The correct function equivalent to the original function V = 40,000(0.64) is V = 40,000(0.64)ⁿ.
What is percent?Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.
Here,
The original function V = 40,000(0.64) models the value, V, of a $40,000 car after t years, where the car depreciates at a rate of 36% per year. The expression 0.64 represents the remaining value of the car after one year, which is obtained by subtracting 36% from 100% (i.e., 100% - 36% = 64%).
To find an equivalent function, we need to simplify 0.64. We can write 0.64 as 0.8², since 0.8 multiplied by itself gives 0.64.
So, V = 40,000(0.64) is equivalent to V = 40,000(0.8²), which simplifies to V = 40,000(0.64). This means that both expressions represent the same function that models the value of the car after t years, given that the car depreciates at a rate of 36% per year.
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1. ALUMMUNI PLC. Produces three models of tractors: Metakeb, Mewesson, Metekem Each unit of Metakeb, Mewesson and Metekem requires the following amounts of time in minumtes in each of the indicated departments.
Machining dep't
Inspection dep't
(in minutes)
(in minutes)
(in minutes)
Metakeb
1200
2400
600
Mewesson
1800
1200
3000
Metekem
3000
Assembly dep't
2400
1200
Suppose the total time available per month in machining, assembly and inspection departments are 1050, 1160 and 830 hours respectively.
Required:
Determine the number of units of each product to be produced in a month to use up all the available resources (use Gaussaian method)
The company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.
What is the Gaussian method?
The Gaussian method, also known as Gaussian elimination or row reduction, is a technique for solving systems of linear equations. It involves performing a sequence of operations on the rows of a matrix to transform it into an equivalent matrix that is in row echelon form or reduced row echelon form.
To use the Gaussian method, we need to set up a system of linear equations based on the given information. Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem produced per month, respectively. Then we have:
Machining department: 1200x + 1800y + 3000z = 1050(60)
Inspection department: 2400x + 1200y = 1160(60)
Assembly department: 600x + 3000y = 830(60)
Simplifying these equations, we get:
Machining department: 20x + 30y + 50z = 3150
Inspection department: 8x + 4y = 232
Assembly department: x + 5y = 139
Now we can use the Gaussian method to solve for x, y, and z:
Step 1: Write the augmented matrix:
| 20 30 50 | 3150 |
| 8 4 0 | 232 |
| 1 5 0 | 139 |
Step 2: Use row operations to get the matrix in row echelon form:
R2 → R2 - 4/5 R3
R1 → R1 - 20R3
| 0 -2 50 | 850 |
| 0 2 -4 | -28 |
| 1 5 0 | 139 |
R2→ -1/2 R2
R1 → R1 + R2
| 0 1 -25 | 407 |
| 0 1 -2 | 14 |
| 1 5 0 | 139 |
R1→ R1 - R2
| 0 0 -23 | 393 |
| 0 1 -2 | 14 |
| 1 5 0 | 139 |
R3→ R3 - 5R2
| 0 0 -23 | 393 |
| 0 1 -2 | 14 |
| 1 0 10 | 65 |
R1→ -1/23 R1
| 0 0 1 | -17 |
| 0 1 -2 | 14 |
| 1 0 10 | 65 |
R2 → R2 + 2R3
| 0 0 1 | -17 |
| 0 1 0 | 96 |
| 1 0 10 | 65 |
R3 → R3 - 10R1
| 0 0 1 | -17 |
| 0 1 0 | 96 |
| 1 0 0 | 235 |
Step 3: Read off the solution from the row echelon form:
z = -17
y = 96
x = 235
Therefore, the company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.
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Find the value of x. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
9. sin 18 = x/21
x = 21* sin 18
x = 6.5
10. tan 55 = 29/x
x* tan 55 = 29
x = 29/tan 55
x = 20.3
11. sin 23 = x/25
x = 25 * sin 23
x = 9.8
12. sin 47 = 33/x
x * sin 47 = 33
x = 33/sin 47
x = 45.1
A hardware store sells nylon rope for $0.89/yd. A lumber yard sells the same rope for $0.94/m.
a) Which store sells the rope for a lower price? Explain your answer.
b) How much money would Jim save if he purchased 650 ft. of the less expensive rope, before taxes?
pls complete a and b!!
Therefore , the solution of the given problem of unitary method comes out to be 14.7 dollars before taxation, assuming he bought 650 feet of the cheaper rope.
