Answer:
Here is how to write and graph an inequality for the budget problem:
Let x be the number of large boxes and y be the number of small boxes. The total cost of the boxes must be less than or equal to the budget of $500. So, we can write the inequality as:
65x + 35y ≤ 500
To graph this inequality, we need to find the boundary line and the shaded region. The boundary line is the equation that we get when we replace the inequality sign with an equal sign, which is:
65x + 35y = 500
To graph this line, we need to find two points on it. We can do this by plugging in some values for x or y and solving for the other variable. For example, if x = 0, then y = 500/35 = 14.29. If y = 0, then x = 500/65 = 7.69. So, two points on the line are (0, 14.29) and (7.69, 0). We can plot these points on a coordinate plane and draw a solid line through them, since the inequality includes the equal sign.
To find the shaded region, we need to test a point that is not on the line and see if it satisfies the inequality. For example, we can test the point (0, 0), which is the origin. Plugging in x = 0 and y = 0 into the inequality, we get:
65(0) + 35(0) ≤ 500
0 ≤ 500
This is true, so the point (0, 0) is a solution to the inequality. This means that the shaded region is the area that includes the point (0, 0) and is below the line.
If Renaldo buys 6 small gift boxes, then y = 6. To find how many large gift boxes he can afford, we need to plug in y = 6 into the inequality and solve for x. We get:
65x + 35(6) ≤ 500
65x + 210 ≤ 500
65x ≤ 290
x ≤ 290/65
x ≤ 4.46
This means that Renaldo can buy at most 4 large gift boxes if he buys 6 small gift boxes. However, since x has to be a whole number, the largest possible value for x is 4. So, Renaldo can buy 4 large gift boxes and 6 small gift boxes and still stay within his budget.
I hope this helps!
Step-by-step explanation:
Somebody pls help, will give points and mark brainliest ! PLS
Answer:
1.07 x 10^8
Step-by-step explanation:
what is 4375 as a fraction?
The value of 0.4375 in fractional form is 7/16.
Parts of a whole numbers are represented by fractions, where the denominator represents the entire object and the numerator the equal part.
By dividing a number by 10 for each digit after the decimal, we may eliminate the decimal and turn it into a fraction.
The decimal point is followed by four integers, thus we will divide it by 10,000.
= 4375 / 10000
Simplifying fraction yields the result
= 4375 ÷ 5 / 10000 ÷ 5
= 875 ÷ 5 / 2000 ÷ 5
= 175 ÷ 5 / 400 ÷ 5
= 35 ÷ 5 / 80 ÷ 5
= 7 / 16
In addition, they are comparable fractions.
The fractional equivalent of 0.4375 is 7/16.
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Complete question - what is 0.4375 as a fraction?
Connie is buying snacks for a hike. She purchased a bag of trail mix for $6.98 and a large bottle of water for $2.15.
What was Connie's total bill?
Connie's total bill is sum of trail mix and water will be $9.13.
What is sum ?
In mathematics, the sum refers to the result of adding two or more numbers together. It is a basic arithmetic operation, often used in many different mathematical concepts and calculations. The symbol for addition is '+', and the sum of a set of numbers is often represented using the capital Greek letter sigma (∑).
According to the question:
Connie's total bill would be the sum of the cost of the trail mix and the cost of the water, which is:
Total bill = cost of trail mix + cost of water
Total bill = $6.98 + $2.15
Total bill = $9.13
Therefore, Connie's total bill was $9.13.
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select all expressions that represent a correct solution to the equation 6(x+4)=20
The expression represents a correct solution to the equation 6(x+4)= 20 is x= -2/3
We know, that the equation is:
6(x+4)=20
6x + 24 = 20
Now, Subtract 24 from both sides
6x + 24 = 20
6x + 24-24 = 20-24
Simplify the expression in the equation
6x + 24-24 = 20-40
6x=-4
Divide both sides by the same factor
6x=-4
6x/6 =-4/6
Simplify the expression
Cancels numbers that are both numerators and denominators X=-4/6 X=-2/3
Therefore, the correct solution to the equation is x=-2/3
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Find the lateral surface area of this triangle prism in cm2 5cm 5cm 4cm 6 cm 12cm
the lateral surface area of the triangular prism with measurement of 5cm, 5cm, 4cm, 6cm and 12cm is 140 cm².
