Marilyn uses a credit card with a 19.9% APR compounded monthly to pay for car repairs totaling $991.38. She can pay $410 per month on the card. What will the total cost of this purchase be?
$1,021.01
$1,188.66
$991.38
$1,192.39
Answers
$991.38 × 0.199/12 = $16.44
The balance subject to the next month's finance charge will be
$991.38 +16.44 -410.00 = $597.82
The finance charge at the end of the second month will be
$597.82 × 0.199/12 = $9.91
The balance remaining after the second payment will be
$597.82 +9.91 -410.00 = $197.73
The finance charge applied at the end of the third month is
$197.73 × .199/12 = $3.28
so Marilyn can make one final payment of
$197.73 +3.28 = $201.01
to pay off the balance.
In all, Marilyn has paid 2×$410.00 +201.01 =
$1021.01 . . . . . . . . corresponds to the first choice
_____
In real life, Marilyn's credit card may not accrue any finance charge until after the first statement on which the charge appears. Thus the total cost of the purchase may be only $1004.02. The attached spreadsheet shows the beginning balance and the finance charges for each month for the two different scenarios.
Related Questions
Which expression is equivalent to 18x + 45
Answers
not sure what you're looking for
9*2X=18X
9*5=45
18X+45=18X+45
Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form an = a1 ⋅ rn−1. explain how you arrived at your answer.
Answers
a ⇒⇒⇒ the first term
r ⇒⇒⇒ common ratio
Given: the fourth term (a4) = 121.5 and the common ratio = 3 and n = 4
∴ [tex]121.5 = a* 3^{4-1} [/tex]
∴ a = 121.5/3³ = 121.5/27 = 4.5
So, The formula for this sequence will be [tex]4.5 * 3^{n-1} [/tex]
Answer:
First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.
In the figure below, lines that appear to be tangent are tangent. Point O is the center of the circle. Which of the following is the value of x?
a. 60 degrees
b. 90 degrees
c. 100 degrees
d. 120 degrees
Answers
Answer:
(D) 120 degrees
Step-by-step explanation:
From the figure drawn, we have
∠ABC=60°
And ∠OAB=∠OCB=90° (angles made by tangent on the circle is 90°)
Thus, ∠AOC+∠OCB∠CBA+∠OAB=360° (Angles sum property of quadrilateral)
[tex]x+90^{\circ}+90^{\circ}+60^{\circ}=360^{\circ}[/tex]
[tex]x+240^{\circ}=360^{\circ}[/tex]
[tex]x=120^{\circ}[/tex]
Therefore, the value of x is [tex]120^{\circ}[/tex]
Hence, option D is correct.
Answer: d. 120 degrees
Step-by-step explanation:
From the given figure drawn, we can see that
∠ABC=60°
Also we know that tangents are radius are perpendicular at the point of tangency
And ∠OAB=∠OCB=90° (∵ tangents are radius are perpendicular at the point of tangency)
Therefore, we have
[tex]\angle{AOC}+\angle{OCB}+\angle{ABC}+\angle{OAB}=360^{\circ}\text{ ( By Angle sum property of quadrilateral)}\\\\\Rightrarrow\ x+90^{\circ}+60^{\circ}+90^{\circ}=360^{\circ}\\\\\Rightarrow\ x=360^{\circ}-240^{\circ}\\\\\Rightarrow\ x=120^{\circ} [/tex]
A circle has a circumference of 324\pi324π324, pi. what is the radius of the circle?
Answers
C = 2πr
=> 324π = 2πR
=> R = ( 324 / 2 ) = 162 units
Bobby is testing the effectiveness of a new cough medication. There are 100 with a cough in the study. Seventy patients received the cough medication, and 30 other patients did not receive treatment. Thirty-four of the patients who received the medication reported no cough at the end of the study. Twenty of the patients who did not receive medication reported no cough at the end of the study. What is the probability that a patiebt chosen at random from this study took the medication, given that they reported no cough?
