The value of tan2[tex]\alpha[/tex] = 6/7 where tan[tex]\beta[/tex] = 5/12 and sin[tex]\alpha[/tex] = 3/5.
What are the trigonometric identities are used to solve?Trigonometric identities allow us to formulate tan 2[tex]\alpha[/tex] in terms of tan[tex]\beta[/tex] and sin[tex]\alpha[/tex] as follows:
[tex]tan 2\alpha = \frac{ 2 tan \alpha }{1 - tan² \alpha }[/tex]
We know sin[tex]\alpha[/tex], so we can use the Pythagorean identity to find cos[tex]\alpha[/tex]
cos² [tex]\alpha[/tex] + sin² [tex]\alpha[/tex] = 1
cos² [tex]\alpha[/tex] = 1 - sin² [tex]\alpha[/tex] = 1 - ([tex]\frac{3}{5}[/tex])² = [tex]\frac{16}{25}[/tex]
cos α = ±[tex]\sqrt{\frac{16}{25} }[/tex]= ±[tex]\frac{4}{5}[/tex]
sin[tex]\alpha[/tex] and tan[tex]\beta[/tex] are both in the first or third quadrants because they are both positive numbers. Since cos[tex]\alpha[/tex] is positive, we can use the following positive root:
cos α = [tex]\frac{4}{5}[/tex]
Now we can use the tangent identity to find tan α:
tan [tex]\alpha[/tex] = [tex]\frac{sin\alpha }{cos\alpha }[/tex]=[tex]\frac{\frac{3}{5} }{\frac{4}{5} }[/tex]= [tex]\frac{3}{4}[/tex]
Next, we can use the Pythagorean identity to find tan² [tex]\alpha[/tex]:
tan² [tex]\alpha[/tex] + 1 = sec² [tex]\alpha[/tex]
tan² [tex]\alpha[/tex] = sec² [tex]\alpha[/tex] - 1
sec [tex]\alpha[/tex] = 1/cos [tex]\alpha[/tex] = 5/4
tan² [tex]\alpha[/tex] = (5/4)² - 1 = 9/16
Now we can use the formula for tan 2[tex]\alpha[/tex]:
tan 2[tex]\alpha[/tex] = 2 tan α / (1 - tan² α)
tan 2[tex]\alpha[/tex] = 2(3/4) / (1 - 9/16)
tan 2[tex]\alpha[/tex]= 6/7
Therefore, tan 2[tex]\alpha[/tex] is equal to 6/7.
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Helpppppppppppppppppp
f(x)=-x+ 2
g(x)=-4x²+x+5
Find (fog)(x)
Show work on how you found answer and then answer
The function (fog)(x) is 4x² - x - 3.
Define functionIn mathematics, a function is a rule that maps each element from a set (called the domain) to a unique element in another set (called the range or codomain).
In other words, a function is a mathematical object that takes one or more inputs, performs a specified operation on them, and produces an output. The input values of a function are called its arguments, and the output value is called the function value.
Starting with g(x):
g(x) = -4x² + x + 5
Now substituting g(x) into f(x):
f(g(x)) = -(g(x)) + 2
= -[-4x² + x + 5] + 2 (substituting g(x) into f(x))
= 4x² - x - 3
Therefore, (fog)(x) = 4x² - x - 3.
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The function f(x) = x + 5 represents the length of a rectangle, and the function g(x) = 7x − 2 represents the width of the rectangle. What is the area of the rectangle if x = 3?
a. 56
b. 27
c. 285
d. 152
Two-thirds of the earth is covered by water and remaining is covered by land. Find the percentage of land and water in the earth.
Answer:
About 71 percent of the Earth's surface is water-covered
and the rest of the percent is 29 percent
Step-by-step explanation:
Area of land: 148 326 000 km2 (57 268 900 square miles), this are 29% of the total surface of Planet Earth. Area of water: 361 740 000 km2 (139 668 500 square miles), this are 71% of the total surface of the Earth.
Step-by-step explanation & Answer
We know that
[tex]\frac{2}{3}[/tex] = Water covering earth
[tex]\frac{1}{3}[/tex] = Land covering earth
We know that there is more water than land.
