There are infinitely many possible locations for your house that would allow you to travel one mile south, one mile east, and one mile north and end up back at your starting point.
As per the question given,
This is a classic puzzle known as the "One-Mile Puzzle". There are actually infinitely many possible locations for your house that satisfy these conditions.
One way to think about it is to consider the fact that the one-mile distances you traveled form the sides of a triangle. Since you traveled one mile due south, one mile due east, and one mile due north, the triangle you formed is an isosceles right triangle, with the right angle at the point where you ended up.
If you let (x, y) be the coordinates of your house, then the point where you ended up after traveling one mile south, one mile east, and one mile north is (x, y-1) + (1, y) + (x, y+1), which simplifies to (2x+1, 2y).
So, any point (x, y) that satisfies the equation 2x + 1 = 2y will work as a possible location for your house. For example:
If x = 0, then y = 1/2, so your house could be located at (0, 1/2).
If x = 1, then y = 3/2, so your house could be located at (1, 3/2).
If x = -1, then y = -1/2, so your house could be located at (-1, -1/2).
And so on...
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You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly.
Answer:
A(t) = 9000(1 + 0.036/12)^12t
[Function formula for the compound interest]
A = 9000(1 + 0.036/12)^12t
[General formula for the compound interest]
A(1) ≈ 9329.40 $
[Compound interest over 1 year]
Step-by-step explanation:
Compound interest formula:
A = P(1 + r/n)^nt.
P is the principal or starting amount.
r is the interest rate.
n is the number of times compounded per year.
t is the period of time.
Given P is 9000, r is 3.6% or 0.036, n is 12 or monthly, and t is variable.
The following function represents the relationship over time:
A(t) = 9000(1 + 0.036/12)^12t
Which of the following statements is true? Uso la computadora en la cafetería. Hago ejercicio en el laboratorio de ciencias. Nado en la piscina..
Answer:
Nado en la piscina..Step-by-step explanation:
ICA 2023
need answers ASAP!!!!!!!!!!!!!!
How does the quantity of shares you own impact your dollar gains and losses?
how does the length of time you hold the shares impact your rate of return?
How does the quantity of shares you own impact your rate of return?
The quantity of shares you own can impact your dollar gains and losses, but not your rate of return. The length of time you hold the shares can have a significant impact on your rate of return, with longer holding periods generally leading to higher returns.
Investing in stocks can be a great way to earn money, but it's important to understand how your investments can impact your gains and losses. Two key factors that can impact your returns are the quantity of shares you own and the length of time you hold the shares. In this article, we'll explore how these factors can affect your rate of return.
Impact of Quantity of Shares:The quantity of shares you own can have a direct impact on your dollar gains and losses. When the stock price goes up, the value of your shares also increases. Similarly, when the stock price goes down, the value of your shares also decreases. If you own more shares, the dollar amount of your gains and losses will be greater.
But, how does the quantity of shares impact your rate of return? Rate of return is the percentage change in the value of your investment over a certain period of time. It takes into account the gains and losses as well as the length of time you held the investment.
Impact of Length of Time:The length of time you hold the shares can have a significant impact on your rate of return. Generally, the longer you hold the shares, the higher your rate of return will be. This is because the stock market tends to go up over time, and the longer you hold the shares, the more time you have to benefit from this growth.
Impact of Quantity and Time on Rate of Return:So, how does the quantity of shares you own impact your rate of return? As we mentioned earlier, the rate of return is only impacted by the percentage change in the stock price, not the quantity of shares. However, owning more shares can provide you with a higher dollar amount of gains, which can lead to a higher rate of return.
Additionally, the longer you hold the shares, the higher your rate of return will be. This means that if you own more shares and hold them for a longer period of time, you can potentially earn a higher rate of return.
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Determine the solutions of the equation:
the absolute value quantity four thirds times x plus 2 end quantity minus 6 equals 0
The solutions of the given absolute value equation |4/3 x + 2| - 6 = 0 are x = 3 and x = -6.
What is Absolute Value Equations?Absolute value equations are kind of equations which includes the absolute value symbol in the expression.
