how many years would it take an amount of money to double if it is invested at 10 % compounded continuously?
Answers
It will take 7 years to double the invested amount if the invested amount is compounded at 10% continuously.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if we have $100 and it generates 5% interest annually, we will have $105 at the end of the first year. We will wind up with $110.25 at the conclusion of the second year.Our investment will double at a 10% interest rate in roughly 7 years (72 x 10% = 7.2); at a 12% interest rate, it will double in roughly 6 years (72 x 12%).Therefore, it will take 7 years to double the invested amount if the invested amount is compounded at 10% continuously.
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Related Questions
What is the length of BC
Answers
Answer:
\(BC \approx 2.24\)
Step-by-step explanation:
We can form a right triangle with BC as the hypotenuse.
Then, we can apply the Pythagorean Theorem to solve for the length of BC.
The dimensions of this right triangle are base: 2, height: 1.
Plugging these values into the theorem:
\(a^2 + b^2 = c^2\)
\(2^2 + 1^2 = BC^2\)
\(4 + 1 = BC^2\)
\(5 = BC^2\)
\(\boxed{\sqrt5 = BC}\)
We can approximate \(\sqrt5\) as:
\(\boxed{BC \approx 2.24}\)
at what point (x,y) is the function f(x)=6−7x closest to the point (−10,−4)? enter an exact answer.
Answers
The exact solution of this equation involves solving a quadratic equation, which may not result in a simple integer value for x.
To find the point (x, y) on the function f(x) = 6 - 7x that is closest to the point (-10, -4), we need to minimize the distance between the two points.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, we want to minimize the distance between the point (-10, -4) and any point on the function f(x) = 6 - 7x. So we can set up the distance equation:
d = sqrt((-10 - x)^2 + (-4 - (6 - 7x))^2)
To find the point (x, y) that minimizes the distance, we can find the value of x that minimizes the distance equation. Let's differentiate the distance equation with respect to x and set it equal to zero to find the critical point:
d' = 0
Differentiating and simplifying the equation, we get:
(-10 - x) + (-4 - (6 - 7x))(-7) = 0
Solving this equation will give us the value of x at the closest point. Plugging this x-value into the function f(x) = 6 - 7x will give us the corresponding y-value.
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Select all the possible names for the shape.
Answers
The possible names for the shape in the image are Parallelogram and Quadrilateral since it has two equal opposite sides which are parallel.
What are the possible names of the given shape?First we take a look of the properties of the likely names;
Properties of Parallelograms
Opposite sides are parallel.Opposite angles and sides are congruent.Same-Side interior angles (consecutive angles) are supplementary.Diagonals of a parallelogram bisect each other,Properties of Quadrilaterals
Has four sides.Two diagonals.some of interior and exterior angle gives 360 degree.Properties of Rectangles
Opposite sides are parallel and equal to each other.Each interior angle is equal to 90 degrees.The diagonals bisect each otherProperties of Rhombus
Rhombus has four interior angles.The opposite angles of a rhombus are equal to each other.All four sides are equalProperties of Trapezoids
The bases (the top and bottom) are parallel to each otherThe base angles and the diagonals of an isosceles trapezoid are equal.The side lines are not parallelFrom the properties, the shape is not a rectangle because each of the interior angle is not 90 degrees. It is not a Rhombus because all its sides are not equal. It is not a Trapezoid because only the bases are parallel to each each other.
Hence, the possible names for the shape in the image are Parallelogram and Quadrilateral since it has two equal opposite sides which are parallel.
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2/3(x+6)=-8 whats the value of x?
Answers
Answer:
x=-18
Step-by-step explanation:
Answer:
The answer is -18
Step-by-step explanation:
STEP 1:
\(3 \times \frac{2}{3} (x + 6) = 3( - 8)\)
2(x+6) = -24
______________________________________
STEP 2:
Divide both sides by 2:
\( \frac{2(x + 6)}{2} = \frac{ - 24}{2} \)
________________________________
STEP 3:
Simplify:
\(x + 6 = - 12\)
Subtract 6 from both sides:
\(x + 6 - 6 = - 12 - 6\)
________________________________
STEP 4:
\(x = - 18\)
Therefore, your answer is -18.
Ask more questions if you don’t understand! :)
The depth of a diver is her distance below sea level because depth represents a distance
Answers
The depth of the diver is 32 feet below sea level.
What is the angle of elevation?The angle of elevation is the angle between the observer's eyesight horizontal line and the object. The complete question can be seen in the image attached below.
The depth of the diver is the absolute value of -32 since it can't be negative.
= |-32|
= 32
Therefore, we can conclude that the depth of the diver is 32 feet below sea level.
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what is the domain???
Answers
The domain is the set of all x-values used by the graph.
