Answer:
[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]
Step-by-step explanation:
Given exponential function:
[tex]f(x)=P(1+r)^x[/tex]
Replace f(x) with y:
[tex]y=P(1+r)^x[/tex]
Divide both sides by P:
[tex]\dfrac{y}{P}=(1+r)^x[/tex]
Take natural logs of both sides:
[tex]\ln \left(\dfrac{y}{P}\right)=\ln (1+r)^x[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\ln \left(\dfrac{y}{P}\right)=x \ln (1+r)[/tex]
Divide both sides by x:
[tex]\dfrac{1}{x}\ln \left(\dfrac{y}{P}\right)=\ln (1+r)[/tex]
[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]
[tex]\ln \left(\dfrac{y}{P}\right)^{\frac{1}{x}}=\ln (1+r)[/tex]
Raise both sides to power of e:
[tex]\large\text{$e^{\ln \left(\frac{y}{P}\right)^{\frac{1}{x}}}=e^{\ln (1+r)}$}[/tex]
[tex]\textsf{Apply the power law}: \quad e^{\ln x}=x[/tex]
[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}=1+r[/tex]
Subtract 1 from both sides:
[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1=r[/tex]
Therefore, the equation to find r is:
[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]
Please help me with this
Answer:
A represents f(x) and B represents g(x)
Step-by-step explanation:
choose a value for x, substitute , say x = 1 into both f(x) and g(x) , then check the values obtained on the graph.
f(x) = 100 × [tex](\frac{3}{5}) ^{1}[/tex] = 100 × [tex]\frac{3}{5}[/tex] = 20 × 3 = 60
thus (1, 60 ) is a point on the graph of f(x)
the point (1, 60 ) is on graph A
g(x) = 100 × [tex](\frac{2}{5}) ^{1}[/tex] = 100 × [tex]\frac{2}{5}[/tex] = 20 × 2 = 40
thus (1, 40 ) is a point on the graph of g(x)
the point (1, 40 ) is on graph B
These points are linear. Find the slope.
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{8 }{2 +4} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4 }{ 3 }[/tex]
hello , please help !
Answer:
4,7
Step-by-step explanation:
4,7
I can’t figure out this problem please help me
Answer:
95 6/7
Step-by-step explanation:
The perimeter can be found by adding the length and width together and then multiplying the sum by 2.
Perimeter = 2(L + W)
Where L is the length and W is the width.
So, using the given measurements:
Perimeter = 2(33 5/7+ 14 3/14) = 94 26/14
94 26/14 -> 95 12/14 -> 95 6/7
Answer:
The perimeter is [tex]95\frac{6}{7}[/tex] inches.
Step-by-step explanation:
The formula for the perimeter of a rectangle is
[tex]P=2L+2W[/tex]
We are given the length and the width. Lets evaluate the perimeter.
First lets convert the length and width to an improper fraction.
Length: [tex]33\frac{5}{7}[/tex]
To write 33 as a fraction with a common denominator, multiply by [tex]\frac{7}{7}[/tex]. Then simplify.
[tex]\frac{33*7}{7} +\frac{5}{7}[/tex]
[tex]\frac{231}{7} +\frac{5}{7}[/tex]
[tex]\frac{231+5}{7}[/tex]
[tex]\frac{236}{7}[/tex]
Width:
To write 14 as a fraction with a common denominator, multiply by [tex]\frac{14}{14}[/tex]. Then simplify.
[tex]\frac{14*14}{14} +\frac{3}{14}[/tex]
[tex]\frac{196}{14} +\frac{3}{14}[/tex]
[tex]\frac{196+3}{14}[/tex]
[tex]\frac{199}{14}[/tex]
Lets enter the 2 fractions into the perimeter equation.
[tex]P=(2*\frac{236}{7} )+(2*\frac{199}{14} )[/tex]
Simplify each term.
[tex]P=\frac{2*236}{7} +2*\frac{199}{14}[/tex]
[tex]P=\frac{472}{7} +2*\frac{199}{14}[/tex]
Factor 2 out of 14.
[tex]P=\frac{472}{7} +2*\frac{199}{2(7)}[/tex]
Cancel the common factor of 2.
[tex]P=\frac{472}{7} +\frac{199}{7}[/tex]
Combine the numerators over the common denominator.
[tex]P=\frac{472+199}{7}[/tex]
[tex]P=\frac{671}{7}[/tex]
[tex]P=95\frac{6}{7}[/tex]
If you decide to select walking at a normal pace as your only physical daily activity, what would be the rate at
which you will be burning calories? Show how you calculated that rate
A 140-pound person will typically burn 4 calories per mile of walking at a rate of 3 miles per hour.
