Step-by-step explanation:
If the stock market declined by an average of 2.5% each month during the first 6 months of Mr. Jones' investment, we can calculate the total percentage decrease using the following formula:
(1 - 0.025)^6 = 0.8938
This means that after 6 months, Mr. Jones' investment would have decreased by approximately 10.62% (1 - 0.8938 = 0.1062).
To calculate how much money Mr. Jones has remaining, we need to multiply his initial investment of $1,500 by the percentage decrease:
$1,500 x 0.1062 = $159.30
Therefore, Mr. Jones would have $1,500 - $159.30 = $1,340.70 remaining after the first 6 months of his investment in the stock market with an average decline of 2.5% each month.
A dog breeder recorded the weight of a puppy during the first eight months after it was born. The breeder created the equation w = 0.25m + 8.3, where w is the weight of the puppy in pounds and m is the number of months since the puppy was born. What is the meaning of the slope from the breeder's equation?
The meaning of the slope from the breeder's equation is that each month, the weight of the puppy increases by 0.25 pounds.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.For the context of this problem, we have that the slope is of 0.25, which is the monthly increase in the weight of the puppy, in pounds.
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4x+2y=8
5x+3y=9
I need the order pairs for both of these
Answer:
(3,-2)
Step-by-step explanation:
What is the inverse of f is f(x) = 3^square root of (x-4)
Answer:
the inverse of f(x) = 3^(sqrt(x-4)) is f^-1(x) = ((ln x)/ln 3)^2 + 4.
Step-by-step explanation:
To find the inverse of f(x) = 3^(sqrt(x-4)), we can follow these steps:
Step 1: Replace f(x) with y:
y = 3^(sqrt(x-4))
Step 2: Swap x and y:
x = 3^(sqrt(y-4))
Step 3: Solve for y:
Take the natural logarithm (ln) of both sides to bring down the exponent:
ln x = ln(3^(sqrt(y-4)))
Using the rule that ln(a^b) = b ln(a), we can simplify the right side:
ln x = (sqrt(y-4)) ln 3
Divide both sides by ln 3:
(sqrt(y-4)) = (1/ln 3) ln x
Square both sides:
y - 4 = ((ln x)/ln 3)^2
Add 4 to both sides:
y = ((ln x)/ln 3)^2 + 4
Step 4: Replace y with f^-1(x):
f^-1(x) = ((ln x)/ln 3)^2 + 4
Therefore, the inverse of f(x) = 3^(sqrt(x-4)) is f^-1(x) = ((ln x)/ln 3)^2 + 4.
The store sold 25% of its books over the holiday, and now it has 600 books in stock.
How many books the store had before holidays?
Answer: If the store sold 25% of its books during the holiday, that means it has 75% of its books left in stock after the holiday. Let's represent the original number of books with the variable "x".
So, if 75% of x is equal to 600 books, we can write an equation:
0.75x = 600
To solve for x, we can divide both sides by 0.75:
x = 600 / 0.75
x = 800
Therefore, the store had 800 books before the holiday.
Step-by-step explanation:
Evaluate the following sum.
∑k=252(3)k
The sum of the series is approximately -2.977069 x 10³⁷.
What is the sum of the series?The sum of the series is calculated by applying the following methods as shown below.
We can write the sum as:
∑k=252(3)k = 3^252 + 3^253 + 3^254 + ...
Notice that this is an infinite geometric series with first term a = 3^252 and common ratio r = 3.
To find the sum of an infinite geometric series, we use the formula:
S = a/(1-r)
Applying this formula, we get:
S = 3^252/(1-3) = 3^252/(-2)
So the sum of the series is -0.5 times 3 raised to the power of 252, which is a very large negative number.
Specifically, it is approximately equal to: -2.977069 x 10³⁷.
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What is the value of sin−1(−3√2)
Answer:
The value of sin^-1(-3√2) is an angle whose sine is -3√2.
Since the sine function is an odd function, sin(-θ) = -sin(θ), we can find the reference angle by taking the inverse sine of the positive value 3√2, which gives:
sin^-1(3√2) ≈ 80.06°
The sine function is also negative in the third and fourth quadrants of the unit circle. Since the given value is negative, the angle must lie in either the third or fourth quadrant.
To determine in which quadrant the angle lies, we can use the fact that sine is negative in the third and fourth quadrants. Since sin^-1(-3√2) gives a positive value, the angle must lie in the third quadrant where the sine is negative.
