The Bank discount and proceeds of the given information is:
$2365.27 and $47634.73 respectively.
Given the face value is $50,000
Discount rate = 13%
No.of term days = April 5 to August 14
= 131 days.
Bank discount = ?
Proceeds = ?
First calculate the bank discount using the formula:
Bank discount = face value × discount rate × time
Bank discount = $50,000 × 0.13 × 131/360
= 50,000×0.13×0.36388
= $2365.27
now calculate the proceeds using the formula :
Proceeds = face value - bank discount
= 50,000 - 2365.27
= $47634.73
Hence the bank discount and proceeds are $2365.27 and $47634.73 respectively.
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Given that f(x)=x²+3+2 write the formula defining the following function:
h if h can be formed by a horizontal translation of f right 4 units followed by a vertical translation up 7 units.
H(X)=?
The new function that can be formed after f(x) transforms horizontally 4 units to the right and then vertically 7 units upwards is
H(x) = h(x) = x² + 11x + 37.
How to shift an equation horizontally?
For a function, f; a brand new function d(x) = f(x - h), where h is a constant, is a horizontal shift of the function f; for positive 'h' the graph shifts right and for negative 'h' the graph shifts left.
How to shift an equation vertically?
For a function, f; a brand new function d(x) = f(x) + k, where k is a constant, is a vertical shift of the function f; for positive 'h' the graph shifts up and for negative 'h' the graph shifts down.
Given, the equation is f(x) = x² + 3x + 2
The new equation formed will be = h(x)
Also, the function horizontally shifts 4 units to the right.
Therefore, h(x) = f(x + 4) = (x + 4)² + 3(x + 4) + 2 = x² + 11x + 30
Again, the function formed in h(x) vertically shifts up by 7 units.
Thus, new equation for h(x) is = h(x) + 7 = x² + 11x + 37
Therefore, the required equation for H(x) = h(x) = x² + 11x + 37
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Select the correct answer.
This table represents function f.
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), which statement is true over the interval (-3, 0]?
The average rate of change of f is less than the average rate of change of g.
The average rates of change of f and g cannot be determined from the given information.
Te average rate of change of f is the same as the average rate of change of g
The average rate of change of f is more than the average rate of change of g
The average rate of change of f is less than the average rate of change of g.
What is average rate ?
This expression represents the average rate of change of the function f over the range a≤x≤b is less than or equal to x, and is less than or equal to b:
f(b)−f(a) / b - a
It is the average amount by which the function changed per unit throughout that time period.
Here, in Average rate of change in function g over [-3, 0]
=> a = -3, b = 0
=> f(a) = 5 , f(b) = 14
Average rate of change = (14 - 5) / (0 - (-3))
= 3
Now, in Average rate of change in function f over [-3, 0]
=> a = -3, b = 0
=> f(a) = -3, f(b) = 0
Average rate of change = (0 - (-3)) / (0 - (-3))
= 1
Therefore, The average rate of change of f is less than the average rate of change of g.
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Simplify: 4/x-2/x^2+1-2/x+1
On simplifying the given expression 4/x-2/x^2+1-2/x+1 we get solution as (2x^2 + 2x - 2)/x^2.
What is the meaning of simplifying a n equation?
To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.
We have given:
[tex]\frac{4}{x} - \frac{2}{x^2} +1 - \frac{2}{x} + 1[/tex]
Adding the numbers:
[tex]\frac{4}{x} - \frac{2}{x^2} - \frac{2}{x} + 2[/tex]
Making a common denominator:
[tex]\frac{4x}{x^2} - \frac{2}{x^2} - \frac{2x}{x^2} + \frac{2x^2}{x^2}[/tex]
Combining the values with common denominator:
[tex]\frac{2x^2 + 2x - 2}{x^2}[/tex]
This the the simplified result of the given expression.
