The change in potential energy of the apple during the fall was approximately 13.72 joules.
What is the name of potential energy?One of the two types of energy is potential energy, which is the latent energy in an object at rest. Kinetic energy, on the other hand, is the energy that an item in motion expresses.
The formula: can be used to determine the change in potential energy (PE) of a mass m object that falls a distance h from the Earth's surface.
ΔPE = mgh
where g is the acceleration brought on by gravity close to Earth's surface, which is roughly 9.8 m/s^2.
In this instance, the apple weighs 0.2 kg, falls 7 metres, and accelerates by gravity at a rate of 9.8 m/s^2. So, the potential energy change is as follows:
PE is equal to (0.2 kg) times (9.8 m/s^2) times (7 m) Equals 13.72 joules (J)
As a result, the apple's potential energy changed by around 13.72 joules during the fall.
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You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 5 or a number greater than 3 (b) Rolling a number less than 4 or an even number (c) Rolling a 4 or an odd number Question content area bottom Part 1 (a) P(5 or number>3)=enter your response here (Round to three decimal places as needed.) Part 2 (b) P(1 or 2 or 3 or 4 or 6)=enter your response here (Round to three decimal places as needed.) Part 3 (c) P(4 or 1 or 3 or 5) =enter your response here (Round to three decimal places as needed.)
a) The probability of rolling a 5 or a number greater than 3 is 1/2.
b) The probability of rolling a number less than 4 or an even number is 5/6.
c) The probability of rolling a 4 or an odd number is 2/3.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
In rolling a six-sided die, the total number of outcomes is 6.
The sample space is {1,2,3,4,5,6}
The probability formula is -
Probability = Number of outcomes corresponding to events / total number of outcomes.
(a) Let A be the event of rolling a 5. Then A = {5}.
Let B be the event of rolling a number greater than 3. Then B = {4,5,6}.
The event of rolling A or B is given by A∪B = {4,5,6}.
So, apply the probability formula -
P(A∪B) = 3/6 = 1/2
Therefore, the probability value is 1/2.
(b) Let C be the event of rolling a number less than 4. Then C = {1,2,3}.
Let D be the event of rolling an even number. Then D = {2,4,6}.
The event of rolling C or D is given by C∪D = {1,2,3,4,6}.
So, apply the probability formula -
P(C∪D) = 5/6
Therefore, the probability value is 5/6.
(c) Let E be the event of rolling a 4. Then E = {4}.
Let F be the event of rolling an odd number. Then F = {1,3,5}.
The event of rolling E or F is given by E∪F = {1,3,4,5}.
So, apply the probability formula -
P(E∪F) = 4/6 = 2/3
Therefore, the probability value is 2/3.
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A recent study reported the mean body mass index (BMI) for adults in the United States was 26. 8. A researcher believes the mean BMI of marathon runners is less than 26. 8. A random sample of 35 marathon runners had a mean BMI of 22. 7 with a standard deviation of 3. 1. The researcher will conduct a one-sample t-test for a population mean. Have the conditions for inference been met
Since the samples of the study are independent, the condition for inference have been met
The body mass index for adults in the United States = 26.8
BMI stands for Body Mass Index
Body mass index of marathon runners = less than 26.8
The random samples = 35
The body mass index of the random samples = 22.7
Standard deviation = 3.1
Then the researchers will conduct a one sample t test for a population mean.
The one sample t-test is is defined as the hypothesis test that check whether the unknow population mean is different from the specific value
Here the samples are independent
Therefore, the condition for inference have been met
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Enter the letter of the graphed function(image)
The given graph is represented by the function ( x + 2 )(x - 1 )³(x - 3 ). The correct option is A.
What is a function?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
Graphing functions involve drawing a curve on the coordinate plane that represents the function. Every point on a curve (graph) that represents a function satisfies the function equation.
The graph is represented by the function,
( x + 2 )(x - 1 )³(x - 3 )
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Proper subset is a set that contains elements contained in another set but not equal
to that set.