For example : |x - 5| = 4 is an absolute value equation.
The given absolute value equation is,
four thirds times x plus 2 end quantity minus 6 equals 0.
|4/3 x + 2| - 6 = 0
Isolating the absolute value quantity on one side,
|4/3 x + 2| - 6 + 6 = 0 + 6
|4/3 x + 2| = 6
This can be written as,
4/3 x + 2 = 6 and 4/3 x + 2 = -6
Solving each of these,
4/3 x + 2 = 6
4/3 x = 4
x = 3
4/3 x + 2 = -6
4/3 x = -8
x = -6
Hence the value of x are 3 and -6.
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After arguing for two weeks, Tony convinced his parents to have his birthday party at FlyZone trampoline park. As soon as he gets there, Tony spends time practicing flips on the trampolines. Then, he spends
3
4
of an hour eating birthday cake with his friends. In all, Tony spends 1
1
4
hours at FlyZone.
Which equation can you use to find the amount of time t Tony practices flips?
The amount of time that Nora practices flips is; t = 1 ¹/₄
How to Solve Algebra problems?
The BODMAS rule would be used to simplify the expression, BODMAS is an abbreviation for bracket, of, division, multiplication, addition and subtraction. It dictates the order in which a mathematical expression should be solved.
We are told that;
Nora spends time practicing flips on the trampolines. Let this be t.
Then, she spends 1/2 of an hour eating birthday cake with her friends.
Thus, total amount of time spent on flips and eating with her friends is;
t + ¹/₂ = 1 ³/₄
t = 1 ³/₄ - ¹/₂
t = 1 ¹/₄
Thus , the amount of time that Nora practices flips is; t = 1 ¹/₄
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Given question is incomplete , Complete Question is;
After arguing for two weeks, Nora convinced her parents to have her birthday party at FlyZone trampoline park. As soon as she gets there, Nora spends time practicing flips on the trampolines. Then, she spends 1/2 of an hour eating birthday cake with her friends. In all, Nora spends 1 3/4 hours at FlyZone. Which equation can you use to find the amount of time Nora practices flips?
Solve this equation for (t) to find the amount of time Nora practices flips
Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
F) (x, y ) → (2x, 2y)
G) (x, y ) → (1. 5x, 1. 5y)
H) (x, y ) → (3x, 3y)
J) (x, y ) → (4x, 4y)
The best way to represents the change in the vertices of rectangle ABCD to rectangle A'B'C'D' in the attached graph is given by :
option A. (x, y ) → (2x, 2y).
From the attached graph we have,
Coordinates of rectangle ABCD are :
Coordinate of vertex A ( -3, -2 )
Coordinate of vertex B ( -3, 2 )
Coordinate of vertex C ( 3, 2 )
Coordinate of vertex D ( 3, -2 )
And coordinates of A'B'C'D' are:
Coordinate of vertex A' ( -6, -4 )
Coordinate of vertex B' ( -6, 4 )
Coordinate of vertex C' ( 6, 4 )
Coordinate of vertex D' ( 6, -4 )
Coordinate of rectangle ABCD gets dilated by the scale factor of :
Scale factor of 'x' coordinate = -6 / -3
= 2
Scale factor of 'y' coordinate = -4 / -2
= 2
Change in the vertices of rectangle ABCD to A'B'C'D' is given by :
( x , y ) → ( 2x , 2y )
Therefore, the vertices of rectangle ABCD changed to A'B'C'D' is equal to option A. ( x , y ) → ( 2x , 2y ).
The above question is incomplete, the complete question is:
Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
A) (x, y ) → (2x, 2y)
B) (x, y ) → (1. 5x, 1. 5y)
C) (x, y ) → (3x, 3y)
D) (x, y ) → (4x, 4y)
Graph is attached.
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let |q|=5 at angle at 45° and |r|=16 at an angle of 300°. what is |q-r|?
Answer:
18.0
Step-by-step explanation:
this is correct!
