To answer this question, first we need to properly understand the definition of median and mean, and also understand what it means to be "roughly symmetrical".
Let's start with the definition of median.
"the median is the value separating the higher half from the lower half of a data sample"
If we have an odd amount of elements in our dataset, the median is literally the middle element of our set.
Example:
[tex]\lbrace1,1,1,2,3,4,7,10,52\rbrace[/tex]We have four elements below 3, and four elements above 3, therefore, the median of this dataset is 3.
If we have an even amount of elements, the median is the mean between the two elements in the middle.
Example:
[tex]\lbrace1,1,1,1,2,2,7,15\rbrace[/tex]The elements in the middle are 1 and 2. This means our median is
[tex]\frac{1+2}{2}=1.5[/tex]1.5.
Now, let's understand the mean.
By definition, The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers, given by the sum of all elements divided by the amount of elements.
Examples:
[tex]\begin{gathered} \lbrace1,2,3\rbrace \\ \bar{x}=\frac{1+2+3}{3}=2 \\ \lbrace1,1,3,5,7,9,9\rbrace \\ \bar{x}=\frac{1+1+3+5+7+9+9}{7}=5 \end{gathered}[/tex]Now that we know what mean and median exactly are, let's try to understand what it means to be "roughly symmetrical".
When talking about histograms, Close to symmetric means the data are roughly the same in height and location on either side of the center of the histogram.
As the histogram gets closer to symmetric, the mean approaches the middle values, to be more specific, If the histogram is close to symmetric, then the mean and median are close to each other.
Since the statement says "roughly symmetrical" this is the only thing we can claim. If we have more values to the right in our roughly symmetrical distribution, the mean will be a little bit bigger than then median, and if we have more values to the left in our roughly symmetrical distribution, the mean will be a little bit smaller than then median.
Write (9m) to the power of 4 without exponents.
6561m⁴ is the value of the expression (9m)⁴ without applying the exponent property.
What is an exponent?
The type of mathematical shorthand known as exponential notation enables us to write complex expressions more concisely. The base, which can be either a number or letter, is an exponent. It implies that the base is to be raised to a specific level of power. While n is the power, X is the base.
The expression is (9m)⁴.
The value of the expression (9m)⁴ without applying the property of the exponent will be
→ 9m × 9m × 9m × 9m
(we've simply expanded (9m)⁴ )
which on further simplifying gives,
→ 6561m⁴
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Alex is fourteen years old and he is also nine years older than his sister Kristen. How old is Kristen?
Answer:
5
Step-by-step explanation:
If Alex is 14 and he's 9 years older than his sister Kristen,then Kristen is 5
14-9=5
Answer:
14-9 = 5, so Kristen is 5 years old
Orlando makes a trail mix for his hiking trip. He uses 1 \frac{5}{6}1 6 5 pounds of cashews, 1.6 pounds of sunflower seeds, 1 \frac{1}{8}1 8 1 pounds of raisins, and 1.625 pounds of pecans. Which answer choice shows these weights in order from least to greatest ? DUE TODAY NEED NOW WILL GIVE BRAINLIEST PART OF TEST REALLY NEED
An answer choice shows these weights in order from least to greatest is:
1 1/8 pounds of raisins.1.6 pounds of sunflower seeds.1.625 pounds of pecans.1 5/6 pounds of cashews.What is a numerical data?A numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.
In order to arrange the given numerical data (weights) in order from least to greatest, we would convert the fractions into a decimal number as follows:
1 5/6 pounds of cashews = 11/6 = 1.8333 pounds.1.6 pounds of sunflower seeds = 1.6 pounds.1 1/8 pounds of raisins = 9/8 = 1.125 pounds.1.625 pounds of pecans = 1.625 pounds.Now, we can arrange the numerical data in order from least to greatest based on the weight of each item:
1.125 pounds = 1 1/8 pounds of raisins.1.6 pounds = 1.6 pounds of sunflower seeds.1.625 pounds = 1.625 pounds of pecans.1.8333 pounds = 1 5/6 pounds of cashews.Read more on greatest numbers here: brainly.com/question/24654699
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Aaden has a bag that contains strawberry chews, apple chews, and watermelon
chews. He performs an experiment. Aaden randomly removes a chew from the bag,
records the result, and returns the chew to the bag. Aaden performs the experiment
31 times. The results are shown below:
A strawberry chew was selected 4 times.
A apple chew was selected 7 times.