We would need to find the percentage which is:
[tex]\frac{2}{3}[/tex] = ?%
?% = 66.6666667% Or roughly 67%
[tex]\frac{1}{3}[/tex] = ?%
?% = 33.33 or 33%
We can see 67% & 33% = 100%!
So the answer to you problem is,
Water covering earth: 67%
Land covering earth: 33%
Investment Portfolio 1 Portfolio 2 Portfolio 3
Stock in Large, Old Corporation $500 $2,000 $2,000
Stock in Emerging Company $5,000 $500 $1,000
U.S. Treasury Bond $3,000 $500 $1,000
Certificate of Deposit $500 $6,000 $3,000
Which of the following shows the portfolios' levels of risk from highest to lowest?
Answer:
P1, P3, P2
Step-by-step explanation:
I'm pretty sure that this is right :/
Part 2
Use your answer above (and more differentiation/integration) to now express the following function as a power series (centered at x = 0).
g(x) = 1/(9+x)³
Therefore , the solution of the given problem of function comes out to be g(x) (-1)ⁿ (n+2)!/n! (9ⁿ⁻²) xⁿ.
What is function?On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
With x = 0, we can use the formula for the geometric series to represent the function g(x) = 1/(9+x)3 as a power series:
=> 1 / (1 - t) =∑ (n = 0 to n) t
where |t| 1 and t is some integer.
In this instance, we have:
=> g(x) = 1/(9+x)³ = [tex](1/9)^{3}[/tex] [tex](1+(-x/9))^{-3}[/tex]
So, using the above calculation and the value of t = -x/9, we can write:
=> G(x) = (1/9)3 n(x/9) (n=0 to infinite)
If we condense this phrase, we get:
=> (n=0 to infinite) = g(x) [tex](-1)^{n}[/tex] (n+2)!/n! ([tex]9^{n-2}[/tex]) [tex]x^{n}[/tex]
Thus, the power series expansion for g(x) with the origin at x = 0 is as follows:
=> (n=0 to infinite) = g(x) (-1)ⁿ (n+2)!/n! (9ⁿ⁻²) xⁿ
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1.Each of these relationships reflects a correlation. Which relationship most likely reflects correlation but not causation?
A.Making pancakes more often is associated with flipping pancakes more often.
B.Having cereal for breakfast more often is associated with having more bowls to wash.
C.Frying eggs more often is associated with cooking bacon more often.
2.Each of these relationships reflects a correlation. Which relationship most likely reflects correlation but not causation?
A.Owning more horses is associated with having a larger stable.
B.Owning more goats is associated with owning more sheep.
C.Owning more chickens is associated with having more eggs.
Having cereal for breakfast more often is associated with having more bowls to wash, which is the relationship that most likely reflects correlation but not causation.
What does a correlation means?Correlation means that there is a statistical relationship between two variables, but it doesn't necessarily mean that one variable is causing the other to occur.
In this case, it's possible that people who eat cereal for breakfast simply prefer to use more bowls or have more bowls available to them, rather than the act of eating cereal causing them to use more bowls. Therefore, this relationship reflects correlation but not causation. In contrast, the other two relationships in the options could be argued to reflect causation.
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Actual lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 11 days. About
what percentage of births would be expected to occur more than 22 days after the mean pregnancy length?
About 2.28% of births would be expected to occur more than 22 days after the mean pregnancy length.
What is percentage?
Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".
Since the lengths of pregnancy terms are nearly normally distributed with a mean pregnancy length and a standard deviation of 11 days, we can use the properties of the normal distribution to answer this question.
Let X be the length of pregnancy terms, then X ~ N(μ, σ) where μ is the mean pregnancy length and σ is the standard deviation.
We want to find P(X > μ + 22), which is the probability that a birth occurs more than 22 days after the mean pregnancy length.
Using the standard normal distribution, we can standardize X as follows:
Z = (X - μ) / σ
Since X ~ N(μ, σ), then Z ~ N(0, 1).
