If the Learning curve rate is 85%, then the painter will need 35.5 hours to pant all 20 rooms.
Learning curve rate tells us that there will be improvement or the time for the task will decrease as the person learn the repetitive task.
The time for completing n units is given by the formula:
Tₙ = T₁ . nᵇ
Where:
T₁ = time to complete 1st task
n = number of units
b = ln (learning curve rate) / ln(2)
The given parameters:
T₃ = 9 hours
learning curve rate = 85%
Hence,
b = ln (0.85) / ln(2) = 0.693
Plug the values into the formula for n = 3
T₃ = T₁ . 3ᵇ
T₁ = T₃ / 3ᵇ = 9 / 3ᵇ
Substitute the parameters for n = 20.
T₂₉ = T₁ . 20ᵇ
= (9 / 3ᵇ) . 20ᵇ
= 9 . (20/3)ᵇ
Substitute b = 0.693
T₂₉ = 35.5 hours
Hence, it takes 35.5 hours for the painter to pant all 20 rooms.
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What is the formula for the equation of a proportional line?
Answer: y=kx
Step-by-step explanation:
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator 45 to 9
Answer:
[tex]\frac{5}{1}[/tex]
Step-by-step explanation:
45 : 9
= [tex]\frac{45}{9}[/tex] ← divide numerator and denominator by 9 )
= [tex]\frac{5}{1}[/tex] ← in simplest form
Find the inverse of each function.
y=log 10 x
The inverse of the function is f ⁻¹(x) = 10ˣ
Given the function is y = log₁₀ x
In relation to the original function f, the inverse function is denoted by the symbol f-1, and both the original function's domain and its range are transformed into the inverse function's domain. By replacing (x, y) with (y, x) with reference to the line y = x, one can obtain the graph of the inverse function.
steps to find the inverse of the function:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now replace y with x.
x = log₁₀ y
change the dependent variables.
f ⁻¹(x) = 10ˣ
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Henry is working two summer jobs, washing cars and walking dogs. He can work at most 15 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours washing cars, ww, and the number of hours walking dogs, dd, that Henry can work in a given week.
y=5x 7.5w+7.5d Answer:
Step-by-step explanation:
The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week is , w + d ≤ 15 .
What is an inequality?The relationship between two expressions or values that are not equal to each other is called 'inequality.
here, we have,
Given that w is the number of hours for washing a car and d is the number of hours to walking dogs.
The work hours at most 15 hours altogether between both jobs in a given in a week.
Hence, w + d ≤ 15 is the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week.
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-4x-1+x4/10-2x2 in standard form
The standard form will be
1/10 x⁴-2x²-4x-1
Polynomials in standard form can also be referred to as the standard form of a polynomial which means writing a polynomial in the descending order of the power of the variable. To write a polynomial in a standard form, the degree of the polynomial is important as in the standard form of a polynomial, the terms are written in decreasing order of the power of x. The standard form of polynomial is given by, f(x) = anxn + an-1xn-1 + an-2xn-2 + ... + a1x + a0, where x is the variable and ai are coefficients.
A mathematical expression of one or more algebraic terms in which the variables involved have only non-negative integer powers is called a polynomial. The terms have variables, constants, and exponents. The standard form polynomial of degree 'n' is
aₙxⁿ+aₙ₋₁xⁿ⁻¹+aₙ₋₂xⁿ⁻²+.......
To write a polynomial in standard form ,simplyfy and then arrange the terms in descending order.
ax²+bx+c
move -1
-4x+x⁴/10-2x²-1
Reorder terms
1/10x⁴-2x²-4x-1
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1. f(x)= (x+4)(x-6) 2. f(x)= (2x-4)(x-3)
Find the x-intercept
FOIL to convert functions to standard
Find the y-intercept
Answer both.
The intercepts and the standard form of each polynomial are listed below:
x-Intercept: x = - 4 or x = 6, Standard form: f(x) = x² - 2 · x - 24, y-Intercept: f(0) = - 24x-Intercept: x = 1 / 4 or x = 3, Standard form: f(x) = 2 · x² - 10 · x + 12, y-Intercept: f(0) = 12How to find the intercepts and the standard form of quadratic equationsIn this case we need to find the intercepts of each quadratic equation and transform each quadratic equation into standard form. The x-intercept correspond with each of the roots of the polynomial and the y-intercept is found by evaluating the expression at x = 0.
Now we proceed to find each element:
Case 1
x-Intercept
x = - 4 or x = 6
Standard form
f(x) = (x + 4) · (x - 6)
f(x) = x² - 2 · x - 24
y-Intercept
f(0) = - 24
Case 2
x-Intercept
x = 1 / 4 or x = 3
Standard form
f(x) = (2 · x - 4) · (x - 3)
f(x) = 2 · (x - 2) · (x - 3)
f(x) = 2 · (x² - 5 · x + 6)
f(x) = 2 · x² - 10 · x + 12
y-Intercept
f(0) = 12
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Adi has a dentist appointment at 09:10 am.
