions. given daisy's ppf, the following production combo, 9 pies and 8 tarts is
The following question is incomplete.
Please complete the question so it can be answered.
Without the actual Production possibility frontier table or chart we cannot determine the exact quantities.
However, based on the information provided, we can determine that the production combo of 9 pies and 8 tarts is a point on Daisy's PPF.
This means that Daisy can produce 9 pies and 8 tarts per week using her available resources of 5 lbs of flour.
To fully analyze production possibilities of Daisy, we would need to see her complete PPF, which would show all possible combinations of pies and tarts that she could produce with her resources.
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An object's _____ are the tasks or functions that the object performs when it receives a command to do so.
a. roles
b. utilities
c. methods
d. instances
An object's methods are the tasks or functions that the object performs when it receives a command to do so.
What are the methods?The methods of an object describe what the object can perform. In object-oriented programming (OOP), objects are a key element of the language. Each object has a collection of methods that it can perform.
Methods are similar to functions or procedures in traditional programming. They're the code that the object executes in response to a command. Because objects have methods, programming in object-oriented programming (OOP) languages involves defining the object classes, which specify the methods and properties that each object in that class will have.
Roles:- Roles specify the various abilities that an object can perform. In object-oriented programming (OOP), these roles are often defined through interfaces, which specify the set of methods that an object must implement in order to fulfill the role. The role of an object is determined by the methods that it implements.
Utilities:- Utilities are typically unrelated to an object's role, but rather are commonly used functions that are available throughout a system or application. They often provide functionality that is required by many different objects in the system.
c. methods is the correct option.
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suppose is a critical point of a function with continuous second derivatives. in each case, what can you say about ?
Yes, if is a critical point of a function with continuous second derivatives, then it is a stationary point.
This means that the function's derivative is equal to 0 at that point and it is neither increasing or decreasing.
A stationary point is a point on the graph of a function where the function's derivative is equal to 0. This is an important property of a function and it can be used to determine the properties of the function.
At a stationary point, the rate of change of the function is equal to 0, so the function is neither increasing or decreasing. In other words, the function is neither increasing or decreasing at that point.
This property can be used to analyze the function and determine its characteristics. For example, it can be used to identify local minima or maxima.
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Please Help i need the full answer
The value of x in the intersected chord is 72.95 degrees.
How to find the inscribed angle using arc angle?If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
The chords intercepts to form two arc angles 42.9 and 103 degrees. The inscribed angle formed by the intersected chord can be found as follows:
Therefore,
x = 1 / 2 (103 + 42.9)
x = 1 / 2 (145.9)
x = 72.95
Therefore,
x = 72.95 degrees
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50 Points
Janey paints a block of wood with gold glitter for an art project. The block measures
8 inches by 10 inches by 20 inches.
After she's done, she decides to make two blocks by cutting through the block on the
red line. She still wants each block to be covered with gold glitter.
What is the total area of the cut surfaces she still needs to paint?
Answer the questions to find out.
1. What is the shape of each cut surface? what are its dimensions?
2. What is the area of each cut surface?
3. What is the total area Jenny needs to paint? Explain how you found your answer.
Answer:
The shape of each cut surface is a rectangle. The dimensions of the first cut surface are 8 inches by 10 inches, and the dimensions of the second cut surface are 10 inches by 20 inches.
The area of the first cut surface is 8 inches x 10 inches = 80 square inches. The area of the second cut surface is 10 inches x 20 inches = 200 square inches.
To find the total area Jenny needs to paint, we need to add the area of the first cut surface to the area of the second cut surface.
Total area = Area of first cut surface + Area of second cut surface
Total area = 80 square inches + 200 square inches
Total area = 280 square inches
Therefore, Jenny needs to paint a total area of 280 square inches.
4. George sails his boat 3.7 miles from the dock at the mainland to Paradise Island. From Paradise Island, a 72 degree angle is formed between the dock at the mainland and shipwreck rock. If the distance between Shipwreck rock and the dock is 5.6 miles, approximately how far does George need to sail from paradise island to reach shipwreck rock?