To find the lateral surface area of a triangular prism, we need to calculate the sum of the areas of all the rectangular faces of the prism. In this case, the triangular prism has two triangular faces and three rectangular faces. The triangular faces have dimensions of 5 cm (base) and 4 cm (height), while the rectangular faces have dimensions of 5 cm (width), 6 cm (height), and 12 cm (length).
To calculate the area of one of the triangular faces, we use the formula for the area of a triangle:
Area = (1/2) x base x height
In this case, the base is 5 cm and the height is 4 cm, so the area of one triangular face is:
Area = (1/2) x 5 cm x 4 cm = 10 cm²
Since there are two triangular faces, the total area of the triangular faces is: Total area of triangular faces = 2 x 10 cm² = 20 cm²
To calculate the area of one of the rectangular faces, we use the formula for the area of a rectangle: Area = length x width
In this case, the dimensions of the rectangular faces are 6 cm (height) x 5 cm (width) and 12 cm (length) x 5 cm (width), so the areas of these faces are: Area of one rectangular face = 6 cm x 5 cm = 30 cm²
Area of another rectangular face = 12 cm x 5 cm = 60 cm²
Since there are three rectangular faces, the total area of the rectangular faces is: Total area of rectangular faces = 30 cm² + 60 cm² + 30 cm² = 120 cm²
Finally, the lateral surface area of the triangular prism is the sum of the areas of the triangular and rectangular faces:
Lateral surface area = Total area of triangular faces + Total area of rectangular faces
Lateral surface area = 20 cm² + 120 cm² = 140 cm²
Therefore, the lateral surface area of the triangular prism is 140 cm².
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A graph of a linear equation is shown below.
Which equation describes the graph?
y = 0.5x − 1.5
y = 0.5x + 3
y = 2x − 1.5
y = 2x + 3
Answer:c
Step-by-step explanation:
Jen left the house at 10:03. She went to the post office, returned books to the library, and bought groceries at the store. Jen was running errands for 59 minutes. What time was it when she returned home?
Jen returned home was 11:02. Below, you will learn how to solve the problem.
When Jen left the house, it was 10:03, she was running errands for 59 minutes. To find out what time it was when she returned home, we need to add the 59 minutes to the time she left the house.
First, we need to convert the time she left the house to minutes, 10:03 is equal to 603 minutes (10 hours x 60 minutes per hour + 3 minutes).
Next, we add the 59 minutes she was running errands to the 603 minutes:
603 minutes + 59 minutes = 662 minutes
Finally, we convert the 662 minutes back to hours and minutes:
662 minutes ÷ 60 minutes per hour = 11 hours with 2 minutes remaining
So, the time when Jen returned home was 11:02.
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what is the rectangular form of 6(cos(225o) i sin(225o))? negative 3 startroot 2 endroot minus 3 startroot 2 endroot i negative 3 startroot 2 endroot 3 startroot 2 endroot i 3 startroot 2 endroot minus 3 startroot 2 endroot i
The rectangular form of 6{(cos225°) +i(sin225°) }is -3√2-3i√2.The shape that complex numbers typically take is referred to as rectangle form: z = a + bi.
What are polar form and rectangular form?Polar notation depicts a complex number in terms of the lengths of the vector and the angular direction from the starting point. In rectangle notation, a complex number is represented by its vertical and horizontal dimensions. The system is referred to be rectangular because the angles made by the axes at the origin and the measurements at point p are both 90 degrees. As a result, the measurement results in a rectangle with sides Xp and Yp.
To determine rectangular form, we obtain,
Let Z=6{(cos225°) +i(sin225°)}
Now, cos225°=-cos( 180°+45°)= -cos45°= -[tex]\frac{1}{√2}[/tex]
sin225°=-[tex]\frac{1}{√2}[/tex]
S0, 6{(cos225°) +i(sin225°)}= 6 ( -[tex]\frac{1}{√2}[/tex])+6i(-[tex]\frac{1}{√2}[/tex])=-3√2-3i√2.
