(4,5) and (4,12) are this pair is allowable to the maximum number of widgets the factory can produce in a day is 4, so x ≤ 4 .
(11,1) and (3,9) are this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12, so x + y ≤ 12.
Let us assume the number of widgets = x
Let us assume the number of zurls = y
According to question,
The combined number of widgets and zurls made each day cannot be more than 12.
That means,
x + y ≤ 12 (Equation-1)
The maximum number of widgets the factory can produce in a day is 4.
That means,
x ≤ 4 (Equation-2)
So,
We can write each pair has,
(4,5)
x = 4,
y = 5
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 5 ≤ 12 ; 4 ≤ 4
9 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
(11,1)
x = 11,
y = 1
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
11 + 1 ≤ 12 ; 11 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(3,9)
x = 3,
y = 9
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
3 + 9 ≤ 12 ; 3 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(4,12)
x = 4,
y = 12
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 12 ≤ 12 ; 4 ≤ 4
16 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
Therefore,
(4,5) and (4,12) are this pair is allowable to the maximum number of widgets the factory can produce in a day is 4, so x ≤ 4 .
(11,1) and (3,9) are this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12, so x + y ≤ 12.
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The maximum number of widgets the factory can create in a day is 4, therefore x 4. (4,5) and (4,12) are this pair is permissible.
The total number of widgets and zurls produced each day is limited to 12, therefore (11,1) and (3,9) are acceptable. Therefore, x + y 12.
Let's assume there are x widgets.
Assume that y is equal to the number of zurls.
According to the inquiry,
There can never be more than 12 widgets and zurls produced each day.
That implies,
x + y ≤ 12 (Equation-1)
The maximum number of widgets the factory can produce in a day is 4.
That means,
x ≤ 4 (Equation-2)
So,
We can write each pair has,
(4,5)
x = 4,
y = 5
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 5 ≤ 12 ; 4 ≤ 4
9 ≤ 12
Hence this pair is not allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is allowable to the maximum number of widgets the factory can produce in a day is 4.
(11,1)
x = 11,
y = 1
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
11 + 1 ≤ 12 ; 11 ≤ 4
12 ≤ 12
Hence this pair is allowable to the combined number of widgets and zurls made each day cannot be more than 12.
Hence this pair is not allowable to the maximum number of widgets the factory can produce in a day is 4.
(3,9)
x = 3,
y = 9
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
3 + 9 ≤ 12 ; 3 ≤ 4
12 ≤ 12
Therefore, this pair is permitted as long as the total number of widgets and zurls produced each day does not exceed 12.
The factory can only manufacture a maximum of 4 widgets per day, so this combination is not permitted.
(4,12)
x = 4,
y = 12
We can substitute values in equation 1 and 2,
x + y ≤ 12 ; x ≤ 4
4 + 12 ≤ 12 ; 4 ≤ 4
16 ≤ 12
Because the maximum daily production of widgets and zurls is limited to 12, this pair is not permitted.
The factory can only make a maximum of 4 widgets every day, hence this pair is permitted.
Therefore,
The maximum number of widgets the factory can create in a day is 4, therefore x 4. (4,5) and (4,12) are this pair is permissible.
The total number of widgets and zurls produced each day is limited to 12, therefore (11,1) and (3,9) are acceptable. Therefore, x + y 12.
Find the coordinate of the midpoint of the segment with the given endpoints.
-8 and -6.
The distance between the points is 2: x2 - x1 = -6 + 8. So, the midpoint would be located on a point that is half of this distance from both points.
2/2 = 1
-6 - 1 = -7
-8 + 1 = -7
-7 has a distance of 1 from both -8 and -6, so this is the midpoint.
What is the percent error if a stick of length 60 inches is measured to be 63 inches long?
If a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .
The Percent Error can be calculated by the formula
Percent Error = (measured value - actual value)/(actual value) ×100
In the question ,
it is given that
the original length of the stick is 60 inches .
the measured length of the stick is 63 inches .
So, the measured value = 63 inches ,
actual value = 60 inches .
Substituting the measured values and actual value in the percent error formula , we get
Percent Error = (63-60)/60 × 100
= 3/60 × 100
= 1/20 × 100
= 100/20
= 5 %
Therefore , if a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .
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(3x²y) . (2xy³) . (4x²y²)
Answer:
24[tex]x^{5}[/tex][tex]y^{6}[/tex]
Step-by-step explanation:
(3x²y) × (2xy³) × (4x²y²)
= 3 × 2 × 4 × x² × x × x² × y × y³ × y²
= 24 × [tex]x^{(2+1+2)}[/tex] × [tex]y^{(1+3+2)}[/tex]
= 24[tex]x^{5}[/tex][tex]y^{6}[/tex]
1.are the events not on a leash and retriever independent 2.what is the probability that a dog that is a retriever is on a leash3.what is the probability that a dog that is not on a leash is not a retriever?4.what is the probability that a dog is not a retriever and is on a leash?
The total number of dogs are 135.
The number of Retrievers dogs are 35.
The number of off leashed playing dogs are 47.
Determine the number of dogs that are not Retrievers.
[tex]\begin{gathered} NR=135-35 \\ =100 \end{gathered}[/tex]Determine the number of dogs that are not retrievers and not lleashed.
[tex]47-10=37[/tex]So table can be filled as,
Not on a leash leashed Total
Retrievers 10 25 35
Not a Retrievers 37 63 100
Total 47 88 135
1.
The events are indpendent if occurence of event does not affect the other event. But it can be observed that not on a leash and retriever depend on each other. So event not on a leash and retriever are not indpendent.
4.
The number of dogs that are not retriever and is on a leash are 63. So probability is,
[tex]\begin{gathered} P\text{ (R'}andL\text{)}=\frac{63}{135} \\ =\frac{7}{15} \end{gathered}[/tex]let a be the area of a circle with radius r that is increasing in size with respect to time. if the rate of change of the area is 3 cm/s, find the rate of change of the radius when the radius is 6 cm.
1/4π is area of a circle when the radius is 6 cm.
What is the circumference of a circle?
The radius squared times pi equals the area of a circle (A = r2). Find out how to apply this formula to determine a circle's area given its diameter.As a result, the circumference of a circle is pi times the diameter or 2 pi times the radius, which is how pi is typically defined as the ratio of a circle's circumference to its diameter. This provides a geometric reason that a circle's surface area is indeed equal to "pi r squared."A = πr²
differentiate both sides with respect to 't'
dA/dt = πr² dr/dt
dA/dt = 2πr dr/dt
dA/dt = 3 , r = 6
3 = 2π * 6dr/dt
dr/dt = 1/4π
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Part A = Gil is shopping for books and CDs. He buys 4 books and no CDs for a total of $32. Write an equation that represents the relationship between the cost of a book, y, and the cost of a CD, x, in standard form.
Part B= what is the slope of the equation?
9 more than the product of 4 and x
Answer:
4x + 9
Step-by-step explanation:
the product of 4 and x is 4x
then 9 more is addition, so 4x + 9
For any long-distance call T-Mobile charges a base rate of $15 per month plus $0.0
that you are on the phone, while Verizon charges a base rate of only $10 per month, but charges $0.10 per minute for long distance calls. Write the equation that represents the total cost for one month of long distance calls for each company, where y is total cost and x is the amount of minutes used
T-Mobile charges a base fee of $15 per month plus $0.05 for each minute. 300 minutes long would you need to call for them to charge the same amount.
How to estimate total cost?Given: While Verizon has a basic rate of only $10 per month but charges $0.10 for long-distance calls, T-Mobile has a base fee of $15 per month plus $0.05 for each minute you are on the phone.
We have to estimate how long would you need to call for them to charge the same amount.
Let the equation be 15 + 0.05 x = 0.10 x
⇒ 0.05 x - 0.10 x = -15
simplifying the above equation, we get
⇒ -0.05 x = -15
⇒ 0.05x = 15
⇒ x = 15 / 0.05
⇒ x = 300 minutes
Therefore, 300 minutes long would you need to call for them to charge the same amount.
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Polly is an artist, and she sells posters at a local café. When she sells x posters, she makes f(x) dollars.
What does f(5)=10 tell you?
The expression f(5)=10 tells us that if Polly is an artist and sells posters at a local cafe then it means that Polly makes 10 dollars when she sells 5 posters.
According to the question,
We have the following information:
Polly sells x posters then she makes f(x) dollars.
We have the following expression:
f(5) = 10
So, it simply means that in place of x in f(x) we have f(5) then we have 5 in place of x.
f(x) is the amount made in dollars. So, the total amount Polly made is 10 dollars.