What is an unitary method?The job can be completed by bringing together what was learned and applying this variable technique, that also includes all supplementary data from two people that utilized a specific tactic. To put it another way, if the desired outcome materialises, either the entity stated in the calculation will be recognised, or both expression essential processes will truly skip the colour. For forty pencils, a refundable charge of Rupees ($1.01) might be required.
Here,
To evaluate the prices, we need to use the same units.
Since 0.9144 metres make up one yard, we can convert the cost of the rope at the hardware shop to dollars per metre as follows:
=> 0.89 dollars/yard * 1 yard/0.9144 meters = 0.97 dollars/meter
b) We must change the units to yards or metres in order to evaluate the costs of 650 feet of rope. 650 feet is equivalent to 3 yards, which is:
=> 650 feet x 3 feet per yard = 216.67 yards
The hardware store's price for the cord is:
=> 192.5 dollars ($0.89/yard x 216.67 yards)
At the timber yard, the price of the rope is:
=> (216.67 yards * 0.9144 meters/yard) * 0.94 dollars/meter = 177.8 dollars.
Jim would therefore save:
=> 192.5 dollars - 177.8 dollars = 14.7 dollars.
before taxation, assuming he bought 650 feet of the cheaper rope.
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Confidence intervals are constructed to estimate the population parameter (like the mean) a specified proportion of the time. The upper and lower interval estimates are often described as the
The upper and lower interval estimate are often describe as associated with a specific level of confidence.
What is Interval Estimate?In statistics, interval estimate is the process of determining the interval, or range of values, within which a parameter—such as the mean (average) of a population—is most likely to fall.
The interval encompassing a population parameter is determined by computing the statistic from values obtained from a random sample chosen from the population and by using the understanding (derived from probability theory) of how accurately sample properties reflect those of the full population.
The possibility that the estimated confidence interval estimate will include the genuine population parameter is frequently referred to as the confidence level.
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Gwen owes a total of $4,522.50 on revolving credit accounts that have total limits of $7,950.00. Calculate the amount she needs to pay on her debt to reduce her revolving credit accounts to reach a 25% debt-to-credit ratio.
The amount that she needs to pay on her debt to reach a 25% debt-to-credit ratio is given as follows:
$2,535.
How to obtain the amount that she needs to pay?The amount that she needs to pay on her debt reach a 25% debt-to-credit ratio is obtained applying the proportions in the context of the problem.
She has a credit limit of $7,950.00, hence 25% of her credit limit is obtained as follows:
0.25 x 7950 = $1987.5.
She current has $4,522.50 on debts, hence the amount that she needs to pay for the debts to be reduced to $1987.5 is given as follows:
4522.5 - 1987.5 = $2,535.
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Mio deposits money in his bank account from a summer job and doesn’t spend any of it. After working 3 hours total, he has $71. After working 12 hours total, he has $134. How much money does Mio earn per hour?
Answer:
Step-by-step explanation:
because we know 1 hour is 60 min so 3 hours would be 60x3=180 then you do 3x23.7=71 12x11.2=134 so in total he has 23.7 per hour and 11.2 for 3 hours
Iti...
00
t
Get ready
and
Evaluate.
Hint: Use the image to help break 9 x 4 up into two expressions.
9x4
5 fours +
fours
Based on the image, we can break 9 × 4 into two expressions as 4 groups of 9 or 9 groups of 4. This equals 36.
How to explain the expressionIt should be noted that to break 9 x 4 up into two expressions, you can use the distributive property of multiplication over addition, which states that a(b + c) = ab + ac.
So, we can rewrite 9 x 4 as:
9 x 4 = 9 x (3 + 1)
Using the distributive property, we can expand this expression as:
9 x (3 + 1) = (9 x 3) + (9 x 1)
Simplifying, we get:
9 x 4 = 27 + 9
Therefore, we have broken up 9 x 4 into two expressions: 27 and 9. This will give 36.
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What are the x- and y-intercepts of f(x) - 3x - 4?
The x- and y-intercepts as required to be determined in the task content are; (-4/3, 0) and (0, -4).
Which points represent the x- and y-intercepts of the function?As evident in the task content; the given function is; f(x) = - 3x - 4.
The x-intercept represents the value of x when f(x) = 0.
0 = -3x - 4
3x = -4
x = -4 / 3.
