Answer:
data given
interest rate 12%
amount to be received 15ooo
time9years
Step-by-step explanation:
from
A=p[1+r/100]^n
where
A is amount
p is principal
r is rate interest
n number of interist period
now,
15000=p[1+12/100]^8
15000/1.12^8 =p×1.12^8/1.12^8
p=6058.24
p=6058)
: .you should invest 6,058
The amount to be invested initially if you want to have fifteen thousand dollars after nine years is $3947.18.
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
We are given that:
A=15000
r=0.12
t=9
We need to find P. You can do this by rearranging the formula:
P=ertA
Then plug in the given values and use a calculator:
P=e0.12×915000
P≈3947.18
Therefore, by the given interest rate the answer will be $3947.18.
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What is the meaning of [tex]\pi (i-j)/n[/tex]?
A regular polygon with n vertices' angle in radians between two consecutive axes of symmetry is referred to by the formula π(i - j) /n in the definition of the dihedral group D.
A regular polygon with n vertices' angle in radians between two consecutive axes of symmetry is referred to by the formula π(i - j) /n in the definition of the dihedral group D.
What is a subgroup?A group G's subgroups are its subsets that are also groups that fall under the same operation as G. The same axioms of G—closure, associativity, identity, and inverse—are satisfied by a subgroup, which is a subset of G that does the same. The identity element of G must be present in a subgroup, and for any element g, the inverse of g must also be present. Every pair of components g1 and g2 in the subgroup must also have their product, g1g2, present in the subgroup.
A regular polygon with n vertices' angle in radians between two consecutive axes of symmetry is referred to by the formula π(i - j) /n in the definition of the dihedral group D.
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find the smallest number that is a multiple off all 2,3,4,5,6,8 and 9
1/2 of 50 of 1/4 of ?
Answer:
[tex] \frac{1}{2} \times 50 \times \frac{1}{4} = 50 \times \frac{1}{8} = \frac{25}{4} = 6 \frac{1}{4} [/tex]
A baseball team has the starting and relief pitchers shown in the table. The manager selects a pitcher at random. Find the probability that the pitcher is left-handed.
Pitchers on Baseball Team (Table)
Pitchers Number
Left-handed starters 1
Right-handed starters 4
Left-handed relievers 2
Right-handed relievers 1
Okay, here are the steps to find the probability the randomly selected pitcher is left-handed:
1) There are 1 left-handed starter, 4 right-handed starters, 2 left-handed relievers and 1 right-handed reliever.
2) In total, there are 1 + 4 + 2 + 1 = 8 pitchers.
3) Of the 8 pitchers, 1 + 2 = 3 are left-handed.
4) So the probability the randomly selected pitcher is left-handed = (3/8) = 3/8 = 0.375
Therefore, the probability that the randomly selected pitcher from the team is left-handed is 0.375.
Let me know if you have any other questions!
in the number below, how many times greater is the number represented by the digit in the thousands place than the number represented by the digit in the hundreds place?
57,762
Answer:
Ten times greater
Step-by-step explanation:
700 x 10 = 7000
Answer:
it will be ten times greater
Step-by-step explanation:
1267.1 ml = L
pls help
1267.1 ml = 1.2671 L.
What are liter and milliliter?A little amount of liquid is measured in milliliters. You can utilize liters for larger amounts of liquid. One milliliter, or 1 ml, is equal to one liter. Milliliter can be written as ml or mL.
Large amounts of liquid are measured in liters. Kg is the unit for measuring mass, m is the unit for measuring length, and km is the unit for measuring distance among the ones provided.
To convert milliliters (ml) to liters (L), we divide the number of milliliters by 1000:
1267.1 ml ÷ 1000 = 1.2671 L
Therefore, 1267.1 ml is equal to 1.2671 L.
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1267.1mL is equal to 1.2671 L.
