A coin sold for $271 in 1976 and was sold again in 1988 for $417. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V, = 271.
k=
(Round to the nearest thousandth.)
Answers
well, let's noticed, the original amount is $271 and 12 years later it turned to $417, so
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$417\\ P=\textit{initial amount}\dotfill &271\\ r=rate\to r\%\to \frac{r}{100}\dotfill &0\\ t=years\dotfill &12\\ \end{cases}[/tex]
[tex]417=271(1 + \frac{r}{100})^{12}\implies \cfrac{417}{271}=\left( \cfrac{100+r}{100} \right)^{12} \implies \sqrt[12]{\cfrac{417}{271}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[12]{\cfrac{417}{271}}=100+r\implies 100\sqrt[12]{\cfrac{417}{271}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{3.657\approx r} \end{array}}[/tex]
Related Questions
question if r and s are positive integers, is r over s less than one third ? (1) r is less than 20. (2) s is greater than 65.
Answers
The correct option e. Statements (1) and (2) TOGETHER are NOT sufficient.
(1) r is less than 20: NOT sufficient.(2) s is greater than 65: NOT sufficient.Define the term positive integers?The counting numbers or natural numbers, which are also known as the positive integers, are the numbers 1, 2, 3,... Any figure higher than zero is considered positive.For the stated question-
1. R is less than 20: insufficient since s is unknown.
2. Because there is no date for r, statement 2 is insufficient because S is bigger than 65.
We now have two conditions when combined. s>0 and s>65, r 20 and r>0.
Using the maximum possible value of r as an example and the least possible value of s as an example, the value is greater than 1/3.
Therefore, every values for r would only decrease, while s will rise.
Therefore, simply stating that it won't be below 1/3 will do.
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The complete question is-
If r and s are positive integers, is r/s less than 1/3 ?
(1) r is less than 20.
(2) s is greater than 65.
a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d. EACH statement ALONE is sufficient.
e. Statements (1) and (2) TOGETHER are NOT sufficient.
John drew a triangle with side lengths of 5, 12 and 13. His friend, Bryan, looked at it and asked John if it is a right triangle. John’s response was yes. Explain or show how John can prove to Bryan that the triangle is a right triangle.
Answers
Using Pythagoras theorem, the numbers are from a right angled triangle
Pythagoras TriplePythagorean triples are a2+b2 = c2 where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.
In this question, to find out if the numbers are a Pythagorean triple, we can use pythagoras theorem while assuming the longer side is the hypothenuse.
13² = 12² + 5²
169 = 144 + 25
169 = 169
The numbers are Pythagorean triple because the sum of square of the two sides is equal to the square of the hypothenuse.
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What is the solution to the equation below? 2(x-3)= 2x+5
A.) X=2 3/4 C.) There is no solution
B) x= 3 3/4 D.) There are infinitely many solution
Answers
The given algebraic equation 2(x-3)= 2x+5 has no solution. Option C is correct.
Given that,
To determine the solution to the equation 2(x-3)= 2x+5.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Given equation,
2(x-3)= 2x+5
2x - 6 = 2x + 5
-6 ≠ 5
Thus, The given algebraic equation 2(x-3)= 2x+5 has no solution. Option C is correct.
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A person casts a shadow that aligns with the shadow of a tree. The person is 5.5 feet tall, and casts a shadow of 8.25 feet long. The tree's shadow measures 22.5 feet long.
How tall is the tree? How far is the person standing from the tree?
Answers
Part a: Height of tree; 15 feet.
Part b: distance of tree from person; 14.25 feet.
What characteristics do related triangles share?When the ratio of two triangles' respective sides is equal in magnitude while their corresponding angles are congruent, two triangles are said to be comparable in geometry.Furthermore, two geometric forms are only regarded as congruent when their associated side lengths and angle magnitudes are congruent.We can now create an equation which can be used to calculate the height of the tree.Part a: Height of the tree;
We get the following mathematical formula (equation) since the ratio of a corresponding sides of similar triangles is equal in magnitude:
22.5/8.25 = x/5.5
In which
x is the height of the tree.