He gets to the dentist's surgery at 08:56 am.
How many minutes early is he?
Answer:
Step-by-step explanation: 14 minutes
Angles A and B are complementary to each other. If m∠A = 41° and m∠B = (2x + 19)°, find the value of x.
x = 15
x = 11
x = 58
x = 30
Given that Angles A and B are complementary to each other, the numerical value of x is 15.
What is the numerical value of x?Complementary angles are angles that sum up to 90 degrees.
Given the data in the question;
Angles A and B are complementary to each other.Measure of angle A = 41°Measure of angle B = (2x + 19)°Since Angles A and B are complementary to each other, the sum of angle A and B is 90 degrees.
Measure of angle A + Measure of angle B = 90°
Plug in the given values and solve for x.
41 + (2x + 19) = 90
41 + 2x + 19 = 90
2x + 60 = 90
2x = 90 - 60
2x = 30
x = 30/2
x = 15
Given that Angles A and B are complementary to each other, the numerical value of x is 15.
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Answer: A is the answer
Step-by-step explanation: i took the test and got it right
For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=1/x²
Answer to this question is:
Domain of given function is (-∞,0)∪(0,∞),{x|x≠0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is √x/x,-√x/x
The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.
This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.
When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.
Interval Notation:(-∞,0)∪(0,∞)
Set-Builder Notation:{x|x≠0}
The set of all valid y values constitutes the range.Graph may be used to find the values.
Interval Notation:(0,∞)
Set-Builder Notation:{y|y>0}
For calculation of inverse:
Interchange the variables x=1/y²Solve for yy=√x/x,-√x/xReplace y with f^-1(x)f^-1(x)=√x/x,-√x/x∴Domain of given function is (-∞,0)∪(0,∞),{x|x≠0}
Range of given function is (0,∞),{y|y>0}
Inverse of given function is √x/x,-√x/x
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Jonathan is buying string to make friendship bracelets. He buys 7 bundles of string in different colors. Each bundle costs $0.56. Tax for the 7 bundles is $0.35. How much money does Jonathan pay in all for the string?
Answer:
4.27
Step-by-step explanation:
1 bundle= $0.56
7bundles=o.56x7=$3.92
Tax=0.35
3.92+0.35=4.27
work out what the values of three consecutive even
integers must be if their sum is 6000.
The values of three consecutive even integers must be if their sum is 6000 will be 1998, 2000, and 2002.
What is an integer?it is defined as a whole number it can be a negative whole number or a positive whole number for example 2, 4, 1, -8, 0, etc. When it comes to integers, even numbers can be divided by two exactly while odd numbers cannot. 2, 6, 10, 20, 50, and other even numbers serve as examples.
Suppose the value of the three consecutive even integers is n, n + 2, and n + 4
The sum of the integers is 6000.
Sum = n + n + 2 + n + 4
Sum = 3n + 6
Sum=6000
3n + 6 = 6000
3n = 5994
n = 5994/3
n = 1998
The three consecutive even integers are,
n=1998
n+2=1998+2=2000
n+4=1998+4=2002
Thus, the values of three consecutive even integers must be if their sum is 6000 will be 1998, 2000, and 2002.
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Solve each equation.
log x-log 3=8
log(x) - log (3) = 8 => x = 299916251.899, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
log (x) - log (3) = 8
=> log (x) = 8 + log (3) = 8 + 0.477
=> log (x) = 8.477
Since, generally the base of log is 10, raising them to 10.
=> [tex]10^{log_{10}x} = 10^{8.477}[/tex]
=> x = 299916251.899 (as [tex]a^{log_a(x)} = x[/tex])
Hence, log(x) - log (3) = 8 => x = 299916251.899, by properties of logarithm.
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The grid above shows the graph of the parent function f(x)= |x| and a translated functions graph.
Use f(x)=|x| f(x) is shifted left 5 and shifted up 2 to create g (x). write the equation g(x).
The equation of the translated graph from the parent function is g(x) = |x + 2| + 1
How to write the equation of the translated graph?The parent function is given as
f(x)= |x|
From the graph, we can see that the parent function f(x) is translated as follows:
2 units left translation1 unit up translationThe above sequence of translation is represented as
(x, y) = (x + 2, y + 1)
So, we have
g(x) = |x + 2| + 1
Hence, the equation of the translated graph is g(x) = |x + 2| + 1
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Which of the binomials below is a factor of this expression?
100A²-498²
OA. A+ 7B
OB. 10A+7B
OC. A + B
OD. 10A+B
Answer: B. 10A + 7B
Step-by-step explanation:
To find the correct binomial, we will factor the given expression. I assume that by "-498²" you mean "-49B²".