What does equal refers to?The term "equal" is used to indicate that two values or expressions have the same numerical value or meaning. When we say that two quantities are equal, we mean that they are exactly the same in terms of their value or magnitude. This is denoted by the symbol "=". For example, if we say that 2 + 3 = 5, we mean that the sum of 2 and 3 is exactly equal to 5. Similarly, if we say that x + 4 = 10, we mean that the value of x that satisfies this equation is exactly equal to 6. The concept of equality is fundamental to many areas of mathematics, including algebra, calculus, and geometry.
1L =1000mL
1mL=(1/1000)L
Therefore 1267.1 mL= (1267.1/1000)L
So, 1267.1 mL= 1.2671L
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ANSWER Quick Due in 5 minutes!!!!!!
The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 18, with an IQR of 16 Bus 47, with an IQR of 24 Bus 18, with a range of 16 Bus 47, with a range of 24
IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers.
Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.
WHAT IS IQR?An indicator of statistical dispersion used to describe the variability of a dataset is the interquartile range (IQR). It is derived by subtracting a dataset's 75th percentile (Q3) from its 25th percentile (Q1). When compared to other measures of variability like range, the IQR represents the middle 50% of the data and is less susceptible to outliers.
We must contrast the measurements of variability for the two buses in order to determine which one is more reliable. We can utilize range and interquartile range as measurements of variability. (IQR).
The range of a dataset is the difference between its maximum and minimum values.
The range for Bus 18 is 16 (22 - 6), whereas the range for Bus 47 is 24. (28 - 4).
As a result, Bus 47's range is greater than Bus 18's.A measure of variability that is less impacted by outliers than the range is the interquartile range (IQR). It is determined as the difference between a dataset's third and first quartiles (Q3 and Q1, respectively).
The IQR is 16 for Bus 18 (Q3 - Q1 = 22 - 6)
The IQR for Bus 47 is 24 (Q3 - Q1 = 28 - 4"). Bus 18 therefore has a lower IQR than Bus 47.IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers. Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.
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7.) Adult tickets for Disney on Ice are $6.50 while a child's ticket is only $2.50. At Tuesday night's
performance, 435 people were there in attendance. The box office brought in $1667.50 for that evening.
How many of each type of ticket were sold?
Answer:
Adult tickets: 145
Child tickets: 290
Step-by-step explanation:
Let x = adults; y = children
[tex]\left \{ {{x + y=435} \atop {6.50x+2.50y=1667.50}} \right.[/tex]
=> x = adults = 145
y = children = 290
Write an Algebraic Equation for each problem (include a let statement) and use it to solve the world problem
On number is eight less than five times another. If the the sum of the two numbers is 28, find the two numbers.
The smaller number is __.
The larger number is __.
The smaller number is 6 .
The larger number is 22
To solve this problem
Let's let x be the smaller number and y be the larger number.
From the problem, we know that one number is eight less than five times the other, so we can write:
y = 5x - 8
We also know that the sum of the two numbers is 28, so we can write:
x + y = 28
Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.
Let's solve the first equation for x
x = (y + 8)/5
Now we can substitute this expression for x into the second equation:
(y + 8)/5 + y = 28
Multiplying both sides by 5 to eliminate the fraction, we get:
y + 8 + 5y = 140
Combining like terms, we get:
6y + 8 = 140
Subtracting 8 from both sides, we get:
6y = 132
Dividing both sides by 6, we get:
y = 22
Now we can use the equation y = 5x - 8 to solve for x:
22 = 5x - 8
Adding 8 to both sides, we get:
30 = 5x
Dividing both sides by 5, we get:
x = 6
Therefore, the smaller number is 6 and the larger number is 22.
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Given cos A = 3/10 and tan A < 0 , find sin A .
