The time required to the nearest day to make the deposit of $1000 to grow to $1 million at 3% compounded continuously is 84044 days.
In the question ,
it is given that
the deposit ( principle amount P) = $1000
the final amount (A) = 1 million = $1000000
the rate of interest (r) = 3% = 0.03
let the time taken to make $1000 to 1 million be " t ".
The continuous compounding interest is given by the formula
[tex]A = P\times e^{r t}[/tex]
where A is the final amount
P is the principle amount
r is the rate of interest
t is the time taken
Substituting the values of A , P , r and t from above , we get
1000000 = 1000×[tex]e^{0.03*t}[/tex]
10000000/1000 = [tex]e^{0.03t}[/tex]
1000 = [tex]e^{0.03t}[/tex]
taking ln on both the sides
㏑(1000) = ㏑([tex]e^{0.03t}[/tex])
㏑(1000) = (0.03t)*㏑(e)
6.9077 = (0.03t)*1 .... as ln(e) = 1 and ln(1000)=6.9077
6.9077 = 0.03*t
t = 6.907755/0.03
t = 230.2585
So , time required is 230.2585 years .
to convert into days , we multiply by 365.
time ( in days) = 230.2585×365
= 84044.3525
≈ 84044 days
Therefore , the time required to make the deposit of $1000 to grow to $1 million at 3% compounded continuously is 84044 days .
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-3×+9=-3(2×+3)+3(×-4)+1
The expression we have is:
[tex]-3x+9=-3(2x+3)+3(x-4)+1[/tex]Step 1. To solve for x, we need to first apply the distributive property on the right-hand side of the equation. The distributive property is to multiply the number outside each pair of parenthesis by the terms inside it. We get the following:
[tex]-3x+9=-3\cdot2x-3\cdot3+3\cdot x+3\cdot(-4)+1[/tex]Solving the multiplications on the right-hand side:
[tex]-3x+9=-6x-9+3x-12+1[/tex]Step 2. Combine the like terms.
We start by combining the terms that contain x:
[tex]-3x+9=-3x-9-12+1[/tex]And then, combine the independent terms:
[tex]-3x+9=-3x+4[/tex]Step 3. Add 3x to both sides of the equation:
[tex]-3x+3x+9=4[/tex]On the left side, we get that -3x+3x cancel each other:
[tex]9=4[/tex]As we can see, this is not true, which means that there is no solution for x.
Answer: There is no solution for x.
I am an odd number. When you multiply me by 6, then
divide the product by 3, the quotient is 10. What number am I?
Answer:
20 hope this is helpful and also enjoy your day
I am 5 when you multiply me by 6, then divide the product by 3, the quotient is 10.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Assuming I am 'n'.
∴ When you multiply me by 6, which is 6n, then divide the product by 3, which is 6n/3 the quotient is 10 which is 6n/3 = 10.
6n/3 = 10.
2n = 10.
n = 5.
So, I am an odd number 5.
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Be Allison has been to the large muffin sale table Chris wants to pay more signs
By proportion, Chris should mix 8/3 parts of the red paint in 2 fluid ounces of blue paint.
Purple paint is made using a combination of red paint and blue paint.
Now Allison made purple paint by mixing 3 parts red [aint and 4 parts blue paint.
Therefore, the ratio for the purple paint is :
= 4 parts blue paint / 3 red paint
Chris has 2 fluid ounces of blue paint.
Let the amount of red paint Chirs have to be x.
Then the proportion should be equal.
So,
4 / 3 = x / 2
By cross multiplication,
4 × 2 = 3 × x
8 = 3x
Dividing each side by 3,
x = 8/3
Chirs should mix 8/3 parts of the red paint with blue paint.
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What is the value of X?What is the value of the radius In circle O?
Answer
x = 4.5 units
Radius = 29 units
Explanation
The center of the circle is point O.
So, any line drawn from that point O to any point on the circumference of the circle is the radius of the circle and will therefore have the same length.
Therefore, OC = OD
OC = 6x + 2
OD = 10x - 16
6x + 2 = 10x - 16
Rewriting this
10x - 16 = 6x + 2
10x - 6x = 2 + 16
4x = 18
Divide both sides by 4
(4x/4) = (18/4)
x = 4.5 units
Then, we can now calculate the radius of the circle now
Radius = OC = OD
= 6x + 2 or 10x - 16
= 6(4.5) + 2 or 10(4.5) - 16
= 27 + 2 or 45 - 16
= 29 units.
