Answer:
11.4
Step-by-step explanation:
Step 1: Calculate the mean.
40, 55, 35, 60, 20, 50, 55
=
315
divided by 7
=
45
Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.
40 - 45 = 5
55 - 45 = 10
35 - 45 = 10
60 - 45 = 15
20 - 45 = 25
50 - 45 = 5
55 - 45 = 10
Step 3: Add those deviations together.
= 80
Step 4: Divide the sum by the number of data points.divided by 7
= 11.428
Step 5: Round to the nearest tenth.
= 11.4
Answer:
The mean absolute deviation is approximately is 11.43.Step-by-step explanation:
The means absolute deviations is define by:
[tex]D_{x} =\frac{\sum |x_{i}-x| }{N}[/tex]
From the formula, we observe that we need to find the mean, and then find the different between that mean and each element. Then, we have to sum all those differences and divide this by the total number of elements.
So, the mean is
[tex]x=\frac{\sum x_{i} }{N}\\ x=\frac{40+55+35+60+20+50+55}{7}=45[/tex]
Now, each difference would be
[tex]40-45=-5\\55-45=10\\35-45=-10\\60-45=15\\20-45=-25\\50-45=5\\55-45=10[/tex]
The sum of all differences, using their absolute value, would be:
[tex]5+10+10+15+25+5+10=80[/tex]
Then, we divide this result by the total number of elements which is 7:
[tex]\frac{80}{7} \approx 11.43[/tex]
Therefore, the mean absolute deviation is approximately is 11.43.
What is the area of the triangle formed from (-2,2), (1,2), and (0,-6)?
A.12 square units
B.48 square units
C.8 square units
D.24 square units
Answer:
Option A.12 square units
Step-by-step explanation:
Let
[tex]A(-2,2), B(1,2), C(0,-6)[/tex]
Plot the vertices
see the attached figure
we know that
The area of triangle is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
where
[tex]b=AB=(1-(-2))=3\ units[/tex]
[tex]h=(2-(-6))=8\ units[/tex]
substitute
[tex]A=\frac{1}{2}(3)(8)[/tex]
[tex]A=12\ units^{2}[/tex]
Answer:
Step-by-step explanation:
A. 12
ABC is a right triangle.If AC=12 and BC=13,find AB
The answer for AB is 5.
To find this answer, you would use Pythagorean Theorem. The equation would be a² + 12² = 13². First, square 12 and 13, to get the equation to say a² + 144 = 169. Next, subtract 144 from both sides. This leaves a² = 25. Finally, square root both sides to a = 5. Thus meaning 5 is the answer.
Here is an image to show how this answer is found. I hope this helps!
Can someone help me plz
Answer:
Half gallon
Step-by-step explanation:
at the least expensive price per ounce (60 cents), half gallon is the answer.
given sin(0)= -1 and cos(0)= 0, what is the angle measurement of 0 in radians
Check the picture below.
What is the approximate value of K? Use the law of sines to find the answer.
A.) 2.9 units
B.) 3.8 units
C.) 5.1 units
D.) 6.2 units
Answer:
C.) 5.1
Step-by-step explanation:
First, solve for J's angle of degrees
180 - (120 + 40) = 20
Second, fill in all the information that you know in the equation
sin(20) / 2 and sin(120) / k
Third, cross multiply
k x sin(20) = 2 x sin(120)
Fourth, solve for k
k x sin(20) / sin(20) = [2 x sin(120)] / sin(20)
k = [2 x sin(120)] / sin(20)
k = 5.0641777.....
Fifth, round to the nearest tenth
k = 5.1
Answer:
its 5.1 on edg
Step-by-step explanation:
Can someone please help me ..
Answer:
The mean of pictures is 2
Step-by-step explanation:
To find the mean we add up all the pictures then divide it by the amount of newspapers, there are 10 and 5 newspapers. 10/5=2.
what are the soultion(s) to the quadratic equation 40- x^2=0
Answer:
40 - x² = 0
x² = 40
x = ±√40 = ±√4√10 = ±2√10
Find the x-intercepts of the parabola with
vertex (-1,-108) and y-intercept (0,-105).
