Answer:
[tex] \huge{ \boxed{r =100( \sqrt[n]{ \frac{A}{P} } - 1)}}[/tex]
Step-by-step explanation:
[tex]A = P(1 + \frac{r}{100} )^{n} \\ [/tex]
First of all in order to make r the subject we have to first divide both sides of the equation by P
That's
[tex] \frac{A}{P} = \frac{P( {1 + \frac{r}{100} })^{n} }{P} \\[/tex]
We'll finally get
[tex] \frac{A}{P} = ( {1 + \frac{r}{100}) }^{n} \\ [/tex]
Next we have to remove the power n and to do that we find the square root of 'n' of both sides as
We have
[tex] \sqrt[n]{ \frac{A}{P} } = \sqrt[n]{( {1 + \frac{r}{100} })^{n} } \\ \\ \\ \sqrt[n]{ \frac{A}{P} } = 1 + \frac{r}{100} [/tex]
Next we subtract 1 from both sides to isolate r/100
We have
[tex]\sqrt[n]{ \frac{A}{P} } - 1 = 1 - 1 + \frac{r}{100} \\ \sqrt[n]{ \frac{A}{P} } - 1 = \frac{r}{100} [/tex]
Finally to isolate r , we multiply both sides by 100
[tex] \frac{r}{100} \times 100 =100 \times (\sqrt[n]{ \frac{A}{P} } - 1)[/tex]
We have the final answer as
[tex]r =100( \sqrt[n]{ \frac{A}{P} } - 1) \\ [/tex]
Hope this helps you
Need help please is do tomorrow
Answer: 39
Step-by-step explanation:
it starts at 11 and adds 7 everytime, assuming its linear (meaning it has a constant rate of change) u would add 7 to 32 to get your 5th value
Answer: y = 39
Step-by-step explanation:
Since the line is linear, the y increases 7 every time x increases 1
Add 7 to 32 and it equals 39
work out the size of angle x 24
The size of angle x in the isosceles triangle is:78°.
What is an Isosceles Triangle?A triangle that has two sides that have congruent lengths is called an isosceles triangle. The base angles of the isosceles triangle are the angles that are opposite the congruent lengths, they are also equal to each other.
The triangle in the image below has two congruent sides, therefore, it is an isosceles triangle and the angles opposite its congruent sides will also be equal to each other.
Therefore:
x = 1/2(180 - 24)
x = 1/2(156)
x = 78°
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The diameter of the circle is 10 centimeters and the measure of is 72º. Find the length of.
Round your calculations to the nearest tenth. Complete your work in the space provided.
The arc length of the segment it 6.28 meters
How to calculate the arc length using?From the question, we have the following parameters:
Central angle, x = 72 degrees
Diameter, d = 10 centimeters
The radius of the circle can be calculated using
r = d/2
So, we have
r = 10/2
Evaluate
r = 5 cm
The exact arc length using the central angle measure is calculated as:
Arc length = x/360 * 2πr
Substitute the known values in the above equation
Arc length = 72/360 * 2π * 5
Evaluate
Arc length = 6.28
Hence, the exact arc length using the central angle measure is 6.28 meters
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Possible question
The diameter of the circle is 10 centimeters and the measure of is 72º. Find the length of arc
Round your calculations to the nearest tenth. Complete your work in the space provided.
It takes 36 pounds of seed to completely plant a 6 acre field. How many acres can be planted per pound of seed?
Answer: 6 lbs per acre
Step-by-step explanation: just divide 36 by 6 and you get 6. To check your answer multiply 6 and 6. Then you get 36 and know your answer is right.
A plant manufactures parts whose links are normally distributed with a mean of 16.3 cm and a standard deviation of 2.5 cm if one part is randomly selected find the probability that the part is between 10.8 and 12.8 cm
The probability that the part is between 10.8 and 12.8 cm is 0.0669.
What is a normal distribution?
Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is symmetric around the mean.