Hence, the expression f(5) = 10 clearly states that Polly sold 5 posters as an artist and made 10 dollars out of it.
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4. Which of the following is a binomial with degree 3?
3x+3x²
2xy²
2+5x-3x³
2x³ + xy
2x³ + XY is a binomial with a degree of 3
What is binomial?An algebraic expression containing only two terms is called a binomial. This is a binomial polynomial. It is also called the sum or difference of two or more monomials. This is the simplest form of a polynomial. A binomial is a polynomial with only terms. For example, x 2 is a binomial where x and 2 are two separate terms. Also, the coefficient of x is 1, the exponent of x is 1, and 2 is a constant here. Therefore, an A-binomial is a two-term algebraic expression that contains a variable, a coefficient, an exponent, and a constant.
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What is the slope of the line that passes through the point (4,7) and (7,16)
Answer: The slope is 3.
Step-by-step explanation: Hope this helps :)
A: What two integers does square root of 37 fall between
B: Estimate The Decimal To The Nearest Tenth
A . [tex]\sqrt{37}[/tex] falls between integers 6 and 7
B. The decimal to the nearest tenth = 6.1
A. How are the two integers calculated?
[tex]\sqrt{37}[/tex] = 6.082 , falls between integers 6 and 7
What are integers?
A collection of integers is created if negative numbers are mixed in with whole numbers.Positive, negative, and zero are all examples of integers. Fractions and decimals are not included in integers. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division.B: Estimate The Decimal To The Nearest Tenth
[tex]\sqrt{37}[/tex] = 6.082
To estimate the decimal to the nearest tenth , we check the number in the hundredth place first which is 8.Since the hundredth place value number 8 is greater than 5 , we add a number to the tenth place .So the tenth place number changes from 0 to 1.[tex]\sqrt{37}[/tex] = 6.082 = 6.1
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3/5-6/10+9/15-12/20=
Answer:
Step-by-step explanation:
0
Use point-slope form to write the equation of a line that passes through the point (20,19)(20,19) with slope 55.
The equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.
As given in the question,
Line passes through the point ( x₁ , y₁ ) = ( 20, 19)
Slope of the line that passes through (20 , 19) is 55
Equation of a line in point-slope form that passes through the point (20,19) with slope 55
y - y₁ = m ( x- x₁)
⇒ y - 19 = 55 (x - 20)
⇒ y -19 = 55x - 1100
⇒ y= 55x - 1091
Therefore, the equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.
The complete question is:
Use point-slope form to write the equation of a line that passes through the point (20,19) with slope 55.
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-1/9 divided by 3/4
-4/27
1/12
1/12
4/27
Answer:
-4/27
Step-by-step explanation:
Which of the following is the prime factorization of 10? a1 x 10 b2 x 2 x 5 c5 x 5 d2 x 5
a=1×10, b=2×2×5, c=5×5 and d=2×5. Option a, b and d are the prime factorization of 10 but option c is not a prime factorization of 10.
Given that,
a=1×10, b=2×2×5, c=5×5 and d=2×5
We have to find the prime factorization of 10.
A natural number other than 1 is said to have a prime factor if its only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on. So, let's take something like the number 20 as an example. That can be divided into two components. We can say, "Well, that's 4 times 5." Note that the number five is a prime.
Option a is 1×10
1×10=10
Option a is a prime factor of 10.
Option b is 2×2×5
2×2×5=10×2
Option b is a prime factor of 10.
Option c is 5×5
5×5=25
Option c is not a prime factor of 10.
Option d is 2×5
2×5=10
Option d is a prime factor of 10.
Therefore, Option a, b and d are the prime factorization of 10 but option c is not a prime factorization of 10.
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The area of the Caribbean Sea is 2.7182 × 10^6 km2. The area of the South Atlantic Ocean is 4.027 × 10^7 km2. Find the total area. Write the final answer in scientific notation with the correct number of significant digits.
The area of the Caribbean Sea is 2.7182 × 10^6 km2, The area of the South Atlantic Ocean is 4.027 × 10^7 km2, then the total area of the Caribbean Sea and the South Atlantic Ocean is 4.29882 × 10⁷ km².
We are to determine the total area of the Caribbean Sea and the South Atlantic Ocean.