George needs to sail close to 3.7 miles from Paradise Island to reach Shipwreck Rock.
How do we calculate?Applying the law of cosines:
c^2 = a^2 + b^2 - 2ab cos(C)
where:
c = the unknown distance
a = 3.7 miles (distance from the dock at the mainland to Paradise Island)
b = 5.6 miles (distance from the dock at the mainland to Shipwreck Rock)
C = 72 degrees (angle formed between the dock at the mainland and Shipwreck Rock)
The we convert the angle from degrees to radians:
72 degrees = (72/360) * 2π radians = 1.2566 radians (approx.)
Substituting the values into the formula and solving for c:
c^2 = 3.7^2 + 5.6^2 - 2(3.7)(5.6)cos(1.2566)
c^2 = 13.69
c ≈ 3.7 miles
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I really need help with this
As Hannah want to arrange the 4 cereal boxes from least to greatest weight, the correct arrangement will be: "Oaties, Bran Flakes, Corn Cornes, Big O's". The Option C is correct.
What is arrangement of weight from least to greatest?Arranging weights from least to greatest is a common task in various situations, such as when weighing ingredients for a recipe or when sorting objects by weight.
To accomplish this, one needs to compare the weights of the objects and order them accordingly. A simple approach is to use a weighing scale to measure the weights accurately and write them down.
The correct arrangement of "Oaties, Bran Flakes, Corn Cornes, Big O's" is correct because they have the weights of 451.5, 453.6, 453.8 and 458.2 respectively.
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a rod placed up against a wall is sliding down. the distance between the top of the rod and the foot of the wall is decreasing at a rate of 9 inches per second. when this distance is 152 inches, how fast is the distance between the bottom of the rod and the foot of the wall changing? the rod is 172 inches long.
when the distance between the top of the rod and the foot of the wall is 152 inches, the distance between the bottom of the rod and the foot of the wall is decreasing at a rate of approximately 19.08 inches per second.
In this case, we are given that the distance between the top of the rod and the foot of the wall is decreasing at a rate of 9 inches per second. We want to find the rate at which the distance between the bottom of the rod and the foot of the wall is changing.
We can start by using the Pythagorean theorem to relate the three distances involved: the height of the rod (h), the distance between the top of the rod and the foot of the wall (x), and the distance between the bottom of the rod and the foot of the wall (y). Specifically, we have:
[tex]h^2 = x^2 + y^2[/tex]
To find the rate at which y is changing, we can take the derivative of both sides of this equation with respect to time (t), using the chain rule:
2h dh/dt = 2x dx/dt + 2y dy/dt
We are given that dh/dt = -9 inches per second (since h is decreasing). We also know that h = 172 inches and x = 152 inches (when y = 0). Substituting these values and solving for dy/dt, we get:
dy/dt = (h/x) * (dx/dt - (x/y) * dh/dt)
dy/dt = (172/152) * (-9 - (152/y) * 9)
dy/dt = -19.08 inches per second (rounded to two decimal places)
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A holiday package is valued at $15000 today. If inflation averages 2% per year, calculate the value of the holiday package indexed for inflation over 4 years
The value of the holiday package indexed for inflation over 4 years is $16,236.00, calculated using the formula Value after inflation = Value before inflation × (1 + inflation rate)ⁿ.
To calculate the value of the holiday package indexed for inflation over 4 years, we can use the formula:
Value after inflation = Value before inflation × (1 + inflation rate)ⁿ
("ⁿ" represents number of years)
where the inflation rate is given as a decimal.
Substituting the given values, we get:
Value after inflation = $15000 × (1 + 0.02)⁴
= $15000 × 1.0824
= $16,236.00
Therefore, the value of the holiday package indexed for inflation over 4 years is $16,236.00.
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Is 4, 5, and 6 a right triangle??..