A watermelon chew was selected 20 times.
Based on these results, express the probability that the next chew Aaden removes
from the bag will be a flavor other than apple as a fraction in simplest form.
The probability that the next chew Aaden removes from the bag will be a flavor other than apple is 24/31.
What is Probability?Probability is a branch of mathematics concerned with determining the likelihood of an event occurring. Probability assesses the likelihood of an event occurring and is equal to the number of favorable events divided by the total number of events.
Given:
Number of times Aaden performs the experiment = 31 times
A strawberry chew was selected 4 times.
An apple chew was selected 7 times.
A watermelon chew was selected 20 times.
So,
Probability of selecting a strawberry chew = 4/31
Probability of selecting an apple chew = 7/31
Probability of selecting a watermelon chew = 20/31
So, the probability that the next chew Aaden removes from the bag will be a flavor other than apple i.e. it can be strawberry or watermelon chew.
Probability of selecting a strawberry chew + Probability of selecting a watermelon chew
= 4/31 + 20/31 = 24/31
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Answer:
24/31
Step-by-step explanation:
Based on these results, express the probability that the next chew Aaden removes from the bag will be a flavor other than apple as a fraction in simplest form.
The experiment occurred 31 times, a flavor other than apple was selected 4+20=24 times. Probability the next chew will be a flavor other than apple:
24/31
=
The probability as a fraction in simplest form is
24/31
(02.05 MC)
Given f(x) and g(x) = f(kx), use the graph to determine the value of k.
-3
-1/3
1/3
3
Using the graph obtained value of k is 1/3. Option C is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that
f(x) and g(x) = f(k-x),
The standard equation of a line is,
y = mx + b
The slope of the line for the coordinate points are (1, 2) and (1.5, 5)
m = 5-2/1.5-1
m = 3/0.5
m = 6
The y-intercept of the line is,
2 = 6(1) + b
2 - 6 = b
b = -4
As a result the obtained equation is g(x) = 6x - 4
For the other coordinate point (3, 2) and (2, 0), the slope is
m = 0-2/2-3
m = -2/-1
m = 2
The y-intercept of the line is,
2 = 2(3) + b
2 - 6 = b
b = -4
As a result the obtained equation will be f(x) = 2x - 4.
Substitute xk at the place of x in the function as
f(xk) = 2(xk)- 4
If g(x) to f(k⋅x)
6x + 4 = 2(xk)- 4
6x = 2xk
6 = 2k
k = 1/3
Thus, using the graph obtained value of k is 1/3. Option C is correct.
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INEED HELP NOW PLS HELP IVE GIVEN EXSAMPlES AND I NEED SNSWeRS With work to it
1) 20 percent of 60 is 12
2) 25 percent of 24 is 6
3) 4 percent of 600 is 24
4) 88 is 110 percent of 80
5) 18 is 20 percent of 90
What is percentage ?To calculate the proportion of value to the original value, the percentage concept is employed. For calculating a company's profit or loss percentage , percentages are frequently employed in business. Additionally, it's a common way for universities and schools to display the grades that pupils have earned. An estimation of the pupils' grades can be made using a percentage calculation. A ratio of any value to the total value multiplied by 100 is how percentages are typically defined. The percentage is shown as % in symbols.
1) [tex]\frac{20}{100}[/tex]×x=12
x=[tex]\frac{1200}{20}[/tex]
x = 60
2) x ×[tex]\frac{24}{100}[/tex] = 6
x=25%
3)[tex]\frac{4}{100}[/tex]×600 = 24
4) [tex]\frac{110}{100}[/tex]×x = 88
x =[tex]\frac{8800}{110}[/tex]
x= 80
5) [tex]\frac{x}{100}[/tex]×90 = 18
x = 20
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The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator. PLEASE HELP ASAP
Answer:
[tex]2\sqrt{2}[/tex]
Step-by-step explanation:
x^2+x^2=16
x^2=8
x= 2sqrt2
:]
I l over here and I have no idea
The diagram shows an intersection of roads. Identify all supplementary, complementary, and vertical angles.
Fast please!!!
Answer:
Supplementary: 2,3
Complementary: 1,4,5
Vertical Angles (VA): 1 is equivalent to 4
Step-by-step explanation:
Supplementary angles are angles that equal up to 180 degrees.
Complementary angles are angles that are 90 degrees.