A. 63%
B. 53%
C. 38%
D. 43%
Answers
[tex]=\frac{34}{54}=63\%[/tex]
The probability that a patient chosen at random from this study took the medication, given that they reported no cough is 63%.
Answer:
The answer to this question is 63%
Dustin is driving his car at speed of 50 kilometres per hour. he going to texas which is located 345 kilometres from his starting point.how long will it take him to reach texas?
Answers
An equation of a function y(t) is shown.
y(t)=−t²+14t−40
Which of the following statements are true about the graph of y(t) for
6≤t≤8 and WHY?
a. The value of y(t) increases over the interval 6≤t≤7
b. The value of y(t) increases over the interval 7≤t≤8
c. The average rate of change over the interval 6≤t≤8 is 0
d. The value of y(t) is constant over the interval 6≤t≤8
e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8
Answers
y(t)=-t^2+14t-40
thus the graph will be as shown in the figure:
From the graph we deduce that the correct statement is:
y'(t)=-2t+14=0
thus
t=7
thus
y(7)=0
thus the correct statement is:
c. The average rate of change over the interval 6≤t≤8 is 0
The graph of y(t) increases over the interval 6≤t≤7 because the derivative is positive. The average rate of change over the interval 6≤t≤8 is 0 due to symmetry about the vertex of the parabola at t=7. The rate of change over the intervals 6≤t≤7 and 7≤t≤8 are equal in magnitude but opposite in direction.
Given the quadratic function y(t)=-t²+14t-40, we need to analyze its behavior over the interval 6≤t≤8. The first derivative y'(t) of the function, which represents the slope of the tangent line to the graph at any point t, is -2t + 14. To determine the intervals of increase and decrease, we can set the first derivative to zero to find the vertex of the parabola, yielding t=7, which means the function increases on the interval 6≤t≤7 and decreases on 7≤t≤8.
The average rate of change over an interval is calculated by taking the difference in the function values at the endpoints of the interval over the difference in t. For the interval 6≤t≤8, since this is a symmetrical interval around the vertex, the average rate of change is 0. Furthermore, it follows from symmetry that the average rate of change over the intervals 6≤t≤7 and 7≤t≤8 should be equal in magnitude but opposite in sign.
Considering the stated properties and analyzing the equation, we can conclude that:
The value of y(t) increases over the interval 6≤t≤7.The value of y(t) decreases over the interval 7≤t≤8, so statement b is false.The average rate of change over the interval 6≤t≤8 is 0, making statement c true.The value of y(t) is not constant over the interval 6≤t≤8.The average rates of change over both intervals 6≤t≤7 and 7≤t≤8 are not equal in value; they are opposite, making e false.The GRE is an entrance exam that many students are required to take in order to apply to graduate school. In 2014, the combined scores for the Verbal and Quantitative sections were approximately normally distributed with a mean of 310 and a standard deviation of 12.
What is the probability that a randomly selected score is greater than 334? Write your answer as a decimal.
Answers
The probability that a randomly selected score is greater than 334 is 0.0228
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have [tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For this case, we're given that:
Combined scores were approximately normally distributed with mean of 310 and a standard deviation of 12.If we take:
X = a randomly selected score obtained in the GRE exam.
Then, by the given data, we have:
[tex]X \sim N(\mu = 310, \sigma = 12)[/tex]
And therefore, we can write:
Probability that a randomly selected score is greater than 334 = P(X > 334)
Converting X to standard normal distribution:
[tex]Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - 310}{12}[/tex]
The probability we need can be calculated as:
[tex]P(X > 334) = 1 - P(X \leq 334)\\P(X > 334) = 1 - P(Z \leq \dfrac{334 - 310}{12})\\\\P(X > 334) = 1 - P(Z \leq 2)[/tex]
From the z-tables, the p-value for Z = 2 is 0.9772
Thus, we get [tex]P(Z \leq 2) = 0.9772[/tex], and therefore,
[tex]P(X > 334) = 1 - P(Z \leq 2) = 1- 0.9772 = 0.0228[/tex]
Thus, the probability that a randomly selected score is greater than 334 is 0.0228
Learn more about z-score here:
https://brainly.com/question/21262765
Triangle RST was dilated by a scale factor of 1/2. The image, triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units. What is the length of a leg of the pre-image, triangle RST?