Write your answer in this form: (x1,71), (x2,y2).
If necessary, round to the nearest hundredth.
Answer:
The x-intercept are (-7 , 0) and (5 , 0)
Step-by-step explanation:
* Lets revise the general form of the equation of the parabola
- The general form of the equation of the parabola is:
y = ax² + bx + c , a , b , c are constant
- The y-intercept is c, because the parabola intersect the y-axis at
point (0 , c)
- The x-coordinate of the vertex point is -b/2a
* Now lets solve the problem
∵ The general form of the equation of the parabola is y = ax² + bx + c
∵ The y-intercept is -105
∴ c = -105
∴ y = ax² + bx - 105
∵ The vertex point is (-1 , -108)
∴ The x-coordinate of the vertex of the parabola = -1
∵ The x-coordinate of the vertex of the parabola = -b/a
∴ -b/2a = -1 ⇒ using cross multiplication
∴ -b = -2a ⇒ multiply two sides by -1
∴ b = 2a
- Substitute the value of b in the equation
∴ y = ax² + 2ax - 105
- Substitute the value of x , y in the equation by the coordinates of
the vertex point
∵ The vertex point lies on the parabola
∴ put x = -1 and y = -108
∴ -108 = a(-1)² + 2a(-1) - 105
∴ -108 = a - 2a - 105 ⇒ add the like term
∴ -108 = -a - 105 ⇒ add 105 to both sides
∴ -3 = -a ⇒ multiply both sides by -1
∴ a = 3
- Substitute the value of a in the equation
∵ y = ax² + 2ax - 105
∴ y = 3x² + 2(3)x - 105
∴ y = 3x² + 6x - 105
- To find the x-intercept put y = 0
∴ 3x² + 6x - 105 = 0
- All the terms have 3 as a common factor
∴ divide all the terms by 3
∴ x² + 2x - 35 = 0
- Now factorize it into two factors
∵ x² = x × x ⇒ the 1st term in the bracket and the 1st term in the
2nd bracket
∵ -35 = -5 × 7 ⇒ the 2nd term in the 1st bracket and the 2nd term in the
2nd bracket
∵ x × - 5 = -5x ⇒ means
∵ x × 7 = 7x ⇒ extremes
∵ 7x - 5x = 2x ⇒ the middle term
∴ (x - 5)(x + 7) = 0
- Equate each bracket by 0
∴ x - 5 = 0 ⇒ add 5 to both sides
∴ x = 5
OR
∴ x + 7 = 0 ⇒ subtract 7 from both sides
∴ x = -7
∴ The x-intercept are -7 , 5
* The x-intercept are (-7 , 0) and (5 , 0)
Answer:
Step-by-step explanation:
The nth term of a sequence is n^2 + 20.
a) work out the first three terms of the sequence
b) how many terms in the sequence are less than 50?
Answer:
[tex]\large\boxed{a)\ 21,\ 24,\ 29}\\\boxed{b)\ \text{five terms}}[/tex]
Step-by-step explanation:
[tex]a_n=n^2+20\\\\a)\\\\\text{Substitute}\ n=1,\ n=2\ \text{and}\ n=3\ \text{to the }\ a_n:\\\\a_1=1^2+20=1+20=21\\\\a_2=2^2+20=4+20=24\\\\a_3=3^2+20=9+20=29[/tex]
[tex]b)\\\\\text{You have to solve the inequality:}\\\\n^2+20<50\qquad\text{subtract 20 from both sides}\\\\n^2<30\to n<\sqrt{30}\to n\leq5\\\\a_1,\ a_2,\ a_3,\ a_4\ \text{and}\ a_5\ \text{are less than 50.}[/tex]
a) The first three terms of the sequence are 21, 24 and 29.
b) The no. of terms less than 50 are 6.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, The nth term of a sequence is n² + 20.
The first three terms we'll get by replacing 1, 2, and 3 in place of n.
The first term is (1)² + 20 = 21.
The second term is (2)² + 20 = 24.