Therefore, sin^-1(-3√2) = -80.06° (rounded to two decimal places).
Step-by-step explanation:
Mrs lam worked a total of 180 hours in 9 months she worked 5 days each month she worked the same number of hours each day how many hours did mrs lam work each day draw a bar diagram and write and equations to help you solve
If Mrs lam worked a total of 180 hours in 9 months she worked 5 days each month then, Mrs. Lam worked 4 hours each day.
What is a bar diagram?Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.
The variable quantity is shown on one of the axes, and the drawn bars are all of the same width. Moreover, the other axes show the variable's measure. These graphs are also used to compare different numbers since the heights or lengths of the bars represent the value of the variable. Bar charts make it simple to grasp the data and show frequency distribution tables, which facilitates computations.
Let us suppose the number of hours worked each day = x.
Given that, Mrs lam worked a total of 180 hours in 9 months she worked 5 days.
Thus,
Total hours = 180 = 5 * 9 * x
180 = 45x
x = 4
Hence, Mrs. Lam worked 4 hours each day.
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Hi can someone help me with math homework
Answer:
Shorter section is (mm):
159
Longer section is (mm):
211
Step-by-step explanation:
Let x represent the longer section length and y the shorter section length
We are given x : y = 4:3
We can rewrite in fractional form as
[tex]\dfrac{x}{y} = \dfrac{4}{3}[/tex]
Multiply both sides by y to get
[tex]\dfrac{x}{y} \cdot y = \dfrac{4}{3}y\\\\x = \dfrac{4}{3}y[/tex]
We know that the combined length of both sections is 370 mm
x + y = 370
Substitute the expression for x in the above equation
[tex]\dfrac{4}{3}y + y = 370\\\\\dfrac{4}{3}y + y = y(\dfrac{4}{3} + 1})\\= y(\dfrac{4}{3} + \dfrac{3}{3})\\\\= y(\dfrac{7}{3})\\\\= \dfrac{7}{3}y[/tex]
Therefore we get
[tex]\dfrac{7}{3} y= 370\\\\[/tex]
Multiply both sides by [tex]\dfrac{3}{7}[/tex]
[tex]\dfrac{7}{3} y \times \dfrac{3}{7} = 370 \times \dfrac{3}{7} \\\\y = 158.57\; mm\\[/tex]
= 159 mm (to 3 significant figures)
Therefore the longer section = 370 - 159 = 211 mm
Check the ratio to verify
211/159 = 1.327 ≈ 1.33 which is 4/3
what continues the pattern, 324,256,196,144, ?
is the answer 100
Answer:
Step-by-step explanation:
324-68=256
256-60=196
196-52=144
144-44=100
Yep...you were correct!
4. Solve the right triangle: B = 72°; b = 24 cm.
Answer:
The right triangle has sides of approximately 7.86 cm, 24 cm, and 24.88 cm, and angles of 90°, 72°, and 18°.
Answer:
A=18 degrees
a=7.80cm
C=24.54cm
Step-by-step explanation:
Canadian restaurant ratings
Attempts 1
12. Order of operations
A set of three scores consists of the values 3, 7, and 2.
Σ(3X - 1) =
(2x)² =
Hint: Remember to follow the order of mathematical operations.
The sigma notations when evaluated are Σ(3X - 1) = 33 and Σ(2X)² = 248
How to evaluate the sigma notationFrom the question, we have the following parameters that can be used in our computation:
3, 7, 2
The notation Σ(3X - 1) can be represented as
Σ(3X - 1) = (3(3) - 1) + (3(7) - 1) + (3(2) - 1)
Evaluate
Σ(3X - 1) = 33
Using the above as a guide, we have the following operation
Σ(2X)² = (2 *(3))² + (2 * (7))² + (2 * (2))²
Evaluate
Σ(2X)² = 248
Hence, the value of Σ(2X)² is 248
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A group of 140 young adults were asked if they use a grocery delivery app instead of going to the grocery store themselves.
According to the table, what is the probability that arándome chosen young adult does not use a grocery delivery app give that they are male? Give your answer in the simplest fraction form.
The probability that a randomly chosen young adult who are male do not use a grocery delivery app is 16.39%.
What is the probability?The probability refers to the chance or likelihood that an expected outcome, event, or success occurs given that there are many possible outcomes, events, or successes.
Probability is a fractional value that lies between zero and one depending on the degree of certainty or otherwise.