Then,
22.5/8.25 = x/5.5
Further simplifying;
8.25x = 22.5 × 5.5
8.25x = 123.75
x = 123.75/8.25
x = 15 feet. (height of the tree)
Part b: distance of tree from person;
These calculations can be used to determine how far away from the tree this individual is:
Distance equals the product of a person's shadow and a tree's shadow
Distance = 22.5 - 8.25
Distance = 14.25 feet.
Thus, distance of tree from person is 14.25 ft.
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An urn has 4 green balls and 6 red balls. A experiment consists of selecting 5 balls from the urn without replacement. Find the expected number of red balls chosen, and its variance.
Answers
The expected variance of red balls chosen is 2/3 from the urn.
Define the term variance?Variability is measured by the variance. The average of the squared variance is used to calculate it. The degree of dispersion within your data set is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.Six red balls and four green balls are in an urn.
Till a urn is empty, we take balls out of it one at a time without replacing them and noting their order of the colors.
Let X represent the proportion of red balls in the initial five drawings.Y represent the proportion in the next five draws.The, the variance is found as-
Variance(X,Y) = E(XY) - E(X).E(Y).E(XY)
E(XY) = 25×(6/10)(4/9)
E(X) = 5×(6/10)
E(Y) = 5×(4/10)
Thus,
Variance(X,Y) = 25(6/10)(4/9) - 25(6/10)(4/10)
Variance(X,Y) = 2/3
Thus, the variance for choosing red balls is 2/3.
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The hydrogen ion concentration, [H+], in a certain cleaning compound is [H+]=3.3x10^-12. Use the formula pH=-log [H+] to find the pH of the cleaning compound.
Answers
The pH of the cleaning compound is 2.51.
What is pH?pH, quantitative measure of the acidity or basicity of aqueous or other liquid solutions.
Given that, The hydrogen ion concentration, [H+], in a certain cleaning compound is [H+]=3.3x10^-12.
[OH-] = 1.0*10^-14/3.3*10^-12 = 0.303*10^-12
pH = -log0.303*10^-12 = 2.51
Hence, The pH of the cleaning compound is 2.51.
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B. If I go to be early, then I sleep well.
Converse:
Inverse:
Contrapositive:
Answers
Inverse: if i dont go to be early, then i dont sleep well
Contrapositive: if i dont sleep well, then i dont go to be early
The converse, inverse and contrapositive statements for the given conditional statement are :
Converse: if I sleep well, then I go to be early
Inverse: if I don't go to be early, then I don't sleep well
Contrapositive: if I don't sleep well, then I don't go to be early.
What is conditional statement?A conditional statement is a part of mathematical reasoning which is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning.
Given is a conditional statement, "If I go to be early, then I sleep well", we need to form its converse, inverse and contrapositive statements,
The rules for the given conditional statement are ;
Let p and q be the parts of the statement,
1) Converse statement = if p then q, converse = if q then p.
Therefore,
Converse: if I sleep well, then I go to be early.
2) Inverse statement = if p then q, inverse = if not p then not q.
Therefore,
Inverse: if I don't go to be early, then I don't sleep well.
3) Contrapositive statement = if p then q, Contrapositive = if not q then not p.
Therefore,
Contrapositive: if I don't sleep well, then I don't go to be early.
Hence, the converse, inverse and contrapositive statements for the given conditional statement are :
Converse: if I sleep well, then I go to be early
Inverse: if I don't go to be early, then I don't sleep well
Contrapositive: if I don't sleep well, then I don't go to be early.
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sam discovered that the pool in his backyard is leaking slowly. the pool holds 15,684 gallons of water, and is leaking at a rate of 8 gallons per day. after how many days will the pool be empty
Answers
Answer:
It will take the pool 1,960.5 days for the pool to become empty.
Step-by-step explanation:
We can find this answer by simply dividing the two numbers together:
15,684 ÷ 8 = 1,960.5 days.