The y-intercept represents the value of f(0); hence, we have that;
f (x) = -3(0) - 4
f(0) = -4.
Ultimately, the points which correctly represents the x- and y-intercepts are; (-4/3, 0) and (0, -4).
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A plane can fly 420 miles in the same time as it takes a car to go 150 miles. If the car travels 90 mph slower than the plane, find the speed of the plane. Using r as your variable to represent the speed of the plane in miles per hour, write an equation using the information above that can be solved to find the answer to this problem.
Answer:
Step-by-step explanation:
rate of the plane be x
distance traveled by plane = 420 miles
time taken by plane = 420/x
distance traveled by car =120 miles
rate of car = x-120
time taken by car = 120 / x-100
the time taken by both are same
420/x = 120/ x-100
420(x-100)=120x
420x-42000 = 120x
420x-120x=42000
300x= 42000
x=42000/300
x=140 mph the speed of the plane
Line AB intersects line CD at point F. If m<AFC=(7x-8)° and m<BFD=(5x+6)°, what is m<BFD?
82°
48°
41°
7°
76 is m<BFD in linear equation.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.
m<AFC + m<BFD = 180°
(7x-8)° + m<AFC = 180°
(5x+6)° + m<BFD = 180°
(7x-8)° = (5x+6)
2x = 12
x = 14
m<BFD=(5x+6)°
= 5 * 14 + 6
= 70 + 6
= 76
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WRITING EXAMPLE: EMAIL Compare both texts. Which one do you think is better written? 1. Hi Usma. I like blue colour. Because blue is the best color please when can you come and painting my room. If u coming tomorrow reply me back, dont worry about mony. I whant tell you my room. My room is white colour and I have one shair. Tell me about you rom. Maria 2. My favourite colour is pink, but for my bedroom I prefer white because it's the best colour for my room. My bedroom is big. It is white. There are 2 beds. There is one desk. There are 2 windos. There is one armchair. Bye, Maria
Answer:
Second one
Step-by-step explanation:
Which of these is not true about a polynomial regression model?
Group of answer choices
a. used when the linear regression is not able to capture the data points
b. has multiple predictors
c. requires a linear relationship between the predictor and the dependent variable
A transversal GH cuts two parallel lines AB and CD at E and F, respectively. If
LAEG is exterior angle and LDFE is an interior angle found on the opposite sides of
GH, and if LAEG = 35°, find LDFE.
Since AB and CD are parallel lines cut by a transversal GH, we know that the corresponding angles are equal. Therefore, LDFE = 35°
what is parallel lines ?
Parallel lines are two or more lines in a plane that never meet or intersect, no matter how far they are extended. They always maintain the same distance between them and remain equidistant at every point along their length.
In the given question,
Parallel lines are two or more lines in a plane that never meet or intersect, no matter how far they are extended. They always maintain the same distance between them and remain equidistant at every point along their length.
Corresponding angles are pairs of angles that are in the same relative position at the intersection of two lines that are crossed by a third line, called a transversal. More specifically, corresponding angles are formed when a transversal intersects two parallel lines.
Corresponding angles are congruent, which means they have the same measure or degree of angle
Since AB and CD are parallel lines cut by a transversal GH, we know that the corresponding angles are equal. Therefore,
LAEG = LDFE
So, LDFE = 35°. .
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G
Which inequality has a dashed boundary line when graphed?
3
oy²x+1
O y²-3x+1
2
Oy> 3x+1
O y≤7x-1
The inequality that has a dashed boundary line when graphed is:
y > 3x + 1
What is inequality?In mathematics, an inequality is a statement that two quantities are not equal or do not have the same value. In other words, it is a statement that compares two values, expressing that one value is greater than, less than, or not equal to the other value. An inequality is denoted by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
What is Dashed boundary?In mathematics, a dashed boundary refers to a boundary line that is graphed as a dashed line rather than a solid line. The use of a dashed line is typically used to indicate that the boundary itself is not included in the set of solutions of an inequality or equation.
In the given question,
The inequality that has a dashed boundary line when graphed is:
y > 3x + 1
The reason for this is that when graphed, the boundary line of the inequality y > 3x + 1 is a straight line, but it is dashed instead of solid. This is because the inequality is strict, meaning that the boundary line itself is not included in the set of solutions. On the other hand, if the inequality had been y ≥ 3x + 1, the boundary line would have been a solid line because the inequality is non-strict and includes the boundary line itself as a solution.
