Kylie changed the ratio of blue to yellow in her paint mixture from 5:3 to 3:4, making the colour more yellowy. She could have started with either 3.5 litres of blue and 2.1 litres of yellow, or 7 litres of blue and 4.2 litres of yellow. She could have added either 0.7 litres of blue and 3.5 litres of yellow, or 1.4 litres of blue and 7 litres of yellow to achieve the new ratio.
The new colour is more yellowy than the first colour because the ratio of blue to yellow has changed. Initially, the ratio was 5:3, or 5 parts blue to 3 parts yellow. After Kylie added more blue and 5 times as much yellow than blue, the ratio changed to 3:4, or 3 parts blue to 4 parts yellow. This means yellow is now the majority colour, which makes the final colour more yellowy than the first.
To calculate the amount of blue and yellow in the new mixture, we can use the equation:
Blue : Yellow = 3 : 4
Therefore, the amount of blue needed is 3/7 of the total, and the amount of yellow is 4/7 of the total.
2a) How many litres of each colour could Kylie have started with?
Possibility 1: Kylie could have started with 3.5 litres of blue and 2.1 litres of yellow (3.5 : 2.1 = 5 : 3).
Possibility 2: Kylie could have started with 7 litres of blue and 4.2 litres of yellow (7 : 4.2 = 5 : 3).
2b) How many litres of each colour could Kylie have added?
Possibility 1: Kylie could have added 0.7 litres of blue and 3.5 litres of yellow (0.7 : 3.5 = 3 : 4).
Possibility 2: Kylie could have added 1.4 litres of blue and 7 litres of yellow (1.4 : 7 = 3 : 4).
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magine that party a is selling a car to party b. party a thinks there is an 80% chance the car will not break down in the first year, while party b thinks there is an 80% chance it will. design a contingency contract that could help them avoid an impasse over this issue.
The steps taken to design a contingency contract are valuating the potential outcomes, consequences and agree on terms of contract.
Identify the potential outcomes. Party A thinks that there is an 80% chance that the car will not break down in the first year, while Party B thinks that there is an 80% chance that it will. These are the two potential outcomes that need to be identified.
Determine the consequences of each outcome. Next, the consequences of each outcome should be determined. For example, if the car breaks down in the first year, then Party A may have to pay for repairs or reimburse Party B for the purchase price of the car. If the car does not break down, then no consequences need to be determined.
Agree on the terms of the contract. Finally, both parties need to agree on the terms of the contract. This may include how much Party A will have to pay if the car breaks down, how long Party B has to wait for reimbursement if the car does break down, and any other terms that are relevant to the situation. Once the terms have been agreed upon, the contingency contract can be signed by both parties, and they can proceed with the sale of the car.
A contingency contract could be designed to help them avoid an impasse over the issue of the car's breakdown. The contingency contract is a contract that is triggered by a specific event or circumstance, such as the car breaking down in the first year. This contract outlines what will happen if the event or circumstance occurs, and both parties agree to the terms in advance.
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Ben purchases 2 drinks and a bag of popcorn at the movie theater, for a total of $9.50. If x represents the cost of the drinks and y represents the cost of the popcorn, which equation represents this situation?
An equation that represents this situation include the following: D. y = -2x + 9.50.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the cost of the drinks and the cost of the popcorn respectively, and then translate the word problem into a linear equation as follows:
Let the variable x represent the cost of the drinks.Let the variable y represent the cost of the popcorn.Since Ben purchased 2 drinks and a bag of popcorn at the movie theater, for a total cost of $9.50, a linear equation that models the situation is given by this mathematical expression:
2x + y = 9.50
By making y the subject of formula, we have:
y = -2x + 9.50
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If you can afford $900 to $1080 apartments. How much do you make a year?
Answer:
$43,200
Step-by-step explanation:
The amount of money you make a year depends on various factors, such as your monthly expenses, debt obligations, and tax liabilities.
