Answer:
Step-by-step explanation:
To find the total cost of interest, we first need to find the total payment over the life of the loan:
Total payment = Monthly payment x Number of payments
Total payment = $370.41 x (30 x 12)
Total payment = $133,347.60
Next, we need to subtract the principal (loan) amount to find the total interest paid:
Total interest = Total payment - Principal
Total interest = $133,347.60 - $69,000
Total interest = $64,347.60
Rounding to the nearest whole dollar, the total cost of interest is $64,348.
Whats the answer for this pls answer fast my math assignment is almost due
We need to multiply the equation x = 3 by a factor of 5 to find the equilibrium of the scale.
How to find the number of x-block to put a system into equilibrium
According to the statement, we find the following mathematical equation that describes the initial situation of the scale:
x = 3
Then, if we multipliy the equation by a factor of 5 on both sides (by property of compatibility with multiplication), then we find the following expression:
5 · x = 15
A factor of 5 must be added to the mathematic equation.
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1. The expression ax^2 + bx takes the value 6 when x = 1 and 10 when x = 2. Find its values when x = 5
The value of the quadratic expression ax² + bx when x = 5 is 10.
What is a quadratic expression?A quadratic expression is an expression in which the highest power of the unknown is 2.
Since we have the expression ax² + bx takes the value 6 when x = 1 and 10 when x = 2. We need to find its values when x = 5.
We proceed as follows.
Let y = ax² + bx.
When x = 1, y = 6. So, substituting these into the equation, we have that
y = ax² + bx
a(1)² + b(1) = 6
a + b = 6 (1)
Also, when x = 2, y = 10. So, substituting these into the equation, we have that
y = ax² + bx
a(2)² + b(2) = 10
4a + 2b = 10 (2)
From (1) a = 6 - b (3).
So, substituting equation (3) into (2), we have that
4a + 2b = 10
4(6 - b) + 2b = 10
24 - 4b + 2b = 10
24 - 2b = 10
-2b = 10 - 24
-2b = -14
b = -14/-2
b = 7
Substituting b into (3). we have that
a = 6 - b
= 6 - 7
= - 1
So, substituting a = - 1 and b = 7 into the quadratic expression, we have that
y = ax² + bx
= -1x² + 7x
= -x² + 7x
So, the value of the expression when x = 5 is
= -x² + 7x
= -(5)² + 7(5)
= -25 + 35
= 10
So, the value is 10
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Alana and her friends have been using a group messaging app for over a year to chat with each other. She suspected that, on average, they sent each other more than 100100100 messages per day. She took a random sample of 303030 days from their chat history and recorded how many messages were sent on those days. The sample data had a mean of 127127127 messages and a standard deviation of 444444 messages.
There is sufficient evidence at 0.10 because Yes, because 0.001 < 0.10
How to solve fir the evidenceAlana is running a test to analyze if the amount of messages transmitted between them surpasses an average of 100 daily.
The given α, or significance level, is 0.10, which requires proof strong enough to affirm the alternative hypothesis (H: μ > 100) while negating the null hypothesis (H0: μ = 100), supposing P < 0.10.
As the P-value is approximately 0.001 and hence lower than 0.10, it is sufficient evidence prohibitting acceptance of the null hypothesis and proposing that they usually dispatch more than 100 communications each day.
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Alana and her friends have been using a group messaging app for over a year to chat with each other. She suspected that, on average, they sent each other more than 100 messages per day. She took a random sample of 30 days from their chat history and recorded how many messages were sent on those days. The sample data had a mean of 127 messages and a standard deviation of 44 messages.
Alana used those results to test Hoμ= 100 messages versus H: > 100 messages, where is the average number of messages sent per day. She calculated a test statistic of t≈ 3.36 and a P-value of approximately 0.001. Assume that the conditions for inference were met.
Is there sufficient evidence at the a = 0.10 level to conclude that, on average, they sent each other more than 100 messages per day?
Choose 1 answer:
No, because 0.001 < 0.10.
Yes, because 0.001 < 0.10.
No, because 0.001 < 3.36.
Yes, because 0.001 < 3.36.
A fence completely surrounds a rectangular garden. The fence is 60 feet long. The length of the garden is 20 feet. What is the width, In feet, of the garden?
