Yuto's measurements are the most accurate since they have the smallest mean absolute deviation from the correct length of 6 mm. Hence Option 3 is Correct
To determine whose measurements are the most accurate, we need to compare each friend’s measurements against the correct value of the grain of rice, which is 6 mm. The accuracy of measurements corresponds to how close they are to this true value.
Let's look at each friend's measurements:
Andrey: 7 mm, 5 mm, 6 mm, 8 mmMariya: 7.41 mm, 8.54 mm, 5.12 mm, 6.23 mmYuto: 6.1 mm, 5.9 mm, 6.3 mm, 7.2 mmMisaki: 5.843 mm, 6.981 mm, 5.334 mm, 7.632 mmTo evaluate accuracy, we calculate the deviation of each measurement from 6 mm, then find the mean absolute deviation for each friend:
Andrey: Mean = ( |7-6| + |5-6| + |6-6| + |8-6| ) / 4 = 1.5 mmMariya: Mean = ( |7.41-6| + |8.54-6| + |5.12-6| + |6.23-6| ) / 4 = 1.52 mmYuto: Mean = ( |6.1-6| + |5.9-6| + |6.3-6| + |7.2-6| ) / 4 = 0.625 mmMisaki: Mean = ( |5.843-6| + |6.981-6| + |5.334-6| + |7.632-6| ) / 4 = 0.906 mmHere, Yuto's measurements are the most accurate since they have the smallest mean absolute deviation from the correct length of 6 mm.
Yuto's measurements are the most accurate.
Andrey: 7 mm, 5 mm, 6 mm, 8 mm
Mean value: [tex]\frac{7 + 5 + 6 + 8}{4} = 6.5[/tex] mm
Absolute errors: [tex]|7 - 6| = 1[/tex] mm, [tex]|5 - 6| = 1[/tex] mm, [tex]|6 - 6| = 0[/tex] mm, [tex]|8 - 6| = 2[/tex] mm
Average error: [tex]\frac{1 + 1 + 0 + 2}{4} = 1[/tex] mm
Mariya: 7.41 mm, 8.54 mm, 5.12 mm, 6.23 mm
Mean value: [tex]\frac{7.41 + 8.54 + 5.12 + 6.23}{4} \approx 6.825[/tex] mm
Absolute errors: [tex]|7.41 - 6| \approx 1.41[/tex] mm, [tex]|8.54 - 6| \approx 2.54[/tex] mm, [tex]|5.12 - 6| \approx 0.88[/tex] mm, [tex]|6.23 - 6| \approx 0.23[/tex] mm
Average error: [tex]\frac{1.41 + 2.54 + 0.88 + 0.23}{4} \approx 1.265[/tex] mm
Yuto: 6.1 mm, 5.9 mm, 6.3 mm, 7.2 mm
Mean value: [tex]\frac{6.1 + 5.9 + 6.3 + 7.2}{4} \approx 6.375[/tex] mm
Absolute errors: [tex]|6.1 - 6| = 0.1[/tex] mm, [tex]|5.9 - 6| = 0.1[/tex] mm, [tex]|6.3 - 6| = 0.3[/tex] mm, [tex]|7.2 - 6| = 1.2[/tex] mm
Average error: [tex]\frac{0.1 + 0.1 + 0.3 + 1.2}{4} \approx 0.425[/tex] mm
Misaki: 5.843 mm, 6.981 mm, 5.334 mm, 7.632 mm
Mean value: [tex]\frac{5.843 + 6.981 + 5.334 + 7.632}{4} \approx 6.448[/tex] mm
Absolute errors: [tex]|5.843 - 6| \approx 0.157[/tex] mm, [tex]|6.981 - 6| \approx 0.981[/tex] mm, [tex]|5.334 - 6| \approx 0.666[/tex] mm, [tex]|7.632 - 6| \approx 1.632[/tex] mm
Average error: [tex]\frac{0.157 + 0.981 + 0.666 + 1.632}{4} \approx 0.859[/tex] mm
It takes 3/4 yards of ribbon to make a bow how many bows can be made with 7 yards
Estimate the value of 97.5 divided by 1.96
The estimated value is 50, which is close to the actual value of approximately 49.74.
To estimate the value of 97.5 divided by 1.96, we can round the numbers to make the calculation simpler.
Rounding 97.5 to 100 and 1.96 to 2 gives us an easier division: 100 divided by 2, which equals 50.
This estimation tells us that the actual value will be close to 50.
If we require more accuracy and use a calculator, we would find that 97.5 divided by 1.96.
= 9.75 / 1.96
= 49.74.
Therefore, our rounded estimate of 50 is reasonably close to the actual value.
There are 40 colas and
20 lemon-lime sodas in the cooler. What is the ratio of colas to lemon-lime sodas?
christina scored a certain number of goals,g, during a soccer season. sarah scored twice as many goals during the same season. write an expression for the nuber of goals sarah scored
Final answer:
The expression for the number of goals Sarah scored, if Christina scored g goals, is 2g, representing that Sarah scored twice as many goals as Christina.