Answer: Since we know that cos A = 3/10, we can use the Pythagorean identity to find sin A:
sin^2 A + cos^2 A = 1
sin^2 A = 1 - cos^2 A
sin A = sqrt(1 - cos^2 A)
Substituting cos A = 3/10, we get:
sin A = sqrt(1 - (3/10)^2)
sin A = sqrt(1 - 9/100)
sin A = sqrt(91)/10
Since we also know that tan A < 0, we know that the sine and tangent of A have opposite signs, and therefore sin A is negative.
Therefore:
sin A = -sqrt(91)/10
Step-by-step explanation:
A group of six student's in Mrs. Turner's class is working on a project. The number of hours that each student worked is shown below.
3 hours
5 hours
4 hours
4 hours
2 hours
5 hours
Which statement describes the mean number of hours worked?
The statement that describes the mean number of hours worked through which the relation is satisfied is The mean is the highest number or hours worked by any students in the group
What about mean?
In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is often called the arithmetic mean, and it is calculated by adding up all the values in the set and then dividing the result by the total number of values.
The formula for the mean is:
mean = (sum of all values) / (total number of values)
For example, suppose we have a set of four numbers: 2, 5, 8, and 11. To find the mean of this set of numbers, we add them up and divide by the total number of values:
mean = (2 + 5 + 8 + 11) / 4
mean = 26 / 4
mean = 6.5
Therefore, the mean of this set of numbers is 6.5. The mean is a commonly used measure of central tendency in statistics and data analysis, and it provides a way to summarize the general trend or average of a data set.
According to the given information:
Mean of the given condition is,
⇒ [tex]\frac{3 + 5 + 4 + 4 + 2 + 5}{6}[/tex]
⇒ [tex]\frac{23}{6}[/tex]
⇒ 3.83 mean of the given condition.
So, it indicate that The mean is the highest number or hours worked by any students in the group.
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Class: Algebra 2
I need help with these Natural Logarithms problems!!!!!
I will give lots of points!!!!
The solutions are: x = ln(2) for 2eˣ = 4, x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.
Solving equations using natural logarithmTo solve these equations using natural logarithm, we can use the following rules:
If a = eᵇ, then b = ln(a).If ln(aᵇ) = b ln(a).Using these rules, we can solve the given equations as follows:
2eˣ = 4
Divide both sides by 2 to get
eˣ = 2.
Take the natural logarithm of both sides to get
ln(eˣ) = ln(2).
Using rule 1 above, we can simplify ln(eˣ) to x, and we get
x = ln(2).
e⁴ˣ = 25
4x = ln(25).
Divide both sides by 4 to get
x = ln(25)/4.
eˣ = 72
Take the natural logarithm of both sides to get
x = ln(72).
e³ˣ = 124
Take the natural logarithm of both sides to get
3x = ln(124).
Divide both sides by 3 to get
x = ln(124)/3.
For the second set of equations, we use the same rule as above
So, we have
ln(x - 3) = 2
x - 3 = e²
x = e² + 3.
x ≈ 10.389.
Therefore, the solution is x ≈ 10.389.
ln(2t) = 4
2t = e⁴
t = 0.5 * e⁴
t ≈ 27.299.
Therefore, the solution is t ≈ 27.299.
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Fresh Produce, Inc. buys white button mushrooms for $0.87 a pack. The selling price is $1.50 a pack. What is the markup rate based on the selling price?
5 points
30%
22%
45%
42%
The markup rate based on the selling price is 42%.
What is markup rate?Markup rate is the percentage of the selling price that is added to the cost price to determine the final selling price. It is calculated as (selling price - cost price) / cost price x 100%.
In the given question,
The markup rate based on the selling price is:
Markup rate = ((Selling price - Cost price) / Selling price) x 100%
Markup rate = (($1.50 - $0.87) / $1.50) x 100%
Markup rate = (0.63 / 1.50) x 100%
Markup rate = 42%
Therefore, the markup rate based on the selling price is 42%.
