As a result, the balance in the account at the end of seven years is, to the closest cent, $116177.20.
What is amount ?The term "amount" in mathematics typically denotes a sum, total, or quantity. It could be a numerical value or some other kind of measurement. Depending on the context, the word "amount" may also be used to refer to quantity, total, sum, volume, or magnitude. \
The term "amount" is used in algebra and calculus to describe the outcome of an operation, such as the amount of change in a function or the quantity of a variable needed to satisfy an equation. In many disciplines, including finance, science, and engineering, the word "amount" is frequently used to refer to quantities or measurements.
given
The amount of money in the account after 7 years can be calculated using the formula V = Pe(rt), where V is the value of a account in t years, P is the principal implementation, e is the base of a natural log, and r is the rate of interest:
V = P*e(rt) = 67700*e(0.077*7)
[tex]V = 67700 * e^{(0.539) (0.539)[/tex]
V = 67700 * 1.716
V = 116177.20
As a result, the balance in the account at the end of seven years is, to the closest cent, $116177.20.
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olve the equation, and check the solutions. (x+6)/(x^(2)-5x+6)-(8)/(x^(2)-7x+10)=(x-6)/(x^(2)-8x+15)
We find that the equation holds true for both solutions. Therefore, the solutions are x = (117 + i√3631)/(10) and x = (117 - i√3631)/(10).
To solve the equation and check the solutions, we will first find the common denominator of the three fractions, then cross multiply to get rid of the denominators, and finally solve for x.
Step 1: Find the common denominator of the three fractions. The common denominator is the product of the three denominators: (x^(2)-5x+6)(x^(2)-7x+10)(x^(2)-8x+15)
Step 2: Cross multiply to get rid of the denominators:
(x+6)(x^(2)-7x+10)(x^(2)-8x+15) - (8)(x^(2)-5x+6)(x^(2)-8x+15) = (x-6)(x^(2)-5x+6)(x^(2)-7x+10)
Step 3: Simplify and solve for x:
(x+6)(x^(4)-15x^(3)+82x^(2)-200x+150) - (8)(x^(4)-13x^(3)+78x^(2)-150x+90) = (x-6)(x^(4)-12x^(3)+67x^(2)-160x+120)
x^(5)-15x^(4)+82x^(3)-200x^(2)+150x - 8x^(4)+104x^(3)-624x^(2)+1200x-720 = x^(5)-12x^(4)+67x^(3)-160x^(2)+120x-6x^(4)+72x^(3)-402x^(2)+960x-720
0 = 5x^(4)-117x^(3)+866x^(2)-1990x
Step 4: Use the quadratic formula to find the solutions for x:
x = (-(-117) ± √((-117)^(2)-4(5)(866)))/(2(5))
x = (117 ± √(13689-17320))/(10)
x = (117 ± √(-3631))/(10)
x = (117 ± i√3631)/(10)
Step 5: Check the solutions by plugging them back into the original equation:
(x+6)/(x^(2)-5x+6)-(8)/(x^(2)-7x+10)=(x-6)/(x^(2)-8x+15)
((117 + i√3631)/(10) + 6)/(((117 + i√3631)/(10))^(2) - 5((117 + i√3631)/(10)) + 6) - (8)/(((117 + i√3631)/(10))^(2) - 7((117 + i√3631)/(10)) + 10) = ((117 + i√3631)/(10) - 6)/(((117 + i√3631)/(10))^(2) - 8((117 + i√3631)/(10)) + 15)
After simplifying, we find that the equation holds true for both solutions. Therefore, the solutions are x = (117 + i√3631)/(10) and x = (117 - i√3631)/(10).
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34. The table below shows the number of new restaurants in a fast food chain that opened during the years
of 1988 through 1992. Using an exponential model, write an equation for the curve of best fit, then
estimate the number of new restaurants that opened in 2005.
1486
Year
1988
1989
1990
1991
1992
New
Restaurants
49
81
112
150
262
Equation:
Answer:
As a result, we can assume that the fast-food business added about 3,454 new outlets in 2005.
