Answer:
For a data set of N elements:
{x₁, x₂, ..., xₙ}
The median is the middle value (or the average of the two middle values)
The average or mean is:
[tex]m = \frac{x_1 + ... + x_n}{N}[/tex]
The mode is the value that is more repeated.
The range is the difference between the largest value and the smallest value.
Now, let's try to construct two sets A and B that meet the required conditions:
Let's suppose two sets of 5 values each:
A = {2, 2, 3, 4, 5}
The median of A is 3.
The range of A is = 5 - 2 = 3
The average of A is: (2 + 2 +3 +4 +5)/5 = 16/5
And the value "2" appears two times, so the mode is 2.
Now, let's try to find a data set B such that:
The mode is smaller than 2 (so for example, we can have a "1" that repeats two times)
The median is smaller than 3 (let's have a median equal to 2)
The average is larger than 16/5
The range is larger than 3
This is ratter simple:
B = {1, 1, 2, 6, 9}
The median of B is 2.
The mode of B is 1
The range of B is: 9 - 1 = 8
The average of B is: (1 + 1 + 2 + 6 + 9)/5 = 19/5
So, we just found an example for two data sets A and B such that A has a greater median and mode, while B has a greater average and range.
So the answer is yes, it is possible.
A dilation has center at the origin. Which of the following is the image of the point P(1.- for a scale
factor of
A
D: (P) = P(x3)
B
D}(P) = P',
C
D:(P) = P1C-
D
D}(P) = PG-)
Answer:
C. [tex]D_\frac{1}{7} (P)=P'(\frac{1}{4},-\frac{5}{14} )[/tex]
Step-by-step explanation:
[tex]\frac{7}{4}*\frac{1}{7}=\frac{7}{28} =\frac{1}{4}[/tex]
[tex]-\frac{5}{2} *\frac{1}{7} =-\frac{5}{14}[/tex]
Matthew has 5 1/4 bags of fertilizer to spread around his yard. Each bag of fertilizer will cover 115.4 ft 2. How many square feet will Matthew be able to cover if he uses all of the fertilizer?
Answer:
605.85 (ft 2)
Step-by-step explanation:
5 1/4 * 115.4 = 605.85 (ft 2)
Integration of ∫(cos3x+3sinx)dx
Answer:
[tex]\boxed{\pink{\tt I = \dfrac{1}{3}sin(3x) - 3cos(x) + C}}[/tex]
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]
Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx . Now , Rewrite using du and u .[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]
At the fair, 2 corn dogs and 3 pretzels cost $13, and 5 corn dogs and 6 pretzels costs $28. How much
would 2 pretzels and a corn dog cost??
A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tallman is walking towards the wall at the rate of 30 feet per second. How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall
Answer:
The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]
Step-by-step explanation:
Given - A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tall man is walking towards the wall at the rate of 30 feet per second.
To find - How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall ?
Proof -
From the given information, the figure becomes
Triangle ABC and Triangle DBE are similar triangle
AC/DE = BC/BE
⇒h/6 = 200/(200-x)
⇒h = 1200/(200 -x)
Now,
Differentiate h with respect to t, we get
[tex]\frac{dh}{dt} = 1200(-\frac{1}{(200-x)^{2} } )(-1)\frac{dx}{dt}[/tex]
⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-x)^{2} } )\frac{dx}{dt}[/tex]
Now,
If the rate of the tip is moving down the wall
At x = 50 feet, dx/dt = 30 feet per second
So,
⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-50)^{2} } )(30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)^{2} } (30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)(150) } (30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{24}{15 }[/tex]
So, we get
The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]
Log(10) u = 3/2 log(10) 4
u = 8
Step-by-step explanation:
log(10) u = log(10) 4^(3/2)
or
u = 4^(3/2)
= [sqrt(4)]^3
= (2)^3
= 8
find 3/5% of $90,000
Choose a method you prefer to solve for a system of linear equations.
2x + 4y = -4
2x-y=6
Answer:
Elimination
x = 2
y = -2
Step-by-step explanation:
Elimination
2x + 4y = -4
2x - y = 6
Subtract the second equation from the first
5y = -10
Divide both sides by 5
y = -2
---------------------
Substitute for y = -2 in the second equation
2x - -2 = 6
2x + 2 = 6
subtract 2 from both sides
2x = 4
Divide both sides by 2
x = 2
It Takes Mike 18 minutes to finish reading 4 pages of a book. How long does it take him to finisn reading 30 pages?
Answer:
135
Step-by-step explanation:
First, divide.
18 ÷ 4 = 4.5
Then, multiply.
4.5 × 30 = 135
Have a great day!
Please help me solve this problem
Answer:
72 in²
Step-by-step explanation:
lateral area: the surface area of a 3D figure, but excluding the area of any bases
the lateral area of this prism is the sum of the three rectangular sides.
calculate the third side of the triangle first because it's also the side of one of the rectangle:
√(5² - 4²) = 3
4 × 6 + 5 × 6 + 3 × 6 = 72
Help me out please???
If G is the incenter of ∆ABC, then GD = GF = GE.
Given, GD is 3x + 5 and GF is 6x - 4.
According to the above statement,
GD = GF
or, 3x + 5 = 6x - 4
or, 5 + 4 = 6x - 3x
or, 9 = 3x
or, 9/3 = x
or, 3 = x
The value of x is 3.