In this graph, all x-values less than or equal to 6 are used, so the domain is
(-infty, 6] or { x | x ≤ 6 }
the description of simple integer arithmetic expressions with addition and multiplication cannot be represented by a context-free grammar.
Answers
Simple integer arithmetic expressions with addition and multiplication cannot be represented by a context-free grammar due to their recursive and hierarchical nature.
Context-free grammars (CFGs) are formal grammars that can be used to generate languages based on a set of production rules. However, CFGs are limited in their ability to represent certain types of languages. One such limitation is the inability to represent the recursive and hierarchical structure of simple integer arithmetic expressions involving addition and multiplication.
In simple integer arithmetic expressions, operands can be combined using addition and multiplication operators. These expressions can be nested, with subexpressions appearing within larger expressions. The recursive nature of these expressions poses a challenge for CFGs because they require an unbounded number of production rules to capture all possible levels of nesting.
CFGs are designed to handle languages with a linear structure, where the order of symbols is important but not their hierarchical relationships. While CFGs can handle addition or multiplication operations individually, they struggle to capture the nested structure and precedence rules inherent in arithmetic expressions.
To represent simple integer arithmetic expressions with addition and multiplication, more powerful formalisms such as context-sensitive grammars or parsing algorithms like recursive descent or operator precedence parsing are typically used. These approaches can handle the recursive and hierarchical nature of arithmetic expressions, allowing for the correct interpretation of operators and operands based on their precedence and associativity.
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The complete question is :
why simple integer arithmetic expressions with addition and multiplication cannot be represented by a context-free grammar?
A rectangle has perimeter 20 m. express the area a (in m2) of the rectangle as a function of the length, l, of one of its sides. a(l) = state the domain of a.
Answers
In rectangle , The domain of A is: 0 ≤ l ≤ 5
To express the area of the rectangle as a function of the length of one of its sides, we first need to use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.
In this case, we know that the perimeter is 20 m, so we can write:
20 = 2l + 2w
Simplifying this equation, we can solve for the width:
w = 10 - l
Now we can use the formula for the area of a rectangle, which is A = lw, to express the area as a function of the length:
A(l) = l(10 - l)
Expanding this expression, we get:
A(l) = 10l - l^2
To find the domain of A, we need to consider what values of l make sense in this context. Since l represents the length of one of the sides of the rectangle, it must be a positive number less than or equal to half of the perimeter (since the other side must also be less than or equal to half the perimeter). Therefore, the domain of A is:
0 ≤ l ≤ 5
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a two digit number is such tht product is 15 . When 18 is added to the numberthe digits interchange .Find the numbers?
Answers
Answer:
35
What are the factors of 15?
1,15
3,5
It is a two digit number so it has to be 35 or 53
Add 18 to both numbers
35 + 18 = 53
53 + 18 = 71
35 became 53 so 35 is the answer
Hope this helps
Step-by-step explanation:
Asif, Sean, Bill, Francis, and Andrew are running against each other in a 100 m race. They all have an equal chance of winning.
Show the possible orders for the first three runners crossing the finish line.
What is the probability of Andrew being one of the first three runners to cross the finish line? Assume that there will not be a tie.
Answers
Answer:
a) see below for a listing of possible orders
b) 0.6
Step-by-step explanation:
You are asked to list the possible permutations of 5 runners, taken 3 at a time. Then, you are asked for the fraction of those that have Andrew among them.
PermutationsThe formula for the number of permutations of n objects taken k at a time is ...
P(n, k) = n!/(n -k)!
Then the number of ways three can place from five contestants is ...
P(5, 3) = 5!/(5 -3)! = 5·4·3 = 60
ListingFor listing purposes, we can represent the runners with the letters ...
A: AndrewB: BillC: FrancisD: AsifE: SeanThe order we choose for listing the permutations is to list a combination of three finishers, followed by the other 5 orders in which they can finish. In order of first, second, third, we can have ...
ABC ACB BAC BCA CAB CBA ABD ADB BAD BDA DAB DBA
ABE AEB BAE BEA EAB EBA ACD ADC CAD CDA DAC DCA
ACE AEC CAE CEA EAC ECA ADE AED DAE DEA EAD EDA
BCD BDC CBD CDB DBC DCB BCE BEC CBE CEB EBC ECB
BDE BED DBE DEB EBD EDB CDE CED DCE DEC ECD EDC
P(Andrew shows)In the above list, the first three of the five lines all have Andrew as one of those who "show" in the race.
