The Arithmetic Mean and Median of the given set of data ( 2, 5, 13, 15, 19, 21 ) are 12.5 and 14 respectively.
What is Arithmetic mean?Arithmetic mean is simply the average of a given set numbers. It is determined by dividing the sum of a given set number by their number of appearance.
Mean = Sum total of the number ÷ n
Where n is number of numbers
Median is the middle number in the data set.
Given the sets;
2, 5, 13, 15, 19, 21n = 6Mean = Sum total of the number ÷ n
Mean = (2 + 5 + 13 + 15 + 19 + 21) ÷ 6
Mean = 75 ÷ 6
Mean = 12.5
Median is the middle number in the data set.
Median = ( 13 + 15 ) ÷ 2
Median = 14
Therefore, the Arithmetic Mean and Median of the given set of data ( 2, 5, 13, 15, 19, 21 ) are 12.5 and 14 respectively.
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10. A garden is to be surrounded by a paved
border of uniform width.
16 m
|-X-
L=16+X+x
L= 2x+16
W=14+x+x
W= 2x+14
14 m
a) Write a simplified expression for the
area of the border.
b) The border is to have an area of
216 m². Find the width of the border.
The length of a rectangular floor is two ft more than its width. If the area of the floor is 63 ft, find the length and the width of the floor.
Answer:
width = 7 and length = 9
Step-by-step explanation:
Let's assume width = w, and length = 2 + w
So area of a rectangle = width * length
63 ft² = w (2 + w)
63 = 2w + w²
w² + 2w - 63 = 0
Use the quadratic formula to solve this
here, a = 1, b = 2 and c = -63
w = 7 or -9
The dimensions of a rectangle cannot be negative. So we take the dimension, w = 7.
Width = 7 and Length = 7+2 = 9
Are the ratios 8:3 and 4:1 equivalent?
Answer:
No.
Step-by-step explanation:
8:3 = 8/3
4:1 = 4/1 = 8/2
8/2 is not = 8/3
Alice, a 16-year-old, gave birth to a baby boy last year. how will this affect the likelihood that her 13-year-old sister, marie, will have a baby
Answer:
I think that the actions of older people/family members around you greatly influence that thoughts/actions of a younger child. Since Marie looks up to Alice, Marie probably thinks that having a child at such a young age is a good idea. Therefore if Alice gave birth at the age of 15, there is a high chance her younger sister will follow in her footsteps.
(I'm not sure how this relates to math)
What is true about the domain and range of the function? the domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1. the domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4. the domain is all real numbers, and the range is all real numbers less than or equal to 4. the domain is all real numbers less than or equal to 4, and the range is all real numbers.
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
How to determine the true statement?The equation of the function is given as:
f(x) = -(x + 3)(x -1)
The above function is a quadratic function, and the domain of a quadratic function is the set of all real numbers
Expand the function
f(x) = -(x² + 3x - x - 3)
f(x) = -(x² + 2x - 3)
Expand
f(x) = -x² - 2x + 3
Differentiate
f'(x) = -2x - 2
Set to 0
-2x - 2 = 0
Add 2 to both sides
-2x = 2
Divide through by -2
x = -1
Substitute x = -1 in f(x)
f(-1) = -(-1 + 3)(-1 -1)
Evaluate
f(-1) = 4
This means that the maximum value of the function is 4
Hence, the domain is all real numbers, and the range is all real numbers less than or equal to 4.
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Answer: C: The domain is all real numbers, and the range is all real numbers less than or equal to 4.
Step-by-step explanation: EDGE 2022
Use the quadratic formula to solve for X.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
There is estimated to be a population of approximately 85 mice on Farmer Jon's Farm, and the population is tripling each year. Does the scenario above represent exponential growth or decay? write an equation to represent the scenario.
Answer:
Exponential growth
Step-by-step explanation:
As it mentions that the population is tripling each year, we can clearly understand that it is exponential growth.
Equation
⇒ Let y be total population of mice and x the number of years
⇒ y = 85(3ˣ)
Hope it helps ~
52 + 6 × (5 − 3) − 10⁄2 =??
Answer:
PEMDAS
Step-by-step explanation:
start with parantheses
52+6×(5-3)-10/2
52+6×2-10/2
no exponents so move on to multiplication
52+12-10/2
followed by division
52+10-5
finally add and subtract
57
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
La respuesta es A
Step-by-step explanation:
simplemente tienes que multiplicar 7 x 3 que te da 21 y luego tienes que sumar el 2 del numerador (siempre multiplica el o los enteros por el denominador y sumale el numerador)
Answer:
A
Step-by-step explanation:
The larger number in a mixed number represents how many "wholes" of the fraction there are. The fraction in a mixed number is sort of like the "leftovers", the amount that doesn't fit into a whole number. In this case, the whole number is 7, meaning there are 7 amounts of 3/3. You would multiply the whole number by the number in the denominator of the fraction, which would equal 21. The improper fraction of the whole number would be 21/3 (21 divided by 3 equals 7). Now you would add that to the fraction 2/3. The answer would be 23/3.