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Answer:
A
Step-by-step explanation:
right on edge
when can a correlation coefficient based on an observational study be used to support a claim of cause and effect?
A correlation coefficient based on an observational study cannot be used to support a claim of cause and effect, as correlation does not imply causation.
Correlation is a statistical measure that describes the strength and direction of a relationship between two variables. A correlation coefficient ranges from -1 to 1, where -1 indicates a strong negative correlation, 0 indicates no correlation, and 1 indicates a strong positive correlation. Correlation does not imply causation, meaning that just because two variables are correlated does not mean that one causes the other.
In an observational study, researchers observe and record data on variables of interest without manipulating them directly. These studies are often used in fields such as epidemiology, social sciences, and psychology to investigate relationships between variables and identify potential risk factors for diseases or other outcomes.
Observational studies can suggest possible relationships between variables, but they cannot prove causation. This is because there may be other factors that are influencing the relationship between the variables, and these factors cannot be controlled or accounted for in an observational study. In order to establish causation, researchers need to conduct experiments where they can manipulate the variables and control for other factors that may influence the outcome.
Therefore, a correlation coefficient based on an observational study cannot be used to support a claim of cause and effect, as correlation does not imply causation.
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There are 300,000 households in Clover City. A local television repair shop takes a random sample of 50 households and finds that the average number of televisions per household from the sample last year that needed to be repaired was 2.53 ± 0.71. Which of the following is an estimate of the total number of televisions that needed repairing last year in Clover City?
Try using Socratic and it may help
Solve the system by substitution
-2x+ 7y = 15
6y=x
The solution to the system of equation is x = -2 and y = -3.
What is system of equations?System of equation can be solved using different method such as elimination method, graphical method and substitution method,
here we have,
Therefore, let's solve the system of equation by using substitution method.
-2x+ 7y = 15
6y=x
substitute the value of x in equation(i)
-2* 6y+ 7y = 15
or, -12y + 7y = 15
or, -5y = 15
or, y = -3
so, we get,
x = 6/ -3
or, x = -2
Hence, The solution to the system of equation is x = -2 and y = -3.
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the pithag tells us how the ____ lengths of ______ triangles are related
Pythagorean theorem tells us how the side lengths of right triangles are related.
The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.
This relationship can be written as the equation:
[tex]a^2 + b^2 = c^2[/tex]
where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.
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Which expression is equivalent to 7k+13-4K+10+5k-6
A.6n+90
B.14+72
C.6n+72
D.14n+90
the expression equivalent to 7k+13-4K+10+5k-6 is 8k + 17. correct option: (B) 14+72
How to do and what is expression equivalent?
Simplifying the expression by combining like terms, we get:
7k + 13 - 4k + 10 + 5k - 6
= (7k - 4k + 5k) + (13 + 10 - 6)
= 8k + 17
Therefore, the expression equivalent to 7k+13-4K+10+5k-6 is 8k + 17. correct option would be : (B)
Two expressions are equivalent if they represent the same mathematical value for all possible values of the variables. In other words, if you substitute any value for the variables in both expressions, the resulting values will be the same.
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the usual price of a bag of oranges was $4. during a promotion, two bags of oranges were sold for $5.99. find the percentage decrease in the price of the two bags of oranges. give your answer correct to 1 decimal place.
The percentage decrease in the price of the two bags of oranges is 25.1 %.
We have been told that the usual price of a bag of oranges was $4 and during the promotion, it became $5.99 for two bags of oranges. We need to find the percentage decrease here.
We can calculate that two bags before the promotion cost = $4 × 2 = $8
As we already know, the two bags during the promotion cost = $5.99
The decrease in price can be calculated as well = $8 - $5.99 = $2.01
Percentage decrease = ($2.01 / $8) * 100 %
Percentage decrease = 25.1 %
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How many groups of 1/3 inch are in 3/4 inch? Write your answer as a mixed number in simplest form.