P(Andrew shows) = 3/5 = 0.6
Use the remainder theorem to find P (3) for P(x) = -x+3x² - 2x-5.Specifically, give the quotient and the remainder for the associated division and the value of P(3).믐Quotient =Х5 ?Remainder = 0p(3) = 0
Answers
We are given the function
\(P(x)=-x^3+3x^2-2x-5\)we are to use remainders theorem to find p(3)
Therefore
Given p(3) then x = 3
Hence
\(\begin{gathered} P(3)=-3^3+3(3)^2_{}-2(3)-5 \\ P(3)=-27+27-6-5 \\ P(3)\text{ = -11} \end{gathered}\)Hence, p(3) = - 11
Therefore, the Remainder is - 11
Finding the quotient
Given
\(\begin{gathered} p(x)\text{ = 3 }\Rightarrow\text{ x = 3} \\ \text{therefore} \\ x\text{ -3 is a factor} \end{gathered}\)Therefore to find the quotient we will use long division method
\(x-3\sqrt[]{-x^3+3x^{^2}-2x-5}\)This gives
\(\begin{gathered} \text{ -x}^2\text{ -2} \\ x-3\sqrt[]{-x^3+3x^2-2x-5} \\ \text{ (-) -}x^3+3x^2 \\ ----------------------- \\ \text{ -2x - 5 } \\ \text{ ( - ) -2x}^{}\text{ + 6} \\ -------------------- \\ \text{ - 11} \end{gathered}\)Therefore, The quotient is
\(-x^2-2\)From the solution above
P(3) = - 11
The first two steps in determining the solution set of the system of equations, y = x2 – 6x + 12 and y = 2x – 4, algebraically are shown in the table.
Which represents the solution(s) of this system of equations?
(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)
Answers
Answer:
(4,4)
Step-by-step explanation:
The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.
x^2 - 6x + 12 = 2x - 4
x^2 - 8x + 16 = 0
(x - 4)^2 = 0
x = 4
Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.
y = 2x - 4 = 2(4) - 4 = 4
Therefore, the solution of this system of equations is (4, 4).
Therefore, the correct answer is (4, 4).
Solve the simultaneous equations
5
x
+
2
y
=
11
−
5
x
+
4
y
=
13
Answers
Answer:
its 13
Step-by-step explanation:
are u try to find out what x and y equal
use the given information to find the values of the remaining five trigonometric functions. sin(x) = 3 5 , 0 < x < /2
Answers
The values of the remaining five trigonometric functions are:
cos(x) = 4/5
tan(x) = 3/4
csc(x) = 5/3
sec(x) = 5/4
cot(x) = 4/3.
Using the given information, we can use the Pythagorean identity to find the value of cos(x):
cos²(x) = 1 - sin²(x)
cos²(x) = 1 - (3/5)²
cos²(x) = 1 - 9/25
cos²(x) = 16/25
cos(x) = ±4/5
Since 0 < x < π/2, we know that cos(x) is positive, so cos(x) = 4/5.
Now we can use the definitions of the remaining trigonometric functions to find their values:
tan(x) = sin(x) / cos(x) = (3/5) / (4/5) = 3/4
csc(x) = 1 / sin(x) = 5/3
sec(x) = 1 / cos(x) = 5/4
cot(x) = 1 / tan(x) = 4/3
Therefore, the values of the remaining five trigonometric functions are:
cos(x) = 4/5
tan(x) = 3/4
csc(x) = 5/3
sec(x) = 5/4
cot(x) = 4/3.
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For National High Five Day, Ronnie’s class decides that everyone in the class should exchange one high five with each other person in the class. If there are 20 people in Ronnie’s class, how many high fives will be exchanged?
Answers
To determine the number of high fives that will be exchanged, we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person .
To calculate the number of unique pairs, we can use the formula for combinations, which is nC2, where n is the number of people .So, for Ronnie's class with 20 people, the number of high fives exchanged is:20C2 = (20 * 19) / (2 * 1) = 190.Therefore, a total of 190 high fives will be exchanged in Ronnie's class on National High Five Day. we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person needs to give a high five to every other person, excluding themselves.
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Which of the following is the best deal? A. 6-oz box of crackers for $1.08c. 8-oz box of crackers for $1.20b. 7-oz box of crackers for $1.19d. 9-oz box of crackers for $1.26
Answers
Answer:
Step-by-step explanation:
The answer is D
1.19/7-.17
1.20/8-.15
1.26/9-.14
1.08/6-.18
i think this is it
Mrs. Ciardiello traveled 322 miles in 7 hours. How many miles did she travel per hour?
100 POINTS AND BRAINLIST
Answers
Answer: 46 mph
Step-by-step explanation:
322 divided by 7 is 46 tyyy stan bts!
Variables on both sides
4x + 9 = 2x + 13
Answers
Answer:
x = 2
Step-by-step explanation:
i guess
Ground Turkey meat costs 1.29 per pound. how much would 1.08 pounds of turkey meat cost.
