1.MAD Calculation: A possible set of data values that yield a mean of 20 and a MAD of 10 is: 10, 20, 20, 20, 30, 40.
2. Five Students' Test Scores: Mean = 85, Median = 85, Range = 10, MAD ≈ 3.33.
3. Survey Data: Students' mean sleep = 7.7 hours; Teachers' mean sleep = 6.7 hours.
let's go through each question step by step:
1. MAD Calculation:
The Mean Absolute Deviation (MAD) is the average of the absolute deviations from the mean of a dataset. Given that the MAD of the set of six data values is 10 and the mean is 20, we need to find the data values that satisfy these conditions.
Let's denote the data values as (x_1, x_2, x_3, x_4, x_5, x_6).
The mean is given as:
[tex]\[ \text{Mean} = \frac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6}{6} = 20 \][/tex]
Multiplying both sides by 6 gives us:
[tex]\[ x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 120 \][/tex]
Now, we need to find a set of values that satisfy this equation and also have a Mean Absolute Deviation of 10.
The Mean Absolute Deviation (MAD) formula is:
[tex]\[ \text{MAD} = \frac{|x_1 - \text{Mean}| + |x_2 - \text{Mean}| + |x_3 - \text{Mean}| + |x_4 - \text{Mean}| + |x_5 - \text{Mean}| + |x_6 - \text{Mean}|}{6} \][/tex]
Given MAD = 10, and Mean = 20, we have:
[tex]\[ 10 = \frac{|x_1 - 20| + |x_2 - 20| + |x_3 - 20| + |x_4 - 20| + |x_5 - 20| + |x_6 - 20|}{6} \][/tex]
Multiplying both sides by 6, we get:
[tex]\[ 60 = |x_1 - 20| + |x_2 - 20| + |x_3 - 20| + |x_4 - 20| + |x_5 - 20| + |x_6 - 20| \][/tex]
Now, we need to find a set of six values that satisfy both equations.
There are multiple possible sets of values that satisfy these equations. One such set could be:
[tex]\[ x_1 = 10, \ x_2 = 20, \ x_3 = 20, \ x_4 = 20, \ x_5 = 30, \ x_6 = 40 \][/tex]
You can verify that these values satisfy both the mean and the MAD conditions.
2. Five Students' Test Scores:
Given:
- Five students scored 80 on a test,
- Five students scored 85, and
- Five students scored 90.
A. The mean:
[tex]\[ \text{Mean} = \frac{(5 \times 80) + (5 \times 85) + (5 \times 90)}{15} = \frac{400 + 425 + 450}{15} = \frac{1275}{15} = 85 \][/tex]
B. The Median:
Since there are an odd number of data points (15), the median will be the 8th value when the data is arranged in ascending order. Since each score (80, 85, 90) appears 5 times, the median is 85.
C. The Range:
The range is the difference between the highest and lowest values:
[tex]\[ \text{Range} = 90 - 80 = 10 \][/tex]
D. The MAD:
To find the MAD, we first calculate the deviations from the mean for each data point, take their absolute values, and then find their mean.
[tex]\[ \text{MAD} = \frac{|80 - 85| + |80 - 85| + \ldots + |90 - 85|}{15} \][/tex]
[tex]\[ = \frac{5|80 - 85| + 5|85 - 85| + 5|90 - 85|}{15} \][/tex]
[tex]\[ = \frac{5(5) + 5(0) + 5(5)}{15} = \frac{50}{15} \approx 3.33 \][/tex]
3. Survey Data:
Given:
Students: 7, 6, 8, 9, 8, 9, 10, 10, 10
Teachers: 6, 6, 4, 5, 7, 8, 7, 8, 8, 8
A. Mean of students' data set:
[tex]\[ \text{Mean} = \frac{7 + 6 + 8 + 9 + 8 + 9 + 10 + 10 + 10}{10} = \frac{77}{10} = 7.7 \][/tex]
B. Mean of teachers' data set:
[tex]\[ \text{Mean} = \frac{6 + 6 + 4 + 5 + 7 + 8 + 7 + 8 + 8 + 8}{10} = \frac{67}{10} = 6.7 \][/tex]
The means tell us that, on average, students get slightly more sleep per night compared to teachers.
The perimeter of a rectangle garden is 54 feet. The width is 5 more feet than the length. What is the length of the garden
The Length of the rectangle is 11 ft and the width is 16 ft
How do you do it please help ASAP and thank you for your support
Answer:
19.38 cm^2
Step-by-step explanation:
base * height = A of parallelogram
3.4 * 5.7 = 19.38
I need help really bad
Volume is found by multiplying the length by the width by the height.
