If Malcolm trains on his kayak every weekend. The speed is 12km/h and the distance is 31.5km.
How to find the speed and distance?Let's call Malcolm's paddling speed in still water "v".
When paddling upstream, Malcolm is fighting the current, so his effective speed is v - 3 km/h. And when paddling downstream, his effective speed is v + 3 km/h.
The time it takes for him to paddle upstream= 3.5 hours
Distance he covers in this time = (v - 3) * 3.5.
The time it takes for him to paddle downstream = 2.1 hours
Distance he covers in this time = (v + 3) * 2.1.
Let set the sum of these two distances equal to each other and solve for v:
(v - 3) * 3.5 = (v + 3) * 2.1
Expanding both sides:
3.5v - 10.5 = 2.1v + 6.3
Subtracting 2.1v from both sides:
1.4v - 10.5 = 6.3
Adding 10.5 to both sides:
1.4v = 16.8
Dividing both sides by 1.4:
v = 12 km/h
So Malcolm's paddling speed in still water is 12 km/h. To find the distance he paddles upstream, we can use the formula (v - 3) * 3.5, which gives us:
(12 - 3) * 3.5 = 9 * 3.5 = 31.5 km
Therefore the distance Malcolm paddles upstream is 31.5 km.
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5). When
Error analysis: Ali factored the above problem, c, and got 2x(10y) she checked it using the distributive property, she got the original problem! Since her check worked, she thinks she has the correct answer. How can that be? Explain her mistake.
+
3. Error analysis: Jamie incorrectly factored 15x20xy. She got 5x(3-4xy).
Factor the expression correctly.
What error did she likely make?
a. She did not have the correct operation inside parentheses.
b. She did not factor the variable from the first term.
c. She did not factor the variable from the second term.
d. She did not simplify the terms inside the parentheses.
30
The error she made is option c. Jamie did not factor the variable from the second term.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is 15x - 20xy.
We have to factor the expression.
Common factor of both the terms 15x and 20xy is 5x.
Taking the term 5x outside and using the distributive property,
15x - 20xy = 5x (3 - 4y)
But Jamie got it as 5x (3 - 4xy)
So the variable in the second term has not been factored correctly.
Hence the error in the process is that She did not factor the variable from the second term.
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What is a unit normal table?
To calculate the z-score, the formula is: z-score = (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation. Once the z-score is calculated, it can be used to look up the area, or probability, in the table.
A unit normal table is a type of probability table that is used to determine the area, or probability, under the normal curve. It is based on the standard normal probability distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. To use the unit normal table, one first needs to calculate the z-score, which is the number of standard deviations away from the mean a given value is. To calculate the z-score, the formula is: z-score = (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation. Once the z-score is calculated, it can be used to look up the area, or probability, in the table.
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How to find the variance of uniform distribution?
We can find the variance of a uniform distribution, using the following formula: Variance = (b - a)² / 12. Here: a is the lower limit of the uniform distribution, b is the upper limit of the uniform distribution.
The formula for the variance of a uniform distribution is based on the fact that the variance of a continuous uniform distribution is equal to the square of the range (i.e., the difference between the upper and lower limits) divided by 12.
For example, let's say we have a uniform distribution between 0 and 10. To find the variance, we would use the formula:
Variance = (10 - 0)² / 12
Variance = 100 / 12
Variance = 8.33
Therefore, the variance of a uniform distribution between 0 and 10 is 8.33.
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Jose's parabola opens downward
A parabola is a mirror-symmetrical, roughly U-shaped planar curve in mathematics. Many seemingly unrelated mathematical descriptions that all correlate to the same curves can be used to define it.
What is a parabola?In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical planar curve.
The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.
A line and a point (the focus) are two components of one definition of a parabola (the directrix).
The directrix is not the main focus.
The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.
A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.