Do you burn the same amount of calories walking as running?Walking at a pace of 3 miles per hour results in an average calorie burn of 4 for a 140-pound person. This person would therefore burn around 112 calories in a period of 30 minutes. On the other hand, a 200-pound person burns roughly 5 calories per minute, or 159 calories every 30 minutes.
An average walking speed of 3 miles per hour (or 120 steps per minute) is recommended for health reasons. That is a mile that takes 20 minutes. You must increase your pace to 4 miles per hour (135 steps per minute), or a 15-minute mile, to walk for weight loss.
Walking and running have about equal calorie burn rates per minute. Walking at 3.5 mph for 40 minutes for a 160-pound person would take 40 minutes.
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Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.
The coordinates are ( , ) and ( , )
Answer: The diagonal AC of a square bisects the square and the midpoint of the diagonal is the center of the square. Since the center of the square is the midpoint of the diagonal, we can find the midpoint of AC by averaging the x-coordinates and y-coordinates of A and C.
The coordinates of the center of the square is ( (2+(-2))/2 , (4+1)/2) = (0, 2.5)
Since a square is a special case of rectangle, which means all sides are equal, the length of the side of the square is the distance between A and C.
Using the distance formula, we can find the length of the side of the square:
d = sqrt( (2-(-2))^2 + (4-1)^2 ) = sqrt(4^2 + 3^2) = sqrt(16+9) = sqrt(25) = 5
The coordinates of the vertex D can be found by subtracting half of the side length from x and y coordinates of the center point.
D(0-5/2, 2.5 - 5/2) = (-2.5, 0.5)
The coordinates of the vertex B can be found by adding half of the side length from x and y coordinates of the center point.
B(0+5/2, 2.5 + 5/2) = (2.5, 5.5)
So the remaining vertices are (2.5, 5.5) and (-2.5, 0.5)
Step-by-step explanation:
Inso ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, how many gallons of ice cream can 4
machines make?
The gallons of ice cream 4 machines can make is 650 gallons.
How to find the number of gallons of ice cream 4 machine can make?Two ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:
Therefore,
If 2 ice cream machine = 320 gallons
4 ice cream machine = ?
cross multiply
Hence,
gallons of ice cream made by 4 machines = 320 × 4 / 2
gallons of ice cream made by 4 machines = 1280 / 2\
Therefore,
gallons of ice cream made by 4 machines = 640 gallons
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In 2018, the population of Sydney was 5.48 million.
This was 22% of the total population of Australia.
Work out the total population of Australia in 2018
Give your answer correct to 3 significant figures.
The population of Australia in 2018 was 24.909 million.
Given: The population of Sydney in 2018 = 5.48 million
This population of Sydney is equal to 22 % of the total population of Australia.
To find: Total population of Australia
Solution:
According to the Question,
Total population of Australia * 22% = total population of Sydney
Total population of Australia * 22/100 = 5.48 million
= 5.48 million * 100/22
= 24.909 million (approx.)
Hence, the population of Australia in 2018 was 24.909 million.
The total population of Australia in 2018 was 24.90 million.
What is percentage?A percent is a dimensionless number, meaning that it has no units of measurement, since it represents a part of whatever whole is being measured.
Given that, the population of Sydney was 5.48 million, which was 22% of the total population of Australia.
We need to find the total population of Australia.
Let the total population of Australia be y.
Therefore,
y × 22% = 5.48
y = 5.48 × 100/22
y = 24.90
Hence, the total population of Australia in 2018 was 24.90 million.
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Anderson multiplies two rational expressions with the
following results. Describe his error. Then find the correct product.
The required correct product is (x + 4)/(x - 4)(x + 1) for the rational expressions.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Anderson multiplies two rational expressions with the given results.
His error is the inequivalent can't be canceled out.
The two rational expressions are given in the question, as follows:
(x² - 16)/(x² - 8x + 16) × (x + 1)/(x² + 2x + 1)
(x² - 4²)/(x² - 2 × 4 × x + 4² ) × (x + 1)/(x² + 2 × 1 × x + 1²)
(x + 4)(x - 4)/(x - 4)² × (x + 1)/(x + 1)²
(x + 4)/(x - 4)(x + 1)
Thus, the required correct product is (x + 4)/(x - 4)(x + 1).
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Please help me solve this i'm not sure what else to do
The equation of the line in point-slope form is obtained as y = -2x + 4.
What is the point-slope form?
Point-slope is the general form of a linear equation which is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
The line passes through point (x1,y1) = (0,4)
The slope of the line is m = -2.
The formula for point-slope form of equation is -
y-y1=m(x-x1)
Substituting the values in the equation -
y - 4 = -2(x - 0)
y - 4 = -2x
y = -2x + 4
Therefore, the equation is obtained as y = -2x + 4.
