The answers below provides the elements of the sets L1 ∪ L2, L1 ∩ L2, L1 concatenation L2, L1*, and L2* where L1 and L2 are languages over Σ = {a, b}.
What are the elements of the following sets?a) L1 ∪ L2:
The union of two sets is the set of all elements that are in either set. Therefore,
L1 ∪ L2 = {a, b, ab, λ, bb}
b) L1 ∩ L2:
The intersection of two sets is the set of all elements that are in both sets. Therefore,
L1 ∩ L2 = {ab}
c) L1 concatenation L2:
The concatenation of two languages is the set of all possible combinations of elements where the first element comes from the first language and the second element comes from the second language. Therefore,
L1 concatenation L2 = {aλ, a bb, aab, bλ, bbb, bab, abλ, abb, abab}
d) L1*:
L1* is the Kleene star of L1, which is the set of all possible combinations of elements from L1, including the empty string λ. Therefore,
L1* = {λ, a, b, ab, aa, bb, aaa, aab, abb, bbb, aaaa, aaab, aabb, abbb, ...}
e) L2*:
Similarly,
L2* = {λ, bb, ab, bbbb, abb, aabb, abbb, aabbb, ...}
Note that the Kleene star of L2 includes only elements made up of b's and λ.
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Divide and give your answer as a decimal. Round your answer to the nearest thousandth (3 digits behind the decimal).
2/9
Answer:
0.222
Step-by-step explanation:
2 divided by 9 is:
0.222 (rounded to the nearest thousandth)
In order to develop a more appealing cheeseburger, a franchise uses taste tests with 11 5 different buns, 3 different cheeses, 4 types of lettuce, and types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?
It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.
Write an absolute value equation that has the following solution set.
-8 and -2
Thank you!
The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3
What is an absolute value equation?
An absolute value equation can be written as |expression| = value
To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.
We can write,
|x + 5| = 3
To solve for x, we have two cases,
Case 1: x + 5 is positive
If x + 5 is positive, then the equation becomes x + 5 = 3
Solving for x,
x = -2
This matches one of the solutions we want.
Case 2: x + 5 is negative
If x + 5 is negative, then the equation becomes -(x + 5) = 3
Solving for x,
x = -8
This also matches the other solution we want.
Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.
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A man bought two pencils and three biros at a cost of 50, Again he bought three pencils and four biros for 70. find the cost of a pencil and a biro
ii) The door is 0.9 m wide and 2.1 m high. Each of the four windows is 1.5 m wide and 1.2 m high work out the toral area of the door and the four windows
Answer: The area of the door can be calculated as:
Area of door = width x height
= 0.9 m x 2.1 m
= 1.89 square meters
The area of one window can be calculated as:
Area of window = width x height
= 1.5 m x 1.2 m
= 1.8 square meters
Since there are four windows, the total area of the four windows is:
Total area of four windows = 4 x Area of window
= 4 x 1.8 square meters
= 7.2 square meters
Therefore, the total area of the door and the four windows is:
Total area = Area of door + Total area of four windows
= 1.89 square meters + 7.2 square meters
= 9.09 square meters
Hence, the total area of the door and the four windows is 9.09 square meters.
Step-by-step explanation:
The Greenfield Community Picnic is today. The organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches.
Answer: What is the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic?
Let's call the number of pulled-pork sandwiches "P" and the number of barbeque chicken sandwiches "C". According to the problem, the organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches. This means that:
P/C = 2/5
To simplify this ratio, we can multiply both sides by a common factor that will make the denominators the same. In this case, the smallest common multiple of 2 and 5 is 10, so we can multiply both sides by 10:
10(P/C) = 10(2/5)
Simplifying this expression, we get:
2P = 4C
Dividing both sides by 2, we get:
P/C = 2/4
Simplifying this fraction, we get:
P/C = 1/2
Therefore, the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic is 1:2.
Step-by-step explanation:
A quadrilateral is shown.
H
6.5
5.51
What is the area of the quadrilateral? Enter the answer in the box.
The calculated area of the quadrilateral is 35.82 square units.
What is the area of the quadrilateral?Given that
BAse = 6.5
Height = 5.51
To find the area of a quadrilateral, we need to multiply the base by the height.
Area of quadrilateral = base x height
Substituting the given values, we get:
Area = 6.5 x 5.51
Area = 35.815
Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.
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Nick's new home had a purchase price of $145,500. He got a 30-year fixed mortgage for 75% of the purchase price. The interest rate on the loan is 3.15%. What is his monthly payment?