Step-by-step explanation:
If they are RIGHT triangles then the Pythagorean theorem would apply
c^2 = a^2 + b^2 where c is the long side ( hypotenuse)
4) does 10^2 = 6^2 + 8^2 ?
100 = 36 + 64 Yes....it is a right triangle
5) does 8^2 = ( sqrt26)^2 + sqrt(28^2) ?
64 = 26 + 28 NO....it is NOT a right triangle
6) you should try this one yourself .....
Solve the system by graphing
Y = 5x + 1
Y = -x - 5
The solution of the system of equtaions:
Y = 5x + 1
Y = -x - 5
is (-1, -4), look at the graph at the end.
How to solve the system of equations graphically?To solve a system of equations graphically just graph both of the equations, in this case are the lines y = 5x + 1 and y = -x - 5, in the same coordinate axis and then identify the point where these two lines intersect.
That point will be the solution of the given system of equations.
Said graph can be seen in the image at the end. There you can see two lines, one orange and one blue, and the lines intersect at the point (-1, -4), so that is the solution of the system.
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an 8 foot ladder is leaning against a wall. the top of the ladder is sliding down the wall at the rate of 2 ft per second. how fast is the bottom of the ladder moving along the ground at the point in time when the botto of the ladder is 4 feet from the wall
The bottom of the ladder is moving at a rate of 4/3 ft per second.
To solve the problem, we can use the Pythagorean Theorem:[tex]$x^2 + y^2 = 64$[/tex], where x is the distance from the wall to the bottom of the ladder and y is the length of the ladder. We differentiate this equation with respect to time t and use the chain rule to get [tex]$\frac{d}{dt} (x^2 + y^2) = \frac{d}{dt} 64$[/tex]
Simplifying, we get
[tex]$2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0$[/tex]
When the bottom of the ladder is 4 feet from the wall, we have x = 4 and y = 8, so we can substitute these values into our equation and solve for [tex]$\frac{dx}{dt}$[/tex]:
[tex]$2(4)\frac{dx}{dt} + 2(8)(-2) = 0$[/tex]
[tex]$\frac{dx}{dt} = \frac{16}{8} = \frac{4}{3}$[/tex]
Therefore, the bottom of the ladder is moving at a rate of [tex]$\frac{4}{3}$[/tex] ft/s.
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use half angle identity. help
pls
Required value of the given expression is (1+√2)
Given expression is [tex]tan \frac{11\pi}{8} [/tex]
We want to solve it.
Now,
[tex] \tan( \frac{11\pi}{8} ) = \tan( \frac{3\pi}{8} + \frac{8\pi}{8} ) \\ = \tan( \frac{3\pi}{8} + \pi ) \\ = \tan( \frac{3\pi}{8} ) [/tex]
Finding [tex] \tan( \frac{3\pi}{4} ) [/tex]
Let,
[tex] \tan(2t) = \tan( \frac{3\pi}{4} ) = - 1[/tex]
Use half angle identity,
[tex] \tan(2t) = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ - 1 = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ {tan}^{2} t - 2tant - 1 = 0[/tex]
Let,[tex]x = tant[/tex]
So,[tex] {x}^{2} - 2x - 1 = 0[/tex]
Now, [tex]x = 1 \pm \sqrt{2} [/tex]
So,
[tex]tant = tan \frac{3\pi}{8} = 1 \pm \sqrt{2} [/tex]
[tex]tan \frac{3\pi}{8} [/tex] is positive,then required value is 1+√2.
So, option D is the correct answer.
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equivalent fractions for 7/12 and 5/6
Answer:
14/24, 21/36, 28/48, 35/60, 42/72, 49/84, 56/96 are equivalent fractions of 7/12.
10/12, 15/18, 20/24, 25/30. are equivalent fractions of 5/6
Step-by-step explanation:
Terrell is a dog trainer. He charges $75 for each training session plus $1.45 per mile that he must drive to and from the session. Write an expression to represent this situation. Explain your answer.