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Answer:
1960.5 days
Step-by-step explanation:
[tex]\boxed{\textsf{Rate (gallons per day)} = \sf \dfrac{Volume\;(gallons)}{Number\; of\; days}}[/tex]
Given:
Volume = 15,684 gallonsRate = 8 gallons per daySubstitute the given values into the formula:
[tex]\implies 8=\dfrac{15684}{\sf Number\;of\;days}[/tex]
[tex]\implies \sf Number\;of\;days=\dfrac{15684}{8}[/tex]
[tex]\implies \sf Number\;of\;days=1960.5[/tex]
Therefore, if the pool is leaking at a rate of 8 gallons per day, the pool will be empty after 1960.5 days.
help help help help help me
Answers
What grade is that?
Step-by-step explanation:
Which form of a linear equation do you prefer to use: slope-intercept form or point-slope form? list advantages and disadvantages of each. Compare your answer with a classmate's and discuss any differences.
Answers
Both slope-intercept form and point-slope form are equally important and useful, and easy to use. The advantages and disadvantages of both forms of linear equations are shown below.
Point-slope form:Advantages: One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form.
This form is helpful since it allows us to find the equation of the line by only knowing the slope and one point along the line.
Disadvantages: Since vertical lines have arbitrary slopes, one limitation of the point-slope form is that it cannot be used to describe the equation of a vertical line.
Standard form and slope-intercept form are two additional frequently used forms.
Slope-intercept:
Advantages: The slope of the line and the y-intercept are both clearly displayed in slope-intercept form.
The slope of the line and the single point the line passes through are both plainly displayed in point-slope form.
When working with equation systems, the standard form is more convenient. (specifically, to locate the intersection with matrices).
Disadvantages: Slope-intercept form has the same drawbacks as a point-slope form in that vertical lines cannot be represented since the slope of a vertical line is ill-defined.
Therefore, both slope-intercept form and point-slope form are equally important and useful, and easy to use. The advantages and disadvantages of both forms of linear equations are shown below.
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out of 240 racers who started the marathon, 209 completed the race, 22 gave up, and 9 were disqualified. what percentage did not complete the marathon?
Answers
The percentage of racers that did not complete the marathon is 12.9 %
What is arithmetic?
Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots
Main Body:
Total racers = 240
racers that completed race = 209
so racers that did not complete the marathon = 240 - 209
= 31
percentage of racers that did not complete the marathon = (31/240)*100
= 12.9 %
Hence percentage of racers that did not complete the marathon is 12.9%
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Write the word sentence as an equation. Then solve the equation.
5 more than a number x is 9.
An equation that represents this word sentence is
The solution is x =
Answers
So the equation would be
5 + x = 9
To solve for x we would isolate x on one side so it would be
X= 9 - 5
X = 4
Meaning that the solution is x = 4
Hopefully this is right just change it to the best of your understanding
Which side is the longest
Answers
Answer:
PR
Step-by-step explanation:
The longest side is opposite the largest angle.
Answer: There are two equal sides
Step-by-step explanation:
Considering P and R are both 48 degrees and the only different angle is Q that would mean there are two equal sides.
Hurry please i have 24 hours to do this. The area of the triangle below is 29.25 square feet. What is the length of the base?
6.5 ft
Answers
Answer:
length of base = 9 feet
Step-by-step explanation:
b= base A= area h= height
[tex]b=2*\frac{A}{h} = 2*\frac{29.25}{6.5} = 9[/tex]
which congruence theorem can be used to prove △bda ≅ △bdc?ahlbssacaasdsss
Answers
To prove △BDA ≅ △BDC, SSS congruence theorem should be used.
What is the Side-Side-Side congruence theorem of triangles?
If all three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by the SSS rule.
Given that ΔBDA is similar to ΔBDC and:
AD ≡ DC
AB ≡ BC
BD ≡ BD (shared side)
△BDA ≅ △BDC
The best postulate to use is the side-side-side (SSS) postulate.
Hence, to prove △BDA ≅ △BDC, the SSS congruence theorem should be used.
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Three cups of baking soda are poured into 9 mixing bowls so that each bowl holds the same amount of baking soda.
This visual model represents the situation, with each letter representing one of the bowls.