Daniella and her 10 friends are collecting shells on the beach to make crafts. After
they have collected the shells and put them in a pile, they split them evenly among
the group. Each person gets 4 shells. How many shells did they collect as a group?
Select the correct equation and solve for s.
4+ s = 11; s = 7
s/10 = 4; s = 40
4s = 11; s = 2.75
s/11 = 4; s = 44
Daniella and her friends collected a total of 44 shells.
What is linear equation ?
Linear equation can be defined as equation in which highest degree is one.
Given ,
Daniella and her 10 friends are collecting shells on the beach to make crafts.
After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.
The correct equation for this problem is:
s = 11 x 4
where s is the total number of shells collected.
Simplifying this equation, we have:
s = 44
Therefore, they collected a total of 44 shells.
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Find the indicated probability. The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of his car and its make (foreign or domestic)A car was randomly selected from the lot. Given that the car selected is older than two years old, find the probability that it is not a foreign car.
The probability that, if the car selected is older than two years old, it is not a foreign car is 57/118, so the correct option is A.
How to find the probability?We want to find the probability that if the car selected is older than two years old, it is not a foreign car.
Looking at the table, we can see that there are 200 - 82= 118 cars older than two years.
And of these 118 cars, 25 + 10 + 26 = 61 are foreign cars.
Then the number of non-foreign cars is:
118 - 61 = 57
And the probability will be equal to the quotient between the number of non-foreigner cars and the total number:
P = 57/118
So the correct option is A.
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B) Mr. S Ralph spends $165. 31 on oranges INCLUSIVE of a 15% sales tax. Her total is $165. 31 with tax. (115% = original price is 100% plus tax of 15%). Calculate the ORIGINAL PRICE of the oranges, which means the cost of the oranges
without the tax
The total cost of the item would be [tex]$115[/tex].The original price of oranges purchased by Mr. S Ralph can be calculated by subtracting the sales tax from the total cost.
Sales tax is calculated as a percentage of the original price. In this case, the sales tax is 15%, meaning that the original price can be found by dividing the total cost (which includes the sales tax) by 1.15.To calculate the original price of the oranges, divide the total cost of $165.31 by 1.15. This gives us a total of $143.87. Thus, the original price of the oranges purchased by Mr. S Ralph is $143.87 without the sales tax included.Sales tax is a form of taxation imposed by governments on goods and services. Generally, for the majority of goods and services, the sales tax is calculated as a percentage of the original price. This means that the total cost of the goods or services can be calculated by adding the percentage of sales tax to the original price.For example, if an item costs $100, and the sales tax rate is 15%, the total cost of the item would be calculated by multiplying the original price by 1.15 (100% + 15% = 115%). The total cost of the item would be [tex]$115[/tex].
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A pyrotechnician plans for two fireworks
to explode together at the same height In the air. They travel
at
speeds shown below. Firework B is launched 0.25 s before Firework A. How many seconds after
B Firework B launches will both fireworks explode?
Firework A
Firework B
340 ft/s
260 ft/s
The mentioned scenario can be calculated using the distance equation, the number of seconds in which explosion would occur is 1.125 seconds.
What is the relationship between time, speed and distance ?The distance covered by the object is equal to the product of the speed of object and the time required for it.
Distance = Time x speed
Firework A :
D = 360xt - - - (1)
Firework B:
D = 280x(0.25) + 280xt
D= 70 + 280xt - - - (2)
Equate equation (1) and (2) :
360t = 280t + 70
Collect like terms
360t - 280t = 70
80t = 70
t = 70/80
t = 0.875 seconds
0.875 + 0.25 = 1.125 seconds
Hence, the fireworks will explode after 1.125 seconds of launching Firework B.
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our company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at a randomly selected time throughout a 12-hour period. Then it calculates the mean systolic (top number) pressure for the sample of measurements. Based on the sample results, the device determines whether there is significant evidence that the individual’s actual mean systolic pressure is greater than 130. If so, it recommends that the person seek medical attention.
(a) State appropriate null and alternative hypotheses in this setting. Be sure to define your parameter.
(b) Describe a Type I and a Type II error, and explain the consequences of each.