By putting the value of x in GD or GF, we get
GD = 3(3) + 5 = 9 + 5 = 14
GF = 6(3) - 4 = 18 - 4 = 14
Therefore, GE = 14.
The point (-8,0) reflected in the x-axis is
Answer:
That would be (8,0) my good sir ( ma'am )
Step-by-step explanation:
Have a nice day
Red Blue Yellow Green What is the probability of a player spinning the color blue and then rolling a 4?
A: 1/4
B: 1/24
C: 1/6
D: 1/16
Answer:
(1/4)×4=1/16
Step-by-step explanation:
Blue is 1 out of the 4 colours, it rolls for 4 times
Clark has two 16-ounce cans of corn. He uses 18 ounces of it to
make a corn soup and the rest to make a casserole.
a. How many ounces of corn did he use to make the casserole?
Answer:
14
Step-by-step explanation:
Answer:
14 Ounces
Step-by-step explanation:
16 x 2 = 32 Ounces of corn
32 - 18 = 14 Ounces
in a class of 24 students, how many different 3 person teams for a group project can the teacher make?
Answer:
The teacher can make 8 different 3 person teams
Step-by-step explanation:
Since there is a total of 24 students and the teacher wants to make as many 3 person groups as he/she can you would just do 24 divided by 3 which would equal 8 different teams of 3 people. So the teacher can make 8 different groups of 3 people
If using the method of completing the square to solve the quadratic equation x2+14x-14=0, which number would have to be added to "complete the square"?
Answer:
49
Step-by-step explanation:
the number would simply be
14÷2=7
7²=49
can someone help me.?!
[tex]{\boxed{\mathcal{\red{h\:=\:9.5}}}}[/tex] ✅
Step-by-step explanation:-[tex]h + \frac{1}{2} = 10 \\ ⇢ h + 0.5 = 10 \\ ⇢ h \: = 10 - 0.5 \\ ⇢ h = 9.5[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
can someone please help I will do anything
Answer:
678.24 cubic centimeters
Step-by-step explanation:
What is the coefficient in this equation? 140 - 6 = 28
Answer:
There is none there is no variable.
Step-by-step explanation:
Hope this helps!!
Answer:
there is no co efficient a co efficient is the constant before the variable when its attached.
You went to a bake sale and bought a whole bunch of
yummies!
Cookies were $1 and Brownies were $2. You spent
$13 total.
What are three combinations of cookies and brownies
that you could have gotten?
Write an equation that represents this situation.
Answer:
If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y
∴ $1*(x*1) + $2*(y*1) = $13
Step-by-step explanation:
1) You can buy 4 brownies for $2 each = 2*4 = $8
The rest you can buy cookies = 5 cookies = $5
$8+$5=$13
2) You can buy 5 brownies and 3 cookies = $10+$3 = $13
3) You can buy 3 brownies and 7 cookies = $6+$7=$13
Equation: -
If cookies are for $1 and brownies are for $2, let number of cookies = x and number of brownies = y
∴ $1*(x*1) + $2*(y*1) = $13
find the mean, median, mode, and range of the data 10, 13, 7, 6, 9, 4, 6, 3, 5
Find the quotient for 5,600÷8
Answer:
700
Hope this helps!!
Answer:
700
Step-by-step explanation:
if 3/5 of a number is 2 more than 2/3 of the same number, then what is the value if the square of the number
9514 1404 393
Answer:
900
Step-by-step explanation:
Let x represent the number. The given relationship is ...
(3/5)x = 2 +(2/3)x
-2 = 1/15x . . . . . . . . subtract 2+3/5x from both sides
-30 = x . . . . . . . . . . multiply by 15
Then the square of the number is ...
x² = (-30)² = 900
A rectangular room is 11 feet by 14 feet. The ceilings are 9 feet high. If a gallon of paint covers 250 square feet. How many gallons of paint are needed to paint the room?
Answer:
3 gallons or 3.032
Step-by-step explanation:
find the total surface area (758)
divide by 250 or subtract 250 till it is under that number
Which expression has a value of 7/12?
1. 2 1/12 + 5 1/12
2. 6/8 + 1/4
3. 1/3 + 1/4
4. 7/8 + 4
Answer: 3. 1/3 + 1/4
Step-by-step explanation:
1/3 = 4/12
1/4 = 3/12
4/12 + 3/12 = 7/12
What value(s) for n will make this expression true?
3.5 and -3.5
3.5 only
nl = 3.5
0 and 3.5
-3.5 only
just need a bit of help
Answer:
35A) arc AC = 360-(100+110+80)=
360-290 = 70°
35B) L D = ½× 70 = 35°
35C) L AEC = ½(100+70)=½×170= 85°
35D) L P = ½(100-70) = ½×30 = 15°
If 2x + 5 = 82, then 12x = ?
A 5
B
10
C 15
D 20
Answer:
2x= 38.5
Step-by-step explanation:
I'm not sure where u got 12x but 2 x = 38.5:
2x + 5 =82
subtract 5 for 82
2x = 77
77 divided by 2 is 38.5
x = 38.5
hope this helps :)
URGENT... please help
7.
Reason The dot plot shows the numbers of pages students
in a class read during their dedicated reading time.
A. How many students are in the class?
B What percent of students read more than 6 pages?
Explain your reasoning
Pages Read During
Dedicated Reading Time
What fraction of the students read less than 5 pages?
D. How many total pages did all of the students read? Show your work
id speaker notes
Step-by-step explanation:
7equitacion h< y ⚽ de los siguientes dominios