The total interest cost to Bette is $145.89
What is exact interest basis?
Exact interest means that the interest is computed on 365-day per year basis rather than a 360-day per year basis, which is the case with financial institutions.
The first task in this case is to determine the number of days from May 19, when the amount was borrowed till October 8, when loan repayment was effected.
There are 142 days between the two dates, hence, we can compute exact interest on the loan as shown by the below formula:
exact interest=loan principal*number of days the borrowing last/365days *interest rate
loan principal=$3000
number of days the borrowing last=142
interest rate=12.5%(1/2%=0.5%)
Exact interest=$3000*142/365*12.5%
Exact interest=$145.89
The amount would have been different if ordinary interest where the number of days in a year is deemed to be 360, was used instead
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You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 3% compounded annually, the second account pays 4% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $34,000 in interest. If you invest four times the money into the account that pays 3% compared to 2%, how much did you invest in each account?
The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000
How to solve for the amount investedWe have x + y + z = 1000000
((1+0.03)x - x)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000
4z + x + z = 1000000
((1+0.03)4z - 4z)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000
((1+0.03)4z - 1)+ ((1+0.04)y - 1) + ((1 + 0.02)z-1) = 34000
12/100z + 4/100y +2/100z = 34000
2y + 7z = 1700000
-2y - 10z = -2000000
2y + 7z = 1700000
Solve through the use of the simultaneous linear equation
z = 100000
y = 500000
x = 400000
The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000
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An oil-drilling company knows that it costs $25,000 to sink a test well. If oil is hit, the income for the drilling company will be $325,000. If only natural gas is hit, the income will be $155,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the probability of hitting gas is 1/20, what is the expectation for the drilling company?
The expected value for the drilling company, using a discrete distribution, is of -$9,125, that is, a loss of $9,125.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Considering the cost that it takes to sink a test well, and the probabilities of each outcome, the discrete distribution is given by:
P(X = 300,000) = 1/40 = 0.025.P(X = 130,000) = 1/20 = 0.05.P(X = -25,000) = 1 - (0.025 + 0.05) = 0.925.Hence the expected value is given as follows:
E(X) = 300000 x 0.025 + 130000 x 0 .05 - 25000 x 0.925 = -$9,125.
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Identify the most reasonable unit to measure the time spent at school on an average school day. Seconds, minutes, or hours?
The most reasonable unit to measure the time spent at school on an average school day is in hours.
How to find the most reasonable unit for a measure?
In anything we are going to measure, we have to pay special attention to the unit. When doing this, we want to keep the absolute value of the measure, that is, the number small, hence the do this conversion of units may be used.
For example, it is easier and more practical to say one day instead of 87,840 seconds. The same logic is applied to this problem, in which the most reasonable unit to measure the time spent at school on an average school day is in hours, as it keeps the numerical measure smaller than it would be in minutes or seconds.
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Craig has a watch that is losing time. For every minute that passes, his watch loses 10 seconds. If Craig set his watch correctly at 9am, what time whould it show when it is 10am on the house clock?
Answer:
9:50 am
Step-by-step explanation:
because 10 x 60 is equal to 1 hour, so you get 600 seconds subtracted from 10am. 600 seconds is equal to 10 minutes. so 10 am - 10 minutes = 9:50am
find derivative of y= sin x sin 3x
The derivative of y= sin x sin 3x is [tex]$=3 \cos x-3 \cos 3 x$[/tex]
What is a derivative?Futures contracts, options contracts, and credit default swaps are typical types of derivatives. Beyond this, a sizable number of derivative contracts satisfy the requirements of a wide range of counterparties.To find the derivative of y= sin x sin 3x:
[tex]$y=3 \sin (x)-\sin (3 x)$[/tex]
[tex]$y^{\prime}=3 \cos x-[\cos (3 x) \cdot 3]$[/tex]
[tex]$y^{\prime}=3(\cos x-\cos 3 x)$[/tex]
[tex]\frac{dx}{dy} =3 cosx - 3 cos x[/tex]
Differentiate [tex]sin 3x[/tex] using the chain rule
Given [tex]y=f^{'} (g(x))*g^{'}[/tex]←chain rule
y=[tex]y=3 sin x-sin 3x[/tex]
[tex]\frac{dx}{dy} =3 cos x - cos 3x*\frac{d}{dx} (3x)[/tex]
[tex]=3cosx-3cos3x[/tex]
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An estimated 40% of all people were born after the year 2000. If two people are selected at random from around the world, what are the chances that NEITHER of these people were born after the year 2000?