The third term is (3)² + 20 = 29.
No. of terms that are less than 50 are
n² + 20 < 50.
n² < 30.
n < ± √30.
n < 6 approx.
learn more about sequences here :
https://brainly.com/question/21961097
#SPJ2
Simplify (3x – 5) - (4x + 6).
Answer: -1x-11
Step-by-step explanation:
I NEED HELP ASAP
The graphs of f(x) = –2x and
g(x) = (1/2)^x are shown.
What are the solutions to the equation
-2x = (1/2)^x ?
Select each correct answer.
-2, -1, 2, 4
Answer:
I have not the slightest clue but there's an app called cam calc and I swear its the best
Answer:
-2!
Step-by-step explanation:
im just finished this exact test and i swear thats the right answer!!
translate the following situation into an inequality statement . Lily has $25 to spend on a charm bracelet for her sisters birthday gift the cost of the bracelet is $12 plus $1.50 per charm
Final answer:
Lily's budget scenario with her sister's charm bracelet is translated into the inequality statement 12 + 1.50c ≤ 25, where c represents the number of charms she can buy. Solving this inequality will show how many charms Lily can afford without exceeding her $25 budget.
Explanation:
The question involves translating a real-life situation into an inequality statement concerning budget and expenses. Lily has $25 to spend on her sister's birthday gift, which is a charm bracelet. The cost structure for the bracelet is $12 for the bracelet itself plus $1.50 for each charm. We let the number of charms she plans to buy be represented by c. The total cost for these charms would be $1.50c, and when added to the initial $12 for the bracelet, the sum should not exceed Lily's budget of $25.
Therefore, the inequality that represents this situation is 12 + 1.50c ≤ 25.
To find the maximum number of charms Lily can afford, we would solve for c in the inequality. This step involves subtracting 12 from both sides and then dividing by 1.50.
Please help! Evaluate 1 + ( - 2/3 ) - (-m) where m - 9/2.
Answer:
[tex]m + \frac{1}{3} [/tex]
Step-by-step explanation:
[tex]1. \: 1 - \frac{2}{3}+m \\ 2. \: m + (1 - \frac{2}{3}) \\ m + \frac{1}{3} [/tex]
Answer:
29/6
Step-by-step explanation:
1+ -2/3 - (-m)
1 - 2/3 + m
1/3 + m
Let m = 9/2
1/3 +9/2
Get a common denominator of 6
1/3 *2/2 = 2/6
9/2 *3/3 = 27/6
2/6 + 27/6
29/6
2/2 - 7x-4
Simplify
- 58+4
2x + 1
2-1
2x + 1
*+1
2-72
Answer:
A or (2x+1)/(x-1)
Step-by-step explanation:
Let's simplify the top of the fraction first.
1. Simplify the numerator.
2x^2 -7x-4=(2x+1)(x-4)
2. Simplify the denominator.
x^2-5x+4=(x-4)(x-1)
Now we have:
((2x+1)(x-4))/((x-4)(x-1))
We see that there is an (x-4) both on the numerator and denominator.
We can remove (x-4) by division.
Doing that, we have:
(2x+1)/(x-1) or A
20. –3 |z| + 2(a + y) what's the answer?
z=-4.2 a=-2 y=3
Answer:
-10.6
Step-by-step explanation:
-3|z| + 2(a + y) =
= -3|-4.2| + 2(-2 + 3)
= -3(4.2) + 2(1)
= -12.6 + 2
= -10.6
EMERGENCY!!
What are the solutions to the equation (x-6)(X + 8) = 0?
x= -6 or x = 8
x=-6 or x = -8
x = 6 or x = -8
x= 6 or x = 8
Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
12x - y = 25
9x + y =17
Answer:
the ordered pair is (2,-1)
Step-by-step explanation:
We need to solve the system of equations using elimination method
12x - y = 25 eq(1)
9x + y = 17 eq(2)
Adding eq(1) and eq(2)
12x - y = 25
9x + y = 17
___________
21x = 42
x = 42/21
x= 2
Now, putting value of x in equation 1
12x - y = 25
12(2) -y = 25
24 -y = 25
Adding -24 on both sides
24 -y-24 = 25-24
-y = 25-24
-y = 1
Multiply both sides by -1
y = -1
the value of x = 2 and y = -1
So, the ordered pair is (2,-1)
Answer:
The solution is: (2, -1)
Step-by-step explanation:
I have the following system of equations
[tex]12x - y = 25[/tex]
[tex]9x + y =17[/tex]
Note that if we add both equations, the variable y is "eliminated".