Since you are given the volume and two of the dimensions, multiply the two dimensions together, then divide the volume by that number.
11 x 5 = 55
Width = 440 / 55
Width = 8 inches.
Did I set up the equation right? Please help me.
Yes you did a little reminder for you from me is that c^2 will ALWAYS be across from the right angle(90 degree)
What is the discriminant of 9x^2+2=10x^2
Answer:
8
Step-by-step explanation:
To find the discriminant, we need to get the equation in standard form
9x^2+2=10x^2
Subtract 10x^2 from each side
9x^2-10x^2+2=10x^2-10x^2
-x^2 +2 =0
This is in the form ax^2+bx +c =0
where a=-1 b=0 and c=2
The discriminant is
b^2 -4ac
0^2 -4*(-1)*2
0+8
The discriminant is 8
the combined area of two squares is 45 square cm. each side one square is twice as long as a side of the other Square. what is the length of each side of the larger square
Answer: it is 45cm^2
Step-by-step explanation:
it is because it is
how much money must be deposited now in an account paying 7% annual interest compounded yearly to have a balance of $1000 after 6 years
To find out how much money must be deposited now in an account paying 7% annual interest compounded yearly to have a balance of $1000 after 6 years, we can use the formula for compound interest. Plugging in the values given, we get an approximate deposit of $665.58.
Explanation:To find out how much money must be deposited now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the future value, P is the principal (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we have A = $1000, r = 7% (or 0.07), n = 1 (compounded yearly), and t = 6 years. Plugging in these values, we can solve for P:
A = P(1 + r/n)^(nt)
$1000 = P(1 + 0.07/1)^(1 * 6)
$1000 = P(1 + 0.07)^6
$1000 = P(1.07)^6
$1000 = P(1.5037)
P ≈ 1000 / 1.5037
P ≈ 665.58
Therefore, approximately $665.58 must be deposited now to have a balance of $1000 after 6 years.
What value is equivalent to 23 · 34?
Answer:
782
Step-by-step explanation:
You have to multiplied 23 and 34
23 X 34 = 782
Answer:
782 is the answer
Step-by-step explanation:
Multiply 23 x 34 and that gives you 782.
Well i forgot so i need help
[tex]2\pi r\\2\pi23\\144.51[/tex]
Answer: 46 in tall for the circle
Plz help i don’t understand it
since you cross multiply, 2 times 4 is 8 and 6 times the p is 6p so divide both sides by 6 and 8/6 is 1.33 so 1.33=p
Answer:
p = 4/3
Step-by-step explanation:
The problem is showing you a proportion and how to solve it.
Let's use the following proportion to explain the cross multiplication method.
[tex] \dfrac{a}{b} = \dfrac{c}{d} [/tex]
Start with the proportion above. To get rid of parentheses, multiply both sides by b and by d.
[tex] bd\dfrac{a}{b} = bd\dfrac{c}{d} [/tex]
Simplify:
[tex] ad = bc [/tex]
Now look again at the proportion we started with.
[tex] \dfrac{a}{b} = \dfrac{c}{d} [/tex]
The two products we ended up with are the same you have circled in your problem. Those products are the result of cross multiplying.
Now let's do your problem and go straight to the cross multiplication.
[tex] \dfrac{6}{2} = \dfrac{4}{p} [/tex]
6 and p are circled together, so the left side becomes 6p.
2 and 4 are circled together, so the right side becomes 2 * 4.
After cross multiplying, we have
6p = 2 * 4
6p = 8
Divide both sides by 6 to find p.
p = 8/6
Reduce the fraction
p = 4/3
What the problem shows you is that to simplify a proportion, set the cross products equal to each other, and solve the equation.
the sum of foir consecutive even integers is -28
Which number line shows the solution set for |s/2+4| < 2
Solution set: s ∈ (-4, -12). The first option shows the correct number line.
Let's find the number line that shows the solution set for the inequality:
[tex]\left|\frac{s}{2}+4\right| < 2[/tex]
We can solve the inequality by splitting it into two cases, one positive and one negative, and then solving each case separately.