Explanation:
If Christina scored a certain number of goals, g, during a soccer season, and Sarah scored twice as many goals during the same season, we can write an expression for the number of goals Sarah scored as 2g. This expression simply states that Sarah's goals are double the quantity of Christina's goals.
To think about this conceptually, if Christina scored 5 goals, we would substitute g with 5 and calculate Sarah's goals as 2 × 5, which equals 10 goals. This expression is a straightforward representation of the relationship between the number of goals scored by Christina and by Sarah.
Are the two triangles below .similar?
1/2b+9/4=7/4 solve the equation
The 5th grade is having a picnic this Friday. There will be 182 students and 274 adults. Each table seats 12 people. How many tables are needed?
Scott was going to sell all of his stamps collection to buy a video game. after selling half of them he changed his mind. he then bought sixteen more. how many did he start with if he now has 29?
To find out how many stamps Scott started with, we can set up an equation. After solving the equation, we find that Scott started with 26 stamps.
Explanation:To find out how many stamps Scott started with, we can set up an equation using the information given. Let's represent the number of stamps he started with as 'x'. After selling half of them, he would have 'x/2' stamps left. But since he changed his mind and bought sixteen more, he now has 'x/2 + 16' stamps. We know that he currently has 29 stamps, so we can set up the equation: x/2 + 16 = 29. We can solve this equation to find the value of x, which represents the number of stamps Scott started with.
To solve the equation, we can subtract 16 from both sides: x/2 + 16 - 16 = 29 - 16. Simplifying, we get: x/2 = 13. To isolate x, we can multiply both sides of the equation by 2: 2 * (x/2) = 13 * 2. Simplifying, we get: x = 26. Therefore, Scott started with 26 stamps.
A fair charges $7.25 for admission and $5.50 for a ride pass. Ten friends visited the fair. Not all of the friends purchased ride passes. If their total cost was $105.50, how many friends purchased ride passes?
tell me pls thank you
The number of friends who purchased ride passes= 6
Step-by-step explanation:It is given that:
A fair charges $7.25 for admission and $5.50 for a ride pass.
Now, if 10 friends visited the fair.
This means that:
Total cost of admission= 7.25×10= $ 72.5
Also, if x friends purchased the ride passes.
Then, the total cost of ride passes= 5.50x
Total cost= 72.5+5.50x
This means that:
72.5+5.50x=105.50
i.e.
5.50x=105.50-72.5
5.50x=33
x=33/5.50
x=6
Hence, 6 friends purchased ride passes.
is this answer right
splashtown charges an entrance fee of $25 plus $1 for each ride. Schlitterbahn charges a $40 entrance fee and all the rose are free. After how many rides would Schlitterbahn be cheaper than splashtown
Schlitterbahn becomes cheaper than Splashtown after more than 15 rides.
Let's define x as the number of rides:
Cost of Splashtown: $25 + $1 * x
Cost of Schlitterbahn: $40
We need to find the value of x for which the cost of Splashtown becomes greater than the cost of Schlitterbahn.
$25 + $1x > $40
$1x > $40 - $25
x > $15
So, after more than 15 rides, Schlitterbahn would be cheaper than Splashtown.
Express 220 as the product of its prime factors. Write the prime factors in ascending order and give your answer in index form.
Factor out the coefficient of the variable 1/2a-1/2
The coordinates of the vertices of quadrilateral JKLM are J(−4, 1) , K(2, 3) , L(5, −3) , and M(0, −5) . Drag and drop the choices into each box to correctly complete the sentences.
after school,Lamar Walker yo the corner Store and bought 2 candy bars for $0.97 cashier $5.15 for his purchase.how much Change did Lamar receive back?
What is the distance between the points (−5, −9) and (−5, 13) ?
A:4 units
B:11 units
C:16 units
D:22 units
The distance between the points (−5, −9) and (−5, 13) would be 22. units.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²]
We have been given two points as (−5, −9) and (−5, 13)
Then the distance formula :
D = √[(x-p)² + (y-q)²]
Now we substitute;
[tex]d = \sqrt{(-5 - (-5)^2 + (13 - (-9)^2}\\d = \sqrt (-5 + 5)^2 + (13 + 9)^2\\d = \sqrt (0^2 + 22^2)\\d = \sqrt (484)\\d = 22[/tex]
Therefore, the distance between the points (−5, −9) and (−5, 13) would be 22. units.
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Marty has a fenced yard in the shape of a rectangle. it's area is 635.4 square feet. The width of the yard is 18 feet. Whatis the length of the fence?
write the linear inequality in slope intercept form -4y-6x>8
About 56% of the 2,553 students are enrolled in at least one honors lass. How many students are enrolled in an honors class?
We are given that about 56% of the 2,553 students are enrolled in at least one honors lass.