True or false
Answer: A proper subset of a set A is a subset of A that is not equal to A
Step-by-step explanation:
I barley know anything about shapes
Answer:
they all have flat sides except for the cylinder
Step-by-step explanation:
Its okay we all are bad on some things
A growing giant pumpkin weighs 40.5 pounds on day 18 and 496.3 pounds on day 50. Which equation can be
used to find the weight gain of the giant pumpkin, (pounds), from day 18 to day 50, and what is the value of x?
The equation of line is y = 14.24375x + 296.8875 , where x is the number of days and y is the total weight gain in x days
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 18 , 40.5 )
Let the second point be Q ( 50 , 496.3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 496.3 - 40.5 ) / ( 50 - 18 )
Slope m = 455.8 / 32
Slope m = 14.24375
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 40.5 = 14.24375 ( x - 18 )
On simplifying the equation , we get
y - 40.5 = 14.24375x - 256.3875
Adding 40.5 on both sides of the equation , we get
y = 14.24375x + 296.8875
where x is the number of days
Hence , the equation of line is y = 14.24375x + 296.8875
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The weight of potato chips in a medium sized bag is stated to be 10 ounces. The amount that
the packaging machine puts in these bags is believed to be normally distributed with a mean of 10.2
ounces and a standard deviation of 0.12 ounces. Is it unusual for a bag to contain 9.8 ounces of
chips? Explain your answer and show work
Answer:
Step-by-step explanation:
Let me explain each step in more detail.
Step 1: Calculate the Z-score
The Z-score is a measure of how many standard deviations a value is from the mean. To calculate the Z-score, we use the following formula:
Z = (x - μ) / σ
Where:
x = 9.8 ounces (the value we want to examine)
μ = 10.2 ounces (the mean of the distribution)
σ = 0.12 ounces (the standard deviation of the distribution)
Plugging in the values, we get:
Z = (9.8 - 10.2) / 0.12 = -3.33
This Z-score tells us that 9.8 ounces is 3.33 standard deviations below the mean of 10.2 ounces.
Step 2: Look up the cumulative probability from a Z-table
A Z-table is a table that lists the cumulative probabilities for various Z-scores. The cumulative probability tells us the probability of getting a value less than or equal to a certain Z-score. To use the Z-table, we need to know the Z-score and whether we want the cumulative probability to the left (for values less than) or to the right (for values greater than). In this case, we want the cumulative probability to the left because we want to find the probability of getting a weight less than or equal to 9.8 ounces.
The cumulative probability for a Z-score of -3.33 is approximately 0.0004. This means that there is a 0.0004 (or 0.04%) chance of getting a weight of 9.8 ounces or less in a bag of chips.
Step 3: Interpret the results
Since the cumulative probability is very small, it is highly unlikely that a bag of chips would contain 9.8 ounces or less of chips. Therefore, we can conclude that it is unusual for a bag of chips to contain 9.8 ounces or less.
If my answer met your requirements, please rate it AWESOME BRAINLY ANSWER.
A rancher raises milking cows and goats which he feeds with two types of mixes, type x and type y. Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein; each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein. The livestock need a minimum of 6,000 units of calcium and 12,000 units of protein per day. What combination of mixes should the rancher buy to minimize daily feed cost?
The combination should be 20 of Brand A and 20 of Brand B.
What is Linear Programming?When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
Given:
Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein.
Each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein.
So, Max Z = 400x + 600 y
Constraints:
100x + 200 y ≤ 6000
or, 400x + 200y ≤ 12000
Solving the Equation:
300x = 6000
x= 20
and, y= 20
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Find the value of each variable. Round to the nearest tenth, if necessary.
16.7, 6.7 and 22 degrees respectively are the measures of a, c and m<C
Solving trigonometry identityThe given diagram is a triangle with the following sides
Hypotenuse = AC = 18
m<A = 68 Degrees
We need to determine the measure of a, b and m<C
Using the trigonometry identity
sin 68 = a/18
a = 18sin68
a = 16.7
Similarly;
cos68 = c/18
c = 18cos68
c = 6.7
Since the sum of angles in a triangle is 180 degrees, hence:
m<C = 90 - m<A
m<C = 90 - 68
m<C = 22 degrees
Hence the measure of a, c and m<C is 16.7, 6.7 and 22 degrees respectively.
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A roller-coaster car is at the top of a hill. The car and its passengers have a combined mass of 1,088 kilograms. If the hill is 62 meters tall, how much potential energy does the car have?
