Suppose that $20,000 is invested at 9% interest, compounded annually. After time t, in years, it grows to the amount A given by the function A(t) = $20,000(1.09)
a) Find the amount of time after which there will be $200,000 in the account.
b) Find the doubling time.
After what amount of time will there be $200,000 in the account?
Answer:
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = [log (200,000) -log (20,000)] / log (1.09)
Years = [5.3010299957 -4.3010299957] / 0.037426497941
Years = 1 / 0.037426497941
Years = 26.7190374471
*************************************************
Finding Doubling Time : (We'll calculate $100 becoming $200)
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Years = log (200) -log (100) / log(1.09)
Years = (2.3010299957 -2) / 0.037426497941
Years = .3010299957 / 0.037426497941
Years 8.0432317278
It takes 8.0432317278 years for money to double at 9% per year.
Source:
http://www.1728.org/compint2.htm
Step-by-step explanation:
HELP ME !!
PLEASE ANSWER !! ILL GIVE BRAINLIEST !!
50 POINTS !!
FAKE ANSWERS WILL GET REPORTED .
Answer:
<1=62
<2=83
<3=35 this is the answer of this question
Please help meeeeeee!!!!!!!!
Answer:
A
Step-by-step explanation:
Hi I don't usually upload pictures but I was too lazy to type so I did it on paper. I had to get the numbers in the parenthesis out so I multiplied the + by everything in the parenthesis following the negative and positive multiplication rules. Then, I combined and subtracted like terms.
Hope this helps !!
-Ketifa
Help?
Describe how to translate the graph of y= x to obtain the graph of y = x – 15.
Answer:
Shift down 15 units
Step-by-step explanation:
the number on the right is the one that determines where the line intersects through the y axis
A hospital near a ski resort records the type of injuries treated during ski season and other seasons and other seasons over a year. the results shown in the table will help determine the medical staff that is required at different times of the year. according to the data in the table, what is the probability that a patient will need to be treated with a broken bone during ski season.
Answer:
The answer is C
Step-by-step explanation:
You have to divide both numerators then the denominater.
So, it would look like: 160 over 90 x 100 over 290
160x100=16 90x290=25 16/25
Mary can make a quilt in 3 days and Eva can make
a quilt in 5 days. In how many days can they make
quilt working together?
Answer: in explanation
Step-by-step explanation
Sandi can perform 1/9 of the task in a day
Eva can perform 1/5 of the task in a day
Working together, they can perform
1/9 + 1/5 of the task per day
= 5/45 + 9/45 = 14/45 of the task in a day
or 45/14 days in the task = 3.2 days
So
It would take about 3.2 days to complete the task working togethe
Below is a dot plot showing how much time customers spent in a store, rounded to the nearest five minutes. Which of the following is a representative sample of this population?
NEED THIS BAD PLEASE HELP ME!!!!!!!
Answer:
D
Step-by-step explanation:
i did a test with the same question
The representative sample of the population displayed by the dot plot is: dot plot D.
What is a Representative Sample of a Population?The representative sample of a population can be described as a subset of a particular population which displays or exhibit similar characteristics of the larger population group.
From the image given, the dot plot that reflects the characteristics of the dot plot of the population is the dot plot in option D.
Dot plot D is a representative sample.
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Consider the following. 12, 7, 18, 23, 24, 27 Compute the population standard deviation of the numbers. (Round your answer to two decimal place.) (a) Double each of your original numbers and compute the standard deviation of this new population. (Round your answer to two decimal place.) (b) Use the results of part (a) and inductive reasoning to state what happens to the standard deviation of a population when each data item is multiplied by a positive constant k.