Answer:3
Step-by-step explanation:
Charlie has $500 in a savings account at the beginning of the summer, but withdraws $25 each week to spend on meals at Duchess (his favorite). He wants to have at least $200 in the account at the end of the summer for the start of school. How many weeks can Charlie withdraw money from the account?
Let's first determine how much Charlie will have in his savings account at the end of the summer if he doesn't withdraw any money. There are 12 weeks in the summer, so he would have:
$500 - $25/week x 12 weeks = $200
So if he withdraws money for more than 0 weeks, he will not have at least $200 in the account at the end of the summer. Therefore, he cannot withdraw any money from the account.
Answer:
12 weeks.
Step-by-step explanation:
Since Charlie has $500, but wants to spend $25 every week, we can set up a problem.
[tex]25[/tex] × [tex]12[/tex] [tex]= 300[/tex]
Thus, he can go 12 weeks and spend $300 while still managing to have $200 left in his account.
Hope it helped!
Which table represents the function y=-3x+2?
Input x 0 1 2
Output y 2 6 10
Input x 0 1 2
Output y 2 3 4
Input x
0 1 2
Output y 3 4 5
Input x 0 1 2
Output y 2 -1 -4
Input x (0 1 2)- Output y( 2 -1 -4) is represents the function y = -3x+2.The relationship between such a collection of input data and each output is how a function is defined.
What is a function, exactly?A function is, to put it simply, a relationship between outputs in which each input is connected to exactly one output. For each function, there is a range, made the request, and domain. Typically, a function is written as f(x), where x stands for the output. It is possible for a function to be declared inside of a class, module, or other function.
To determine Function , we obtain,
y = -3x+2
y = -3(0)+2=2
y = -3(2)+2=-1
y = -3(2)+2=-4
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PLEASE HELP!!!!!!!!!! Use an algebraic method (substitution or elimination) to solve the system of equations. Show your work.
4 − 2 = 16
2 + 3 = 32
The requried solution to the system of equations is x = 7, y = 6.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
To solve the system of equations:
4x - 2y = 16 - - -- - -(1)
2x + 3y = 32 - - - - - - (2)
We can use the method of substitution:
Solve one of the equations for one of the variables in terms of the other variable.
Let's solve the first equation for y:
4x - 2y = 16
-2y = -4x + 16
y = 2x - 8
Substitute the expression found in step 1 into the other equation 2.
2x + 3(2x - 8) = 32
Solve the resulting equation for the remaining variable.
2x + 6x - 24 = 32
8x - 24 = 32
8x = 56
x = 7
Substitute the value of x into one of the original equations to find the value of the other variable.
Using the first equation:
4x - 2y = 16
4(7) - 2y = 16
28 - 2y = 16
-2y = -12
y = 6
Therefore, the solution to the system of equations is x = 7, y = 6.
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Natalie’s mom gave her $40.00 to buy a pair of jeans. She found a pair of jeans originally priced at $45.00, but marked down with a 20% discount. A sales tax of 8% will be added to the sale price of the jeans. Which expression can Natalie use to determine if she has enough money to purchase the jeans?
The expression that can be used to determine if she has enough money to purchase the jeans would be discussed below.
How to calculate the actual price of the jeans after tax?The total amount of money given to Natalie by her mom= $40.
The original price of the jeans = $45
The discount percentage = 20% of 45
= 20/100 ×45/1
= 900/100 = $9
The price of the jeans after discount = $36
The percentage of tax deduction = 8% of 45
= 8/100 × 45
= 360/100
= $3.6
The price of the jeans after tax = 36+ 3.6 = $39.6
Therefore, the amount of money that the money gave to Natalie to purchase jeans will be enough.
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Complete the ratio table.
82 19
164 38
57
328 76
410
The complete ratio table is
Hours Weeks
168 1
1008 6
840 5
How to complete the table?
The mathematical operation that would be used to determine the missing values are division and multiplication. In order to convert hours to weeks, divide by 168 hours. To convert weeks to hours, multiply by 168.