What are equations used for?
A mathematical equation, such as 6 x 4 = 12 x 2, states that two variables or values are equivalent. a meaningful noun. An equation is used when two or maybe more factors must be considered jointly in order to understand or explain the whole situation.
We can apply the following formula to find an exponentially model that matches the data:
y = abˣ
Where x is the length of time after 1988, y is the number of fresh restaurants that open each year, and a and b are undetermined constants.
We may use the information from the years 1988 and 1989 to get the constants a and b:
49 = ab⁰
81 = ab¹
As a result of the first equation, a = 49. When we put it in the second equation, we obtain this result:
81 = 49b¹
b = 81/49
The following is the exponentially model that best matches the data:
y = 49(81/49)ˣ
Since 2005 is 17 years after 1988, we need to determine the value of y when x = 17 in order to figure out the number of new eateries that debuted in 2005:
y = 49(81/49)¹⁷
y ≈ 3,454
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Jai went to the store to buy some chicken. The price per pound of the chicken is $3.75 per pound and he has a coupon for $1.75 off the final amount. With the coupon, how much would Jai have to pay to buy 5 pounds of chicken? Also, write an expression for the cost to buy p pounds of chicken, assuming at least one pound is purchased.
Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥ 1.
what is unitary method ?The unitary method in mathematics is a strategy for resolving proportional issues. Finding the value of one unit of a quantity and using that value to calculate the value of a second quantity that is proportional to the first includes this technique. The unitary technique is frequently employed in a variety of real-world contexts, including engineering, finance, and food preparation. The unitary method can be used to determine the amount of flour required to make a different number of cookies, for instance, if a recipe asks for 2 cups of flour to make 12 cookies.
given
The price of 5 pounds of poultry without the coupon is:
$5 for five pounds at $3.75 per pound.
Jai saves $1.75 thanks to the coupon, making the total price for 5 pounds of chicken:
$18.75 - $1.75 = $17.00
Jai would therefore need to spend $17.00 in order to purchase 5 pounds of poultry using the coupon.
With the assumption that at least one pound is bought, we can use the following formula to write an expression for the price to buy p pounds of chicken:
Expense is equal to (price per pound) x (pounds) - (coupon amount)
where p is the number of pounds, $3.75 is the price per pound, and $1.75 is the value of the voucher.
Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥ 1.
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Tyler took out a five-year loan with a principal of $12,000. He made monthly payments of $215 for the entire period, at which point the loan was paid off. How much did Tyler pay in interest?
Responses
$15
$60
$75
$900
Answer:
D, $900
Step-by-step explanation:
and monthly payments of $215, we can use the following formula:
Total interest = Total amount paid - Principal
where:
Total amount paid = Monthly payment x Number of payments
Number of payments = Number of years x 12
In this case, Tyler made monthly payments of $215 for 5 years, which is a total of 5 x 12 = 60 payments.
Substituting these values into the formula, we get:
Total amount paid = $215 x 60 = $12,900
Total interest = $12,900 - $12,000 = $900
Therefore, Tyler paid $900 in interest over the five-year period. The answer is option D: $900.
Henry has 342 marbles in bags. If 9 marbles are in each bag. how many bags does Henry have? How many bags will he have if he gives 15 bags to his brother?
What is the answer to this problem i have
The quotient of the given values when expressed in a scientific notation would be = 1.7 × 10⁵
What is scientific notation?A scientific notation is defined as a means of representation of too large or too small values in a most convenient form.
The quotient of 3.91× 10⁷ and 2.3 × 10² means the division of 3.91× 10⁷ and 2.3 × 10².
That is ;
= 3.91× 10⁷/ 2.3 × 10²
= 3.91/2.3 × 10⁷/10²
= 1.7 × 10⁵ ( it is 10⁵ because since it's division the superscripts attached to 10 will be subtracted)
Therefore, the quotient value of the given expression above would be = 1.7 × 10⁵.