(c) The blood pressure device can be adjusted to decrease one error probability at the cost of an increase in the other error probability. Which error probability would you choose to make smaller, and why?i
What is Null hypothesis?
The null hypothesis assumes that any difference between the selected attributes in a set of data is attributable to chance. For example, if the predicted earnings for the gambling game are genuinely zero, then any discrepancy between the data's average earnings and zero is due to chance.
(a) The appropriate null and alternative hypotheses for this setting are:
Null hypothesis: The actual mean systolic pressure (μ) of the individual is not greater than 130 (μ ≤ 130).
Alternative hypothesis: The actual mean systolic pressure (μ) of the individual is greater than 130 (μ > 130).
(b) Type I error occurs when the null hypothesis is rejected when it is actually true. In this case, it means that the device recommends that the person seeks medical attention when they do not actually need it. The consequence of this error is that the person may undergo unnecessary medical tests or treatments, which can be costly, time-consuming, and can cause anxiety or other negative effects.
Type II error occurs when the null hypothesis is not rejected when it is actually false. In this case, it means that the device does not recommend medical attention when the person actually needs it. The consequence of this error is that the person may not receive the necessary medical attention and treatment, which can lead to serious health problems, including organ damage or failure, stroke, or heart attack.
(c) In this scenario, the cost of making a Type II error is likely to be much higher than the cost of making a Type I error. The reason is that failing to detect high blood pressure in a person can have serious health consequences. Therefore, it is better to make the Type I error probability smaller and the Type II error probability larger. This means that the device should be adjusted to have a higher threshold for recommending medical attention, which would decrease the likelihood of a false alarm, even if it increases the likelihood of missing some cases where medical attention is needed.
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The initial assertion that forms the null hypothesis frequently rests on research from the past or expert knowledge. According to the alternative hypothesis, a population parameter is either less, larger, or different from the value predicted by the null hypothesis.
What are the distinctions between Type I and Type II errors and what impact do they have?A type I error (false-positive) occurs when a researcher rejects a null hypothesis that is actually true in the population; if the researcher does not do this When a null hypothesis is rejected even when it is false in the population, this is known as a type II error (false-negative).
What does a hypothesis parameter mean?Parameter Hypothesis testing is a second sort of statistical inference.
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Estelle is having her birthday party at Gold Frames Art
costs $265
Museum this year. A party package
and covers the entrance fee for guests, a private party room, and an activity
guide. Estelle
upgraded her package to include a favor for each of her 8 guests, bringing the
total to $305.
Answer:
Step-by-step explanation:
im guessing youre finding the price of the favour.
(305-265)/8=answer
"/" means divide.
9 A square is graphed on the set of axes below, with vertices at
(-1,2), (-1,-2), (3,-2), and (3.2).
Which transformation would not carry the square onto itself
Answer:
With the information given, I would say a dialation.
Step-by-step explanation:
Rotation of 180 degree around point (1, 0). Therefore, option (3) is the correct answer.
What is a transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
Given that, the square with vertices (-1, 2), (-1, -2), (3, -2) and (3, 2).
(1) Reflection over the y-axis
Then the vertices become (1, 2), (1, -2), (-3, -2) and (-3, 2)
So, the transformation carries the square onto itself.
(2) Reflection over the x-axis
Then the vertices become (-1, -2), (-1, -2), (3, 2) and (3, -2)
So, the transformation carries the square onto itself.
(3) Rotation of 180 degree around point (1, 0)
(x, y) becomes (-y, x) 180° clockwise
So, the coordinate points are (-2, -1), (2, -1), (2, 3) and (-2, 3)
So, the transformation does not carries the square onto itself.
Therefore, option (3) is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
A square is graphed on the set of axes below, with vertices at (-1,2), (-1,-2), (3,-2), and (3.2). Which transformation would not carry the square onto itself.