Hope this Helps!!!
this morning the temperature was "-12" degrees. the temperature will rise 5/8 degree every hour for 3 hours before dropping 1/2 degree each hour for 5 hours. what is the temperature after 8 hours
Using proportions, it is found that the temperature after 8 hours is of -12.63 degrees.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using arithmetic operations such as multiplication or division considering the given rates in the function.
The temperature is of -12 degrees, and rises by 5/8 every hour for 3 hours, hence the temperature in 3 hours will be given by:
-12 + 3 x 5/8 = -12 + 15/8 = -10.13 degrees.
Then, for each of the next 5 hours, the temperature drops by 0.5 degrees, hence the temperature after 8 hours will be given by:
-10.13 degrees - 5 x 0.5 = -10.13 - 2.5 = -12.63 degrees.
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how do I write a function that describes the given transformation
1) Considering that this is our parent function:
[tex]f(x)=2^x[/tex]2) Then let's visualize what happens when we transform it to :
[tex]g(x)=2^{x-3}+1[/tex]3) So now let's reflect that across the y-axis, and vertically shrink that by 1/3:
4. What is the value of y in the system of equations shown below?
z+y+z=22
y+z=16
z-2=7
Answer:
Step-by-step explanation:
Y = 22 - 2Z
22 - 2Z + Z = 16
22 - Z = 16
Z = 6
Y + Z = 16
Y + 6 = 16
Y = 10
NO LINKS!! Part 4: Please help me with this Similarity Practice
Answer:
C' = (10, 1)
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 3 units down.
Step-by-step explanation:
If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.
Given vertices of triangle ABC:
A = (0, 0)B = (1, 4)C = (5, 2)To maintain similarity but not maintain congruence, dilate triangle ABC (since dilation keeps the corresponding angles of both triangles the same).
Given vertex of triangle A'B'C':
B' = (2, 5)If ΔABC is dilated by a scale factor of 2, with the origin as the center of dilation, B' = (2, 8). If the triangle is then translated 3 units down, B' = (2, 5), which matches the given coordinate of point B'.
Therefore, the series of transformations is:
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation.Translation of 3 units down.Mapping Rule: (x, y) → (2x, 2y - 3)
Therefore, the coordinates of point C' are:
⇒ C' = (2(5), 2(2) -3) = (10, 1)
Which of the following inequalities would have the solution set graphed below?
t - 2 ≤ 0
t - 3 ≤ 5
t + 2 ≤ 0
t + 3 ≤ 1
Answer:
t - 2 ≤ 0
Step-by-step explanation:
Given inequality
t- 2 ≤ 0
Add 2 on both sides of the inequality without changing the meaning
t - 2 + 2 ≤ 0 + 2
or
t ≤ 2
Looking at the number line given, we can see that all numbers to the left of 2 including 2 are part of the solution set
Hence the solution set graphed is t- 2 ≤ 0
90 divided by 5(3x2)-1=
The solution of expression 90 ÷ [5 (3×2) - 1} is,
90 ÷ [5 (3×2) - 1} = 3.10
We have to given that,
An expression to simplify as,
⇒ 90 ÷ [5 (3×2) - 1}
We can simplify the expression as,
⇒ 90 ÷ [5 (3×2) - 1}
⇒ 90 ÷ [5 ×6 - 1]
⇒ 90 ÷ [29]
⇒ 3.10
Therefore, The solution of expression 90 ÷ [5 (3×2) - 1} is,
90 ÷ [5 (3×2) - 1} = 3.10
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Using Euler's formula, how manyedges does a polyhedron with 20faces and 12 vertices have?? ] edgesEuler's Formula: F + V = E + 2Enter
SOLUTION:
Case: Euler's formula
Given:
Faces= 20
Vertices =12
Euler's formula: F + V = E + 2
Required: To find the number of Edges
Method:
Step 1: Recreate the formula to isolate E
F + V = E + 2
E = F+V - 2
Step 2: Plug in the value of the variables
E = F+V - 2
E= 20 + 12 - 2
E = 30
Step 3:
The value of E is 30
Final answer:
The Polyhedron has 30 edges
can someone pls help with this problem?
Answer:
(6√13)/13
Step-by-step explanation:
You want the exact value of cot(arcsin(√13/7)).
Trig ratiosThe relevant trig ratios are ...