The total number of young adults surveyed = 140
The total number of young adults who do not use the app = 78
The number of male young adults who do not use the app = 5
The total number of male young adults surveyed = 17
The probability of a young adult not using the app = 78/140
The probability of a male young adults not using the app = 5/17
Thus, the probability that a randomly chosen young adult who are male do not use a grocery delivery app = 5/17 x 78/140 = 16.39%.
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Which expression is equivalent to 6(1/3x+2/3
Answer: 2x + 4 (I'm not sure because you didn't show the choices)
In a right triangle ABC, AC = 24, AB = 45, and BC = 51. Find the measure of angle C to the nearest degree.
Answer:
C⁰ = 28⁰
Step-by-step explanation:
^^^^ The answer of the question is given above in the image
solve for x: 2(3x-3)=-18
Answer:
[tex]\huge\boxed{\sf x = -2}[/tex]
Step-by-step explanation:
Given equation:2(3x - 3) = -18
Distribute 2 to 3x and 36x - 6 = -18
Add 6 to both sides6x = -18 + 6
6x = -12
Divide both sides by 6x = -12/6
x = -2[tex]\rule[225]{225}{2}[/tex]
Answer: x=-2
Step-by-step explanation:
Step 1. Multiply the 2×3x and 2×3 which would make the problem 6x-6=-18
Step 2. Add the -6 to the -18 and multiply that answer of -12 by 6 to get your final answer of x=-2
I kinda lost on this question, please help
Answer:
increasing: (0, π/2) ∪ (3π/2, 2π)decreasing: (π/2, 3π/2)relative maximum: (π/2, 1/2)relative minimum: (3π/3, -1/2)Step-by-step explanation:
You want to know the intervals on which f(x) = sin(x)/(2+cos(x)²) is increasing and decreasing, and the relative extremes.
DerivativeThe quotient rule can be used to find the derivative of f(x). Where the derivative is positive, the function is increasing.
f'(x) = ((2+cos(x)²)cos(x) +sin(x)(2cos(x)sin(x)))/(2+cos(x)²)²
f'(x) = (cos(x)(2 +cos(x)² +2sin(x)²)/(2+cos(x)²)²
f'(x) = cos(x)(3+sin(x)²)/(2+cos(x)²)²
We observe that the factors (3+sin(x)²) and (2+cos(x)²) are both positive for all x. This means the sign of the derivative will match the sign of cos(x).
IncreasingThe function is increasing where cos(x) > 0, on the intervals ...
(0, π/2) ∪ (3π/2, 2π)
DecreasingThe function is decreasing where cos(x) < 0, on the interval ...
(π/2, 3π/2)
Relative maximumThe first derivative test tells us the function will have a relative maximum where the function goes from increasing to decreasing, at x = π/2. The function value at that point is ...
f(π/2) = sin(π/2)/(2 +cos(π/2)²) = 1/2
The relative maximum is at (π/2, 1/2).
Relative minimumThe first derivative test tells us the function will have a relative minimum where the function goes from decreasing to increasing, at x = 3π/2. The function value at that point is ...
f(3π/2) = sin(3π/2)/(2 +cos(3π/2)²) = -1/2
The relative minimum is at (3π/2, -1/2).
The graph represents a relation where x represents the independent variable and y represents the dep -5 -4 -3 -2 5 4 3 2 1 -1 0 -1 -2 -3 -4 -5 What is the domain of the relation? 1 2 3 4 5
The set representing the domain of the relation is given as follows:
{-4,-2,0,3,5}.
How to find the domain and the range of a function?The domain of a function is the set that contains all the values assumed by the input of the function, hence on a graph it is given by the values of x assumed by the graph.The range of a function is the set that contains all the values assumed by the output of the function, hence on a graph it is given by the values of y assumed by the graph.For the relation in this problem, the x-coordinates of each point are given as follows:
x = -4.x = -2.x = 0.x = 3.x = 5.Hence the set representing the domain of the relation is given as follows:
{-4,-2,0,3,5}.
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You are conducting a study testing whether depression symptoms are lower after participating in therapy compared to before. Given this information, complete the hypotheses in symbols:
H o: [tex]\mu_{post[/tex] - [tex]\mu_{pre[/tex] = 0 This is the null hypothesis, which states that there is no difference in the mean depression symptoms before and after therapy.