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HELP PLS
Factor the trinomal or stage that the trinomal is prime
The correct answer is x² - 7x - 18 = (x - 9)(x + 2)
Find the perimeter of the image below: (4 points)
37 units
38 units
39 units
40 units
38, 39, 40, 37, 38, and so forth. The perimeter of the supplied figure must be determined. = 38.97 units. As a result, 38.97 units make up the perimeter.
How do you find the perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter.
The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:
d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
There are points that correspond to each vertex in the polygon:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So, using the distance formula and the vertex positions of side PT, we can determine its length: The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:
d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)\x^{2} }[/tex] ≤ b r/≥ d=[tex]\sqrt{(8-(-2)^{2})+(7-11)^{2} }[/tex] ≤b r/≥
d=[tex]\sqrt{116}[/tex]
There are points that correspond to each vertex in the polygon:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So, using the distance formula and the vertex positions of side PT, we can determine its length:
P = (-2, 11)
T = (8, 7)
The length of PT is [tex]\sqrt{116}[/tex]
The other 4 sides are handled in the same way, and the results are as follows:
TS = [tex]\sqrt{49}[/tex]
SR = [tex]\sqrt{50}[/tex]
RQ = [tex]\sqrt{61}[/tex]
QP = [tex]\sqrt{40}[/tex]
You may calculate the perimeter by adding all the sides:[tex]\sqrt{116}[/tex]+[tex]\sqrt{49}[/tex]+[tex]\sqrt{50}[/tex]+[tex]\sqrt{61}[/tex]+[tex]\sqrt{40}[/tex] = 38.97
The solution is 39 units if you round off.
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Help please will give brainliest!
Answer:24.353333333
Step-by-step explanation:
5) Is the sequence geometric?
a) 100, 25, 6.25, 1.5625,....
b) 3, -8, -19, -30,...
The sequence of 100, 25, 6.25, 1.5625 is geometric.
What is meant by geometric?The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers.
In essence, we multiply the numbers together and calculate their n[tex]th[/tex]root, where n is the total number of data values.
A succession of shapes are used to create geometric patterns.
Because the pattern is governed by a rule, patterns created from shapes are comparable to patterns created from numbers.
The dimensions, perimeter, area, surface area, volume, etc. of geometric shapes are determined using geometry formulas.
Mathematics' branch of geometry examines the connections between points, lines, angles, surfaces, solids' measurements, and qualities.
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1.5 (-2)^(n-1) > -6000
Find n (n is integer)
Answer:
что там а? я даже не знаю hehe
Jason likes to play video games. His parents allow him to play for 20 min plus 10
min for each half hour he does chores or studies. He can never play for more
than 90 min/day.
The function f(x)=20+10x models the number of minutes per day Jason could
play where x represents the number of half hour increments he has done chores
or studied.
What is the practical range of the function?
A. all multiples of 10 greater than or equal to 20 and less than or equal to 90
B. all integers
C. all real numbers greater than or equal to 20
D. all real numbers
Answer:all integers
Step-by-step explanation:
the correct is all integers
HELPP PLSSS
factor by grouping
The required factors of the polynomial by grouping are (x-3)(x^2 + 2).
What is grouping to solve cubic polynomial?To factor polynomial equations, a specialized approach is called grouping. It can be applied to polynomials with four terms as well as quadratic equations. Although they differ significantly, the two approaches are comparable.The first two terms and the final two terms are combined: p(x)=(x3 - 4x2) + (3x - 12), and we then identify the shared
factors as follows: p(x) = x2(x - 4) + 3(x - 4). (x - 4).
According to question:x^3 - 3x^2 + 2x -6
(x-3)(x^2 + 2)
Thus, required factors are (x-3)(x^2 + 2).
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Help Please!
Who ever answers right gets brainliest
An exponential decay function to model the situation is f(x) = 49(0.7)^x.
The average rate of change over 1 ≤ x ≤ 4 is -7.5.
The average rate of change over 5 ≤ x ≤ 7 is -1.4.
The rate of change decreases as x increases.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since the initial value is 49 and the decay factor is 0.7, an exponential function that models the situation is given by:
f(x) = ab^x
f(x) = 49(0.7)^x
When x = 1, the value of f(x) is:
f(1) = 49(0.7)^1
f(1) = 34.3.
When x = 4, the value of f(x) is:
f(4) = 49(0.7)^4
f(4) = 11.7649.
For the average rate of change over 1 ≤ x ≤ 4, we have:
Average rate of change = [f(b) - f(a)]/(b - a)
Average rate of change = [11.7649 - 34.3]/(4 - 1)
Average rate of change = -22.5351/3
Average rate of change = -7.5
For the average rate of change over 5 ≤ x ≤ 7, we have:
Average rate of change = [f(b) - f(a)]/(b - a)
Average rate of change = [49(0.7)^7 - 49(0.7)^5]/(7 - 5)
Average rate of change = [4.0354 - 8.2354]/2
Average rate of change = -4.2/3
Average rate of change = -1.4.