The chances that NEITHER of these two selected people were born after the year 2000 is 0.36
How to determine the probability?The given parameters are:
Year = 2000
Proportion of people born after 2000, p = 40%
Sample size = 2
The chances that NEITHER of these two selected people were born after the year 2000 is calculated as:
P = (1- p)^2
Substitute the known values in the above equation
P = (1 - 40%)^2
Evaluate the exponent
P = 0.36
Hence, the chances that NEITHER of these two selected people were born after the year 2000 is 0.36
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The price of a product is reduced by 30%. By what percentage should be increased to make it 100%?
it should be 70 percent
Step-by-step explanation:
100 subtract by 30 is 70 percent
Round 219.371 to the nearest one tenth and hundredths
Answer:
219.4
Step-by-step explanation:
Find the number in the tenth place 3 and look at the one place to the right for rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5. So the answer is 219.4
ONE HUNDRED LOTTERY TICKETS ARE SOLD FOR $5.00 EACH. ONE PRIZE OF $300
WILL BE AWARDED. STEVE PURCHASES ONE TICKET. FIND HIS EXPECTATION.
How to make 3 dimensional object become 4 dimensional object
Using Hinton's method;
Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distanceThen draw lines between their equivalent vertices.The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.What is a 4 dimensional shape?A four-dimensional shape (4D) is a mathematical extension of a three-dimensional or 3D space.
Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects.
Using Hinton's method;
Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distanceThen draw lines between their equivalent vertices.The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.Learn more about dimensional shapes here:
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HELP ME WITH THIS PLEASEEEE
Answer:
the perpendicular bisector
Explanation:
The perpendicular bisector will intersect the segment at its midpoint.
200 divided by 115.3597
Answer:
Step-by-step explanation:
1.733707699
could you brainlyest me?
A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.
a) The slope of the secant lines are: q = 5, f(q) = 2,076: m = - 131.1, q = 10, f(q) = 1,299: m = - 106.8, q = 20, f(q) = 357: m = - 81.6, q = 25, f(q) = 84: m = - 68.1, q = 30, f(q) = 0: m = - 51.
b) The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.
How to estimate the slope of a tangent line by averaging two adjacent secant lines
In this problem we must determine the slope of several lines based on the information given by the table and using the secant line formula:
m = [f(q) - f(p)] / (q - p) (1)
If we know that a = 15 and p = 765, then the slope of the secant lines are:
q = 5, f(q) = 2,076
m = [2,076 - 765] / (5 - 15)
m = - 131.1
q = 10, f(q) = 1,299
m = [1,299 - 765] / (10 - 15)
m = - 106.8
q = 20, f(q) = 357
m = [357 - 765] / (20 - 15)
m = - 81.6
q = 25, f(q) = 84
m = [84 - 765] / (25 - 15)
m = - 68.1
q = 30, f(q) = 0
m = [0 - 765] / (30 - 15)
m = - 51
The slope of the line tangent to the curve at the point (x, y) = (15, 765) can be estimated by averaging the slopes of the closest secant lines:
m' = [(- 106.8) + (- 81.6)] / 2
m' = - 94.2
The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.
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use a graphing device to find all solution of the question rounded to two decimal places.
x^3-x=log(x+1)
0.00.1.14
Answer:
Step-by-step explanation:
....
A tower that is 114 feet tall casts a shadow 121 feet long. Find the angle of elevation of the sun to the
nearest degree
Answer:
43 degrees
Step-by-step explanation:
First, notice that we can draw a right triangle to represent this situation. The vertical leg of the triangle corresponds to the tower, and the horizontal leg corresponds to the shadow. The height of the tower, 114, is OPPOSITE, and the length of the shadow, 121, is ADJACENT to the angle of elevation to the top of the tower. Remember SOH CAH TOA, we can use TAN to find the angle since we know the values of O and A.
TAN(x) = O/A
TAN(x) = 114/121
x = ARCTAN(114/121)
x = 43
If f(x) = -1x + 1and g(x) = x4, what is (f º g)(x)?