Therefore, a parabola is a mirror-symmetrical, roughly U-shaped planar curve in mathematics. Many seemingly unrelated mathematical descriptions that all correlate to the same curves can be used to define it.
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Complete question:
What is a parabola?
Find the value of the variable x. If your answer is not an integer, write it in simplest radical form with
the denominator rationalized h
The value of the variables y and z are 18
How to determine the value of the variablesFrom the question, we have the following parameters that can be used in our computation:
The special right triangle
The special right triangle has one of its angles to be 45 degrees
This means that
Legs = Hypotenuse/√2
Using the above as a guide, we have the following:
Legs = 18√2/√2
Evaluate
Legs = 18
Hence, the value of y and z are 18
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What are the coordinates of the point on the directed line segment from (-1,-9) to (8,9) that partitions the segment into a ratio of 4 to 5
Answer: To find the point on the directed line segment that partitions it into a ratio of 4 to 5, we can use the formula for a point on a line given two endpoints and a ratio. The formula is:
(x, y) = (1 - t) * (x1, y1) + t * (x2, y2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and t is a value between 0 and 1 that determines the location of the point along the line.
In this case, (x1, y1) = (-1, -9) and (x2, y2) = (8, 9), and we want the point that partitions the line segment into a 4 to 5 ratio, so:
t = 4 / (4 + 5) = 4 / 9
Plugging in the values into the formula:
x = (1 - t) * x1 + t * x2 = (1 - 4/9) * (-1) + (4/9) * 8 = (5/9) * 8 - (4/9) * 1 = 44/9 - 4/9 = 40/9
y = (1 - t) * y1 + t * y2 = (1 - 4/9) * (-9) + (4/9) * 9 = (5/9) * 9 - (4/9) * (-9) = 45/9 + 36/9 = 81/9
So the point that partitions the line segment into a 4 to 5 ratio is (40/9, 81/9).
Step-by-step explanation:
Write and simplify an expression
for the perimeter of the triangle.
8x-4
x+5
6x
Will give Brain liest
Answer:
= 15x + 1.
Step-by-step explanation:
Sum and the length of all three sides
8x - 4 + x + 5 + 6x
8x + x + 6x - 4 + 5
15x + 1.
What is the Systematic Approach algorithm?
The Systematic Approach algorithm is a problem-solving methodology that is widely used in many different fields, such as engineering, business, and science.
It is a structured and systematic process that involves identifying a problem, analyzing it, generating possible solutions, evaluating these solutions, and selecting the best one. The algorithm is also known as the "systems engineering process" or "systems analysis and design."
The algorithm is typically divided into several phases, including:
Problem identification: This involves defining the problem, its boundaries, and its scope. This step also involves identifying the objectives and constraints of the problem. Analysis: This step involves gathering data and information related to the problem, and identifying the root cause of the problem. This may involve conducting surveys, interviews, or experiments. Design: In this step, potential solutions are generated, and a conceptual design is created. The design should be flexible enough to allow for the incorporation of new information and changes. Evaluation: The potential solutions are evaluated based on predetermined criteria, and the best solution is selected. Implementation: The selected solution is implemented and monitored to ensure it is working effectively. Any necessary modifications or adjustments are made during this phase.
The Systematic Approach algorithm is a powerful tool for problem-solving as it provides a structured, step-by-step approach to analyzing and solving complex problems. It also allows for a thorough understanding of the problem and its potential solutions, as well as the ability to evaluate and select the best solution based on predefined criteria.
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Write the expression in quadratic form. If possible. Otherwise, write NOT POSSIBLE.
16x^10 + 2x^5 + 6
Answer:
5X^4 + 2X^2 – 8
Step-by-step explanation
Its quadratic form is 5(x²)² +2x² -8
Let be X²=p, so the final expression is 5p²+2p-8
hope this help's
A hotel had 45 guests call for room service, and 200 who did not. What percentage of the guests called for room service?