I hope this makes some type of sense, I didn't explain it very well.
what is 9 - 3 dived by 1/3 + 1 =
Shawna is going out of town for the day, so she asks a friend to watch her 3 dogs. She wants to leave
1/2 of a pound of food for each dog. If a can of dog food has 0.75 pounds of food, how many cans should Shawna leave?
Answer:
2cans
Step-by-step explanation:
1/2 = .5 so .5×3=1.5 and 1.5 ÷ .075 =2
Please help me with question 36. I don’t know the answer
Answer:
Period = [tex]\frac{\pi }{4}[/tex]
Amplitude = 4
Step-by-step explanation:
To find the answer, use the form acos(bx - c) + d:
a = -4
b = 8
c = 0
d = 0
The amplitude is the absolute value of a, so:
|a| = |-4| = 4
To find the period, use this equation:
[tex]\frac{2\pi }{b}[/tex]
Replace b with 8 in the formula and solve:
[tex]\frac{2\pi }{8} = \frac{\pi }{4}[/tex] Simplify
So, the period is equal to [tex]\frac{\pi }{4}[/tex]
Hope this helps!!
If you were going to buy a $60 game, which would save you more money: a coupon for 30% off or a
$20 off coupon?
Answer:
A coupon for 30%
Step-by-step explanation:
A coupon takes the a certain percentage of a price and subtracts it (a discount). A coupon for 30% off takes 30% of the price which is $60 and subtracts it, same goes for the $20 off coupon. Because a greater percentage is being taken off of the price, the 30% off coupon would save someone more money.
WILL MARK BRAINLIEST IF THERES WORK SHOWN AND ITS RIGHT PLEASE
An expression is shown below:
2x³ + 10x² - 4x2y - 20xy
Part A: Rewrite the expression by factoring out the greatest common factor
Part B: Factor the entire expression completely. SHOW THE STEPS OF YOUR WORK.
Write and solve an addition or subtraction equation to find the missing angle measure
Answer:
n = 60°
Step-by-step explanation:
60° + n + 60° = 180° ( straight line angles)
-> n + 120° = 180°
-> n = 180° - 120°
-> n = 60°
The measure of the missing angle can be found using the equation 120 + n = 180 and the value of n is 60°.
What are Linear Pair of Angles?Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.
Sum of the measures of angles of linear pair is supplementary.
Given is a line on which some shapes are drawn.
Clearly, it can be seen that,
The three angles 60°, n and 60° forms a linear angles since all are formed on a line.
So the sum is 180°.
60 + 60 + n = 180
120 + n = 180. is the required equation.
Solving,
n = 180 - 120 = 60°
Hence the value of n is 60 degrees.
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Solve x^2 =-25, where x is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Answer: x = ±5i
Step-by-step explanation:
√x2 = √−25
x = √−1 ∗ 25
x = i√25
x = ±i5
Greg bought a new tv on sale the sale price was 45% off of the original price the tv greg bought had an original price of 320$ if mike gave the cashier 200$ how much money did he receive back
Answer:
$24
Step-by-step explanation:
320 x 0.45=144
320-144=176
200-176=24
What is the completely factored form of f(x)=x^3+5x^2+16x+80 ?
f(x)=(x−5)(x−4i)(x+4i)
f(x)=(x+5)(x−4i)(x+4i)
f(x)=(x−5)(x−4)(x+4)
f(x)=(x+5)(x−4)(x+4)
Answer:
B) [tex]f(x)=(x+5)(x-4i)(x+4i)[/tex]
Step-by-step explanation:
[tex]f(x)=x^3+5x^2+16x+80\\\\f(x)=x^2(x+5)+16(x+5)\\\\f(x)=(x^2+16)(x+5)\\\\f(x)=(x-4i)(x+4i)(x+5)[/tex]
Thus, the second choice is correct.
In a class of 35 students, 20 offer Physics, 18 offer Chemistry and 2 offer neither Physics nor Chemistry. i) Illustrate the information on a Venn diagram. ii) How many students offer all the two subjects? ii) How many students offer Physics? iv) How many students offer only one subject?
Answer:
Given:
35 = Total number of students20 = Physics students18 = Chemistry students2 = Neither Physics or Chemistry studentsTo construct the Venn diagram:
Draw 2 circles overlapping.As 2 students study neither subject, place the number 2 in the box outside the circles.
Calculate the number of students who study both subjects (central overlapping section):
Physics students + Chemistry students + neither students - Total students
= 20 + 18 + 2 - 35 = 5
Place the number 5 in the central overlapping section.
⇒ Left section = Physics students - both subjects
= 20 - 5
= 15
⇒ Right section = Chemistry students - both students
= 18 - 5
= 13
i) See attachment
ii) Physics and Chemistry = 5 students
iii) Physics only = 15 students
iv) One subject only = 15 + 13 = 28 students
In a Crystal Light container, the ratio of strawberry flavored packages to orange flavored packages are 8 to 4. Based on this ratio, how many orange flavored packages will you find in a Crystal Light container with a total of 96 packages?
Answer:
32
Step-by-step explanation:
With the ratio 8:4 we can assign variables.
