1. The five-number summary of the data set is: 20, 27, 29.5, 39, 45.
b. Range = 25
c. Interquartile range (IQR) = 12
How to Find the Five-Number Summary?Given the data set for fuel efficiencies for vehicles featured in a car-buying guide as: 27, 30, 41, 27, 20, 22, 36, 37, 44, 45, 29, 29, we have five-number summary solved as shown below.
a. Minimum: 20 (smallest data point.)
First Quartile: 27 (center of the first part/half of the data set when ordered)
Median: 29.5 (center of the data set when ordered)
Third Quartile: 39 (center of the 2nd half of the data set when ordered)
Maximum: 45 (largest data point.)
Thus, the five-number summary of the data set is: 20, 27, 29.5, 39, 45.
b. Range = max - min
Range = 45 - 20
Range = 25
c. Interquartile range (IQR) = Third Quartile - First Quartile
Interquartile range (IQR) = 39 - 27
Interquartile range (IQR) = 12
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Simplify the expression. NEED HELP FAST
The simplification of the expression 3a(15 + 3 - 3²) + 7a(8/4) gives 41a
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
3a(15 + 3 - 3²) + 7a(8/4)
Simplifying the exponents:
3a(15 + 3 - 9) + 7a(8/4)
Simplifying the terms in the bracket:
3a(9) + 7a(2)
Opening the parenthesis:
27a + 14a
Adding:
= 41a
The simplification of the expression 3a(15 + 3 - 3²) + 7a(8/4) gives 41a
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Select one of the factors of 3x2 + 4x − 4.
(x + 4)
(3x + 2)
(3x − 2)
(x − 2)
The factors of the polynomial 3x² + 4x - 4 are (3x - 2) and (x + 2)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Polynomial is an expression that involves the operations of addition, subtraction, multiplication of variables.
Given the polynomial:
3x² + 4x - 4
Factorizing the polynomial gives:
= 3x² + 6x - 2x - 4
= 3x(x + 2) - 2(x + 2)
= (3x - 2)(x + 2)
The factors of the polynomial 3x² + 4x - 4 are (3x - 2) and (x + 2)
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Help please I need help
Answer:
okay!
Step-by-step explanation:
3x5=15+4=19 so I think 10 5 5 10 hope it he,ped I tried!
A student has these scores on their assignments. The teacher is considering
The arithmetic mean of a given data is the sum of all observations divided by the number of observations.
For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:
Mean = Sum of all observations/Number of observations
Mean = Sum of all observations/Number of observations
Mean = (12 + 34 + 45 + 50 + 24)/5
Mean = 165/5 = 33
The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus
median = middle value i.e. 4.
suppose Given data:
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
a)Mean without '0' = 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/9
= 700/9
= 77.777
Median without '0' = 80
Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/10 = 70
Median with '0' = 80
b)standard deviation= 18.121673811445. (without '0')
standard deviation with 0 = 28.982753492379
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Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
x+10=5
we conclude that the equation x + 10 = 5 has only one solution, which is x = -5
How many solutions has the given equation?Here we have the linear equation:
x + 10 = 5
In general, linear equations have only one solution, but let's solve this to see how many solutions it has.
If we subtract 10 in both sides of the linear equation, we will get:
x + 10 - 10 = 5 - 10
x = -5
So there is a single solution, which is x = -5.
Then we conclude that the equation below has only one solution.
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Find a polynomial of degree n that has only the given zero(s). (There are many correct answers.
x = -3, -1;
n = 4
The required polynomial function is x^4 + 8x³ + 22x² + 24x + 9
In this question,
We have been given the zeros of a polynomial and the degree of a polynomial.
We need to find the polynomial of degree 4 and has zeros x = -3, -1
If a polynomial function f(x) has zeros x = -3, x = -1, then it has factors
(x + 3), (x + 1).
If these were its only factors, then polynomial would be a quadratic.
This means, both the zeros must be of multiplicity 2.
So, the roots of the polynomial must be of the form f(x) = (x + 3)²(x + 1)²
f(x) = (x + 3)²(x + 1)²
f(x) = (x² + 6x + 9)(x² + 2x + 1)
f(x) = x^4 + 8x³ + 22x² + 24x + 9
Therefore, the required polynomial function is x^4 + 8x³ + 22x² + 24x + 9
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At a concert, Nabila purchased three t-shirts and a concert program that cost $15. In total, Nabila spent $90. Find the cost of a single t-shirt if they all had the same price.