So add the first equation to the second and solve for the variable x
[tex]12x - y = 25[/tex]
[tex]9x + y =17[/tex]
----------------------------------
[tex]21x=42[/tex]
[tex]x=\frac{42}{21}\\\\x=2[/tex]
Now substitute the value of x in any of the two equations and solve for the variable y
[tex]9(2) + y =17[/tex]
[tex]18 + y =17[/tex]
[tex]y =17-18[/tex]
[tex]y =-1[/tex]
The solution is: (2, -1)
The table shows the number of candies packed by machine c. the equation shows the number of candies packed by machine D. In both representations, x is a measure of the number of minutes and y is a measure of the number of candies packed. How many more candies could machine d pack than machine c in 11 minutes
Answer: 605 candies
Step-by-step explanation:
Machine C shows a table where 150 candies are added every 2 minutes (which equals 75 candies per minute). Extend the table to show how many candies are made in 11 minutes:
x y
(minutes) (candies)
2 150
4 300
6 450
8 600
10 750
11 825
Machine D productivity is given by the equation y = 130x
when x = 11 minutes, y = 130(11)
= 1430 candies
The difference between machines C and D is: 1430 - 825 = 605
Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 minutes to reach mile marker 3. When she reaches mile marker 6, she notes that 8 minutes total have passed since mile marker 0.
What is the average speed of the car in miles per minute?
mile(s) per minute
What is an equation of the line that represents n, the number of mile marker passed, as a function of t, time in minutes?
Answer:
0.75 and n-6= 0.75(t-8)
Step-by-step explanation:
To find the average speed of Ava's car, divide the total distance traveled by the total time taken. Ava travels 6 miles in 8 minutes, so the average speed is 0.75 miles per minute. The equation of the line representing the number of mile markers passed as a function of time is n = (3/4)t.
Explanation:To find the average speed of Ava's car in miles per minute, we can use the formula:
Average speed = total distance / total time
First, we need to find the total distance traveled. Ava travels from mile marker 0 to mile marker 6, which is a distance of 6 miles.
Next, we need to find the total time it took Ava to travel this distance. Ava notes that 8 minutes have passed when she reaches mile marker 6, but it took her 4 minutes to travel from mile marker 0 to mile marker 3. This means it took her 4 minutes to travel 3 miles. Therefore, it would take her an additional 4 minutes to travel the remaining 3 miles from mile marker 3 to mile marker 6.
So, the total time taken by Ava to travel 6 miles is 4 minutes + 4 minutes = 8 minutes.
Now, we can use the formula to calculate the average speed:
Average speed = total distance / total time = 6 miles / 8 minutes = 0.75 miles per minute.
Equation of the line:
To find the equation of the line that represents the number of mile markers passed as a function of time, we can use the equation:
n = mt + b
Here, 'n' represents the number of mile markers passed, 't' represents time in minutes, 'm' represents the slope of the line, and 'b' represents the y-intercept.
In this scenario, Ava starts checking her car's clock at mile marker 0, which means the y-intercept is 0. We also know that Ava takes 4 minutes to travel from mile marker 0 to mile marker 3, which means she passes 3 mile markers in 4 minutes. Therefore, the slope of the line is 3/4.
So, the equation of the line is: n = (3/4)t.
Learn more about average speed here:https://brainly.com/question/12322912
#SPJ2
Review: To simplify an expression, combine like terms by adding or
subtracting coefficients only. Like terms have the same variable (letter or
symbol that represents a quantity).
