The quartiles of each data set are explained below.
How to Find the Quartiles of a Data Set?To find the quartiles of a data set, first ordered the data. Thereafter, determine the following:
First quartile (Q1): the middle value of the first half of the dataSecond quartile (Q2): The center value that divides the data set into equal halves.Third quartile (Q3): The middle value of the second part of the data.1. Order the data set, 4, 6, 5, 6, 2, 7, 6, 8:
2, 4, 5, 6, 6, 6, 7, 8
The center of the data is between 6 and 6. Therefore, the middle = (6 + 6)/2 = 6. This means the median or second quartile = 6
Middle value of the first part of the data = (4 + 5)/2 = 4.5.
Middle value of the second part of the data = (6 + 7)/2 = 6.5
First quartile = 4.5
Second quartile = 6
Third quartile = 6.5
The same way we will also find the quartiles of the other given data set as stated below.
2. For 17, 14, 20, 29, 12, 24, 10, 19, we have:
First quartile = 13
Second quartile = 18
Third quartile = 22
3. For 68, 88, 44, 68, 50, 68, 37, 50, we have:
First quartile = 47
Second quartile = 59
Third quartile = 68
4. For 52, 60, 24, 36, 48, 52, 72, we have:
First quartile = 36
Second quartile = 52
Third quartile = 60
5. For 102, 78, 312, 170, 250, 40, 52, 38, 125, we have:
First quartile = 46
Second quartile = 102
Third quartile = 210
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Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent.
Continent Number of cities
Europe 101010
Asia 888
Africa 444
Australia 333
How many different combinations of cities does Elyse have to choose from
Elyse has the option of combination of 960 cities, or another to choose from. If Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit.
Define permutation and combination.Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.
Given,
Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent.
To determine how many options Elyse will have, we use permutations and combinations.
We can say that she has a choice of any of the eight cities in Asia for every ten cities in Europe. Similar to how she can select any of the 4 cities in Africa for every 8 cities in Asia. The same is true for Australia and Africa.
Elyse has a choice of a total:
10×8×4×3
960
Elyse has the option of combination of 960 cities, or another.
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what is the answer for 3(m+5)-2(-9+m)=29
solving for m
distribute into parentheses
3m + 15 + 18 -2m = 29
simplify
m + 33 = 29
subtract
m = -4
verify
3(-4+5) -2(-9-4) = 29
3 + 26 = 29
29 = 29
true
m = -4
hope this helps :)
jeron
Pls helpp i really need help pleaseee
Answer:
P/mh
Step-by-step explanation:
P = mgh to solve for g Divide both sides by mh
[tex]\frac{P}{mh}[/tex] = [tex]\frac{mgh}{mh}[/tex] On the right side of the equation the m and h cancel out and you are left with
[tex]\frac{P}{mh }[/tex] = g
12. How much tax would I pay on a Nintendo Wii (cost of $150) if the tax is 8%?
Answer:
$162
Step-by-step explanation:
8% of 150 = 12 + 150
Which shape DOES NOT have the same perimeter as the other shapes?
Measure the angles of ABC and its three images, and record the measurements in the table. Round each answer to the nearest degree.
Type your response here:
ABC
Measure
A'B'C'
Measure
A'1B'1C'1
Measure
A'2B'2C'2
Measure
ABC
A'B'C'
A'1B'1C'1
A'2B'2C'2
ACB
A'C'B'
A'1C'1B'1
A'2C'2B'2
CAB
C'A'B'
C'1A'1B'1
C'2A'2B'2
The approximate measures of the angles of ΔABC and the images formed by translation, reflection, and rotation of ΔABC, which are rigid transformations are;
ΔABC [tex]{}[/tex] ΔA'B'C' ΔA''B''C'' ΔA'''B'''C'''
∠A = [tex]{}[/tex] 22° ∠A' = 22° ∠A'' = 22° ∠A''' = 22°
∠B = [tex]{}[/tex] 120° ∠B' = 120° ∠B = 120° ∠B''' = 120°
∠C [tex]{}[/tex] = 38° ∠C' = 38° ∠C = 38° ∠C''' = 38°
What is a rigid transformation?A rigid transformation, also known as congruence transformation, in geometry, is one in which the length of the pre-image is preserved, such that the image and the pre-image have the same side lengths, and are therefore congruent.