(in the expression let x represent the number of miles.)
The expression 75 + 1.45x represents the total cost of a training session with Terrell
The expression to represent this situationLet x be the distance (in miles) that Terrell must drive to and from the training session.
Then the total cost C of the training session, in dollars, can be expressed as:
C = 75 + 1.45x
The first term, 75, represents the base fee that Terrell charges for each training session. The second term, 1.45x, represents the additional cost that Terrell incurs due to the distance he has to drive. This second term is calculated by multiplying the distance x by the rate of $1.45 per mile.Therefore, the expression 75 + 1.45x represents the total cost of a training session with Terrell, including both the base fee and the additional cost for driving.
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Q5. For all values of x, b) Solve fg(x) = gf(x)
g(x)=x-5
f(x)=x²+1
Answer:
To solve fg(x) = gf(x), we need to find the values of x that satisfy this equation. First, let's calculate fg(x):fg(x) = f(g(x)) = f(x-5) = (x-5)² + 1 Now, let's calculate gf(x):gf(x) = g(f(x)) = g(x² + 1) = (x² + 1) - 5 = x² - 4So, we have the equation:(x-5)² + 1 = x² - 4 Expanding (x-5)², we get:x² - 10x + 26 = x² - 4 Simplifying, we get:-10x + 26 = -4-10x = -30x = 3 Therefore, the solution to fg(x) = gf(x) for all values of x is x = 3.
A reservoir is 90% filled with liquid. The reservoir holds 1,330 gallons of liquid. How many gallons of liquid are needed to fill the reservoir to the top?
Choose the correct answer below.
A. 1,197 gallons
B. 133 gallons
C. 74 gallons
D. 1,330 gallons
Answer: B. 133 gallons
Step-by-step explanation: 90% of 1330 is 1197. you can take 10% which is 133 and multiply it by 9 to get that answer. then you have to subtract 1197 from 1330 to get you 133
how to factor a trinomial when a is greater than 1
To factor a trinomial when a is greater than 1, we can use the AC method
To factor a trinomial when a is greater than 1, follow these steps
Multiply the coefficient of a (the first term) by the constant (the third term).
Find two numbers that multiply to the product obtained in step 1 and add up to the coefficient of b (the second term).
Replace the middle term with the two terms found in step 2.
Factor the resulting four-term polynomial by grouping.
Factor out the greatest common factor from each group.
Factor the resulting binomials.
Combine the factors to obtain the final factorization of the trinomial.
This method is known as the AC method, and it can be used to factor trinomials of the form ax^2 + bx + c, where a is greater than 1.
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There is exactly 111 pair of parallel sides in the following shape.what is the area of the shape? \text{ units}^2 units 2 start text, space, u, n, i, t, s, end text, squared
Therefore, the answer is not possible to determine without additional information.
There are exactly 111 pair of parallel sides in the shapeTo find:
Area of the shape Formula used:Area of the parallelogram= base × height Explanation: We know that the parallelogram has two pairs of parallel sides. Since we are given that there are 111 pairs of parallel sides in the shape, we can infer that there are 55.5 parallelograms.
But the problem does not specify whether these parallelograms are of the same size or not. Hence we do not know if they will form a single shape or multiple shapes.In the absence of the above information, we cannot determine the area of the shape.
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A forecaster would like to use the 2-period moving average method on data below to make forecasts. Before doing this, she would like to test the performance of this method on past data. Which of the following could represent past forecasts for this method? (In the options below note that F1 represents the forecast for time period 1, and so on.)