To get a rough estimate of your annual income based on the range of affordable rent provided, you can use the rule of thumb that suggests spending no more than 30% of your gross income on housing expenses. Assuming you are willing to spend between $900 and $1080 per month on rent, we can calculate the range of annual incomes that would allow you to meet this guideline:
$900/month rent x 12 months = $10,800/year rent
$10,800/year rent / 0.3 = $36,000/year gross income
$1080/month rent x 12 months = $12,960/year rent
$12,960/year rent / 0.3 = $43,200/year gross income
Therefore, based on the assumption that you can afford rent between $900 and $1080 per month, your estimated annual gross income would need to be in the range of $36,000 to $43,200. However, this is only a rough estimate and may not take into account all of your individual financial circumstances.
3.6.2 Reflect the plane in the x-axis, and then in the line y = 1/2. Show that the resulting isometry sends (x,y) to (x,y+1), so it is the translation to.1. 3.6.3 Generalize the idea of Exercise 3.6.2 to show that the combination of reflec- tions in parallel lines, distance d/2 apart, is a translation through distance d, in the direction perpendicular to the lines of reflection. 3.6.4 Show, by a suitable picture, that the combination of reflections in lines that meet at angle 8/2 is a rotation through angle 0, about the point of intersec- tion of the lines. Another way to put the result of Exercise 3.6.4 is as follows: Reflections in any two lines meeting at the same angle 0/2 at the same point P give the same outcome. This observation is important for the next three exercises (where pictures will also be helpful).
The transformation as a whole is given by P → Q → R → S. A rotation through angle, about the intersection point of the lines, results from the combination of reflections in lines that meet at angle /2.
Two reflections across intersecting lines equal what?Two reflections across intersecting lines have the same composition as one rotation with the junction point as the centre of rotation.
By (0,-1/2), the initial translation is provided.
Given by is the reflection along the x-axis (x,-y)
By (0,1/2), the final translation is indicated. Hence, the transformation as a whole is provided by
(x,y) → (x,-y) → (x,-y+1/2) → (x,y+1)
This demonstrates that the resulting isometry moves the values of (x,y) by one unit in the positive y-direction to (x,y+1).
The whole transformation is provided by:
P → P + (0,d/2) → Q → Q - (0,d/2)
The total transformation is given by:
P → P + (d/2,0) → (x,-y) → (x,y) → Q
where Q is positioned (x,y). Adding the two transformations together, we obtain:
P → P + (0,d/2) → Q → Q - (0,d/2) = P + (d,0)
This demonstrates that a translation across distance d, in the direction perpendicular to the lines of reflection, results from the combination of reflections on parallel lines spaced d/2 apart.
The total transformation is given by:
P → Q → R → S
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how to rewrite the mixed number as an improper fraction. draw please help me bc it do tomorrow PLEASE HELP PLEASE IT DO TOMORROW.
Answer:
To rewrite a mixed number as an improper fraction, you need to multiply the whole number by the denominator of the fraction, then add the numerator. The resulting sum is the numerator of the improper fraction, while the denominator remains the same.
For example, to rewrite the mixed number 3 1/2 as an improper fraction, you would:
Multiply the whole number 3 by the denominator 2: 3 x 2 = 6
Add the numerator 1 to the product: 6 + 1 = 7
Write the sum 7 as the numerator of the improper fraction, with the denominator 2: 7/2
So, the improper fraction equivalent of the mixed number 3 1/2 is 7/2.
Step-by-step explanation:
A right triangle is removed from a rectangle to create the shaded region shown below find the area of the shaded region be sure to include the correct unit and your answer 3 ft 3 ft 8ft 10ft
The area of shaded region is 45 square units.
How to determine the area of shaded region?The complete question is added as an attachment
The area of the shaded region is calculated as
Shaded region =Area of rectangle - Area of triangle
Using the above as a guide, we have the following:
Area of rectangle = 8 * 6 = 48
Area of triangle = 1/2 * 2 * 3 = 3
Substitute the known values in the above equation, so, we have the following representation
Shaded region = 48 - 3
Evaluate the difference
Shaded region = 45
Hence, the shaded region is 45 square units.
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The numbers 1 through 10 are put in one bag. The numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number? Enter your answer as a fraction.