Sin = Opposite/Hypotenuse
Tan = Opposite/Adjacent
Cot = 1/Tan = Adjacent/Opposite
Pythagorean theoremThe Pythagorean theorem can be used to find the side adjacent to the angle whose sine is √13/7. Using the sine ratio, we can take the opposite side to be √13, and the hypotenuse to be 7. Then the adjacent side is ...
adjacent² +opposite² = hypotenuse²
adjacent² +(√13)² = 7²
adjacent² = 49 -13 = 36
adjacent = √36 = 6
CotangentThen the cotangent of the angle is ...
cot(arcsin(√13/7)) = adjacent/opposite = 6/√13
cot = (6√13)/13
Line RQ is a perendicular bisector to line PS at Q between P and A. By which of the five congruence statements HL, AAS, ASA, SAS, SSS, can you immediatley conclude that triangle PQR is congruent toe triangle SQR
Figure it out ur self
This month, a vegetarian restaurant used 9,168 ounces of spinach. That is 20% more than last month, when the restaurant had a different menu. How much spinach did the restaurant use last month?
Consider 9,168 ounces of spinach is 20% more than the amount of spinach of the last month. If x is such unknown amount of spinach, you can write:
[tex]x+(\frac{20}{100})x+9,168[/tex]where (2/100)x factor represents the 20% of x.
Simplify the pervious equation and solve for x:
[tex]\begin{gathered} x+0.2x=9,168 \\ 1.2x=9,168 \\ x=\frac{9,168}{1.2} \\ x=7,640 \end{gathered}[/tex]Hence, last month the restaurant used 7,640 amount of spinach.
PLEASE HELP ASAP!!!!! DUE SOON!!! FULL ANSWER!!!!!
A woman can bicycle 44 miles in the same time as it takes her to walk 8 miles. She can ride 9 mph faster than she can walk. How fast can she walk?
She can walk _____________ mph
Answer: 4 mph
Step-by-step explanation:
If woman can walk xmph, then she can ride {x + 10} mph (because she can ride 10 mph faster than she can walk)
Woman ride 28 miles by 28 hours, and can walk 8 miles by 8 hours.
x+10 x
28 =8 [tex]28x=8%28x%2B10%2928x=8x%2B8020x=80x=80%2F20x=4[/tex]
x+10 x
Prove that if x and y are real numbers, then max(x, y) +
min(x, y) = x + y. [Hint: Use a proof by cases, with
the two cases corresponding to x ≥ y and x
Real numbers contain the number zero and can be either positive or negative.
If x > y, then max (x, y) = x and min (x, y) = y.
So, max (x, y) + min (x, y) = x + y
What is meant by real numbers?Real numbers contain the number zero and can be either positive or negative. Because they exists not imaginary, which exists a separate type of number system, they are directed to as real numbers. Unquantifiable quantities, like the square root of -1, are referred to as imaginary numbers.
A "actual" and practical idea, infinity. Infinity, on the other hand, is not a number on the real number line since it is not a part of the mathematically defined set of "real numbers."
If x > y, then max (x, y) = x and min (x, y) = y.
So, max (x, y) + min (x, y) = x + y
If x ≤ y , then max (x, y) = y and min (x, y) = x.
And we have, max (x, y) + min (x, y) = y + x = x + y
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The measure of an angle is 28.5°. What is the measure of its complementary angle?
When the measure of an angle is 28.5° then the angle measure of its complementary angle will be 61.5°.
What is complementary angle?They are referred to as complementary angles when the sum of two angles is 90 degrees. For instance, the angles of 30 degrees and 60 degrees complement one another.
If we know the measurement of one angle, we can easily find the unknown angle because the sum of complementary angles equals 90 degrees.
As an illustration, if one of the two angles is 45 degrees, then the formula is:
x + 45 = 90
x = 90 - 45 = 45°.
If 2 complementary angles adds up to 90°
So the complementary angle of 28.5° is
90° - 28.5° = 61.5°
Thus, the angle measure of its complementary angle will be 61.5°.
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Solve each system by graphing. If the lines are parallel, write no solution. If the lines coincident, write infinitely many solutions.
Answer:
No Solution
Explanation:
Given the system of equations:
[tex]\begin{gathered} y-2x=4 \\ y=5+2x \end{gathered}[/tex]First, graph each equation using the x and y-intercepts.
Equation 1
[tex]\begin{gathered} y-2x=4 \\ \text{When }x=0,y=4\implies\text{Point (0,4)} \\ \text{When y}=0,x=-2\implies\text{Point (-2,0)} \end{gathered}[/tex]Join the points (0,4) and (-2,0) as done below:
Equation 2
[tex]\begin{gathered} y=5+2x \\ \text{When }x=0,y=5\implies\text{Point (0,5)} \\ \text{When y}=0,x=-2.5\implies\text{Point (-2.5, 0)} \end{gathered}[/tex]Join the points (0,5) and (-2.5, 0) as done below:
We observe that the two lines are parallel.
