The hours that it take a pipes to feel the same pool is 120 hours.
How to calculate the value?Rate demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this situation, 5 pipes can fill the pool in 24 hours.
The rate for a pipe will be:
= Number of hours × Number of pipe
= 24 × 5
= 120 hours
The time taken is 120 hours.
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Please help me with this question
To derive the formula that goes through these two points, we use the general equation for an exponential equation.
Y = a(b)^x
There we will substitute the two points into this equation to get two equations
45 = a(b)^2
5/9= a(b)^-1
By dividing the first equation by the second, we obtain:
27 = b^3
Therefore b= 3
We plug b=3 into the first equation using the second point:
45 = a(3)^2
We get a = 5
Therefore the equation is y = 5(9)^x
We can verify this equation by plugging in the two points given to see if it works.
5/9 = 5(9)^-1
5/9 = 5/9
And:
45 =5(9)^2
45 = 45
It does, so the equation is correct.
The answer is y =5(9)^x
What is exponential equation?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.Exponential equations are equations in which variables occur as exponents.For example, exponential equations are in the form a x = b y .To solve exponential equations with same base, use the property of equality of exponential functions .To learn more about exponential equation refer to:
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Kevin has an annual salary of $41,732, and he earned $33.52 interest from his savings account. He also paid $1050 in student loan interest and contributed $3900 to an IRA retirement account. Calculate Kevin’s adjusted gross income.
Kevin's adjusted gross income is $36, 815. 52
What is adjusted gross income?Adjusted gross income is simply described as gross income minus certain adjustments from the income.
These adjustments includes;
Educator expensesStudent loan interestAlimony paymentsContributions to an account, etcIt is calculated as;
Adjusted gross income = sum total of income - expenses
Now, let's substitute the values into the formula, we have;
Adjusted gross income = $(41,732 + 33.52) - $(1050 + 3900)
Add the values
Adjusted gross income = $(41, 765. 52 - 4950)
Subtract the values
Adjusted gross income = $36, 815. 52
Hence, the value is $36, 815. 52
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Heights are generally normally distributed. Men have a mean of 69.5 inches and standard deviation 2.4 inches. Women have
a mean of 63.8 inches and standard deviation 2.6 inches. The US Air Force has a height requirement for their pilots to be
between 64 inches and 77 inches.
Make sure you are rounding z-scores properly to two places.
Part A: Find the two z-scores for women who meet this height requirement z =
and z=
I
(larger value)
For Blank 1
Part B: Using the z-scores from part A, find the proportion of women who meet the height requirement. Give this answer as a
decimal.
Z=
(smaller value)
Part C: Find the two z-scores for men who meet this height requirement z =
(larger value)
Part D: Using the z-scores from part C, find the proportion of men who meet the height requirement. Give this answer as a
decimal.
QUESTION 2
(smaller value) and
Part E: If the height requirement were changed to exclude only the shortest 1% of women and tallest 1% of men, what are the
new heights? The short value would be
in inches and the tall value would be
in inches. Please give these two values rounded properly to one decimal place.
Normal distribution curve is symmetric around the mean, it shows that values close to the mean happen more frequently than those distant from the mean.
What is meant by normal distribution curve?A bell-shaped (symmetric) curve, the normal probability distribution or the normal curve. The mean of it is represented by and the standard deviation by σ.
In this example, the mean and median are both equal and lie in the center of the distribution; they are 64, and the standard deviation is 7, with 68% of the values falling within the first standard deviation, 95% within the second standard deviation, and 99.7% within the third. Once more, variance is equal to the standard deviation squared.
According to the normal distribution curve:
"the percent of women whose heights are between 64 and 69.5 inches" represents the values within 2 standard deviation.