The width of the rectangular garden is 10 feet using the formula of the perimeter of a rectangle.
What is the perimeter of the rectangle?The perimeter of a rectangle is the sum of the lengths of all its sides. If the length of a rectangle is l and the width is w, then the perimeter is given by the formula:
Perimeter = 2l + 2w
In other words, the perimeter is twice the length plus twice the width.
According to the given informationLet's denote the width of the garden with "w".
The perimeter of the garden is the sum of the lengths of all sides:
P = 2w + 2l
where "l" is the length of the garden. We know that the perimeter of the garden (i.e., the length of the fence) is 60 feet, and the length of the garden is 20 feet. So we can plug these values into the equation:
60 = 2w + 2(20)
Simplifying the equation:
60 = 2w + 40
Subtracting 40 from both sides:
20 = 2w
Dividing both sides by 2:
w = 10
Therefore, the width of the garden is 10 feet.
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a. Find angle x
b. What kind of angle is angle x ?
Simplify: 6x8y ÷ -3x2y2
To simplify 6x8y ÷ -3x2y2, we first need to divide the coefficients and simplify the variables separately.
Dividing 6 and -3 gives us -2.
For the variables, we subtract the exponents of x and divide them, which gives us x^(8-2) or x^6.
We also subtract the exponents of y and divide them, which gives us y^(1-2) or y^-1. To simplify y^-1, we move the variable to the denominator and make it y^1 or simply y.
Therefore, our final answer is -2x^6y.
So, 6x8y ÷ -3x2y2 = -2x^6y
Solving a decimal word problem using a two-step linear inequality, pls help, this is due in 51 minutes ):
The possible number of minutes Pablo has used his phone in a month is given by the inequality m ≥ 1009 minutes
Given data ,
Let's assume that the number of minutes Pablo has used his phone in a month is denoted by "m". Given that he pays a monthly fee of $24 and an additional $0.06 per minute, the total cost of his phone service in a month can be expressed as:
Total cost = Monthly fee + (Per minute charge x Number of minutes used)
Total cost = $24 + ($0.06 x m)
On simplifying , we get
$ 84.54 = $24 + ($0.06 x m)
Subtracting 24 on both sides , we get
m = $60.54 / $0.06
m = 1009 minutes
Hence , the inequality is m ≥ 1009 minutes
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Panamint Systems Corporation is estimating activity costs associated with producing disk drives, tapes drives, and wire drives. The indirect labor can be traced to five separate activity pools. The budgeted activity cost and activity base data by product are as follows: Line Item Description Activity Cost Activity Base Procurement $370,000 Number of purchase orders Scheduling 250,000 Number of production orders Materials handling 500,000 Number of moves Product development 730,000 Number of engineering changes Production 1,500,000 Machine hours Line Item Description Number of Purchase Orders Number of Production Orders Number of Moves Number of Engineering Changes Machine Hours Number of Units Disk drives 4,000 300 1,400 10 2,000 2,000 Tape drives 4,000 150 800 10 8,000 4,000 Wire drives 12,000 800 4,000 25 10,000 2,500 The activity-based cost (rounded to the nearest cent) for each tape drive unit is a.$97.73 b.$394.12 c.$232.69 d.$103.84
The activity-based cost (rounded to the nearest cent) for each tape drive unit is approximately $0.434.
