If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:
Total number of hours of work / Number of hours of work done by 4 men in a day
= 224 / (4 x 8)
= 7
So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.
II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:
Total number of men x Total number of days x Number of hours worked by each man per day
= 4 x 7 x 8
= 224 hours
Therefore, the total cost of employing all 4 men is:
Total number of hours x Rate per hour
= 224 x $57.50
= $12,880
III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:
Total number of hours of work / Total number of days to complete the project
= 224 / 4
= 56 hours
Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:
Number of hours of work per day - Number of hours worked by each man per day
= 56 - 8
= 48 hours
Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.
IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:
l x $57.50
= $57.50l
Let the overtime rate of payment be $r per hour. Then:
r = $57.50l
The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:
Number of regular hours x Regular hourly rate
= 4 x 8 x 7 x $57.50
= $16,240
The cost of overtime hours is:
Number of overtime hours x Overtime hourly rate
= 4 x 6 x 7 x $57.50l
= $12,180l
So, the total cost of the project is:
Total cost = Cost of regular hours + Cost of overtime hours
= $16,240 + $12,180l
Answer:
Step-by-step explanation:
(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:
Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days
So it will take 4 men, each working 8 hours per day, 7 days to complete the project.
(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:
Total cost = 4 men x $57.50/hour x 56 hours = $12,320
(iii) If the project is to be completed in 4 days, each man will need to work for a total of:
224 total hours / (4 men x 4 days) = 14 hours per day
Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.
(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:
Overtime rate = $57.50 x 1.5 = $86.25/hour
To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:
Regular hours cost = 224 regular hours x $57.50/hour = $12,880
The cost of the overtime hours is:
Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour
= 96 x $86.25
Therefore, the total cost of the project is:
Total cost = Regular hours cost + Overtime cost
= $12,880 + $8,280
= $21,160
where the overtime rate is 1.5 times the regular hourly rate.
Can anyone help me with this quickly?????
The table of the piecewise function is shown below and the point of maximum growth rate for the function is (8.96, 7.5)
Completing the table of the piecewise function
Given that
g(x) = x² - 1 if x ≤ 3
g(x) = x - 5 if x > 3
For values greater than 3, we use the function g(x) = x - 5;
Otherwise, we use g(x) = x² - 1
This means that
x Workings g(x)
-2 g(-2) = (-2)² - 1 3
0 g(0) = (0)² - 1 -1
1 g(1) = (1)² - 1 0
3 g(3) = (3)² - 1 8
5 g(5) = 5 - 5 0
The point of maximum growth rateGiven that
f(x) = 15/(1 + 6e⁻⁰°²ˣ)
The point of maximum growth rate for a logistics function represented as f(x) = c/(1 + ae⁻ᵇ⁺) is
t = ln(a)/b
y(t) = c/2
So, we have
t = ln(6)/0.2 = 8.96
y(t) = 15/2 = 7.5
Hence, the point is (8.96, 7.5)
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Solve by Completing the Square
Matalea created a rectangle where the length was eight more than the width. She then determined that the area of a rectangle could be found by using the function A(x)= x2+8x where x is the width of the rectangle. If the area of the rectangle is 33 in.2, what is the width of the rectangle?
The width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.
What is Area of rectangle ?
Area of rectangle can be defined as product of length and breadth.
We know that the area of the rectangle is given by the function A(x) = x² + 8x, where x is the width of the rectangle. We also know that the area of the rectangle is 33 in². So we can set up the equation:
x² + 8x = 33
To solve for x, we can rearrange the equation and set it equal to zero:
x² + 8x - 33 = 0
We can now use the quadratic formula to solve for x:
[tex]x = (-b\±\sqrt{(b^2 - 4ac)}) / 2a[/tex]
where a = 1, b = 8, and c = -33. Substituting these values, we get:
[tex]x = (-8\±\sqrt{(8^2 - 4(1)(-33))}) / 2(1)[/tex]
[tex]x = (-8\± \sqrt{(256)}) / 2[/tex]
x = (-8 ± 16) / 2
So x = -12/2 or x = 4.
Therefore, the width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.
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I don’t know how to find x
The angles on the diagram are vertical angles and the value of x is 25.
What is the numerical value of x?The two angles are said to be adjacent angles when they have a common vertex and side.
On the other hand, vertical angles are angles that are opposite of each other when two lines cross and they are conguent.
Therefore, the angles on the diagram are vertical angles.
Now, since vertical angles are congruent.
Angle 75 and angle (4x - 25 ) are equal.