Answers
Triangle RST was dilated by a scale factor of 1/2
Given: triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units.
Pre-image: measure of pre-image * scale factor = measure of resulting image
measure of pre-image = measure of resulting image / scale factor
measure of pre-image = 8 / 1/2measure of pre-image = 8 * 2/1
measure of pre-image = 16 units.
Answer:
16 units
Step-by-step explanation:
RST was dilated by a scale factor of 1/2. This means R'S'T' has sides that are 1/2 the length of the sides of RST.
Since the legs of R'S'T' are 8 units, this gives us the equation
8 = 1/2x
Divide both sides by 1/2:
8÷1/2 = x
8 × 2/1 = x
16 = x
Each leg in RST is 16 units.
You are required to choose two topics from a list of six to write about on your science test. How many different pairings are possible?
10
15
20
12
Answers
The answer is 12 :)
ONE LAST QUESTION!!!!!!!!!!WILL GIVE THE BRAIN!!!!!!!!!!
Answers
Shifting upwards by 3 units means, adding 3 to the function value. So the resulting function after these two transformations will be:
[tex]g(x)=- \sqrt{x}+3 [/tex]
Thus, option C gives the correct answer
help me please...
Problem: The standard form of a circle is (x-h)2+(y-k)2=r2 and for the parabola, y-k=a(x-h)2. The (h,k) pair will be the center of the circle and the vertex of the parabola. The radius of the circle is ‘r’ and the focal length of the parabola is f=1/(4a). For the following General Conic Equation: x2+y2-4x-6y-12=0 complete the following problems showing all your work:
Complete the square showing all your work to convert to Standard Form:
If this is a circle, state the coordinates of the center and give the radius. If this is a parabola, state the coordinates of the vertex and give the focal length. Show all your work.
Sketch the Conic. Label the values you found in part B. Be sure to draw or show the radius or focal length.
Answers
x²+y²-4x-6y-12=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x²-4x)+(y²-6y)=12
Complete the square twice. Remember to balance the equation by adding the same constants to each side
(x²-4x+4)+(y²-6y+9)=12+4+9
Rewrite as perfect squares
(x-2)²+(y-3)²=25
the answer part A) is
(x-2)²+(y-3)²=5²-----> this is the standard form of the equation of a circle
Part B) (x-2)²+(y-3)²=5²
the center is the point (2,3) and the radius is r=5 units
Part C)
using a graph tool
see the attached figure
Need this geometry answer
Answers
so according to this
7x+x-4 = 180
8x = 184
x= 23
therefore angle DBC 23-4 = 19
SO 19 IS THE ANSWER
Uppose it costs $10 to roll a pair of dice. you get paid the sum of the numbers in dollars that appear on the dice. what is the expected value of this game?
Answers
Are the two events “choosing a sophomore” and “choosing someone who replied ‘Yes’” independent events?
Answers
If you prove that ∆WXZ is congruent to ∆YZX, which general statement best describes what you have proved?
A.Diagonals of a parallelogram bisect each other.
B. Diagonals of a parallelogram are congruent.
C. Opposite sides of a parallelogram are congruent.
D. The diagonal of a parallelogram connects two non-consecutive vertices.
Answers
Proving that ΔWXZ is congruent to ΔYZX does not directly prove any of the provided statements about a parallelogram without additional context. Likely, it could imply that diagonals of a parallelogram bisect each other, but more information is needed.
Explanation:If you prove that ΔWXZ is congruent to ΔYZX, you have demonstrated the congruence of triangles within a geometric figure, likely referencing elements of a parallelogram. However, the specific elements such as sides or diagonals are not indicated in the proof of congruence between the triangles in question.