Area from a value (Use to compute p from Z)
Value from an area (Use to compute Z for confidence intervals)
Let the parameters be
Mean 64
Standard deviation 2.75
Above 1.96
Below 1.96
Between 64 and 69.5
Outside -1.96 and 1.96
Area (probability) 0.4772
And that value is 95 % of the whole data
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according to wine-searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. random ratings of a pinot noir recently produced by a newly established vineyard in follow: excel file: data07-11.xlsx 87 91 86 82 72 91 60 77 80 79 83 96 a. develop a point estimate of mean wine score for this pinot noir (to decimals). 82.00 b. develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals). 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.
Below table showing calculation of Point Estimate of Mean and Standard Deviation:
Score X-X’ (X-X’)^2
87 5 25
91 9 81
86 4 16
82 0 0
72 -10 100
91 9 81
60 -22 484
77 -5 25
80 -2 4
79 -3 9
83 1 1
96 14 196
984 1022
Mean(X’) = Total Score/n
n = Total number = 12
X’ = 984/12 = 82
Standard Deviation (σ) = √∑(X-X’)^2/(n-1)
σ = √1022/(12-1)
σ = √1022/ 11
σ = 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389
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LMNO is a parallelogram. If NM\ =\ x+32\ and\ OL=2x+22,\NM = x+32 and OL=2x+22, find the value of x and then find NM and OL
Answer:
the value of x is 10
Step-by-step explanation:
Since LMNO is a parallelogram, the opposite sides are parallel and have the same length. This means that NO and LM have the same length, which we can call y. We can write the following equations to represent the given information:
NM = x + 32
OL = 2x + 22
NO = y
LM = y
Since NO and LM have the same length, we can set their lengths equal to each other to find the value of y:
x + 32 = y
2x + 22 = y
We can solve this system of equations by setting the two equations equal to each other and solving for x:
x + 32 = 2x + 22
-x = -10
x = 10
Substituting the value of x back into the equations for NM and OL, we find that:
NM = 10 + 32 = 42
OL = 2(10) + 22 = 32
Therefore, the value of x is 10, and the lengths of NM and OL are 42 and 32.
what number is 16 2/3% more than 240
280 is the number which is 16 2/3% more than 240
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.
(1/6) th of 240 = 240/6 = 40
40 more than 240 = 280
So, 280 is the number which is 16 2/3% more than 240
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The angle formed between one side and another, always less than 180 degrees.
Answer:obtuse angle
Step-by-step explanation:
An obtuse angle is an angle of greater than 90° and less than 180°. It is bigger than an acute angle. It is smaller than a straight angle, which measures 180°. Angles are measured with a protractor obtuse angle is specifically present in hexagon and pentagon and others.
O MEASUREMENT AND DATA
Introduction to the probability of an event
A spinner with 12 equally sized slices has 5 red slices, 3 blue slices, and 4 yellow slices. The dial is spun and stops on a slice at random. What is the probabili
that the dial stops on a slice that is not red?
Write your answer as a fraction in simplest form.
Explanation
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The probability that the dial stops on a yellow or blue slice will be 0.6667.
What is probability?
Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A spinner with 12 similarly measured cuts has 5 yellow cuts, 3 blue cuts, and 4 red cuts. The dial is turned and stops on a cut indiscriminately.
The total number of the event is given as,
Total events = 5 + 3 + 4
Total events = 12
The probability that the dial stops on a yellow or blue slice will be given as,
P = 3 / 12 + 5 / 12
P = 0.25 + 0.4167
P = 0.6667
The probability that the dial stops on a yellow or blue slice will be 0.6667.
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What is the quotient of
102 and 5?
The leftover after dividing 102 by 5 is the quotient, which is:
Quotient 20
Remainder 2
102 5: Quotient and Remainder
The quotient and remainder method is one way to determine the quotient and remainder of a division. The dividend (102) and the divisor are already known to us (5). Now, we need to determine the residual and the quotient:
The Quotient and Remainder procedure is as follows:
20 quotient, 5 | 102 dividend, -10 2, and a reminder
As can be seen:
The remainder is 2, while the quotient is 20.