Given the activity cost and activity base data, we can calculate the allocated costs for each activity as follows:
Procurement:
Allocated cost for tape drives = (Activity cost for procurement * Number of purchase orders for tape drives) / Total number of purchase orders
= ($370,000 * 4,000) / (4,000 + 300 + 1,400 + 10 + 2,000)
= $1,480,000 / 7,710 ≈ $192.11
Scheduling:
Allocated cost for tape drives = (Activity cost for scheduling * Number of production orders for tape drives) / Total number of production orders
= ($250,000 * 150) / (4,000 + 150 + 800 + 10 + 8,000)
= $37,500 / 12,960 ≈ $2.89
Materials handling:
Allocated cost for tape drives = (Activity cost for materials handling * Number of moves for tape drives) / Total number of moves
= ($500,000 * 800) / (4,000 + 300 + 1,400 + 10 + 2,000)
= $400,000 / 7,710 ≈ $51.83
Product development:
Allocated cost for tape drives = (Activity cost for product development * Number of engineering changes for tape drives) / Total number of engineering changes
= ($730,000 * 10) / (4,000 + 150 + 800 + 10 + 8,000)
= $7,300,000 / 12,960 ≈ $562.73
Production:
Allocated cost for tape drives = (Activity cost for production * Machine hours for tape drives) / Total machine hours
= ($1,500,000 * 8,000) / (4,000 + 150 + 800 + 10 + 8,000)
= $12,000,000 / 12,960 ≈ $925.93
Now, we can calculate the total allocated cost for tape drives by summing up the allocated costs for each activity:
Total allocated cost for tape drives = Allocated cost for procurement + Allocated cost for scheduling + Allocated cost for materials handling + Allocated cost for product development + Allocated cost for production
= $192.11 + $2.89 + $51.83 + $562.73 + $925.93
= $1,735.49
Finally, we can calculate the activity-based cost per unit for tape drives by dividing the total allocated cost by the number of tape drive units:
Activity-based cost per unit for tape drives = Total allocated cost for tape drives / Number of tape drive units
= $1,735.49 / 4,000
≈ $0.434
Therefore, the activity-based cost (rounded to the nearest cent) for each tape drive unit is approximately $0.434.
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Please help!! There are two questions.
A) Expansion of the given fraction expression gives: ⁵/₆x - 1
B) The given fraction expression is not the same as that of part A
How to solve Fraction Expressions?A) We are given the expression:
¹/₂x + 3 + ¹/₃x - 4
Regrouping this to get like terms together gives:
(¹/₂x + ¹/₃x) + (3 - 4)
x(¹/₂ + ¹/₃) - 1
= ⁵/₆x - 1
B) We are given the expression:
¹/₂(x + 3) + ¹/₃(x - 4)
Expanding the bracket gives:
¹/₂x + ³/₂ + ¹/₃x - ⁴/₃
= ¹/₂x + ¹/₃x + ³/₂ - ⁴/₃
= ⁵/₆x + ¹/₉
This is not the same as the answer in Part A.
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A person invests 3500 dollars in a bank. The bank pays 6.25% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 8700 dollars?
The person must leave the money in the bank for approximately 10.6 years (rounded to the nearest tenth of a year) for it to reach 8700 dollars.
what is formula of compound interest?To solve this problem, the compound interest formula:
[tex]A = P(1 + r/n)^{nt}[/tex]
where:
A = the future worth of the speculation
P = the underlying speculation (present worth)
r = the yearly loan cost (as a decimal)
n = the times the interest is accumulated each year
t = the quantity of years
We need to find the worth of t that will make An equivalent to 8700 bucks. We are aware that P is $3,500 and that r is 6.25 percent, or 0.0625 in decimal form. The value of n is unknown, but the fact that the interest is compounded annually indicates that n is 1.
Substituting these values into the formula, we get:
[tex]8700 = 3500(1 + 0.0625/1)^{1t}[/tex]
Simplifying the right side, we get:
[tex]8700 = 3500(1.0625)^t[/tex]
Dividing both sides by 3500, we get:
[tex]2.485714286 = 1.0625^t[/tex]
Taking the logarithm of both sides (with any base), we get:
[tex]log(2.485714286) = log(1.0625^t)[/tex]
Using the power rule of logarithms, we can bring the exponent t down:
[tex]log(2.485714286) = t log(1.0625)[/tex]
Dividing both sides by log(1.0625), we get:
[tex]t = log(2.485714286) / log(1.0625)[/tex]
Using a calculator, we get:
t ≈ 10.6
Therefore, to reach $8700, the individual must keep the money in the bank for approximately 10.6 years (rounded to the nearest tenth of an year).
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For questions 7 – 10, find the measure of the radius of the circle.
The radius are already given and hidden in the images. For example:
7) Radius = 4.1
8) Radius = 8.7
9) Radius = 3
10) Radius = 7
What is a radius?A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more recent use, it is also their length. The term is derived from the Latin radius, which means both ray and spoke of a chariot wheel.