Therefore, P(X > μ + 22) = P(Z > (22/σ)) = P(Z > (22/11)) = P(Z > 2)
Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 2 is approximately 0.0228.
So, about 2.28% of births would be expected to occur more than 22 days after the mean pregnancy length.
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The U.S. Department of Labor annually publishes an Occupational Outlook Handbook, which reports the job outlook, working conditions, and earnings for thousands of different occupations. The handbook reports both the mean and median annual earnings. For most occupations, which is larger, the mean or the median? Why do you think so? Which do you think is a better measure of central tendency? [3 sentences]
i need help with this question
Answer:(2I3O-9247)
Step-by-step explanation:
Explain the relationship between prejudice and discrimination? What are some ways to combat both prejudice and
discrimination? Identify and provide an example of two of the following intergroup relationships: assimilation, segregation,
pluralism, expulsion, amalgamation, or genocide.
Answer:
Prejudice and discrimination are related concepts that are often seen together in intergroup relations. Prejudice refers to preconceived opinions, attitudes, or beliefs about a group or individual based on their membership in a particular social group. Discrimination, on the other hand, refers to actions that are based on prejudice and that result in unequal treatment or opportunities for individuals or groups.
The relationship between prejudice and discrimination is that prejudice often leads to discrimination. When individuals or groups hold prejudiced beliefs about others, they are more likely to engage in discriminatory actions towards them. Discrimination can take many forms, including social exclusion, harassment, violence, and unequal access to resources and opportunities.
One way to combat both prejudice and discrimination is through education and awareness-raising campaigns. By educating individuals and communities about the harmful effects of prejudice and discrimination, people can learn to recognize their own biases and work to eliminate them. Other strategies include promoting diversity and inclusion in workplaces, schools, and other social settings, and providing equal opportunities for all individuals regardless of their background.
An example of intergroup relationships could be segregation and pluralism. Segregation refers to the physical separation of different groups within society, often based on factors such as race or ethnicity. An example of segregation is the historical segregation of African Americans in the United States, where they were denied access to many public spaces, such as schools and restaurants.
Pluralism, on the other hand, refers to the coexistence of different cultural and ethnic groups within society. In a pluralistic society, individuals and groups are free to express their cultural identities and customs without fear of discrimination or prejudice. An example of pluralism is Canada, which has a multicultural policy that recognizes and celebrates the diversity of its citizens while promoting equal opportunities and rights for all.
Helpppppppppp
In the month of January, Sasha had a balance of 3200$ on her credit card. She made a payment of $300 and left the Remaining balance to be paid later. How much interest will she pay this month if her APR is 18.75% round to the nearest cent.
$46.19
$35.10
$4.50
$543.75
Answer:
543.75
Step-by-step explanation:
How long did it take to pay of the loan? What is the answer?
The time it would take to pay back the loan is 16 years.
How long would it take to pay back the loan?When a loan earns a simple interest, it means that the interest that would be paid by the borrower grows as a linear function of the amount borrowed, interest rate and the duration of the loan.
Simple interest = loan amount x time x interest rate
Interest = amount repaid - loan value
$678,400 - $320,000 = $358,400
Duration of the loan = simple interest / (loan amount x interest rate)
$358,400 / (0.07 x 320,000) = 16 years
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Find the volume of the solid enclosed by the paraboloids z = 4 ( x^2 + y^2 ) and z = 32 − 4 ( x^2 + y^2 ) .
After answering the presented question, we can conclude that circle Therefore, the volume of the solid enclosed by the two paraboloids is 512π cubic units.
What is circle?A circle appears to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically depicted with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle.
The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.
To find the volume of the solid enclosed by the given paraboloids,
This is the equation of a circle with radius 2 centered at the origin.
So, we can set up our triple integral as follows:
V = ∫∫∫ E dz dy dx
where E is the region enclosed by the circle and the two planes z = 0 and z = 16.
V = ∫2 ∫2π ∫6 z r dz dθ dr
V = ∫2 ∫2π [1/2 2]6 dθ dr
V = ∫2 ∫2π 128 dr dθ
V = ∫2 256π dr
V = 512π
Therefore, the volume of the solid enclosed by the two paraboloids is 512π cubic units.
