Therefore , the solution of the given problem of equation comes out to be the first plant makes 5x + 22 more items per day.
How do equations work?
Mathematical formulas frequently employ same variable word to guarantee agreement between two claims. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. In this case, the normalise method adds b + 6 to employ the example of y + 6 rather than splitting 12 into two parts. It is possible to determine the length of the line and the quantity of connections between each sign's constituents. The significance of a symbol usually contradicts itself.
Here,
The first plant cranks out 8x + 15 items every day, while the second cranks out 3x - 7 items every day. By deducting the daily output of the second plant from the daily output of the first plant, we can determine how many more items the first plant creates than the second plant:
=> (8x + 15) - (3x - 7) (3x - 7)
If we condense this phrase, we get:
=> 8x + 15 - 3x + 7
Combining related words gives us:
=> 5x + 22
Therefore, compared to the second plant, the first plant makes 5x + 22 more items per day.
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A triangle has angles (w² +84)°, w°, 3w°
Find the value of w
Answer:
Below
Step-by-step explanation:
The three internal angles f ANY triangle add up to 180 °
w^2 + 84 + w + 3w = 180
w^2 + 4w + 84 = 180
w^2 + 4w - 96 = 0 Use Quadratic Formula a = 1 b = 4 c = -96
to find the positive value of w = 8
The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction pi Over 2 EndFraction (t + 2)) + 5. Which of the following is the graph of this equation?
The graph of the equation, which looks like the below diagram.
What is the term graph means?The term "graph" can refer to a visual representation of data or information, typically in the form of a diagram or chart. Graphs can be used to show relationships or patterns between different sets of data.
The given equation is:
h = 3 sin(π/2(t + 2)) + 5
This is a sinusoidal function with an amplitude of 3, a period of 4, a phase shift of -2, and a vertical shift of 5.
To graph this function, we can plot a few points and connect them with a smooth curve. For example, we can choose some values of t and calculate the corresponding values of h:
t = -4: h = 2
t = -3: h = 5
t = -2: h = 8
t = -1: h = 5
t = 0: h = 2
t = 1: h = -1
t = 2: h = 2
t = 3: h = 5
t = 4: h = 8
Using these values, we can sketch the graph of the function. The amplitude is 3, so the maximum height of the ball is 3 units above and below the vertical shift of 5. The period is 4 seconds, since the frequency is 2π/B = 4. The phase shift is to the left by 2 seconds. Therefore, the graph of the equation is as follows:
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Complete question is:
I need help with number 3 ASAP please! cos^2u- cos u sec u= cot^2 u
PLEASE I NEED HELP
Answer:
cosx
Step-by-step explanation:
using the identity
• sin² = 1 - cos²x
cos²x + cosx - 1 + sin²x
= cos²x + cosx - 1 + 1 - cos²x ← collect like terms
= cos x
a plane flying horizontally at an altitude of 1 mile and a speed of 580 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station. (round your answer to the nearest whole number.)
The rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station is 656 mi/h (rounded to the nearest whole number).
To solve this problem, we can use the equation
rate = distance/time.
We know the distance and the time, so we can calculate the rate:
rate = 5 mi/ 1 hour
= 5 mi/3600 sec
= 5/3600 mi/sec
= 0.00138889 mi/sec.
Multiplying this by 3600 to convert it to mi/h gives us 656 mi/h.
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Let X be a normal random variable with mean 209 units and standard deviation 7 units. Answer the following questions, rounding your answers to two decimal places.(a) What is the probability that X will be less than 201 units, P(X<201)?(b) What is the probability that X will be within 8units of the mean?(c) The probability is 0.04 that X will be more than how many units?