Answer:
6/100=3/50
Step-by-step explanation:
The first bag contains the numbers 1 through 10, which is a total of 10 numbers. The second bag contains the numbers 5 through 14, which is also a total of 10 numbers.
The probability of picking the same number from both bags is the number of ways of picking the same number divided by the total number of possible outcomes. There are 10 possible outcomes in each bag, so the total number of possible outcomes is 10 × 10 = 100.
To count the number of ways of picking the same number, we can simply count the number of numbers that appear in both bags. There are six numbers that appear in both bags: 5, 6, 7, 8, 9, and 10.
Therefore, the probability of picking the same number from both bags is:
6/100
Simplifying this fraction by dividing both the numerator and denominator by 2 yields:
3/50
So the probability of picking the same number from both bags is 3/50.
find the area of a figure with 4cm 3 cm and 10 cm
help me with this question please
Answer:
2.50 p + 1.50p
Step-by-step explanation:
if you buy an item x amount of times you would times the two to figure out the total cost of that type of item then add with the other
How can you show that two fractions are reciprocals?
Subtract the fraction from its reciprocal. Their difference will be 1.
Divide a fraction by its reciprocal. This will show that the quotient is always 1.
Multiply a fraction by its reciprocal to show that their product is always 1.
Add the fraction and its reciprocal. Their sum will be 1.
Answer:
To show that two fractions are reciprocals, you can multiply them together and check if the product is equal to 1. That is, if we have two fractions a/b and b/a, their product is:
(a/b) * (b/a) = ab / ba = 1
Therefore, if the product of two fractions is equal to 1, they are reciprocals of each other.
For example, let's say we have the fractions 2/5 and 5/2. We can multiply them together to check if they are reciprocals:
(2/5) * (5/2) = 1
Since the product is equal to 1, we can conclude that 2/5 and 5/2 are reciprocals of each other.
Conner worked on Monday, M, and Friday, F, for a total of 12 hours. He charges $5 per hour on Monday and $8 per hour on Friday. If the total amount Conner received was $81, how many hours did he work on Monday
Conner worked 5 hours on Monday.
Let's use the letters "m" and "f" to denote the number of hours Conner worked on Monday and Friday, respectively.
Conner worked a total of 12 hours, and since we know this from the issue statement, we may write:
m + f = 12
Also, we are aware that Conner received $81 and charged $5 on Mondays and $8 on Fridays. Hence, we can write:
5m + 8f = 81
To determine one of the variables in terms of the other, we can utilise the first equation. To solve for "f," we obtain:
f = 12 - m
We can now solve for "m" by substituting this expression for "f" in the second equation:
5m + 8(12 - m) = 81
After simplifying and finding "m," we obtain:
5m + 96 - 8m = 81
-3m + 96 = 81
-3m = -15
m = 5
Conner spent 5 hours at work on Monday as a result.
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In the given the figure above, m∠BAC= 64° and m∠CBA=56°.
Part I: Find the m∠DEC .
Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.
I. The measure of angles DEC is: 60°
II. The theorems used are corresponding angles and triangle sum theorems.
What is the Triangle Sum Theorem?
We are given the following:
m∠BAC = 64°
m∠CBA = 56°
AB║CD
BC║DE
Considering triangle ABC, we have:
m∠BCA = 180 - m∠BAC - m∠CBA [triangle sum theorem]
Substitute:
m∠BCA = 180 - 64 - 56
m∠BCA = 60°
Therefore, based on the corresponding angles theorem,
m∠DEC = m∠BCA
Substitute:
m∠DEC = 60°
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A city bus collected $780 in fares in one day. The price of a regular fare was $0.80, and the price of a discount fare was $0.40. If a total of 1200 paid the fares on this bus, write a system of equations that represents this situation.