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Which missing x-value would make the table a function?
we can replace the second occurrence of x = -2 with x = 1:
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
For the table to be a function, each x-value must correspond to a unique y-value. To determine the missing x-value, we need to find if there are any repeated x-values with different y-values.
The x-value 3 is paired with y-values -3 and -1, which means that the table is not a function. Therefore, we need to replace one of the x-values that appears twice with a different value.
Since x = 0 is already paired with y = 5, we cannot use 0 as the replacement. The only other x-value that appears more than once is x = -2. Therefore, we can replace one of the occurrences of x = -2 with a different value.
For example, we can replace the second occurrence of x = -2 with x = 1:
x y
3 -3
1 4
-2 -1
-2 -2
0 5
Now each x-value corresponds to a unique y-value, so the table represents a function.
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Does standard deviation means independent events
Standard deviation does not mean independent events.
Does standard deviation means independent events?No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.
Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.
Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.
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Nate is renting a compact car for 8 days and wants to buy the additional insurance. Using the information below, what is the total cost of the car rental if Nate fills the gas tank before he returns the car? Vehicle Type Daily Rental Rate Compact $56 Luxury Sedan $75 SUV $98 Minivan $90 Optional insurance cost is $10 per day. Gasoline charge of $3.50 per gallon if car returned not full.
the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $[tex]570.[/tex]
What is the total cost?To calculate the total cost of the car rental, we need to first determine the rental rate for a compact car for 8 days, including the optional insurance.
The daily rental rate for a compact car is $ [tex]56,[/tex] and the optional insurance costs $10 per day. Therefore, the total daily cost of renting a compact car with insurance is:
[tex]56 + 10 = 66[/tex]
To determine the total cost of renting the compact car for 8 days, we simply multiply the daily cost by the number of days:
[tex]66 \times 8 = $528[/tex]
Next, we need to determine the cost of gasoline if Nate returns the car without a full tank. The gasoline charge is $ [tex]3.50[/tex] per gallon, but we don't know how many gallons Nate will need to fill up the tank.
If we assume that a compact car has a gas tank capacity of around 12 gallons, and that Nate will need to refill the tank to its full capacity, then the gasoline charge would be:
$[tex]3.50 \times 12 = $42[/tex]
Finally, we can calculate the total cost of the rental, including the optional insurance and the gasoline charge if Nate returns the car without a full tank:
$[tex]528 + $42 = $570[/tex]
Therefore, the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $[tex]570[/tex].
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Find the area of the figure. Round to the nearest hundredth when necessary.
6in
14in
26in
15in
The answer is 1,764 in^2
At a local play, student tickets cost $6 each and adult tickets cost $11 each. If ticket sales were $3,000 for 400 tickets, how many students attended the play?
120
180
220
280
Answer:
If ticket sales were $3,000 for 400 tickets then 280 students attended the play.
Step-by-step explanation:
14. Type the correct answer in each box.
A41 represents the element at the line 4 and column 1, which is the same for B41.
When two matrices are added or subtract, we add or subtract the elements at the same position.
The elements are:
A41 = 7.B41 = 2.Hence:
(A - B)41 = 7 - 2 = 5.(A + B)41 = 7 + 2 = 9.When a matrix is multiplied by a constant, each element is multiplied by a constant, hence:
c41 = -3 x 5 = -15.d41 = -3 x 9 = -27.More can be learned about operations with matrices at https://brainly.com/question/16901354
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PLSSS HELP ME ITS DUE TOMORROW!!!!!
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answer: option (a) and option (e).
Step-by-step explanation:
Answer:
(a) and (e) are correct
Step-by-step explanation:
(a) x² + (y - 3)² = 6²
(b) x² + (y - 5)² = (√6)²
(c) (x - 4)² + y² = 6²
(d) (x + 6)² + y² = 12²
(e) x² + (y + 8)² = 6²
The general equation of a circle is:
(x - a)² + (y - b)² = r², where (a, b) represents the x-y coordinates of the centre, and r represents the radius.