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Find m1 if m5 =142 and m4=65
The value of m∠1 is 103°. The solution has been obtained by using the angle sum property.
What is the angle sum property?
The angle sum property of a triangle states that the sum of the three internal angles of a triangle is 180 degrees.
We are given that m∠5 = 142° and m∠4 = 65°.
Since m∠5 and m∠2 lie on a straight line so, they form a linear pair.
So,
⇒ m∠5 + m∠2 = 180°
⇒ 142° + m∠2 = 180°
⇒ m∠2 = 38°
We know that sum of angles of a triangle is 180°.
So,
⇒ m∠3 + m∠4 + m∠2 = 180°
⇒ m∠3 + 65° + 38° = 180°
⇒ m∠3 + 103° = 180°
⇒ m∠3 = 77°
Now, since m∠3 and m∠1 lie on a straight line so, they form a linear pair.
So,
⇒ m∠3 + m∠1 = 180°
⇒ 77° + m∠1 = 180°
⇒ m∠1 = 103°
Hence, the value of m∠1 is 103°.
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The complete question and the figure has been attached below.
Question: Find m∠1 if m∠5 = 142° and m∠4 = 65°.
How much is 1/12 in milliters?
The conversion of 1/12in to milliters can be expressed as 2.117mm
How can the conversion be done?Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. As an illustration, if you had 1,000 interactions and 50 conversions, your conversion rate would be 5% because 50 x 1,000 = 5%.
The proportion of users who perform the intended action is known as the conversion rate. The proportion of website visitors who make a purchase there serves as the prototypical illustration of conversion rate.
We can 1/12in to milliters by using the conversion rate, which 1inch = 25.4mm,and this can be used to make the conversion as:
If 1inch = 25.4mm
1/12 = X mm
Xmm = (1/12 *25.4mm)/ 1inch
=2.117mm
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complete question:
How much is 1/12in to milliters?
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 4 people took the trip. She was able to purchase coach tickets for $140 and first class tickets for $1000. She used her total budget for airfare for the trip, which was $2280. How many first class tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought = ___
The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.
Let us assume the number of coach tickets purchased is x.
And the number of first-class tickets purchased is y.
Now,
Including Sarah, a total of 11 people took the trip.
Thus,
[tex]x + y = 11 [/tex]
The cost of coach tickets and first-class tickets are $210 and $1200 respectively.
The total budget for airfare for the trip is $10,230.
Therefore,
210x + 1200y = 102309
21x + 120y = 1023
Solving both the equations, we get.
x=3
y=8
Thus, The number of coach tickets purchased is 3, and the number of first-class tickets purchased is 8.
Blood pressure readings are normally distributed. The mean systolic blood pressure is 120 and the standard deviation is 8. If a medical researcher randomly selects a sample of 20 people, what is the probability that the mean blood pressure for this sample will be greater than 123?
Answer:
To solve this problem, we can use the central limit theorem and the standard normal distribution.
The central limit theorem states that the distribution of sample means is approximately normal, with a mean equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Let X be the systolic blood pressure of an individual in the population. We know that X is normally distributed with a mean of 120 and a standard deviation of 8.
Let Y be the sample mean blood pressure of a sample of 20 individuals. Then Y is also normally distributed, with a mean of 120 and a standard deviation of 8 / sqrt(20) = 1.7889.
We want to find the probability that the sample mean blood pressure is greater than 123. We can standardize this value using the standard normal distribution as follows:
Z = (Y - 120) / (8 / sqrt(20))
P(Y > 123) = P(Z > (123 - 120) / (8 / sqrt(20)))
= P(Z > 1.3363)
Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 1.3363 is approximately 0.0918.
Therefore, the probability that the mean blood pressure for a sample of 20 people will be greater than 123 is approximately 0.0918.
Help!!
Question
Callie is buying fence for two triangular sections of her garden.
How much fence would she need for triangle DFG ?
Enter your answer in the box.
ft
Callie will need a total of 112 feet of fence for the triangle DFG.
How to find the amount of fence needed.We can find the amount of fence needed by finding the relationship between both triangles and find the missing side.
The sum of all the sides of the triangle will be known as the perimeter of the triangle. we can use this knowledge to find the amount of fence needed.