(1) Reflection over the y-axis
(2) Reflection over the x-axis
(3) Rotation of 180 degree around point (1, 0)
(4) Reflection over the line y=x-1
David and Alec are comparing the international calling plans on their cell phones. On his plan,
David pays $4 just to place a call and $1 for each minute. When Alec makes an international
call, he pays $1 to place the call and $2 for each minute. A call of a certain duration would
cost exactly the same under both plans. What is the duration?
Write a system of equations, graph them, and type the solution.
3 minutes is the cost of the call that is same for both plans
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's assume the call duration in minutes is represented by x.
For David, the cost of the call can be represented by the equation: C(d) = 4 + x
For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x
Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:
4 + x = 1 + 2x
Solve for x.
3 = x
Hence, the call duration that costs the same on both plans is 3 minutes.
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Jamarie and DJ go bowling. Jamarie knocks a total of 26 pins. DJ knocks down three times as
many. How many did they knock down together?
Show your work
In total they knocked down 104 pins.
I got this by multiplying 26 by 3, which equals 78, then adding 26 to 78 to get the final answer, 104.
Hope this helps!
a bin of 50 manufactured parts contains 3 defective parts and 47 nondefective parts. a sample of 6 parts is selected from the 50 parts. write down an expression for the number of different samples of size 6 that contain exactly 2 defective parts.
The expression for the number of different samples is: C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x
(47! / (4! x 43!)).
The number of different samples of size 6 that contain exactly 2 defective parts can be calculated using the binomial coefficient formula:
C(3, 2) x C(47, 4)
where C(n, k) represents the number of ways to choose k objects from a set of n objects.
In this case, we first choose 2 defective parts from the 3 defective parts in the bin, which can be done in C(3, 2) ways. Then we choose 4 nondefective parts from the 47 nondefective parts in
the bin, which can be done in C(47, 4) ways. We multiply these two quantities together to obtain the total number of different samples of size 6 that contain exactly 2 defective parts.
Therefore, the expression for the number of different samples of size 6 that contain exactly 2 defective parts is:
C(3, 2) x C(47, 4) = 3 x C(47, 4) = 3 x (47! / (4! x 43!))
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Question 7(Multiple Choice Worth 2 points) (09.06 LC) How many hectometers are in 580 millimeters? O 0.0058 hectometers O0.058 hectometers O58,000 hectometers O 580,000 hectometers
Answer: B. 0.058 hectometers
Step-by-step explanation: To convert millimeters to hectometers, you need to divide the number of millimeters by 10,000.
Given that there are 580 millimeters, the conversion to hectometers can be calculated as follows:
580 millimeters ÷ 10,000 = 0.058 hectometers
Here are some transformation rules. For each transformation, first predict what the image of triangle ABC will look like. Then compute the coordinates of the image.
(x, y) —-> (x -4, y -1)
A’ = ???
B’ = ???
C’ = ???
(x, y) —-> (y, x)
A’ = ???
B’ = ???
C’ = ???
(x, y) —-> (1.5x, 1.5y)
A’ = ???
B’ = ???
C’ = ???
Answer:
See below
Step-by-step explanation:
Givens:
A (2,3)
B (4,2)
C (3,5)
1. Subtract each x and y value by 4: (x-4,y-4)
A (-2,-1)
B (0,-2)
C (-1,1)
2. Flip the x and y values: (y,x)
A (3,2)
B (2,4)
C (5,3)
3. Multiply each point by 1.5: (1.5x,1.5y)
A (3,4.5)
B (6,3)
C (4.5,7.5)
Find the equation of the line that cuts the x-axis at x = 1 and whose slope is -1.
The equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.
What is slope-intercept form?The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
Since the line has a slope of -1 and cuts the x-axis at x = 1, we can find the y-intercept by using the point-slope form of the line equation:
y - y₁ = m(x - x₁)
y - 0 = -1(x - 1)
y = -x + 1
So the equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.
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Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
We can simplify the expression to get:
[tex]\sqrt[4]{x^3}[/tex]
How to simplify the expression?Here we want to simplify the following expression:
[tex]\sqrt[]{x} *\sqrt[4]{x}[/tex]
Remember that a square root is equivalent to a power of 1/2, and the fourth root is equivalent to a power of 1/4.