Hence, by process of elimination, the options that have a diameter of 12 units and therefore, a radius of 6 units, are (a), (c), and (e).
Therefore, the correct choices are (a), and (e), as (c) has a circle centre of (4,0) and does not lie on the y-axis.
A bakery owner wants to keep his bakery open a few more hours every evening. He wants to
conduct a survey to determine whether extending the bakery's hours would be what customers
want. Which survey method would likely produce the most representative sample?
A. Ask 20 of the bakery's employees as they arrive for work.
B. Ask the first 20 customers who enter the bakery tomorrow.
C. Ask 20 of the bakery's regular suppliers as they make deliveries.
D. Ask 20 customers as they visit the bakery over the course of a day.
"Ask 20 customers as they visit the bakery over the course of a day." would likely produce the most representative sample.
What is sample?In statistics, a sample refers to a group of individuals or objects that are selected from a larger population and used to represent that population for the purpose of statistical analysis and inference. A sample is often used because it is impractical or impossible to examine every member of the population, so a smaller group is chosen that is expected to be representative of the larger population. The goal of sampling is to obtain accurate and reliable information about the population by studying the characteristics of the sample.
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Hurry please combine Leon’s results and Celia’s results to find the experimental probability of spinning a 4
The experimental probability of spinning a 4 will equals to 0.3.
How to find the experimental probability of spinning a 4?Outcome Tally Frequency
1 IIII 4
2 III 3
3 IIIIIIII 7
4 IIIIII 6
Total 20
The probability of spinning a 4:
= 6/20
= 3/10
= 0.3
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Whats the answer. There is a sreenshot attached.
Answer:
a) 5x/16
b) x = 32
Step-by-step explanation:
a) x/8 + 3x/16 can be simplified by getting a common denominator. x/8 can be changed like this:
x/8 × 2/2 is 2x/16
now we have:
2x/16 + 3x/16
= 5x/16
b) solve x/8+3x/16=10
change the left side of the equation as in part a.
5x/16 = 10
multiply both sides of the equation by 16
5x = 160
divide by 5
x = 32
Consider the statement “If you are under age 17, then you cannot attend this movie.”
a. Write the converse.
b. Write the inverse.
c. Write the contrapositive.
a. The converse, inverse and contrapositive are "If you cannot attend this movie, then you are under age 17.", "If you are over age 16, then you can attend this movie." and "If you can attend this movie, then you are not under age 17."
Writing the other versions of the statementThe original statement is an example of a conditional statement, which is a statement of the form "if A, then B." The part that comes after "if" is called the hypothesis, and the part that comes after "then" is called the conclusion.
To find the converse of the statement, we switch the hypothesis and conclusion. The converse of a conditional statement may or may not be true. In this case, the converse is not true.
To find the inverse of the statement, we negate both the hypothesis and conclusion. The inverse of a conditional statement may or may not be true. In this case, the inverse is not true.
To find the contrapositive of the statement, we switch and negate both the hypothesis and conclusion. The contrapositive of a conditional statement is always true if the original statement is true. In this case, the contrapositive is true.
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Select Repeating or Nonrepeating to correctly classify each decimal.
The correct Repeating or Non-repeating decimals are-
Repeating - 2.23(bar) , 3.426(bar) , 4.321321....
Non-repeating - 1.01011
Explain about the Repeating or Non-repeating decimals:As fractions and decimals both represent portions of a whole, many decimals can be expressed as fractions. "Rational numbers" are defined as decimals that can be expressed as fractions. "Irrational numbers" are decimals that cannot be expressed as a fraction.
A decimal number that never ends and never repeats itself is known as a non-terminating, non-repeating decimal.Such decimals are irrational numbers since they cannot be expressed as fractions.Repeating decimals: The decimals which will not end and the number will repeat again and again.
Repeating - 2.23(bar) , 3.426(bar) , 4.321321....