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4. c^(3)v^(9)c^(-1)c^0
6. 9y^(4)j^(2)y^(-9)
8. 2y^(-9)h^(2)(2y^(0)h^(-4))^(-6)
10. (-3q^(-1))^(3)q^(2)
expression has the least vitive"? B. n^(n)
D. −n^(n)n^(-4)
vitive is D: −nnn−4.
To answer the question, the expression with the least vitive is D: −nnn−4.
For reference, the expressions in the question are:
4. c3v9c−1c0
6. 9y4j2y−9
8. 2y−9h2(2y0h−4)−6
10. (−3q−1)3q2
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Solve by using Cramer's Rule: \[ \begin{array}{l} -3 x-4 y-4 z=-8 \\ x-3 y-3 z=-19 \\ -x+y-2 z=3 \end{array} \]
The solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]
To solve this system of equations using Cramer's Rule, we will begin by finding the determinant of the coefficient matrix, which is an array of the coefficients of the variables in the equations. We will then find the determinants of the matrices that result from replacing each column of the coefficient matrix with the constant terms of the equations. Finally, we will use these determinants to find the values of x, y, and z.
The coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} \]
The determinant of the coefficient matrix is: \[ \begin{array}{ccc} -3 & -4 & -4 \\ 1 & -3 & -3 \\ -1 & 1 & -2 \end{array} = (-3)(-3)(-2) - (-4)(-3)(-1) - (-4)(1)(1) - (-4)(-3)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = -6 + 4 + 4 + 4 - 12 + 8 = -2 \]
The matrix that results from replacing the first column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -8 & -4 & -4 \\ -19 & -3 & -3 \\ 3 & 1 & -2 \end{array} = (-8)(-3)(-2) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(3) - (-4)(-19)(1) - (-4)(-3)(-2) = 48 - 36 - 76 + 36 - 76 + 24 = -80 \]
The matrix that results from replacing the second column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -8 & -4 \\ 1 & -19 & -3 \\ -1 & 3 & -2 \end{array} = (-3)(-19)(-2) - (-8)(-3)(-1) - (-4)(1)(3) - (-4)(-19)(-1) - (-4)(-3)(1) - (-4)(1)(-2) = 114 + 24 + 12 + 76 - 12 + 8 = 222 \]
The matrix that results from replacing the third column of the coefficient matrix with the constant terms is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} \]
The determinant of this matrix is: \[ \begin{array}{ccc} -3 & -4 & -8 \\ 1 & -3 & -19 \\ -1 & 1 & 3 \end{array} = (-3)(-3)(3) - (-4)(-19)(-1) - (-8)(1)(1) - (-8)(-3)(-1) - (-8)(-19)(1) - (-8)(1)(3) = 27 + 76 + 8 + 24 - 152 + 24 = 7 \]
Using these determinants, we can find the values of x, y, and z: \[ x = \frac{-80}{-2} = 40 \] \[ y = \frac{222}{-2} = -111 \] \[ z = \frac{7}{-2} = -3.5 \]
Therefore, the solution to this system of equations is: \[ \begin{array}{l} x=40 \\ y=-111 \\ z=-3.5 \end{array} \]
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7. 05 circles discussion-based assessment discussion-based assessment a student using a computer to study once you have completed the lesson and assignments, please contact your instructor to complete your discussion-based assessment. You and your instructor will discuss what you have learned up to this point in the course to make sure you're ready to move on
The discussion-based assessment is meant to provide you with an opportunity to reflect on the topics and skills you have learned, as well as identify any areas you may need additional support in.
The conversation should be guided by your instructor, who will ask questions to ensure you understand the material, as well as provide feedback and advice on how to improve your understanding and performance.
At the end of the assessment, you and your instructor should have a clear understanding of your progress and where you need to focus your efforts moving forward.
The instructor should also provide feedback on your performance and suggest strategies for improvement. Additionally, you should have an understanding of the topics you need to work on and the resources available to you to help you improve.