Answers
Answer:
1.194
Step-by-step explanation:
its just keeps going with the four
can someone answer all that's question....I really² need the answer
Answers
1.
In the triangle that contains x (call the other 2 angles as a and b, where a is the angle that is supplemetary to the center angle.)
a = 180 - 110 = 70 (supplemetary angles add up to 180)
b = 30 (b and the angle measures 30 are in the same segment.)
-> x = 180 - 70 - 30 = 80.
2. In triangle PRT, v = 180 - 40 - 70 = 70.
Since P,Q,S,T all lies on the circumference, PQST is a cyclic quadrilateral.
-> w = 180 - PQS = 180 - (180 - 70) = 70.
3.
i) A 1:2 scale means that all sides of P must be shortened by twice the lengths.
Since D is the only shape with the sides shortened from P, it's the correct option.
ii) A 1:1/2 scale means that all sides of P must be enlarged by twice the lengths.
Therefore, the measures of the sides become sqrt(20),6,4,6 (clockwise from diagonal), which is B.
4. Using the Pythagoras' theorem, we can find the hypotenuse PR : \(\sqrt{12^{2} + 5^{2} } = 13\)
sin(x) = QP/PR = 5/13 = 0.385 (rounded to 3 d.p)
tan(y) = QP/QR = 5/12 = 0.417 (rounded to 3 d.p)
Camila drew a triangle with a side that is 24 inches long and a side that is 18 inches long. Which of the following could be the length of the third side of the triangle that Camila drew? Select THREE that apply
A
42 inches
B
40 inches
C
18 inches
D
7 inches
E
6 inches
F
5 inches
Answers
Answer:
The answer is a b and there is one more but I don’t know it I’m sorryyyy
Step-by-step explanation:
X+y=150/2
x+y=75 find the solution using cramers rule
Answers
Answer:
I didn’t know if I was solving for x or for y but I believe that the answer is x=75-y
Step-by-step explanation:
Solve by simplifying both sides of the equation, then isolating the variable.
The mean of 35,25,45,30,45,30,25,4030,35
Answers
Answer:
You're mean should be 34.
Step-by-step explanation:
The mean of a set of numbers is the sum divided by the number of terms.
Hope this helps.
The table represents a function.
What is f(5)?
A. -8
B. -1
C. 1
D. 8
Answers
Answer:
A. -8
Step-by-step explanation:
We can look at the table and figure out how we get f(5)
really its just the x value pugged into the x value for the function
after that we look on the table, f(5) is -8 because at the bottum of the table it shows 5 and -8
High Hopes^^
Barry-
The length of a rectangle is 3 inches more than its width. If the perimeter is 42 inches find the demensions of the rectangle
Answers
Answer:
W-18inches L-21inches
Step-by-step explanation:
42-6 = 36/2 = 18
Width is 18 inches
and
Length is 21 inches
Find the missing side lengths of each triangle.
Answers
4d - 13 = 12 - d
5d = 25
d = 5
hence,
LK = d + 6
= 5 + 6
= 11
help me on this questioj pelase
Answers
Answer:
A
A
Step-by-step explanation:
8) because of the rules of angles we know that all angles found on a line are equal to 180 degrees, and all angles opposite one another are equal. because of this A is not possible. 90 and 40 do not add up to 180 degrees, and are not equivalent to each other.
9) using the same rules as above, we know that the two angles have to add up to 180 degrees (they can't be equal this time). A is not possible.
Write an equation of the line that passes through (1,-2) and (-5,4)
Answers
Answer: x+y+1=0
Step-by-step explanation:
m=y2-y1/x2-x1
= 4-(-2) /-5-1
=6/-6
=-1
equation of line
y-y1=m(x-x1)
y-(-2) =-1(x-1)
y+2=-x+1
x-1+y+2=0
x+y+11=0
What Is The Slope Of The Line Passing Through (-3, 5) and (5, -3)?
A. Slope = -1
B. Slope = 0
C. Slope = 1
D. No Slope
Answers
Answer:
Answer choice A. Slope -1
Step-by-step explanation:
If we plot the two points on a graph we can see that the points go from left to right, starting from a higher point to a lower point. This means the slope is negative. B and D are the same choice, but just in different words, and 0 cannot be positive or negative. and C is positive, not negative. So it is A. I hope this helps, and I hope it's not wrong, but I don't think it is.
What is the value of x in the equation 0.7x – 1.4 = –3.5?
–7
–3
3
7
Answers
Answer: easy x=−3
Step-by-step explanation:
gotchu bro
Answer:
-3
Step-by-step explanation:
0.7x-1.4=-3.5
0.7x=-3.5+1.4
0.7x=-2.1
x=-2.1/0.7
x=-3