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write 0.0000072 in scientific notation
Answer:
7.2 × 10^-6
Step-by-step explanation:
7.2 are the two last digits of the notation
and the reason its to the power of -6 is because there are 6 digits until you reach 7
You buy a container of cat litter for $13.75 and a bag of cat food for x dollars. The total purchase is $20.80, which includes 4% sales tax. Write and solve an equation to find the cost of the cat food.
The cost of the bag of cat food is $6.22
What is cost prize ?
The prize at which the good and services have been bought is known as cost prize.
here, the given information is :
Cost of a container of cat liter = $13.75
Cost of a bag of cat food = X dollars
Total amount of money required to purchase the items = $20.80
Percentage of sales tax that had to be given = 4%
Then,
Amount of sales tax given = (4/100) * 20.8 dollars
= 20.8/25 dollars
= 0.83 dollars
Then the total purchase price for the two items = 20.80 - 0.83 dollars
= 19.97 dollars
Now we can easily find the cost of the cat food by subtracting the cost of the liter from the total purchase amount :
Cost of the cat food = 19.97 - 13.75 dollars
= 6.22 dollars
Therefore, the cost of the bag of cat food is $6.22
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HELP PLS I NEED THIS ANSWERED QUICKLY
A membership at Gym A costs $50 for 5 months. A membership at Gym B down the street costs $40 for 3 months. You write two equations in the form of y=kx to try and figure out which membership would be cheaper for a year. What is the value of k for the cheaper membership?
The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A linear equation is an equation that increases at a constant rate.
An equation in the form y = kx is called a linear equation.
In the equation of form y = kx
y = dependent variable which is the total cost
x = number of months
k = constant of proportion / cost per month
Thus k = y/x
The Cost per month at Gym A = $50 / 5 = $10
The Cost per month at Gym B = $40 / 3 = $13.33
The Membership cost at Gym A for a year = $10 x 12 = $120
The Membership cost at Gym B for a year = $13.33 x 12 = $160
Hence, The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.
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Please see image below I am checking my wirk I think the answer is -119
-119
1) Let's evaluate that polynomial when y=4, note that to evaluate is to find out the corresponding value when we plug into that another one:
[tex]\begin{gathered} -5y^2-8y-7,y=4 \\ -5(4)^2-8(4)-7 \\ -5(16)-32-7 \\ -119 \end{gathered}[/tex]2) Hence, the answer is -119
Finding Missing Angles !
Answer: m11= 180-90= 90 (linear pair)
m12= 180-90= 90 (linear pair)
m13= 90 linear pair
x³-8x+8 =0
[tex]x ^3 - 8x + 8 = 0[/tex]
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a 8-meter ladder is leaning against the wall of a building, and the base of the ladder is sliding away from the building at a rate of 5 meters per second. how fast is the top of the ladder sliding down the wall when the base of the ladder is 6 meters from the wall?
Height of the ladder on the wall in decreasing at the rate of ≈ 6m/s
What is differentiation ?Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilizing only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
Calculationlet ym be the height of wall at which ladder touches
Also let the foot of ladder be xm away from the wall
then by the pythagoras theorem we have ,
[tex]x^{2} +y^{2} =[/tex] 64 [ length of ladder = 8 m ]
⇒ y = [tex]\sqrt{64 - x^{2} }[/tex]
then , the rate of change of height (y) with respect to time (t) is given by
[tex]\frac{dy}{dt}=\frac{-x}{\sqrt{64 - x^{2} }} . \frac{dx}{dt}[/tex]
it is given that [tex]\frac{dx}{dt}[/tex] = 5 m/s
∴ [tex]\frac{dy}{dt}=[/tex] [tex]\frac{-5x}{\sqrt{64 - x^{2} }}[/tex]
now when x = 6m , we have :
[tex]\frac{dy}{dt} = \frac{-5 * 6}{\sqrt{64 - 6^{2} }}[/tex]
= -30 / 5 .3
= -5.660377358490566
therefore height of the ladder on the wall in decreasing at the rate of ≈ 6m/s
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A local jewelry store sells class rings, which it purchases for $60 each. The store engraves a name and date on the ring and sells it using a markup rate of 340%.