Answer:
Step-by-step explanation:
Number of guests who called for room service = 45
Total number of guests = 45 + 200 = 245
Percentage of guests who called for room service = (45/245) x 100% ≈ 18.4%
Therefore, approximately 18.4% of the hotel's guests called for room service.
(11 × 4) ÷ 2 × 1 = [?]
Answer:
22
Step-by-step explanation:
(11 x 4) / 2 x 1
= 44/2 x 1
= 22 x 1
= 22
F(x) has zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1 find the degree of polynomial?
The degree of polynomial is 3
How to find the degree of polynomial?From the question, we have the following parameters that can be used in our computation:
zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1
The degree of a polynomial is the sum of the multiplicities
Using the above as a guide, we have the following:
Degree = 2 + 1
Evaluate
Degree = 3
Hence, the degree is 3
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Jake worked on his garden for 3 hours. Adrian worked on his garden 3 times as long as Jake. Precious worked on her garden 2% times as long as Jake. Select all that are true: Adrian worked longer than Jake in his garden. O Precious worked less time in her garden. Precious worked more time than Adrian. □ Adrian worked the least amount of time.
Answer:
The answer is to get it wrong on khan academy the go-to progress report(click on the percent to get to it and find the problem and go to hints and it should show the answer.
Step-by-step explanation:
Answer:
Adrian worked the least amount of time. (False, Precious worked the least amount of time with 0.06 hours)
Step-by-step explanation:
The following statements are true:
Adrian worked longer than Jake in his garden. (Adrian worked 3 times as long as Jake, so Adrian worked 3 hours * 3 = 9 hours)
Precious worked less time in her garden. (Precious worked 2% of the time that Jake worked, which is 2% of 3 hours = 0.06 hours, which is less than both Jake and Adrian)
The following statement is false:
Precious worked more time than Adrian. (As calculated above, Precious worked 0.06 hours, which is less than Adrian's 9 hours)
And finally:
Adrian worked the least amount of time. (False, Precious worked the least amount of time with 0.06 hours)
Draw a triangle with vertices A(0, 4), B(2, -2), and C(-2, -2). Apply a dilation centered at the origin with scale factor to this triangle and draw the resulting triangle,A'B'C'. In complete sentences, describe the following:
a,The relationship between corresponding sides in terms of their lengths.
b.The relationship between corresponding sides in terms of their orientations.
c.The relationship between corresponding angles in terms of their measures.
a) Relationship between corresponding sides: the corresponding sides are parallel and have a ratio of k in length.
b) Relationship between corresponding sides' orientations: The corresponding sides will still be parallel to the original sides.
c) Relationship between corresponding angles:the corresponding angles are congruent.
What do you mean by congruent angles?
Congruent angles are angles that have the same measure or size. In other words, if two angles have the same number of degrees or radians, they are said to be congruent. When we say that two angles are congruent, it means that they are exactly the same shape and size, and they can be superimposed on each other without any rotation or scaling. Congruent angles play an important role in geometry, as they allow us to prove that two figures are similar or congruent.
To apply a dilation with scale factor k centered at the origin, we multiply the coordinates of each vertex by k. So, to find the coordinates of A', B', and C', we will multiply the coordinates of A, B, and C by the scale factor.
a) The relationship between corresponding sides in terms of their lengths:
Let's denote the scale factor by k. The distance between two points (x1, y1) and (x2, y2) is given by the distance formula, which is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
When we multiply each coordinate by k, the distance between the two points is multiplied by k as well. So, if AB has length dAB and A'B' has length dA'B', we have:
dA'B' = k * dAB
Similarly, we can find the relationship between the lengths of BC and B'C', as well as between the lengths of AC and A'C'.
b) The relationship between corresponding sides in terms of their orientations:
The orientation of a line is given by its slope. If two lines have the same slope, they are parallel or collinear. If they have slopes that are negative reciprocals of each other, they are perpendicular. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. So, if the slope of AB is mAB and the slope of A'B' is mA'B', we have:
mA'B' = k * mAB
We can use this to find the relationship between the slopes of BC and B'C', as well as between the slopes of AC and A'C'.
