The volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is 16π/3.
What is the bounded region?
A territory is said to be bounded if it has a boundary or other restrictions applied to it. In other words, a bounded shape is limited by a set of measurements or characteristics and cannot be an indefinitely huge area.
Here, we have
Given: x = 1+(y−2)², x=2
We have to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
Rotating with the cylinder method about the x-axis means it must be a dy integral. The given parabola equation is already solved for x. Find the intersections:
2 = 1 + (y−2)²
0 = (y -1)(y-3)
y = 1, 3
We will integrate from
y = 1 to 3
The radius of each cylinder will be r=y and the height will be (greater minus lesser, i.e. right minus left).
h = 2 - (1 + (y-2)²)
h = 1 - y² + 4y -4
h = - y² + 4y - 3
Volume = [tex]\int\limits^a_b {2πrh} \, dy[/tex]
= 2π∫₁³ y.( - y² + 4y - 3)dy
= 16π/3
Hence, the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is 16π/3.
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use substitution to solve the system of equations -1=2x-y 8x-4y=-4
Given System of equation has multiple solution.
What are Systems of equations?Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given a system of equation:
-1 = 2x - y and 8x - 4y = -4
From equation 1
-1 = 2x - y
y = 2x + 1
Substitute this value on equation 2
8x - 4y = -4
8x - 4(2x + 1) = -4
-4 = -4
An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.
Thus, Given System of equation has multiple solution.
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3
=
Find the width of floor space covered by 38 boards with 7 3/4-in. exposed surface each.
Answer: The width of the floor space covered by 38 boards with 7 3/4-in exposed surface each is 298 inches.
To find this, you would multiply the number of boards (38) by the width of the exposed surface of each board (7 3/4 inches).
38 x 7.75 = 298 inches.
Step-by-step explanation:
A researcher plans to use a random sample of n=500 families to estimate the mean monthly family income for a large population. A 99% confidence interval based on the sample would be ______ than a 90% confidence interval. (a) narrower and would involve a larger risk of being incorrect, (b) wider and would involve a smaller risk of being incorrect, (c) narrower and would involve a smaller risk of being incorrect, (d) wider and would involve a larger risk of being incorrect, (e) wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller.
A researcher plans to use a random sample of n = 500 families to estimate the mean monthly family income for large population. A 99% confidence interval based on the sample would be wider and would involve a smaller risk of being incorrect than a 90$ confidence interval.
What is random sample?A simple random sample is a subset of people selected at random from a larger group of people, all with the same probability, in statistics. This procedure involves choosing a sample at random. A simple random sample is a population subset that has been chosen at random. This sampling technique minimizes the possibility of selection bias by giving every member of the population an exact equal probability of being chosen. The use of random sampling assures that the results of your study should be close to those that would have been obtained from measurements of the complete population (Shadish et al., 2002). The most basic random sample gives every unit in the population an equal probability of being chosen.The mean monthly family income for a sizable population will be calculated using a researcher's random sample of n = 500 families. An interval with a 99% confidence level based on the sample would be larger and carry a lower risk of error than one with a 90% confidence level.To learn more about random sample refer to:
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table 2.6 shows the average hourly compensation of production workers in manufacturing for several years. let x be the number of years since 1970, so that x
The formula for the average hourly compensation of production workers in manufacturing is C = 40.25x + $6.81.
For example, in 1975 (x = 5), the average hourly compensation of production workers in manufacturing was calculated using the formula as follows:
C = 40.25(5) + $6.81
C = $202.81
Therefore, the average hourly compensation of production workers in manufacturing in 1975 was $202.81. The same formula can be used to calculate the average hourly compensation of production workers in manufacturing for any year since 1970.
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B...
Launch realize. 5-4: Lesson Quiz (LMS graded)
Which of the following side-angle relationships in AABC are true? Select all that apply.
OA The largest angle is opposite the smallest side.
OB. The smallest angle is opposite the largest side.
OC. The smallest angle is opposite the smallest side.
OD. The largest angle is opposite the largest side.
The biggest angle in the triangle is opposite the largest side, which is how they actually relate to one another. The right answer is D.