Three equally sized rectangles. Each rectangle is divided into 9 equal parts. Longer lines separate every 3 parts. The first 3 parts of the first rectangle are each labeled A. The second 3 parts of the first rectangle are each labeled B. The third 3 parts of the first rectangle are each labeled C. The first 3 parts of the second rectangle are each labeled D. The second 3 parts of the second rectangle are each labeled E. The third 3 parts of the second rectangle are each labeled F. The first 3 parts of the third rectangle are each labeled G. The second 3 parts of the third rectangle are each labeled H. The third 3 parts of the third rectangle are each labeled I.
How much baking soda does each mixing bowl hold?
Responses
19 cup
1 over 9, cup
16 cup
1 over 6, cup
14 cup
1 fourth, cup
13 cup
Answers
Answer:
Answer: 3 or 2 1/2 ethier is right
Step-by-step explanation:
V+6>5
how do you solve this equation?
Answers
Answer:
v > -1
Step-by-step explanation:
v + 6 > 5
We want to work backwards to solve this, therefore we must subtract 6 on both sides to isolate v.
v + 6 > 5
(- 6) (-6)
v > -1
a farmer wants to fence an area of 3750 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. what should the lengths of the sides of the rectangular field be so as to minimize the amount of fencing needed?
Answers
The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 3750, hence:
Area = length * width = x * y
3750 = xy
y = 3750/x
A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:
Amount of fencing needed (P) = x + x + y + y + y = 2x + 3y
Amount of fencing needed (P) = 2x + 3(3750/x) = 2x + 1800/x
To minimize the amount of fencing needed, dP/dx = 0, hence:
dP/dx = 2 - 1800/x²
2 - 1800/x² = 0
2 = 1800/x²
2x² = 1800
x² = 900
x = 30 feet
y = 600/x = 600/30 = 20 feet
Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet
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Solve 4x³ 40x2 +96x = 0 by factoring. List the answers
from least to greatest separated by commas with no spaces.
-
Answers
Answer:
x=0,4,6
Step-by-step explanation:
How can the triangles be proven similar by the SAS similarity theorem? I give brainiest
Answers
Answer:
Show that the ratios UV/XY and WV/ZY are equivalent, and ∠V ≅ ∠Y.
if the classroom supplies, outdoor games, toys for the playground and paint for all three classrooms are represented by 3x2, xy3, 2x3y, and 4xy respectively, multiply the polynomial expressions. write your answer in descending order according to the x variable. please use the palette below to enter your answer.
Answers
To represent outside games, playground equipment, and paint for all three classrooms, multiply the polynomial expressions by 3x2, xy3, 2x3y, and 4xy, accordingly.
This polynomial's formula is 12x^5y^3 + 24x^4y^3 + 18x^3y^3
Numerous branches of mathematics and science use polynomials. used to approximate other functions in calculus and numerical analysis to approximate other functions in calculus and numerical analysis. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics.Algebraic varieties and polynomial rings, two core concepts in algebra and algebraic geometry, are constructed using polynomials in higher mathematics.
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a ladder reaches a maximum length of about 23 m. for any ladder to be safe, the angle it makes with the ground should be between 65° and 70°. one storey of a building is about 4 m. a fire breaks out on the fifth storey of a building. will the extension ladder reach the fifth storey safely?
Answers
Answer:
Given,
Let's assume the maximum safe height of wall = h
angle formed between ladder and ground = 70°
length of ladder = 16 ft
From the given data, it can be seen that ladder will form a right angle triangle structure with the wall
So,from the concept of trigonometry,
Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70
o
=
length of ladder
maximum safe height of wall
= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70
o
=
16 ft
h
= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70
o
=> h = 16 x 0.9396
=> h = 15.03 ft
So, the maximum safe height that can be reached by the ladder will be 15.03 ft.
Sorry I put the wrong answer.
solve for the variable c in this equation: a(c + b) = d question 2 options: or c = d/a - b or c = d/a + b or c = b - d/a or c = d/b - a
Answers
Solving the equation a(c + b) = d for variable c, the variable c = (d/a) – b. (Option A)
Equation refers to a statement that represents an equality of values of two mathematical expressions and is indicated by the sign =.