PE=mgh
A) 67,456 J
B) 330,534.4 J
C) 1,159.8 J
D) 661,068.8 J
The potential energy of the roller coaster car at the top of a hill is 661,068.8 J.
The correct answer choice is option D
What is potential energy?Potential energy is a form of energy which is dependent on the relationship between different system components.
The gravitational constant, g = 9.8 m/s².
Mass, m = 1088 grams
Height, h = 62 meters
So, The amount of potential energy the car has;
PE = mgh.
PE = 1088 × 9.8 × 62
PE = 661,068.8J
Ultimately, the car has a potential energy of 661,068.8J.
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Please help me! Factor Each Polynomial Completely.
x^2-y^2-3.5(x+y)
The polynomial x^2-y^2-3.5(x+y) is factored completely to xy(x - y)
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of coefficients, variables, terms, factors and constants.
They are also composed of arithmetic operations, such as;
SubtractionMultiplicationDivisionAdditionBracketParenthesesx^2-y^2-3.5(x+y)
expand the brackey
x² - y² - 3.5x + 3.5y
Factor the common terms
xy(x - y - 3.5 + 3.5)
collect lie terms
xy(x - y)
Hence, the expression is xy(x - y)
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what is v=u+at
u=17 a=4 t=8
Answer: 65
Step-by-step explanation:
17 + 48
Question 3
Sam built the model shown below. It is composed of two rectangular prisms. What is the volume of the figure?
Answer:
44 in^2
Step-by-step explanation:
V = L×W×H
Bottom rectangle prism
L= 6 W= 4 H= 1
V = 6×4×1
V=24
Top rectangle prism
L= 2 W= 2 H= 5
V=2×2×5
V= 20
Add both of the rectangle prisms
24+25= 44
What equation would you use to solve x
Answer: X^2+6.8^2=10.6^2
Step-by-step explanation:
The pythagorean theorem can be used to find the missing sides of triangles.
The formula is:
a^2+b^2=c^2, where c^2 is always the hypotenuse (the biggest and diagonal line) and a^2 and b^2 are the other side lengths
In this problem, plug in the values. So in this case, you have:
a^2+6.8^2=10.6^2
Hope this helps
a tire of a moving bicycle has a diameter of 18 inches, if the tire is making 4 rotations per second find the bicycle's speed in miles per hour.
Speed of bicycle in miles per hour will be 12.85 mi/h.
What is the definition of speed?
The following is the definition of speed:
The rate at which the position of an item changes in any direction.
The ratio of distance travelled to time spent travelling is described as speed. Speed is a scalar number since it has just one direction and no magnitude.
Formula for Speed
The speed formula is as follows:
s=d/t
Where,
s denotes the speed in metres per second, d the distance travelled in metres, and t the time in seconds.
Now,
Given Diameter=18 inch
then distance covered by cycle in 4 rotation in one second =4*π*diameter
=4*22/7*18
=226.28
Then Speed=226.28 in/s
As 1 mike=63360 inch and 1 hour= 3600 seconds
then Speed in miles/hour=226.28*3600/63360
=12.85 mi/h
hence,
Speed of bicycle in miles per hour will be 12.85 mi/h.
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By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol. By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol. How much cholesterol is in each item? The quantity of cholesterol in an egg is.....mg, the quantity of cholesterol in a cupcake is.....mg, and the quantity of cholesterol in a slice of pizza is.....mg. (Simplify your answers. Type mixed numerals, if possible. Otherwise, type integers or fractions.)
The quantity of cholesterol in an egg is 272 mg
The quantity of cholesterol in a cupcake is 18 mg
The quantity of cholesterol in a slice of pizza is 9 mg
How to find the amount of cholesterol in each itemLet the amount of egg be e
Let the amount of cupcake be c
Let the amount of pizza be p
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol
e + c + p = 299
The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol
3c + 4p = 90
By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol
3e + c = 834
e + c + p = 299
3c + 4p = 90
3e + c = 834
solving the simultaneous equation gives
e = 270
c = 18
p = 9
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Yusef drove 130 miles in 2.5 hours. Which equation can be used to calculater, the average
speed at which Yusef drove?