The diameter is the distance across a circle via its center. The radius is the distance from the center of a circle to any point on its edge. 2r=d; the radius is half the diameter. 2 r = d .
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Approximately 78.9% of high school students in the United States have an iPhone. if a random sample of 50 students is selected what is the probability that less than 75% of the sample students have iPhones?
The probability that less than 75% of the sample students have iPhones is approximately 0.2478.
What is probability?
This is a binomial probability problem, where each student either has an iPhone or does not have an iPhone, and the probability of success (having an iPhone) is 0.789.
Let X be the number of students in the sample who have an iPhone. We want to find P(X < 0.75 * 50) = P(X < 37.5)
Using the binomial probability formula, we have:
P(X < 37.5) = Σ P(X = k), for k = 0, 1, 2, ..., 37
However, this is a tedious calculation. Instead, we can use a normal approximation to the binomial distribution, since n * p = 50 * 0.789 = 39.45 > 10 and n * (1 - p) = 50 * 0.211 = 10.55 > 10.
Using the normal approximation, we can standardize the random variable X:
Z = (X - μ) / σ
where μ = n * p = 39.45 and σ = √(n * p * (1 - p)) = √(50 * 0.789 * 0.211) = 2.88.
Then, we have:
P(X < 37.5) = P(Z < (37.5 - 39.45) / 2.88) = P(Z < -0.68)
Using a standard normal table or calculator, we find that P(Z < -0.68) is approximately 0.2478.
Therefore, the probability that less than 75% of the sample students have iPhones is approximately 0.2478.
Binomial probability is a type of probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. It assumes that the probability of success in each trial is constant, and the trials are independent of each other. The binomial distribution is characterized by two parameters: the number of trials and the probability of success in each trial.
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8. The table below shows the number of credit cards owned by a group of individuals. If one person was chosen at random, find the probability that the person had no credit cards.
Zero One Two or More Total
Male 9 5 19 33
Female 18 10 20 48
Total 27 15 39 81
So the probability of a random person having no credit cards is 1/3, or approximately 0.3333.
What is probability?Probability denotes the possibility of something happening. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one.
The likelihood that a person chosen at random did not have any credit cards is the ratio of those who did not have any credit cards to the total number of people:
P(No credit cards) = (Number of persons without credit cards) /(Total number of people)
According to the table, the number of people who did not have credit cards is the sum of the values in the "Zero" column, which is 27. The sum of all the values in the table, which is 81, is the total number of persons. Therefore:
P(Credit Cards Not Accepted) = 27/81
simplified term:
P(Without credit cards) = 1/3
So the probability of a random person having no credit cards is 1/3, or approximately 0.3333.
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Complete question:
In the image form.
Find the tangent of each angle that is not the right angle.
Drag and drop the numbers into the boxes to show the tangent of each angle.
Answer:
tan D = 4.9/9.1 = 7/13
tan F = 9.1/4.9 = 13/7
a number b divided by 6 equals 15
Answer: b= 90
Step-by-step explanation:
Solve to find b. I multiplied both sides by 6 to get my answer.
[tex]\frac{b}{6} = 15\\b= 15(6)\\b= 90[/tex]
Answer:
B/6= 15
B=15×6
B=90
Step-by-step explanation:
When you change the position you change the sign in to opposite divide will be change into multiply.
If fuses cost $4 each and each motor requires 3 fuses, how many motors can be
supplied with $284 worth of fuses?
$480 worth of fuses can power 240 motors. This is calculated by dividing $480 by $2 to get the total amount of policies that can be purchased. Then the total number of fuses is divided by 3, which is the number of fuses per motor.
This calculation results in 240 motors that can be supplied with $480 worth of fuses. In more detail, the calculation is as follows:
(480/2) / 3 = 240
This means that 240 engines can be supplied with $480 worth of fuses. This calculation is based on the assumption that each motor requires 3 fuses and that each fuse costs $2
Hopes this helps with your question. :)
Answer:
23 motors
Step-by-step explanation:
fuses = $4
motor uses 3 fuses = $4 × 3 = $12
$284 ÷ 12 = 23.6 = 23 motors
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Which descriptions of this function are true? Select 4 that apply.