What are a triangle's properties?A triangle is a three-sided shape with two dimensions. The three angles add up to 180 degrees.A triangle's characteristics are:
A triangle has three vertices, three angles, and three sides.The sum of the internal angles of a triangle is always 180 degrees. The triangle's angle sum attribute describes this.Any two triangle sides can be added together to equal a length greater than the third side.The side of a triangle facing the biggest angle is its largest side.The sum of the triangle's internal opposite angles is equal to any of its outer angles. This is referred to as the triangle's outside angle property.The biggest angle is therefore opposite the largest side, which is the actual connection between the triangle's sides. The right answer is D.To Learn more About triangle Refer To:
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The Salk vaccine field trials were conducted only in certain experimental areas (school districts), selected by the Public Health Service in consultation with local officials. In these areas, there were about 3 million children in grades 1, 2, or 3; and there were about 11 million children in those grades in the United States . In the experimental areas, the incidence of polio was about 25% higher than in the rest of the country. Did the Salk vaccine filed trials cause children to get polio instead of preventing it? Answer yes or no, and explain briefly.
Based on the information provided, it can be concluded that the vaccine trials most likely did not cause children to get polio as these are independent variables.
What is causality bias?This type of bias implies people believe two events are related as a cause or effect. This often happens when one event follows another, and therefore people believe one event causes the other.
In this case, people are likely to believe the vaccine caused higher polio rates just because after the vaccine, polio rates seemed to increase. However, these two variables are independent as vaccines produce immunization against polio.
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Points B, D, and J are midpoints of the sides of right triangle ACG. Points K, E, I are midpoints of the sides of triangle J DG, etc. If the dividing and shading process is done 100 times (the first three are shown) and AC=CG=6, then the total area of the shaded triangles is nearestA. 6B. 7C. 8D. 10
The area of the shaded triangles is nearest to 10
The total area of the shaded triangles can be calculated using the following equation:
[tex]Total Area = (AC∧2)÷2 × (2∧n)[/tex]
Where AC is the length of the original triangle's hypotenuse and n is the number of iterations.
Given that AC = 6 and n = 100, the equation becomes
[tex]Total Area = (6^2)/2 × (2^100)[/tex]
Total Area = 18 × (2^100)
Total Area = 18 × 1.26 x 10^31
Total Area ≈ 10
Therefore, the total area of the shaded triangles is nearest to 10
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Amanda is currently in the market for a new job as a mechanical engineer. To get a sense of what the typical salary is for the position she is interested in, Amanda did some research and found a database showing salary information from mechanical engineers across the county. Amanda had access to both the average national salary and the average local salary for mechanical engineers. Which of the following is an example of a parameter in Amanda's scenario?
In Amanda's case, an example of a parameter is the national average income for mechanical engineers.
What is the parameter in Amanda's scenerio ?As a mechanical engineer, Amanda is now seeking employment. Additionally, she is paid in line with both the national average for Mechanical engineers as well as the average for Mechanical engineers in our community. In Amanda's instance, a parameter example is needed, thus that is what the question asks for. The population's traits are referred to as a parameter, whereas the sample's characteristics are referred to as statistics.
Due to its gifts and the information it provided that was close to the average population slurry, it constitutes a parameter here. A representative sample of mechanical engineers is Amanda's city. In Amanda's city, the slurry from a sample is the mechanical engineers' average annual pay. They have therefore taken a representative sample of all the mechanical engineers in the city from the larger population.
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1. Fractions equal to 1/2
Answer: Answers vary…
Step-by-step explanation:
Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. Some fractions equivalent to 1/2 are: 2/4, 3/6, 4/8, 5/10, 6/12, etc. This is because equivalent fractions have the same value in reduced form.
a survey has to be taken to estimate the proportion of voters who favored stem cell research among the
The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / Total Number of voters) x 100.
Proportion of favor stem cell research = (Number of voters who favor stem cell research / Total Number of voters) x 100
In order to estimate the proportion of voters who favor stem cell research, a survey has to be taken. Suppose the survey results indicate that out of a total of 500 voters, 300 of them favor stem cell research. Then, the proportion of favor stem cell research would be calculated as follows: Proportion of favor stem cell research = (300/500) x 100 = 60%. This means that 60% of the total voters favor stem cell research.
The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / +++Total Number of voters) x 100.
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Find the slope-intercept equation for a line with a slope of 3 that passes through (1, 7).
Answer:
y=3x+4
slope is the slope obviously and insert the point into the y=3x+b
itll be 7=3(1)+b
so itll be 4=b
based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true?
Based on the graph of the general solution to the differential equation dy/dx = 2x + y, the option C: The slopes are all positive in Quadrant 1, is true.
What is a differential equation?
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.
The given the differential equation is dy/dx=2x+y.
The graph for the function is drawn.
dy/dx=2x+y
Now slope=2x+y
Along x-axis, y=0.
So, slope=2x≠0.
Since it depends upon x hence the slope along the y-axis are not horizontal.
Along y-axis, x=0.
So, slope=y≠0.
Since it depends upon y the slope along the x-axis are also not horizontal.