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(9, 23) is a point on the graph y = f(x)
Which point must be on the graph of y = f(x) + 4 ?
A (9, 19) B (13, 23) C (5, 23)
D (9, 27)
Answer:Option (d)
Step-by-step explanation: D (9, 27)
Find the probability of numbers lying between 500 and 900 inclusive with exactly two consecutive figures are identical.
Answer:
To find the probability of numbers lying between 500 and 900 inclusive with exactly two consecutive figures that are identical, we can use the following steps: Step 1: Count the total number of three-digit numbers between 500 and 900 inclusive. There are 400 three-digit numbers between 500 and 900 inclusive. Step 2: Count the number of three-digit numbers between 500 and 900 that have exactly two consecutive figures that are identical. We can break this down into cases based on the middle digit of the three-digit number. Case 1: The middle digit is not 0 or 9. In this case, there are 8 possible digits that can be used for the middle digit (i.e., 1, 2, 3, 4, 5, 6, 7, or 8). For each possible middle digit, there are
3 of 4
Type an algebraic expression for each of the verbal expressions.
a. 8 less than the product of 3 and j
b. The quotient of f and the quantity of g increased by 11
Step-by-step explanation:
a.8<3+j
b.f+g=11
Hope it help
find the magnitude x-Component = -6 units, y-component = -8 units
Thus, the magnitude of vector with the given x-Component = -6 units and y-component = -8 units is found as: 10 units.
Explain about the magnitude of vectors:The length of a vector determines its magnitude. The letter "a" stands for the vector's magnitude.
We shall take the square root of sum of the squares of each component of a two-dimensional vector to estimate its magnitude from its coordinates. For instance, the following formula can be used to determine a vector's magnitude: U = (x1, y1).
|U| = √[x1² + y1²]
The Pythagorean theorem serves as the basis for this formula.
given vectors:
x-Component = -6 units, y-component = -8 unitsmagnitude = √[x² + y²]
magnitude = √[(-6)² + (-8)²]
magnitude = √[36 + 64]
magnitude = √100
magnitude = 10 units
Thus, the magnitude of vector with the given x-Component = -6 units and y-component = -8 units is found as: 10 units.
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Complete question:
find the magnitude of vector?
x-Component = -6 units, y-component = -8 units
A proportion often shows the relationship between:
Answer: two related quantities by comparing their ratios and establishing equivalence.
Step-by-step explanation: A proportion is a mathematical statement that equates two ratios. It is commonly used to express the relationship between two related quantities or sets of data. A proportion consists of four values: two ratios, where each ratio is made up of a numerator and a denominator.
Proportions are useful for comparing and understanding the relationship between different quantities. They can be used to solve various real-life problems, such as determining equivalent values, finding unknown quantities, or making predictions based on known information.
For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion would be 2:1. This proportion shows the relationship between the amount of flour and water needed in the recipe.
In a proportion, the ratios are equivalent, meaning they have the same value. This equality allows us to solve for unknown quantities by cross-multiplying and finding the missing value.
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4. San Antonio, Texas, depends on the Edwards Aquifer for its water supply. The graph shows the
decline of the water level of the aquifer over a two-week period beginning on May 20, 2012.
Aquifer Level (ft)
664
663
662
661
660
659
658
657
656
655
654
653
652
0
7
Water Level of
Edwards Aquifer
A -1.6
B. -0.8
C. 0.625
D. 1.25
8 10 12 14
Days since May 20th
Based on the graph, which of the following is the best estimate of the change in the water level.
in feet per day, during this time period?
Answer:
d=9
Step-by-step explanation:
9x1
Need help with question #3
On solving the provided question we can say that As a result, the matrix following provides a foundation for V': { [1, 1, 0] }
what is matrix ?A matrix is a collection of numbers that are organised in rows and columns. Learns about matrix elements and dimensions and introduces them for the first time. A matrix is a rectangular grid of numbers in rows and columns. Matrix A, for example, has two rows and three columns. Its name is derived from its single row and 1 n row matrix order. For example, A = [1 2 4 5] is a row matrix of order 1 by 4. Another example of a row matrix is P = [-4 -21 -17] of order 1-by-cubic.