Nick's monthly mortgage payment is $482.16.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To calculate Nick's monthly mortgage payment, we first need to find out the amount he borrowed from the bank, which is 75% of the purchase price:
$145,500 x 0.75 = $109,125
Next, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate (3.15%) by 12:
3.15% / 12 = 0.002625
Now we can use the following formula to calculate Nick's monthly payment:
M = P [ [tex]i(1 + i)^{n}[/tex] ] / [ [tex](1 + i)^{n}[/tex] – 1]
Where:
M = Monthly payment
P = Loan amount (principal)
i = Monthly interest rate
n = Number of payments (in months)
Plugging in the values we have:
M = $109,125 [ 0.002625 [tex](1 + 0.002625)^{360}[/tex] ] / [ [tex](1 + 0.002625)^{360}[/tex] – 1]
M = $482.16
Therefore, Nick's monthly mortgage payment is $482.16.
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Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
The total net amount the supermarket owes the wholesaler for the order is $231.31.
What does discount mean?A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.
According to the given informationTo find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.
The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:
Discounted cost = List price - (Discount rate x List price)
For the soup, the discounted cost per case is:
$18.90 - (0.39 x $18.90) = $11.51
For the baked beans, the discounted cost per case is:
$33.50 - (0.39 x $33.50) = $20.42
Now we can calculate the total net amount owed by the supermarket to the wholesaler:
Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)
Total net amount = (13 x $11.51) + (4 x $20.42)
Total net amount = $149.63 + $81.68
Total net amount = $231.31
Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.
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Find the equation of the linear function
represented by the table below in slope-intercept
form.
X: -3,1,5,9
y: -8,0,8,16
By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.
what is slope?A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).
To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.
With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:
slope = (y change) / (change in x)
slope = (16 - (-8)) / (9 - (-3))
slope = 24 / 12
slope = 2
We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:
y = mx + b 0 + b b = 2(1) + b b = -2
Hence the linear function's slope-intercept equation is:
y = 2x - 2
As a result, the linear function denoted by the table is y = 2x - 2.
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Mohal plans to repaint some classroom bookcases. He has 1 1 /8 gallons of paint. All of the bookcases are the same size and each requires 1/8gallon of paint. How many bookcases will he be able to paint?
Mohal will be able to paint 9 bookcases for the amount of paint.
What is fraction?An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.
Given that, he has 1 1 /8 gallons of paint.
Thus, number of bookcases are:
1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9
Hence, Mohal will be able to paint 9 bookcases for the amount of paint.
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When two sample means are significantly different
Group of answer choices
The pooled variance estimate should not be used
The difference is too great to attribute to chance
The corresponding population means are significantly different
The difference is of practical importance
When two sample means are significantly different, "the difference is too great to attribute to chance".
What is statistical significance?The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).
Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.
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Prove: DC = 6 units
A
6 units
D
Statements
AD || BC
ZDAC ZBCA
C
?
DC BA
DC = BA
given
alternate interior angles theorem
AC AC
reflexive property of congruence
ZDCA ZBAC alternate interior angles theorem
DC = 6 units
Which step is missing?
B
O A. ADAC
OB. ADCA
O C. ADCA
Reasons
?
CPCTC
definition of congruent sides
substitution property of equality
ABCA by SAS
ABCA by ASA
ABCA by SAS
The missing step in the proof is: D. ADCA
What is the missing step and reason of the proof?In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).
Therefore, we have the following proportional sides:
DC/AC = AC/BC
Given that DC = BA (given statement), we can substitute BA for DC in the proportion:
BA/AC = AC/BC
Now, we can cross-multiply to get:
BA * BC = AC²
Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:
BA * BC = AC * AC
Use the definition of congruent sides to replace BA with DC:
DC * BC = AC * AC
And finally, use the substitution property of equality to replace BC with 6 units (given statement):
DC * 6 = AC * AC
From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.
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Becky ate 7.5 x 10^5 milligrams of rice. Carter ate 3.1 x 10^6 milligrams of rice. who ate more?
Answer:
The Correct answer is Carter
find the factors to this polynomials i need help SHOW YOUR WORK.
Answer:
hope this will help you...
When an athlete hits a ball all of the following would make a difference in the height and distance that the ball goes. ball How hard you hit the swing ● The angle of the is blowing air Which way the wind How hard the wind is blowing Temperature of the Humidity of the air How high you hit the ball
All options except "How high you hit the ball" would affect the ball's height and distance.
Selecting which would make a difference in the height and distanceThe following factors would make a difference in the height and distance that the ball goes when an athlete hits a ball:
How hard you hit the swingThe angle of the swingWhich way the wind is blowingHow hard the wind is blowingTemperature of the airHumidity of the airTherefore, all options except "How high you hit the ball" would affect the ball's height and distance.