In quadrant I -
x,y≥0
So, dy/dx≥0
Hence the slopes are all positive in quadrant I.
In quadrant IV -
x≥0,y≤0
So, dy/dx is not always positive.
Therefore, the slopes are not all positive in quadrant IV.
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Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true? The slopes along the y-axis are horizontal. The slopes along the x-axis are horizontal. The slopes are all positive in Quadrant 1. The slopes are all positive in Quadrant 4.
3. Ato Liku purchases a house for Br. 250, 000. He makes a 20% down payment, with a balance amortized by a 30 year mortgage at an annual interest rate of 12% compounded monthly. a) Determine the amount of the monthly mortgage payment. b) What is the total amount of interest Ato Liku will pay over the life of the mortgage? c) Determine the amount of the mortgage Ato Liku will have paid after 10 years?
Answer:
a) To determine the monthly mortgage payment, we first need to calculate the amount of the loan, which is equal to the purchase price of the house minus the down payment. In this case, the loan amount is 250,000 * 0.8 = 200,000. Next, we need to calculate the monthly interest rate, which is equal to the annual interest rate divided by 12. In this case, the monthly interest rate is 0.12/12 = 0.01. Using the formula for the monthly mortgage payment (P = L[i(1+i)^n]/[(1+i)^n-1]), where P is the monthly payment, L is the loan amount, i is the monthly interest rate, and n is the number of payments (in this case, 30 years * 12 = 360), we can calculate the monthly payment as:
P = 200,000[0.01(1+0.01)^360]/[(1+0.01)^360-1] = 1326.91
b) To calculate the total amount of interest Ato Liku will pay over the life of the mortgage, we can subtract the original loan amount from the total amount of payments made over the life of the mortgage. In this case, that would be 360 * 1326.91 - 200,000 = 480,596.
c) To determine the amount of the mortgage Ato Liku will have paid after 10 years, we can multiply the monthly mortgage payment by the number of payments made in 10 years (10 years * 12 = 120). In this case, that would be 120 * 1326.91 = 159,223.20.
The graph of f(x) = RootIndex 3 StartRoot x EndRoot is shown with g(x). Which equation represents the graph of g(x)?
g(x) = RootIndex 3 StartRoot x minus 2 EndRoot
g(x) = RootIndex 3 StartRoot x + 2 EndRoot
g(x) = RootIndex 3 StartRoot x EndRoot + 1
g(x) = RootIndex 3 StartRoot x EndRoot–1
The graph of g(x) is represented by the equation g(x) = Root Index 3 Start Root x EndRoot-1.
What is meant by mathematical equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, the point-slope form, and the slope-intercept form are the three primary kinds of linear equations.An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is something like 4 + 6 = 10.A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A formula declares that two things are equal. In this case, 10 + 2 equals 6 + 6. Simply put, this means that 10 + 2 is equivalent to or the same as 6 + 6. For example, the equation 10 + x = 6 + 6 may have an unknown.Hence, the correct option is D) g(x) = RootIndex 3 Start Root x End Root–1
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Suppose a researcher compiled a data set consisting of the following variables for a sample of 200 women. For each variable, select whether it is discrete or continuous. Variable Discrete Continuous
The number of countries ever visited Pounds of chocolate consumed in the past year Shoe size Height in inches The number of pets currently living in the household
The number of countries ever visited is a discrete variable. Discrete variables are variables that can only take specific values, rather than any value within a range. The number of countries ever visited can only be a whole number, such as 0, 1, 2, 3, and so on, and not a fraction or decimal.
Pounds of chocolate consumed in the past year is a continuous variable. Continuous variables are variables that can take any value within a range. Pounds of chocolate consumed in the past year can be any value between 0 and a maximum value, such as 0.5, 1.5, 2.7, and so on.
Shoe size is a discrete variable. Shoe size is typically measured in whole numbers, such as 5, 6, 7, 8, and so on, and not in fractions or decimals.
Height in inches is a continuous variable. Height in inches can take any value within a range, such as 60, 61, 62, and so on.
The number of pets currently living in the household is a discrete variable. The number of pets can only be a whole number, such as 0, 1, 2, 3, and so on, and not a fraction or decimal.
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Hotel P offers two types of rooms for its customers: a Deluxe room and a Suite room. The price per night for the suite room for check-in on Sunday until Thursday is 70% higher than the price per night for a Deluxe room for the exact check-in period. The price per night for the Deluxe room for check-in on Friday and Saturday is 25% higher than for price per night for the Deluxe room for check-in on Sunday until Thursday. If the hotel management wants to maintain the price difference between the two types of space, and the price per night for a Suite room for check-in on Sunday until Thursday is $223, what should be the price per night for a Suite room for check-in on Friday and Saturday?