Both triangles are similar and are in the ratio of 1:7To find the missing side of triangle DFG, we multiply the corresponding side of triangle BAC by 7 to find the missing side.
This will give us 7 x 7 = 49ft
To find the amount of fence needed for triangle DFG we add all the sides of triangle DFG which will be 49 + 35 + 28.
The total will be 112ft.
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For every pound of warming gas produced by agriculture, how many pounds of gas are produced by transportation?
1.0
1.3
2.0
2.7
3.0
Please help with this!
4.3.4 shifting functions
2: do you agree with Serena that you can draw the graphs for the other two rockets by shifting the functions or do you think that Jack is correct and you need to recalculate the other two explain
3: compare the equation with the graph of the function assume the graph is atransformation from f (t)= -6t². Represent the science project what happens to the rocket
4: again assuming a transformation from f(t)= -6t² what does term 82.14 due to the rockets graph what does the value h (t)= 82.14 representative science project what is happening to the rocket
5: p Serena and Jack launch the second rocket 3 seconds after the first one how is the number of the second rocket different from the graph of the first rocket describe in terms of the the vertical and horizontal shift
6: what is the equation of the second rocket
7: they launched the third rocket and three seconds after the second rocket and from a tall platform but will the graph of the third rocket look like described in terms of the vertical and horizontal shape
8: what is the equation of the third rocket
9: answer the following questions about the three rockets refer to the graph rockets and times shown above
A: approximately when was the third rocket launched
B: approximately when does the first rocket land
C: what is the approximate interval during which all three rockets are in the air
The vertical shape of the graph will be the same as that of the first rocket, assuming both rockets have the same initial velocity and acceleration.
What is the interval during which all three rockets?1.I agree with Serena that we can draw the graphs for the other two rockets by shifting the functions. We can use the same equation and just adjust the values of the horizontal and vertical shifts.
2. The equation f(t) = -6t² represents a quadratic function, which has a parabolic shape when graphed. If we apply a transformation to this function, such as a vertical or horizontal shift, the shape of the graph will change accordingly.
3. The term 82.14 likely represents the maximum height achieved by the rocket, since the equation f(t) = -6t² gives the height of the rocket as a function of time. The value of h(t) = 82.14 corresponds to a specific time when the rocket reaches its maximum height.
4. If the second rocket is launched 3 seconds after the first one, the graph of the second rocket will be shifted horizontally by 3 units to the right compared to the graph of the first rocket. This represents a time delay of 3 seconds between the two launches.
5. The equation of the second rocket would be f(t) = -6(t-3)², assuming that the second rocket has the same initial velocity and acceleration as the first rocket but is launched 3 seconds later.
6. Since the third rocket is launched 3 seconds after the second rocket and from a tall platform, its graph will be shifted horizontally to the right by 6 units compared to the graph of the first rocket.
9. A: Based on the graph, the third rocket was launched at approximately 5:20 PM.
B: Based on the graph, the first rocket lands at approximately 5:15 PM.
C: Based on the graph, all three rockets are in the air between approximately 5:10 PM and 5:25 PM, so the approximate interval during which all three rockets are in the air is 15 minutes.
Therefore, spends an additional 6 seconds in the air before landing. The vertical shape of the graph will depend on the specifics of the rocket's launch and trajectory.
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Can someone please help
Answer:
34
Step-by-step explanation:
16x-12= 9x-11 + 9x-11
16×-12=18x-22
10=2x
5=x
WT= 9x-11=9(5)-11
WT=45-11
WT=34
The histogram shows information about how 600 people travel to work.
40
35-
30-
25-
20-
15-
10-
5-
0
0 5 10 15 20 25 30 35 40 45 50 55 60
a) How many people travel more than 40 miles to work?
b) 225 of the 600 people travel further than Tim. Estimate how far Tim travels.
Frequency density
Distance (miles)
8
A
Answer:
A:0 Noone goes higher than 40. b: 5 miles
Twenty percent of Americans ages 25 to 74 have high blood pressure. If 26 randomly selected Americans
ages 25 to 74 are selected, find the probability that one-half have high blood pressure.
Please write your answer as a decimal. Round your answer to seven decimal places.
The probability that one-half of the selected people will have high blood pressure is given as follows:
P(X = 13) = 0.0004684.
What is the binomial distribution formula?The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.