When an athlete hits a ball, there are several factors that can affect the ball's trajectory, including the force and angle of the swing, as well as external environmental factors such as wind, temperature, and humidity.
The harder the athlete hits the ball, the more force will be imparted to the ball, and the farther it will travel.
Similarly, the angle of the swing can affect the trajectory of the ball, with a higher or lower angle resulting in different heights and distances traveled.
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50pts!!!!
Many investors use interest-only loans to buy shares or property. For such loans the principal stays constant and only the interest is paid back each month.
She buys an investment property for $300 000 and borrows the full amount at 7% p.a. simple interest. She rents out the property at $1500 per month and pays $3000 per year in rates and other costs to keep the property.
Find the amount of interest she needs to pay back every month.
Find her yearly income from rent.
By considering the other costs in keeping the property, calculate her overall loss in a year.
she hopes that the property’s value will increase enough to cover any loss she is making. By what percentage of the original price will the property need to increase in value per year?
Step-by-step explanation:
to find the interest she needs to pay back every month, we need to use this formula:
I = PRT/12
in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:
I = (300,000)(7)(1)/12 = $17,500 in interest every month
to find her yearly income from rent, we have to multiply the monthly rent by 12
1500 × 12 = $18,000
to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000
she said that she hopes the property's value will increase to cover the loss she made.
to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as
Percentage increase = (difference in increase/Original price) × 100
so
percentage increase = (15000/300000) × 100 = 5%
so the property needs to increase in value by at least 5% per year to cover the loss.
The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.
Explanation:First, let's calculate the monthly interest she needs to pay. 7% of $300,000 is $21,000 for a year. To find the monthly interest, we divide this by 12, resulting in $1750.Her yearly income from rent is $1500 multiplied by 12, giving us $18,000.To calculate her overall loss, we add the yearly interest and the costs to keep the property, then subtract the yearly rent income. So, $21,000 + $3000 - $18,000 = $6000 loss per year.Lastly, to find out by what percentage the property value needs to increase, we divide the loss by the original price and multiply by 100, giving us 2% increase per year.Learn more about Interest and Profit Calculation here:https://brainly.com/question/32651816
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Rewrite 6x2 + 2xy + 9x + 3y in factored form. (2x + 3)(3x + y) (2x + y)(3x + 3) (3x + 2)(3x + y) (3x + y)(2x + 1)
Answer:
(3x + y)(2x + 3)
Step-by-step explanation:
Factorizing the expression:6x² = 2 * 3 * x * x
2xy = 2*x * y
Common factor = 2x.
9x = 3 * 3 * x
3y = 3 * y
Common factor = 3
Take out the common factor 2x from the first and second term & take out the common factor 3 from third and fourth term.
6x² + 2xy + 9x + 3y = 2x(3x + y) + 3(3x + y)
= (3x + y)(2x + 3)
Equipment accusers on January 8 at cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight line method
Answer: To calculate the annual depreciation expense of the equipment using the straight-line method, we need to first determine the depreciable cost of the asset, which is the cost of the asset minus its estimated residual value.
Depreciable Cost = Cost of asset - Estimated Residual Value
Depreciable Cost = $212,000 - $14,000
Depreciable Cost = $198,000
Next, we can use the following formula to calculate the annual depreciation expense:
Annual Depreciation Expense = Depreciable Cost / Useful Life
Annual Depreciation Expense = $198,000 / 15 years
Annual Depreciation Expense = $13,200 per year
Therefore, the annual depreciation expense of the equipment using the straight-line method is $13,200 per year.
Step-by-step explanation:
28) The number of hours per week that high school students spend on computers is normally distributed, with a mean
of 5 hours and a standard deviation of 2 hours. 70 students are chosen at random. Let y represent the mean number
of hours spent on the computer for this group. Find the probability that y is between 5.1 and 5.7.
The probability that y is between 5.1 and 5.7 is approximately 0.4292.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.
According to question:Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.
Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:
z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24
The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:
z1 = (5.1 - 5) / 0.24 ≈ 0.42
and
z2 = (5.7 - 5) / 0.24 ≈ 2.92
Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.
Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.
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Which expresion has the greatest value when n is equal to 4
The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.
How do we calculate?To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.
A. 5n = 5(4) = 20
B. n + 30 = 4 + 30 = 34
C. 50 - n = 50 - 4 = 46
D. 80 ÷ n = 80 ÷ 4 = 20
The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n
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Colleen is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Hartford was $250. Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer: Increase in percentage by 42% and with baggage 43.2%.