From the given information,
The area of the Caribbean Sea is 2.967 × 10⁶ km² and
The area of the South Atlantic Ocean is 4.149 × 10⁷ km²
To determine the total area, we will add the given areas together,
2.7182 × 10⁶ km²
+ 4.027 × 10⁷ km²
So, That is,
2.7182 × 10⁶ km²
+ 40.27 × 10⁶ km²
----------------------------
42.9882 × 10⁶ km²
So,
We can write,
= 4.29882 × 10⁷ km²
Therefore,
The total area of the Caribbean Sea and the South Atlantic Ocean is 4.29882 × 10⁷ km².
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Functions W and Z are both linear functions of x. Which statement comparing the functions is true? Select all that apply. A. The slope of Function W is less than the slope of Function Z. B. The slope of Function W is equal to the slope of Function Z. C. The slope of Function W is greater than the slope of Function Z. D. The y-intercept of Function W is less than the y-intercept of Function Z. E. The y-intercept of Function W is equal to the y-intercept of Function Z. F. The y-intercept of Function W is greater than the y-intercept of Function Z
The correct options are:
B. The slope of Function W is greater than the slope of Function Z.
F. The y-intercept of Function W is greater than the y-intercept of Function Z.
Let's find the slope (m) and y-intercept (b) of each function to see which one compares the two functions accurately.
Function W:
The slope of Function B, using two points on the line, (0, -1) and (2, 0):
m = ( y₂ - y₁ )/ (x₂ - x₁ )
m = [ 0 - (- 1 )]/( 2- 0 ) = 0.5
The y-intercept will be when x = 0. Therefore, from the graph, the y-intercept is b = -1.
For Function Z:
The slope of Function Z, using two pairs of values from the table of values for function Z, ( 0, - 2 ) and ( 2, - 1.5 ):
m = ( y₂ - y₁ )/ (x₂ - x₁ )
m = ( - 1.5 - ( -2 ) )/( 2 - 0 )
m = 0.5/2 = 0.25
The y-intercept is the value of y when x = 0.
From the table when x = 0, y = - 2. Therefore, the y-intercept is b = - 2.
Thus, the following statements that compare both functions are TRUE:
B. The slope of Function W is greater than the slope of Function Z.
This is TRUE because 0.5 is greater than 0.25.F. The y-intercept of Function W is greater than the y-intercept of Function Z.
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Need help college math algebra
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 16 feet
more than the length of the shortest side. Find the dimensions if the perimeter is 156 feet.
The length of three sides will be 35 feet, 70 feet and 51 feet
Define Perimeter of triangle
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.
Perimeter of Triangle = side1 + base + side2
Let, the shortest side of the triangle = x
The other side length is = 2x
and, the length of third side is = x + 16
given perimeter = 156 feet
We know, perimeter of triangle = a + b +c
where, 'a' and 'c' stands for sides of triangle
and, b stands for base
hence, the expression will be according to formula,
x + 2x + x + 16 = 156
solve for 'x'
4x + 16 = 156
4x = 156 - 16
x = 140/4
x = 35
2x = 2 * 35 = 70
x + 16 = 35 + 16 = 51
Therefore, the length of three sides will be 35 feet, 70 feet and 51 feet.
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Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are
(
3
x
−
4
)
feet,
(
x
2
−
1
)
feet, and
(
2
x
2
−
15
)
feet.
What is the perimeter of the triangle if
x
=
4
?
Responses
16
feet
16 feet
40
feet
40 feet
76
feet
76 feet
80
feet
The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively. The perimeter of the triangle is 42 feet.
Given that,
Kat is using reflective orange paint to outline a triangle stage prop. The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively.
We have to find if x = 4, what is the triangle's perimeter.
The perimeter of the triangle is equal to sum of the three sides of the triangle.
=3x - 4 + x² - 1 + 2x² - 15
=3x²+3x-20
Take the x value as 4
We get,
=3(4)²+3(4)-20
=3×16+3×4-20
=48+14-20
=62-20
=42
Therefore, The perimeter of the triangle is 42 feet.
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if the sample size were to increase, all other numbers remaining the same, what would be the impact on the standard error? the standard error would:
If the sample size were to increase, and all other numbers remaining stays the same, then the standard error would be less.
Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.
SE = SD / √n
where SE = standard error
SD = sample standard deviation
n = sample size
Increasing the sample size, n, while the samples remain the same(hence, the standard deviation will be the same), will result to smaller standard error.
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Asymptote (horizontal) of f(x)=2(3)^-x
The Value of the horizontal asymptote is 0
What is horizontal asymptote?