its b
i have covid and want to know what to do
The Central Limit Theorem states that The sampling distribution of the sample standard deviation will be approximately normal as long as the sample size is large enough. The sampling distribution of the sample mean will be approximately normal as long as the original population is normal. The distribution of the sample will be approximately normal as long as the sample size is large enough. The sampling distribution of the sample mean will be approximately normal as long as the sample size is large enough regradless of the underlying population distribution. QUESTION 14 Assume that the time spent on social media daily by ZU students has a mean of 130 minutes and a standard deviation of 43 minutes. If random samples of 246 students are selected, find the standard error of the mean? Round your answer to 2 decimal places. QUESTION 15 Assume that the speed of vehicles traveling on MBZ Highway is normally distributed with a mean of 108 km/h with a standard deviation of 5.5 km/h. According to the empirical rule, 95.44% of the speeds of vehichles traveling on MBZ Highway will be between 97 and 119 km/h 86 and 130 km/h 102.5 and 113.5 km/h 91.5 and 124.5 km/h
14: 2.38 minutes
15: lower bound is 97 km/h and the upper bound is 119 km/h
Question 14: The standard error of the mean (SE) can be calculated using the following formula: SE = s/√n, where s is the standard deviation of the population (43 minutes) and n is the sample size (246 students). Plugging in the values, SE = 43/√246 ≈ 2.38. Therefore, the standard error of the mean is 2.38 minutes and it should be rounded to 2 decimal places, giving us 2.38 minutes.
Question 15: According to the empirical rule, 95.44% of the speeds of vehicles traveling on MBZ Highway will be between 97 and 119 km/h. Therefore, the lower bound is 97 km/h and the upper bound is 119 km/h.
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what is the surface area of the rectangular prism below
Answer: A=490
Step-by-step explanation:
Formula - A = 2 ( wl + hl + hw)
2(7•14+7•14+7•7) = 490
How would i find percent of a number in this case 81% of 108 The work part i have the answer
I dont know how to do this
pls answer if u know with simple working
i dont know if u add 4 each time it didnt work for last questionn
The 3rd term of the linear sequence above is 14.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 18 - 22
Common difference, d = -4
For the third term, we have:
a₃ = a₁ + (n - 1)d
a₃ = 22 + (3 - 1)-4
a₃ = 22 - 8
a₃ = 14.
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What is the answer in the photo
The sales price of the item after deduction of percentage discount is: $18
How to find the discounted price?The regular price is defined as the price at which similar goods or services are regularly sold on the market.
The discount is defined as an amount or perhaps percentage deducted from the normal selling price of something.
The sales price is defined as the actual amount for which a good is sold after deduction of discount if any.
The parameters given are:
Regular Price = $20
Percentage Discount = 10%
Thus:
Discount = 10% * 20
Discount = $2
Thus:
Sales Price = $20 - $2
= $18
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Is 12 a integer and is 55.3 a integer and is 18 over 2 a integer and is -260.43 a integer and is 12 over 17 a integer ?
Answer:
yes
no
yes
no
no
Step-by-step explanation:
An integer is a positive or negative whole number or zero.
Examples of integers:
-1000, 993, 12, -19, 1000000, -79, 0, 1, 221
Examples of numbers that are not integers:
-5/4, -223.25, 1000.1, 45.2, 1000000.45, 32/7
Is 12 a integer yes
and is 55.3 a integer no
and is 18 over 2 a integer = 9, so yes
and is -260.43 a integer no
and is 12 over 17 a integer =0.70588..., so no
solve using elimination
5x-y=-6
x-y=-2
Answer: 5x/5 = -6/5 + y/5
Step-by-step explanation:
x = -6 + y/5
and then x = -2 +y
Given Matrices A and B shown below, find B - 2A. Let B - 2A = C.
The value of C(22) =
We need to look at the element in the second row, second column of C, which is -3. Therefore, C₂₂ = -3.
Describe Matrix?In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are used to represent linear transformations, as well as to solve systems of linear equations.
A matrix with m rows and n columns is called an m x n matrix. The individual entries of a matrix are denoted by a subscript, with the first subscript indicating the row and the second subscript indicating the column. For example, the entry in the second row and third column of a matrix A would be denoted by A[2,3].
Matrices can be added, subtracted, multiplied, and divided (by a scalar). Addition and subtraction of matrices is done element-wise, while matrix multiplication involves taking the dot product of rows and columns. Multiplying a matrix by a scalar involves multiplying every entry in the matrix by that scalar.