The coordinates of the vertices of triangle ΔABC, obtained from a similar question online are;
A(-6, -1), B(-3, -3), C(-1, -2)
The lengths of the sides of triangle ΔABC are;
AB = √((-3 - (-6))² + (-3 - (-1))²) = √(13)
BC = √((-1 - (-3))² + (-2 - (-3))²) = √5
AC = √((-1 - (-6))² + (-2 - (-1))²) = √(26)
The law of cosines can be used to fined the measure of an angle of the triangle as follows;
Let a represent the side BC, let b represent the side AC, and let c represent the side AB, the formula for the law of cosines is presented as follows;
a² = b² + c² - 2·b·c·cos(A)
Where;
∠A = The angle at the vertex A
Therefore;
(√5)² = (√(26))² + (√(13))² - 2 × √(26) × √(13) × cos(A)
5 = 26 + 13 - 2 × √(26) × √(13) × cos(A)
cos(A) = (5 - (26 + 13))÷ (-2 × √(26) × √(13))
∠A = arccos((5 - (26 + 13))÷ (-2 × √(26) × √(13))) ≈ 22°
Similarly, we get:
cos(B) = (26 - (5 + 13))÷ (-2 × √(5) × √(13))
∠B = arccos((26 - (5 + 13))÷ (-2 × √(5) × √(13))) ≈ 120°
cos(C) = (13 - (26 + 5))÷ (-2 × √(5) × √(26))
∠C = arccos((13 - (26 + 5))÷ (-2 × √(5) × √(26))) ≈ 38°
The transformation from ΔABC to ΔA'B'C', obtained from a similar question online, is a translation 5 units to the right and 2 units up
The transformation from ΔA'B'C' to ΔA''B''C'' is a reflection across the line y = -x
The transformation from ΔA''B''C'' to ΔA'''B'''C''' is a counterclockwise rotation by 270° about the origin
The translation, reflection, and rotation transformations are rigid transformations, such that the shape and sizes of the pre-images are preserved, and we get;
[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\Delta ABC &Measure & \Delta A'B'C' &Measure & \Delta A''B''C'' & Measure & \Delta A'''B'''C''' & Measure \\\angle ABC & 120^{\circ} & \angle A'B'C' & 120^{\circ} &\angle A''B''C'' &120^{\circ} &\angle A'''B'''C''' &120^{\circ} \\\angle ACB &38^{\circ} & \angle A'C'B' & 38^{\circ} &\angle A''C''B'' &38^{\circ} &\angle A'''C'''B''' &38^{\circ} \\\\end{bmatrix}[/tex]
[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\Delta ABC &Measure & \Delta A'B'C' &Measure & \Delta A''B''C'' & Measure & \Delta A'''B'''C''' & Measure \\\angle CAB & 22^{\circ} &\angle C'A'B' & 22^{\circ} &\angle C''A''B'' &22^{\circ} &\angle C'''A'''B''' &22^{\circ} \end{bmatrix}[/tex]
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need help on these math questions
The evaluation of the table, equations, and graphs in the question are as follows;
First question;
Part A; The table does not represent a function
Part B; The value of f(300) is $123 represents the total cost for driving 300 miles
Second question;
Part A; The equation is; y = -2·x + 8
Part B; The graph can be obtained by finding the ordered pair of values for the first five hours and plotting the result on a graph, to form a straight line graph.
Third question;
Part A; The solution is; (2, -1)
Part B; Two solutions for f(x) are; (1.5, 0) and (0, 3)
Part C; The solution for the equation, g(x) = f(x) is the point (0, 3)
What is a function?A function is rule, law or expression that maps the elements of one set A unto the elements of another set B such that each element of the set A maps unto exactly one element of the set B.