Answer:
(f º g) = [tex]-x^4+1[/tex]
Step-by-step explanation:
So it's important to note that the notation: "(f º g)" isn't f(x) * g(x), it's a composite function, where you essentially have two functions, with one of the functions being the argument of one of the functions.
This means we can plug in the function g(x) as x into the function f. So let's do that
Original Function:
f(x) = -1x + 1
Plug in x^4 (this is the value of g(x)) as x into the function
f(g(x)) = [tex]-(x^4)+1[/tex]
Distribute the negative sign
f(g(x)) = [tex]-x^4+1[/tex]
11/3=
7/2=
14/5=
21/4=
Answer:
1 (3.66)
2(3.5)
3(5.25)
Can u guys please give me the correct answer
Answer:
27°Step-by-step explanation:
in the smallest triangle (BCD) you have an angle of 90° and one of 63°, the sum of the internal angles in a triangle is 180°, remove the known angles from 180 ° and you will have the measure of the CBD angle
180 - 63 - 90 =
27°
Answer:
27°
Step-by-step explanation:
180°-90°-63° = 27°
Question 8
What is wrong with the following equation: 8 + (6/2) = 17-5
The loft
Answer:
11=12
they are not equal to each other
Step-by-step explanation:
8+(6/2)=17-5
8+3=12
11=12
hope this helps
Add the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.
x 4 -3x + 1, 4x 2 - 2x + 8, and x 3 - 9
The addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.
Polynomialx⁴ - 3x + 14x² - 2x + 8x³ - 9Adding the polynomial
(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)
Open parenthesis= x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9
Collect like terms in descending powers= x⁴ + x³ + 4x² - 3x - 2x + 1 + 8 - 9
= x⁴ + x³ + 4x² - 5x
Therefore, the addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.
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What is the standard form equation of the ellipse that has vertices (-15, 4) and (5, 4) and co-vertices (-5, -3) and
(-5, 11)?
Step-by-step explanation:
Notice that the main vertices (-15,4) and (5,4) both have the same y coordinate. This means that the focal axis is horizontal so we have a horizontal ellispe.
Equation of a horizontal ellipse is
[tex] \frac{(x - h) {}^{2} }{ {a}^{2} } + \frac{(y - k) {}^{2} }{ {b}^{2} } = 1[/tex]
I'll explain the variables.
Step 1: Find the center.
The center (h,k) is the midpoint of either the main or co vertices. It doesn't matter because of the definition of an ellipse.
So using the midpoint formula, let find the midpoint of the main vertices.
[tex]( \frac{ - 15 + 5}{2} ) = - 5[/tex]
[tex] \frac{4 + 4}{2} = 4[/tex]
So our center is (-5,4) so as of right now we have
[tex] \frac{(x + 5) {}^{2} }{ {a}^{2} } + \frac{(y - 4) {}^{2} }{ {b}^{2} } = 1[/tex]
Step 2: The variable a represents the semi major axis. This
basically means what is the distance from the center to either main vertex.
Here, let use (5,4). Using (5,4), our main vertex and (-5,4), our center.
Use the distance formula
[tex]a= \sqrt{(5 - ( - 5) {}^{2} + (4 - 4) {}^{2} } [/tex]
[tex]a = \sqrt{100} [/tex]
[tex]a= 10[/tex]
So our distance is 10, this means a=10
Step 3: The variable b represent the semi minor axis. This basically the distance from the center to either co vertex.
Using the distance formula,
[tex]b = \sqrt{ (- 5 - ( - 5) {}^{2} + (4 - 11) {}^{2} } [/tex]
[tex]b = \sqrt{49} [/tex]
[tex]b = 7[/tex]
So b=7, so finally we plug a=10, b=7
[tex] \frac{(x + 5) {}^{2} }{100} + \frac{(y - 4) {}^{2} }{49} = 1[/tex]
√3018+√36+√169 can you solve this for me please
Answer:
55
Step-by-step explanation:
[tex]\sqrt{3018+\sqrt{36+\sqrt{169} } }[/tex]
= [tex]\sqrt{3018+\sqrt{36+13} }[/tex]
= [tex]\sqrt{3018+\sqrt{49} }[/tex]
= [tex]\sqrt{3018+7}[/tex]
= [tex]\sqrt{3025}[/tex]
= 55
PLEASE HELP!!! WILL MARK BRAINLIEST!!!!!