1008 hours to weeks = 1008 / 168 = 6 weeks
5 weeks to hours = 5 x 168 = 840 hours
Hence , The complete ratio table is
Hours Weeks
168 1
1008 6
840 5
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what is 2x4 actual size?
The actual size of 2×4 is 1.5 inches by 3.5 inches
The measurement is 2 × 4
Assuming you are referring to lumber sizes, a 2x4 piece of lumber has actual dimensions of 1.5 inches by 3.5 inches
If we convert to the centimeter then the actual size will be 3.81 cm by 8.89 cm
The name "2x4" refers to the rough dimensions of the lumber before it is planed and smoothed, which are typically about 2 inches by 4 inches. However, the planing process reduces the size of the lumber by about 0.5 inches in both dimensions.
Therefore, the actual size is 1.5 inches by 3.5 inches
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an
, the n^{\text{th}}n
th
term of the sequence 17, 15, 13, 11, ...17,15,13,11
Therefore, the n-th term of the sequence is 19 - 2n.
What is arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant value to the previous term. This constant value is called the common difference of the arithmetic sequence. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is obtained by adding 3 to the previous term.
The nth term of an arithmetic sequence can be expressed using the following formula:
an = a1 + (n - 1)d
where an is the nth term of the sequence, a1 is the first term, n is the number of the term, and d is the common difference.
The sum of the first n terms of an arithmetic sequence can also be calculated using the formula:
Sn = n/2(2a1 + (n - 1)d)
where Sn is the sum of the first n terms, a1 is the first term, n is the number of terms, and d is the common difference.
Here,
The first term of the sequence is 17 and the common difference between consecutive terms is -2 (i.e. subtracting 2 from the previous term to get the next term). So, we can write the n-th term of the sequence as:
a_n = 17 + (n-1)(-2)
Simplifying this expression, we get:
a_n = 19 - 2n
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Chen made a table to track the savings he builds up over the first three weeks of doing chores. He's decided to not spend
any of the money.
If the sequence of values for the money that he has saved over the first three weeks follows an arithmetic pattern, how
much money will he have saved by the fourth and fifth weeks?
Type the correct answer in each box. Use numerals instead of words. Do not use $.
Week
1
2
3
4
5
Dollars Saved
12
18
24
Answer:
36
Step-by-step explanation:
Find the length of X
Answer:
[tex]x=3, x=\frac{17}{4}[/tex]
Step-by-step explanation:
The side opposite to the length of 20 is 7x - 11, whereas the side opposite to an unknown length is 4x - 2. To solve this unknown length, we are given 35 as the total length, so we can do 35-20 = 15, which is the opposite of the length of 4x-2.
Since we know the opposite sides of each side, we can set up these equations since we notice that the lengths are parallel based on what is diagrammed:
[tex]7x-11=20[/tex]
[tex]4x-2=15[/tex]
Now, let's solve for x in [tex]7x-11=20[/tex]:
[tex]7x-11=20[/tex]
[tex]7x=20+11\\7x=21\\x=3[/tex]
Let's solve for x in [tex]4x-2=15[/tex]:
[tex]4x-2=15[/tex]
[tex]4x=15+2\\4x=17\\x=\frac{17}{4}[/tex]
Two pools are being filled with water. To start, the first pool contains 1920 liters of water and the second pool contains 2500 liters of water. Water is being added to the first pool at a rate of 34. 75 liters per minute. Water is being added to the second pool at a rate of 20. 25 liters per minute
After 10 minutes, the first pool will contain a volume of 2267.5 liters of water and the second pool will contain 2702.5 liters of water.
It is important to first identify the information given in the question. We have the starting amounts of water in both pools, as well as the rates at which water is being added to each pool. Using this information, we can set up an equation to determine how much water will be in each pool after a certain amount of time.
Let t represent the amount of time in minutes that the pools are being filled. The equation for the first pool will be 1920 + 34.75t and the equation for the second pool will be 2500 + 20.25t.