Non-repeating: These decimals will not have the repeating numbers after the decimal poins.
Non-repeating - 1.01011
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What is the least whole number that rounds to 570 when rounded to the nearest ten?
What is the greatest whole number that rounds to 570 when rounded to the nearest ten?
Use the number pad to enter your answers in the boxes.
Least number:
Greatest number:
Answer:
Least: 565
Greatest: 574
Step-by-step explanation:
564 would round down to 560 and 575 would round to 580
Helping in the name of Jeus.
The least whole number that rounds to 570 when rounded to the nearest ten is 570. The greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
Explanation:To find the least whole number that rounds to 570 when rounded to the nearest ten, we need to look at the digit in the tens place. In this case, the tens digit is 7. Since the number can only round up or down, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 570 than to 580, we can round down to 570. Therefore, the least whole number that rounds to 570 when rounded to the nearest ten is 570 itself.
On the other hand, to find the greatest whole number that rounds to 570 when rounded to the nearest ten, we again need to look at the digit in the tens place. Since the tens digit is 7, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 580 than to 570, we can round up to 580. Therefore, the greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
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Have vehicles gotten more fuel-efficient over the years? Between 1960 and 1999 the size and shape of automobiles in the United States has changed almost annually. The amount of fuel consumed by these vehicles has also changed. The following table describes the average fuel consumption per year per passenger car in gallons of gasoline.
B is wrong
The average rate of change in fuel consumption per year from 1995 to 1997 will be option c.) 4 gallons per year
What is average rate of change?The average rate of change, sometimes referred to as the average rate of variation, is a measurement of the average rate of change of a quantity over a certain period of time or space. It is frequently used in physics, mathematics, and other academic fields to explain how quickly one quantity changes with relation to another.
For given problem,
[tex]\text{Average fuel consumption per year per passenger car in 1995} = 530\; gallons[/tex]
[tex]\text{Average fuel consumption per year per passenger car in 1997} = 538\; gallons[/tex]
[tex]\text{Change in fuel consumption } \delta g= 538 - 530 = 8 \;gallons[/tex]
[tex]\text{Change in years} \; \delta t= 1997 - 1995 = 2 \;years[/tex]
We can now determine the average annual change in fuel consumption:
[tex]\text{Average rate of change} = \text{Change in fuel consumption} /\text{ Change in years}[/tex]
[tex]\delta g/ \delta t[/tex]= [tex]8\; gallons / \;2 \;years= 4 \;gallons\; per\; year[/tex]
Hence, 4 gallons per year is the accurate average rate of change in gasoline usage per passenger automobile between 1995 and 1997. This shows that, on average, fuel efficiency declined throughout this time for passenger cars in the United States, with average gasoline usage rising.
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please help and please show step by step :)
(3,4) , (5,80) ,(7,188)
(10,245), (13,305)
(1,9), (2,15), (4,87) , (6,279)
for each data set above
a)State the degree of the interpolant
b) Write each system of the equations that must be solved to find the interpolant
c) Find the Vandermonde matrix corresponding to the system of equations
a) The degree of the interpolant is 3.
b) Required system of equations are
[tex]a_0 + 3a_1 + 9a_2 = 4 \\ a_0 + 5a_1 + 25a_2 = 80 \\ a_0 + 7a_1 + 49a_2 = 188 \\ a_0 + 10a_1 = 245 \\ a_0 + 13a_1 = 305 \\ a_0 + a_1 + a_2 + a_3 = 9 \\ a_0 + 2a_1 + 4a_2 + 6a_3 = 15 \\ a_0 + 4a_1 + 16a_2 + 36a_3 = 87 \\ a_0 + 6a_1 + 36a_2 + 216a_3 = 279[/tex]
c) Required Vandermonde matrix corresponding to the system of equations are [ 1 3 9; 1 5 25; 1 7 49], [1 10; 1 13], [1 1 1 1; 1 2 4 6; 1 4 16 36; 1 6 36 216].
a) How to determine the degree of the interpolant?