The piecewise defined function is
f(t) = 800 * 1.5^t for 0 - 2
f(t) = 2700 * 1.05^t-3 for 3 to 9
How to determine the piecewise functions?On the domain of t = 0 to 2, we have:
f(0) = 800
f(1) = 1200
f(2) = 1800
The above function is a piecewise function with the following definition
f(0) = 800 --- initial value
r = 1200/800 = 1.5 --- rate
The function is then represented as:
f(t) = f(0) * r^t
This gives
f(t) = 800 * 1.5^t
On the domain of t = 3 to 9, we have:
f(3) = 2700
f(4) = 2835
The above function is a piecewise function with the following definition
f(3) = 800 --- initial value
r = 2835/2700 = 1.05 --- rate
The function is then represented as:
f(t) = f(3) * r^t-3
This gives
f(t) = 2700 * 1.05^t-3
Hence, the piecewise defined function is
f(t) = 800 * 1.5^t for 0 - 2
f(t) = 2700 * 1.05^t-3 for 3 to 9
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A bird flies 50km everyday to collect food for his offspring and 20km to drink water. To fly this distance takes him 1 hour and 40 minutes. What’s his average speed over the whole day?
Answer:
42km/h
Step-by-step explanation:
70km=100 minutes
7km= 10min
42km=60min
42km/h
G wants to get over 9000 comments on his videos. He gets the same number of comments for each cat video that he uploads, and he gets the same number of comments for each dog video that he uploads. Let C represent the number of cat videos and D represent the number of dog videos that G should upload to achieve his goal.
750C+450D>9000 According to the inequality, how many comments does each cat video get, and how many comments does each dog video get?
can G achieve his goal by uploading 8 cat videos and 7 dog videos?
Answer:
Each Cat video gets 750 comments
Each dog video gets 450 comments
Hope this helps you!
Answer:
He gets 750 comments on the cat videos and 450 on the dog videos the answer to the second question is yes
Step-by-step explanation:
khan :)
I neeeeed heeeelp please
Answer:
10b/y^2
Step-by-step explanation:
Hope this helps! :)
24 is what percent of 480?
Answer:
5%.
Step-by-step explanation:
That is
(24/480 * 100
Now 480 / 24 = 20 so we have
(1/20) * 100
= 100/20
= 5%.
Answer:
24 is 5% of 480
Step-by-step explanation:
24 / 480 = 0.05
Percent is "for each 100"
Then:
0.05 * 100 = 5%
Checking account A charges a monthly service fee of $12 and a wire transfer
fee of $10.50, while checking account B charges a monthly service fee of $21
and a wire transfer fee of $8.50. Which checking account is the better deal if
4 wire transfers are made per month?
A. Checking account B IS the better deal, because its total monthly
fees amount to $55, while those for checking account A amount to
$54.
B. Checking account B is the better deal, because its total monthly
fees amount to $54, while those for checking account A amount to
$55.
C. Checking account A is the better deal, because its total monthly
fees amount to $55, while those for checking account B amount to
$54.
c
D. Checking account A is the better deal, because its total monthly
fees amount to $54, while those for checking account B amount to
$55.
For only 4 wire transfers, Checking account A has a monthly fee of $54, while checking account B has a monthly fee of $55, so the correct option is D.
Which checking account is better?Checking account A charges a monthly fee of $12, plus $10.50 for each wire transfer, then the total cost if you make 4 wire transfers is:
C = $12 + $10.50*4 = $54
For checking account B, we have a fixed cost of $21, plus $8.50 per each wire transfer, then the total cost for 4 wire transfers is:
C' = $21 + 4*$8.50 = $55
So, if you make only 4 wire transfers per month, checking account A is a better option.
Then we can see that the correct option is D.
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Which of the following would be an acceptable first step in simplifying the expression
sinx/1- cosx?
A. sinx - sinx/1- cos x
B. 1/cscx - cosx
C. Cannot be simplified further
D. sin x(1+cosx)/(1-cosx)(1+cosx)
Answer: A
Step-by-step explanation: Because it can be simplified twice.
Why my foot keep makin cheese?!?!?!?
Answer:i am not sure
Step-by-step explanation:
This question is very hard to answer
Answer: I think your brain needs cheese but..............................................
Step-by-step explanation:
Don't know