Sometimes, the remaining part is referred to as the "modulo," or simply "mod." This notation is used to say that:
102 mod 5 = 2
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a 9 foot ladder is leaning against a wall. if the top of the ladder is sliding down the wall at a rate of
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]
Given that,
Length of the ladder is, [tex]l=9ft[/tex]
Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.
Now, from triangle ABC,
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
[tex]h^{2} +b^{2} =l^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = 81 (Equation-1)
Differentiating the above equation with respect to time, 't'.
So,
We can write,
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0
[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0
[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0 (Equation-2)
In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.
Let us assume,
h = 3 ft and db/dt = 3 ft/s
We can substitute values in equation-1,
[tex]3^{2} +b^{2}[/tex] = 81
9 + [tex]b^{2}[/tex] = 81
[tex]b^{2}[/tex] = 81-9
[tex]b^{2}[/tex] = 72
b = [tex]\sqrt{72}[/tex]
b = 8.48 ft
Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]
3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0
3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0
3*[tex]\frac{dh}{dt}[/tex] = - 25.44
[tex]\frac{dh}{dt}[/tex] = -25.44/3
[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s
Therefore,
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
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-y + 7y -54 = 0 what is the linear equation for y
The linear equation for y is y=9.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
-y+7 y-54=0
Add similar elements: -y+7 y=6 y
6 y-54=0
Move 54 to the right side
6 y=54
Divide both sides by 6
[tex]\frac{6 y}{6}=\frac{54}{6}[/tex]
Simplify
y=9
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what is the circumference
The circumference is 12.56
1,458, 486, 162, 54, … patterns
1,458, 486, 162, 54,
Every succeeding number is getting divided by 3.
What is patterns ?
A recurring arrangement of numbers, shapes, colors, and other elements is known as a pattern. The Pattern may be connected to any kind of occasion or thing. When a group of numbers are arranged in a certain way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Pattern of even numbers: 2, 4, 6, 8, 10, 1, 14, 16, 18...
Pattern of odd numbers: 3, 5, 7, 9, 11, 13, 15, 17, 19.
Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, and 21. so on.
The patterns among our 1,458, 486, 162, and 54 data must be found.
1458/3 = 486
486/3 = 162
162/3 = 54
54/3 = 18
18/3 = 6
6/3 = 2
so the patterns is Every succeeding number is getting divided by 3.
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1. A tire has the specification 225/60R14. What is the sidewall of the tire in inches (1 inch = 25.4 mm)?
a. 9.3in b. 60in
c. 8.9 in
d. 5.3in
2. If the diameter of a tire is 25 inches, approximate what distance does the tire cover in 8 rotations?
a. 628in
b. 392in
c. 60 in
d. 225in
The distance that tire covered in 8 rotations with diameter 25 inches is 628in using circle circumference's formula .
What is circumference of circle ?
The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.
The formula is :
2πr where r is the radius of the circle.
We know that diameter = 2*radius.
Given diameter = 25 inches
So, the radius = 25/2 inches.
So, the circumference = 2*(22/7)*(25/2)
Circumference of circle = distance covered by tire in one rotation.
So, the distance covered in 8 rotations = 8 * circumference
= 8* 2*(22/7)*(25/2)
= 628.5 inches
≈ 628 in
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ecall that one of the ten parts of the definition of a vector space says that if is a vector space, then there exists a vector in such that for all in hceggg
This means that for any vector v in the vector space V, there is a vector 0 in V such that v + 0 = v.
This is known as the identity property, and it states that adding 0 to any vector in V does not change the original vector. The identity property is an essential part of the definition of a vector space.
In general, a vector space is a set of objects called vectors that can be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field.
A vector space is a set V together with two operations that satisfy the eight axioms listed below.