To find B - 2A, we need to multiply every element of A by 2 and then subtract the resulting matrix from B:
2A = [(-4)*2 (-3)*2 ; (-2)*2 (-3)*2 ; (-3)2 32 ; (-2)2 42] = [-8 -6 ; -4 -6 ; -6 6 ; -4 8]
B - 2A = [6 -9 ; 7 12 ; -3 -3 ; 2 -7] - [-8 -6 ; -4 -6 ; -6 6 ; -4 8] = [14 -3 ; 11 18 ; 3 9 ; 6 -15]
So C = B - 2A = [14 -3 ; 11 18 ; 3 9 ; 6 -15]
To find C₂₂, we need to look at the element in the second row, second column of C, which is -3. Therefore, C₂₂ = -3.
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The total revenue, in dollars, from the sale of x units of a product is given by 2200x R(x) = in(8x + 8) (a) Find the marginal revenue MR function. x In((8x+8)2200) – 2200x + ln((8x + 8)2200) in?(8x + 8)(x+1) MR = (b) Find the marginal revenue when 100 units are sold. (Round your answer to the nearest cent.) $ Interpret your result. O The cost of producing one additional unit is approximately this amount. O Selling one additional unit yields approximately this amount. O The total cost of producing 100 units is this amount. O The total revenue from selling 100 units is this amount.
The marginal revenue when 100 units are sold is approximately $17.12. Selling one additional unit at this point would yield approximately $17.12 in additional revenue.
To find the marginal revenue, we first need to find the derivative of the total revenue function with respect to x, which is the definition of marginal revenue:
R(x) = 2200x/(ln(9x+9))
Using the quotient rule, we get:
R'(x) = (2200(ln(9x+9)) - 2200x(1/(9x+9))(1/(9x+9)))/(ln(9x+9))^2
Simplifying this expression, we get:
R'(x) = 2200(9x)/(9x+9)^2ln(9x+9)^2
Substituting x=100, we get:
R'(100) = 2200(9(100))/((9(100)+9)^2ln(9(100)+9)^2 = $9.77 (rounded to the nearest cent).
Interpretation: The marginal revenue when 100 units are sold is $9.77. This means that selling one additional unit of the product will increase the total revenue by approximately $9.77.
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Complete question:
The total revenue, in dollars, from the sale of x units of a product is given by R(x)=2200x/(ln(9x+9)). Find the marginal revenue when 100 units are sold. (Round your answer to the nearest cent.) Interpret your result.
in a group of 23 people, what is the probability at least 2 have the same birthday? you may assume no one was born on a leap year and that each of the 365 days is equally likely. (suggestion: use the rule for complements)
The probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.
The probability of at least 2 people having the same birthday in a group of 23 people can be calculated using the rule for complements. The complement of this event is that all 23 people have different birthdays. We can calculate the probability of this event and then subtract it from 1 to find the probability of at least 2 people having the same birthday.
The probability of the first person having a different birthday from the others is 1. The probability of the second person having a different birthday from the first is 364/365, since there are 364 days left that are not the first person's birthday. The probability of the third person having a different birthday from the first two is 363/365, and so on.
The probability of all 23 people having different birthdays is:
1 * (364/365) * (363/365) * ... * (343/365)
This simplifies to:
364! / (36522 * 341!)
Using a calculator, we find that this is approximately 0.4927.
Therefore, the probability of at least 2 people having the same birthday is:
1 - 0.4927 = 0.5073
So, the probability of at least 2 people having the same birthday in a group of 23 people is 0.5073.
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In a group of 23 persons, the probability that at least two of them share the same birthday is around 0.5073, or 50.73%.
The probability that at least 2 people in a group of 23 have the same birthday, can be calculated by using the rule for compliments. First, we can calculate the probability that no two people share a birthday in a group of 23.
The first individual will have any birthday, however the 2nd individual have to have a distinct birthday, which has a probability of 364/365 (since there are 365 days in a year and one day has already been "used" by the first person). The probability that the third individual will have a different birthdate from the previous two is 363/365. Continuing in this way,
The probability that all 23 people have different birthdays is:
(365/365) x (364/365) x (363/365) x ...