Example: 17a + 4 - 5a - 3 = (17a - 5a) + (4-3) = 12a + 1
Simplify this expression. 10b + 7 - 3 - 2
Answer:
10b + 2
Step-by-step explanation:
To simplify this expression. 10b + 7 - 3 - 2 use the sample you demonstrated above to simplify it
10b + 7 -3 -2
combine the like terms
10b + 7 - 5
10b + 2
The expression 10b + 7 - 3 - 2, when simplified by grouping and adding or subtracting like terms, becomes 10b + 2.
Explanation:To simplify an expression, like the one you've given which is 10b + 7 - 3 - 2, it is necessary to group like terms and combine them.
First, let's combine like terms. In this case, you only have a single term with a variable:
10b (which we will leave as is since there are no other terms with 'b' in them)
Then, you have constants (numbers without variables) 7, -3, and -2. We can combine these by adding or subtracting them: 7 - 3 - 2 = 2
So your simplified expression becomes: 10b + 2
Learn more about Simplify Expression here:https://brainly.com/question/29003427
#SPJ3
y= -3/4x+3 and y=-12
Answer:
x = 20, y = -12Step-by-step explanation:
[tex]y=-\dfrac{3}{4}x+3\ and\ y=-12\\\\\text{Substitute the value of y to the first equation:}\\\\-12=-\dfrac{3}{4}x+3\qquad\text{multiply both sides by 4}\\\\-48=-3x+12\qquad\text{subtract 12 from both sides}\\\\-60=-3x\qquad\text{divide both sides by (-3)}\\\\20=x\to x=20[/tex]
Answer:
x = 20, y = -12
Step-by-step explanation:
y= -3/4x+3 and y=-12
x = 20, y = -12
Answer ASAP!!It takes 1 1/2 cups of flour, cups of sugar, and 1 1/4 cup of butter to bake fifteen shortbread cookies. If Ramon has 5 cups of flour, 4 cups of sugar, and 13/4 cups of butter, how many shortbread cookies can he bake? Plz don't copy and paste the answer from another site. I need it to be answered in fraction form and well explained. Brainliest for first correct!
Answer:
Up to 39 shortbread cookies.
Step-by-step explanation:
Start by considering: how many cookies can Ramon make if
Flouring runs out first,Sugar runs out first, and Butter runs out first?Assume that flour runs out before the other two ingredients. How many cookies can Ramon make?
It takes 1 1/2 = 3/2 cups of flour to bake fifteen cookies. 5 cups of flour is available. How many batches of fifteen cookies will that 5 cups of flour make?
[tex]\displaystyle \frac{5}{3/2}\right = \frac{10}{3}[/tex].
That's
[tex]\displaystyle 5\times \frac{10}{3} = 50\;\text{cookies}[/tex].
Similarly, assume that sugar runs out before the other two ingredients. How many cookies can Ramon make?
It takes one cup of sugar to bake fifteen cookies. 4 cups of sugar is available. That 4 cups of sugar will make up to four batches of fifteen cookies. That's 60 cookies.
Assume that butter runs out before the other two ingredient. How many cookies can Ramon make?
It takes 1 1/4 = 5/4 cups of butter to bake fifteen cookies. 13/4 cups of butter is available. That 13/4 cups of butter will make up to 13/5 batches of fifteen cookies. That's
[tex]\displaystyle 15 \times \frac{13}{5} = 39\;\text{cookies}[/tex].
These three numbers differ. How many cookies will these materials actually make? The ingredient that will make the smallest number of cookies will run out before other ingredients. In this case, butter runs out first. These materials will make up to 39 shortbread cookies.
Help pls !!! A waitress kept track of whether her customers ordered and appetizer and dessert
The 0.3 in the highlighted cell mean 30% ordered dessert but no appetizer.
The correct option is (D).
What is mean?The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values.
As, the number is in the column with no appetizer and row with dessert
So, 0.3 = 0.3*100/100
= 30/100
= 30% ordered dessert but no appetizer.
Hence, 30% ordered dessert but no appetizer.
Learn more about mean here:
https://brainly.com/question/17060266
#SPJ2
A line has a slope of –3/2 and has a y-intercept of 3. What is the x-intercept of the line?