Hence;
4x - 25 = 75
Solve for x
4x - 25 = 75
Add 25 to both sides
4x - 25 + 25 = 75 + 25
4x = 75 + 25
4x = 100
Divide both sides by 4
4x/4 = 100/4
x = 100/4
x = 25
Therefore, the value of x is 25.
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I’ll give BRAINLIEST if correct as well as 5star ratings
Answer:
Below
Step-by-step explanation:
If the 'y'-axis is # larvae and the 'x' axis is °C then the peak would show the greatest # larvae (450) would be at 5 °C
Answer:
B) This means that the number of larvae is greatest at 5 degrees Celsius.
Step-by-step explanation:
On the given graph:
The x-axis represents the temperature in degrees Celsius.The y-axis represents the number of larvae.The curve is a parabola that opens downwards. Therefore, its vertex is the maximum value.
From observation of the graph, the vertex (peak) is (5, 450).
This means that the number of larvae reaches its maximum value of 450 at a temperature of 5 degrees Celsius.
the base of a solid right pyramid is a square with an edge length of n units. the height of the pyramid is n-1 units
There for the answer is the volume of the pyramid is equal to V = 1/3 (n³ - n²).
What do math lengths mean?
The measurement or size of a thing end to end is referred to as its length. In other words, it is the larger of an object's upper two or three geometric dimensions. The dimensions of a rectangle, for instance, are its length and width.
We know that.
The volume of pyramid is equal to
V =1/3 (area of base) × height
In this problem
Area of base = n² units²
Height = (n - 1) units
Substitute in the formula above
V = 1/3 n² × (n - 1)
V = 1/3 (n³ - n²) units³
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Please help! Easy geometry question!
a) If the slant range of the plane in the image is 14.5 km, and the ground range is 10.15 km, find the altitude of the plane to the nearest meter. Show your work and explain your thinking.
b) If this plane loses power and descends suddenly at a rate of 750 meters per minute, how much time will the pilot have before he has to land?
The altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.
What is right angled triangle ?
A right-angled triangle is a triangle that has one angle that measures 90 degrees (a right angle). This means that the other two angles must add up to 90 degrees as well. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The Pythagorean theorem, which states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse, is a fundamental concept in mathematics and has many practical applications. Right-angled triangles are used in fields such as engineering, architecture, and physics to calculate distances, heights, and angles.
a) Let's use the Pythagorean theorem to find the altitude of the plane. We have a right triangle with the slant range as the hypotenuse, the ground range as one leg, and the altitude as the other leg. So, we can use:
altitude² + ground range² = slant range²
altitude² + 10.15² = 14.5²
altitude² = 14.5² - 10.15²
altitude² = 84.9025
altitude ≈ 9.21 km or 9210 meters (rounded to the nearest meter)
b) If the plane descends at a rate of 750 meters per minute, the pilot will have:
time = altitude / descent rate
time = 9210 / 750
time ≈ 12.28 minutes (rounded to two decimal places).
Therefore, the altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.
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Rounding to nearest 10th
Given - the system of the equations as
[tex]y=-2x+1\\y=-11x-3[/tex]
To find - the solution of the set of equation
Explanation- given the set and we can see that left hand side of the equation is equal.
we get
[tex]-2x+1=-11x-3\\-2x+11x=-3-4\\9x=-7\\x=-7/9=-0.77[/tex]
we get
[tex]y=-2(0.77)+1\\y=-1.54+1\\y=-0.54[/tex]
Hence the value is x =-0.77, y=0.54
Final answer- the value of x = 0.77, y = -0.54
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The same solutions equations are B)2.3p – 10.1 = 6.49p-4 and C)230p-1010=650p-400-p.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is,
=> 2.3p – 10.1 = 6.5p – 4 – 0.01p
To remove decimal we need to multiply by 100 on both side of the equation then,
=> (2.3p – 10.1)*100 = (6.5p – 4 – 0.01p)*100
=> 2.3*100p-10.1*100=6.5*100p-4*100-0.01*100p
=> 230p-1010=650p-400-p
And simplifying then,
=>2.3p – 10.1 = 6.5p – 4 – 0.01p
=>2.3p – 10.1 = 6.49p-4
Hence the correct options are, B)2.3p – 10.1 = 6.49p-4 and C)230p-1010=650p-400-p.
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two mechanics worked on a car. the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. together they charged a total of $2175. what was the rate charged per hour by each mechanic if the sum of the two rates was $120 per hour?