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The complete question is:
Discussion-based Assessment
A student using a computer to study once you have completed the lesson and assignments, please contact your instructor to complete your discussion-based assessment. You and your instructor will discuss what you have learned up to this point in the course to make sure you're ready to move on to the next lesson. What does it mean?
George looks at Kara's work and says she made a mistake.
He says she should have divided by 2 before she added.
Which student is correct? Explain how you know.
Answer:
George will be right by the rule of BODMAS
Step-by-step explanation:
If the students use BODMAS rule, division comes before addition
In a class 45% of the students are girls. If there are 18 girls in the class, then find
the total number of students in the class.
Answer:
i dont think its possible
Lee wants to make at least $400 profit from selling t-shirts. The initial start up costs for making t-shirts is $125. Write an inequality that represents the amount of sales, s, that Lee must have to reach the goal. Please answer!!
Answer:4
Step-by-step explanation:
Identify then number of solutions of the polynomial equation. Then find the solutions. z^(3)+10z^(2) + 28z + 24=0
The solutions are: z = -3, -2, and -1. This equation is a third-degree polynomial equation and it can have up to three solutions. To find these solutions, you can use the Rational Root Theorem.
This theorem states that all rational solutions of a polynomial equation can be written in the form a/b, where a is a divisor of the coefficient of the constant term, and b is a divisor of the coefficient of the leading term.
For this equation, the constant term is 24 and the leading term is 1, so the possible solutions can be expressed as a/b, where a is a divisor of 24 and b is a divisor of 1. Therefore, the possible solutions are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. To find the exact solutions, substitute these values for z into the equation and solve for each value.
The solutions are: z = -3, -2, and -1.
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A number y, when rounded to 2 decimal places, is equal to 9. 68. Find the upper and lower bound
If the number when rounded to 2 decimal places is equal to 9.68, then the upper bound is 9.685 and lower bound is 9.675 .
In order to find the upper bound of the number y, we need to add 0.005,
and to find the lower bound of the number y, we need to subtract 0.005 ,
We know that, the number y, when rounded to 2 decimal places is equal to 9.68 ;
So, the Upper Bound is = 9.68 + 0.005 = 9.685, and
The Lower Bound is = 9.68 - 0.005 = 9.675.
Therefore, the lower bound of y is 9.675 and upper bound of y is 9.685.
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The height of "Cokakola" soft drink cans are normally distributed with mean 3.7 centimeters and a standard deviation of 0.3 centimeter. 1. Find the probability that a randomly selected Cokakola can has the height below 3.55 centimeter. (4 marks) 1. Suppose that a Cokkola can is called "defective" if it has bright below 3.56 centimeter or above 3.06 centimeter. Find the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans. (6 marks) ki. Uning the normal approximation to the binomial distribution, estimate the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm? (5 marks) (b) Suppose that, on average, the number of car accidents in Hong Kong are 6 per day (which bas 24 hours) i. Determine the probability that at least x accidents will occur in 12 hour period. (4 marks) ii. In a two days, if there were 8 car accidents in Hong Kong, what is the probability that 2 accidents have occurred in the first 12 hours of the two days?
1. To find the probability that a randomly selected Cokakola can has the height below 3.55 centimeters, we need to use the z-score formula:
z = (x - μ) / σ
where x is the value we are looking for, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z = (3.55 - 3.7) / 0.3
z = -0.5
Now we can use the standard normal table to find the probability that corresponds to this z-score. The probability is 0.3085. So the probability that a randomly selected Cokakola can has the height below 3.55 centimeters is 0.3085.
2. To find the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans, we can use the binomial probability formula:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of defective cans. The probability of a can being defective is the sum of the probabilities of it being below 3.56 centimeters or above 3.06 centimeters. Using the z-score formula and the standard normal table, we can find these probabilities to be 0.3085 and 0.0013, respectively. So the probability of a can being defective is 0.3098. Plugging in the values into the binomial probability formula, we get:
P(X < 3) = (0.3098)^0 * (0.6902)^10 + 10 * (0.3098)^1 * (0.6902)^9 + 45 * (0.3098)^2 * (0.6902)^8
P(X < 3) = 0.5738
So the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans is 0.5738.