VA (Vertical Angles) are angles that are basically across from other (take a look at 1 and 4) AND NO, 2,3 or 5 would be considered as Vertical angles as they do not Aline.
a triangle with a base of 6cm has an area of 30cm squared. What is its perpendicular height?
The area of a triangle is 1/2bh. We know the area, a, the base, b, and we are attempting to find the height, h. So, we simplify the area formula with the value of b and solve for h, given a.
1/2(6)h = 30
3h = 30
Isolate h.
3h/3 = 30/3
h = 10
Mr majors ordered 6 boxes of candy and a bucket of pop corn at the concession stand. if the pop corn was $3.20 and the total was $18.20, what was the price of one candy box
The price of one candy box was $2.50 if the popcorn were of $3.20 and the total amount was $18.20.
The price of one candy box can be determined using an algebraic expression. An algebraic expression can be defined as one that consists of both numbers and letters.
As he ordered 6 boxes of candy and a bucket of popcorn and the popcorn was of $3.20 and the total was $18.20, an algebraic expression can be given as;
6(x) + 3.20 = 18.20
Here x is the price of one candy box
Solving for x;
6x = 18.20 - 3.20
6x = 15
x = 15 / 6
x = 2.50
Hence the price of one candy box is calculated to be $2.50.
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The graph of an exponential function has a y-intercept of 9 and contains the point (2,144). Construct the function that describes the graph.
The graph of an exponential function has a y-intercept of 9 and contains the point (2,144). the function that describes the graph.
y=9(4)^x
This is further explained below.
What is the function that describes the graph.?Generally, the Standard form of an exponential function
y=a b^x
Where
y= is the y component of the graph
x= is the x component of the graph
a and b are equation vaiables
Given the y-intercept (0,9) and the point (2,144) Applying both.
a=9,
144=9 b^2
Solve further by making b the subject of formular
b^2=144/9
b^2=16
b[tex]= \sqrt{ 16}[/tex]
Therefore b=4
So, y=9(4)^x
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Dominique paid $15.50 to join an online music service. She purchases 10 songs each month at a cost of $0.99 per song. Dominique thinks that after 8 months, she will have spent around $75.00 total. Is Dominique's estimate reasonable?
If she thinks that after 8 months, she will have spent around $75.00 total. Dominique's estimate is not reasonable?
Determining whether the estimated amount is reasonableWe have to make use of the given data to find whether amount of $75 which she estimated that she will spent after 8 months is reasonable
Total cost:
Total cost =$15.50 + 10 × $0.99 × 8
Total cost = $15.50 + 9.9 × 8
Total cost = $15.50 +$79.2
Total cost = $94.7
Hence,
$94.70 ≥ $75.00
Based on the above calculation the amount she estimated is not a reasonable amount because the total cost is greater that the estimated amount.
Therefore we can conclude that the estimate is unreasonable.
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The estimate of the Dominique's is not reasonable.
Given that,
Dominique paid $15.50 to join an online music service. She purchases 10 songs each month at a cost of $0.99 per song. Dominique thinks that after 8 months, she will have spent around $75.00 total. Is Dominique's estimate reasonably is to be justified.
Here,
According to the question,
The total cost of the song for 8 months = 8 (0.99 x 10)
= $ 79.2
Total cost = 15.50 + 79.2 = $94.7
Since the total cost exceeds Dominique's estimate so her estimate is not reasonable.
Thus, the estimate of the Dominique's is not reasonable.
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What equation could be used to solve the problem below?
If three times a number is increased by 24, the result is 4 less than seven times the number.
"Every angle subtended at the circumference of a semicircle by the diameter is a roght angle." Which other circle theorem proves this?
The angle subtended by an arc is twice the angle it subtends.
The angle is 90 degrees.
What is diameter of circle?
diameter is circle is twice the radius of circle.
The theorem to solve the given statement is :
The angle subtended by an arc is twice the angle it subtends.
let suppose, O be the center of circle,
The diameter AB forms on the circle and point P on the periphery of circle ,
so we have:
To prove : ∠APB=90°
We know that angle subtended by an arc at center is double the angle subtended at any point or circumference.
that is:
Angle subtended by arc AB at O = Double the angle subtended at P
⇒∠AOB=2∠APB
∵AOB is a straight line.
∠AOB=180°
2∠APB=180°
∠APB=90°
Angle formed by arc AB or semi circle is 90°
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I messed up and didn’t show this for my last question, so sorry on my part.