This is a difference of squares:
(10A + 7B)(10A - 7B)
The binomial 10A + 7B is an answer option, so our answer is:
B. 10A + 7B
2. Order the numbers from least to
greatest.
45, 4.5, √20, √45
Answer:
√20, 4.5, √45, 45
Step-by-step explanation:
find your square roots first, then group based on the value of the square roots
Eva went miniature golfing with Taylor. She shot
4 under par and Taylor shot 2 under par. By how
many strokes did Eva beat Taylor?
i will give yall 100 points if this get answered fast:
HELP ME PLEASE FAST
write a linear function to model the following situation:
An airplane is 30,000 ft. in the air and descending 1,000 ft. for each mile it travels.
descending means its going ____.
write the equation.
Y= _____________
or as a function
f(x) = 30,000 - 1,000x
the question is: How far away from the airport does the airplane have to start to descend to land safely? To answer that, we need to find the x- intercept
Answer:
x = 30
Step-by-step explanation:
To find the x intercept, you need to substitute [tex]y = 0[/tex], as all points on the x axis's y-coordinate is 0.
[tex]0 = 30000 - 1000x\\ \\ \to 0 + 1000x = 30000 \cancel{- 1000x + 1000x} \\\\ \to 1000x = 30000 \\ \\\to \frac{1000x}{1000} = \frac{30000}{1000} \\ \\\to x = 30[/tex]
Answer: Its x= 30
Step-by-step explanation:
translation: 7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
Answer: 7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(5, -1)
Step-by-step explanation:
If you want to translate a point 7 units right, you'll need to add 7 to its x-coordinate. If you want to translate a point 1 unit down, you'll need to subtract 1 from its y-coordinate. Do both of these things to perform a translation 7 units right and 1 unit down.
So, we can write,
7 units right means add the +7
1 unit down means subtract the -1
Then,
J(-3, 1) = J'(-3 + 7, 1 - 1)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(-2 + 7, 3 - 1)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(-2 + 7, 0 - 1)
N(-2, 0) = N'(5, -1)
Therefore,
These points to make sure they have shifted 7 units right and 1 unit down.
7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(5, -1)
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Which expression is equivalent to -1/2 ( 1/4x - 3/8)?
The expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.
Which expression is equivalent to the expression given as in the task content?It follows from the task content that the expression which is equivalent to that given in the task content be determined.
On this note, by distributing the coefficient of.tne parents; we have;
-1/2 ( 1/4x - 3/8)
= {(-1/2) × (1/4)x} + {-1/2 × -3/8}
= (-1/8)x + 3/16
Ultimately, the expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.
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Question 1 (1 point)
Willorie Ford moves to Lake Havasu City Arizona to try out a food truck. She sets up shop
under London Bridge and notices that her business is "seasonal".
On December 1, she makes $450 per day.
On March 1, she makes $800 per day.
On June 1, she makes $450 per day.
On September 1, she makes $100 per day.
On December 1, she makes $450 per day.
Estimate how much she would make on certain days and draw a model.
By this model, she would make $
By this model, she would make $
By this model, she would make $
By this model, she would make $
on February 1. (Round to the nearest dollar)
on May 1. (Round to the nearest dollar)
on July 1. (Round to the nearest dollar)
on August 1. (Round to the nearest dollar)
Step-by-step explanation:
2,250 was made in a month
Samantha claims that 4x + 2 is equivalent to the expression x + 17 + 3x - 15.
Check whether Samantha's equivalent expression is correct using x = 2.
A.)Samantha S incorrect because when
using x = 2, the resulting values in
both expressions are different
B.)Samantha is
incorrect because the expressions cannot be checked using x = 2.
C.)Samantha is correct
because when using x 2, the resulting values in
both expressions are equal.
Option C: Samantha is correct because when using x=2, the resulting values in both expressions are equal.
Consider, 4x + 2
When x = 2,
=> 4x + 2 = 4*2 + 2
=> 10
Now consider, x + 17 + 3x - 15
When x = 2,
=> 2 + 17 + 3*2 - 15
=> 10
Therefore, Samantha is correct as both expressions equal 10 when x=2.
In other words, if we consider, x + 17 + 3x - 15
=> x + 17 + 3x - 15
=> x(1+3) + 17 - 15
=> 4x + 2
This shows that for any value of x, the expression x + 17 + 3x - 15, simplifies to 4x + 2.
Therefore, both the expressions, 4x + 2 and x + 17 + 3x - 15, are equal.
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What is the amplitude of y = 3sin4θ ? (F) 4/3 (G) 3 (H) 4 (I) 2π
Answer:
a sin(bθ−c)+d
→ Using this, find the amplitude based off of the given formula. Use the expression as a reference to help you identify a.
a = 3
b = 4
c = 0(no defined value)
d = 0(impossible to identify)
→ Find a.
