Step-by-step explanation:
x = the number
1/4 * x = 1/8 <====given, Multiply both sides of the equation by 4
4 * 1/4 x = 4 * 1/ 8
x = 4/8 = 1/2
Step-by-step explanation:
Let the given number Be X
SO given thatone fourth of X is one eighth
x/4 = 1/8
x = 1/2
x = 0.5
so the given number is 0.57. Fill in the bubbles to indicate whether
each expression is linear or not linear.
5x Linear or Nonlinear
6x+1 Linear or Nonlinear
10xy Linear or Nonlinear
17 Linear or Nonlinear
4x^2 Linear or Nonlinear
The type of the relation are
Linear: 5x, 6x + 1 and 16Nonlinear: 10xy and 4x^2Indicating whether each expression is linear or not linearA linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.
In the given expressions:
"5x" and "6x + 1" have only the variable "x" raised to the power of 1, making them linear."10xy" has the variables "x" and "y" both raised to the power of 1, making it nonlinear."17" is a constant term and has a degree of 0, making it linear."4x^2" has the variable "x" raised to the power of 2, making it nonlinear.Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".
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Help me thank you
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Answer: The actual difference between the numbers is:
87.71 - 5.8 = 81.91
Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?
Step-by-step explanation:
To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.
Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.
The actual difference between the numbers is:
87.71 - 5.8 = 81.91
Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.
Answer:
Yasmine estimated the difference to be 82. The actual difference is 81.91.
Step-by-step explanation:
The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.
So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be
(88 - 6) = 82.
The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.
Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.
A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 176 feet of fencing,
what is the largest area the farmer can enclose?
Answer: 46 ft by 92 ft
Step-by-step explanation:
The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.
Find each value or measure.
x = _____
mJK=_____ degrees
mMJ=_____ degrees
mLMK=______ degrees
(30 points) will give brainiest for effort
The value or measure of following are :-
x = 17.18°
∠JK = 143.78°
∠MJ = 116.48°
∠LMK = 47.17°
What is an arc?A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.
Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:
∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°
∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°
We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:
∠MNJ = ∠LNK
The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:
½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK
2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ
11x - 9° = 2∠MNJ
∠MNL = ∠JNK
The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:
½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK
2.75x + 1.5° = 2∠JNK
1.375x + 0.75° = ∠JNK
Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:
2∠MNJ + 2∠JNK = 360°
Substituting the expressions we found for ∠MNJ and ∠JNK, we get:
22x - 18° = 360°
22x = 378°
x = 17.18° (rounded to two decimal places)
Now that we know x, we can find the values of the other angles of arc-
∠JNK = 1.375x + 0.75° = 24.43°
∠KNL = 8.5x - 20.5° = 119.35°
∠MNJ = (11x - 9°)/2 = 92.05°
∠LNK = ∠MNJ = 92.05°
∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°
∠JK = ∠JNK + ∠KNL = 143.78°
∠MJ = ∠MNJ + ∠JNK = 116.48°
∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°
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The ratio of union members to nonunion members working for a company is 4 to 5. If there are 140 nonunion members working for the company,
what is the total number of employees?
The total number of employees is 112.
Explain numbers
Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.
According to the given information
Let's use x to represent the total number of employees.
According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.
So, we can set up the following proportion:
4/9 = x/(x - 140)
To solve for x, we can cross-multiply and simplify:
4(x - 140) = 9x
4x - 560 = 9x
560 = 5x
x = 112
Therefore, the total number of employees is 112.
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On January 1, Year 2, Kincaid Company's Accounts Receivable and the Allowance for Doubtful Accounts carried balances of $74,600 and $3,700, respectively. During Year 2, Kincaid reported $208,000 of credit sales, wrote off $2,000 of receivables as uncollectible, and collected cash from receivables amounting to $258,900. Kincaid estimates that it will be unable to collect one percent (1%) of credit sales.
What effect will recognizing the uncollectible accounts expense for Year 2 have on the elements of the financial statements?
Multiple Choice
Decrease total assets and net income
Decrease total assets and increase retained earnings
Increase total assets and decrease net income
Increase total assets and retained earnings
The correct answer is: Decrease total assets and net income.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.
When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.
Therefore, the correct answer is: Decrease total assets and net income.
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Is the graph increasing, decreasing, or constant?