Steps to solve:
1. Split the inequality into two cases:
[tex]\frac{s+8}{2} < 2[/tex]
[tex]-\frac{s+8}{2} < 2[/tex]
2. Solve the first case:
[tex]2 \cdot \frac{s+8}{2} < 2 \cdot 2[/tex]
s + 8 < 2⋅2
s + 8 < 4
s < −4
3. Solve the second case:
[tex]2 \cdot \frac{-(s+8)}{2} < 2 \cdot 2[/tex]
−(s + 8) < 2⋅2
−s − 8 < 2⋅2
−s − 8 < 4
−s < 12
[tex]\frac{-s}{-1} > \frac{12}{-1}[/tex]
s > −12
4. Combine the solutions from both cases:
s < −4 or s > −12
The number line that shows the solution set for the inequality is the one with the shaded regions between −4 and −12.
Use 12 x 5 = 60 and 12 x 2 = 24 to help you multiply 12 x 7.
Uh... 84 is correct. Add 60 & 24 and you get 84. Hopefully that helps
Answer:
84
Step-by-step explanation:
12*7=84
12*5=60
7-5=2
84-60=24
Which of the following do not describe a residual?
Answer:
A and C do not describe a residual
Step-by-step explanation:
A residual in least squares regression is defined as the difference between the actual value and the predicted value. Symbolically, this definition is represented by alternative B.
solve the inequality -5x<15
x > -3 divide by -5 on both sides and then switch the sign bc everytime u divide by a negative number u have to switch the sign
Answer:
x < -3
Step-by-step explanation:
All you have to do is divide -5 on both sides.
-5x < 15
------ ------
-5 -5
x < -3
Sometimes, you might have to flip the < sign. So it will be like:
x > -3
If you want to graph the inequality, here's how it will look:
(Graph shown on bottom of answer)
Mathematics is a great, beautiful, and important thing in life! With math, you can do anything when you out your mind to it!
- Jamal Josecite
8th Grade Student
(Please give me brainliest! I need to level up!)
miguel recently started a new hourly wage job. The equation y= 18.75x + 2500 models his total pay, y, in dollars as it relates to the number of hours, x, that he has worked.
Answer:
Step-by-step explanation:
Y=18.75x + 2500
Change the addition sign to a subtraction = Y=18.75x - 2500
Then bring 18.75x and divide it by 2500 = 133.33 so Y=133.33 if you were to round it would be 133.00
The total wage will be equal to $2593.75.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Miguel recently started a new hourly wage job. The equation y= 18.75x + 2500 models his total pay.
The total wage at 5 hours will be calculated as below:-
y= 18.75x + 2500
y = ( 18.75 x 5 ) + 2500
y = ( 93.75 ) + 2500
y = $2593.75
Therefore, the total wage will be equal to $2593.75.
The complete question is given below:-
Miguel recently started a new hourly wage job. The equation y= 18.75x + 2500 models his total pay, y, in dollars as it relates to the number of hours, x, that he has worked. Calculate the total wage at 5 hours working.
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Chris is making a tabletop. He has 9 tiles that are each 3 1/8 long by 2 3/4 inches wide.
What is the area of all the tiles
How much would all the blouses cost?
Answer:
$392
Step-by-step explanation:
We are buying 16 blouses. Each one costs 24.50
16*24.50 =392
The total cost of the 16 blouses is $392
Answer:
$392.00 all together
Step-by-step explanation:
$24.50 times 16
Hope This Helps! Have A Nice Day!!
A school is arranging a field trip to the zoo. The school spends 654.36 dollars on passes for 34 students and 4 teachers. The school also spends 303.96 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The school spent approximately $26.16 per student for a zoo pass and lunch during their field trip.
Explanation:The total amount spent on passes for the 34 students and 4 teachers is $654.36. The total amount spent on lunch for just the students is $303.96. It means for each student, the school spent a combined amount on passes and lunch. To find this, first, we need to identify how much was spent per student for the pass, then add this to the amount spent per student on lunch.
First, we calculate the cost of a pass for each student. Since the total cost of passes is for both students and teachers, we need to find only the cost for the students. We accomplish this by subtracting the teachers’ share. It assumes the cost of a pass for a student and a teacher is the same.
The cost per person (student or teacher) for the pass is: $654.36 / (34 students + 4 teachers) = $654.36 / 38 = $17.22 (approximately, rounding to the nearest penny).
To determine the cost per student for lunch, we just need to divide the total lunch cost by the number of students: $303.96 / 34 = $8.94 (approximately).
In the end, the total cost per student for both the pass and lunch is: $17.22 + $8.94 = $26.16
Therefore, the school spent approximately $26.16 per student for a zoo pass and lunch.