So we basically need to find the value of 56% of 2553
converting 56% to decimal we get 56/100 =0.56
now multiplying 0.56 with 2553, we get
0.56*2553=1429.68
Rounding off we get 1430
Answer : 1430 students are enrolled in an honors class
Answer:
Answer : 1430 students are enrolled in an honors class
Step-by-step explanation:
Simplify: 3x(-11x + 1) A) -33x2 + 3x B) -33x2 + 1 C) -33x + 1 D) -30x
To simplify [tex]\(3x(-11x + 1)\)[/tex], we distribute [tex]\(3x\)[/tex] to both terms inside the parentheses, resulting in [tex]\(-33x^2 + 3x\)[/tex]. Thus, the simplified expression is [tex]\(-33x^2 + 3x\)[/tex]. Therefore, the correct answer is option A) [tex]\(-33x^2 + 3x\)[/tex].
To simplify the expression [tex]\(3x(-11x + 1)\)[/tex], we'll use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex].
1. **Apply the distributive property**:
We distribute [tex]\(3x\)[/tex] to both terms inside the parentheses:
[tex]\[3x \cdot (-11x) + 3x \cdot (1)\][/tex]
2. **Perform multiplication**:
[tex]\[= -33x^2 + 3x\][/tex]
Now, let's break down each step in detail:
- **Step 1: Apply the distributive property**:
We distribute [tex]\(3x\)[/tex] to both terms inside the parentheses: [tex]\(-11x\) and \(1\)[/tex]. This results in two separate terms.
- **Step 2: Perform multiplication**:
Multiply each term inside the parentheses by [tex]\(3x\)[/tex]. This results in:
[tex]\[3x \cdot (-11x) = -33x^2\][/tex]
[tex]\[3x \cdot (1) = 3x\][/tex]
Combining these two terms, we get [tex]\(-33x^2 + 3x\)[/tex].
Therefore, the simplified form of the expression [tex]\(3x(-11x + 1)\) is \(-33x^2 + 3x\).[/tex]
Hence, the correct answer is option A) [tex]\(-33x^2 + 3x\)[/tex].
Movie rental at a video store, you have two options for renting movies. You can pay $4 per movie,or you can pay a one time membership fee of $20 and then pay only $1.50 per movie. After how many movie rentals will she cost of renting movies with the membership be less than the cost of renting movies without the membership?
can some one help solve this?
A cruise ship can cover 17 nautical miles in 306 minutes. How many nautical miles will it travel in 198 minutes?
Just number 24s answer please
a compound inequality is graphed, and its graph consists of all real numbers. which open sentence could have resulted in this solution set?
r<6 or r>4
r<6 or r<4
r>6 or r<-4
Compound inequalities are used to group at least two inequalities
The open sentence that could result in the solution set is r<6 or r>4
From the question, we understand that the solution set consists of real numbers
From the list of options, only the open sentence r<6 or r>4 satisfy the given condition.
This is so because;
r<6 or r>4 = {4.0...... to 5.99...}
The solution set of other open sentence are not true
Hence, the open sentence that could result in the solution set is r<6 or r>4
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The complement of an acute angle is an obtuse angle.
A.) True
B.) False
solve for Z.
3z - 5 = 2z + 2
Lina bought 4 smoothies at a health food store. The bill was less than $16.
Write and solve an inequality to represent the cost of each smoothie.
What values make sense for this situation?
The inequality representing the cost of each smoothie is 4x < 16, which simplifies to x < 4, denoting that the cost of each smoothie is less than $4. Sensible values are any positive numbers less than $4.
To represent the cost of each smoothie with an inequality, let's designate the cost of one smoothie as x. Since Lina bought 4 smoothies and the total cost was less than $16, the inequality to represent this situation is:
4x < 16
To solve this inequality, we'll divide both sides by 4:
x < 16 / 4
x < 4
The cost of each smoothie is less than $4.
Values that make sense for this situation would be any positive price per smoothie that is less than $4, as Lina's total purchase for 4 smoothies must not exceed $16. So, x could be any positive real number less than 4.
Two lines intersect to form a linear pair of congruent angles. The measure of one angle is (7x + 34)° and the measure of the other angle is (2y/3)°. Find the values of x and y.
To find the values of x and y, we need to set up and solve a system of two equations based on the fact that the angles form a linear pair and are congruent.
Explanation:You are asked to find the values of x and y in two congruent angles which are linear pairs. A linear pair is a set of adjacent angles whose uncommon sides form a straight line, thus their sum is 180 degrees. Therefore, we can form the equation (7x + 34)° + (2y/3)° = 180°.
Since the two angles are also congruent (meaning they have the same measure), we can also form the equation (7x + 34)° = (2y/3)°. Now you have a system of two equations that you can solve to find the values of x and y.
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In a week, 27 hens laid 81 eggs. What is the unit rate for eggs per hen?