Then we can write:
[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4}[/tex]
Now in the product we just add the exponents:
[tex]\sqrt[]{x} *\sqrt[4]{x} = x^{1/2}*x^{1/4} = x^{1/2 + 1/4} = x^{3/4} = \sqrt[4]{x^3}[/tex]
That is the expression si,plified.
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how many ways can aileen choose 2 pizza toppings from a menu of 18 toppings if each topping can only be chosen once?
The number of ways to choose 2 toppings from a menu of 18 toppings is a classic example of a combinatorial problem.
We have a set of 18 items (toppings), and we want to know how many ways there are to choose 2 of these items. The answer is given by the binomial coefficient C(18, 2), which is the number of ways to choose 2 items from a set of 18 items, where order does not matter and repetition is not allowed.
The formula for a binomial coefficient is:
C(n, k) = n! / (k! * (n - k)!)
where n! means n factorial, which is the product of all positive integers from 1 to n. So, for example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
Using this formula, we can calculate the number of ways to choose 2 toppings from a menu of 18 toppings:
C(18, 2) = 18! / (2! * (18 - 2)!) = 18 * 17 / (2 * 1) = 153 ways
So there are 153 different ways to choose 2 toppings from a menu of 18 toppings.
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if there are 12 strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?
The probability that no two of them celebrate their birthday in the same month is very low.
There are 12 months in a year, so the probability that the first person has a birthday in a particular month is 1/12. The probability that the second person does not have a birthday in the same month is 11/12, since there are 11 months left that the second person's birthday can fall in. The probability that the third person does not have a birthday in any of the two previously chosen months is 10/12, and so on.
Therefore, the probability that none of the 12 people have a birthday in the same month is:
P = (1/12) x (11/12) x (10/12) x ... x (2/12) x (1/12)
which is approximately 0.00010578, or about 0.01%.
So the probability that no two of them celebrate their birthday in the same month is very low.
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What is the solution to this equation? 5(x-3)=21 what does x equal
Answer:7.2
Step-by-step explanation:
x-3=21/5=4.2
x=4.2+3=7.2
Mae Ling earns a weekly salary of $320 plus a 6. 0% commission on sales at a gift shop. How much would she make in a work week if she sold $4,500 worth of merchandise?
Mae Ling make $590 in a work week if she sold $4,500 worth of merchandise.
The given is:
We need to find how much she would earns in a work week
Mae Ling earns a weekly salary of $320
She earns a 6.0% commission on sales
She sold by $4,500 in that week
Add $320 to the product of 6.0% and $4,500
She made = 320 + (6.0% × 4,500)
6.0% = 6.0 ÷ 100 = 0.06
She made = 320 + (0.06 × 4,500)
She made = 320 + 270
She made = 590
She would make $590 in a work if she sold $4,500 worth of merchandise.
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The diameter of a fountain is 9 meters. A sidewalk that is 0.7 meters will be built around it. Find the diameter
Round to the nearest tenth
An estimated Rs. 1863.40 will be needed to cement the route.
What is meant by Cost?A mathematical formula known as a cost function can be used to determine the overall cost of production for a given quantity of goods produced. We'll go into more detail about the cost function below. Representation of unit expenses in relation to the production of 1 or more units during a construction project. For instance, the most popular cost function has the formula y = a + bx, where y is the total cost, an is the total fixed cost, b is the variable cost per unit of production or sales, and x is the number of units produced or sold. This formula sums the fixed costs and the variable costs to represent the total cost.Diameter of park [tex]$=7 \mathrm{~m}$[/tex]
so, radius of park [tex]$=\mathrm{r}_1=3.5 \mathrm{~m}$[/tex]
Width of park [tex]$=0.7 \mathrm{~m}$[/tex]
Bigger radius of park [tex]$=\mathrm{r}_2=0.7+3.4=4.2 \mathrm{~m}$[/tex]
Now, Area of path = area of bigger circle -area of smaller circle
[tex]$=\pi r_2^2-\pi r_1^2=$ $\pi\left(r_2^2-\mathrm{r}_1^2\right)=\frac{22}{7}\left(4.2^2-3.5^2\right)=\frac{22}{7}(17.64-12.25)=16.94 \mathrm{~m}^2$[/tex]
Also, Cost of expenditure = rate [tex]$\times$[/tex] area [tex]$=110 \times 16.94=1863.40$[/tex]
Cost of Expenditure of cementing the path is Rs. 1863.40.