Answer:
(a) [tex]\sigma = 7.04[/tex]
(b) [tex]\sigma = 14.1[/tex]
(c) The population standard deviation is multiplied by k
Step-by-step explanation:
Given
[tex]Dataset: 12, 7, 18, 23, 24, 27[/tex]
Solving (a): The population standard deviation
Start by calculating the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{12+7+18+23+24+27}{6}[/tex]
[tex]\mu = \frac{111}{6}[/tex]
[tex]\mu = 18.5[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
This gives:
[tex]\sigma = \sqrt{\frac{(12-18.5)^2 + (7 - 18.5)^2 + (18-18.5)^2 + (23-18.5)^2 + (24 - 18.5)^2 + (27 - 18.5)^2}{6}}[/tex]
[tex]\sigma = \sqrt{\frac{297.5}{6}}[/tex]
[tex]\sigma = \sqrt{49.5833}[/tex]
[tex]\sigma = 7.04[/tex]
Solving (b): Double the dataset and calculate the new population standard deviation
The new dataset is:
[tex]Dataset: 24, 14, 36, 46, 48, 54[/tex]
Start by calculating the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{24+ 14+ 36+ 46+ 48+ 54}{6}[/tex]
[tex]\mu = \frac{222}{6}[/tex]
[tex]\mu = 37[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
This gives:
[tex]\sigma = \sqrt{\frac{(24-37)^2 +(14-37)^2 +(36-37)^2 +(46-37)^2 +(48-37)^2 +(54-37)^2}{6}}[/tex]
[tex]\sigma = \sqrt{\frac{1190}{6}}[/tex]
[tex]\sigma = \sqrt{198.33}[/tex]
[tex]\sigma = 14.1[/tex]
Solving (c): What happens when the dataset is multiplied by k
In (a), we have:
[tex]\sigma = 7.04[/tex]
In (b), when the dataset is doubled,
[tex]\sigma = 14.1[/tex]
This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:
i.e.
[tex]New \sigma = k * \sigma[/tex]
A group of friends went to lunch. The bill before sales tax and tip was $37.50. A sales tax of 8% was added. The group then tipped 18% on the amount after the sales tax was added. What was the amount, in dollars, of the sales tax?
What was the total amount the group paid, including tax and tip?
Sales Tax = $3.00
The total amount paid by the group was $48.15
The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:
Sales tax = $37.50 * 8% = $3.00
The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:
Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15
So the total amount paid by the group was $48.15.
2) 45+ 17 = 62
3) X + 5/6 = 7/16
4) Y + 1/7 = 5/8
9514 1404 393
Answer:
2) true
3) X = -19/48
4) Y = 27/56
Step-by-step explanation:
3) Subtract 5/6 from both sides
X = 7/16 -5/6 = (7·6 -16·5)/(16·6) = (42 -80)/96
X = -19/48
__
4) Subtract 1/7 from both sides
Y = 5/8 -1/7 = (5·7 -8·1)/(8·7)
Y = 27/56
Given that the polynomial x² - 10x + 14 leaves the same remainder when divided by x + 2b orx + 2c where 3b - 2c = 0 and b # c . Find the values of b and c.
Step-by-step explanation:
please refer to the 3 pages of sketch for details
What is 1/4 : 3/4 :: 75 : =
Answer:
75 : 225
Step-by-step explanation:
[tex]\frac{\frac{1}{4} }{\frac{3}{4} } :\frac{75}{y}[/tex]
0.25 × y = 0.75 × 75
0.25y = 56.25
0.25y ÷ 0.25 = 56.25 ÷ 0.25
y = 225
In the following problems the values of sin(θ)and cos(θ)are given. Determine the value of tan(θ).
a. sin(θ)=0.1 and cos(θ)=0.995
tan(θ)=
b. sin(θ)=−0.158 and cos(θ)=−0.987
tan(θ)=
c. sin(θ)=−0.631and cos(θ)=0.776
tan(θ)=
Answer:
a) ≈ 0.1
b) ≈ 0.2
c) ≈ 0.9
Step-by-step explanation:
GIVEN :-
Values of sinθ & cosθTO FIND :-
Value of tanθFACTS TO KNOW BEFORE SOLVING :-
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex]SOLUTION :-
a) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.1}{0.995}[/tex] ≈ 0.1
b) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{-0.158}{-0.987} = 0.16 (appx)[/tex] ≈ 0.2
c) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.631}{0.776} = 0.81 (appx)[/tex] ≈ 0.9
Multiply: (–4 + i)(2 – 3i)
a. –5 – 10i
b. –8 + 11i
c. –5 + 14i
d. –11 + 14i
The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.