To find out how much water is in each pool after a certain amount of time, we can simply plug in the value of t and solve for the amount of water. For example, if we want to know how much water is in each pool after 10 minutes, we can plug in t = 10 and solve:
First pool: 1920 + 34.75(10) = 1920 + 347.5 = 2267.5 liters
Second pool: 2500 + 20.25(10) = 2500 + 202.5 = 2702.5 liters
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In the figure below, DG is parallel to EF and ZFDG =
D
OD. 75°
G
Note: picture not drawn to scale
If m/FDG = 66° and m/EDG = 100°, what is m/FED?
OA. 100°
OB. 90°
OC. 80°
Answer:
m∠FED = 80°
Step-by-step explanation:
We have m∠FDG = m∠DFE = 66°m∠EDG = 100°Since ∠EDG is formed from the two angles ∠FDG and ∠FDEDetermine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct.a. dydt=3y−y2b. dydt=y(2−y)2c. dydt=y2|y−2|d. dydt=y2−3ye. dydt=4y−y3f. dydt=2y−y2g. dydt=y(y−2)h. dydt=y3−4y
to determine the stability of the equilibrium solutions Consider the autonomous differential equation
dydt=f(y).
The equilibrium solutions are obtained by solving
f(y)=0 for y.
Let
c1,c2,⋯,cn
be the equilibrium solutions.
Plot
c1,c2,⋯,cn
on the real number line, and create a phase line using the signs of
f(y)
by drawing a left arrow on the interval where
f(y)<0
, and right arrows where
f(y)>0.
Use the phase line to determine the stability of the equilibrium solutions as follows.
If both arrows point toward the equilibrium solution, it is stable.
If both arrows point away from the equilibrium solution, it is unstable.
If one arrow points towards the equilibrium solution and one points away from it, it is semi-stable.
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What is the solution of Chinese Remainder Theorem?
The solution of the Chinese Remainder Theorem can be calculated by using the formula: [tex]{\displaystyle x=\sum _{i=1}^{k}a_{i}M_{i}N_{i}.}[/tex]
According to the Chinese remainder theorem, if one knows the remainders of the Euclidean division of an integer n by multiple numbers, one may uniquely calculate the remainder of the division of n by the product of these integers, provided that the divisors are pairwise coprime (no two divisors share a common factor other than 1).
For example, if we know that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, we may calculate the remainder of n divided by 105 (the product of 3, 5, and 7) without knowing the value of n. This tells us that if n is a natural number less than 105, then the only possible value of n is 23.
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What determines which numerical measures of center and spread are appropriate for describing a given distribution of a quantitative variable? Which measures will you use in each case?
The appropriate numerical measures of center and spread to describe a given distribution of a quantitative variable depend on the shape, symmetry, and presence of outliers in the data.
Measures of center include mean, median, and mode. The mean is affected by extreme values, while the median is resistant to outliers. The mode is useful when looking for the most common value or values in a distribution.
Measures of spread include range, interquartile range (IQR), variance, and standard deviation. The range is the difference between the maximum and minimum values, but it is sensitive to outliers. The IQR is the range of the middle 50% of the data and is resistant to outliers. Variance and standard deviation both measure the spread of the data around the mean, with the variance being the average squared deviation from the mean and the standard deviation being the square root of the variance.
In general, if the data is approximately symmetric and without outliers, the mean and standard deviation are appropriate measures of center and spread, respectively.
If the data is skewed or has outliers, the median and IQR are more appropriate. If the distribution has multiple modes, the mode may be useful to describe the distribution, but it should be used with caution as it may not be unique or well-defined for certain distributions.
Ultimately, the choice of measures of center and spread depends on the characteristics of the data and the research question being investigated. It is always a good practice to use multiple measures of center and spread and to visualize the distribution of the data using histograms or boxplots to gain a better understanding of the data.
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I Need help on number 15 pls
Using the fact that the figures are similar, we will get z = 4.
How to find the value of z?We know that the two figures are similar, then the correspondent quotients between sides must be equal.
That means that we can write the equation:
10/15 = z/6
And we can solve that equation for z, we will get:
z = 6*(10/15) = 4
That is the value of z.
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