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Sharel has opened a new bake shop in town selling cakes. Sharel sells
each cake for $11 and has spent $606 on rent and maintenance this
month. How many cakes did Sharel sell if she made $494 profit this
month?
Answer:
she sold 100 cakes in all
Step-by-step explanation:
606 + 494 = 1100 ÷ 11 = 100
In a geometric sequence, the first term, a_1, is equal to 3, and the third term, a_{3}, is equal to 192 Which number represents the common ratio of the geometric sequence?
Answer:
r = 8
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
given a₁ = 3 and a₃ = 192 , then
a₁ = 3 → (1)
a₁r² = 192 → (2)
divide (2) by (1) on both sides
[tex]\frac{a_{1}r^2 }{a_{1} }[/tex] = [tex]\frac{192}{3}[/tex] ( cancel a₁ on numerator/ denominator of left side ), then
r² = 64 ( take square root of both sides )
r = [tex]\sqrt{64}[/tex] = 8
an advertising company designs a campaign to introduce a new product to a metropolitan area of population 5 million people. let p(t) denote the number of people (in millions) who become aware of the product by time t. suppose that p increases at a rate proportional to the number of people still unaware of the product. the company determines that no one was aware of the product at the beginning of the campaign, and that 10% of the people were aware of the product after 10 days of advertising. the number of people who become aware of the product at time t is:
The number of people who become aware of the product at time t is [tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]
The advertising company wants to introduce a new product to a population of 5 million people. They assume that no one was aware of the product at the beginning of the campaign. They also know that after 10 days of advertising, 10% of the people became aware of the product. To find out how many people become aware of the product at time t, they use a function called p(t).
The function p(t) represents the number of people (in millions) who become aware of the product by time t. The company assumes that the rate at which p increases is proportional to the number of people still unaware of the product. This means that the more people who are unaware of the product, the faster the number of people who become aware of it will increase.
To express the proportionality mathematically, we can use the equation:
p'(t) = k [5 - p(t)]
Where p'(t) is the rate of change of p with respect to time t, and k is the proportionality constant that determines the speed of the increase. The quantity (5 - p(t)) represents the number of people who are still unaware of the product at time t. This means that as p(t) gets closer to 5 million, the rate of increase of p(t) will slow down.
To solve this equation, we need to use calculus. Integrating both sides of the equation, we get:
ln|5 - p(t)| = kt + C
Where C is the constant of integration. To determine the value of C, we use the initial condition that p(0) = 0. This means that at the beginning of the campaign, no one was aware of the product. Substituting this into the equation, we get:
ln|5 - 0| = k(0) + C
Simplifying, we get:
C = ln(5)
Substituting this value into the equation, we get:
ln|5 - p(t)| = kt + ln(5)
To find the value of p(t) at a specific time t, we can solve for p(t) by taking the exponential of both sides of the equation:
[tex]|5 - p(t)| = e^{kt+ln(5)}[/tex]
Simplifying, we get:
[tex]5 - p(t) = 5e^{kt}[/tex]
Or:
[tex]p(t) = 5(1 - e^{kt})[/tex]
To find the value of k, we can use the fact that 10% of the people were aware of the product after 10 days of advertising. This means that:
p(10) = 0.1(5) = 0.5
Substituting this into the equation, we get:
[tex]0.5 = 5(1 - e^{10k})[/tex]
Solving for k, we get:
k = -0.1 ln(0.9)
Substituting this value into the equation for p(t), we get:
[tex]p(t) = 5(1 - e^{-0.1ln(0.9)t})[/tex]
Simplifying, we get:
[tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]
This is the formula that tells us how many people will become aware of the product at time t.
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