Here, we have
Mean = 16.3cm
Standard deviation = 2.5cm
We have to find the probability that the part is between 10.8 and 12.8 cm
Now,
we know that z = (x−μ)/σ
putting values in the normal distribution formula, we get
P( 10.8 < x < 12.8) = P( (10.8 - 16.3)/2.5 < z < (12.8 - 16.3)/2.5)
= P ( -2.2 < z < -1.4)
P( 10.8 < x < 12.8) = 0.0669, by normal distribution table
Hence, the probability that the part is between 10.8 and 12.8 cm is 0.0669.
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There was 3/5 of a gallon of paint in the bucket. Dr. Wu used 2/5 of that. How much paint was left?
Answer:
1/5
Step-by-step explanation:
equation: 3/5-2/5=x
we can multiply the whole equation by 5 so that we can easily subtract the numbers
3-2=1
now we divide it by 5 so that we get our number in a fraction
after we divide we get 1/5
The first section of a newspaper has 16 pages. Advertisements take up 3 and 3/8 of the pages. How many pages are not advertisements?
A total of 12 5/8 pages is not meant for advertisement
How to determine the number of pages that are not for adverts?From the question, we have the following parameters
First section = 16 pages
Pages for advertisement = 3 and 3/8 pages
Rewrite the above parameters as
First section = 16 pages
Pages for advertisement = 3 3/8 pages
The number of pages that are not for adverts is then calculated as
Pages not for adverts = First section - Pages for advertisement
Substitute the known values in the above equation
So, we have the following equation
Pages not for adverts = 16 - 3 3/8
Evaluate the difference
Pages not for adverts = 12 5/8
Hence, the number of pages that are not for adverts is 12 5/8 pages
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(x-2x³-29x² - 43x+8)÷(x-7)
Answer:
-2x^2 - 43x - 343 - 2393/x-7
Select the correct answer.
Which set of absolute values is compared correctly?
A. -71 <181<|9|<1-10|
B.1-41 <1-3/<13<|4|
C. 1211-51> |-7|>1-81
D. 1-41>19> |-31 >|-10|
In actuality, "absolute value" refers to thinking of all numbers as positive and removing all negative signs from front of them (or zero). Symbol for absolute value. -71<181<|9|<1-10| set of absolute values
Explain about the absolute values?Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0.
The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.
The exact distance of an integer or number from zero on a number line is its absolute value. As a result, the absolute value is never negative and is always positive.
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The Fitness Studio, Inc.’s, 2021 income statement lists the following income and expenses: EBITDA = $686,000, EBIT = $547,000, interest expense = $94,000, and net income = $426,000.
Based on the data on the income statement, the amount of the tax equals to $27,000.
What is a taxes?Generally, a taxes refers to those mandatory contributions levied on individuals or corporations by a government entity either from local, regional, or national government.
Given that: EBIT = $547,000 Interest expense = $94,000 Net income = $426,000
EBT = EBIT - Interest expense
EBT = $547,000 - $94,000
EBT = $453,000
The tax reported in Income statement:
= EBT - Net income
= $453,000 - $426,000
= $27,000
In conclusion, the 2021 taxes reported on the income statement equals to $27,000.
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Katyhas$100,000inasavingsaccount.Theinterestrateis8%peryearandisnotcompounded.Howmuchwillshehaveintotalin2years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $
The amount that Katy would have saved in her savings account in 2 years is $16, 000
How to find the amount saved?Given that the interest on the savings account is not compounded, the amount that Katy would have saved in 2 years can be found by the formula:
= Principal x Interest Rate x Time
Principal = $100, 000
Interest rate = 8%
Time = 2 years
The amount that Katy would have saved is:
= Principal x Interest Rate x Time
= 100, 000 x 8% x 2
= $16, 000
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Which algebraic expression represents the amsplit the cost of a $20.00 gift?
A. f + 20
B. 20f
C. 20 ÷ f
D. f ÷ 20
Answer:
The answer is C: 20 ÷ f
Step-by-step explanation:
Ryan is going to spin the spinner 80 times.