Step-by-step explanation:
we know that the price is increased from $250 to $ 335
the percentage change by increasing the price is
$355 - $ 250 = $105
percentage change will be change/original = 105/250*100 = 42%
additional charges $ 50, $105+ $50 = 155
percentage change = 155/355*100 = 43.2%
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Please help me please tysm and have a great day :)
Answer:
mean: 20mins
Step-by-step explanation:
add them all together to get 240
then divide by how many there are
240÷12=20
so the mean is 20mins
carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
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Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.
Answer: The formula for compound interest is:
A = P(1 + R/100)^t
where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.
Here, P = Rs. 3,500, R = 8%, and t = 2 years.
So, the amount after 2 years will be:
A = 3,500(1 + 8/100)^2
= 3,500(1.08)^2
= 3,892.32
Therefore, the compound interest for 2 years will be:
CI = A - P
= 3,892.32 - 3,500
= 392.32
Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.
Step-by-step explanation:
Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero
The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.
Describe Comparison Algebra?Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.
Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.
In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.
The statements that provide support for Chloe's claim are:
A. A<0 because A is to the left of zero.
F. B>0 because B is to the right of zero.
Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.
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The owner of a stereo store wants to advertise that she has many different sound systems in stock. The store carries 5 different CD players, 8 different receivers, and 10 different speakers. A sound system consists of one of each item. How many different sound systems can the store owner advertise?
The owner can advertise 400 different sound systems. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers can be explained using the four fundamental operations, generally known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.
We are given that the owner of a stereo store carries 5 different CD players, 8 different receivers, and 10 different speakers and each sound system consists of one of each item.
So, the different sound systems that the owner can advertise is obtained by using the multiplication operation, which gives:
⇒ Different sound systems = 5 * 8 * 10
⇒ Different sound systems = 400
Hence, the owner can advertise 400 different sound systems.
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Given f’(x)=4x-3 compute f(5)-f(-1)
Answer:
To solve this problem, we need to integrate the derivative f'(x) to obtain the function f(x).
∫f'(x) dx = ∫(4x - 3) dx
f(x) = 2x^2 - 3x + C
where C is the constant of integration.
To find the value of C, we need to use the fact that f(0) = 5. Substituting x = 0 into the above equation, we get:
f(0) = 2(0)^2 - 3(0) + C = C
Therefore, C = 5.
Hence, the function f(x) is:
f(x) = 2x^2 - 3x + 5
Now, we can find f(5) and f(-1) and compute their difference:
f(5) - f(-1) = (2(5)^2 - 3(5) + 5) - (2(-1)^2 - 3(-1) + 5)
f(5) - f(-1) = (50 - 15 + 5) - (2 + 3 + 5)
f(5) - f(-1) = 35 - 10
f(5) - f(-1) = 25
Therefore, f(5) - f(-1) = 25.
A car park changes £1.50 to each car entering.
The payment station only accepts £1 coins and 50p coins.
Here are the coins collected from the payment station on particular day:
Number of £1 coins 172
Number of 50p coins 256
Assuming each driver paid the exact amount due on that day, work out the percentage of the drivers that paid with three 50p coins.
Answer:
84 paid with three 50p coins.
50 Points! Multiple choice algebra question. If r(x)=x^3-2x+1, find r(2a^3). Photo attached. Thank you!
Answer:
D
Step-by-step explanation:
Answer:
D. [tex]8a^{9} -4a^{3} +1[/tex]
Step-by-step explanation:
Given [tex]r(x)=x^{3} -2x+1[/tex] and find [tex]r(2a^{3} )[/tex] :
[tex]r(2a^{3} )[/tex] is the same as saying [tex]x=2a^{3}[/tex]So, we have [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]Solve for [tex]r(2a^{3} )[/tex] :
1. [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1[/tex]
Start with simplifying [tex](2a^{3})^{3}[/tex][tex](2a^{3})^{3}=2^{3}*(a^{3})^{3}=8*a^{3*3}=8a^{9}[/tex]When you have a quantity raised to a power, or an exponent, you have to distribute the exponent to each term multiplied.When you multiply two terms that are raised to a power, you add the powers.When you divide two terms that are raised to a power, you subtract the power in the numerator from the power in the denominator.When you have a power raised to a power, you multiply the powers.2. [tex]r(2a^{3} )=8a^{9} -2(2a^{3})+1[/tex]
Simplify [tex]2(2a^{3})[/tex]Multiply two times the quantity[tex]2(2a^{3})=4a^{3}[/tex]3. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]
Answer:
So, if [tex]r(x)=x^{3} -2x+1[/tex], then [tex]r(2a^{3} )=(2a^{3})^{3} -2(2a^{3})+1=8a^{9} -4a^{3}+1[/tex].
Then the answer is D. [tex]r(2a^{3} )=8a^{9} -4a^{3}+1[/tex]