Evaluate the function for the following values
f(-2)=
f(0)=
f(3)=
Answer:
1 , 7 , 7
Step-by-step explanation:
to evaluate f(- 2) means what is the value of y when x = - 2
locate x = - 2 on the x- axis , go vertically up to meet the graph at (- 2, 1)
f(- 2) = 1
similarly
f(0)
locate x = 0 , at the origin, go vertically up to meet the graph at (0, 7 )
f(0) = 7
f(3)
locate x = 3 on the x- axis , go vertically up to meet the graph at (3, 7 )
f(3) = 7
the difference of the squares of two positive integers is 325 and their difference is 3. what are the numbers
Answer:
figure it out best of luck tho.
A farmer needs to enclose three sides of a garden with a fence (the fourth side is a river). The farmer has
30 feet of fence and wants the garden to have an area of 108 sq-feet. What should the dimensions of the
garden be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides);
the length with be the longer dimežision (needing one side). Additionally, the length should be as long as
possible.)
length×width = 108
length + 2×width = 30
length = 30 - 2×width
using that in the first equation
(30 - 2×width)×width = 108
-2×width² + 30×width - 108 = 0
the general solution to such a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
so,
width = (-30 ± sqrt(30² - 4×-2×-108))/(2×-2) =
= (-30 ± sqrt(900 - 864))/-4 =
= (-30 ± sqrt(36))/-4 = (-30 ± 6)/-4
width1 = (-30 + 6)/-4 = -24/-4 = 6 ft
width2 = (-30 - 6)/-4 = -36/-4 = 9 ft
for width = 6 ft
length = 30 - 2×width = 30 - 12 = 18 ft.
for width = 9 ft
length = 30 - 2×width = 30 - 18 = 12 ft
given the request that the length sound be as long as possible,
width = 6 ft
length = 18 ft
is our solution.
solve for x
3/4=x-4/6
simply as much as possible
The value of x is 17/12.
Given equation:-
3/4 = x - 4/6
We have to find the value of x from the given equation.
Rearranging the terms to find the solution, we can write,
x = 3/4 + 4/6
Least Common Multiple (LCM) of 4 and 6 = 12
Hence, we can write,
x = (3*3) + (2*4)/12
x = (9 + 8)/12
x = 17/12
Least Common Multiple (LCM)
In arithmetic, Least Common Multiple (LCM) of two or more numbers is the least positive number that can be divided by both the numbers, without leaving the remainder. It is also known as Lowest Common Multiple (LCM), Least Common Denominator, and Smallest Common Multiple.
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at a certain college there are twice as many english majors as history majors and three times as many english majors as mathematics majors. what is the ratio of the number of history majors to the number of mathematics majors?
The ratio of the number of history majors to the number of mathematics majors is 3 to 2.
When two objects are related using numbers or amounts, the relationship is known as a ratio.
Let E be the number of English majors, H be the number of history majors, and M is the number of math majors.
Now,
There are twice as many English majors as history majors.
E = 2 × H
There are three times as many English majors as mathematics majors.
E = 3 × M
Now, let's assume E = 6.
Then,
6 = 2 × H
H = 3 and,
6 = 3 × M
M = 2
Therefore, the ratio of the number of history majors to the number of mathematics majors will be:
H: M = 3 : 2
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Calculate the height of a pyramid if the volume is 168 cm³ and the area of the base in 36 cm².
V
=
Bh, V = volume, B = area of the base, h = height
The volume of a pyramid is v = 1/3base area × height
height = 3volume/ base area
height = 3×168cm^3/ 36cm^2
height = 14cm
What is a pyramid?A pyramid is a three-dimensional shape. It has a flat polygon base. All the other faces are triangles which are called lateral faces. The number of lateral faces equals the number of sides on its base.
The volume of a pyramid is given by
v= 1/3base area × height
= 3×168 = 36h
therefore the height =3x168/36
= 14cm
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PLEASE HELP I LITERALLY HAVE 10 MINUTES!! 40 POINTSSS
The graph that matches the data on the table, representing the altitude and time of a hawk is the straight line graph in the second option.
What is a straight line graph?A straight line graph is the graph of a linear function or relationship
From the he values in the given, we have;
The difference between the consecutive altitude values (the first difference) = 70 - 80 = 60 - 70 = 50 - 60 = -10 is constant
The difference between consecutive time values = 1
Therefore;
The relationship is a linear relationship and the graph is a straight line.