Answer: $25
Step-by-step explanation:
t = t-shirts
3t + 15 = 90
3t = 75
t = 25
yall can u help out whts 2(2/9) = (-4/5m)
Answer:
Step-by-step explanation:
(2/1)(2/9) = (-4/5m)
4/9 = (-4/5m)
(-5/4)4/9 = ((-4/5)(-5/4))m cancel out common factor on both sides
-5/9 = M or M = -5/9 use symmetric property of equality either one is fine for answer.
f(x) -7x - 4; shifts 5 units down.
Graph the image of rectangle ABCD after a dilation with a scale factor of 1/2 
Answer:
I took the time to graph the image onto the image that you had used, I hope this helps! <3
Step-by-step explanation:
Dilating by 1/2, is a contraction, it makes the pre-image smaller than the image.
Write the ratio of frogs to flies in simplest form.
*
Captionless Image
The ratio of frogs to flies in simplest form., 4 frogs and 8 flies in simplest form is 2:4.
What is a ratio and how can it be calculated?A ratio can be described as the ordered pair of numbers in mathematics which do comes in form of a and b, and this can be written as a / b as well as a:b which is the ratio of two terms where both of them is not equal to zero.
In the case above, 4 frogs and 8 flies =4:8 =2:4
Therefore, the ratio of frogs to flies in simplest form., 4 frogs and 8 flies in simplest form is 2:4.
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Complete question:
Write the ratio of frogs to flies in simplest form., 4 frogs and 8 flies in simplest form.
The sidewalk around the lake is 9/10 mile long. You walk 3 laps around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 1 1/2 mile track. How many laps does your friend walk
The number of miles that he walked is 4.5 miles. Then the number of laps that your friend walks will be 3 laps.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A 9/10 miles long walkway around the lake. In the morning you walk three laps around the lake, and in the evening you walk two. On a 1 1/2 mile track, your companion walks the same overall distance as you do.
The number of miles that you walked will be
⇒ 9/10 x (3 + 2)
⇒ 9 x 5 / 10
⇒ 4.5 miles
Then the number of laps that your walk will be
⇒ 4.5 / (1 1/2)
⇒ 4.5 / (3/2)
⇒ 4.5 x 2 / 3
⇒ 3 laps
The number of laps that your friend walks will be 3 laps.
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A school system employs teachers at salaries between $38,000 and $70,000. The teachers’ union and school board are negotiating the form of next years’ increase in the salary schedule. Suppose that every teacher is given a $1000 raise.
Which of the following choices correctly describes the effect this raise will have on each of the following characteristics of the resulting distribution of salary:
Shape
Mean and median
Standard deviation and interquartile range (IQR)
Answer:By adding a constant value to every salary amount, the measures of
central tendency are increased by the amount, while the measures of
dispersion, remains the same
The correct responses are;
(a) The shape of the data remains the same
(b) The mean and median are increased by $1,000
(c) The standard deviation and interquartile range remain the same
Reasons:
The given parameters are;
Present teachers salary = Between $38,000 and $70,000
Amount of raise given to every teacher = $1,000
Required:
Effect of the raise on the following characteristics of the data
(a) Effect on the shape of distribution
The outline shape of the distribution will the same but higher by $1,000
(b) The mean of the data is given as follows;
Therefore, following an increase of $1,000, we have;
Therefore, the new mean, is equal to the initial mean increased by 1,000
Median;
Given that all salaries, , are increased by $1,000, the median salary, , is also increased by $1,000
Therefore;
The correct response is that the median is increased by $1,000
(c) The standard deviation, σ, is given by ;
Where;
n = The number of teaches;
Given that, we have both a salary, , and the mean, , increased by $1,000, we can write;
Therefore;
; The standard deviation stays the same
Interquartile range;
The interquartile range, IQR = Q₃ - Q₁
New interquartile range, IQR = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR
Therefore;
The interquartile range stays the same
Step-by-step explanation:
Lisa wants to take a trip during her vacation. She has 8 months to save towards a trip that she
expects will cost her $4,775 including airfare, hotels, and food. Her monthly income is $3,742
with monthly costs of: $304 for taxes, $750 for housing, $631 for transportation, $521 for
food, and $803 for miscellaneous expenses, such as phone and loan payments. How much
will she be able to save in 8 months?
Answer:
$5,864
Step-by-step explanation:
If you subtract all of the monthly costs from her monthly income, it will drop down to $733 and multiply that by 8.