The price for the Suite room for check-in on Friday and Saturday is given as follows:
$278.75.
How to obtain the price for the room?The price for the room is obtained applying the proportions in the context of this problem.
The price for the room on the period from Sunday until Thursday is given as follows
$223.
The price for the room on Friday and Saturday is 25% higher than from Sunday until Thursday, hence the price is given as follows:
1.25 x 223 = $278.75.
(as an increase of 25% is equivalent to a proportion of 1.25).
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A horse-drawn carriage tour company has found that the number of people that take their tour depends on the price charged per customer. The more the company charges for a tour, the fewer people decide to take the tour.
The function c(x)=50+5x represents the price charged per customer where x is the number of $5 increases they charge over a rate of $50 per person.
The function p(x)=100−2x represents the number of customers expected for the day, where x is the number of $5 increases they charge over a rate of $50 per person.
What does (p⋅c)(2) mean about the horse-drawn carriage tour company?
The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.
The horse-drawn carriage tour company can expect to take in $3760 when the charge per customer is $40.
The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $40.
The horse-drawn carriage tour company can expect to take in $3760 when the charge per customer is $60.
The meaning of (p⋅c)(2) for the horse-drawn carriage tour company is: A. the horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.
How to determine the meaning of (p⋅c)(2) for the horse-drawn carriage tour company?In this scenario, a function which represents the price charged per customer c(x) is given by this mathematical expression;
c(x) = 50 + 5x.
where:
x represents the number of $5 increases they charge over a rate of $50 per person.
When x = 2, the price charged per customer c(x) is given by;
c(2) = 50 + 5(2)
c(2) = $60.
Furthermore, a function which represents the number of customers expected for the day is given by:
p(x) = 100 - 2x
where:
x represents the number of $5 increases they charge over a rate of $50 per person.
When x = 2, the number of customers expected for the day is:
p(2) = 100 - 2(2)
p(2) = 96.
Now, (p⋅c) can be calculated as follows;
(p⋅c) = p(2) × c(2)
(p⋅c) = 96 × 60
(p⋅c) = $5760.
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solve the quadratic equation by completing the square x^2+8x+6=0 first choose the appropriate form and fill in the blanks with the correct numbers then solve the equation
By completing squares we will see that the solutions of the quadratic equations is:
x = -4 ± √10
How to solve the quadratic equation?Here we want to solve the quadratic equation:
x^2 + 8x + 6 = 0
Remember the perfect square trinomial:
(a + b)^2 = a^2 + 2ab + b^2
We can rewrite the quadratic equation as:
x^2 + 2*4x + 6 = 0
To complete squares we need to add 4^2 = 16 in both sides, then we will get:
x^2 + 2*4x + 16 + 6 = 16
(x + 4)^2 + 6 = 16
(x + 4)^2 = 16 - 6
(x + 4)^2 = 10
x = -4 ± √10
That is the solution.
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Suppose the natural level of output is $60 billion of real GDP and that people expect a price level of 100. On the following graph, use the purple line (diamond symbol) to plot this economy's long-run aggregate supply (RAS) curve. Then use the orange line segments (square symbol) to plot the economy's short-run aggregate supply (AS) curve at each of the following price levels: 90, 95, 100, 105, and 110
The purple line would be plotted at the level of output $60 billion, and the orange line segments would be plotted at 90, 95, 100, 105, and 110 respectively.
1. Plot the purple line at the level of output $60 billion.
2. Plot the orange line segments at 90, 95, 100, 105, and 110 respectively.
The long-run aggregate supply (RAS) curve is used to represent the natural level of output for an economy. In this case, the natural level of output is $60 billion of real GDP with a price level of 100. Therefore, the purple line should be plotted at the level of output $60 billion on the graph. The short-run aggregate supply (AS) curve is used to show how the level of output reacts to the price level. Therefore, the orange line segments should be plotted at 90, 95, 100, 105, and 110 respectively. This will show how the level of output changes when the price level is different from the natural level. This will help to illustrate how the economy may react when the price level is different than expected.
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plss help asap, my assignment is due today and I have been trying to solve this for the past 3 days
Answer:
see i have a same solution not exactly though
Step-by-step explanation:
so check and solve good luck
3629
You can used the digit twice to make the smallest 4 digit number
The smallest four-digit number with one digit used twice is 2236.
What is Digit?
A positional numeral system uses a single symbol, the numerical digit, either individually or in combination to represent numbers. The term "digit" refers to the ten symbols of the conventional base-10 numeral system, or decimal digits, which the ten digits of the hands correspond to.