→ Since a is already given, we know that a = 3, therefore, the amplitude is 3
The perimeter of a rectangular pool is 160 meters. The length of the pool is 20 meters more than its width. What is the length?
Answer:
50 meters
Step-by-step explanation:
Width is x
So length will be x + 20
Perimeter = 2 (W + L) = 2 (x + x + 20) = 2 (2x + 20) = 4x + 40
so 4x + 40 = 160
4x = 120
x = 30
so length = x + 20 = 30 + 20 = 50
Find the product of (134−2.4)⋅[0.5⋅(25+2.6)]
Answer: the product is 1816.08
Step-by-step explanation:
The required product of the expression is 1816.08.
Given that,
To determine the product and simplified value of the expression (134−2.4)⋅[0.5⋅(25+2.6)]
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= (134−2.4)⋅[0.5⋅(25+2.6)]
= (131.6) * [0.5 * 27.6]
= 131.6 * 13.8
= 1816.08
Thus, the required product of the expression is 1816.08.
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Please help me with the blanks.
Each answer can be used more than once, by the way.
Completing the Automatic grading is used for empty questions. If a student's response corresponds to the right response you give, you will receive credit for that answer. The technique you use to assess the responses is up to you.
100% exact
Comprised comprises a portion of the right response
meets the criteria you define for a pattern
Enter your query in text form, then enclose the response in brackets. To format the text and add formulas, files, photos, and links, utilize the editor's formatting options.
Using a semicolon, divide several right responses.
Example: Red, blue, and yellow are three examples of primary colors.
A regular expression might also be used. Each blank will only accept one expression at a time. Remember to enclose both the regular expression and the solution in brackets.
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Oh no! Mike solved the equation below for y:
10x - 3y = 6
Let's help him fix it!
1. Circle the mistake within the problem (on the
whiteboard at the left).
2. Describe his mistake in the box below (be sure to
be specific).
The mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y
How to determine the mistake in the equation solution?The solution of the equation is given as
10x - 3y = 6
+3y +3y
----------------------------
10x = 3y + 6
-6 -6
----------------------------
(10x - 6)/3 = 3y/3
10x - 2 = y
In the above steps, we have the following equation
(10x - 6)/3 = 3y/3
When the above equation is expanded, we have
10x/3 - 6/3 = 3y/3
Evaluate the quotient in the above equation
So, we have
10x/3 - 2 = y
The abvoe equation is different from Mike's result
Hence, the mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y
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Divide and simplify. √128/8
The simplest form of the expression is √2 .
Expressions in science square measure mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by degree operator in between.Simplifying expressions mean redaction an identical maths expression with no like terms and through a compact manner.To change expressions, we tend to tend to combine all kind terms and solve all the given brackets, if any, so at intervals the simplified expression, we tend to square measure about to be exclusively left with not like terms that cannot be reduced any.We have given an expression √128/8 . .....(1)
Factors of 128 is given by
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
Put this factors in equation (1) , we get
√128/8 = [tex]\frac{\sqrt{2\times2\times2\times2\times2\times2\times2} }{8}[/tex]
On simplifying , we get
√128/8 = 2 ×2 × 2√2 / 8
= 8√2 /8
= √2
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How do the domains and ranges of the functions f(x)=√x-1 and g(x)=√x-1 compare?
The domain and range of the function f(x) is [1, ∞) and (0, ∞) and g(x) is (0,∞) and [-1, ∞).
Domain of function f(x) :
√ (x - 1) ≥ 0
So, we get that:
x ≥ 1
= [1, ∞)
Range = (0, ∞) as square of a number is always positive.
Domain of function g(x):
√ x ≥ 0
on adding 1 both sides we get
x ≥ 0
= (0,∞)
Range = [-1, ∞).
Therefore, the domain and range of the function f(x) is [1, ∞) and (0, ∞) and g(x) is (0,∞) and [-1, ∞).
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If someone could help soon that would be great
Answer:
a,b,c and no d
Step-by-step explanation:
welcome
Answer:
a, b, and c.
Step-by-step explanation:
Use the line test. :)
Solve the compound inequality
|x-3|<4 and |x+2|>8
The solution of the compound inequality are:
| x - 3 | < 4 -1 < x < 7
| x + 2 | > 8 -10 < x or x >6
How to solve the inequality
Given data
| x - 3 | < 4 and | x + 2 | > 8
Solution the first inequality | x - 3 | < 4
| x - 3 | < 4
x < 4 + 3 OR x > - 4 + 3
x < 7 OR x > - 1
-1 < x < 7
Solution for the second inequality | x + 2 | > 8
| x + 2 | > 8
x < -8 - 2 OR x > 8 - 2
x < - 10 OR x > 6
-10 < x or x >6
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