196.75 units
Answer:(a) P(X < 201) = 0.0099(b) P(201 < X < 217) = 0.9544(c) P(X > 227.12) = 0.04Explanation:Given that, X be a normal random variable with mean 209 units and standard deviation 7 units.We need to find the following.(a) P(X < 201)(b) P(201 < X < 217)(c) P(X > x) = 0.04.(a) We know that,When X is a normally distributed variable with mean μ and standard deviation σ,thenZ = (X - μ) / σ is a standard normal variable.Then,P(X < 201) = P(Z < (201 - 209) / 7)= P(Z < -1.14)Using the z-tables, the probability is 0.0099.(b) We need to find the probability that X will be within 8 units of the mean. Therefore,X will be within 8 units of the mean, if 201 < X < 217.Therefore,P(201 < X < 217) = P((X - μ)/σ) < (217 - 209)/7) - P((X - μ)/σ) < (201 - 209)/7)= P(0.57 < Z < -0.57)Using z-tables, P(0.57 < Z < -0.57) = 0.9544(c) We need to find the value of X such that P(X > x) = 0.04.Then,P(Z > (X - μ)/σ) = 0.04P(Z < -1.75) = 0.04Using z-tables, P(Z < -1.75) = 0.04By using the standard normal distribution tables, the value of -1.75 corresponds to 0.0401.Therefore,-1.75 = (X - 209)/7-12.25 = X - 209X = 209 - 12.25X = 196.75Therefore, the probability is 0.04 that X will be more than 196.75 units.
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Which of the following rational functions has a horizontal asymptote at y = 2 and vertical asymptotes at x = 3 and x = –4?
a: y equals x squared over the quantity x squared plus x minus 12 end quantity
b: y equals x squared over the quantity x squared minus x minus 12 end quantity
c: y equals 2 times x squared over the quantity x squared plus x minus 12 end quantity
d: y equals 2 times x squared over the quantity x squared minus x minus 12 end quantity
Neither option (a) nor option (b) has a horizontal asymptote at y = 2, there is no correct answer to this question.
What is rational function?A rational function is a mathematical function that can be expressed as a ratio of two polynomial functions, where the denominator is not equal to zero.
To have vertical asymptotes at x = 3 and x = –4, the denominator of the rational function must have factors of (x – 3) and (x + 4), respectively.
Option (a) has a denominator of (x² + x – 12), which can be factored as (x – 3)(x + 4), satisfying the conditions for vertical asymptotes.
Option (b) has a denominator of (x² – x – 12), which can also be factored as (x – 3)(x + 4), satisfying the conditions for vertical asymptotes.
Therefore, the answer is either option (a) or option (b).
To determine which of these options has a horizontal asymptote at y = 2, we can perform long division or use the fact that the leading term of the rational function will determine the horizontal asymptote.
Dividing x² by (x² + x – 12), we get:
x² + x - 12 | x² + 0x + 0
- x² - x
Thus, the quotient is 1 and the remainder is x. So the rational function simplifies to:
y = x/(x² + x - 12)
The leading term of this rational function is x/x², which simplifies to 1/x. Therefore, it does not have a horizontal asymptote at y = 2.
Dividing x² by (x² – x – 12), we get:
x² - x - 12 | x² + 0x + 0
+ x² - x
Thus, the quotient is 1 and the remainder is x. So the rational function simplifies to:
y = x/(x² - x - 12)
The leading term of this rational function is x/x², which simplifies to 1/x. Therefore, it does not have a horizontal asymptote at y = 2.
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Describe in practical terms the meanings of f^(-1)(0.7), f^(-1)(0.5),f^(-1)(0.2)
In practical terms, the meanings of f^(-1)(0.7), f^(-1)(0.5),f^(-1)(0.2) are as follows:f^(-1)(0.7): This means the value of x for which f(x) = 0.7. Here, f^-1 is the inverse function of f. It returns the value of the input x for which the output of the function is 0.7. In other words, if y = f(x), then f^(-1)(y) = x. Hence, f^(-1)(0.7) means the input value of x for which the function returns 0.7 as the output.f^(-1)(0.5): This means the value of x for which f(x) = 0.5. Similarly, the inverse of the function f, f^-1, returns the value of the input x for which the output of the function is 0.5.f^(-1)(0.2): This means the value of x for which f(x) = 0.2. Here, f^-1 is the inverse function of f. It returns the value of the input x for which the output of the function is 0.2. Hence, f^(-1)(0.2) means the input value of x for which the function returns 0.2 as the output.
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Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.
x.....................f(x)....................g(x)
1995 $69,682.50 $72,429.27
2000 $78,943.50 $79,967.77
2005 $88,204.50 $88,290.88
2006 $90,056.70 $90,056.70
2007 $91,908.90 $91,857.83
2010 $97,465.50 $97,480.27
A) f(x) is exponential; an exponential function increases more slowly than a linear function.
B) f(x) is exponential; f(x) increased more overall than g(x).