Since the probabilities of all conceivable outcomes must sum up to 1, subtract the likelihood that at least two persons will have the same birthdate from one:
P(at least 2 people have the same birthday) = 1 - (365/365) x (364/365) x (363/365) x ... x (344/365)
P(at least 2 people have the same birthday) = 0.5073
Therefore, the probability that at least 2 people in a group of 23 have the same birthday is approximately 0.5073 or 50.73%
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Approximate, to the nearest 0.1˚, all angles θ in the interval [0˚, 360˚)[0˚, 360˚) that satisfy the equation. (Enter your answers as a comma-separated list.)
(a) sinθ=0.6264
(b) cosθ=−0.6405
(c) tanθ=−1.5519
(a) 40.4° or 139.6°
(b) 137.6° or 222.4°
(c) 124.2° or 304.2°
(a) sinθ=0.6264:θ=40.4° or 139.6°
(b) cosθ=-0.6405:θ=137.6° or 222.4°
(c) tanθ=-1.5519:θ=124.2° or 304.2°.What is interval? An interval is a set of real numbers with the property that every number that lies between two numbers in the set is also included in the set. Let's look at some of the most popular sets of numbers: the integers, the real numbers, and the natural numbers. What is an angle? An angle is a figure formed by two rays starting at a common endpoint called the vertex. The rays are known as sides of the angle, and the point of their intersection is known as the vertex. Angles are usually classified based on their size: acute angles, right angles, obtuse angles, and straight angles are examples. The following is how to solve the problem; 1. In each of the cases given, use the inverse function of sin, cos, or tan to calculate the value of the angle.2. Ascertain if the angle you've calculated is in the required interval.3. Since this question asks for an approximation to the nearest 0.1 degrees, express your solutions to one decimal point.Let's look at the following options:(a) sinθ=0.6264θ = 40.4° or 139.6°(b) cosθ=−0.6405θ = 137.6° or 222.4°(c) tanθ=−1.5519θ = 124.2° or 304.2°.Therefore, to the nearest 0.1 degrees, all angles θ in the interval [0˚, 360˚) that meet the equation are 40.4°, 139.6°, 137.6°, 222.4°, 124.2°, and 304.2°.
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what is the answer to this?
[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response as Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression.
what is polynomial ?Using just the methods of addition, elimination, and multiplication as well as ou pas integer exponents, a polynomial is a mathematical equation made up of variables and coefficients. A polynomial, for instance, is 3x2 - 2x + 5, where x has been the component and 3, -2, and 5 are now the coefficients. This polynomial's highest exponent is 2, which also happens to be its degree. Polynomials can have coefficients that are either constants or other polynomials, as well as many variables. Due to their usage in representing a variety of mathematical relations and functions, polynomials play a significant role in mathematics. Several disciplines, including algebra, algebra, geometry, and physics, make extensive use of them.
given
To make [tex]5x^2-x-8x^2 + 3x^3[/tex]simpler, we can rearrange the terms and join comparable terms:
[tex]0 + 3x^3 - x - 3x^2 = 5x^2 - 8x^2 + 3x^3 - x[/tex]
The following step is to factor the final three terms to remove a common factor of x:
[tex]3x^3 - x - 3x^2 = x\\(3x^2 - 1 - 3x)[/tex]
Hence, the abbreviated form is:
[tex]3x^2 - 1 - 3x^3 = 5x^2-x-8x^2 + 3x^3.[/tex]
Due to the fact that Option C,[tex]3x^3 + x^2 = 0[/tex], does not equal the supplied expression, it is incorrect.
Due to their failure to simplify to the specified formula, options A, [tex]-5x^3+ x^2 = 0,[/tex] and D, [tex]3x^3 -3x^2 =6x[/tex], are likewise incorrect.
[tex]3x^3 + x^2 = 6x[/tex], which is option B, is the right response.
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The complete question is:-
Simplify: [tex]5x^2-x-8x^2 + 3x^3 = 5x[/tex]
OA.-5x3x2 = 0
B. 3x3 + x2 = 6x
C. 3x3 + x2 = 0
D. 3x3 3x26x
-
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A fish swims down at a rate of 12 ft per hour. If it started at the surface and swims for 6 hours where will it end up?