3. (a) To estimate the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm, we can use the normal approximation to the binomial distribution. The mean of the binomial distribution is np, where n is the number of trials and p is the probability of success. The standard deviation of the binomial distribution is √(np(1-p)). Using the z-score formula and the standard normal table, we can find the probability of a can having height above 3.95cm to be 0.0013. So the mean and standard deviation of the binomial distribution are:
μ = 110 * 0.0013 = 0.143
σ = √(110 * 0.0013 * (1 - 0.0013)) = 0.377
Now we can use the z-score formula to find the z-score for 25:
z = (25 - 0.143) / 0.377
z = 65.95
Using the standard normal table, we can find the probability that corresponds to this z-score to be 0. So the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm is 0.
(b) (i) To determine the probability that at least x accidents will occur in 12 hour period, we can use the Poisson distribution formula:
P(X ≥ x) = 1 - P(X < x)
where X is the number of accidents. The mean of the Poisson distribution is λ, which is the average number of accidents per unit of time. Since the average number of car accidents in Hong Kong are 6 per day, and we are looking for the probability in a 12 hour period, the mean is:
λ = 6 * (12 / 24) = 3
Plugging in the values into the Poisson distribution formula, we get:
P(X ≥ x) = 1 - (e^(-3) * 3^0 / 0! + e^(-3) * 3^1 / 1! + ... + e^(-3) * 3^(x-1) / (x-1)!)
This formula can be used to find the probability that at least x accidents will occur in 12 hour period.
(ii) To find the probability that 2 accidents have occurred in the first 12 hours of the two days, we can use the Poisson distribution formula:
P(X = 2) = e^(-λ) * λ^2 / 2!
where X is the number of accidents and λ is the mean. Since the average number of car accidents in Hong Kong are 6 per day, and we are looking for the probability in a 12 hour period, the mean is:
λ = 6 * (12 / 24) = 3
Plugging in the values into the Poisson distribution formula, we get:
P(X = 2) = e^(-3) * 3^2 / 2! = 0.224
So the probability that 2 accidents have occurred in the first 12 hours of the two days is 0.224.
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Isabella is deep-sea diving with two friends. Stacy is exploring a coral reef 6.3 meters in front of Isabella, and Jayla is floating on the surface directly above Isabella. If Jayla and Stacy are 9 meters apart, how far apart are Isabella and Jayla? If necessary, round to the nearest tenth.
Isabella and Jayla are thus separated by about 11.0 metres.
What is the idea of the Pythagorean Theorem?The Pythagorean Theorem states that the spaces on the right triangle (the side across from the right angle) of a right triangle, or, in common mathematical notation, a2 + b2, are equal to the spaces on the legs.
The Pythagoras formula can be used to resolve this issue. Let's call the distance between Isabella and Jayla "x". Then we have:
x² = (6.3)² + (9)²
Simplifying:
x² = 39.69 + 81
x² = 120.69
Taking the square root of both sides:
x ≈ 10.98
Rounding to the nearest tenth, we get:
x ≈ 11.0
Therefore, Isabella and Jayla are approximately 11.0 meters apart.
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Derivations (20 marks): For each of the questions in this section provide a derivation. Other methods will receive no credit i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks) iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)
Proof:
1. ∃x(Fx & Gx) [Premise]
2. Fx & Gx [∃-Elimination, 1]
3. ∃xFx [∃-Introduction, 2]
4. ∃xGx [∃-Introduction, 2]
5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]
6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]
ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)
Proof:
1. ¬ 3x(Px v Qx) [Premise]
2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]
3. Vx ¬ Px [∀-Introduction, 2]
4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]
iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)
Proof:
1. ¬ Vx(Fx → Gx) v 3xFx [Premise]
2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]
3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]
4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]
5. Fx → Gx [Resolution, 3, 4]
6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]
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Evaluate each expression using the values given in the table. X -3 -2 -1 0 1 2 3
F(x) 8 7 6 5 4 3 2
G(x) -7 -3 0 1 0 -3 -7
a. (f∘g)(1) b. (f∘g)(2) c. (g∘f)(2) d. (g∘f)(3) e. (g∘g)(1) f. (f∘f)(3)
Using the values given in the table to evaluate each expression, the value of each expression is (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.