Closure under addition. For all vectors u and v in V, the vector u + v is also in V.Closure under scalar multiplication. For all vectors u in V and all scalars c, the vector cu is also in V.Associativity of addition. For all vectors u, v, and w in V, (u + v) + w = u + (v + w).Commutativity of addition. For all vectors u and v in V, u + v = v + u.Existence of an additive identity. There exists a vector 0 in V such that for all vectors u in V, 0 + u = u + 0 = u.Existence of additive inverses. For every vector u in V, there exists a vector -u in V such that u + (-u) = (-u) + u = 0.Compatibility of scalar multiplication with field multiplication. For all vectors u and v in V and all scalars c and d, (c + d)u = cu + du and c(dv) = (cd)v.Compatibility of scalar multiplication with field addition. For all vectors u and v in V and all scalars c and d, c(u + v) = cu + cv.To learn more about vectors, visit:
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Marco has $16.72. He spends $9.21 on a movie ticket. How much money does Marco have left?
Responses
A $7.68$7.68
B $7.51$7.51
C $7.48$7.48
D $7.61
Answer:
7.51
Step-by-step explanation:
16.72 - 9.21
Find the value of the expression. x(x–y)–y(y^2–x) for x=4 and y=2
PLEASE ANSWE NOW
In △XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ.
AC = 7, AB = 5, and XY = 24. What is the perimeter of △XYZ?
Enter your answer in the box.
The perimeter of triangle XYZ is calculated as: 48 units.
What is the Perimeter of a Triangle?The perimeter of a triangle is found by summing all the lengths of the three sides of the triangle.
Given the following measures as shown in the image below as:
AC = 7
AB = 5
XY = 24
The perimeter of triangle XYZ = XY + YZ + XZ
Based on the triangle midsegment theorem, we have:
YZ = 2(AC) = 2(7)
YZ = 14
XZ = 2(AB) = 2(5)
XZ = 10
Therefore:
The perimeter of triangle XYZ = 24 + 14 + 10
The perimeter of triangle XYZ = 48 units.
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1. Find the slope and the y-intercept of each equation.
a. y = 2x - 6
m=
b=
The equation y = 2x - 6 is a line in the form known as Slope-Intercept Form. This form organizes the equation so that you can easily discern the y-intercept and slope.
Slope-intercept form is y = mx + b. So here, m = 2, b = -6.
Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long. Each wreath requires 5 yards of uncut ribbon. How many wreaths can Ms. Brooks make?
The number wreaths that Ms. Brooks make will be 7 wreaths.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It should be noted that an expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features. People make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects
Here, Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long.
Since each wreath requires 5 yards of uncut ribbon, the number of wreaths that Ms. Brooks make will be:
= (18 + 17) / 5
= 35 / 5
= 7 wreaths.
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Question 3
Evaluate g(x)=-3x+1, when x=10
Give a numerical answer.
Dan has a jar full of quarters and dimes. He has 21 more dimes than he has quarters. Overall, Dan has 67 coins. How many of each coin does Dan have?
The number of dimes and quarters that Dan has will be 44 and 23, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Dan has a container loaded with quarters and dimes. He has 21 additional dimes than he has quarters. Generally, Dan has 67 coins.
Let 'x' be the number of dimes and 'y' be the number of quarters. Then the equations are given as,
x = y + 21 ...1
x + y = 67 ...2
From equations 1 and 2, then we have
y + 21 + y = 67
2y = 46
y = 23
Then the value of the variable 'x' is calculated as,
x = 23 + 21
x = 44
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|x+9|=|-x-9|
How do I solve this equation and graph it?
The value of x is :
x≤ -9 or x > -9
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
|x+9|=|-x-9|
Both the sides have absolute symbols, consider as below:
x+9 = -x-9
=> 2x = -9 - 9 = -18
=> 2x = -18
=> x= -9
This means, x≤ -9 or x > -9
For graph:
consider as below:
y = |x+9|
y = |-x-9|
graph them without absolute symbols
consider upper v shaped graph. ignore downward v shaped graph
By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).
By plotting and joining those points, we get the graph as shown in the attachment.
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Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered
.Mich statement is correct based on the data?