What is the product of the given complex numbers?It follows from the task content that the result of the product of the given complex numbers is to be determined.
On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).
We can therefore multiply as follows;
-8 + 12i + 2i - 3i².
However, it is noteworthy to know that; i² = -1.
Hence, we have that;
-8 + 14i + 3
= -5 + 14i
On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.
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Solve algebraically the simultaneous equations 2x^2-y^2=17 x+2y=1
Here we go...
= 2x² - y² = 17
= 2x² = 17 + y²
= x² = 17 + y²/2
= x = √17+y²/2
= x + 2y = 1
= x = 1 - 2y
___________________
Sry,if i misunderstood the question.. do let me know in the comment section
A biologist tags ducks living at a pond for her research. She uses 14 blue tags, 19 red tags, 27 white tags, and 6 yellow tags on individual ducks before releasing them back into the wild. When the biologist returns to the pond to continue the study, she is more likely to find a duck with a blue tag than a duck with a ...
A red tag
B white tag
C yellow tag
D yellow or red tag
In this figure question attached
Answer:
x = 20°
Step-by-step explanation:
x = 180 - (70 + 90)
x = 180 - 160
x = 20°
Hope this helps!
Two of the statements are true; one is a lie.
Select the one that is a lie.
Then explain your reasoning.
∠GAF ≌ ∠TAE.
∠TAE and ∠FAH are complementary.
∠TAF is obtuse.
Answer: Choice A
angle GAF = angle TAE is the lie (aka false statement)
========================================================
Explanation:
Let's go through each answer choice to see which is true or which is false.
-----------------------------
Choice A
The markers for angles GAF and TAE are different. Both would need to have a single angle marker, or a double angle marker. The differing markers indicates the angles aren't the same.
Also, note that angle TAG isn't a 180 degree angle, or that point G isn't on line TA. We need this to be the the case, so that two vertical angles form. However, such a thing doesn't happen.
So that's why angles TAE and GAF aren't the same measure.
Choice A is the answer. You can stop here if you wanted.
-------------------------------
Choice B
Let
x = measure of angle TAE
y = measure of angle TAH
z = measure of angle HAF
We can see that x+y+z = 180, since angle EAF is a straight angle. The diagram gives y = 90 and z = 50, so,
x+y+z = 180
x+90+50 = 180
x+140 = 180
x = 180-140
x = 40
Angle TAE is 40 degrees. It adds with angle FAH to get 40+50 = 90, showing that the two angles are indeed complementary.
Choice B is a true statement, so we can rule it out.
-------------------------------
Choice C
Angle TAF is composed of angles TAH and HAF
Adding the two angles gets us 90+50 = 140, which is larger than 90.
Therefore angle TAF is obtuse.
Choice C is a true statement, and it can be ruled out as well.
Technically you could have stopped at choice A once you found the lie, but I figured to show why choices B and C could be ruled out.
is 9.307 greater than 9.37
Answer:
No because 9.307 is less than due the facts that the seven in 9.307 is in the thousandth while the seven in 9.37 is in the hundredths
What are the solutions of the equation (5x –
- 2)(x + 6) = 0?
9514 1404 393
Answer:
-2/5, -6
Step-by-step explanation:
We assume you're asking for solutions to ...
(5x -(-2))(x +6) = 0
This can be simplified to ...
(5x +2)(x +6) = 0
__
The solutions are the values of x that make the factors zero. (The product can only be zero if a factor is zero.) Here, we'll find the zeros of the factors one at a time.