To evaluate the expressions, we need to use the values given in the table for f(x) and g(x). The composition of functions (f∘g)(x) means that we plug the value of g(x) into the function f(x).
a. (f∘g)(1) = f(g(1)) = f(0) = 5
b. (f∘g)(2) = f(g(2)) = f(-3) = 8
c. (g∘f)(2) = g(f(2)) = g(3) = -7
d. (g∘f)(3) = g(f(3)) = g(2) = -3
e. (g∘g)(1) = g(g(1)) = g(0) = 1
f. (f∘f)(3) = f(f(3)) = f(2) = 3
Therefore, the answers are (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.
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Find the remainder on dividing 12-5x+3x^(2)+2x^(3) by x+3. Compare this with P(-3) where P(x)=12-5x+3x^(2)+2x^(3).
The remainder on dividing 12-5x+3x^(2)+2x^(3) by x+3 is -39.
This can be found by using long division or synthetic division. The result of the division is 2[tex]x^{(2)}[/tex]-11x+21 with a remainder of -39.
To compare this with P(-3), we need to plug in -3 for x in the original polynomial P(x)=12-5x+3[tex]x^{(2)}[/tex]+2[tex]x^{(3)}[/tex].
This gives us:
P(-3)= 12-5(-3)+3(-3)[tex]^{(2)}[/tex]+2(-3)[tex]^{(2)}[/tex]
=12+15+27-54=-39
Therefore, the remainder is the same as P(-3) for the given polynomial.
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answer quick please!!
Match the reasons with the statements in the proof to prove AB || DC, given that AD is parallel to BC and AD = CB.
Given:
AD || BC
AD = CB
Prove:
AB || DC
1. AD || BC, AD = CB
Reflexive Property of Equality
2. AC = AC
Given
3. 2 = 3
If Alternate Interior Angles are Congruent, then Lines are Parallel.
4. ACD = CAB
If Lines are Parallel, then Alternate Interior Angles are Equal.
5. 1 = 4
SAS (Side-Angle-Side)
6. AB || DC
CPCTE (Corresponding Parts of Congruent Triangles are Equal)
onetary policy below.
AB is parallel to DC because they are equal and corresponding sides of similar triangles.
What is the reflexive property of equality?
The reflexive property of equality is a basic principle in mathematics that states that any quantity is equal to itself. In other words, if we have a variable, say "a", then a is always equal to a. Similarly, if we have an equation such as 2 + 3 = 5, we can use the reflexive property of equality to say that 5 = 5, since any quantity is equal to itself. The reflexive property is used frequently in mathematical proofs to simplify expressions and make them easier to work with.
AD || BC, AD = CB - Reflexive Property of Equality
Explanation: This reason uses the reflexive property of equality, which states that a quantity is equal to itself. In this case, the reason is stating that the given information is true and using the reflexive property of equality to restate it in a different way.
2 = 3 - If Alternate Interior Angles are Congruent, then Lines are Parallel.
Explanation: This reason uses the angle congruence property that if the alternate interior angles are congruent, then the lines are parallel. This property is used to show that angles ACD and CAB are congruent because they are alternate interior angles.
ACD = CAB - If Lines are Parallel, then Alternate Interior Angles are Equal.
Explanation: This reason uses the angle equality property that if the lines are parallel, then the alternate interior angles are equal. This property is used to show that lines AD and BC are parallel because they are given to be parallel, and therefore the alternate interior angles ACD and CAB are equal.