To identify a basis for the R3 subspace V' spanned by the vector v = [1, 1, 0], we must first determine a set of linearly independent vectors that span V'.
One option is to row-reduce the augmented matrix [v|0] using the Gaussian elimination method, where 0 is the zero vector in R3.
[1 1 0 | 0]
[1 1 0 | 0]
[0 0 0 | 0]
This demonstrates that the vector v = [1, 1, 0] spans an R3 one-dimensional subspace, implying that any nonzero scalar multiple of v is also in V'.
As a result, a basis for V' is the set v, which consists solely of the vector v itself.
As a result, the following provides a foundation for V':
{ [1, 1, 0] }
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For a fixed location, the number of sunlight hours in a day fluctuates throughout the year. Suppose that the number of daily sunlight hours in a particular location can be modeled by the following.
Using trigonometric equation, we can find that on January 25th, 218 days after June 21st, there will be 11 hours of sunlight.
Define trigonometric equation?The trigonometric equations can be linear, quadratic, or polynomial equations and are conceptually related to algebraic equations. Trigonometric equations substitute the Sin, Cos, and Tan trigonometric ratios for the variables found in a typical polynomial equation. Sinθ, Cosθ, or Tanθ are the trigonometric ratios that are employed in trigonometric equations.
The number of daily sunlight hours of a particular location is modelled by the trigonometric equation,
l(t) = 12 + 3.5sin (2/365t)
L(t) denotes the number of hours of sunlight in a day.
t is the number of days after June 21st.
In order to find the day during the first 365 where there are 11 hours of sunlight, we must know the value of "t" for which L(t) = 11 hours. The result of solving for t in the given equation with L(t)=10 is as follows:
l(t) = 12 + 3.5sin (2/365t)
11 = 12 + 3.5sin (2/365t)
11-12 = 3.5sin (2/365t)
-1 = 3.5sin (2/365t)
-1/3.5 = sin (2/365t)
-0.285 = sin (2/365t)
For the inverse function of y = sin x
sin ⁻¹(y) =x + 2n
Given that we must determine the day with 11 hours of sunlight in the first 365 days, we get the following results when we set n=0: t = -35.3521 or t =217.9422.
Now, t cannot be negative since we want to discover that the day after June 21st will have 10 hours of sunlight. therefore, ignoring t=-35.3521. We now have t=217.9422.
By rounding, we arrive at the necessary response, t=218.
So, it will have 11 sunlights on January 25th—218 days after June 21st.
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4x + 14 + 4x = 38+77-1
Answer:
x=25/2 or 12.5
Step-by-step explanation:
8x=115-15
8x=100
x=100/8
x=25/2 or 12.5
Answer:
x = 12.5
Step-by-step explanation:
4x + 14 + 4x = 38+77 - 1
8x + 14 = 38 + 77 - 1
8x + 14 = 114
8x = 100
x = 12.5
(1/6)30x+(1/6)24-(1/7)63-(1/7)7x
Answer: 15 IF X=5 // OR its 4x-5 IF youre looking for an equivalent answer
A Large group is throwing a party. There are enough people attending to fill 8 tables, each with 5 seats. Each person will be served 3 glasses of leomonade. How many cups of leomonade will be served at the party
Answer:
120 cups of lemonade
Step-by-step explanation:
1. Multiply 8 x 5 which will give you 40
2. Multiply 40 x 3 which equals 120
As an introduction to probability, a student
As an introduction to probability, Probability is the measure of the likelihood of an event occurring, and it is used to analyze the chances of different outcomes in an experiment or situation.
What is an experiment?
A student can start by understanding the basic concepts and terminology used in probability. Some of the key concepts include:
Experiment: An experiment is any process that produces a set of outcomes.
Outcome: An outcome is the result of an experiment.
Sample Space: The sample space is the set of all possible outcomes of an experiment.
Event: An event is a subset of the sample space.
Probability: Probability is a measure of the likelihood of an event occurring.