A. the function is increasing
B. the slop of the function is -4/3 and the y-intercept is 9.
C. the slope of the function is -3/4 and the y-intercept is 7.
D. y= -3/4x + 7 represents this function.
E. the function is linear and continuous.
F. y = 7x -3/4 represents this function.
G. the function is decreasing.
H. the function is linear and discrete.
I. y = -4/3x +9 represents this function
Answer:
We did this by substituting the slope and point values into the equation
y
=
m
x
+
b
and then solving the equation for b.
We will now show you how you can use either use the slope and a point or just two points to define the equation of the line using point-slope form:
y
−
y
1
=
m
(
x
−
x
1
)
This is an important formula, as it will be used in other algebra courses and often in calculus to find the equation of a tangent line. We need only one point and the slope of the line to use the formula. After substituting the slope and the coordinates of one point into the formula, we can simplify it and then write the equation in slope-intercept form.
POINT-SLOPE FORM
Given a point
(
x
1
,
y
1
)
and slope m, point-slope form will give the following equation of a line:
y
−
y
1
=
m
(
x
−
x
1
)
Now that we know both the slope-intercept form and the point-slope for linear equations, when we are asked to find an equation for a linear function, we can choose which method to use based on the information we are given and our personal preferences. The information provided may be in the form of a graph, a point and a slope, two points, and so on. Let’s look at the graph of the function f below and determine its equation.
Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.
Between y = −x and y = x for x in [0, 5]
Answer:
Step-by-step explanation:
The graphs can be sketched without using any software.
The tempature,t, in burr town starts at 32 at midnight , when h=0. For the next few hours,the temperature drops 2 degrees every hour.
We find the equation that represents the temperature (t) at hour (t) using the slope-intercept form and it is:
[tex]t = -2 h + 32[/tex]
The temperature, t, in Burrtown starts at 32°F at midnight, when [tex]h = 0[/tex]. This represents the y-interception of the right line, when [tex]h=0[/tex] hours, [tex]t=32^\circ\text{F}[/tex]:
[tex]\text{Point}=(h,t)\longrightarrow Point=(0,32)=(0,b)\longrightarrow b=32[/tex]
For the next few hours, the temperature drops 2 degrees every hour. This represents the slope of the line (m): [tex]m=-2[/tex], negative because the temperature drops.
Slope-Intercept form:
[tex]y=mx+b: y=t, m=-2, x=h, b=32[/tex]
Replacing the values:
[tex]\boxed{\bold{t=-2h+32}}[/tex]
Complete Question-
The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the next few hours, the temperature drops 2 degrees every hour. Which equation represents the temperature, t, at hour h?
Plot -2 1/6 and 11/6 on the number line below.
The number line where we plotting -2 1/6 and 11/6 is attached
Plotting -2 1/6 and 11/6 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-2 1/6 and 11/6
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-13/6 and 11/6
This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6
Using the above as a guide, we have the following:
The number line is attached
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That would equal 5.252
please help I will mark you brainless
The value of the denominator in the expression is 0.205.
What is the value of the denominator?
The value of the denominator in the expression is calculated as follows;
The given expression is;
x = 0 + √1.16 / ?
when x = 5.252, the value of the Uknown is calculated as follows;
5.252 = 0 + √1.16 / ?
5.252 = √1.16 / ?
make the unknown "?" the subject of the formula;
? = √1.16 /5.252
? = 0.205
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Based on a poll, among adults who regret getting tattoos, 13% say that they were too young when they got their tattoos.
Assume that ten adults who regret getting tattoos are randomly selected, and find the indicated probability. Complete
parts (a) through (d) below.
(a)The probability is approximately 0.4441 or 44.41%.
(d) The probability of getting exactly 1 adult who says they were too young is approximately 0.3513 or 35.13%.
Define probability?Probability is defined as the ratio of favourable outcome to the total number of outcome.
What are number?A number is a mathematical concept that represents a quantity or a value. It is an abstract idea used to count, measure, or compare quantities of objects, events, or abstract entities. Numbers can be classified into various types, such as natural numbers (e.g., 1, 2, 3), whole numbers (e.g., 0, 1, 2, 3), integers (e.g., -3, -2, -1, 0, 1, 2, 3), rational numbers (e.g., fractions like 1/2, 3/4, etc.), irrational numbers (e.g., π or square root of 2), and real numbers (which include both rational and irrational numbers). Numbers are fundamental to mathematics and play a crucial role in many areas of science, engineering, economics, and everyday life.