1 = 4 - SAS (Side-Angle-Side)
Explanation: This reason uses the similarity property that if two triangles have the same side-angle-side, then they are similar. This property is used to show that triangles ABD and CBD are similar because they have the same side AD = CB and the same angles ABD and CBD.
AB || DC - CPCTE (Corresponding Parts of Congruent Triangles are Equal)
This reason uses the CPCTE property that the corresponding parts of congruent triangles are equal. This property is used to show that sides AB and DC are equal because they are corresponding sides of similar triangles ABD and CBD. Therefore, AB is parallel to DC because they are equal and corresponding sides of similar triangles.
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How to write 3/4 with a denominator of 12? Please help
Answer:
9/12
Step-by-step explanation:
3/4 converted is 9/12 3x3 is 9 and 4x3 is 12.
u think u guys can help with this?
The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 4 - 1 = 3 hours.
The presented graph displays a line or dot plot of a data set that indicates the average daily activity time of a group of individuals over the previous week.
We must locate the data set's middle value in order to get the median. As there are 20 data points in this instance, the median is calculated as the average of the 10th and 11th values, both of which are 2 hours. As a result, 2 hours is the median amount of exercise per day.
We must determine the difference between the data set's maximum and minimum values in order to determine the range. The ranges are 0 hours for the minimum and 5 hours for the highest. The range is therefore 5 - 0 = 5 hours.
Finding the difference between the third quartile (Q3) and the first quartile is necessary to calculate the interquartile range (IQR) (Q1). The data set can be divided into the lower half and the upper half because the median is 2 hours. 10 data points are present in the upper half and 10 data points are present in the lower half.
The median of the lower half of the data set must be located in order to determine Q1. The median is the average of the fifth and sixth values, both of which are one hour because there are ten data points in the lower half. Q1 is therefore 1 hour.
We must determine the median of the upper half of the data set in order to determine Q3. The median is the average of the fifth and sixth values, which are both 4 hours, as there are 10 data points in the upper half. Q3 is therefore 4 hours.
The IQR represents the variation between Q3 and Q1: IQR is equal to Q3 - Q1 (4 - 1 = 3 hours).
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Warm-Up: Suppose you have 60 dollars to deposit into a savings account. If you put your money into Bank A, they will deposit an additional 6 dollars per year into your account. If you put your money into Bank B, they will increase your balance by 10 percent per year.
How much money would you have after one year if you put your money into Bank A? How about Bank B?
Bank B may be a better option because the 10 percent increase is applied to the new balance each year, whereas Bank A only adds a flat 6 dollars each year.
If you put your money into Bank A, you will have to equate it as 60 + 6 = <<60+6=66>>66 dollars after one year.
If you put your money into Bank B, you will have 60 + (60 * 0.10) = 60 + 6 = <<60+(60*0.10)=66>>66 dollars after one year of the investment.
So, after one year, you will have the same amount of money in both Bank A and Bank B.
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How many angles are created when two parallel
lines are cut by a transversal? How many different
angle measures are there?
Answer:
eight angles
Step-by-step explanation:
Retention rates (the percentage of freshmen who return for their sophomore year) are of great interest to colleges and universities. One university's retention rate is typically about 80%. This year, they have 3,000 freshmen. How many of those do we expect to return for their sophomore year?
2,400 freshmen will return for his sophomore year, per the referenced statement.
What is a business interest?The cost a company pays a bank (creditor) for a loan is called interest. Although many other arrangements are available, interest payments are typically based on the remaining balance of both a loan and paid on a monthly basis. With a predetermined interest rate, interest is often computed as a portion of the loan balance.
80 of every 100 undergraduates are anticipated to back for their second year if the percentage is 80%.
We may multiply the overall amount of newcomers by a retention rate to get the number of undergraduates anticipated to return:
80 percent of 3,000 freshman equals 0.80 x 3,000, or 2,400.
So we may anticipate 2,400 freshman coming back for our sophomore year.