A r = 130 - 2.5
B 130 = r/2.5
C r = 130/2.5
D 130 = r + 2.5
The equation can be used to calculate the average speed at which Yusef drove is (c) r = 130/2.5
How to determine the speed equationThe formula to calculate average speed is:
Average speed = distance traveled / time taken
In this problem, Yusef drove 130 miles in 2.5 hours.
So, we can substitute the values in the formula:
Average speed = 130 miles / 2.5 hours
Simplifying this expression, we get:
Average speed = 52 miles per hour
Therefore, the correct equation to calculate the average speed at which Yusef drove is:
r = 130/2.5 or r = 52
Option C matches this equation, so the answer is C.
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A lighthouse is situated 10m back from a 35m high cliff. If the beacon is 8m above the base of the lighthouse, how far from the cliff does the shadow extend?
Answer: the shadow will extend 43.75m
Step-by-step explanation:
A sign for truck drivers states that the road ahead has a constant slope of 2 in 11. This means that for every 11m horizontally its rises 2m.
a. Over what horizontal distance will the road rise 300m?
b. What is the length of the road [AB]?
Can you please help me!!!Please
The company will be able to purchase enough pens while staying within the budget by purchasing 10 mugs only not more than that.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
A company has a budget of $305
Company needs to purchase either a mug or a pen for each of its 100 clients.
Price per Mug $5.55 Price per Pen $2.50
Now,
Price of pen = 100*2.50=250
When the number of employees are 10
=10*5.50=55.0
Mugs can be purchased
When the number of employees are 15
=15*5.50=82.5
Mugs cannot be purchased
Therefore, by algebra the answer will be 10 mugs only.
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5. Now, that you have your answers for questions 1 & 2. Explain what the difference between finding the
mean of the given numbers and finding the value that is half-way between a given set of numbers.
It should be noted that finding the mean gives the average value of a set of numbers, while finding the halfway point gives a value that is equidistant between the two extreme values in the set.
How to explain the meanFinding the mean of a set of numbers involves adding up all the numbers in the set and then dividing the sum by the total number of numbers in the set. The mean represents the average value of the set.
Finding the value that is halfway between a set of numbers involves taking the two extreme values in the set and finding the arithmetic average (i.e., adding the two values and dividing by 2). This value represents the midpoint between the two extremes.
In summary, finding the mean gives the average value of a set of numbers, while finding the halfway point gives a value that is equidistant between the two extreme values in the set.
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Please help question below
The required equation that Nandita used to make the given graph is y = -3x + 2. Option B is correct.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
Here,
From the graph, we need to identify the y-intercept and then match that intercept with each given in the options So,
From the graph, the y-intercept is ordered where the x coordinate of the pair is zero, So,
(0, y) = (0, 2)
Thus, the required equation among the option is y = -3x + 2.
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Kate had some stickers.
She kept 2/5 of them for herself and gave 5/6 of the remaining stickers to 6 of her
friends equally.
(a) What fraction of her stickers did Kate give to her 6 friends?
(b) What fraction of Kate's stickers did each of her 6 friends receive?
a) The fraction of the stickers that Kate gave to her 6 friends was 1/2.
b) The fraction of Kate's stickers that each friend received from the 1/2 of stickers was 1/12.
What is the fraction?The fraction is the portion or part of a whole.
Fractions can be proper, improper, and complex fractions, depending on the relative value of the numerator and the denominator.
The total number of stickers that Kate possesses = 1/1
The fraction Kate kept for herself = 2/5
The remaining portion of Kate's stickers = 3/5 (1 - 2/5)
The fraction Kate gave to her 6 friends to share equally = 5/6 of 3/5 = 1/2
The fraction of Kate's stickers that each friend received = 1/2 ÷ 6 = 1/12
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Find the slope between the two points.
(2,10) and (6,30)
Please help what’s the slope between the two points
Answer:
The slope between the two points would be 5.
Answer: The slope would be 5
Step-by-step explanation:
The graph shows Felix's English scores versus the number of hours he studies:
What will Felix's English scores most likely be if he spends 7 hours a week studying English?
a 64 points
b 72 points
c 84 points
d 92 points
Felix's English score would be around 72 points if he spends 7 hours a week studying English.
the answer is option b, 72 points.