17. TRAFFIC SIGNS The diagram shows a sign used to warndrivers of a school
zone or crossing. Measure and classifyeach numbered angle.
each numbered angle is
1. right angle
2. obtuse angle
Road signs, often known as traffic signs, are posted along the side of roadways or above them to inform and direct drivers. Simple wooden or stone milestones were the oldest types of signs. Later, directional signs with arms were developed, such as the fingerposts used in the United Kingdom and their wooden equivalents in Saxony. Since the 1930s, as traffic volumes have increased, many nations have adopted pictorial signs or have similarly standardized and simplified their signs in an effort to overcome linguistic barriers and improve traffic safety. Such pictorial signals are typically based on international norms and use symbols (often silhouettes) in place of words. These signs were initially created in Europe and have since been adopted in varied degrees by the majority of nations.
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The complete question is attached below
(3). In an election contested by two (2) parties A and B. Party A Secuired 12% of the total votes more than party B. If party B got 132000 votes and there are no invalid votes votes, by how many & did it loose the election.
B lost the election by 15,840 votes.
Since A got 132000+12% of 132000 votes=147840 votes.
What is the solution to 12x+31 = 15?
OA. X = 6
O
O
B. X = 6 or X=-6
C. X = 6 or x = -9
D. No solutions exist.
The solution of the equation 12x + 31 = 15 is x = -4/3
In this question we have been given an equation.
12x + 31 = 15
We need to find the solution of the given equation.
12x + 31 = 15
12x + 31 - 31 = 15 - 31 ..............(Subtract 31 from each side)
12x = -16
x = -16/12 .............(Divide each side by 12)
x = -4/3
Therefore, the solution of the equation 12x + 31 = 15 is x = -4/3
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In which areas were there many labor shortages during the war?
A. Automotive industry
B. Teachers, nurses, and doctors
C. Farm and military industries
D. Industrial luxury production
Question Subtract. 3 1/3−5 Enter your answer as a simplified mixed number by filling in the boxes.
Answer:5/3
Step-by-step explanation:
first u need to change is mixed fraction in to normal fraction
3 1/3-5
3 1/3 means 3*3+1 =10
therefor 10/3-5
u need to find the lcm or the common for the two factor (3 and 1 )
the lcm is 3
so 10-5/3 =5/3
Find the value of |-8| + 4(-5 + 9) ÷ 2.
0
24
12
16
The value of the given expression is 16. The correct option is the fourth option 16
Evaluating an ExpressionFrom the question, we are to find the value of the given expression
The given expression is
|-8| + 4(-5 + 9) ÷ 2
Simplifying by applying PEMDAS
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Simplifying
|-8| + 4(-5 + 9) ÷ 2
8 + 4(4) ÷ 2
8 + 16 ÷ 2
8 + 8
= 16
Hence, the evaluation of the expression is 16
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Unlock all answers START FREE TRIAL agustinas0320 12/11/2020 Mathematics High School answered Ella works two part-time jobs, one before school and one after school. Before school, she earns$11.25/hour, and after school she earns $11..75/hour. Last week, she earned a total of $278. She works twice as many hours after school. How many hours did she work at each job last week?
Last week, Ella worked 16 hours after school and 8 hours before school using the concept of algebraic equations.
What is a mathematical equation?The equality of two mathematical expressions is demonstrated by a mathematical statement called an equation.
Algebraic equations in mathematics frequently have one or more variables.
Given: Ella makes $11.25 per hour before school and $11.75 per hour after.
Total earnings of Ella from = $278
Let x be the number of hours Ella worked before school.
Let y be the number of hours Ella worked after school.
11.25x + 11.75y = 278
Given that she works twice as long after school, it follows that
y = 2x
Substituting in the equation, we get
11.25x + 11.75(2x) = 278
11.25x + 23.5x = 278
34.75x = 278
x = 8
Similarly, y= 2x
y = 16
Ella accordingly worked 16 hours after school and 8 hours before school.
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Last month, a retailer sold 120 jar candles at $30 per candle. This month the retailer is considering putting the candles on sale. They estimate that for each $2 decrease in price, they will sell 10 additional candles.
a. How much should the retailer charge for each candle in order to maximize its profit?
b. Find the domain and the range in the context of this situation.
A) The amount that the retailer should charge for each candle in order to maximize its profit is; $27
B) The domain of the function is; x ≥ 120
The range of the function is; P(x) ≥ 3645
How to find the domain and range of the problem?
A) Let the total sales be represented by P(x).
Let the number of candles sold be x.