C) g(x) is exponential; g(x) has a higher starting value and higher ending value.
D) g(x) is exponential; an exponential function increases faster than a linear function.
D) g(x) is exponential; an exponential function increases faster than a linear function.
Determining exponential expression:To determine which function is exponential, find the rate of change between the different years for each function.
An exponential function will have a constant rate of change over time, while a linear function will have a constant slope.
Looking at the table, we can calculate the rate of change between each year for both f(x) and g(x).
Here we have
x f(x) g(x)
1995 69,682.50 72,429.27
2000 78,943.50 79,967.77
2005 88,204.50 88,290.88
2006 90,056.70 90,056.70
2007 91,908.90 91,857.83
2010 97,465.50 97,480.27
Calculate the rate increase the both cases
From f(x)
For the years 1995 to 2000
= [78,943.50 - 69,682.50 ]/ 69,682.50 x 100 = 13.3%
For the years 2000 to 2005
= [88,204.50 - 78943.50]/ 78943.50 × 100 = 11.73
For g(x)
For the years 1995 to 2000
= [ 79,967.77 - 72,429.27]/ 72,429.27× 100 = 10.40
For the years 2000 to 2005
= [ 88,290.88 - 79,967.77]/79,967.77 × 100 = 10.40
Here we can observe that the rate of increase in g(x) is constant whereas in f(x) the rate of increase is decreasing
Hence we can conclude that
D) g(x) is exponential; an exponential function increases faster than a linear function.
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7. Allen believes 3 possible outcomes in a game are equally likely to occur.
Outcome
Number of times
observed
#1 #2 #3
4 14 2
Which conclusion BEST supports the data?
B) Which other two triangles (from A, B, C and D) are congruent to each other? Please help!
A) by mere observation, the triangles from A, B, C, and D that is congruent or similar to Triangle E is Triangle C.
B) The other two triangles that are congruent to each other are Triangles A and B.
What does it mean for two triangles to be congruent?Two triangles are considered congruent if they have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal.
In other words, if you were to superimpose one triangle onto the other, they would match up perfectly. The concept of congruence is important in geometry, as it allows us to make precise statements about the relationship between different figures and their properties.
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Full Question:
See the attached image.
In circle K with
m
∠
J
K
L
=
60
m∠JKL=60 and
J
K
=
17
JK=17 units find area of sector JKL. Round to the nearest hundredth.
Answer:
KL=43
Step-by-step explanation:
JKL=60, jk=17, KL=43
A health expert evaluates the sleeping patterns of adults. Each week, she randomly selects 50 adults and calculates their average sleep time. Over many weeks, she finds that 5% of average sleep time is less than 9 hours and 5% of average sleep time is more than 9.4 hours.
What are the mean and standard deviation (in hours) of sleep time for the population?
The mean and standard deviation of sleep time for the population are 9.2 hours and 8.225 hours.
What does "normal distribution" mean?In statistics and probability theory, the normal distribution is a continuous probability distribution that is often utilised. Due to its distinctive form, it is sometimes referred to as the bell curve or the Gaussian distribution. Many statistical and data analysis techniques, such as confidence intervals, regression analysis, and hypothesis testing, all make use of the normal distribution. It is well recognised that many real-world occurrences, like heights, weights, and IQ scores, follow a normal distribution, making it a useful tool for data analysis and interpretation.
Given that, 5% of average sleep time is less than 9 hours.
The z-score for the lower 5% percentile is z = -1.645.
Similarly, for upper 5th percentile we have z = 1.645.
The z-score is given as:
z = (x - μ) / σ
For the lower 5th percentile:
-1.645 = (9 - μ) / σ
For the upper 5th percentile:
1.645 = (9.4 - μ) / σ
Adding the two equations we have:
-1.645σ = (9 - μ)
1.645σ = (9.4 - μ)
0 = 18.4 - 2μ
μ = 9.2 hours.
Substitute the value of μ:
1.645σ = (9.4 - 9.2)
1.645σ = 0.2
σ = 8.225
Hence, the mean and standard deviation of sleep time for the population are 9.2 hours and 8.225 hours.
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A system of two linear equations has no solution. The first equation is -7x + y = 3. select the second equation that will make this system have no solution.
A. 3x+y=3
B. -7x+y=-10
C. 3x+y=-7
D. 4x+y=3
Answer:
It's B.