Slope of the graph = -10/1 = -10
The equation in point and slope form is therefore;
(y - 80) = (-10) × (x - 1) = -10•x + 10
(y - 80) = -10•x + 10
y = 80 + 10 - 10•x = 90 - 10•x
y = 90 - 10•x
The y–intercept = 90
The slope = -10
The correct option is therefore the second graph that has the altitude (ft) on the the vertical axis and the time (s) on the horizontal axis, with a straight line decreasing from left to right starting at the point (0, 90) on the left
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A ring is now reduced to £840.
This is a saving of 40% of the original price.
b) Work out the original price of the ring.
Answer:
The original price was $864
Step-by-step explanation:
if the ring is now $840 $40 u do $40 - %40 = %24
$24 + $840 = $864
PLEASE HELP DUE IN A FEW MINUTES! THANK YOU!!
Step-by-step explanation:
5 - (-7) = 5 + 7
because 2 negatives added together make positive.
Answer:
+ 7
Step-by-step explanation:
the rule of signs for addition/ subtraction
a + (- b ) = a - b
a + (+ b) = a + b
a - (+ b) = a - b
a - (- b) = a + b
Then
5 - (- 7 ) = 5 + 7
Wendy is paid $9 per hour and plans to work between 20 and 25 hours per week. Identify the independent and dependent quantity in the situation. Find reasonable domain and range values.
The domain of the given question is; 20 to 25.
If she is paid $9 per hour, the range is; $180 to $225.
How to find the domain and range?The independent quantity is defined as the quantity that causes a change in the dependent quantity.
Now, In this question, the defined quantities are hours worked and weekly pay. Applying the concept of independent and dependent quality, the number of hours she works causes her weekly pay to change. This means that hours worked is the independent quantity and weekly pay is the dependent quantity.
We are told that she plans to work between 20 and 25 hours. This means that;
The domain is 20 to 25.
Now, as she is paid $9 per hour, this makes the range;
9(20) = $180 to 9(25) = $225.
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If f(x) = (x^2 - 4)/(x + 2), find f(- 1)
Please work it out or explain how you got answer!!! I’ll mark brainliest!
Answer:
-3
Step-by-step explanation:
f(x) = (x^2 - 4)/(x + 2)
Substituting x = -1,
f(-1) = (1 - 4)/(-1 + 2)
f(-1) = -3
PLEASE HELP IMMEDIATELY
What is the equation of the line that passes through Point (-2, 1) and has a Slope of 1.
Answer:
[tex]y=x+3[/tex]
Step-by-step explanation:
Using Point-Slope form: Y-y1=m(X-x1)
Slope(m) = 1, Point(x1,y1) = (-2,1)
y-1=1(x+2)
y=x+2+1
y=x+3
:]
(ps. Brainliest would be greatly appreciated lol)
Step-by-step explanation:
1.given gradient (slope) make formula of straight line
[tex]y = 1x + c[/tex]
2.substitute in y and x values in order to work out c
[tex]1 = 1( - 2) + c[/tex]
[tex]c = 3[/tex]
3. equation of line is
[tex]y = 1x + 3[/tex]
5÷6?what is it long division picture please
The solution is ; 5/6 = 0.833... (recurring decimal)
I need help so I get good grades
Answer: 9
Step-by-step explanation:
I am assuming that the grid units equal 1 inch.
We have to solve for x. For the width,
60 = 20/3 x
To divide by a fraction is to multiply by its reciprocal.
x = 60 * 3/20 = 180/20 = 9
A new minivan costs $24,897. About how much would 4 minivans cost?
Answer: about $100,000.
Step-by-step explanation: i gave an estimate because your answer calls for an estimate, not an exact answer. $100,000 is correct because 24,897*4 = 99,588.
Juniper has a monthly budget that breaks down as follows 40% for rent 15% for food 18% free utilities 15% for savings for person for entertainment and 8% for personal items juniper has a net income of 3,250 each month calculate the amount of money that juniper has each month for rent
Juniper spends $1300 out of the monthly income of $3250 on rent
Total income of Juniper = 3250 each month
Income is the money that an individual or organization receives in return for their services or goods. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.
Percentage of expenditure on rent = 40%
Percentage of expenditure on food = 15%
Percentage of expenditure on utilities = 18%
The percentage for savings = 15%
Percentage of expenditure for personal items = 8%
Money Juniper spends on rent each month out of total income:
= Income per month*40%
3250*40%
= $1300
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