Therefore, the system of equations has No Solution.
6 1/9to a mixed number is?
Answer: It's already a mixed number; if your talking about improper fractions it is 55/9
Step-by-step explanation:
6x9+1
6x9=54+1=55/9
Answer:
55/9
Step-by-step explanation:
Because 9 x 6 is 55 then + 1 is 55
A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses.
4, 19, 7, 15, 13, 4
Find the mean number of hours for these students.
If necessary, round your answer to the nearest tenth.
Answer:
10.3
Step-by-step explanation:
To calculate the mean we need to:
(4 + 19 + 7 + 15 + 13 + 4)/6
10.33333,...
Round to nearest tenth: 10.3
A company surveyed 1200 people. Twice as many females as males. How many each were surveyed
Females: X
Males: Y
X=2Y because "Twice as many females as males"
The total surveyed are:
[tex]x+y=1200[/tex][tex]2y+y=1200[/tex]Then we have:
[tex]3y=1200[/tex][tex]y=\frac{1200}{3}=400[/tex]From the first equation:
[tex]x=1200-y=1200-400=800[/tex]So, males are 400 and females are 800.
MODELING WITH MATHEMATICS The top of the slide is 12 feet from the ground and has an angle of depression of 53°.What is the length of the slide? Round your answer to the nearest whole number.12 ft53AThe slide is aboutfeet long.
Solution:
From the given figure;
[tex]\begin{gathered} Opposite=12\text{ feet} \\ Hypotenuse=length\text{ of slide} \\ \theta=53\degree \end{gathered}[/tex]Applying SOHCAHTOA
[tex]\begin{gathered} \sin\theta=\frac{Opposite}{Hypotenuse} \\ \sin53\degree=\frac{12}{Hypotenuse} \\ Hypotenuse=\frac{12}{\sin53\degree} \\ Hypotenuse=15.02562=15\text{ feet \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, the slide is about 15 feet long
Find the length of the hypotenuse of the triangle pictured below. Give your answer accurate to at least 2 decimal places. 8. 7 hypotenuse =
We can use the Pythagoras Theorem:
[tex]\begin{gathered} 8^2+7^2=hypotenusa^2 \\ \text{hypotenusa}=\sqrt[\square]{8^2+7^2}=\sqrt[]{64+49}=\sqrt[]{113}\approx10.63 \end{gathered}[/tex]The hypotenuse is 10.63
can you explain the steps to letter a which is above the word solution i dont understand them
Given the series:
[tex]1-\frac{1}{3}+\frac{1}{9}-...[/tex]State if the series is convergent or divergent and if convergent, find its sum.
The sequence of terms forms a geometric pattern. Each term is found by multiplying the previous term by a constant number (the common ratio).
Let's find the value of the common ratio by dividing any two successive terms, for example:
[tex]r=\frac{-\frac{1}{3}}{1}=-\frac{1}{3}[/tex]The common ratio is greater than -1 and less than 1, so the series is convergent.
Now we find the sum of the infinite series by using the formula:
[tex]S=\frac{t_1}{1-r}[/tex]Where t1 is the first term, that is, t1 = 1.
Substituting:
[tex]S=\frac{1}{1-\left(-\frac{1}{3}\right)}[/tex]Now we add the numbers to the denominator:
[tex]S=\frac{1}{1+\frac{1}{3}}[/tex]We have a sum of an integer and a fraction:
[tex]1+\frac{1}{3}[/tex]To add these numbers, we must get them to have the same denominator, thus:
[tex]1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}[/tex]Operating:
[tex]S=\frac{1}{\frac{4}{3}}[/tex]To divide by a fraction, we multiply by its reciprocal:
[tex]S=1\cdot\frac{3}{4}=\frac{3}{4}[/tex]May I please get help with this for I am confused S to hash by my original and final points of the figure and where I should Rotate it to 270° clockwise
ANSWER:
Point in original figure (2, -3)
Point in final figure (-3, -2)
STEP-BY-STEP EXPLANATION:
The first thing is to determine the original point of the figure on the graph, which would be:
[tex]P(2,-3)[/tex]The rule for 270° counterclockwise rotation is as follows:
[tex](x,y)\rightarrow(y,-x)[/tex]We apply it in this case, and the new point would be:
[tex]P(2,-3)\rightarrow P^{\prime}(-3,-2)[/tex]We represent the result on the graph, as follows
A) In how many years will both companies have the same profit ?
B) Approximately what will that profit be ?