Mech #1 charged 45$/hr and Mech #2 charged 75 $/hr. We can find the solution in the following manner:
Let's make,
mechanic #1's rate = x
mechanic #2's rate = y
Their rate is dollars per hour ($/hr)
Mechanic #1 worked for 20 hours (hr × $/hr = $)
20x = money earned by mechanic #1
And mechanic #2 worked for 15 hours
15y = money earned by mech#2
Together they charged a total of $2175. So the amount of money earned by both mechanics.
20x + 15y = 2175
The sum of the two rates was $120 per hour.
x + y = 120
which means
x = 120- y
Putting (120 - y) in for "x" in the other equation to get everything in terms of one variable.
20(120 - y) + 15y = 2175
Now we can solve for y and get the solution:
20(120 - y) + 15y = 2175
y=45 $/hr
Now use this to solve for x
x + y = 120
x + 45 = 120
x =75
x = 75 $/hr
Mech #1 charged 45$/hr
Mech #2 charged 75 $/hr
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Sara is making 3 batches of chocolate chip cookies and 3 batches of oatmeal cookies each batch of chocolate chip cookie uses 2 1/4 cups of flour. She will use 12 3/4 cups of flour for all six batches.
Which equation can be used to determine how many cups of flour are needed for each batch of oatmeal cookies?
Answer:
Step-by-step explanation:
If Sara is making 3 batches of chocolate chip cookies using 2 1/4 cups of flour per batch, then the total amount of flour she uses for the chocolate chip cookies is:
3 batches x 2 1/4 cups per batch = 6 3/4 cups of flour
Since she will use 12 3/4 cups of flour for all six batches, the amount of flour used for the oatmeal cookies can be found by subtracting the amount of flour used for the chocolate chip cookies from the total amount of flour:
12 3/4 cups - 6 3/4 cups = 6 cups
To determine how many cups of flour are needed for each batch of oatmeal cookies, we can divide the total amount of flour used for the oatmeal cookies by the number of batches:
6 cups ÷ 3 batches = 2 cups per batch
Therefore, the equation that can be used to determine how many cups of flour are needed for each batch of oatmeal cookies is:
Flour needed per batch of oatmeal cookies = Total flour needed for oatmeal cookies ÷ Number of oatmeal cookie batches
Or, in this case:
Flour needed per batch of oatmeal cookies = 6 cups ÷ 3 batches = 2 cups per batch.
43 rail cars is ___ % of 50 rail cars
Step-by-step explanation:
What we do here is divide 43 by 50
[tex] \frac{43}{50} = 0.86 = 86\%[/tex]
To solve one-step equations, you have to use the ________________ operation.
Answer:
Inverse Operation
Step-by-step explanation:
4+-2=5 what is the answer
The true statement of the equation 4+-2=5 is false
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
4+-2=5
To determine the trie statement, we evaluate the expression 4 + (-2)
Using the above as a guide, we have the following:
The sum of 4 and -2 is:
4 + (-2) = 2
So, we have
2 = 5
The above is not true
Hence, the statement "4 + (-2) = 5" is false.
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What is the answer to this photo
The required number of tubs are 17.55 tubs.
How to find number of tubs?To solve the problem, we need to find the total amount of ice cream used in ounces and then convert it to pounds to find the number of tubs used.
Number of scoops for regular cones = 2 scoops/cone
Number of scoops for large cones = 3 scoops/cone
Total number of scoops of ice cream used for regular cones = 2 scoops/cone x 234 cones = 468 scoops
Total number of scoops of ice cream used for large cones = 3 scoops/cone x 156 cones = 468 scoops
Total number of scoops of ice cream used = 468 scoops + 468 scoops = 936 scoops
Total amount of ice cream used in ounces = 936 scoops x 3 ounces/scoop = 2808 ounces
Total amount of ice cream used in pounds = 2808 ounces / 16 ounces/pound = 175.5 pounds
Number of tubs of ice cream used = 175.5 pounds / 10 pounds/tub = 17.55 tubs
Rounding up to the nearest whole number, we get:
Answer: (C) 17.55 tubs.
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Please help me!
Its a geometry question i need to get right but i dont understand D:
Answer:
(1 , -2)
Step-by-step explanation:
We are told that there is a translation of (x-4 , y-3)
This simply means that the x-axis moves to the left by 4 points and that the y-axis moves down 3 points. (if it was a plus not minus then points would move up and to the right)
1) Move the x-axis
We can see that the x-axis of b is 5. To move it to the left 4 we subtract 5 by 4
5 - 4 = 12) Move the y-axis
We can see that the y-axis of b is 1. To move it down we subtract 1 by 3
1 - 3 = -2This leaves us with (1 , -2)
Hope this helps, have a lovely day! :)
Find the missing ratio
3 4
9 ?