Now, since the retailer 120 jar candles at $30 per candle and estimated that or each $2 decrease in price, they will sell 10 additional candles.. Thus;
P(x) = (30 - 2 * (x - 120)/10)x
P(x) = 30x - x²/5 + 24x
P(x) = - x²/5 + 54x
Using -b/2a, we can get the number of candles that maximizes profit as;
-54/(2 * -1/5) = 135 candles
Plugging 135 for x into the P(x) equation gives;
P(135) = $27
B) The domain of the function is; x ≥ 120
The range of the function is; 135 * 27 = 3645
P(x) ≥ 3645
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is 4 33/100 a repeating decimal
Answer:
no
Step-by-step explanation:
4 33/100 is equal to 4.33, it is 4.33, not 4.33 with the dot on it, it means recurring decimal. It is jot a recurring decimal. :)
Is this relation a function? Justify your answer.
A. Yes, because every x-and y-value is positive.
• B. Yes, because the number of x values is the same as the number of
y-values.
• C. No, because two points with the same x-value have different y
values.
• D. No, because two points with the same y-value have different x-
values.
Answer:
C.
Step-by-step explanation:
• C. No, because two points with the same x-value have different y
values. Points with coordinates (7;4) and (7;6).
If KL = 3x, LM = 2, and KM = x + 4, what is KM?
The value of KM is equal to 5.
A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on the line located within.
Consider a point L on a line segment KM such that:
We have the values,
KL = 3x ;
LM = 2
Now, we know,
KL + LM = KM
KM = 3x + 2 ---------(1)
Now, KM = x + 4 ---------(2)
Equating the equations (1) and (2),
We get,
3x + 2 = x + 4
Now, subtract 2 from each side of the equation.
3x + 2 - 2 = x + 4 - 2
3x = x + 2
Subtracting x from each side of the equation.
3x - x = x + 2 - x
2x = 2
Dividing each side of the equation by 2.
( 2x / 2 ) = ( 2 / 2)
x = 1
Therefore,
KM = x + 4
KM = 1 + 4
KM = 5
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what is the percentage of the population under 20 in japan 2018
Answer:
about 4.89% is the percentage of population under 20 in Japan 2018
What is the answer to 811.4 + 215.5=?
Answer:
1026.9
Step-by-step explanation:
Use a calculator!
Answer:
1026.9
Step-by-step explanation:
Line the two numbers up, and start adding from the tenths place and carry numbers if needed. This could also be done with a calculator or online.
A car's fuel consumption is 7.0 litres per 100km. What is
this in miles per gallon? (A gallon is about 4.5 litres, and
a mile is about 1.6km)
Please help.
The car's fuel consumption is 1.6 gallons per 62.50 miles
What is the car's fuel consumption is miles per gallon ?The mathematical operation that would be used to solve this question is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.
The first step is to convert litres to gallons. To convert to gallons, divide 7.0 liters by the unit of conversion.
7 / 4.5 = 1.6 gallons
The second step is to convert kilometer to mile. To do this, divide 100 by the unit of conversion
100 / 1.6 = 62.50 miles
The car's fuel consumption is 1.6 gallons per 62.50 miles
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Solve the following compound inequality.
x+8≥9 andand 2x−6≥8
The solution set in interval notation
The solution set in interval notation [7, ∝)
How to solve the compound inequality?The compound inequality is given as:
x+8 ≥ 9 and 2x − 6 ≥ 8
Take the like terms
x ≥ 9 - 8 and 2x ≥ 8 + 6
Evaluate the like terms
x ≥ 1 and 2x ≥ 14
Divide by 2
x ≥ 1 and x ≥ 7
The solution set of x ≥ 7 is greater than x ≥ 1
So, we have
x ≥ 7
In interval notation, it is [7, ∝)
Hence, the solution set in interval notation [7, ∝)
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A prism has a volume of 528 cubic feet, a length of 6 feet, and a height of 11 feet. What is the width of the prism rounded to the nearest foot?
Given the volume, length and height, the width of the rectangular prism rounded to the nearest foot is 8ft.
What is the width of the given rectangular prism?The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length.
Given the data in the question;
Volume of the rectangular prism V = 528 ft³Length l = 6ftHeight h = 11ftWidth w = ?To determine the with of the rectangular prism, plug the given values into the formula above and solve for w.
V = w × h × l
528 ft³ = w × 11ft × 6ft
528 ft³ = w × 66ft²
Reorder the equation and divide both sides by 66ft²
w × 66ft = 528 ft³
( w × 66ft )/66ft² = 528 ft³ / 66ft²
w = 528 ft³ / 66ft²
w = 8ft
Given the volume, length and height, the width of the rectangular prism rounded to the nearest foot is 8ft.
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