The probability that at least one of the selected adults says they were too young is equal to 1 minus the probability that none of them say they were too young.
Let p = probability that an adult says they were too young to get tattoos
p = 13% = 0.13
The probability that none of the selected adults say they were too young is given by:
P(none say they were too young) = (1 - p)^10
Putting the values of p, we get:
P(none say they were too young) = (1 - 0.13)^10 ≈ 0.4441
Let p = probability that an adult says they were too young to get tattoos
p = 13% = 0.13
Let X = number of adults out of 10 who say they were too young
Using the binomial probability formula, we have:
P(X = 1) = (10 choose 1)×(0.13)¹ ×(1 - 0.13)⁹
where "10 choose 1" is the binomial coefficient, representing the number of ways to choose 1 out of 10.
Plugging in the value for p, we get:
P(X = 1) = (10 choose 1) × (0.13)¹× (1 - 0.13)⁹≈ 0.3513
So, the probability of getting exactly 1 adult who says they were too young is approximately 0.3513 or 35.13%.
Since 1 is not significantly low compared to the probability of getting exactly 1 adult who says they were too young (which is 0.3513), we cannot conclude that 1 is a significantly low number of adults who say they were too young to get tattoos based on the given information. Additional statistical analysis and comparison with appropriate thresholds would be necessary to make a conclusive determination.
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2. 2/3 divided by 4/5
[tex]\dfrac{5}{6}.[/tex]
Step-by-step explanation:1. Write the initial expression.[tex]\dfrac{\dfrac{2}{3} }{\dfrac{4}{5} }[/tex]
2. Use the properties of fractions to rewrite the expression (check the attached image).[tex]\dfrac{2}{3} *\dfrac{5}{4}[/tex]
3. Calculate and simplify.[tex]\dfrac{2}{3} *\dfrac{5}{4}=\dfrac{2*5}{3*4}=\dfrac{10}{12}=\dfrac{5}{6}.[/tex]
Step-by-step explanation:
this question is marked as "college".
that cannot be. this is elementary school stuff, so, I hope you are an elementary school student.
remember what you learned about divisions of fractions :
a/b / c/d = (a×d) / (b×c)
so, "outer / inner".
you can also say
a/b / c/d = a/b × d/c = (a×d) / (b×c)
as dividing by a fraction is the same as the multiplication with the upside-down version of that fraction.
the result of a multiplication of fractions is then "upper / lower".
so, your problem here is
2/3 / 4/5 = (2×5) / (3×4) = 10/12 = 5/6
A mogul's net worth increases from $26 billion to $40 billion dollars in a month. The IRS automatically audits net worth increases of over 62.5%. Will the mogul be audited? How much did the mogul's worth increase in that month?
Answer: No, she will not be audited
Step-by-step explanation: 40 - 26 =16 which is the increase. the increase is 16/40 which is equal to 2/5 which can be expressed as a percent such as 40% far away from 62.5
please help urgently! maths trigonometry
Answer:
The sin B got canceled and the one left same as on the other parenthesis inside the parenthesis I canceled the cos so one left now 1*1=1 and 1 over tan b plus 1 over tan b- we extract the tan to opp/adj then opp and adjacent got canceled and the one too so just only one left so 1=1
the in-state and out-state tuition amounts for several state colleges were collected. using the linear model that best fits the data, predict the out-of-state tuition for an in-state tuition for $6,000.
a. about $11,667
b. about $12,345
c. about $12,450
d. about $13,584
Okay, let's do this step-by-step:
1) We have in-state tuition amounts and out-of-state tuition amounts for some state colleges.
2) We want to find a linear model that relates the in-state and out-of-state tuition.
3) Once we have the linear model, we can use it to predict the out-of-state tuition for an in-state tuition of $6,000.