-8 -6 4
A. Decreasing
B. Increasing
C. Constant
-2
4-
2
-2
AY
2
4
6
8
SUBMIT
Is the graph increasing, decreasing, or constant: C. Constant.
What is a graph?In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.
In conclusion, the above is constant, rather than increasing or decreasing.
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A principal of $1500 is invested at 8.5% interest, compounded annually. How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
A particular sound wave can be graphed using the function y= -1sin 5x. Find the period of the function
Answer:
The period of a sine function of the form y = a sin bx is given by:
period = (2π) / |b|
In this case, the function is y = -1 sin 5x, which can be rewritten as y = -sin(5x). So, we can see that b = 5.
Substituting b = 5 into the formula, we get:
period = (2π) / |5|
period = π / 5
Therefore, the period of the function is π/5.
Approximately of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
The fraction of Earth that is not made up of ocean = 1/4.
Explain about the fraction:The numbers we are familiar with are whole numbers, such as 1, 2, and so on.
Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.
In essence, a fraction explains how a portion of a group interacts with the entire group.
Given that-
fraction of Earth made up of water = 3/4The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water
The fraction of Earth that is not made up of ocean = 1 - 3/4
The fraction of Earth that is not made up of ocean = (4 - 3)/4
The fraction of Earth that is not made up of ocean = 1/4
Thus, the fraction of Earth that is not made up of ocean = 1/4.
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Complete question:
Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
Simplify 6^2/6 x 6^12/6^8
Step-by-step explanation:
6^2 / 6^1 x 6^12 / 6^8 =
6^(2-1) x 6^(12-8) =
6^1 x 6^4 =
6^(1+4) = 6^5 or = 7776
Identify the correct equation of the graph.
-10
O f(b) = (6+4)² +8
O f(b) = (b+8)² +4
Of(b)=(6-8)²-4
O
-5
10
5
-5
-10
V
5
O f(b) = (b-8)² +4
Of(b) = (6-4)²-8
Of(b) (6-4)² +8
10
Check
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Explain about the quadratic function in vertex form:A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Vertex form of a quadratic function:
f(x) = a(x – h)² + k, where a, h, and k are constants.
The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).
(h,k) are the vertex of parabola.
From the given graph:
f(b) is the given function:
Vertex (h,k) = (8, 4)
Thus, h= 8 and k = a = 1, x = b.
Put the values in quadratic function:
f(b) = 1(b – 8)² + 4
f(b) = (b – 8)² + 4
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
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A walk alongside a railway track is represented on a map by an 86 mm straight line.
The walk is 17.2 km.
What is the scale of the map?
First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.
In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
A) 20%
B) 24%
C) 25%
D) 28%
Therefore , the solution of the given problem of percentage comes out to be D) 28% is the right response.
What is percentage?The shorthand "a%" is used in statistics to represent a number or metric that may be expressed as a percentage of 100. Additionally strange spelling include "pct," "pct," as "pc." The approach that is most frequently employed for this is the percentage symbol ("%"). Any hints or set proportions of any part for the total are also unknown. Since numbers commonly add up to 100, they are effectively integers.
Here,
According to the facts provided, 30% of the male population and 60% of the people in Math Town are male.
This suggests that between 30% and 60% of people have brown eyes.
Let's figure out what proportion of the entire population is equal to 30% of 60%:
=> 30% of 60% = (30/100) * (60/100)
=> 0.3 * 0.6
=> 0.18 or 18%
Therefore, brown eyes are present in Math Town's overall population of 18%.
Since the only other gender listed is females and we are aware that 18% of the population as a whole has brown eyes, we can infer that 18% of women also have brown eyes.
Therefore, D) 28% is the right response.
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Home values in a town have declined 26% per year for each of the past
four years. What was the total percentage decrease in home values
during the four-year period?
Answer: 104%
Step-by-step explanation: 26% times 4 years
if the pink lines are parallel, solve for n
The option that is true about the equations for these two lines iis that they represent the same lines.
How to explain the informationThe trick to questions like this is to get both equations into the slope-intercept form. That is done for our first equation (y = 3x + 5). However, for the second, some rearranging must be done:
5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5
Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.
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Two lines are described by the equations:
y = 3x + 5 and 5y – 25 = 15x
Which of the following is true about the equations for these two lines?They represent perpendicular lines.