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The school spent approximately $17.22 on passes and $8.94 on lunch for each student.
Now, let's plug in the values and calculate:
Step 1:
Total spent on passes = $654.36
Step 2:
Amount spent on passes for teachers = 4 * (Amount spent on each teacher's pass)
To find the amount spent on each teacher's pass, divide the total spent on passes by the total number of passes.
Step 3:
Calculate the amount spent on passes for students.
Number of students = 34
Number of teachers = 4
Total number of passes = 34 + 4 = 38
Amount spent on each pass = Total spent on passes / Total number of passes
[tex]\[Amount\ spent\ on\ each\ pass = \frac{654.36}{38}[/tex] ≈ 17.22
Step 4:
Find the total amount spent on lunch for students.
Total spent on lunch for students = $303.96
Step 5:
Calculate the amount spent on lunch for each student.
[tex]\[Amount\ spent\ on\ lunch\ for\ each\ student[/tex] = [tex]\frac{303.96}{34}[/tex] ≈ 8.94
So, the school spent approximately $17.22 on passes and $8.94 on lunch for each student.
a 24-ft. hallway is just 8in on the blueprint. what is the scale?
1 inch is to 3 feet
1 in. : 3 ft.
a. I, III, II
b. II, I, III
c. II, III, I
d. III, I, II
The logical order for the proof is as follows: [tex]\( \overline{UV} \parallel \overline{WZ} \)[/tex] (Given), [tex]\( m\angle SQV + m\angle VQT = 180^\circ \)[/tex] (Substitution Property of Equality), [tex]\( m\angle SQT = 180^\circ \)[/tex] (Definition of a Straight Angle), and [tex]\( m\angle SQV = m\angle ZRS \)[/tex] (Subtraction Property of Equality). The correct choice is: c. II, III, I
The logical order of statements and reasons in the proof is as follows: First, it's given that [tex]\( \overline{UV} \parallel \overline{WZ} \)[/tex]. Then, by the Substitution Property of Equality, we have [tex]\( m\angle SQV + m\angle VQT = 180^\circ \)[/tex]. The Definition of a Straight Angle is applied to conclude that [tex]\( m\angle SQT = 180^\circ \)[/tex].
The Angle Addition Postulate supports [tex]\( m\angle SQV + m\angle VQT = m\angle SQT \)[/tex]. The Same-Side Interior Angles Theorem establishes [tex]\( m\angle VOT + m\angle ZRS = 180^\circ \)[/tex]. Using the Substitution Property of Equality, [tex]\( m\angle SQV + m\angle VQT = m\angle VQT + m\angle ZRS \)[/tex]. Finally, the Subtraction Property of Equality yields [tex]\( m\angle SQV = m\angle ZRS \)[/tex], and, by the Definition of Congruency, [tex]\(\angle SQV = \angle ZRS\)[/tex].
The correct answer is:
c. II, III, I
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the length of a rectangle playground in a scale drawing is 12 inches. if the scale is 1 inch = 10 feet, what Is the actual length. please show me how you got the answerrr
Answer:
120 feet
Step-by-step explanation:
12 x 10 = 120
The points (-2, -1), (5, -4), and (-2, -4) are vertices of a polygon. What is the best name for the polygon?
obtuse triangle
isosceles triangle
right triangle
acute triangle
Answer:
the answwee is right triangle
Step-by-step explanation:
Answer:
Right triangle,
Step-by-step explanation:
The points (-2,-1) and (-2,-4) joined make a vertical line.
Also the line between (-2,-4) and (5, -4) is horizontal.
The 3 points make a right triangle.
A triangle has sides 42, 4x, and 2x−6. What is the possible range of x?
? < x < ?
Answer:
[tex]8\ units< x < 18\ units[/tex]
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Applying the Theorem
case 1) [tex]42+4x > 2x-6[/tex]
[tex]4x-2x > -6-42[/tex]
[tex]2x > -48[/tex]
[tex]x > -24\ units[/tex]
case 2) [tex]42+(2x-6) >4x[/tex]
[tex]42-6 >4x-2x[/tex]
[tex]36 >2x[/tex]
[tex]18 >x[/tex] -----> rewrite
[tex]x<18\ units[/tex]
case 3) [tex]4x+(2x-6) > 42[/tex]
[tex]4x+2x > 42+6[/tex]
[tex]6x > 48[/tex]
[tex]x > 8\ units[/tex]
therefore
[tex]8\ units< x < 18\ units[/tex]
I need help with 25-46 Can someone please help me with any of them or all? 50 POINTS
Answer:
firs
Step-by-step explanation:
John spent $75 on a shopping trip for new clothes last week. He had expected to spend $100 on clothes. table How much was the absolute error in his estimate? $
Answer:
[tex]\$\ 25[/tex]
Step-by-step explanation:
By definition, the absolute error is defined as:
[tex]\epsilon = |x_a - x_e|[/tex]
Where:
[tex]\epsilon[/tex]: is the error
[tex]x_a[/tex]: is the approximate value
[tex]x_e[/tex]: is the exact value
In this problem the approximate value was 100 and the exact value was 75. Then we substitute these values in the formula to find the error.