The ratio of smoothie size to mangos used for Kim is 1.7, and the ratio of smoothie size to mangos used for Bri is 3: 28.
The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
The ratio of smoothie size to mangos used for Bri is 7:1, and the ratio of smoothie size to mangos used for Angela is 4: 28.
The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.
The solution is Option D.
The ratio of smoothie size to mangoes used for Kim is the same as the ratio of smoothie size to mangoes used for Angela
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the equation be represented as A
Now , the value of A is
The number of mangoes used by Bri = 1 mango
The amount of smoothie size of Bri = 7 oz
The number of mangoes used by Kim = 3 mangoes
The amount of smoothie size of Kim = 21 oz
The number of mangoes used by Angela = 4 mangoes
The amount of smoothie size of Angela = 28 oz
Now , the proportion is given by
The ratio of smoothie size to mangoes used by Kim = amount of smoothie size of Kim / number of mangoes used by Kim
Substituting the values in the equation , we get
The ratio of smoothie size to mangoes used by Kim = 21 / 3
The ratio of smoothie size to mangoes used by Kim = 7 : 1
Now , the proportion is
The ratio of smoothie size to mangoes used by Angela = amount of smoothie size of Angela / number of mangoes used by Angela
Substituting the values in the equation , we get
The ratio of smoothie size to mangoes used by Angela = 28 / 4
The ratio of smoothie size to mangoes used by Angela = 7 : 1
So , The ratio of smoothie size to mangoes used by Kim = The ratio of smoothie size to mangoes used by Angela = 7 : 1
Hence , ratio of smoothie size to mangoes used by Kim is equal to ratio of smoothie size to mangoes used by Angela
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Answer:
d
Step-by-step explanation:
i took the test and its right :)
explain the difference between arithmetic growth and exponential (geometric growth). would you recognize them if they were described in writing and/or by picture?
When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.
When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. An illustration of arithmetic growth is the ongoing elongation of roots. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.
The amounts added grow by a fixed rate of growth, expressed in percentages. Due to the fact that these remain constant while the amounts added rise, growth is then typically measured in doubling times.
Due to the fact that all populations of organisms have the potential to experience exponential growth, the concept of exponential growth is particularly intriguing in the field of population biology.
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A ball is dropped from a height of 80 ft. The elasticity of this ball is such that it rebounds three-fourths of the distance it has fallen. How high does the ball rebound on the fifth bounce? Find a formula for how high the ball rebounds on the nth bounce.
Formula for how high the ball rebounds on the nth bounce is 80 (3/4)ⁿ ft and the rebound on 5th bounce is 14.24 ft.
It is given that the ball is dropped from 80 ft and it rebounds (3/4)th of the height it has fallen.
Firstly , using logic ,
The height reached by the ball on its 1st rebound = 80(3/4) = 60 ft
Similarly , calculating on it's 2nd rebound = 60(3/4) = 45 ft
and on 3rd rebound = 45(3/4) ft.
This forms a sequence , known as GP (Geometric Progression).
A Geometric Progression in mathematics, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Hence , here the first term : a = 60 ft
and common ratio is : r = 3/4
the general term for rebound on nth bounce
= 60 * (3/4)ⁿ⁻¹ = 80 (3/4)ⁿ ft
Using the above expression , the rebound on 5th bounce = 60 * (3/4)⁵ = 14.24 ft.
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15. Suppose an economy's marginal propensity to consume (MPC) is 0.6. Then, the multiplier must be
a. 1.96.
b. 3.
c. 1.67.
d. 2.5.
The investment multiplier must be 2.5 i.e.Option (d).
What is an Investment multiplier?
The amount by which the growth in output or income exceeds the increase in investment is referred to as the investment multiplier. It is represented by the letter "k" and is calculated as the ratio of changes in investment and income.