Class rings are sold by a nearby jewelry store, which buys them for $60 each. The amount of markup is y=204.
Given that,
Class rings are sold by a nearby jewelry store, which buys them for $60 each. The ring has a name and date engraved on it, and the retailer markup it up by 340% before selling it.
We have to find the equation that can be used to find the amount of markup y.
So,
We can write the equation as
Amount of markup=340% of the purchases amount
Taking amount of the markup as y and purchases amount is $60.
y=340%×60
y=340/100×(60)
y=34×6
y=204
Therefore, The amount of markup is y=204.
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XYZ and LMN are complementary angles. XYZ = (3x+14)° and LMN= (5x+24)°. What is LMN in degrees?
Write your answer as a decimal.
Answer:
6.5°
Step-by-step explanation:
We know that both XYZ and LMN are complementary angles.
Complementary angles add up to 90°.
So,
we can simply add both of the expressions and set it equal to 90 (degrees).
(3x+14) + (5x+24) = 90
-> add the variables and constants
8x+38=90
-> subtract the 38 from both sides (90-38)
8x=52
-> divide out the coefficient to isolate the variable
x=6.5
So, the answer is 6.5 degrees.
Hope this helped :)
Evaluate the following expressions picture attached 100 POINTS
Answer:
3 5/14 (second choice)
Step-by-step explanation:
c = -3 1/7
d = 6.5 (6 1/2 as fraction)
-3 1/7 as improper fraction: -22/7
6 1/2 as improper fraction: 13/2
Now put both fractions into a common denominator
-22/7 = -44/14
13/2 = 91/14
Now add:
-44/14 + 91/14 = 47/14
Change 47/14 back to fraction
47/14 = 3 5/14
$55 set of headphones for 15% off. What is amount of discount? What is the total amount you pay?
Answer:
discount = $8.25 Total=$46.75
Step-by-step explanation:
[tex]\frac{x}{55}[/tex] = [tex]\frac{15}{100}[/tex] 55.00-8.25= $46.75
[tex]\frac{100x}{100}[/tex] = [tex]\frac{825}{100}[/tex] total= $46.75
x=8.25
discount = 8.25
Answer: The discount is $8.25, the total price you pay is $46.75
Step-by-step explanation:
To find the discount, you multiply the decimal of the percent, which is .15 by the total. So 55*.15=8.25. That is how much of a discount you get.
To find the total amount you pay after the discount you simply subtract the discount from the total, so 55-8.25=46.75
Juanita wants to buy a computer. She needs to earn at least 400 dollars. If she makes 9 dollarsan hour and has already saved 40 dollars, how many hours does she need to work? Write an inequality and solve.
Problem
Juanita wants to buy a computer. She needs to earn at least 400 dollars. If she makes 9 dollars an hour and has already saved 40 dollars, how many hours does she need to work?
Solution
Let x the number of hours required we can set up the following inequality:
40 + 9x > 400
And now we can solve for x we can subtract 40 and we got:
9x > 360
And then we got:
x> 40
So then Juanita needs to work at least 40 hours
And the graph of the inequality is given by:
Alex and Patty are tracking the number of steps they walk. Alex records that he can walk 5750 steps in 50 minutes. Patty
writes the equation y = 1142, where y is the number of steps and x is the number of minutes she walks, to describe her
step rate. This week, Alex and Patty each walk for a total of 4 hours. Who walks more steps? How many more?
walks
more steps.
By solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.So, the distance that Andre traveled.
He demonstrated his ability to take 6000 steps in 50 minutes.
The pace at which Andre can walk is:
= 6000/50= 120 steps per minuteThe 5 hours in minutes conversion: 5 × 60 minutes = 300 minutes
Then,
The distance traveled by Andre is:
120 × 300 = 36000 stepsSo, Andre walks 36000 steps.And, Priya enters the formula y = 118x.Where x represents the number of minutes and y is the number of steps.