What is hypothesis?A hypothesis is a proposed explanation for a phenomenon. It is a testable statement about the relationship between two or more variables that can be used to generate further investigation and research. Hypotheses are developed from research questions and provide a basis for predicting outcomes and testing theories. Hypotheses are not guesses or hunches; rather, they are educated statements that are backed up by evidence.
Ha: [tex]\mu_{post[/tex] - [tex]\mu_{pre[/tex] ≠ 0 This is the alternative hypothesis, which states that there is a difference in the mean depression symptoms before and after therapy.
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Determine the percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $242,300.00 and a 6.5% APR. Round the final answer to the nearest tenth. (4 points)
30.0%
31.1%
45.0%
45.1%
The percentage decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with an APR of 6.5% and a principal balance of $242,300.00 is about 31.1%
What is an APR?An APR is an acronym for the Annual Percentage Rate, which is the interest on al loan amount expressed as a percentage of the amount on loan annually.
The loan amount, the annual percentage rate, and the term of the loan are presented as follows;
Loan amount, P = $242,300.00
Term of the loan, t = 30 years and 15 years
Annual Percentage Rate (APR), r = 6.5%
The amount of the loan after the period can be obtained by using the formula;
A = P·(1 + r)^t
The amount of each loan can therefore be calculated as follows;
The monthly payment is; M = P·(r·(1 + r)^t)/((1 + r)^t - 1)
M = 242,300×((0.065/12) × (1 + (0.065/12))^(30×12))/((1 + ((0.065/12)))^(30×12) - 1) ≈ 1531.5
The total payment on the 30-year loan ≈ 360 × 1531.5 = 551,340
The monthly payment for the 15-year loan is therefore;
M = 242,300×((0.065/12) × (1 + (0.065/12))^(15×12))/((1 + ((0.065/12)))^(15×12) - 1) ≈ 2110.7
The total payment on the 15-year loan ≈ 360 × 2110.7 = 379962
551,340
The percentage change is therefore;
((551,340 - 379962)/551,340) × 100 ≈ 31.1%
The percentage decrease in the total principal and interest paid between the 30-year term mortgage and a 15-year mortgage is about 31.1%
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A Set S with two or more vectors is linearly independent if and only if no vector in S is expressible as a linear combination of the other vectors in S
Prove this Statement/Theorem
Answer:
Step-by-step explanation:
To prove the statement "A Set S with two or more vectors is linearly independent if and only if no vector in S is expressible as a linear combination of the other vectors in S," we must show that both directions of the statement are true. That is, we must show that if a set S is linearly independent, then no vector in S is expressible as a linear combination of the other vectors in S, and conversely, if no vector in S is expressible as a linear combination of the other vectors in S, then the set S is linearly independent.
First, let's assume that the set S is linearly independent. This means that for any vectors v1, v2, ..., vn in S, the equation a1v1 + a2v2 + ... + anvn = 0 has only the trivial solution a1 = a2 = ... = an = 0. We will prove that no vector in S is expressible as a linear combination of the other vectors in S.
Suppose, for the sake of contradiction, that there exists a vector v in S that can be expressed as a linear combination of the other vectors in S. That is, there exist vectors v1, v2, ..., vn-1 in S such that v = b1v1 + b2v2 + ... + bn-1vn-1, where not all of the bi's are zero. Without loss of generality, assume that b1 is nonzero. Then we can write v1 as a linear combination of the other vectors in S:
v1 = (1/b1)v - (b2/b1)v2 - ... - (bn-1/b1)vn-1
Substituting this expression for v1 in the equation a1v1 + a2v2 + ... + anvn = 0, we get:
a1[(1/b1)v - (b2/b1)v2 - ... - (bn-1/b1)vn-1] + a2v2 + ... + anvn = 0
Multiplying both sides by b1 and rearranging, we get:
(a1/b1)v + (-a1b2/b1)v2 + ... + (-a1bn-1/b1)vn-1 + a2v2 + ... + anvn = 0
This is a linear combination of vectors in S that equals the zero vector, and not all of the coefficients are zero, since a1 is nonzero. But this contradicts the assumption that S is linearly independent, so our assumption that there exists a vector in S that can be expressed as a linear combination of the other vectors in S must be false. Therefore, no vector in S is expressible as a linear combination of the other vectors in S.