Multiplier(k) = Change in income / change in investment = 1/ {1-MPC}
where MPC is the marginal propensity to consume
Given, MPC = 0.6
Then, the multiplier(k) = 1/( 1 - 0.6) = 1/ 0.4 = 10/4 = 2.5 times
Hence, the investment multiplier is 2.5 i.e.Option (d).
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Is 8y-5xy=9 linear or nonlinear
Answer: The equation 8y-5xy=9 is nonlinear because it contains the product of the variables x and y. In general, an equation is linear if it can be written in the form ax + by = c, where a and b are constants and x and y are variables. Equations that cannot be written in this form are nonlinear.
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 9200(1.018)²
Answer:
growth
1.8%
Step-by-step explanation:
If the number raised to the power x is between 0 and 1, it is decay since as the exponent increases, the value of the power expression decreases.
For example, think of 0.1, a number between 0 and 1.
0.1^x
x = 1, 0.1^1 = 0.1
x = 2, 0.1^2 = 0.01
x = 3, 0.1^3 = 0.001
As you see, as x increases, the value of the expression decreases from 0.1 to 0.01 to 0.001
Now look at a power in which the base is greater than 1.
If the number raised to the power x is greater than 1, it is growth since as the exponent increases, the value of the power expression increases.
For example, look at 1.5^x
1.5^x
x = 1, 1.5^1 = 1.5
x = 2, 1.5^2 = 2.25
x = 3, 1.5^3 = 3.375
As you see, as x increases, the value of the expression increases from 1.5 to 2.25 to 3.375.
Now our problem:
y = 9200(1.018)^x
What base is raised to x?
Answer: 1.018
Since 1.018 is greater than 1, as the exponent, x, increases, the value of 1.018^x increases. Therefore, this is exponential growth.
1.018 = 1 + 0.018 = 1 + 1.8%
The percentage is 1.8%
One way to measure the amount of energy that a moving object (such as a car) possesses is by finding its Kinetic Energy. The Kinetic Energy (Ex, measured in Joules) of an object depends on the object's mass (m, 2Ek measured in kg) and velocity (v, measured in meters per second), and can be written as v = . m What is the kinetic Energy of an object with a mass of 1,700 kilograms that is traveling at 50 meters per second? Ek Joules The volume of a cone of sand moved by harvester ants given it's radius can be found with the following 3V formular = A mound of gravel is in the shape of a cone with the height equal to twice the radius. 2л Calculate the volume of such a mound of gravel whose radius is 4.92 ft. Use = 3.14. V = (round to the nearest whole number)
The body has a kinetic energy of 2125000 joules, and the gravel mold has a volume of 11.9 cubic units.
Given that,
The Kinetic Energy of an object depends on the object's and velocity , and can be written as v = m
Kinetic Energy of an object with a mass = 1,700 kilograms
Traveling = 50 meters per second
Radius = 4.92 ft
Kinetic energy, which may be seen in the movement of an item or subatomic particle, is the energy of motion. Kinetic energy is present in every particle and moving object. Examples of kinetic energy in action include a person walking, a baseball soaring through the air, a piece of food falling from a table, and a charged particle in an electric field.
Kinetic Energy of a body is given by ,
1/2 mv²
Where m = mass = 1700 kg
v = velocity = 50m/s
Therefore ,
KE = 1/2 * 1700kg * 50m/s
KE = 2125000 J.
Now to calculate the volume
Let's assume that the solution to the problem will be found using your formula. If so, let's carry out the following operations when solving for v in the equation:
On multiplying the equation by 2, the outcome is
2[tex]r^{2}[/tex]
=3[tex]\sqrt{3V}[/tex]
To find volume
enter (v=(2[tex]r^{2}[/tex])/33)
rationalize the right side of the equation's numerator.
v=(2π[tex]r^{2}[/tex] )
A simplified version of 3/333 is
v=(2[tex]r^{2}[/tex])3/9.
Substitute
v=(23.143.1523)/9
v=11.9.
Therefore,
The body has a kinetic energy of 2125000 joules, and the gravel mold has a volume of 11.9 cubic units.
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