The effective annual rate you'll actually be paying on the credit card is 31.38%.
To find the effective annual rate (EAR) when the interest rate is given as an APR with monthly compounding, we can use the following formula:
EAR = (1 + APR / Number of Compounding Periods)^(Number of Compounding Periods) - 1
In this case, the APR is 28.2% and the compounding is done monthly, so the number of compounding periods is 12.
EAR = (1 + 0.282 / 12)^12 - 1 = 0.3138
The effective annual rate is 0.3138, which is equivalent to 31.38% when rounded to 2 decimal places.
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5) Evaluate the algebraic expression for the given value or values of the variable(s)
8x² + 2y; x = 6 and y = 9
a)2736 b) 660 c) 306 d) 2322
6) The formula C = (F - 32) expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. Use the formula to convert 104°F to its equivalent temperature on the Celsius scale.
a) 40°C
b) 76°C
c) 8°c
d) 130°c
In the first question, we are asked to evaluate the algebraic expression 8x² + 2y for the given values of x = 6 and y = 9. The options provided are a) 2736, b) 660, c) 306, and d) 2322.
In the second question, we are asked to use the formula C = (F - 32) to convert 104°F to its equivalent temperature on the Celsius scale. The options provided are a) 40°C, b) 76°C, c) 8°C, and d) 130°C.
For the first question, we substitute the given values into the expression 8x² + 2y:
8(6)² + 2(9) = 288 + 18 = 306.
Therefore, the correct answer is c) 306.
For the second question, we use the given formula C = (F - 32) and substitute F = 104:
C = (104 - 32) = 72.
Therefore, the equivalent temperature of 104°F on the Celsius scale is 72°C.
The correct answer is not among the options provided, as none of the options matches the calculated value of 72°C.
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The correlation coefficient for a certain set of data is r=-0.41. The scatter plot for this data is most likely to be ... Scatter 1 700 60.0 500 400 300 200 100 300 Scatter 4 O. O 160.0 140.0 120.0 10
Option 3 (Scattered) is the correct answer. Option 1 (Clustered), option 2 (Linear), and option 4 (Random) are not correct as they indicate different types of scatter plots that are not appropriate for the given correlation coefficient.
The correlation coefficient of a certain set of data is given as r = -0.41.
The scatter plot for this data is most likely to be scattered.
The correlation coefficient for a certain set of data is given by the ratio of the covariance of the two variables and the product of their standard deviations. It is represented by the letter 'r'.
The value of 'r' ranges between -1 to +1. If r is positive, it represents a positive correlation, and if r is negative, it represents a negative correlation.
In the given question, the value of 'r' is negative. Therefore, it represents a negative correlation.
The absolute value of the correlation coefficient indicates the strength of the correlation.
The closer the value of 'r' is to 1, the stronger the correlation between the two variables.
In this case, the value of 'r' is 0.41. This indicates a moderately weak negative correlation between the variables.
Since the correlation is weak, the scatter plot for this data is most likely to be scattered.
Therefore, option 3 (Scattered) is the correct answer. Option 1 (Clustered), option 2 (Linear), and option 4 (Random) are not correct as they indicate different types of scatter plots that are not appropriate for the given correlation coefficient.
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If f(x)=3x^(5)+4x^(3)+3, then what is the remainder when f(x) is divided by x-3 ?
The Remainder when dividing f(x) by x - 3 is 840
The remainder when dividing the polynomial f(x) = 3x^5 + 4x^3 + 3 by the binomial x - 3, we can use the polynomial remainder theorem. According to the theorem, if we substitute the divisor, x - 3, into the polynomial f(x) and evaluate it at x = 3, the resulting value will be the remainder.
Let's calculate the remainder using this approach:
Substituting x = 3 into the polynomial f(x), we have:
f(3) = 3(3)^5 + 4(3)^3 + 3
= 3(243) + 4(27) + 3
= 729 + 108 + 3
= 840
Therefore, when f(x) = 3x^5 + 4x^3 + 3 is divided by x - 3, the remainder is 840.
In summary, the remainder when dividing f(x) by x - 3 is 840.
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According to a recent poll, 80% of adults enjoy watching TV. Choose a group of 3 adults at random. The probability that all of them enjoy watching TV is: O a. 0.267 Ob. 0.512 c. 0.333 d. 2.400
Answer:
B) 0.512
Step-by-step explanation:
Use the binomial probability formula
[tex]P(X=x)=C(n,x)p^xq^{n-x}\\P(X=3)=C(3,3)(0.80)^3(0.20)^0\\P(X=3)=(0.80)^3\\P(X=3)=0.512[/tex]
Therefore, B is the correct option.
Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.03q² +6q – 48, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing a pairs of sunglasses. A) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) Answer: thousand pairs of sunglasses need to be sold. B) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) Answer:
$102 thousand is the actual maximum profits that can be expected.
A) The given profit function is,P(q) = – 0.03q² +6q – 48
We need to find out the number of pairs of sunglasses (in thousands) should be sold to maximize the profit.
The profit function is in the quadratic form ax² + bx + c.
Hence, it represents a parabola where "a" is negative.
So, the graph will be downward which means it will have a maximum point.
Therefore, to maximize the profit, we need to find the vertex of the parabola.
To find the vertex of the parabola, we use the following formula,
Vertex = (-b / 2a, P(-b / 2a))From the given function, a = -0.03 and b = 6Substituting the values in the above formula,
Vertex = (-6 / 2(-0.03), P(-6 / 2(-0.03)))= (100, P(100))
Therefore, 100 thousand pairs of sunglasses should be sold to maximize the profits.
B) Now, to find the actual maximum profits that can be expected, we need to substitute q = 100 in the given profit function.
P(q) = – 0.03q² + 6q – 48P(100)
= – 0.03(100)² + 6(100) – 48
= $102.
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Find the dot product v•w and the angle between v and w. v=4i - 3j + k, w = i +43 +4k vow=0 (Simplify your answet Type an exact value, using radicals as needed.) The angle between V and wis 0 = 0 (Do not round until the final answer. Then round to the nearest tenth as needed.)
To find the dot product v • w, we multiply the corresponding components of v and w and sum them up.
v = 4i - 3j + k
w = i + 4j + 3k
v • w = (4)(1) + (-3)(4) + (1)(3)
= 4 - 12 + 3
= -5
So, the dot product of v • w is -5.
To find the angle between v and w, we can use the formula:
cosθ = (v • w) / (||v|| ||w||)
where ||v|| and ||w|| are the magnitudes of vectors v and w, respectively.
||v|| = √(4² + (-3)² + 1²) = √(16 + 9 + 1) = √26
||w|| = √(1² + 4² + 3²) = √(1 + 16 + 9) = √26
cosθ = (-5) / (√26 * √26) = -5 / 26
To find the angle, we take the inverse cosine (arccos) of cosθ:
θ = arccos(-5 / 26)
Therefore, the angle between v and w is θ ≈ 98.4 degrees (rounded to the nearest tenth).
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mBEA =
148⁰
212°
74°
180°
B
C 74 A
E
D
Answer:
(b) 212°
Step-by-step explanation:
You want the measure of major arc BEA intercepted by tangent AD and chord AB.
Angle"Inscribed" angle DAB is the supplement of the one given, so is ...
∠DAB = 180° -74° = 106°
ArcThe measure of the arc that angle intercepts is double the measure of the angle:
arc BEA = 2×∠DAB = 2×106°
arc BEA = 212°
__
Additional comment
An inscribed angle is half the measure of the arc it intercepts. If you consider a point D' on arc EA, angle BAD' will have half the measure of arc AED'. This is true for D' located anywhere on arc EA, including at point A.
In the limit, as point D' approaches A, chord AD' approaches tangent AD. It should be no surprise, then, that angle DAB is half the measure of arc AEB.
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In a corporation, 63% of the employees are female, executives,
or both. Furthermore, 58% of the employees are female, and 5% are
female executives. Find the percentage of employees who are male
execut
The percentage of employees who are male executives is 5%.
Let's denote, A = event that an employee is female and B = event that an employee is an executive.
We are given the following probabilities:
P(A ∪ B) = 63% = 0.63 (percentage of employees who are female, executives, or both)
P(A) = 58% = 0.58 (percentage of employees who are female)
P(A ∩ B) = 5% = 0.05 (percentage of employees who are female executives)
We want to find the percentage of employees who are male executives, which is equivalent to finding P(~A ∩ B), where ~A represents the complement of A (i.e., not A or male employees).
Using the concept of the complement, we know that:
P(~A) = 1 - P(A)
Therefore, P(~A ∩ B) = P(B) - P(A ∩ B)
Since P(B) is not given directly, we need to find it using the given information:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.63 = 0.58 + P(B) - 0.05
0.63 - 0.58 + 0.05 = P(B)
0.10 = P(B)
Now, we can find P(~A ∩ B):
P(~A ∩ B) = P(B) - P(A ∩ B)
= 0.10 - 0.05
= 0.05
Therefore, the percentage of employees who are male executives is 5%.
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A particle moves in the coordinate plane with position vector (x(t). y(t))such that x(t) = R-4t+3 and y(t) = 4 - 5t + 3+ in the time interval Osts 4. Part A: Find the equation of the tangent line to the path of the particle when t= 4.