(b)
Work out an estimate for the number of times he should expect the spinner to land on 2
The estimate for the number of times Ryan should expect the spinner to land on 2 is 13.
How to calculate the number of times?From the information, the spanner has numbers labeled 1 - 6 and Ryan is going to spin the spinner 80 times.
It should be noted that the fraction for getting a 2 is 1 out of 6. This will be 1/6.
Therefore, when it's spinned 80 times, the expected number will be:
= 1/6 × 80
= 13
The number of times is 13.
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Complete question
A spanner has numbers labeled 1 - 6. Ryan is going to spin the spinner 80 times. Work out an estimate for the number of times he should expect the spinner to land on 2
a certain washing machine uses 29 gallons of water for each load of laundry washed. How many gallons of water would the washing machine use for 156 loads of laundry?
Answer:156
Step-by-step explanation:
1. Given segment AB with A(-3, 2) and B (5, -4). If point P lies on segment AB such that the ratio of
AP to PB is 2:6. Find the coordinates of p
The coordinates of P is ( -1 , 0.5) .
What is section formula ?
We can get a point's coordinates using the section formula when it divides a line segment externally or internally in a certain ratio. It is a useful tool for determining the coordinates of the point that divides the line segment in a particular ratio. The midpoint of a line segment can be found using this section formula, and it can also be used to derive the midpoint formula.
Here Using the section formula, if a point P(x,y) divides the line joining the points A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio of m:n then,
=> (x,y) = [tex](\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )[/tex]
Here A[tex](x_1,y_1)[/tex] =( -3,2) and B[tex](x_2,y_2)[/tex] = (5,-4) and m:n = 2:6
Then,
=> ( x,y ) = [tex](\frac{2(5)+6(-3)}{2+6} ,\frac{2(-4)+6(2)}{2+6})[/tex]
=> (x,y) = [tex](\frac{10-18}{8},\frac{-8+12}{8} )[/tex]
=> (x,y) = [tex](\frac{-8}{8} ,\frac{4}{8})[/tex]
=> (x,y) = (-1,0.5)
Hence the coordinates of P is (-1 , 0.5) .
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student enrollment at a local school is concerning because the number of student has dropped to 504, which is 20% decrease from the previous year. what was the student enrollment the previous year?
The student enrollment the previous year is 630 students.
How to calculate the number of students?Sine the percentage given is 10% decrease, us implies that the percentage for the previous year will be x
Based on the information given, this will be illustrated as:
x - (20% × x) = 504
x - 0.2x = 504
0.8x = 504.
Divide.
x = 504 / 0.8
x = 630
There were 630 students.
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Does anyone know the answer to this problem?
It is a scalene triangle .
What is a scalene triangle?A triangle called a Scalene Triangle in geometry is one with equally spaced-apart sides. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.The sides and angles of the triangles are used to define them. A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional plane object having three sides and three angles. There are three edges and three vertices.acc to our quesion-
all the sides of triangle are unequal
if all sides are unequal ,it is called scalene triangle.
hence,It is a scalene triangle .
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3.) Johannes sold an order of 3 Strawberry pies
for $12.50 each. She paid her assistant
$1.10 for each Strawberrye pie sold. How much
money did Johannesearn from the pies sold?
Answer:
$34.20
Step-by-step explanation:
Since each pie is $12.50 but the assistant gets $1.10 for each pie, Johannes will get $11.40 for each pie sold.
We know that there were 3 pies sold so you must solve the equation below
11.40*3
The answer is $34.20
Assessment Practice
5. A science teacher has $225 to spend on lab equipment.
He buys 4 posters with a guide to classifying rocks, for
$19 each. Student rock collections cost $9 each. How
many rock collections can he buy? Explain how you solve.