From the options you have provided and general geometric principles, proving congruent triangles within a figure doesn't necessarily directly prove any of those statements without additional context. If we assume ΔWXZ and ΔYZX are created by a diagonal of a parallelogram, congruent triangles might imply that diagonals of a parallelogram bisect each other (Option A). However, it could also relate to the congruence of opposite sides depending on the specifics of the figure, not the diagonals being congruent (Option B), because congruence of triangles does not guarantee equal length of diagonals, just segments within the triangles.
An archway is modeled by the equation y = -2x^2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?
A. 8 units
B. 6 units
C. 5 units
D. 3 units
Answers
1. You have that the the archway is modeled by the equation y=-2x^2+8x and the angle mentioned in the problem is defined by the equation x−2.23y+10.34=0.
2. Therefore, you must susbtitute y=-2x^2+8x into x−2.23y+10.34=0, as below:
x−2.23(-2x^2+8x)+10.34=0
3. When you apply the distributive property, you obtain:
x−2.23(-2x^2+8x)+10.34=0
x+4.46x^2-17.84x+10.34=0
4.46x^2-16.84x+10.34=0
4. When you solve the quadratic equation, you obtain:
x=3 units
Therefore, the answer is the option D: D. 3 units.
Answer
The answer is 6
Step-by-step explanation:
Given a possible triangle ABC with a=5,b=11,and a=23, find a possible value for
Answers
Given a possible triangle ABC with a=5, b=11, and A=23 degrees, find a possible value for angle B. Round to the nearest tenth.
A. 10.2° B. 11.2° C. 59.3° D. no solution
========================================================
a = 5 , b = 11 , and ∠A = 23°
By applying the Law of Sines:
[tex] \frac{sin \ A}{a} = \frac{sin \ B}{b} [/tex]
[tex] \frac{sin \ 23}{5} = \frac{sin \ B}{11} [/tex]
∴ sin B = 11* (sin 23°)/5 ≈ 0.8596
∴ ∠B = [tex] sin^{-1} 0.8596 [/tex] ≈ 59.3°
∴ The correct choice is option (C)
C. 59.3°
For f(x)=3x+1 and g(x)=x²-6, find (f o g)(4)
Answers
so, we can simply first find g(4), and then plug that in f(x),
[tex]\bf \begin{cases} f(x)&=3x+1\\ g(x)&=x^2-6\\ (f\circ g)(4)&=f(~~g(4)~~) \end{cases} \\\\\\ g(4)=(4)^2-6\implies g(4)=16-6\implies g(4)=10 \\\\\\ f(~~g(4)~~)\implies f(~~10~~)=3(10)+1\implies f(~~10~~)=31[/tex]
Find the exact value. tan240°
Answers
[tex] \sqrt{3} [/tex]
The exact value of tan 240° is found by recognizing that 240° is in the third quadrant with a reference angle of 60°. The sine and cosine values are both negative in this quadrant. Therefore, tan 240° simplifies to √3.
To find the exact value of tan 240°, we need to consider its position on the unit circle. The angle 240° is in the third quadrant, where both sine and cosine are negative.
First, recognize that 240° is 60° beyond 180°, making its reference angle 60°.The sine and cosine of 60° are given by sin 60° = √3/2 and cos 60° = 1/2, but since 240° is in the third quadrant, these values will be negative.Thus, sin 240° = -√3/2 and cos 240° = -1/2.Tangent is the ratio of sine to cosine: tan 240° = (sin 240°) / (cos 240°) = (-√3/2) / (-1/2).Simplifying this, we get tan 240° = √3.Therefore, the exact value of tan 240° is √3.
A drawer of loose socks contains 2 red socks, 2 green socks, and 6 white socks. Which best describes how to determine the probability of pulling out a white sock, not replacing it, and pulling out another white sock?
Answers
So, if you were to not replace the first drawn white sock, your percentage goes to 55.5556%! This is because you now have 5/9 socks remaining in the drawer being white!
Answer:
The probability that the first sock is white is 6/10 and that the second sock is white is 5/9, so the probability of choosing a pair of white socks is 30/90 = 1/3! Hope that helps.