Now let's assume that no vector in S is expressible as a linear combination of the other vectors in S. We will prove that the set S is linearly independent. Suppose, for the sake of contradiction, that there exist vectors v1, v2, ..., vn in S such that the equation a1v1 + a2v2 + ... + anvn = 0 has a nontrivial solution, where not all of the ai's are zero. Without loss of generality, assume that a1 is nonzero. Then we can write v1 as a linear combination of the other vectors in S:
v1 = (-a2/a1)v2 - ... - (an/a1)vn
Substituting this expression for v1 in the equation a1v1 + a2v2 + ... + anvn = 0, we get:
0 = a1(-a2/a1)v2 + ... + a
Use the limit definition of the derivative to find a formula for f'(x) given f(x) = 3x^2 − 5
B. Use your result from part a to evaluate f'(− 1).
Answer:
Step-by-step explanation:
A. To find the formula for f'(x) using the limit definition of the derivative, we need to evaluate the following limit:
f'(x) = lim(h->0) [f(x + h) - f(x)] / h
Substituting f(x) = 3x^2 - 5, we get:
f'(x) = lim(h->0) [3(x + h)^2 - 5 - (3x^2 - 5)] / h
Expanding the square, simplifying, and canceling out the constant terms, we get:
f'(x) = lim(h->0) [6xh + 3h^2] / h
Canceling out the h's, we get:
f'(x) = lim(h->0) (6x + 3h)
Taking the limit as h approaches 0, we get:
f'(x) = 6x
Therefore, the formula for f'(x) is:
f'(x) = 6x
B. To evaluate f'(-1), we simply substitute x = -1 into the formula we found in part A:
f'(-1) = 6(-1) = -6
Therefore, f'(-1) = -6.
What is the surface area of the rectangular prism below?
Answer:
72 cm^2
Step-by-step explanation:
2(3 x 2) + 2(6 x 3) + 2(6 x 2) = 2(6) + 2(18) + 2(12)
= 12 + 36 + 24 = 72 cm^2
PLEASE HELP!!!
Aidan is 5.5 ft tall and casts a shadow that is 9 ft long. He notices that a nearby tower casts a shadow that is 305 ft long.
What is the height of the tower (h)?
The height of the tower (h) is approximately 186.4 feet.
What is the height (h) of the tower?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
Given the data in the quesion;
Aidan's height = 5.5ftlength of Aidan's shadow = 9ft height of the tower = ?length of the tower's shadow = 305ftWe can set up a proportion to solve for the height of the tower:
Aidan's height / length of Aidan's shadow = height of the tower / length of the tower's shadow
Plugging in the values we know, we get:
5.5 / 9 = h / 305
To solve for h, we can cross-multiply and simplify:
9h = 5.5 × 305
9h = 1667.5
h = 1667.5 / 9
h = 186.4 ft
Therefore, the value of h is 186.4 feet.
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Solve the system
y=2x-2
y=2x+9
Answer:
y=2 x=-13
Step-by-step explanation:
Pascals triangle is named after the French mathematician Blaise Pascal despite the fact that its documented existence pre-dated him by over 600 years. Though he did not invent Pascals triangle he did invent a type of machine in 1642 that would end up being historically significant. What was this invention?
Answer:
Blaise Pascal is known for inventing the mechanical calculator, also called Pascaline, in 1642. The Pascaline was a type of mechanical calculator that could perform addition and subtraction by using a series of gears and wheels. It was one of the first machines capable of performing arithmetic operations automatically and quickly, without the need for manual calculations. The invention of the Pascaline was a significant contribution to the field of mathematics and engineering, and it paved the way for the development of more advanced calculating machines in the future.
Step-by-step explanation:
in 1970, the population of Kern County, California, was about 330,000. from 1970 to 2000, the county population grew at an average annual rate of about 2.4%. about how many people lived in kern county in 1990
Answer: 792,000
Step-by-step explanation: 330,000 x 2.4%by 20 years = 792,000
The account balance on April 1st is $50.51. On April 15th a payment of $15.00 is made. On April 25th a purchase of $19.27 is made. The annual rate is 18%. What is the unpaid balance? What is the finance charge using the unpaid balance method? What is the new balance? Unpaid balance = $ Finance charge = $ New balance = $
describe me in 3 words ;-;
The new balance is the sum of the unpaid balance, the finance charge, and any new purchases or fees:
New balance = Unpaid balance + Finance charge + Purchase
= $35.51 + $0.84 + $19.27
= $55.62.
We must first identify the balance remaining after the payment and purchase in order to calculate the outstanding balance:
Balance after payment = $50.51 - $15.00 = $35.51
Amount remaining after payment: $35.51 + $19.27 = $54.78
The balance remaining after the payment is made, which comes to $35.51, is the unpaid balance.