To determine the degree of the interpolant, we count the number of data points in each set, subtract one, and take the minimum of the resulting values. This is because a polynomial of degree n can exactly interpolate n+1 distinct data points.
For the first set, we have 3 data points, so the interpolant can have degree at most 2.
For the second set, we have 2 data points, so the interpolant can have degree at most 1.
For the third set, we have 4 data points, so the interpolant can have degree at most 3.
b) How to find the interpolant for each set?
To find the interpolant for each set, we need to solve a system of equations. Let f(x) be the interpolant for each set, and let [tex]x_i[/tex] be the x-coordinate of the ith data point, and yi be the corresponding y-coordinate. Then we need to find the coefficients [tex]a_0, a_1, ..., a_n[/tex] such that [tex]f(x_i) = a_i(x_i)^n + a_{i-1}(x_i)^{(n-1)} + ... + a_1 \times x_i + a_0 = y_i[/tex] for i = 1, 2, ..., m, where m is the number of data points in the set. This gives us m equations in n+1 unknowns.
For the first set,
[tex]a_0 + 3a_1 + 9a_2 = 4 \\ a_0 + 5a_1 + 25a_2 = 80 \\ a_0 + 7a_1 + 49a_2 = 188[/tex]
For the second set,
[tex]a_0 + 10a_1 = 245 \\ a_0 + 13a_1 = 305[/tex]
For the third set,
[tex]a_0 + a_1 + a_2 + a_3 = 9 \\ a_0 + 2a_1 + 4a_2 + 6a_3 = 15 \\ a_0 + 4a_1 + 16a_2 + 36a_3 = 87 \\ a_0 + 6a_1 + 36a_2 + 216a_3 = 279[/tex]
c) The Vandermonde matrix corresponding to the system of equations is an m x (n+1) matrix V, where the ith row is [tex] [x_i^n, x_i^{(n-1)}, ..., x_1, 1] [/tex] for i = 1, 2, ..., m. The columns of the matrix correspond to the coefficients of the interpolant.
For the first set,
V = [ 1 3 9; 1 5 25; 1 7 49]
For the second set,
V = [1 10; 1 13]
For the third set,
V = [1 1 1 1; 1 2 4 6; 1 4 16 36; 1 6 36 216]
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A random sale of 40 flower shop customers was surveyed to find customers' favorite flowers. The table shows the results. The shop expects to sell 50 bunches of flowers on Sunday. How many bunches of each flower should the shop order?
Answer:
below
Step-by-step explanation:
To find out how many bunches of each flower the shop should order, we need to calculate the percentage of customers who preferred each flower, and then use that percentage to estimate the number of bunches needed for each flower.
First, we need to calculate the total number of customers who were surveyed:
Total customers surveyed = 8 + 4 + 8 + 20 = 40
Next, we can calculate the percentage of customers who preferred each flower:
Percentage of customers who preferred daisy = (8/40) x 100% = 20%
Percentage of customers who preferred gardenia = (4/40) x 100% = 10%
Percentage of customers who preferred mum = (8/40) x 100% = 20%
Percentage of customers who preferred rose = (20/40) x 100% = 50%
Now, we can use these percentages to estimate how many bunches of each flower to order.
Let's assume that each bunch contains 10 flowers (this is just an example, the actual number may vary):
Number of bunches of daisy to order = 20% of 50 bunches = 10 bunches
Number of bunches of gardenia to order = 10% of 50 bunches = 5 bunches
Number of bunches of mum to order = 20% of 50 bunches = 10 bunches
Number of bunches of rose to order = 50% of 50 bunches = 25 bunches
So, the shop should order 10 bunches of daisy, 5 bunches of gardenia, 10 bunches of mum, and 25 bunches of rose to meet the expected demand on Sunday.