Once the student understands these concepts, they can move on to learning about the different types of probability, such as classical probability, empirical probability, and subjective probability. They can also learn about the different methods of calculating probability, such as using the formula:
P(E) = number of favorable outcomes / total number of outcomes
where P(E) is the probability of an event E occurring.
The student can then apply these concepts and methods to solve simple probability problems, such as finding the probability of flipping a coin and getting heads, or rolling a die and getting an even number. They can also explore more complex probability problems, such as conditional probability and the multiplication rule.
Overall, learning about probability is an important part of understanding how to make decisions and analyze data in many fields, including science, finance, and engineering.
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Complete question is: As an introduction to probability, a student should start by understanding the basic concepts of probability theory, such as the sample space, events, and probabilities.
The equation d = m/v can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an
equivalent equation solved for V?
Odm = V
Od/m = V
Om/d = V
Om-d=V
Therefore, an equivalent equation solved for V is:
V = m/d.
None of the options given in the question are equivalent to this equation.
What do you mean by the volume?In general, "volume" refers to the amount of space occupied by a three-dimensional object or substance. It can also refer to the amount or quantity of something, such as the volume of water in a swimming pool, the volume of air in a room, or the volume of a book.
In the context of mathematics, the term "volume" is often used to refer specifically to the measure of the amount of space enclosed by a solid object, typically measured in cubic units such as cubic meters (m³) or cubic feet (ft³). For example, the volume of a cube with sides of length 1 meter would be 1 cubic meter (1 m³).
To solve for V in terms of the given equation, we need to isolate V on one side of the equation.
Starting with d = m/V, we can rearrange the terms as follows:
[tex]d = m/V[/tex]
Multiplying both sides by V, we get:
[tex]dV = m[/tex]
Dividing both sides by d, we get:
[tex]V = m/d[/tex]
Therefore, an equivalent equation solved for V is:
[tex]V = m/d.[/tex]
None of the options given in the question are equivalent to this equation.
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Margo borrows $200, agreeing to pay it back with 8% annual interest after 16 months. How much interest will she pay?
Margo will pay $21.28 in interest for the loan. The formula I = Prt is used to calculate the interest for a loan.
What is interest rate?It is expressed as a percentage of the total amount borrowed and is typically noted as an annual percentage rate (APR).
The interest that Margo will pay can be calculated by using the formula I = Prt, where I is the interest, P is the principal (the initial amount borrowed), r is the interest rate, and t is the length of time.
In this case, the principal is $200, the interest rate is 8%, and the time is 16 months.
Therefore, the interest that Margo will pay is
I = 200 x 8% x (16/12)
= $21.28
Therefore, Margo will pay $21.28 in interest for the loan.
The formula I = Prt is used to calculate the interest for a loan.
Here, I is the interest, P is the principal (the initial amount borrowed), r is the interest rate, and t is the length of time.
This formula can be used to calculate interest for any loan, no matter the principal, interest rate, or length of time.
By simply substituting the values into the formula, the interest can be easily calculated.
Therefore, in this case, Margo will pay $21.28 in interest for the loan.
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1 Write the recursive formula for the following. Do not include spaces in your answer. 13, 15, 17, 19...
Answer:
add 2 or find following odd number
Step-by-step explanation:
+2 moves 13 to 15, 15 to 17, 17 to 19, ...
the ratio of pickups to cars sold at a dealership is 2 to 3. If the dealership sold 142 more cars than pickups in 1999, then how many of each did it sell
The number of pickups is 284.
and the number of cars is 142 more than that = 426.
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given: The ratio of pickups to cars sold at a dealership is 2 to 3. If the dealership sold 142 more cars than pickups in 1999
Let y = the number of cars.
x/y = 2/3.
The dealership sold 142 more cars than pickups.
We get y = x + 142
In the equation of x/y = 2/3, replace y with x + 142 to get:
x/(x+142) = 2/3
cross multiply to get:
3x = 2*(x+142)
simplify to get:
3x = 2x + 284
subtract 2x from both sides of the equation to get:
x = 284.
Hence, the number of pickups is 284.
and the number of cars is 142 more than that = 426.
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