A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.
Given digit is ;
3629
Digits are 3 6 2 9
Digits in ascending order
2 3 6 9
Minimal 4 digit number
We can employ a number Twice
So, we'll use the smallest digit, 2, twice.
at positions 1000th and 100th.
The smallest four-digit number with one digit used twice is 2236.
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25 people gathered to watch a baseball game while talking they realized that 5 of them were New York Mets fans what is the probability that the favorite team of a randomly selected person in the group is the New York mets
The probability that the favorite team of a randomly selected person in the group is the New York Mets is 1 / 5.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given that 25 people gathered to watch a baseball game while talking they realized that 5 of them were New York Mets fans.
The probability will be calculated as:-
Probability = 5 / 25
Probability = 1 / 5
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The circle below has center S. Suppose that mZQSR=42°. Find the following.
(a)m QR
(b)m ZQPR
I Don't Know
Submit
D
m QR =
0-
mZQPR = 0
Part (a)
[tex]42^{\circ}[/tex] since the angle intercepted by a central angle is the same as the measure of the arc.
Part (b)
[tex]21^{\circ}[/tex] by the inscribed angle theorem.
Greg purchased a baseball bat at a 20% discount. The original cost of the bat was $95. How much will Greg pay for the bat if there is a 6% sales tax?
Answer:
$80.56
Step-by-step explanation:
First determine the cost of the bat after the discount.
20% of 95 = .20x 95 = 19
95-19= $76
Next, you will calculate the additional cost of sales tax.
Sales tax rate = Sales tax percent / 100 (6/100) = .06
Sales tax = List price x Sales tax rate (76 x .06) = 4.56
Total tax equals $4.56
76+4.56= $80.56
HELP!!
In the figure below, TW and TU are tangent to the circle centered at O. The segment WU passes through the center of the circle. Given that TW=17.4 and WU=12, find WV.
Answer:
WU=4.8
Step-by-step explanation:
put it in the box WU =4.8
A garden is rectangular with a width of 7 feet in a length of 9 feet. If it's surrounded by a walkway, 2 feet wide, how many square feet of area does a walkway cover?
PLEASE HELP!!!
The walkway encircling the garden has a 64-square-foot area.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given, A garden is rectangular with a width of 7 feet in a length of 9 feet.
From the general formula of Area:
Area = Length * width
Area of garden = 7 * 9
Area of garden = 63 Square feet
Perimeter of garden = 2(length * width)
Perimeter of garden = 2(7 + 9)
Perimeter of garden = 32
Since a 2 feet wide rectangular sidewalk is made surrounded the garden So, the area of the walkway will be
Area of walkway = perimeter * width
Area of walkway = 32 * 2 = 64
Therefore, the area of the walkway surrounding the garden is 64 square feet.
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Please please look at the picture and answer the question thank you for your help
Answer:
20 for both
Step-by-step explanation:
hope this helps
*THE ANSWER IS A* 1.5.3 Test (CST): Polynomials Question 25 of 25 Which of these is a binomial? O A. 2x³-7y³ O B. 5xy C. x+2y²-7 O D. ab
Step-by-step explanation:
The correct option is A
Because,
A Binomial is defined as a polynomial containing 2 terms in it.
In option c there are three terms they are x, 2[tex]y^{2}[/tex], -7
In option A There are only two terms That satisfy the definition of binomial.
Richard opened an account in Trust Bank. The equation R=350(1+0.025)" can be used to calculate the amount of money in the account, with 'n' representing the number of years. He also opened another account in Value Savings Bank, with the equation Q=350(1+0.03)" representing the amount of money. What are the interest rates in percent?
The interest rate of the bank R is 2.5% and interest rate of the bank Q is 3%.
What is compound interest?
Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.
Here the given equation represents the amount in compound interest.
Using compound interest formula then
=> A = P[tex](1+\frac{R}{100})^n[/tex]
According to the question the equation for trust bank is
=> R =350 [tex](1+0.025)^n[/tex]
comparing with compound interest formula then
=> [tex]\frac{R}{100}= 0.025[/tex]
=> R = 0.025× 100 =2.5%
Now the equation of other bank is
=> Q = 350[tex](1+0.03)^n[/tex]
Comparing with compound interest formula then
=> [tex]\frac{R}{100}= 0.03[/tex]
=> R = 0.03×100 = 3%
Hence the interest rate of the bank R is 2.5% and interest rate of the bank Q is 3%.
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Please help me with all I’ll mark you brainly
Answer:
Step-by-step explanation:
y = 1x + 2
y = 3x + 3
y = 1/2x + 2
y = -3x + 12