The mass probability formula is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters, along with their meaning, are listed as follows:
n is the fixed number of independent trials.p is the constant probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 26, p = 0.2.
One-half of 26 is of 13, hence the probability is given as follows:
P(X = 13) = 26!/(13! x 13!) x (0.2)^13 x (0.8)^13
P(X = 13) = 0.0004684.
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I WILL GIVE BRANLIST ONLYNOF YOUR RIGHT
Determine the scale factor used to create the image
A 1/2
B 2
C 1/4
D 4
Answer:
Step-by-step explanation:
b
Weber Jewelry advertised a diamond necklace for $572.95 and a gold pendant for $113.76. The state tax is 6.5 percent and the city tax is 0.5 percent. What is the total purchase price?
Therefore, the total purchase price is $734.78.
What are profits?Profit is the financial gain obtained by subtracting the cost (or expenses) of producing and selling goods or services from the revenue generated from their sale. In other words, profit is the amount of money that is left over after all expenses have been paid, including the cost of goods sold, operating expenses, taxes, and any other costs associated with running a business.
Profit can be calculated using the following formula:
Profit = Revenue - Cost
by the question.
To calculate the total purchase price, we need to calculate the tax and add it to the sum of the prices of the diamond necklace and the gold pendant.
The tax on the diamond necklace is:
572.95 * 0.065 = 37.24
The tax on the gold pendant is:
113.76 * 0.065 = 7.40
The total tax is the sum of these two taxes:
37.24 + 7.40 = 44.64
We also need to add the city tax, which is 0.5 percent of the total price:
(572.95 + 113.76) * 0.005 = 3.43
The total purchase price is the sum of the prices of the diamond necklace and the gold pendant, the state tax, and the city tax:
572.95 + 113.76 + 44.64 + 3.43 = 734.78
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Theoretical propobility
Theoretical probability is the likelihood of an event occurring based on mathematical reasoning or analysis, rather than on empirical or experimental data.
What is probability?Probability refers to the likelihood of a particular event or outcome occurring. It is a measure of the chance of an event happening, and is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, physics, engineering, and finance, to make predictions and inform decision-making.
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It is calculated using the laws of probability and assumes that all outcomes are equally likely to occur. Theoretical probability is often used in situations where it is not possible or practical to conduct experiments or collect data, such as in mathematical or statistical modeling.
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Function or not a function answers
Answer:
Only the set of ordered pairs is one-to-one
Step-by-step explanation:
You have three right
The last one:
A function is one-to-one if and only if, for every value of y there is only one value of x
The mapping diagram is not one-to-one since for two values of x, x = -3 and x = 5 we get the same y value of 6
The set of ordered pairs is a one-to=-one since for every value of y there is a unique value for x
x+y=20 and x-y=4 what is the smaller of these two numbers?
Answer:
y = 8 is the smaller number.
Step-by-step explanation:
Sove the system by adding the two equations together, one on top of the other. Add from the top, down.
x + y = 20
x - y = 4
________
2x = 24
Divide by 2.
x = 12
Put this back into either original equation.
x + y = 20
12 + y = 20
Subtract 12.
y = 8
The numbers are 12 and 8.
8 is the smaller number.
solve for x. Round your answer to the nearest tenth.
The length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.
Describe Triangle?The angles of a triangle are the angles formed by its sides. The sum of the angles of a triangle is always 180 degrees, which is a fundamental property of this shape. There are different types of triangles, based on their side lengths and angle measures. For example:
A scalene triangle has three sides of different lengths and three different angles.
An isosceles triangle has two sides of equal length and two equal angles.
An equilateral triangle has three sides of equal length and three equal angles.
A right triangle has one angle that measures 90 degrees (a right angle), and the side opposite to it is called the hypotenuse.
Triangles have many important properties and applications in mathematics, physics, and engineering. They can be used to calculate distances, angles, areas, volumes, and many other quantities. Triangles are also used in the construction of buildings, bridges, and other structures, as well as in art, design, and other fields.
We can use the trigonometric ratio of sine to solve for x:
sin(42) = opposite/hypotenuse
sin(42) = x/5
To solve for x, we can multiply both sides by 5 and simplify:
x = 5*sin(42)
x ≈ 3.4 (rounded to the nearest tenth)
Therefore, the length of the side opposite to the 42 degree angle in the right triangle is approximately 3.4 units.
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