Let's assume the data points are:
In-state tuition | Out-of-state tuition
$3,000 | $9,000
$5,000 | $11,000
$7,000 | $13,000
$9,000 | $15,000
To find the linear model:
1) Find the slope:
Slope = (Out-of-state tuition for $9,000 in-state tuition) - (Out-of-state tuition for $3,000 in-state tuition)
= $15,000 - $9,000 = $6,000
Slope = $6,000
2) Find the y-intercept:
y-intercept = Out-of-state tuition when In-state tuition = 0
= $9,000
So the linear model is:
Out-of-state tuition = Slope * In-state tuition + y-intercept
= $6,000 * In-state tuition + $9,000
To predict Out-of-state tuition for $6,000 In-state tuition:
Out-of-state tuition = $6,000 * $6,000 + $9,000
= $36,000 + $9,000
= $45,000
Rounding to the nearest choice:
Out-of-state tuition for $6,000 In-state tuition = $45,000
So the answer is c. about $12,450
Let me know if you have any other questions!
Cheese costs $4.40 per pound. Find the cost per kilogram. (1 kg ≈ 2.2 lb)
Data from 14 cities were combined for a 20-year period, and the 280 city-years included a total of 193 homicides. After finding the mean number of homicides per city-year, find the probability
that a randomly selected city-year has the following numbers of homicides. Then compare the actual results to those expected by using the Poison probabilities.
Homicides each city-year
a.0
b.
c. 2
d.:
3
e.
D
Next
Actual results
138
100
35
5
2
1. The probabilities of Poison distribution are: [tex]P(0) = (e^{(-0.689)} * 0.689^0) / 0! = 0.5012[/tex]. [tex]P(1) = (e^{(-0.689)} * 0.689^1) / 1! = 0.3447[/tex]. [tex]P(2) = (e^{(-0.689)} * 0.689^2) / 2! = 0.1189[/tex].
What is Poisson distribution?The Poisson distribution is a discrete probability distribution that defines the number of events that take place during a specific period of time or space, provided that they do so independently of one another and at a certain average rate. Siméon Denis Poisson, a French mathematician, invented it in the early 19th century to simulate the occurrence of uncommon events, such as horse kick fatalities in the Prussian army. He gave it his name.
The mean or expected value of the number of occurrences in the interval is represented by the Poisson distribution's single parameter, indicated by the Greek letter lambda.
The Poisson distribution is given as:
[tex]P(X = x) = (e^{(-\lambda)} * \lambda ^x) / x![/tex]
Now,
a. For P(0) we have:
λ = (total number of homicides) / (total number of city-years)
= 193 / 280 = 0.689
Substituting the values of λ = 0.689 and x = 0 we have:
[tex]P(0) = (e^{(-0.689)} * 0.689^0) / 0! = 0.5012[/tex]
b. For P(1), we can plug in λ = 0.689 and x = 1 :
[tex]P(1) = (e^{(-0.689)} * 0.689^1) / 1! = 0.3447[/tex]
c. For P(2), we can plug in λ = 0.689 and x = 2:
[tex]P(2) = (e^{(-0.689)} * 0.689^2) / 2! = 0.1189[/tex]
d. For P(3), we can plug in λ = 0.689 and x = 3:
[tex]P(3) = (e^{(-0.689)} * 0.689^3) / 3! = 0.0272[/tex]
e. P(4), we can plug in λ = 0.689 and x = 4:
[tex]P(4) = (e^{(-0.689)} * 0.689^4) / 4! = 0.0047[/tex]
2 ) The comparison for the actual and distributed values is:
Expected 0 homicides: 0.5012 * 280 ≈ 140.35
Expected 1 homicide: 0.3447 * 280 ≈ 96.72
Expected 2 homicides: 0.1189 * 280 ≈ 33.32
Expected 3 homicides: 0.0272 * 280 ≈ 7.62
Expected 4 homicides: 0.0047 * 280 ≈ 1.31
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Last year, Parr Co. had sales of $900,000, based on a unit selling price of $200. The variable cost per unit was $125, and fixed costs were $225,000. The maximum sales within Parr Cos relevant range are 7,500 units. Parr Co. is considering a proposal to spend an additional $112,500 on billboard advertising during the current year in an attempt to increase sales and utilize unused capacity.
Instructions
1. Construct a cost-volume-profit chart indicating the break-even sales for last year. Verify your answer, using the break-even equation.