8x+4x=96
12x=96
x=8
Subsitute to ratio: 8x:4x
64:32
32 orange packages
Hope this helps
What is the equation for the function shown in FACTORED FORM?
Answer:
f(x) = (x + 1)(x - 4)
Step-by-step explanation:
let f be the function
FACTORED FORM of f :
f(x) = a(x - p)(x - q)
Where p and q are the roots/zeros of f
and ‘a’ is a real number.
=================================
Find p and q :
The roots of f are the x-coordinates where the graph crosses the x-axis, which can be read from the graph: x = -1 and x = 4 ⇒ p = -1 and q = 4.
then f(x) = a(x + 1)(x - 4)
Find ‘a’ :
f(3) = -4 ⇒ a((3) + 1)((3) - 4) = -4 ⇒ a(4)(-1) = -4 ⇒ -4a = -4 ⇒ a = 1
Therefore, f(x) = (x + 1)(x - 4)
Reuben has bought 30 pounds of dog food. He feeds his dog 3/5 pounds for each meal. For how many meals will the food last?
Answer:
50
Step-by-step explanation:
3*50=150. 150/5=30 pounds
Identify coordinate point B. (0, 2) (1, 5) (7, 3) (6, 7)
Answer:
i think 1.5 imagine a dot so its on 5 and 1 then you get 1.5 thats what i think
Step-by-step explanation:
pls dont get mad if i got it wrong D:
Answer:(1, 5)
Step-by-step explanation:
Solve these pls I will give 25 points
Answer:
108 minutes
Step-by-step explanation:
because 45/5=9 and 180/20=9 so multiply 12 by 9 12x9=108
Reggie has $240 in a savings account at the beginning of the summer. He wants to have at least $450 in the account by the end of the summer. He deposits $35 each week. What is the shortest amount of time Reggie needs to deposit money into his account?
Answer:
6 weeks
Step-by-step explanation:
Since Reggie has $240 in the account already we first subtract this $240 from the $450. 450 - 240 = 210. Now since he deposits $35 a week and needs to hit at least 210 to reach is goal of $450 for the summer then we need to divide 210/35 to see the amount of weeks. 210/35 = 6. So 6 weeks is the shortest time.
Use the information in the diagram to find the length of segment AD. Round your answer to the nearest hundredth.
If the length of the side AB is 39.21 then the length of the side AD will be 21.61. Then the correct option is B.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function. The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The length AD is given as
AD = AB - BD
AD = AB - 17.6
Then the value of AB will be given by the Pythagoras theorem.
AB² = BC² + CA²
AB² = 26.5² + 28.9²
AB² = 1537.46
AB = 39.21
Then the value of AD will be
AD = 39.21 - 17.6
AD = 21.61
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convert 12 minutes 35 seconds to seconds
:_
Answer:
755s
Step-by-step explanation:
60*12+35=755
This is the way
Answer:
755 seconds
Step-by-step explanation:
1min = 60 sec
12 x 60 = 720
720+35 = 755
:)
Find the y-intercept of the line 11x - 8y = -1.
write your answer as an integer or as a simplified proper or improper fraction, not as an
ordered pair.
submit
Answer:
1/8
Step-by-step explanation:
I'd start by rearranging the terms for y:
11x-8y=-1
-8y=-1-11x
y=[tex]\frac{-1-11x}{-8}[/tex]
The x-intercept is found when x equals 0, so substitute 0 for x in this new equation to find the y-intercept:
[tex]y=\frac{-1-11x}{-8} \\y=\frac{-1-11(0)}{-8}\\ y=\frac{-1-0}{-8} \\y=\frac{-1}{-8}\\ y=\frac{1}{8}[/tex]
The y-intercept is 1/8
Jimmy has a new job and plans to start saving some money. he decides to use his knowledge of geometric series to set up a savings plan that will start off with him setting aside a small amount each week, and end with him saving a large amount. in each of the first 5 weeks of his job, he wants to raise $2 to the number of weeks he has been working, multiply it by 3, and add that amount to the savings account. use summation notation to write this as a sum and find the total amount jimmy will save in 5 weeks.
The equation that represents the amount saved is T(n) = 3 * (2^n), and the total amount saved in 5 weeks is $186
How to determine the sum of total amount?The statement is given as:
raise $2 to the number of weeks he has been working, multiply it by 3,
Let the number of weeks be n.
So, we have:
T(n) = 3 * (2^n)
For week 1 to 5, we have:
T(1) = 3 * (2^1) = 6
T(2) = 3 * (2^2) = 12
T(3) = 3 * (2^3) = 24
T(4) = 3 * (2^4) = 48
T(4) = 3 * (2^5) = 96
The sum is then calculated as:
Sum = 6 + 12 + 24 + 48 + 96
Evaluate the sum
Sum = 186
Hence, the total amount saved in 5 weeks is $186
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The volume of a sphere is V=4/3 pie r 3
where r is the radius of the
sphere. Determine the volume of the sphere where the radius is
measured at 6 inches.
a 288pie 3
b 216 pie 3
C 144 pie 3
d 48 pie 3
Answer:
A. 288pi in^3
Step-by-step explanation:
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