What is a graph of an equation?
A graph of an equation is a visual representation of the relationship between the variables in that equation. In mathematics, an equation typically involves one or more variables, and the graph of that equation shows how the value of one variable changes as the value of another variable change.
Look at the horizontal axis of the graph to find the point that corresponds to 7 hours of studying per week. In this case, it is approximately halfway between 6 and 8, so we can estimate it to be around 7.
From that point, draw a vertical line up to the graph to find the corresponding English score.
Follow the line until it intersects with the blue line representing Felix's English scores.
From that intersection point, draw a horizontal line over to the y-axis to read the corresponding score.
Based on this analysis, we can estimate that Felix's English score would be around 72 points if he spends 7 hours a week studying English.
Therefore, Felix's English score would be around 72 points if he spends 7 hours a week studying English.
the answer is option b, 72 points.
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Graph the system of inequalities.
y> 4x-2
2y-x≤8
The solution of inequalities is (1.714 , 4.857).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
y > 4x-2
2y-x ≤ 8
Now, solving the inequalities.
y > 4x-2 is given by purple region and 2y-x ≤ 8 is shown by Grey region.
The two lines of inequalities intersect at (1.714 , 4.857).
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A shipping container is in the form of a right rectangular prism and it can hold 1800 cubic feet of shipped goods when it is full. Its length is 30 ft and its height is 7 ft 6 inches. Find the width of the container in feet. Round your answer to the nearest tenth if necessary.
The width of the container can be calculated by dividing the product of the length and height by the volume. The width is 28.1 ft.
[tex]30 ft x 7.5 ft = 225 ft^3[/tex]
[tex]1800 ft^3 / 225 ft^3 = 8[/tex]
[tex]225 ft^3 / 8 = 28.125 ft[/tex]
Width = 28.1 ft
To calculate the width of the shipping container, you need to divide the product of the length and height by the volume. The length of the container is given as 30 ft, and the height is given as 7 ft 6 inches or 7.5 ft. Thus, the product of the length and height is [tex]225 ft^3[/tex]. The volume of the container when it is full is given as [tex]1800 ft^3[/tex]. To find the width, divide the product of length and height by the volume. Thus,[tex]225 ft^3 / 1800 ft^3 = 8[/tex]. Then, divide the product of length and height by the result you got in the previous step, that is,[tex]225 ft^3 / 8 = 28.125 ft[/tex]. This is the width of the container. Round this value to the nearest tenth and you get 28.1 ft as the width of the container.
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WILL MARK BRAINLIST A one of a kind necklace is worth $3200. The value of the necklace increases by 9% each year.
Which explicit and recursive formulas can be used to model the situation.
Drag and drop each formula to the corresponding box.
The Formula will be in form of exponential function that is y=$3200(1.09)ˣ
where x= no. of years.
What exactly are exponential functions?
An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.
Growth that is exponential
The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".
The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.
Now,
Initial value=$3200
% increase=9%
then
Amount in x years will be =3200(1+9/100)ˣ
=3200(109/100)ˣ
=3200(1.09)ˣ
Hence,
The Formula will be in form of exponential function that is y=$3200(1.09)ˣ
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Does the following table represent equivalent ratios?
Answer:
D
Step-by-step explanation:
We can see that we are not increasing by the same amount.
[tex]\frac{1}{25}= \frac{2}{50} \neq \frac{3}{70} \neq \frac{5}{168}[/tex]
Erin has a set of 10 index cards. Each index card is 3 ½ inches long. If she were
to lay the index cards in one long row, how long would the row be?
*
If Erin were to lay the index cards in one long row, the row would be 35 inches long.
What is Multiplication?
Multiplication is an arithmetic operation that is used to find the result of combining equal groups of a given quantity. It involves repetitive addition of equal groups, where one factor represents the number of groups, and the other factor represents the number of items in each group.
Solution:
If Erin has 10 index cards, and each index card is 3 ½ inches long, then the total length of the row would be:
10 cards x 3 ½ inches per card = 35 inches
Therefore, if Erin were to lay the index cards in one long row, the row would be 35 inches long.
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