First question;
Part A: The value of x = 4 has two values of y = 2, and -2
The value of x = 9 has to values of output, y = 3 and -3
The function therefore is; y = f(x) = ±√x
The above function indicates that a value of x returns two values of y, which indicates that a vertical line drawn through the graph of the function f(x) = ±√x intersects the graph twice for values of x > 0, therefore, the equation, f(x) = ±√x, represented by the values in the table is not a function
Part B: The function for the total cost of driving a car is f(x) = 90 + 0.11·x
Where; f(x) = The total cost in dollars
x = The distance the car is driven in miles
Therefore, f(300) is obtained by plugging in x = 300 as follows;
f(300) = 90 + 0.11 × 300 = 123
The value of f(300) = $123
f(300) represents the total cost of driving the car for 300 miles
Second question set;
The velocity of the runner after one hour = 6 km/h
The velocity of the runner after three hours = 2 km/h
Part A: The ordered pair of points of the function are; (1, 6) and (3, 2)
Making use of a linear model, we get;
Slope of the equation of the model, m = (2 - 6)/(3 - 1) = -2
The equation of the model is therefore; y - 6 = (-2) × (x - 1) = -2·x + 2
y = -2·x + 2 + 6
y = -2·x + 8
Where: y = The speed of the runner
x = The number of hours the runner has been running
Part B:
The graph of the equation can be plotted from the values of y obtained from the corresponding values of x for the first 5 hours as follows;
[tex]\begin{array}{|c|c|}x & y \\1 & 6 \\2 & 4\\3 & 2 \\4 & 0 \\5 & -2\\\end{bmatrix}[/tex]
Please find attached the graph of the velocity of the runner with time created using the above table of values found with MS Excel
Third Question;
Part A; The solution to pair of equation can be found from the point of intersection of their graphs
Therefore, the solution of the pair of equations represented by p(x) and f(x) is the point of intersection of the graph of f(x) and p(x), which is the point (2, -1)
Part B; Two solutions for the function f(x) can be obtained by the point of intersection of the x- and y-axis as follows;
The x-intercept of f(x) = (1.5, 0)
The y-intercept of f(x) = (0, 3)
Part C; The solution for g(x) = f(x), is the point of intersection of g(x) and f(x), which is the point (0, 3)
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A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water. What is the velocity of the boat relative to shore?
The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
Define velocity.The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity. Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. The rate of change of displacement is known as velocity. The rate at which velocity changes is called acceleration. Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. As the rate at which velocity changes, acceleration is likewise a vector quantity.
Given
A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
Velocity,
v = √(1.65)² + (10.7)²
v = √2.722 + 114.49
v = √117.212
v = 10.82
The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.
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Help pls i need it
Determine which integer will make the inequality 2(n + 1) ≤ 3(n − 2) true.
S:{0}
S:{4}
S:{6}
S:{8}
Please help you get 100 points and brainly
You have points R(2, 10) and S(6, - 8).
There two ways to construct a right triangle with RS being a hypotenuse.
Please see both ways reflected in the attached.
One triangle is RST and another one is RSU with red or blue legs.
I need help with my math homework
Answer: for the first one, the one that says 7 x 5 = 5 x 7, as the blank is 7.
for the second one, 10 x 11 = 11 x 10, the blank is 10
for the third one, which is Julia's candy, draw 6 pieces of candy in each box and do 4 x 6, which is 24 pieces of candy [4 being the amount of bags].
for the fourth one, draw 5 pieces of candy in each box, then do 5 x 6 = 30.
for the fifth one, it is 4 x 6 = 6 x 4
for the final box, it is 5 x 6 = 6 x 5
Step-by-step explanation:
math
Answer: Hope this helps..
Step-by-step explanation:
7 * 5 - 5 = 30
10 * 11 - 11 = 99
For the candy questions the answers are:
Julia has 24 pieces of candy.
Tommy has 30 pieces of candy.
The equation for Julia is: 4 * 6 = 24
The equation for Tommy is: 5 * 6 = 30
olve the equation 2x + 3y = 5 for x.
A. x equals negative 3 times y plus 5 over 2
B. x equals negative 3 over 2 times x plus 5
C. x equals the quantity negative 3 times y plus 5 end quantity over 2
D. x equals the quantity 3 times y plus 5 end quantity over 2
By solving a linear equation, it can be calculated that
x = [tex]\frac{-3y + 5}{2}[/tex]
Option A is correct
What is a linear equation?
At first, it is important to know about algebraic expression.
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
Now we need to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Linear equation is a very important tool in mathematics
The given linear equation is
2x + 3y = 5
Now,
2x + 3y = 5
2x = -3y + 5
x = [tex]\frac{-3y + 5}{2}[/tex]
Option A is correct
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MATHEMATICAL CONNECTIONS Solve a system of linear equations to find the values of x and y.
The values of x and are 28° and 58° respectively
How to determine the valuesIt is important to note the properties of a trapezium;
Bases are parallel to each otherAdjacent interior angles sum up to 180°Sum of all the interior angles is 360°Length of both diagonals are equalDiagonals intersect each otherWe then have that;
2y + (y + 6) = 180
4x + 2x + 12 = 180
From equation (1), we have;
3y + 6 = 180
collect like terms
3y = 180 -6
3y = 174
y = 58°
From equation (2), we have;
6x = 180 -12
6x = 168
x = 28°
Hence, the values are 28° and 58°
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Suppose that you have $4000 to invest. Which investment yields the greater return over a 10 year period: 7.83% compounded daily or 7.9% compounded quarterly?