None of the other answers
They represent non-perpendicular, intersecting lines.
They represent the same lines.
They represent parallel lines.
Workout 461÷4 give your answer as a whole number and a reminder
Step-by-step explanation:
the answer is 115 remainder 1
what is the weight of a 38kg child
Don has an album that holds 700 photos. Each page of the album holds 7 photos. If 24% of the album is empty, how many pages are filled with photos?
Answer: 76 pages
Step-by-step explanation:
700 photo spaces = 100%
-The total
168 photo spaces = 24%
-The number of empty spaces in the album.
- Find 24% of 700:
70(10%) x 2 = 140
7(1%) x 4 = 28
140 + 28 = 168
532 photo spaces = 76%
- The number of photos in the album
700 - 168 = 532
Finding the number of pages.
-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.
532 ÷ 7 = 76.
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
y² -5y = 750750 -y(y -5) = 0(y +25)(y -30) = 0Step-by-step explanation:
You want three equations that can be used to solve for the length (y) of a room that is whose width is 5 feet less than its length and whose area is 750 square feet.
AreaThe area of the room is the product of its length and width. We are given that the length is y, so the width is (y-5) and that product is ...
A = LW
750 = y(y -5)
This equation can be rearranged into several different forms:
y² -5y = 750 . . . . . . . multiply it out
750 -y(y -5) = 0 . . . . . subtract the right side expression
(y +25)(y -30) = 0 . . . . factor it
Find three consecutive integers such that 4 times the first added to the third is 92
Solve quickly Thanks
The three consecutive integers are 18, 19, and 20.
What is consecutive integers?Consecutive integers are integers that follow each other in order, without any gaps, and differ by 1. For example, 3, 4, and 5 are consecutive integers because they follow each other in order and differ by 1.
According to question:Let's assume that the three consecutive integers are x, x+1, and x+2. Then, according to the problem statement:
4x + (x+2) = 92
Simplifying this equation, we get:
5x + 2 = 92
Subtracting 2 from both sides, we get:
5x = 90
Dividing both sides by 5, we get:
x = 18
Therefore, the three consecutive integers are 18, 19, and 20. We can check that these integers indeed satisfy the condition given in the problem:
4 times the first integer is 4*18 = 72, and when we add the third integer 20 to it, we get 72 + 20 = 92, as required.
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5. Apply Math Models A science teacher uses a fair spinner
simulate choosing 1 of 5 different field trips for her classes.
spinner has 5 equal sections, each representing a different
trip. The teacher spins the spinner 50 times and records the
results in the table below.
Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.
What is frequency?
Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).
The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.
The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.
The experimental and theoretical probabilities do not match exactly. For example, the experimental of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.
The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.
Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).
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Commplete Question:
A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:
Field Trip Number of times selected
A 8
B 16
C 9
D 12
E 5
Apply math models to analyze the data and answer the following questions:
What is the experimental probability of selecting each field trip?
What is the theoretical probability of selecting each field trip?
Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?
What is the relative frequency of selecting each field trip?
Based on the data, which field trip appears to be the most popular?
Alex scored 7/20 of the points in a basketball game. How many of the team's 120 points did Alex score?
Answer:
Step-by-step explanation:
I think its 42 because 7/20ths of 120 is 42
7/20 x 120 =42
A right rectangular prism has a base with an area of 25 1/2 square feet and a volume of 153 cubic feet. What is the height, in feet, of the right rectangular prism? Please help!!
Answer:
[tex]25.5h = 153[/tex]
[tex]h = 6[/tex]
The height is 6 feet, so A is correct.
4.4.3 Quiz: Stretching and Compressing Functions
f(x) = x². What is g(x)?
10
g(x)
Y
5- f(x)
O B. g(x) =
(2,2)
Click here for long description
2
O A. g(x) = (x)²
O c. g(x) =
OD. g(x) = 2x²
2
5
x²
x²
X
The equation of the function g(x) is g(x) = 1/2x²
Calculating the function g(x)If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.
Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).