The formula to convert 5 hours to minutes is:
x = 5 × 60 minutesx = 300 minutesReplace x with its value in the equation:
y = 118xy = 118 × 300y = 35400 steps35400 steps are taken by Priya.
Therefore, by solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).
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The correct question is given below:
Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walked for a total of 5 hours. Who walks more steps?
Gabriel practices for a local marathon. If the
marathon is 42.195 kilometers long, how
many miles does Gabriel need to run in order
to condition himself? Round the answer to
the nearest tenth.
(1 mile ≈ 1.61 kilometers)
Answer:
26.208 miles
Step-by-step explanation:
42.195 / 1.61 = 26.208 miles
The diagram shows the positions of three turbines A, B and C.
A is 6 km due north of turbine B.
C is 4.5 km due west of turbine B.
(a) Calculate the distance AC.
nathan is making a beaded bracelet. for every 5 red beads there are 3 white beads. what is the ratio of red to white beads?
Answer:
5;3
Step-by-step explanation:
the temperature has been dropping 2 1/2 degrees every hour and the current tempter is -15 degrees Ferin height how many hours ago was the temperature 0 degrees Ferin height
The number of hours ago was the temperature 0 degrees is 6 hours.
What is temperature?Temperature simply means the degree if hotness and coldness in a body.
In this case, the temperature has been dropping 2 1/2 degrees every hour. Let the number of hours be h.
This will be illustrated as:
-15 = -2.5h
where h = number of hours
Divide
h = -15 / -2.5
h = 6
Therefore, the correct option is 6 hours.
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Is the following shape a rectangle? How do you know?
A building is in the shape of a square pyramid. each side of the base is 54 meters long and the height is 260 meters. what is the volume of the building? enter your answer in the box. m³
The volume of the building in the shape of a square pyramid is 252720 m³
In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a type of polyhedron with three or more triangle faces that meet above its base (the apex).
The building is in the shape of a square pyramid.
The base of the building is 54 meters long.
The height of the building is 260 meters.
The volume of the right square pyramid is given as:
V = ( 1/3)a²h
Where a is the base and h is the height.
Now we have,
a = 54 meters and h = 260 meters
Then the volume of the building is:
V = ( 1/3)a²h
V = ( 1/3 ) × ( 54 )² × 260
V = ( 1/3 ) × 54 × 54 × 260
V = 758160/3
V = 252720 m³
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1) Calculate the perimeter of
this triangle
7cm
4cm
10cm
6cm
Answer:
27
Step-by-step explanation:
length+base+heigth+breath
=6cm+10cm+4cm+7cm
=27cm
but I am not very sure so when it is correct the give me thanks or rate the answer so I will know it is correct
Help please its due tonight
Answer:
[tex]\sf 12-5x+6x=4[/tex] (Given)
[tex]\sf 12+x=4[/tex] (Combine like terms)
[tex]\sf x=-8[/tex] (Subtraction property of equality)
--------------------------------------------------
Hope this is what you're looking for!
Answer:
1. given
2. combine like terms,
3. subtraction property of equality
Step-by-step explanation:
a sunflower is planted in a garden and the height of the sunflower increases by 10% per day. 2.66 days after being planted the sunflower is 10.3 inches tall. what is the 1-day growth factor for the height of the sunflower? 0.10 incorrect how tall is the sunflower 3.66 days after being planted? incorrect inches how tall is the sunflower 4.66 days after being planted? incorrect inches what is the 2-day growth factor for the height of the sunflower?
Two day growth factor for the height of the sun flower is 1.1449
Take the current number and subtract it from the prior value to determine the growth rate. The growth rate is then expressed as a percentage by multiplying the difference by the previous number and dividing by 100.