c) The relationship between corresponding angles in terms of their measures:
The measure of an angle is determined by the slope of the line that contains the angle. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. This means that the measure of any angle that includes the origin is unchanged by the dilation. However, the measure of any angle that does not include the origin is multiplied by a factor of k. So, if angle ABC has measure x and angle A'B'C' has measure y, we have:
y = k * x
We can use this to find the relationship between the measures of angles BAC and B'A'C', as well as between the measures of angles CBA and C'B'A'.
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Bailey is asked to draw a circle. She is given the center and two points on the circle, but she isn't told which point is which. The points are (-6, 3), (-15, 3), and (3,3). Bailey draws an accurate circle from this information. What is the equation of the circle she drew?
O (= - 6)3 + (3 - 3)? = 3
O (= - 3)? + (y - 3)? = 3
O (* + 6)3 + (y - 3)? = 81
О (= - 3)3 + (y - 3)? = 81
〇(c+15)+(- 3) = 81
O (= - 6)? + (3 - 3)? = 81p
The Equation of Circle is (x+ 6)² + (y - 3)² = 9².
What is Equation of Circle?The equation for a circle is given by:
(x-h)² +(y-k)² = a²
Where (h,k) is the center and a is the radius of the circle.
Given:
We have the points A(-6, 3), B(-15, 3), and C(3,3).
Using Distance Formula
AB = √(-15 + 6)² + (3-3)²
AB = √9²
AB= 9 unit
BC= √(3 + 15)² + (3-3)²
BC = 18 unit
and, AC = √(3+6)² + (3-3)²
AC = 9 unit
As, AB = AC then A has to be the center (-6, 3) with radius 9 unit.
Thus, the Equation of Circle is
(x+ 6)² + (y - 3)² = 9²
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Lebo buys seven icecreams for R37,65 how much will five icecreams cost?
Answer:
R2689 IS THE CORRECT ANSWER
Find the values of x and y for which △ABC and △XYZ are congruent.ABC: side lengths of 4x+3, 5, and 8y−1
XYZ: side lengths of 6x−1, 5, and y+6
Enter the correct values in the boxes.
Answer: Two triangles are congruent if and only if all corresponding sides are equal in length. So, to find the values of x and y for which ΔABC and ΔXYZ are congruent, we need to equate the corresponding side lengths:
4x + 3 = 6x - 1
5 = 5
8y - 1 = y + 6
Solving the first equation for x:
4x + 3 = 6x - 1
2x = -4
x = -2
Solving the third equation for y:
8y - 1 = y + 6
7y = 7
y = 1
So, the values of x and y that make ΔABC and ΔXYZ congruent are x = -2 and y = 1.
Step-by-step explanation:
What is cluster sampling?
Cluster sampling is a sampling technique used in statistics and research methodology where a population is divided into groups, or clusters, and a sample is randomly selected from each cluster to be included in the study.
This method is often used when it is difficult or impractical to obtain a simple random sample of individuals from a large and diverse population. For example, in a study of public schools in a state, it may be easier to randomly select a sample of schools and then include all students in those schools in the study, rather than attempting to randomly select individual students from the entire state.
The advantages of cluster sampling include lower costs and greater efficiency than other sampling techniques, particularly when working with large populations. However, it can also increase the risk of sampling bias and decrease the precision of estimates if the clusters are not representative of the larger population. Therefore, it is important to carefully choose clusters that are as heterogeneous as possible within and as similar as possible between clusters.
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Ravi buys candy that costs $5 per pound. He will spend at least $45 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Ravi will buy.
Write your answer as an inequality solved for p.