We must first determine the average daily balance before we can calculate the finance charge using the unpaid balance technique. Finding the daily balance and dividing the total by the number of days in the billing cycle will allow us to achieve this:
$50.51 times 14 days in April equals $707.
14 April 15–24: $35.51 multiplied by 10 days equals $355.
10 April 25–30: $54.78 multiplied by six days is $328.68
Balance total: $707.14 plus $355.10 plus $328.68 ($1,390.92)
Average daily balance: $1,390.92 divided by 30 equals $46.36.
Hence, the finance charge can be determined as follows:
Finance fee equals $46.36 * (0.18 / 365) * 30 = $0.84. Finance charge formula: Average daily balance * Daily periodic rate * Number of days in billing cycle
The total of the unpaid debt, the finance charge, and any additional purchases or fees is the new balance:
Purchase + Finance fee + New balance = $35.51 + $0.84 + $19.27 = $55.62.
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Answer:
The account balance on April 1st is $50.51. On April 15th a payment of $15.00 is made. On April 25th a purchase of $19.27 is made. The annual rate is 18%. What is the unpaid balance? What is the finance charge using the unpaid balance method? What is the new balance? Unpaid balance = $ Finance charge = $ New balance = $
Step-by-step explanation:
To calculate the unpaid balance, we first need to calculate the balance after the payment and the balance after the purchase:
Balance after payment on April 15th: $50.51 - $15.00 = $35.51
Balance after purchase on April 25th: $35.51 + $19.27 = $54.78
Next, we need to calculate the average daily balance for the billing period. The billing period runs from April 1st to April 30th, which is 30 days. We can split this into two parts:
April 1st to April 15th (15 days)
April 16th to April 30th (15 days)
For the first part of the billing period, the balance is $50.51 for 15 days. For the second part of the billing period, the balance is $54.78 for 15 days. The average daily balance is therefore:
($50.51 x 15 + $54.78 x 15) / 30 = $52.64
The unpaid balance is the average daily balance minus the payment, so:
$52.64 - $15.00 = $37.64
The finance charge using the unpaid balance method is the unpaid balance multiplied by the daily periodic rate and the number of days in the billing cycle. The daily periodic rate is the annual rate divided by 365 days, so:
Daily periodic rate = 0.18 / 365 = 0.000493
Finance charge = $37.64 x 0.000493 x 30 = $0.56
The new balance is the previous balance (after the purchase) plus the finance charge, so:
New balance = $54.78 + $0.56 = $55.34
Therefore, the unpaid balance is $37.64, the finance charge is $0.56, and the new balance is $55.34.
Part D
Record the measures of the angles of Δ ABC and Δ DEF
This is because congruent triangles' corresponding angles are identical, and since triangle ABC and triangle DEF are congruent, their corresponding angles are equal.
What precisely is a triangle?A triangle is a two-dimensional closed geometric object that consists of three line segments called sides that intersect at three places called vertices. Triangles can be distinguished by their angled sides. Triangles, depending on their sides, can be mutually perpendicular (all sides equal), ellipse, or scalene. Triangles are classed as acutely (all angles less than 90 degrees), equal (one angle equal to 90 degrees), or ambiguous (all angles more than 90 degrees) (all angles greater than 90 degrees). The area of a triangle may be determined by applying the formula A = (1/2)bh, wherein There is the area, b is the base of the triangle, and h is the height of the triangle.
In triangle ABC, we have:
Angle A = 60°Angle B = 80°Angle C = 40°In triangle DEF, we have:
Angle D = 60°Angle E = 80°Angle F = 40°This is because congruent triangles' corresponding angles are identical, and since triangle ABC and triangle DEF are congruent, their corresponding angles are equal.
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Which matrix represents the system of equations shown below?
6x +11y = -4
5x-9y=1
Answer: I took the test and got it right
Tthe matrix representing this system of equations is:
[6 11 | -4]
[5 -9 | 1]
The equations in the image can be expressed as a matrix as follows:
[6 11] [x] [-4]
[5 -9] * [y] = [1]
The constants on the right-hand side of each equation are represented by the matrix on the right, while the coefficients of the variables x and y are represented by the matrix on the left. We use square brackets to surround the coefficients matrix and vertical bars to demarcate the variables and constants in order to represent this in matrix form. As a result, the matrix used to describe this set of equations is:
[6 11 | -4]
[5 -9 | 1]
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