[tex]\epsilon = |100 - 75|\\\epsilon = \$\ 25[/tex]
Answer:
$25
Step-by-step explanation:
|25|=25
For people doing this in 2020
−3x+3y=12
3x+6y=−57
find the solution
First solve the equation for 3x
-3x+3y=12
3x=-57-6y
Now substitute the given value into the equation
-(-57-6y)+3y=12
Then solve for y
Y=-5
Then substitute the given value of y
3x=-57-6✖️(-5)
Now solve for x
X=-9
Ordered pairs
(X,Y)=(-9,-5)
Then you are left with your answer:
(-9,-5)
Hope this helps! :3
First we need to solve for X.
Solve for xx.
-3x+3y=12−3x+3y=12
Divide both sides by -3−3.
x-y=-\frac{12}{3}x−y=−
Simplify \frac{12}{3}
x-y=-4x−y=−4
Add y to both sides.
x=-4+yx=−4+y
Regroup terms.
x=y-4x=y−4
Step two:
Let's start with the normal equation.
3x+6y=-573x+6y=−57
Let x=y-4x=y−4.
3(y-4)+6y=-573(y−4)+6y=−57
Simplify.
9y-12=-579y−12=−57
Great! Now we are on step 3.
Solve for y.
9y-12=-579y−12=−57
Add 1212 to both sides.
9y=-57+129y=−57+12
Simplify -57+12−57+12 to -45−45.
9y=-459y=−45
Divide both sides by 99.
y=-\frac{45}{9}y=−
Simplify \frac{45}{9} to 55.
y=-5y=−5
Step 4! Boom!!
Now let's start with what we have.
x=y-4x=y−4
Let y=-5y=−5.
x=-5-4x=−5−4
Simplify.
x=-9x=−9
Then our answers are:
x=−9
y=-5y=−5
Have an amazing day and thanks for using Brainly!
lenear programming equation
Answer: Its where the variable functions matches an output, for example *(modelvariable)=(output((x))
Step-by-step explanation:
Answer:
Linear programming
Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.
Step-by-step explanation:
Given f(x)=7x-9 and g(x) =x^2, choose the expression for (f*g)(x)
ANSWER
[tex](f\circ g)(x)=7 {x}^{2} - 9[/tex]
EXPLANATION
It was given that;
[tex]f(x) = 7x - 9[/tex]
and
[tex]g(x) = {x}^{2} [/tex]
We want to find an expression for the composition function;
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x)=f( {x}^{2} )[/tex]
We substitute x² into f(x)=7x-9
This will give us:
[tex](f\circ g)(x)=7 {x}^{2} - 9[/tex]
The figure shows two triangles on the coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A’B’C’
Its the third option :)
Answer: the correct option is
(D) A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.
Step-by-step explanation: We are given two triangles ABC and A'B'C' on the co-ordinate grid.
We are given to select the set of transformations is performed on triangle ABC to form triangle A’B’C’.
From the graph, we note that
the co-ordinate of the vertices of triangle ABC are A(-4, -1), B(-3, -1) and C(-4, -4).
And, the co-ordinates of the vertices of triangle A'B'C' are A'(-1, 1), B'(-2, 1) and C'(-1, 4).
We know that if a point (x, y) is translated 5 units right, followed by a rotation of 180-degrees clockwise about the origin, then its new co-ordinates becomes
(x, y) ⇒ (-x-5, -y).
So, after these two transformations, the co-ordinates of the vertices of triangle ABC will become
A(-4, -1) ⇒ (4-5, 1) = (-1, 1),
B(-3, -1) ⇒ (3-5, 1) = (-2, 1)
and
C(-4, -4) ⇒ (4-5, 4) = (-1, 4).
The new co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.
Thus, the required set transformations is
A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.
Thus, option (D) is CORRECT.