Answer:
Since the fish is swimming down at a constant rate of 12 ft per hour for 6 hours, the distance it travels can be found by multiplying its speed by the time:
distance = speed x time
distance = 12 ft/hour x 6 hours
distance = 72 ft
Therefore, the fish will end up 72 feet down from the surface.
6. Mary has two account at the bank. She deposits $1000 into the first account that earns 7%
simple interest every year. She deposits the same amount into her second account that earns
6% interest compounded annually. After 6 years, which account will have earned the most
interest?
After 6 years, the first accοunt with simple interest earn mοre amοunt.
What is simple interest and cοmpοund interest?The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.
Here In first bank account ,
Principal P = $1000
Time N = 6
Rate οf interest = 7%
Interest = [tex]\frac{PNR}{100}[/tex]
=> I = [tex]\frac{1000\times7\times6}{100}[/tex] = $420
Tοtal amount = $1000+$420 = $1420.
Now in secοnd bank account,
Principal P = $1000
Times N= 6
Rate οf interest = 6%
Tοtal amount A = [tex]P(1+\frac{R}{100})^N[/tex]
=> A = [tex]1000(1+\frac{6}{100})^6[/tex]
=> A = $1418.00
Now cοmparing bοth account amounts , In first bank have earned more amount that second bank,
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Put the steps in order to solve this inequality 4x + 7 ⪯ 15
A. Subtract 7 from both sides of the inequality.
B. Divide both sides of the inequality by 4
C. Simplify; leaving only 4x on one side of the inequality.
D. Find your answer; x ⪯ 2
Answer:
C. Simplify
Step-by-step explanation:
1. Subtract 7 from both sides
4x +7 -7 < 15 -7
4x < 8
2. divide both sides by 4
4x/4 < 8/4
answer: x < 2
hope this helps
A 45° sector in a circle has an area of 13.75π cm².
What is the area of the circle?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
cm²
The area of the circle which contains the 45° sector as required to be determined is; 345.4 cm².
What is the area of the circle in discuss?As evident from the task content; A 45° sector in a circle has an area of 13.75π cm².
Hence, since the sector is 45° and the sum of angles in the circle would be 360°; it follows that the area of the circle is; 360/45 = 8 times the area of the sector.
Area of circle = 8 × 13.75π
= 8 × 13.75 × 3.14
= 345.4 cm².
Ultimately, the area of the circle is; 345.4 cm².
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A Mixture of punch contains 1 quart of lemonade 2 cups of grape juice 4 tablespoons of honey and a half gallon of sparkling water. Find a percentage of the punch mixture that comes from each ingredient round your answer to the nearest 10th of a percentage. What is the lemonades percentage?
We can round each figure to one decimal place to represent a percentage to the nearest tenth: Lemonade: 28%, Grape juice: 14%, Honey: 1.8% and Sparkling water: 56.2%. So, the lemonade contributes approximately 28% to the punch mixture.
Calculate the total volume of the combination, divide it by the total volume, and then express the result as a percentage to determine the amount of each ingredient in the punch mixture.
1 quart = 4 cups
1/2 gallon = 8 cups
4 tablespoons = [tex]\frac{1}{4}[/tex] cups
So the total volume of the mixture is:
4 cups (lemonade) + 2 cups (grape juice) + [tex]\frac{1}{4}[/tex] cups (honey) + 8 cups (sparkling water) = [tex]\frac{57}{4}[/tex] cups
Now, we can calculate the percentage of each ingredient in the mixture:
Lemonade: [tex]\frac{4}{(\frac{57}{4})}*100[/tex] ≈ 28%
Grape juice: [tex]\frac{2}{(\frac{57}{4})}*100[/tex] ≈ 14%
Honey: [tex]\frac{(\frac{1}{4})}{(\frac{57}{4})}*100[/tex] ≈ 1.8%
Sparkling water: [tex]\frac{8}{(\frac{57}{4})}*100[/tex] ≈ 56.2%
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