The horizontal asymptote of a function y = f(x) is a line y = k and to calculate the horizontal asymptote please substitute [tex]x=[/tex]±∞. We can also find the vertical asymptote.
now we are given a function
[tex]f(x)=2(3)^{-x}[/tex]
Now substitute x=±∞ in the equation, as the x in denominator we get
f(x)= 0
This is the value of the horizontal asymptote
Hence the value of horizontal asymptote comes out to be 0
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Find the 61st term of the arithmetic sequence -12, -28, -44, ...
The sequence's 61st term is -972.
The sequence is -12 , -28 , -44.
Solution:The following arithmetic sequence is: -12, -28, -44, ..
Find the common difference between the succeeding and preceding terms.
c.d = first term - second term
-28 - (-12) = -28 + 12 = -16
-44 - (-28) = -44 + 28 = -16
As a result, the distinction between the terms remains constant.
This is a mathematical sequence.
The formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1 ) d
Where,
an is the sequence's nth term.
a1 is the sequence's first term.
The common difference between terms is denoted by d.
-12, -28, -44 are the numbers in the given sequence.
By changing the values in the formula,
a1 = -12
d = -16
Substituting values,
an = -12 + (n - 1 )(-16)
an = -12 - 16n + 16
an = 4 - 16n
Substitute n = 61 to find the 61st term.
a61 = 4 - 16 x 61
a61 = 4 - 976
a61 = -972
As a result, the sequence's 61st term is -972.
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before the early 1990s, a telephone area code in the us consisted of three digits, where the first was not 0 or 1, the second was 0 or 1, and the third was anything except 0. how many area codes were possible?
Number of possible area codes = 144
The telephone area codes consist 3 digits.
The possible digits are 1, 2, 3,4,5,6,7,8,9,0. That is, a total of 10 digits.
The first digit was not 0 or 1. So the remaining are 2,3,4,5,6,7,8,9. There are 8 possibilities in first place.
The second digit is either 0 or 1. So there are only two possibilities for second place.
The third digit was anything except 0. So the third digit has 9 possibilities.
The total possibilities of the three digit number is the product of possibilities of digits in each place.
Hence, Number of possible area codes = 8 x 2 x 9 = 144
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At the toy store you could get 2 board games for $8.36. Online the price for 3 board games is $12.84. Which place has the highest price for a board game?
An online place has the highest price for a board game because it costs $4.28 and a store costs $4.18 for each game respectively.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
From the data given:
At the toy store, you could get 2 board games for $8.36.
Each board game cost = 8.36/2 = $4.18
Online the price for 3 board games is $12.84.
Each board game costs = 12.84/3 = $4.28
4.28 > 4.18
Thus, an online place has the highest price for a board game because it costs $4.28 and a store costs $4.18 for each game respectively.
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(Please help) Write an equation of the line
The equation of the line is y = -x + 3
How to find the equation of a line
Equation of a straight line is usually of the form y = mx + c
where:
m = slope
c = y intercept
slope = ( 5 - -2 ) / ( -2 - 5 )
= ( 5 + 2 ) / -7
= 7 / -7
= -1
The y intercept is found from the graph to be 3
the equation of lthe line is
y = -1 ( x ) + 3
y = -x + 3
Therefore the equation of the line as gotten from the graph is y = -x + 3
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buffy opens a savings account with $100 that earns 9% interest per year, not compounded. how much interest will buffy earn in 2 years?
Answer:
She will earn 18 dollars in interest.
Step-by-step explanation:
0.09*(100*2)
0.09*(200)
18
You start at (-5, 0). You move down 1 unit and right 2 units. Where do you end?
Answer:
(- 3, - 1 )
Step-by-step explanation:
1 down means subtract 1 from the y- coordinate
2 units right means add 2 to the x- coordinate
(- 5, 0 ) → (- 5 + 2, 0 - 1 ) → (- 3, - 1 )
What is the answer pls
Answer: 11.2
Step-by-step explanation: In order to find the length of n, you can use the given angle measure and base length as well as a trig ratio. Since 6.2 is adjacent to angle N, you can use tangent (opposite/ adjacent).
tan (61) = n/6.2
(multiply by 6.2 on both sides to isolate n)
• 6.2 • 6.2
tan (61) • 6.2 = n
11.185 = n
~11.2 = n.