Answer:
90p or 9p
Step-by-step explanation:
if he will spend 5p per pound then do 5x9P=45P
This is Math and Science together for My Ap class environmental science class picture is below please help
The study of population growth is important because it helps us understand the factors that drive changes in population size, and the impacts that population growth can have on the environment, economy, and human well-being.
Understanding population dynamics is essential for developing sustainable policies and managing natural resources effectively.
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1. Typically, the lowest number your credit score can be is:
Franco has a hat with 9 blue marbles, 4 yellow marbles, and 12 green marbles. He designs a binomial experiment by drawing a marble from the hat, recording whether the marble is green, and then laying the marble aside. He then repeats the process seven times. Which statement must be true?
The experiment is not a binomial experiment because there is not a fixed number of drawings.
The experiment is not a binomial experiment because the probability of choosing a green marble is the same for each drawing.
The experiment is not a binomial experiment because the probability of choosing a green marble is not the same for each drawing.
The experiment is not a binomial experiment because there are only two possible outcomes for each drawing.
Answer: c
Step-by-step explanation:
a cone is sliced such that the cross section is perpendicular to its base and the cross section intersects its vertex. what is the shape of the cross section?
The cross section is shaped like a circle.
A cone is a three-dimensional geometric object with a flat base and a smooth transition to the apex or vertex.
If a cone is sliced such that the cross section is perpendicular to its base and intersects its vertex, the cross section will be a circular shape. This is because the cross section cuts through the entire cone at a right angle, producing a circle that is defined by the curved surface of the cone and the slicing plane. The diameter of the circle is equal to the base diameter of the cone, and its center is located at the midpoint of the base.
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What is the solution for : y=-2/3x+7
4x+6y=42
The equation y =-2/3x+7 , 4x+6y=42 has many solution.
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's solve the system of equation using substitution method.
y = -2/3 x + 7
4x + 6y = 42
Let's substitute the value of y in equation 2
Therefore,
4x + 6(- 2/3 x + 7) = 42
4x - 12 / 3 x + 42 = 42
4x - 4x + 42 = 42
4x - 4x = 42 - 42
0 = 0
Therefore, it numerous solution
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Terri estimates that 30% of 123 is about 60.
Which statement correctly describes why this is not a reasonable estimate?
O The answer should be close to
O The answer should be close to
O The answer should be exactly
O The answer should be close to
of 120, which is 60.
of 120, which is 34.
of 120, which is 40.
of 120, which is 40.
The correct option regarding the estimate of the percentage is of:
The answer should be close to 1/3 of 120, which is 40.
How to estimate the percentage?The percentage is estimated applying the proportions in the context of the problem.
To estimate 30% of 123, we must multiply the total amount of 123 by the decimal equivalent of the percentage of 30%, which is 30/100 = 0.3, hence the estimate is given as follows:
0.3 x 123 = 36.9.
This is close to 1/3 of 120, which is of 40, hence the last option is correct.
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help me this is like something else i dontunderstand it
The correct matching according to the given question is given in the image below.
What is the value of an expression?The value of an expression is obtained by substituting the variables with the specific values. The value may be any real number if the specific values are constants.
Substitute x=6 into the expression -2+2x/3.
-2+(2×6)/3=-2+12/3
=-2+4
=2
Substitute x=-3 into the expression 5-x/3.
5-(-3)/3=5-(-1)
=5+1
=6
Substitute x= 6 into the expression -3+x/2.
-3+6/2=-3+3
=0
Substitute x=4 into the expression 2-3x/4.
2-(3×4)/4=2-12/4
=2-3
=-1
Therefore, the answers are correctly matched by an arrow line.
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HELPPPP ASAP 25 POINTSSS AND I WILL MARK YOU BRAINLIEST2. For a school Project, Ron recorded how much TV he watched in one weekend and what kinds of programs he watched. This chart shows the time he watched TV: SATURDAY: 9:30-10:30AM, 1:00-3:30PM; 8:00-10:00 PM SUNDAY: 1:00-2:30PM and 8:00-10:00PM Ron watched sports programs for one half of the time. He watched movies for one third of the time. He watched cartoons with his sister Ronnette the rest of the time. How many minutes did Ron watch cartoons? Show all work:
Ill try my best to "show my work" in text
First, we need to calculate the total amount of time Ron spent watching TV over the weekend.