Find the total amount of the investment after 10 years if $4000 is invested at 7.83% compounded daily.
The investment yields a greater return over a 10-year period if he invested 7.83% compounded daily.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Suppose that you have $4000 to invest.
The total amount of the investment after 10 years in each case will be given as,
At = r = 7.83% compounded daily, then we have
[tex]\rm A = \ \$4,000 \times \left (1 + \dfrac{0.0783}{365} \right)^{10\times 365}[/tex]
A = $4,000 × (1.000214521)³⁶⁵⁰
A = $4,000 × 2.1878
A = $8,751.37
At = r = 7.9% compounded quarterly, then we have
[tex]\rm A = \ \$4,000 \times \left (1 + \dfrac{0.079}{4} \right)^{10\times 4}[/tex]
A = $4,000 × (1.01975)⁴⁰
A = $4,000 × 2.186
A = $8,745.98
The investment yields a greater return over a 10-year period if he invested 7.83% compounded daily.
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A merchant mixed 20 pounds of a cinnamon tea with 10 pounds of a spice tea. The 30-pound mixture sells for $80. A second
mixture included 12 pounds of the cinnamon tea and 8 pounds of the spice tea. The 20-pound mixture sells for $54. What is the
price per pound of the cinnamon tea?
A.$3.50
B.$2.50
C.$5.50
D.$0.50
Answer:10x+2y=38, where x is the dollar cost of cinnamon and y the dollar cost of the spice.1
6x+8y=80multiply the top by -4-40x-8y=-15216x+8y=80.
Add them and y is eliminated.-24x=-72
Step-by-step explanation:
A 6-sided polygon is classified as a heptagon.
True
False
Answer:
true 6=hepti
Step-by-step explanation:
Question 1Mutple Choice Worth 2 points)
(Angle Relationships MC)
One angle measures 24", and another angle measures (7d-4). If the angles are complementary, what is the value of off
Od=80
Od=17
Od=10
Od=3
As two angles are Complementary Angles they sum up to 90.
So value of d is 10.
What are Complementary angles?Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.
If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.
60° + 30° in the figure below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,
The opposite of 30° is 60°.
The opposite of 60° is 30°.
Calculation:Given;
24,(7d-4) are complementary angles
So, 24°+7d-4 =90°;
⇒7d-4=90-24;
⇒7d-4=66;
⇒7d=70;
⇒d=10.
As two angles are Complementary Angles they sum up to 90.
So value of d is 10.
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I have 3 red balls, 3 blue balls and 3 yellow balls in a box. Total of 9 balls. Let's say that I randomly pick 3 balls, what are the chances of having at least 2 red balls in the 3 that I picked?
The probability of having at least 2 red balls in the 3 that I picked will be 1/3.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
I have 3 red balls, 3 blue balls, and 3 yellow balls in a crate. All out of 9 balls.
If the three balls are picked randomly, then the probability of having at least 2 red balls in the 3 that I picked will be given as,
P = 3/9
P = 1/3
The probability of having at least 2 red balls in the 3 that I picked will be 1/3.
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Jordan had a bake sale. Muffins cost $3 each and cookies cost $2 each. Jordan earned $24.
(Select all)
- 0 muffins and 8 cookies
- 9 muffins and 2 cookies
- 2 muffins and 9 cookies
- 6 muffins and 4 cookies
- 4 muffins and 6 cookies
Answer:
0 muffins and 8 cookies
6 muffins and 4 cookies
Explain:
These are the only two combinations of muffins and cookies that Jordan could have sold to earn $24. If Jordan sold 0 muffins and 8 cookies, they would have earned $24 because 0 x $3 + 8 x $2 = $24. If Jordan sold 6 muffins and 4 cookies, they would have earned $24 because 6 x $3 + 4 x $2 = $24.
Find the radius of the circle containing 36° arc of a circle whose length is 13 m.
Answer:
20.69 m
Step-by-step explanation:
36/360 * 2πr = 13
r = 130/2π = 20.69 m
Find the area of a circle if the radius is 5 feet.