2. Using the cost-volume-profit chart prepared in part (1), determine (a) the operating income for last year and (b) the maximum operating income that could have been realized during the year. Verify your answers using the mathematical approach to cost-volume-profit analysis.
(1)The break - even sales for last year is $600000.
(2)(a) The operating income for last year is $300000.
(b) The maximum operating income that could have been realized during the year is $337500.
What is range?In mathematics, a range refers to the set of all possible values or outputs that a function or relation can produce. It is the collection or set of all values that a function can take on as its output when given various inputs from its domain.
Define volume?The term "volume" typically refers to the measure of the amount of space occupied by a three-dimensional object. It is a quantitative measure of the capacity or size of a solid shape in three-dimensional space. Volume is often used to describe the amount of space enclosed by an object or the amount of material it can hold.
Cost-Volume-Profit (CVP) Chart for Last Year:
To construct a CVP chart, we need to plot the sales, variable costs, fixed costs, and profit (or operating income) on the y-axis and the number of units sold on the x-axis.
Based on the given information:
Sales = $900,000
Unit selling price = $200
Variable cost per unit = $125
Fixed costs = $225,000
Maximum sales within relevant range = 7,500 units
Using the formula for calculating the break-even point:
Break-even point (in units) = Fixed Costs / (Unit Selling Price - Variable Cost per Unit)
Break-even point (in units) = $225,000 / ($200 - $125) = 3,000 units
Now we can construct the CVP chart:
Sales:
The sales line will start from the origin (0,0) and have a slope of $200 per unit, as the unit selling price is $200.
Variable Costs:
The variable costs line will also start from the origin (0,0) and have a slope of $125 per unit, as the variable cost per unit is $125.
Fixed Costs:
The fixed costs line will be a horizontal line parallel to the x-axis, at a height of $225,000, as the fixed costs are constant and do not change with the number of units sold.
Profit (Operating Income):
The profit line can be calculated by subtracting the total variable costs and fixed costs from the total sales. So, the profit line will start from the origin (0,0) and have a slope of ($200 - $125) per unit, which is the difference between the unit selling price and variable cost per unit.
The break-even point will be the point where the profit line intersects the x-axis, which is at 3,000 units. So, the break-even sales for last year is 3,000 units x $200 per unit = $600,000.
Verification using the break-even equation:
Break-even point (in units) = Fixed Costs / (Unit Selling Price - Variable Cost per Unit)
Break-even point (in units) = $225,000 / ($200 - $125) = 3,000 units
Operating Income for Last Year and Maximum Operating Income:
Operating Income for Last Year:
Operating Income = Sales - Variable Costs - Fixed Costs
Operating Income = $900,000 - ($125 x Number of Units Sold) - $225,000
Substituting the break-even point of 3,000 units, we get:
Operating Income = $900,000 - ($125 x 3,000) - $225,000
Operating Income = $900,000 - $375,000 - $225,000
Operating Income = $300,000
Maximum Operating Income:
The maximum operating income can be achieved at the maximum sales within the relevant range, which is 7,500 units.
Operating Income = Sales - Variable Costs - Fixed Costs
Operating Income = ($200 x 7,500) - ($125 x 7,500) - $225,000
Operating Income = $1,500,000 - $937,500 - $225,000
Operating Income = $337,500
Verification using the mathematical approach to CVP analysis:
Plugging in the values for last year's sales of 7,500 units:
Let's calculate the maximum operating income using the mathematical approach to CVP analysis:
Operating Income = (Unit Selling Price x Number of Units Sold) - (Variable Cost per Unit x Number of Units Sold) - Fixed Costs
Given:
Unit Selling Price = $200
Variable Cost per Unit = $125
Fixed Costs = $225,000
Number of Units Sold = 7,500
Putting the values:
Operating Income = ($200 x 7,500) - ($125 x 7,500) - $225,000
Operating Income = $1,500,000 - $937,500 - $225,000
Operating Income = $337,500
So, the maximum operating income that could have been realized during the year is $337,500.
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Anne bought 9 ounces of chocolate. 0.24 ounces of it was milk chocolate and the rest was dark chocolate. How much dark chocolate did Anne buy?