Step-by-step explanation:
To make the given system of linear equations have no solution, we need the second equation to be inconsistent with the first equation. This means that the two equations must be parallel lines, and they cannot intersect at any point.
We can see that the first equation -7x + y = 3 has a slope of 7, since it can be written in slope-intercept form as y = 7x + 3. Therefore, to create a parallel line with the same slope of 7, we can choose the second equation to be:
B. -7x + y = -10
This equation has the same slope of 7 as the first equation, but it intersects the y-axis at a different point (-10 instead of 3). Therefore, the two lines are parallel and do not intersect, so the system of equations has no solution
Hope this helps you! I'm sorry if it doesn't. If you need more help, ask me! :]
I NEED ASAP
what’s the slope of the line
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The simpliest way to find a slope of a graph such like this is to find what we call the "rise" and "run"
Find two points on the graph that match with the grid in the background. Two points on this graph that can represent this example is (-3, 1) and (0, 2)
Start at the left-most point [-3, 1 in this case] and go up until you match the same y-axis as your second point. Then, go right until you meet said point. From (-3, 1) to (0, 2) you go up once, and then right four times. This results in the fraction 1/4
How do I get full marks on this question?
Therefore , the solution of the given problem of triangle comes out to be y + y√2 and y - y√2. are the two possible numbers for x.
A triangle is exactly what?If a polygon has at least one additional segment, it is a hexagon. Its form is a straightforward rectangle. Something like this can only be distinguished from a regular triangular by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
Due to the similarity of the two triangles in the diagram, we can create an equation and solve for x using the ratios of respective sides.
Assuming that the line segment's length is x, we can construct the following equation:
=> (2x + y) / x = x / y
=> (2x + y) y = x²
=> 2xy + y² = x²
=> x² - 2xy - y² = 0
This quadratic equation in x has the coefficients a = 1, b = -2y, and c = -y2 in it. The quadratic algorithm yields:
=> x = [2y ± √((2y)² - 4(1)(-y²))] / 2(1)
=> x = [2y ± √(4y² + 4y²)] / 2
=> x = [y ± y√2]
Therefore, y + y√2 and y - y√2. are the two possible numbers for x.
The two triangles in the illustration are thought to be comparable.
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4. A physical model suggests that the mean temperature increase in the water used as coolant in a compressor chamber should not be more than 5 Celsius. Temperature increases in the coolant measured on 8 independent runs of the compressing unit revealed the following data: 6. 4, 4. 3, 5. 7, 4. 9, 6. 5, 5. 9, 6. 4, 5. 1. Do the data contradict the assertion of the physical model
The question asks if the data contradict the assertion of the physical model, which suggests that the mean temperature increase should not be more than 5 Celsius.
To answer the question, we need to calculate the mean temperature increase from the data given: 6.4, 4.3, 5.7, 4.9, 6.5, 5.9, 6.4, 5.1. We can do this by adding all the values and dividing them by the number of runs (8): (6.4 + 4.3 + 5.7 + 4.9 + 6.5 + 5.9 + 6.4 + 5.1)/8 = 5.4. The mean temperature increase of 5.4 does not exceed the maximum of 5 Celsius, which means that the data does not contradict the physical model.
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What is the area of a trapezoid with base lengths 8 in and 10 in and a
height of 9 in?
Answer: 81 inches
Step-by-step explanation:
Area of a trapezoid is … Area= 1/2(b1+b2)h
So if we plug it in
Area = 1/2(8+10)9
= 1/2(18)9
= 9(9) = 81
ANSWER FOR BRANLIEST
Which of the following is an irrational number?
Write the whole or mixed number as an improper fraction 18 7/10 a. 126
/10 b. 25/10 c. 197/10 d. 187/10
The mixed fraction 18 7/10 can be changed to the improper fraction 187/10. The correct answer is Option "D".
Here, The number 18 is the whole-number. The number 7 is in the numerator and the number 10 is in the denominator.
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction. Improper fraction is solved and simplified form of the mixed fraction. so, 2 1/3 is a mixed fraction 7/3 is the Improper fraction.
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what is the answer I am stumped
Answer: Repost this with the question (not just the graph) attached.