Use one or more equations and bar diagrams in your
explanation. Tell what your variables represent. 4.AR.1.1.4.AR.2.2
Answer:
Assessment Practice 5. A science teacher has $225 to spend on lab equipment. He buys 4 posters with a guide to classifying rocks, for $19 each. Student rock collections cost $9 each. How many rock collections can he buy? Explain how you solve
Let
x -----> number of rock collections that he can buy
so
the algebraic expression that represents this situation is
Solve the inequality for x
subtract 76 both sides
Divide both sides by 9
therefore
The maximum number of rock collections that he can buy is 16
Step-by-step explanation:
The equation is 9x+76=225 and the number of rock collections he can buy is 17.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a science teacher has $225 to spend on lab equipment.
Let the number of rocks collected be x.
He buys 4 posters with a guide to classifying rocks, for $19 each.
That is 19×4=76
Student rock collections cost $9 each.
Now, 9×x=9x
So, the equation is 9x+76=225
Subtract 76 on both the sides of equation, we get
9x=149
Divide 9 on both the sides of equation, we get
x=16.5
x≈17
Therefore, the number of rock collections he can buy is 17.
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Function Notation - Function Machines
#1. Find the following...
f(1) =
f(0) =
f(-3)=
f(8)=
x - input
?
4x + 1
f(x) - output
The function notation of the following are:
f(1) = 5
f(0) = 1
f(-3) = -11
f(8) = 33
Given:
x is the input.
the function is 4x+1
f(x) is the output.
we are asked to determine the values of the following :
a. f(1)
x = 1
so f(x) = 4x+1
f(1) = 4(1)+1
f(1) = 4+1
f(1)=5
b. f(0)
x = 0
so f(x) = 4x+1
f(0) = 4(0)+1
f(0) = 0+1
f(0)=1
c. f(-3)
x = -3
so f(x) = 4x+1
f(-3) = 4(-3)+1
f(1) = -12+1
f(1)= -11
d. f(8)
x = 8
so f(x) = 4x+1
f(8) = 4(8)+1
f(8) = 32+1
f(1)=33
Hence we get the required values.
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i need some help on these, can anybody help me?
v+8w=4v,for v
-m+5n=-2, for n
Answer:
v = 8w/3,n = (m - 2)/5.---------------------------
Given equationsv + 8w = 4v and - m + 5n = - 2Solve the first equation for vv + 8w = 4v4v - v = 8w3v = 8wv = 8w/3Solve the second equation for n- m + 5n = - 25n = m - 2n = (m - 2)/5Answer:
Value of v = (8w)/3Value of n = (m - 2)/5Step-by-step explanation:
1) v + 8w = 4v, for v?
→ v + 8w = 4v
→ 8w = 4v - v
→ 8w = 3v
→ [ v = (8w)/3 ]
Thus, value is (8w)/3.
2) -m + 5n = -2, for n?
→ -m + 5n = -2
→ 5n = -2 + m
→ 5n = m - 2
→ [ n = (m - 2)/5 ]
Thus, value is (m - 2)/5.
The sum of two odd consecutive integers is 88. Find the integers.
Answer:
43, 45 are the numbers
Step-by-step explanation:
Find the dimensions of the rectangle with the largest area; it has two vertices on the x-axis and two vertices above the x-axis on the graph of
y = 5 − x^2.
Answer:
(2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333
Step-by-step explanation:
You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.
DimensionsThe graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².
AreaThe area will be the product of the width and height:
A = WH
A = (2x)(5 -x²) = 10x -2x³
Maximum areaThe area will be a maximum where the derivative of the area function is zero.
dA/dx = 10 -6x² = 0
x² = 10/6
x = (√15)/3
The corresponding rectangle dimensions are ...
width = 2x = (2/3)√15
height = 5 -x² = 5 -5/3 = 10/3
The rectangle with largest area is (2/3)√15 wide by 10/3 tall.
Kyle buys $50,000 of company XYZ's shares, at a share price of
$100. A year later, XYZ's share price is $110, and Kyle sells all his
shares. How many dollars did Kyle's investment gain?