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Basic geometric shapes 3. Triangle Abc has angle measure as shown
The value of x, given the angle measures in Triangle ABC, can be found to be 22.
How to find the value of x ?Triangle ABC is a right angled triangle which means that ACB has the angle measure of 90 degrees. This means that the angle measures left will add up to :
= Sum of interior angles in triangle - Angle ACB
= 180 - 90
= 90 degrees
If the sum of 2 x and ( 3 x - 20 ) adds up to 90 degrees, the value of x would then be:
90 = 2 x + ( 3 x - 20 )
2 x + 3 x - 20 = 90
2 x + 3 x = 90 + 20
5 x = 110
x = 110 / 5
x = 22
In conclusion, the value of x is 22.
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The question is:
What is the value of x?
I need a so please don,t get it wrong
Answer: 48 square inches
Step-by-step explanation:
To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.
area of triangle L x W = 6x4=24
area of rectangle LxW =6x4=24
24+24=48
Divide R240 in the ratio 2:3?
Answer:
96:144
Step-by-step explanation:
240/5=48
48*2=96
48*3=144
So your answer is 96:144
A,B,C,E,F et G sont du plan Simplifier l’écriture de chacun des sommes 1)AB+CE+BC+EF 2) AB+DE+AB+EG 3) AB-BC-AB+BE 4) AB+DE+CD+AD+BC+ED
Please help me with this question.
Answer:
Step-by-step explanation:
put the 2x and make it 2
find the size of the angles marked by letter X and Y in the diagram below you point q a point of tangency 1/4 equals 20 cm calculate the length of the tangents TP and the radius OP
Answer:Angle
Step-by-step explanation:
Why is the denominator of each fraction 12?
Pls help me
12 is the denominator because it represents the total number of times Nicanor selects a diving ring from the bag
Explaination:
Nicanor randomly selects a ring from the bag a total of 12 times. 3 times he selects a red ring, 4 times a yellow one, and 5 times a blue one.
When he selects a red ring, he selects it 3 times out of the 12 times total, which is represented as the fraction 3/12.
When he selects a yellow ring, he selects it 4 times out of the 12 times total, which is represented as the fraction 4/12.
When he selects a blue ring, he selects it 5 times out of the 12 times total, which is represented as the fraction 5/12.
Hope this helps you!
5, Infigure 4.48 • vertical cliff IS Hom high and is absor ved from about which is from from the foot of the cliff calculate the angle of elevation of the top of the cliff from boak ?
Therefore , the solution of the given problem of elevation comes out to be
X = 21.23°.
What is the elevation and depression angle?When it is between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.
Here,
Given : tan X = P/ B
tan X = 68 / 175
X = tan⁻¹ (68 /175)
X = 21.23
Therefore , the solution of the given problem of elevation comes out to be
X = 21.23°.
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10. When cycling 2.4km to the beach, the wheels on Sue's bike
rotated 1255 times. Find the diameter of the wheels.
Therefore , the solution of the given problem of circle comes out to be
the diameter is 62 cm.
A circle is what?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetrical about the center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.
Here,
Given : Sue covered 2.4 km distance and
bike wheel rotated 1225 times.
Thus,
To find the value of diameter of the wheel
=>2400=2πr*1225
=> 2400/2 = πr*1225
=> 1200 = πr*1225
=>r=31
Diameter = 2*31 = 62cm
Therefore , the solution of the given problem of circle comes out to be
the diameter is 62 cm.
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Find the factors of the number 36
Answer:
1,2,3,4,6,12,18
Step-by-step explanation:
uh
A local salesman receives a base salary of $925 monthly. He also receives a commission of 8% on all sales over $1250. How much would he have to sell in a month if he needed to have a monthly income of $2900?
He would need to sell $
to reach his needed monthly income needs.
The salesman needs to sell $25937.5 to reach his needed monthly income needs.
What is commission?Commission, also known as sales commission, is a payment given to employees based on the sales they make.
Given that, A local salesman receives a base salary of $925 monthly. He also receives a commission of 8% on all sales over $1250.
Monthly salary = fixed part + commission part
The fixed salary is $925.
The commission part is 8% on all sales over $1250
Let x = amount of sales, and x must be greater than $1250.
Then, the amount of sales over $1250 is x - 1250.
He earns 8% on that amount, so the commission part is 8%(x - 1250),
or 0.08(x - 1250).
Monthly salary = fixed part + commission part
Monthly salary = 925 + 0.08(x - 1250)
925 + 0.08(x - 1250) = 2900
0.08x = 2075
x = 25937.5
Therefore, he needs to sell $25937.5.
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