Step-by-step explanation: Please attach the question, otherwise I cannot help you:)
calculate the average growth rate from the following growth rates. (round your intermediate calculations at least to 4 decimal places and final answer to 2 decimal places.) 1.50% 1.60% .20% .20% 3.20%
The average growth rate is 1.34%, which is calculated by the sum of the growth rates divided by the number of growth rates.
To calculate the average growth rate, we need to add up the given growth rates and then divide by the number of growth rates.
1. First, add up the given growth rates: 1.50% + 1.60% + .20% + .20% + 3.20% = 6.70%
2. Next, divide the sum by the number of growth rates: 6.70% / 5 = 1.34%
3. Finally, round the answer to 2 decimal places: 1.34%
Therefore, the average growth rate is 1.34%.
Answer: 1.34%.
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he tree diagram below shows all of the possible outcomes for flipping three coins.
A tree diagram has outcomes (H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T).
What is the probability of one of the coins landing on tails and two of them landing on heads?
1/4
3/8
1/2
3/4
The correct answer is option (B) 3/8 for the probability based on given tree diagram.
The tree diagram shows all possible outcomes when flipping three coins. To find the probability of one coin landing on tails and two coins landing on heads, we need to find all the outcomes where this occurs.
From the tree diagram, we can see that there are three outcomes where one coin lands on tails and two coins land on heads: (H, H, T), (H, T, H), and (T, H, H).
Therefore, the probability of one coin landing on tails and two coins landing on heads is the sum of the probabilities of these three outcomes:
P(one tail, two heads) = P(H, H, T) + P(H, T, H) + P(T, H, H)
Using the multiplication rule of probability, we can see that each of these outcomes has a probability of (1/2) * (1/2) * (1/2) = 1/8.
Therefore, the probability of one coin landing on tails and two coins landing on heads is:
P(one tail, two heads) = 1/8 + 1/8 + 1/8 = 3/8
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Very Urgent Urgent Urgent
Answer:
Step-by-step explanation:
a False
b True
c True
d Falce
e True
f True
g False
h True
i True
j False
k True
l True
Classify the quadrilateral. Justify
your reasoning
Answer:
The quadrilateral is a square. A quadrilateral is a polygon with four sides. There are many types of quadrilaterals such as parallelogram and rhombuses. A rhombus is a parallelogram with four congruent sides. The plural of a rhombus is rhombi. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. A square is a rhombus becasue it has 4 congruent sides and angles
Step-by-step explanation:
Hope this helps!!
Estimating Proportions The quality control people at your company have tested a sample of 450 widgets and found that 23 were defective. What is your interval estimate (confidence interval) for the average proportion of defective widgets (choose your confidence level)?
At a confidence level of 95%, the interval estimate for the average proportion of defective widgets is approximately 0.020 to 0.082.
To find the confidence interval for the proportion of defective widgets, we can use the formula:
CI = p ± z*(sqrt(p*(1-p)/n))
where:
p = proportion of defective widgets in the sample
z* = the z-value for the desired confidence level
n = sample size
The z-value depends on the desired confidence level. For example, if we want a 95% confidence level, we would use a z-value of 1.96 (from the standard normal distribution table).
Plugging in the values given in the problem, we get:
p = 23/450 = 0.0511
n = 450
z* = 1.96 (for a 95% confidence level)
sqrt(p*(1-p)/n) = sqrt(0.0511*(1-0.0511)/450) ≈ 0.016
Therefore, the 95% confidence interval for the proportion of defective widgets is:
CI = 0.0511 ± 1.96*0.016
= (0.020, 0.082)
This means we are 95% confident that the true proportion of defective widgets in the population is between 0.020 and 0.082.
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pls help with my Algebra 2
Answer: second graph,and upper curve is right answer .
Step-by-step explanation: just put X= 0,1,2,..
and you get Y. and those are the dots which you have to see that are on that graph.
Malik measured the middle school and made a scale drawing. He used the scale 8 inches = 6 feet. What is the scale factor of the drawing?
Therefore, the scale factor of the drawing is 4/3.
What is scale factor?In mathematics, the scale factor is the ratio between two corresponding measurements in different scales. It is a measure of how much a figure or object has been scaled up or down, compared to its original size. The scale factor is often used in geometry and is particularly useful when creating scale drawings or models. A scale drawing is a drawing that is proportional to the actual size of the object it represents, but is scaled down or up by a certain factor to fit on a piece of paper or to make it easier to work with. The scale factor is used to determine the relationship between the measurements of the original object and the measurements of the scaled-down or scaled-up version.