To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):
[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]
So, we have
a = 1/2
Recall that
g(x) = f(ax)
So, we have
g(x) = f(1/2x)
This means that
g(x) = 1/2x²
Hence. the function is g(x) = 1/2x²
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Michelle did an anyonymous survey and collected her friends' credit scores. The scores she found are listed in the table below. What is the
mean credit score in this group? (Round to the nearest whole point, if applicable.)
a. 698
b. 695
c. 676
d. 703
to find the mean you add al the numbers together and divide it by how many numbers there were. so to find the mean it would be (682+612+756+674+714+790+668+652+776)÷9=702.6 which can be rounded up to 703. Also pls mark as brainliest answer
The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.8 years and a standard deviation of 15.1months. Complete parts (a) through (d).
The answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?
To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,
Z = (X - mean) / standard deviation
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.
(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?
We need to standardize the values of 16 and 18 using the mean and standard deviation provided.
Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.
(c) What is the age at which growth plates fuse for the top 5% of males?
We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).
Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.
Then, we can solve for X using the formula:
Z = (X - mean) / standard deviation
1.645 = (X - 18.8) / (15.1/12)
Simplifying the equation, we get:
X = 18.8 + (1.645)(15.1/12) = 20.24
Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.
(d) What percentage of males have growth plates that fuse before the age of 16?
We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).
Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.
Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.
hence, the answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
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x=10 3x+5y=20 in the system of equations, what is the value of x
You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each
month to save or pay down your debts.
a. How many months will it take to pay off the credit card if you only put half of the available money
toward the credit card each month and make the payments at the beginning of the month?
b. How many months will it take to pay off the credit card if you put all of the available money toward the
credit card each month and make the payments at the beginning of the month?
Be sure to include in your response:
the answer to the original question
• the mathematical steps for solving the problem demonstrating mathematical reasoning
a. It will take 7 months to pay off the credit card. b. it will take 4 months to pay off the credit card.
Define APR?APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.
a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance. We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:
PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)
where:
PV is the present value of the debt
PMT is the payment amount per period
r is the monthly interest rate
n is the number of periods
Substituting the values, we get:
754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV ×r / PMT)) / log(1 + r)
= log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)
= 6.18
Therefore, it will take approximately 7 months to pay off the credit card if you put half of the available money each month toward the credit card.
b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.
754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV × r / PMT)) / log(1 + r)
= log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)
= 3.43
Therefore, it will take approximately 4 months to pay off the credit card if you put all of the available money each month toward the credit card.
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Find the surface Area
Math step by step Answer
(a) The total surface area of the triangular prism is 560 in².
(b) The surface area of the cuboid is 944 ft².
(c) The surface area of the cylinder is 678.58 in².
What is the surface area of the cuboid, cylinder and prism?Cuboid;
The surface area of the cuboid is calculated as;
S.A = 2(12 x 16 + 12 x 10 + 16 x 10)
S.A = 944 ft²
Cylinder:
The surface area of the cylinder is calculated as follows;
S.A = 2π x 6 (6 + 12)
S.A = 678.58 in²
The surface area of a triangular prism can be calculated by summing the areas of its individual faces.
A triangular prism has three rectangular faces and two triangular faces.
The formula for the surface area of a triangular prism is:
Surface Area = Area of triangular faces + Area of rectangular faces
To calculate the area of a triangular face, we can use the formula for the area of a triangle:
Area of a triangle = (base × height) / 2
Given that S₁ = 8 in, S₂ = 12 in, S₃ = 8 in, and the length between the two triangular faces is 18 in, we can proceed with the calculations.
The area of the triangular face with dimensions S₁ = 8 in and S₂ = 12 in is:
Area of triangular face 1 = (8 in × 12 in) / 2 = 48 in²
The area of the triangular face with dimensions S₂ = 12 in and S₃ = 8 in is:
Area of triangular face 2 = (12 in × 8 in) / 2 = 48 in²
The area of the triangular face with dimensions S₃ = 8 in and S₁ = 8 in is:
Area of triangular face 3 = (8 in × 8 in) / 2 = 32 in²
Now, let's calculate the area of the rectangular faces.
Area of rectangular face 1 = 18 in × 12 in = 216 in²
Area of rectangular face 2 = 18 in × 12 in = 216 in²
Finally, we can sum up all the areas to get the total surface area of the triangular prism:
Surface Area = Area of triangular faces + Area of rectangular faces
Surface Area = 48 in² + 48 in² + 32 in² + 216 in² + 216 in² = 560 in²
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