Part B: At what time (if any) is the particle at rest? Justify your answer.
Part C: Is the speed of the particle increasing or decreasing when t = 42 Justify your answer.
Part D: Write an expression for the total distance traveled by the particle on the interval Osts 4.
Given x(t) = R-4t+3 and y(t) = 4 - 5t + 3. A particle moves in the coordinate plane with position vector (x(t), y(t)).
Part A: Find the equation of the tangent line to the path of the particle when t= 4.Tangent line is defined as the line that touches a point on a curve but is different from the curve at the point.
Therefore, first, we will differentiate the given position vector with respect to time to obtain the derivative of the position vector.r(t) = (x(t), y(t))r′(t) = (x′(t), y′(t))= (-4, -5)
Therefore, the tangent line to the curve at t = 4 is given by:r(t) = r(4) + r′(4)(t - 4)r(t) = (R-13, -13) + (-4, -5)(t - 4)r(t) = (-4t + R - 29, -5t - 17)
Part B: At what time (if any) is the particle at rest? Justify your answer.Using the given velocity function, we can set it to zero to get the time at which the particle is at rest.
To find the velocity function, we differentiate the position function with respect to time.v(t) = (x′(t), y′(t))= (-4, -5)The speed function is given by:s(t) = √x′(t)² + y′(t)²= √16 + 25= √41s(t) is a constant function.
Therefore, the particle never comes to rest.
Part C: Is the speed of the particle increasing or decreasing when t = 42? Justify your answer. The speed of the particle is constant. Therefore, it is neither increasing nor decreasing when t = 42.
Part D: Write an expression for the total distance traveled by the particle on the interval Osts 4.The distance traveled by the particle between t = 0 and t = 4 is given by the integral of speed function on
[0, 4].∫[0,4] s(t) dt= ∫[0,4] √41 d[√41t]₀¹³= 3√41
The distance traveled by the particle between t = 4 and t = t is given by the integral of speed function on [4, t].∫[4,t] s(t) dt= ∫[4,t] √41 dt= [√41t]₄ᵗ= (t - 4) √41
The total distance traveled by the particle on the interval Osts 4 is given by the sum of the distance traveled between t = 0 and t = 4 and the distance traveled between t = 4 and t = t.d = 3√41 + (t - 4) √41= (√41t - √41 + 3√41) units.
The equation of the tangent line to the path of the particle when t = 4 is y = -5x + R - 57.The particle never comes to rest.The speed of the particle is neither increasing nor decreasing when t = 42.The expression for the total distance traveled by the particle on the interval Osts 4 is d = (√41t - √41 + 3√41) units.
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Find dy/du, du/dx, and dy/dx. y = u, u³, u = 2x2 - 4 dy / du = du / dx = dy / dx =
So, the derivatives are: dy/du = 1, du/dx = 4x, dy/dx = 4x.
To find dy/du, du/dx, and dy/dx, we can use the chain rule of differentiation.
Given:
y = u
u = u³
u = 2x² - 4
dy/du:
Since y = u, the derivative of y with respect to u is simply 1.
dy/du = 1
du/dx:
To find du/dx, we need to differentiate the equation u = 2x² - 4 with respect to x.
du/dx = d/dx(2x² - 4)
= 4x
dy/dx:
To find dy/dx, we can use the chain rule by multiplying dy/du and du/dx.
dy/dx = (dy/du) * (du/dx)
= (1) * (4x)
= 4x
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Calculating Interest Rates [LO3] Assume the total cost of a college education will be $300,000 when your child enters college in 18 years. You presently have $71,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Annual rate of interest %
To cover the cost of your child's college education, you need to calculate the annual interest rate on your $71,000 investment over 18 years to reach a total of $300,000.
To find the annual interest rate required, we can use the compound interest formula:
[tex]Future Value = Present Value * (1 + Interest Rate)^{Number of Periods[/tex]
In this case, the future value (cost of college education) is $300,000, the present value (initial investment) is $71,000, and the number of periods is 18 years. We need to solve for the interest rate.
Rearranging the formula, we have:
[tex]Interest Rate = ((Future Value / Present Value)^{(1 / Number of Periods) }- 1) * 100[/tex]
Plugging in the values, we get:
[tex]Interest Rate = (($300,000 / $71,000)^{(1 / 18)} - 1) * 100[/tex]
Calculating this expression, the annual interest rate required to cover the cost of your child's college education is approximately 5.62%. Therefore, you would need to earn an annual interest rate of 5.62% on your $71,000 investment to reach the desired amount.
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