C) Which company’s profits are growing more quickly
Answer: 3 years
$60,000
Company B
Step-by-step explanation: Analyze the data on the graph
if the probability of a airplane flight arrives on time is 0.75 find the probability that out of 3 flights ALL arrive on time? and out of 3 flights at least one of them arrives on time?
ANSWER
[tex]P(\text{all}-3)=0.42[/tex]EXPLANATION
We want to find the probability that all 3 flights will arrive on time.
To do that, we have to find the product of the probability that each plane will arrive on time three times.
That is:
[tex]\begin{gathered} P(\text{all}-3)=0.75\cdot0.75\cdot0.75 \\ P(\text{all}-3)=0.42 \end{gathered}[/tex]That is the answer.
helppppppppppppppppppppppppp
Answer:
No
Step-by-step explanation:
V/3 is -35, which is smaller than 5
B. -3/4x-4=-6C. Is 0 solution to -3/4x-4>-6Select answerYes. No.D. Using interval Notation, solve: -3/4x-4>-6
Explanation:
Part A:
The question is given below as
[tex]\begin{gathered} whenx=0,evaluate \\ -\frac{3}{4}x-4= \end{gathered}[/tex]By putting x=0, we will have that
[tex]\begin{gathered} \begin{equation*} -\frac{3}{4}x-4 \end{equation*} \\ -\frac{3}{4}(0)-4 \\ =-4 \end{gathered}[/tex]Hence,
The final answer for part A is
[tex]\Rightarrow-4[/tex]Part B:
[tex]\begin{gathered} solve, \\ -\frac{3}{4}x-4=-6 \end{gathered}[/tex]add 4 to both sides
[tex]\begin{gathered} -\frac{3}{4}x-4=-6 \\ -\frac{3}{4}x-4+4=-6+4 \\ -\frac{3}{4}x=-2 \\ coess\text{ multiply, we will have} \\ -3x=-2\times4 \\ -3x=-8 \\ divide\text{ both sides by -3} \\ \frac{-3x}{-3}=-\frac{8}{-3} \\ x=\frac{8}{3} \end{gathered}[/tex]Hence,
The final answer for part B is
[tex]\Rightarrow x=\frac{8}{3}[/tex]Part C:
[tex]-\frac{3}{4}x-4>-6[/tex]Add 4 to both sides, we will have
[tex]\begin{gathered} -\frac{3}{4}x-4\gt-6 \\ -\frac{3}{4}x-4+4\gt-6+4 \\ -\frac{3}{4}x>-2 \\ cross\text{ multiply} \\ -3x>-2\times4 \\ -3x>-8 \\ divide\text{ bth sides by -3} \\ \frac{-3x}{-3}>-\frac{8}{-3}(the\text{ sighn will be reversed\rparen} \\ x<\frac{8}{3}(0\text{ is a solution\rparen} \end{gathered}[/tex]Hence,
The final answer for part C is YES
Part D:
[tex]\begin{gathered} -\frac{3}{4}x-4\gt-6 \\ -\frac{3}{4}x-4+4\gt-6+4 \\ -\frac{3}{4}x>-2 \\ cross\text{ multiply} \\ -3x>-2\times4 \\ -3x>-8 \\ divide\text{ bth sides by -3} \\ \frac{-3x}{-3}>-\frac{8}{-3}(the\text{ sighn will be reversed\rparen} \\ x<\frac{8}{3} \\ hence,in\text{ interval notation we will have the final answer be} \\ (-\infty,\frac{8}{3}) \end{gathered}[/tex]Hence,
The final answer for part D is given below as
[tex]\Rightarrow(-\infty,\frac{8}{3})[/tex]
Three cards are drawn with replacement from a standard deck of 52 cards. Find the the probability that the first card will be a spade, the second card will be a red card, and the third card will be a face card. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Given:
The total cards is: 52
Number of spade cards: 13
Number of red cards: 26
Number of face cards: 12
Therefore,
[tex]P(\text{spade)}=\frac{13}{52}=\frac{1}{4}[/tex][tex]P(red)=\frac{26}{52}=\frac{1}{2}[/tex][tex]P(\text{face)}=\frac{12}{52}=\frac{3}{13}[/tex]The probability that the first card will be a spade, the second card will be a red card, and the third card will be a face card is given by:
[tex]P(spade\text{ and red and face)=P(spade)}\cdot P(red)\cdot P(face)[/tex]Substitute:
[tex]=\frac{1}{4}\cdot\frac{1}{2}\cdot\frac{3}{13}=\frac{1\cdot1\cdot3}{4\cdot2\cdot13}=\frac{3}{104}[/tex]Answer: 3/104