Period 1 2 3 4 5 Actual Sales 5582 5122 5755 6320 5153
a. F1 = 5582 F2 = 5352 F3 = 5438.5 F4 = 6037,5 F5-5736.5 b. F1 = 5586.4 F2 = 5586.4 F3 = 5586.4 F4 = 5586.4 F5-5586.4 c. F2=5352 F3=5352 F4 = 5348.5 F5 - 6037.5 d. F3=5352 F4 = 5438.5 F5 = 6037.5 e. F3 = 5438.5 F4 = 6037.5 F5 = 5736.5 ________ encompasses the irregular changes in a time series that are not caused by any other component - Long-term trend - Cyclical effect - Random variation - Seasonal effect
The correct option for the past forecasts using the 2-period moving average method is:
A. F1 = 5582 F2 = 5352 F3 = 5438.5 F4 = 6037.5 F5 = 5736.5
Step-by-step explanation:
1. To calculate F2, take the average of Period 1 and Period 2 actual sales: (5582 + 5122) / 2 = 5352.
2. For F3, average Period 2 and Period 3 actual sales: (5122 + 5755) / 2 = 5438.5.
3. For F4, average Period 3 and Period 4 actual sales: (5755 + 6320) / 2 = 6037.5.
4. For F5, average Period 4 and Period 5 actual sales: (6320 + 5153) / 2 = 5736.5.
"Random variation" encompasses the irregular changes in a time series that are not caused by any other component. Some common example of random variation is coin toss. It is independent of the effects of systematic biases. In general, the larger the sample size is, the lower the random variation is of the estimate of a parameter. As random variation decreases, precision increases.
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a slow-moving barge travels at a rate of 4 km per hour in still water. going upstream it travels 8 miles in the same time it takes the barge to travel 24 miles with the current. how fast is the current?
A slow-moving barge moves through the sea at a speed of 4 km/h. It travels 8 miles upstream in the same amount of time as a barge traveling 24 miles downstream with the current. The current moves at a 2 km/h rate.
Let’s start by using the formula for distance, rate, and time:
Distance = rate x time
Let’s assume that the rate of the current is r km per hour.
Going upstream (against the current), the effective rate of the barge is:
4 – r km per hour
Going downstream (with the current), the effective rate of the barge is:
4 + r km per hour
We are told that the time it takes the barge to travel 8 miles upstream is the same as the time it takes to travel 24 miles downstream. Using the formula, we can set up the following equation:
8 / (4 – r) = 24 / (4 + r)
We can simplify this equation by cross-multiplying:
8(4 + r) = 24(4 – r)
Expanding and simplifying, we get:
32 + 8r = 96 – 24r
Adding 24r and subtracting 32 from both sides, we get:
32r = 64
Dividing both sides by 32, we get:
R = 2
Therefore, the rate of the current is 2 km per hour.
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does this table represent a proportional relationship
Yes its i Think If its not sorry
help please i’ll give brainliest!!!
Answer:
Apparently it's 4800 according to desmos.
Step-by-step explanation:
Step-by-step explanation:
x y
-3 150
-2 300
-1 600
0 4800
As you can see, for negative values of x, the area burned becomes smaller and smaller as x becomes more negative. This is because the equation y = 4800(2)^x has a base of 2, which means that as x becomes more negative, 2^x becomes smaller and smaller, causing y to become smaller and smaller as well.
factor the expression 6x^3 + 5x
Answer:
x(6x^2 + 5)
Step-by-step explanation:
To factor the expression 6x^3 + 5x, we can first factor out the greatest common factor of the two terms, which is x. This gives:
x(6x^2 + 5)
We can see that 6x^2 + 5 cannot be factored any further using integer coefficients, so the final factored form of the expression is:
x(6x^2 + 5)
Can someone please help me these questions are due tn
Answer:
$10.98
Step-by-step explanation:
$10.98
0.06 x 183 = $10.98
A candy store uses 10. 3 grams of sugar each hour. How many grams of sugar will the store use in 10 hours?
The candy store will use 103 grams of sugar in 10 hours.
To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).
To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.
We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.
So the calculation would be:
10.3 grams/hour x 10 hours = 103 grams
Therefore, the candy store will use 103 grams of sugar in 10 hours.
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I need help with this please