In the given equation a(c + b) = d, in order to solve for the variable c, we must isolate the c variable at one side and collect other variables on the other side of the equation.
Given equation is:
a(c + b) = d
Divide both sides by a:
(1/a)*a(c + b) = d/a
c + b = d/a
Subtract b from both sides:
c + b – b = (d/a) - b
c = (d/a) – b
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Please help :') ty ty ty ty ty. Show your work too! :)
Answers
a farmer needs to enclose three sides of a garden with a fence (the fourth side is a river). the farmer has 47 meters of fence and wants the garden to have an area of 266 sq-meters. what should the dimensions of the garden be?
Answers
The dimensions of the garden would be length = 28 meters and width = 9.5 meters.
What are quadratic equations?
A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, and b, are the coefficients, c is the constant term, and x is the variable. Since the variable x is of the second degree, there are two roots or answers for this quadratic equation.
Let the width be = w
Let the length be = L
enclose three side ( 2w+L) = 47 meter
L = 47-2w
Area of field = w*L
Area = w(47 - 2w)
266 = 47w - 2w²
2w² - 47w + 266 = 0
Solving this, we get
w = 14 or w = 9.5
The width should be less than the length so w = 9.5
Length = 47 - 2(9.5)
= 47 - 19
= 28 meters.
Hence, the dimensions of the garden would be length = 28 meters and width = 9.5 meters.
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some stickers were divided among avea, brianna, and carson in the ratio 1:3:4. brianna recieved 21 stickers. how many stickers did ava receive?
Answers
Avea received 28 stickers when brianna, and carson in the ratio 1:3:4 and brianna received 21 stickers.
What is a ratio?The ratio is defined as the comparison of two or more quantities of the same units, which shows how much bigger one quantity is than another.
Equating the ratios :Given,The ratio of the distribution of stickers among Avea, Brianna and Carson is 1:3:4
The number of stickers Briana received is 21
Let us consider x as the common factor of the given ratio then, The number of stickers received by the girls are
Avea = xBriana = 3x
Carson = 4x
As we know 3x = 21 x
= 21/3
= 7
then,4x
= 4×7
= 28
The number of stickers that Avea received is 28. Hence, the answer is 28
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Simplify the following expression completely. 3(2x-1)+5(2x-1)
Answers
Answer:
= 16x - 8
Step-by-step explanation:
3(2x - 1) + 5(2x - 1)
8(2x - 1)
16x - 8
Answer:
16x - 8
Step-by-step explanation:
Given expression,
→ 3(2x - 1) + 5(2x - 1)
Simplifying the expression,
→ 3(2x - 1) + 5(2x - 1)
→ 6x - 3 + 10x - 5
→ (6x + 10x) + (-3 - 5)
→ 16x +(-8)
→ 16x - 8
Hence, solution is 16x - 8.
Function g can be thought of as a translated (shifted) version of f(x) = x2.
++
-7-6-5-4-3-2
ल
1
उक्त
-2-
-3-
-5-
-6-
Write the equation for g(x).
9 (x) = [
9
+2
2 3 4 5 6 7
Answers
Answer: 3
Step-by-step explanation:
what is the answer i need an answer pls
Answers
Answer: The first option
Step-by-step explanation: Once you multiply all the denominators to make them the same, the numerators (in the original order they are given in) become 63, 16, and 44.
16<44<63, which is the first option.
a rectangle is 4 times a long as it is wide. if the length of the third side?
Answers
the length and breadth of the rectangle is L = 4, B =16
Let L and B stand for length and width, respectively.
a rectangle is 4 times a long as it is wide
L=4B …….(1) (1)
L1 and B1 should represent the revised length and width.
L1=(L+4)
B1=(B-1)
Area = L1 + B1 + 60.
=> (L+4)×(B-1)=60 …….(2) (2)
Using (1)-
=> (4B+4)×(B-1) =60
=> 4×(B^2–1) = 60
=> B^2–1 = 15
=> B^2 = 16
=> B = +4 or -4
B=4 inches because breadth is always positive.
L = 4 B = 16 inches.
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