Step-by-step explanation:
Hugo is 6 feet 4 inches tall, weighs 225 pounds, and very muscular. if you think hugo is more likely to be a professional football player rather than a professional ballroom dancer, you are using:
Answers
An inductive argument is intended to show that its conclusion is probably or likely true, though not certainly true, if its premises all are true. The author of an inductive argument (if sincere) only aims to establish the intended conclusion with a high degree of probability although not with complete certainty.
Words such as “probably,” “likely,” and “it is reasonable to conclude” suggest that you intend your argument to show that the conclusion is probably, but not certainly, true. The statement above use the words "more likely", then this word tell us that this is, in fact, an inductive argument.
Answer:
I think it is the option "representative heuristic"
Step-by-step explanation:
Heuristics are kind of like "mental shortcuts" that we use to make assumptions quickly. They are based off of our category prototypes and what we believe are typical examples of a certain object or group. The reason why it would be representative heuristic is because when you use this, you are comparing the new situation to an already existing image of the object. In this case, you are comparing Hugo to the "typical" image of a football player.
Hope this helps you :)
The _____ is a measure of variability that is simply the difference between the highest score and the lowest score. variance standard deviation median range
Answers
The answer to this is range! Because when you are figuring out the range, you subtract the lowest score from the highest score. Good luck on your test!
The range is a measure of variability that is simply the difference between the highest score and the lowest score. which is the correct answer would be option (D).
What is the range of the data?The range of the data is defined as the difference between the maximum number of data to the minimum number of data.
The range of given data = maximum number - minimum number
The range is the correct answer to this because you subtract the lowest score from the highest score to determine the range.
Therefore, the range is a measure of variability that is simply the difference between the highest score and the lowest score.
Hence, the correct answer would be an option (D).
To learn more about the range of the data click here:
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A shipping box in the shape of a rectangular prism has a volume of 18x^3+5x^2-2x. what are three expressions that can represent possible dimensions of the shipping box?
Answers
Volume=length×width×height
but
V=18x^3+5x^2-2x
V=x(18x^2+5x-2)
V=x(9x-2)(2x+1)
Hence the possible expression for the dimensions of the shipping box is x by (9x-2) by (2x+1)
Answer:
[tex](x), (9x-2), (2x+1)[/tex]
Step-by-step explanation:
[tex]18x^3+5x^2-2x=x(18x^2+5x-2)=x(9x-2)(2x+1)[/tex]
Consider the function graphed below
Answers
For x <1:
In this interval we have the following equation:
f (x) = x ^ 2
For x> 1:
In this interval we have the following equation:
f (x) = (1/3) x + 2/3
Answer:
The graph represents the following function:
f (x) = x ^ 2 (x <1)
f (x) = (1/3) x + 2/3 (x> 1)
Square root of -1 divided by (3+8i)-(2+5i)
Answers
Used:[tex](a+b)(a-b)=a^2-b^2[/tex]
The cost of printing the football roster for games was 25 for 4.00 what is the cost per copy
Answers
STEPS:
Divide 4 by 25
= $0.16
CHECK YOUR ANSWER:
Each copy costs $0.16. You decided to get 25 copies.
25 * $0.16
= $4.00
Frank owns 250 acres of land. If he divides the land into 1/3 acre plots, how many plots will he have?
Answers
Hope this helps you.
All you really have to do is 250 divided by 1/3 and you get 83.3333 (repeating) but you can just say 83.3.
Will mark 5 stars
The variable used to show correlation is r, which is also known as the correlation complement.
A.True
B.False
Answers
B. False
What are the lengths?
Answers
Two sides of the right angled triangles are given and we are to find the Third side. This can be done using the Pythagoras Theorem, which states:
Hypotenuse² = Base² + Perpendicular²
For 1st figure, we have
Base = 21
Perpendicular = 20
So,
Hypotenuse² = 20² + 21² = 841
⇒
Hypotenuse = 29 (1st option is correct)
For 2nd Image, we have
Base= 6
Hypotenuse = 10
So, we can write:
10² = 6² + Perpendicular²
Perpendicular² = 64
⇒
Perpendicular = 8 (Option Fourth)