18 24
Answer:
the missing ratio is 12
Step-by-step explanation:
essentially all of these ratios should simplify to 3:4
what is the distance between A and B.
A.
B.
C.
D.
The distance between points A and B is: A. 4√5 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given parameters into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-4))² + (-2 - 2)²]
Distance = √[(8)² + (-4)²]
Distance = √(64 + 16)
Distance = √80
Distance = √16 × √5
Distance = 4√5 units.
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Answer:
none of them are right it is 4 to the 10
Step-by-step explanation:
Please solve i really need help
2 quart of blue paint and 5/4 quart of red paint is needed to make 3 1/4 quart purple paint
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
2/5 quart of blue paint is mixed with 1/4 quart of red paint to make purple paint. Hence:
Ratio of blue paint to red paint = (2/5) : (1/4) = 8 : 5
Therefore for 3 1/4 quart of purple paint:
Amount of blue paint = (8/13) * 3 1/4 = (8/13) * 13/4 = 2 quart
Amount of red paint = (5/13) * 3 1/4 = (5/13) * 13/4 = 5/4 quart
2 quart of blue paint and 5/4 quart of red paint is needed to make the purple paint
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The amount you must add to 8 to increase 8 by 25% is
Answer:
2
Step-by-step explanation:
Take out 25% of 8
25/100*8= 2
Required Amount=2
Cason wants to read at least 45 books. He has already read one book. If he reads 2 books a week, how many weeks will he need to read to meet his goal? Solve a linear inequality to find the number of weeks Cason must read.
A. x < 22
B. x > 22
C. x ≤ 22
D. x ≥ 22
I need an explanation to
Cason must read for at least 22 weeks to meet his goal. The correct answer is D. x ≥ 22
Solving by InequalityLet x be the number of weeks Cason needs to read to meet his goal. In each week, he can read 2 books. Therefore, the total number of books he will read in x weeks is:
2x
Since Cason has already read one book, the total number of books he will have read after x weeks is:
2x + 1
We want Cason to read at least 45 books, so we can set up an inequality:
2x + 1 ≥ 45
Subtracting 1 from both sides, we get:
2x ≥ 44
Dividing both sides by 2, we get:
x ≥ 22
Therefore, Cason must read for at least 22 weeks to meet his goal.
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Which of the following can be used to evaluate the series 8 E k=1 5 (2/3) k-1
5[1-[tex](2/3)^{8}[/tex]/1-2/3] can be used to evaluate the series 8 E k=1 5 (2/3) k-1 through geometric series.
What do you mean by geometric series?A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios. In other words, the following term is obtained by multiplying each phrase in a geometric series by a constant.
Hence, a geometric series has the formula a, ar, ar2, where an is the first term and r are the sequence's common-ratio. Either a positive or negative integer can be used to describe the common ratio.
The given series is:
Now,we want to write an expression that can be used to evaluate this series.
Since this is a geometric series, we use the formula for the sum of the first k terms: Sk = a (1-[tex]r^{k}[/tex]/1-r)
From the given series the first term a= 5 is, and the common ratio is r =2/5 and k=8
We substitute the values to obtain:
S8= 5[1-[tex](2/3)^{8}[/tex]/1-2/3]
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PLS PLS PLS PLS PLS HELP
The best interpretation of the y-intercept of the linear function is given as follows:
D. The model indicates that 1-bedroom apartments in New York had an average rent of 800 dollars in 2000.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.The variables for this problem are given as follows:
x is the number of years since 2000.y is the cost of renting.Hence option D gives the correct interpretation of the intercept of the line.
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Write an equation
Vertically stretched by a factor of 2, reflected across the x-axis, then translated 1 unit left and 8 units up.
The equation for the function with the described transformations is y(x) = -2f(x+1) + 8.
What is the new equation of the function?Starting with the basic function of f(x), we can apply the described transformations in the following order:
Vertical stretching by a factor of 2: We multiply the output of the function by 2. This results in a new function g(x) = 2f(x).
Reflection across the x-axis: We flip the sign of the output of the function. This results in a new function h(x) = -g(x) = -2f(x).
Translation 1 unit left and 8 units up: We shift the graph of the function 1 unit to the left and 8 units up. This can be achieved by replacing x with (x+1) and adding 8 to the output.
This results in a new function y(x) = h(x+1) + 8 = -2f(x+1) + 8.