A height increases by 7% per day
So the growth factor for height of sun flower is 107/100 =1.07
For 2.7 days - 12 inch
3.74 days increase by 7% by day
⇒ 12 + 7/100 x 12
⇒ 12 ( 107/100 )
⇒ 12.84 inches
3.74 days 12.84 inches
4.74 days increase by 7 % by day
⇒ 12.84 + 7/100 x 12.84
⇒ 12.84 x 107/100
⇒ 13.73 inches
Two days growth factor
⇒ 107/100 x 100/107
⇒ 1.1449
Hence Two day growth factor for the height of the sun flower is 1.1449
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to collect these data, the researchers randomly selected american households to visit and interviewed the adult member of the household whose birthday was nearest. is this an experiment or an observational study?
In an observational study, we measure or survey members of a sample without trying to affect them. In an experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.
This is clearly an observational study
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solve each system of inequalities
Answer:
x < 6
Step-by-step explanation:
x/3 + x/4 < 7 | * 12
4x + 3x < 84
7x < 84 | : 7
x < 12
1 - x/6 > 0
1 > x/6 | * 6
6 > x
x < 6
x < 6 and x < 12 gives x < 6
⦁ At store A, 3 pounds of apples cost $12. ⦁ At store B, the cost is given by y = 2x where y is the cost in dollars and x is the number of pounds of apples. ⦁ The cost of apples at store C is shown in the graph. Answer the questions to find out which store's apples are the least expensive. 1. What is the unit price of apples at store A? Explain how you found this unit price. (2 points) 2. What is the unit price of apples at store B? How did you use the equation to find the unit price? (2 points) 3. What is the unit price of apples at store C? How did you use the graph to find the unit price? (3 points) 4. Which store has the lowest unit price for apples? (3 points)
1. The unit price of apple in store A is $4
2. The unit price of apple in store B is $2
3. The unit price of apple in store C is $3
4. The store with the lowest unit price is store B
1. How to determine the unit price at store A
We can obtain the unit price at store A by doing the following:
3 pounds of apples cost $12.
Therefore,
1 pound will cost = (1 × pound $12) / 3 pounds = $4
Thus, the unit price is $4
2. How to determine the unit price at store B
We can obtain the unit price at store B by doing the following:
y = 2x
Number of pound (x) = 1Cost (y) = ?y = 2x
y = 2 × 1
y = $2
Thus, the unit price is $2
3. How to determine the unit price at store C
We can obtain the unit price at store C by obtaining the slope of the graph. This can be obtaioned as follow:
x coordinate 1 (x₁) = 1x coordinate 2 (x₂) = 3y coordinate 1 (y₁) = 3y coordinate 2 (y₂) = 9Slope (m) =?m = (y₂ – y₁) / (x₂ – x₁)
m = (9 – 3) / (3 – 1)
m = 6 / 2
m = 3
Thus, the unit price is $3
4.How todetermine the store with the lowest unit price
Unit price at store A = $4Unit price at store B = $2Unit price at store A = $3From the above, we can conclude that store B has the lowest unit price
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34. G and H are complementary angles.
If the measure of G = (6x-15)° and the measure of H = (3x + 6), find the measure of H.
Answer: the measure of H is 39 the measure of G is 51
Step-by-step explanation:
6x-15+3x+6=90
9x-9=90
9x=99
x=11
6(11)-15=51
3(11)+6=39
Tell whether it shows growth or decay and graph by using a table of values
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given exponential function
[tex]f(x)=0.5^x[/tex]STEP 2: Compare with the standard exponential function to determine whether it shows growth or decay.
If a is positive and b is greater than 1 , then it is exponential growth.
If a is positive and b is less than 1 but greater than 0 , then it is exponential decay.
[tex]\begin{gathered} f(x)=a\cdot b^x_{} \\ \text{Comparing with }f(x)=0.5^x,\text{ it can be written as }f(x)=1\times0.5^x, \\ It\text{ can be se}en\text{ that }a=1,b=0.5 \\ \text{ Since }a\text{ is positive and b is less than 1 but greater than 0, then it is an exponential decay.} \end{gathered}[/tex]Hence, the given function shows an exponential decay.
STEP 3: Graph the values by using a table of values
We generate a table of values first
STEP 4: Plot the graph of the data values