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83 divided by 17 pls answer my calculator is worse than my brain
83/17 = 4.88235294118
Answer:
4.88, and 4.9 rounded to the nearest 10th and 5 round to the nearest whole number.
Step-by-step explanation:
14
Nadia was considering two different vacation packages. For each, she wrote a linear equation
to model the cost of airfare and'n nights in a hotel. She graphed the corresponding lines and
found the two packages cost the same only when the vacation includes 5 nights in a hotel.
Which statement about Nadia's graph must be true?
AThe lines are parallel.
BThe lines are not parallel.
CThe x-intercepts are the same.
D The y-intercepts are the same.
Answer:
Step-by-step explanation:Which is the equation of a line that has a slope of 1/2 and passes through point (2, -3)?
(8x^(3)+24x^(2)+14x+2)-:(2x+5) Your answer should give the quotient and the remainder.
4x^(2)+2x+2 with a remainder of -8.
The quotient and remainder of the given expression can be found by performing polynomial long division.
First, divide the leading term of the dividend, 8x^(3), by the leading term of the divisor, 2x. This gives a quotient of 4x^(2).
Next, multiply the divisor, (2x+5), by the quotient, 4x^(2), to get 8x^(3)+20x^(2).
Then, subtract this product from the dividend to get a new dividend of 4x^(2)+14x+2.
Repeat this process by dividing the leading term of the new dividend, 4x^(2), by the leading term of the divisor, 2x, to get a new quotient of 2x.
Multiply the divisor, (2x+5), by the new quotient, 2x, to get 4x^(2)+10x.
Subtract this product from the new dividend to get a new dividend of 4x+2.
Finally, divide the leading term of the new dividend, 4x, by the leading term of the divisor, 2x, to get a new quotient of 2.
Multiply the divisor, (2x+5), by the new quotient, 2, to get 4x+10.
Subtract this product from the new dividend to get a remainder of -8.
So, the final quotient is 4x^(2)+2x+2 and the final remainder is -8.
Therefore, the answer is: (8x^(3)+24x^(2)+14x+2)-:(2x+5) = 4x^(2)+2x+2 with a remainder of -8.
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A representative sample of 50 customers at the restaurant is surveyed during a weekend
The answer to this question is as follows e. Untrue. It is not possible to equation predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
A prediction that 13 of the first 100 clients the next weekend will purchase baked chicken is not plausible.
b. Untrue. This weekend, 20% of consumers didn't purchase eggplant parmesan,
c. Untrue. Based on the information in the table, we are unable to determine with any degree of accuracy how many grilled fish meals the chef should cook.
d. True. This previous weekend, 100% of customers Minus 10% = 90% did not order pasta with veggies.
e. Untrue. It is not possible to predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.
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(1 point) LetA=[6514] and b=[−9−17]. Define the linear transformationT:R2→R2byT(x)=Ax. Find a vectorxwhose image underTisb.x=[Is the vectorxunique?
The vector x whose image under T is b is x = [23/19 -129/19].
A linear transformation is a function that maps one vector to another vector while preserving the operations of vector addition and scalar multiplication. In this case, the linear transformation T is defined as T(x) = Ax, where A is a matrix and x is a vector.
To find a vector x whose image under T is b, we need to solve the equation Ax = b for x. This can be done by multiplying both sides of the equation by the inverse of A, which gives us x = A-1b.
Using the formula for the inverse of a 2x2 matrix, we can find A-1:
A-1 = (1/(6*4 - 5*1)) * [4 -5-1 6] = [4/19 -5/19-1/19 6/19]
Now we can multiply A-1 by b to get x:
x = A-1b = [4/19 -5/19-1/19 6/19] * [−9−17] = [(4/19)*(-9) + (-5/19)*(-17) (−1/19)*(-9) + (6/19)*(-17)] = [23/19 -129/19]
Therefore, the vector x whose image under T is b is x = [23/19 -129/19].
The vector x is unique because the inverse of A is unique, and therefore the solution to the equation Ax = b is also unique.
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