78.5 ft2
31.4 ft2
72 ft2
15 ft2
The area of the circle is obtained as 78.50 square feet. The correct option is (A).
What is a circle?A circle is a geometric shape, all of which points are equidistant from a fixed point called as the Centre.
The Centre of the circle does not lie on it.
Given that,
The radius of the circle is 5 feet.
The expression for the area of the circle is given as πr².
Substitute the value of r and take π = 3.14 to obtain,
Area = πr²
= 3.14 × 5²
= 3.14 × 25
= 78.50
Hence, the area of the circle with given radius is obtained as 78.50 square feet.
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Solve equation:
-6-3k+8=5
if you solve the equation you get k=-1
Please help ASAP!!
50 Points + Brainliest if correct!
(Also, I know that my answer is incorrect)
Answer:
5
Step-by-step explanation:
We have f(x) = 10x^3 and g(x) = 4x^(8/3) given. We need to find f/g, evaluating at x = 8. So how do we do this?
First, let's put our x value into the function f. f(8) = 10*8^3 = 5120.
Next, let's put our x value into the function g. g(8) = 4*8^(8/3) = 1024.
Now we just need to find f/g, which is just the result from our function f divided by our result from function g. This is f(8) / g(8). Substituting our solutions in, we have 5120/1024 = 5.
Answer:
5120/1024 = 5
Step-by-step explanation:
5120/1024 = 5
40 POINTS ASAP!!!!!!!!!!!!!!!! 40 POINTS ASAP!!!!!40 POINTS ASAP!!!!!40 POINTS ASAP!!!!!!!!!!!!!!!! 40 POINTS ASAP!!!!!40 POINTS ASAP!!!!! PLEASE HELP !!!!! PLEASE
In the diagram, the measures of ∠2, ∠6, and ∠7 are 25°. The measure of ∠1 is 155°. Are lines c and d parallel?
Answer:
Step-by-step explanation:
Yes, the lines are parallel.
so its d. trust me :)
In Exercises 1 and 2, complete the proof.
1. Given PQ=RS
Prove PR=QS
2. Given ∠1 is a complement of ∠2.
∠2≅∠3
Prove ∠1 is a complement of ∠ 3
In Exercises 3-6, name the property that the statement illustrates.
3. If PQ≅ ST and ST≅UV, then PQ≅UV
1. For the given line segment if PQ = RS then it is proved that PR = QS .
2. From the given angles if ∠1 is complement to ∠2 (∠1 + ∠2 = 90° ) then angle 1 is complement to angle 3.
As given in the question,
1. Given : PQ = RS
To prove : PR = QS
Proof:
PQ = RS ( given )
Add both the side QR we get,
PQ + QR = QR + RS
From the diagram, it is given P - Q - R - S are collinear points
PR = QS ( PQ + QR = PR and QR + RS = QS)
Hence, PQ = RS implies that PR = QS.
2. Given: ∠1 is a complement of ∠2
∠2 ≅ ∠3
To prove : ∠1 is a complement of ∠3
proof: ∠1 is a complement of ∠2
⇒∠1 + ∠2 = 90°
⇒∠1 + ∠3 = 90° ( given ∠2 = ∠3 )
⇒∠1 is a complement of ∠3.
Hence, it is proved that ∠1 is a complement of ∠2 implies that ∠1 is a complement of ∠3.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
(4,-10)
Step-by-step explanation:
Graphing calculator
Will mark brainliest
I want to know what is 2/5 x -3
Answer:
I think your answer is [tex]\frac{2}{5} x-3[/tex]
Step-by-step explanation:
4 - (2x + 4) = 5
Solve for x
Vue wonders how long the ball was in the air when it was 54 feet in the air so he writes the equation 54=-16s2+96s. Solve the equation for time(s) to determine how long the ball was in the air when it was 54 feet above the ground . Round your answer to the nearest hundredth of a second . On a piece of paper , Identify which of the following methods you used to solve this question : factoring , completing the square, the Quadratic Formula, using a graph. Then explain how your solution helps Vue answer his question
Answer:
0.63 or 5.37 seconds
Step-by-step explanation:
You want to know how long a ball was in the air when its height is 54 feet, and its height is described by -16s^2 +96s, for time (s) in seconds.
SolutionA graph shows the value of the height function is 54 when s = 0.63 or 5.37.
These solutions mean the ball was in the air 0.63 seconds when it passed 54 feet going up, and it was in the air 5.37 seconds when it was 54 feet in the air on the way down.