Putting it all together, the equation for the function with the described transformations is:
y(x) = -2f(x+1) + 8
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The complete question is below:
Write an equation for f(x) when it is vertically stretched by a factor of 2, reflected across the x-axis, then translated 1 unit left and 8 units up.
Linear Inequality
X >/ -2
X-y >/ 1
The solution to the system of inequalities is:
{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.
What is linear inequality?A linear inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
First, let's graph the line x = -2, which is a vertical line passing through -2 on the x-axis.
Next, let's graph the line x - y = 1, which can be rewritten as y = x - 1. This is a line with a slope of 1 (meaning it goes up 1 unit for every 1 unit it goes to the right) and a y-intercept of -1 (meaning it passes through -1 on the y-axis).
Now, we need to shade in the region that satisfies both inequalities. We know that x has to be greater than or equal to -2, so we shade to the right of the vertical line x = -2. We also know that x - y has to be greater than or equal to 1, so we shade above the line y = x - 1.
The shaded region is the overlapping region that satisfies both inequalities. It is the region above the line y = x - 1 and to the right of the vertical line x = -2.
Therefore, the solution to the system of inequalities is:
{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.
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The complete question is as follows:
What is the solution to the system of inequalities?
x ≥ -2
x - y ≥ 1
Assume you take out a $3000 loan, compounded monthly, for 2 and a half years at 8.5% APR. What is the last month’s interest? Answer rounded to the nearest penny.
In response to the aforementioned query, we may say that The interest for the previous month, rounded to the nearest cent, is $289.84.
what is interest ?By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.
The Annual Percentage Rate (APR) can first be changed to a monthly interest rate as follows:
r = APR/12 = 0.085/12 = 0.0070833
Then, we may determine how many months the loan will last:
n = 2.5 years * 12 months a year = 30 months.
We can now calculate the total amount owing at the conclusion of the loan term using the compound interest formula:
A= P(1 + r)^n
where P is the loan's principle, r is the interest rate each month, and n is the number of months.
A = $3000(1 + 0.0070833)^30\s= $3,789.64
At the conclusion of the loan period, there will be a balance of $3,789.64.
B = $3000(1 + 0.0070833)^(30-1) - [((1 + 0.0070833)^30 - 1)/(0.0070833)]
= $3,499.80
I = $3,789.64 - $3,499.80\s= $289.84
The interest for the previous month, rounded to the nearest cent, is $289.84.
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Rotation: 180° about the origin
Answer:
A rotation about the origin 180 degrees means that the pre-image essentially rotates half an actual circle
The rule for 180 degrees rotation is (x,y)-->(-x, -y)
So the points of this quadrilateral are now
(1,3) = (-1, -3)
(4,1)=(-4, -1)
(4,4)=(-4, -4)
(1,4)=(-1,-4)
So it moves from 1st to 3rd quadrant
HOPE THIS HELPS
Pls give simple working
Screen shot this and then mark when it should go tyy
Answer:
How?
Step-by-step explanation:
Pls calculate the areas
The area of the circle with a radius of 10 meters is given as follows:
314.16 m².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr².
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle, on a segment that passes through the center. Hence, the diameter’s length is twice the radius length.
Considering the above concept, the measure of the radius for the circle in this problem is given as follows:
r = 10m.
Thus the area of the circle is given as follows:
A = π x 10²
A = 314.16 m².
More can be learned about the calculation of the area of a circle at https://brainly.com/question/15673093
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Gabriel's father has a garden in the back yard. The dimensions of the garden are shown here.
A green rectangle is shown. The width is labeled as 2 and two-thirds feet. The length is labeled as 7 and three-fourths feet.
Part A
Calculate the area of the garden. Show at least one step before you show your solution.
Part B
You found the area of the garden in Part A. Explain briefly, without doing any calculations, how you would find
5/6 of this area.
The Area of Garden is 62/3 feet².
What is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm² and m² are used to measure area. A shape's area is a two-dimensional measurement.
Given:
Length = 7 3/4 feet = 31/4 feet
Width = 2 2/3 feet = 8/3 feet
So, Area of Garden
= l w
= 31/4 x 8/3
= 62/3 feet²
and, Now, 5/6th of the Garden
= 62/3 x 5/6
= 31 / 3 x 5 / 2
= 155 / 6 feet²
Learn more about Area here:
https://brainly.com/question/27683633
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The perimeter of a rectangle is 100 cm. The length is 5 more than twice the width. What are the dimensions of the rectangle?
Answer:
in image...
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