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
Given,
The share bought by Kyle of company XYZ = $50,000
The share price = $100
The share price after an year = $110
We have to find the gain amount by Kyle when Kyle sells all his shares.
Here,
We can apply Unitary method;
100 ⇒ 110
50000 ⇒ x
Compute;
100x = 110 x 50000
x = (110 x 50000) / 100
x = 110 x 500
x = $55000
Now,
Kyle gains,
55000 - 50000 = $5000
That is,
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
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Peter and Parker work for a cleaning crew. Peter can clean a room in 15 minutes less time than it takes Parker to do the same job. Working together,
they can clean two rooms in 110 minutes. Approximately how long does it take Peter to clean a room by himself?
Peter will take 47.5 minutes to clean the room.
In the question ,
it is given that ,
Peter and Parker are working for a cleaning crew ,
let the time taken by Parker to clean the room is = x minutes .
So ,according to the question ,
time taken by Peter to clean the room is = (x - 15) minutes .
Working together, they clean two rooms in 110 minutes
which is represented , by the equation ,
x + x - 15 = 110
2x = 110 + 15
2x = 125
x = 125/2
x = 62.5
Parker takes 62.5 minutes and Peter takes 47.5 minutes .
Therefore , Peter will take 47.5 minutes to clean the room .
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Simplify 5^3 x 5 please
Answer:
5^4
Step-by-step explanation:
5^3x5
5x5x5x5
5^4
Hopes this helps please mark brainliest
The simplified form of the expression, 5³.5 will be 625.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that the expression is, 5³.5
=5³.5
The base should remain constant and the exponents added when multiplying like bases. Keep the base constant when raising a base with power to another power, and multiply the exponents instead. Keep the base constant and deduct the exponents in the denominator and numerator when dividing like bases.
Apply the law of exponent as
xᵃ × xᵇ = xᵃ⁺ᵇ
=5³⁺¹
=5⁴
=5x5x5x5
=625
Thus, the simplified form of the expression, 5³.5 will be 625.
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x/2=8/5
what is x???
Answer:
x = 3.2
Step-by-step explanation:
[tex] \sf \frac{x}{2} = \frac{8}{5} \\ [/tex]
Use cross multiplication.
[tex] \sf5x = 8 \times 2 \\ \sf 5x = 16[/tex]
Divide both sides by 5.
[tex] \sf \: x = 3.2[/tex]
What is the solution to the equation 1/3x + 2/9x =10
The solution to x in the equation is 1/3x + 2/9x =10 is 18
To solve for x we follow the step;
Step 1: Combine the equation multiple into single fraction
1/3x + 2/9x =10
[tex]\frac{x}{3}[/tex] +[tex]\frac{2x}{9}[/tex] =10
Step 2: Find the common denominator
[tex]\frac{3x}{9}[/tex] + [tex]\frac{2x}{9}[/tex] =10
Step 3: Add the fraction with common denominator
[tex]\frac{3x +2x}{9}[/tex]= 10
[tex]\frac{5x}{9}[/tex] =10
Step 4: Cross multiply
5x = 9(10)
5x = 90
Step 4: Divide both 5
[tex]\frac{5x}{5}[/tex] =[tex]\frac{90}{5}[/tex]
x= 18
Therefore, the solution for x in the equation is 18
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The formula for finding the surface area of a cube is 6s2, where s is the length of each side of the square. Evaluate for s=10 to find the number of square centimeters (cm2) for the surface area of a cube with a side length of 10 cm. i need helpp
The surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].
Given:
The formula for finding the surface area of a cube is 6s2.
side length s = 10 cm.
Surface area of a cube = 6[tex]s^{2}[/tex] = 6*s*s
= 6 * 10 * 10
= 60 * 10
= 600 [tex]cm^{2}[/tex].
Therefore the surface area of a cube with a side length of 10 cm is 600 [tex]cm^{2}[/tex].
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