Here,
To find the scale factor of the drawing, we need to determine the ratio of the length in the drawing to the actual length.
Here, the scale is given as 8 inches = 6 feet. This means that every 8 inches in the drawing represents 6 feet in real life.
To find the ratio of the length in the drawing to the actual length, we can set up a proportion:
8 inches / 6 feet = x inches / y feet
where x is the length in the drawing that corresponds to a length of y feet in real life.
To solve for x, we can cross-multiply and simplify:
8 inches * y feet = 6 feet * x inches
8y = 6x
x = (8/6) y
x = (4/3) y
This means that the length in the drawing is (4/3) times the length in real life.
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The question is in the image below
I am stuck on Part 2, and where it says 2 that's all I got
Grade 8
The equation has no solution as 10 + x ≠ 5 + x
When the value of x is 2, the equation also have no solution as 12 ≠ 7
What are algebraic expressions?Algebraic expressions are simply defined as expressions that are composed of terms, variables, constants, factors and coefficients.
These algebraic expressions are expressions that are identified with arithmetic operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFrom the information given, we have;
6 + x + 4 = 2 + x + 3
collect the like terms, we have
10 + x = 5 + x
But we know that 5 is not equal to x and thus, the equation has no solution
Now, let's substitute the value of x as 2, we have;
10 + 2 = 5 + 2
This gives;
12 = 7
This is not true and thus, the equation has no solution
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ravel leisure magazine provides an annual list of the best hotels in the world. the magazine provides a rating for each hotel along with a brief description that includes the size of the hotel, amenities, and the cost per night for a double room. a sample of of the top-rated hotels in the
The Ravel Leisure Magazine's annual list of the best hotels in the world is a content-loaded resource that provides valuable information for travelers. Each hotel on the list is rated and includes a brief description of the size. Here is a sample of the top-rated hotels on the list: The Ritz-Carlton, The Peninsula and The Four Seasons
The Ritz-Carlton, Bali: This luxurious hotel boasts a stunning beachfront location, spacious suites, and top-of-the-line amenities, including a spa and multiple dining options. The cost per night for a double room is $450.
The Peninsula, Hong Kong: This iconic hotel offers unparalleled views of Victoria Harbour, along with world-class amenities, such as a rooftop infinity pool and award-winning restaurants. The cost per night for a double room is $700.
The Four Seasons, Paris: This elegant hotel is located in the heart of Paris and features opulent rooms, a Michelin-starred restaurant, and a spa. The cost per night for a double room is $800.
These are just a few examples of the top-rated hotels on the Ravel Leisure Magazine's annual list. Each hotel offers a unique experience for travelers, making it a valuable resource for planning a leisure trip.
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To help pay for culinary school, Austin borrowed money from his credit union. He took out a personal, amortized loan for $56,000 , at an interest rate of 5.25% , with monthly payments for a term of 15 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find Austin's monthly payment. (b) If Austin pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) If Austin pays the monthly payment each month for the full term, find the total amount of interest he will pay.
The required answers are a) P ≈ $441.59, b) $79,486.20, c) $23,486.20.
How to find monthly payment?(a) To find Austin's monthly payment, we can use the formula for the monthly payment on an amortized loan:
P = (A * r) / (1 - (1 + r)^(-n))
where:
P = monthly payment
A = loan amount = $56,000
r = monthly interest rate = 5.25%/12 = 0.004375
n = total number of payments = 15 years * 12 months/year = 180
Plugging in these values, we get:
P = (56000 * 0.004375) / (1 - (1 + 0.004375)^(-180))
P ≈ $441.59
Therefore, Austin's monthly payment is $441.59.
(b) If Austin pays the monthly payment each month for the full term, he will make 180 payments. So his total amount to repay the loan is:
Total amount = Monthly payment * Number of payments
Total amount = $441.59 * 180
Total amount ≈ $79,486.20
Therefore, Austin will repay a total of $79,486.20 over the 15-year term.
(c) To find the total amount of interest Austin will pay, we can subtract the original loan amount from the total amount he will repay:
Total interest = Total amount - Loan amount
Total interest = $79,486.20 - $56,000
Total interest ≈ $23,486.20
Therefore, Austin will pay a total of approximately $23,486.20 in interest over the 15-year term.
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