Answer:
x = 2 → (2, 0)Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept (0, b)
We have the slope m = -3/2 and the y-intercept b = 3.
Substitute:
y = -3/2x + 3
The x-intercept is for y = 0. Substitute:
0 = -3/2x + 3 add 3/2x to both sides
3/2x = 3 multiply both sides by 2
3x = 6 divide both sides by 3
x = 2
A system of equations is shown below. Which ordered pair represents the solution to the system
Answer:
The correct answer is (-5,-5)
Step-by-step explanation:
1. Both of the equations are in standard form, so first you set them equal to each other.
2. Solve for x as a normal algebraic equation.
3. Back substitute your answer for x into one of the original equations. (back substitution is just putting the x back into the equation and solving for y.)
4. Now you have your x and y coordinates, and the point of intersection of the two lines.
The ordered pair represents the solution to the system is (-5, -5), and the correct option is A.
What is the ordered pair?A pair of numbers that are written in a particular order, enclosed in brackets are known as ordered pairs.
The given system of equation is;
y = 3x + 10
y = 5x +20
Subtraction equation 1 from 2
y - y = 3x + 10 - 5x -20
0 = -2x -10
2x = -10
x = -10/2
x = -5
Substitute the value of x in equation 1
y = 3x + 10
y = 3(-5) +10
y = -15 +10
y = -5
Hence, the ordered pair represents the solution to the system is (-5, -5), and the correct option is A.
Learn more about ordered pairs here;
https://brainly.com/question/14220121
#SPJ2
For the graph of function f shown below, which of the following is true?
Answer:
A
Step-by-step explanation:
Because it touches the x axis 3 times as shown in your graph
Hope it helps you..☺
What is the value of the digit 1 in the number 13?
Answer:
the value of the digit 1 in the no. 13 is 10
Step-by-step explanation:
cuz it's in the tens place
1 3tens ones
hope u understood
and helps u
and ur welcm
:D
The value of digit 1 in the number 13 is 10 because it is located in the 'tens' place.
Explanation:The value of the digit 1 in the number 13 corresponds to its place value in the number. In the number 13, 1 is in the 'tens' place, thus its value is 10. Place value is determined by the position of a digit in a number. It shows the mathematical worth of each digit at their respective places. Zeroes play a significant role in deciding the place value of digits in a number, acting as placeholders that help identify decimal points.
Learn more about Place Value here:https://brainly.com/question/27734142
#SPJ2
5 1/8 - 2/ 78 my little sister's homework
Answer:
5 1/8 - 2 7/8 =
3 -6/8 =
2 2/8 =
2 1/4 =
2.25
Step-by-step explanation:
The ratio of the height of two similar cylinders is 4 to 3 What is the ratio of their volumes
Answer:
64 : 27
Step-by-step explanation:
When using scale factors
Length = scale factor
Area = scale factor squared
Volume = scale factor cubed
The ratio is 4:3
The ratio of the volume is 4^3 : 3^3
64 : 27
HELP Geometry does anyone know this
Answer: second option.
Step-by-step explanation:
You need to remember the following identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
In this case, we can observe that:
[tex]\alpha=45\°\\opposite=6\\hypotenuse=x[/tex]
Now you must substitute these values into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for the hypotenuse. Then:
[tex]sin(45\°)=\frac{6}{x}\\\\(x)(sin(45\°))=6\\\\x=\frac{6}{sin(45\°)}\\\\x=6\sqrt{2}[/tex]
Answer:
The correct answer is second option
6√2
Step-by-step explanation:
From the figure we can see a right angled triangle, with angles 45°, 45° and 90°
The height of triangle is 6 units
Points to remember
If the angles of a right angled triangle are 45°, 45° and 90° then the sides are in the ratio, 1 : 1 : √2
To find the value of x
From the figure we can see that, the angles are 45°, 45° and 90°
Therefore the two sides are equal and one side is x
The equal side is 6 units
Therefore 6 : 6 : x = 6 : 6 : 6√2
The value of x = 6√2
The second option is the correct answer.