5x +2 = 0
5x = -2 . . . . . subtract the constant
x = -2/5 . . . . divide by the x-coefficient
__
x +6 = 0
x = -6 . . . . . .subtract the constant
The solutions of the equation are x = -2/5 or -6.
__
The graph shows the x-values that make the product zero.
I just need help appreciate it and have a great day
On solving the provided question, we can say that - by doing the fraction we have 3/12 = 1/4
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
balloons is 12
blew up is 1/3
friend blew up is 5
1/3*12 = 4
4+5 = 9
3/12 = 1/4
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how do you get 3/8 from 13/8
You can get 3/8 from 13/8 by subtraction. The solution is 10 / 8
How to get 3/8 from 13/8In order to get 3/8 from 13/8 we would have to carry out a subtraction of fractions.
That is we would have: 13/8 - 3/8
take the lcm of the denominator
[tex]\frac{13 - 3}{8}[/tex]
= 10 / 8
Hence when we take 3 / 8 from 13 / 8, the solution that we would have would be from subtraction. This is 10 / 8
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2. What number is a common multiple of
5 and 9?
What IS the approximate length of arc s on the circle below? Use 3.14 for T Round your answer to the nearest
tenth.
Answer:
14.1 inches
Step-by-step explanation:
The formula to be used to find the arc length is Ф = s(arc length) / r(radius)
First we rearrange the formula to find the arc length which would be s = Ф * r
This formula only works in radians so the first step is converting 135° to radians so we would do 135° * π radians/180° which would give us 3π/4
We would then multiply 3π/4 * 6 and get 18π/4, plugging that value into a calculator returns us a value of ≈ 14.137
We then round to the nearest tenth and get an answer of 14.1 inches for the arc length of the circle below
Answers are
(-1,3)
(0,2)
(1,2)
(2,-1)
(2,2)
HAVE A NICE DAY
WILL GIVE BRAINLST :)
Answer:
1. A
2. C
Step-by-step explanation:
The perimeter of a rectangular field is 74 yards. The length of the field is 27 yards. What is the width in yard of the field
Answer:
width = 10 yds
Step-by-step explanation:
perimeter = 2L + 2W
74 = 2(27) + 2W
74 = 54 + 2W
subtract 54 from both sides of the equation:
2W = 20
divide both sides by 2:
W = 10
The width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards
How to find the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Perimeter of the rectangle = [tex]2(L + W) \: \rm units[/tex]
For this case, let we assume that:
The width of the considered rectangular field = W yards
Then, as we're provided that:
Perimeter of the rectangular field = 74 yardsLength of the rectangular field = 27 yards.Putting these in the formula for perimeter of a rectangle, we get;
[tex]Perimeter = 2( L + W)\\74 = 2(27 + W)\\\\\text{Dividing both the sides by 2}\\\\\dfrac{74}{2} = \dfrac{2(27+W)}{2}\\\\37 = 27 + W\\\\\text{Subtracting 27 from both the sides}\\\\37 - 27 = W\\W = 10 \: \rm yards[/tex]
Thus, the width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards
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Irregular polygons has sides that are not equal lenght and angles that are not equal?
TRUE OR FALSE?
Answer:
yeah it's true
Step-by-step explanation:
regular polygon have all equal side and all equal angleIRREGULAR polygon have atleast one unequal side and one unequal angle............THANKS.........
Factorise 2(x-y)-a(y-x)
Answer:
( a + 2 ) ( x - y )
Step-by-step explanation:
2 ( x - y ) - a ( y - x )
= 2 ( x - y ) + a ( x - y )
= ( 2 + a ) ( x - y )
= ( a + 2 ) ( x - y )
Hence factorised.
You stand 25 m from the base of a tree and the angle of elevation from the ground to the top of the tree is 48 degrees. How tall is the tree?
Answer:
ffyftxrrxrrxcvcmuvcyztzxvujgyh
Step-by-step explanation:
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