On Saturday, he watched TV for 1 hour and 0 minutes from 9:30-10:30AM, 2 hours and 30 minutes from 1:00-3:30PM, and 2 hours from 8:00-10:00PM, for a total of 5 hours and 30 minutes on Saturday.
On Sunday, he watched TV for 1 hour and 30 minutes from 1:00-2:30PM, and 2 hours from 8:00-10:00PM, for a total of 2 hours and 30 minutes on Sunday.
The total time he spent watching TV over the weekend is 5 hours and 30 minutes on Saturday + 2 hours and 30 minutes on Sunday = 8 hours.
Next, we need to calculate the time he spent watching sports programs and movies.
He watched sports programs for half of the total time he spent watching TV, so he spent 8 hours / 2 = 4 hours watching sports programs.
He watched movies for one third of the total time he spent watching TV, so he spent 8 hours / 3 = 2 hours and 40 minutes watching movies.
Finally, we can calculate the time he spent watching cartoons with his sister.
He spent 8 hours watching TV total, and 4 hours watching sports programs and 2 hours and 40 minutes watching movies, so he spent 8 hours - 4 hours - 2 hours and 40 minutes = 1 hour and 20 minutes watching cartoons.
Since there are 60 minutes in an hour, the total time Ron spent watching cartoons is 1 hour and 20 minutes = 80 minutes.
Answer:
So Ron spent 1 hour and 40 minutes watching cartoons with his sister Ronnette.
Step-by-step explanation:
First, we need to calculate the total time that Ron spent watching TV. On Saturday, he watched TV for 1 hour in the morning, 2 hours and 30 minutes in the afternoon, and 2 hours in the evening, which adds up to 6 hours and 30 minutes. On Sunday, he watched TV for 1 hour and 30 minutes in the afternoon and 2 hours in the evening, which is a total of 3 hours and 30 minutes. So over the weekend, Ron watched TV for 6 hours and 30 minutes on Saturday and 3 hours and 30 minutes on Sunday, which adds up to a total of 10 hours.
Since Ron watched sports programs for half the time he watched TV, he spent 10 hours / 2 = 5 hours watching sports.
And since he watched movies for one-third of the time he watched TV, he spent 10 hours / 3 = 3 hours and 20 minutes watching movies.
Finally, we can calculate the time Ron spent watching cartoons by subtracting the time he spent watching sports and movies from the total time he spent watching TV:
10 hours - 5 hours - 3 hours and 20 minutes = 1 hour and 40 minutes
So Ron spent 1 hour and 40 minutes watching cartoons with his sister Ronnette.
If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
cosΘ= -1/2
Answer:
There are two possible solutions for angle Θ, as cosine is negative in the second and third quadrants.
Using the inverse cosine function on a calculator, we can find the two possible solutions for Θ:
Θ = 120° (in the second quadrant)
Θ = 240° (in the third quadrant)
Therefore, the possible angles for Θ are 120° and 240°.
cambia 89° a radianes
Answer:
acute angle
Step-by-step explanation:
Which statement correctly compares the values of the 7s in 7.825 and 3.7?
Answer:
Step-by-step explanation:
The statement that correctly compares the values of the 7s in 7.825 and 3.7 is:
The 7s in 7.825 are greater than the 7s in 3.7.
The 7s refer to the units place (the "ones" place) in decimal numbers. In 7.825, the 7s are 7 and in 3.7, the 7s are 7. When comparing the two numbers, we can see that the number 7.825 is greater than 3.7, which means the 7s in 7.825 are greater than the 7s in 3.7.