If the population of Town B is 50% greater than the population of Town A and the populations of Town C is 20% greater than the population of Town A, then what percent greater is the population of Town B tan the population of Town C
Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that 7 cups of water and 3 liters of water filled 9.8 pints. Later, they find that if they start with 5 liters of water and remove 9 cups of water, they end up with 6 pints of water. Model the given two situations as a system of linear equations. Based on your equations, determine the relationship between;
●cups and liters,
●cups and pints,
●and pints and liters.
Show all your work and submit your work along with the resulting relationships.
Here's work you can copy and paste:
7 cups + 3 liters = 9.8 pints
7c+3l=9.8p
5 liters - 9 cups = 6 pints
5l+9c=6p
Cups and Liters
7c+3l=9.8p
p= 7c+3l/9.8 (put in equation 2)
5l-9c= 7c+3l/9.8
49l-88.2c=7c+3l
49l-3l=7c-88.2c
46l=45.2c
1Liter = 2.1 Cups
Cups and Pints
7c+3l=9.8p
3l=9.8p-7c
l=9.8p-7c/3 (put in equation 2)
5(9.8p-7c/3)-9c=6p
(49p-35c/3)-9c=6p
49/3p-35/3c-9c=6p
49/3p-6p=35/3c+9c
31/3p=62/3c
1 Pint = 2 Cups
Pints and Liters
7c=9.8p-3l
c=9.8p-3l/7 (put in equation 2)
5l-9(9.8p-3l/7)=6p
5l-63/5p+27/7l=6p
5l+27/7l=6p+63/5p
62/7l=93/5p
1 Liter = 2.1 Pints
express this sentence as a formula: z varies directly with the square of s.
Which best describes the range of the function f(x) = 2(1/4) after it has been reflected over the y-axis? all real numbers all real numbers less than 0 all real numbers greater than 0 all real numbers less than or equal to 0
Answer:
All real numbers greater than 0.
Step-by-step explanation:
We have the function, [tex]f(x) = 2(\frac{1}{4})^{x}[/tex].
'Reflection over y-axis means to flip the graph over y-axis', which changes the function by f(x) becomes f(-x).
So, after reflection, the given function transforms into,
[tex]g(x)=f(-x)[/tex]
i.e. [tex]g(x)=2(\frac{1}{4})^{-x}[/tex]
According to the graph of the function g(x), we see that,
Range of [tex]g(x)=2(\frac{1}{4})^{-x}[/tex] is the 'Set of all real non-negative numbers' i.e. {x | x > 0} i.e. [tex](0,\infty)[/tex]
Is 7/2 the same thing as 3.5
Solve the inequality.
15 + 12c ≥ 9(c + 15)
you buy a box of sugar-free gum that has 12 packs each pack has five pieces which expression represents the total number of pieces of gum
What is the value of x?
give and example of a repeating decimal where two digits repeat
3x-2y=13 2x+3y=-16 are these lines parallell or perpendicular or neither
what is the inverse of the function f(x) = 2x + 1
the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x - 1}{2} \).[/tex]
To find the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex], we'll switch the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] and solve for [tex]\( y \)[/tex].
1. Start with the original function:
[tex]\[ f(x) = 2x + 1 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = 2y + 1 \][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[ x - 1 = 2y \][/tex]
[tex]\[ \frac{x - 1}{2} = y \][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{x - 1}{2} \][/tex]
Therefore, the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x - 1}{2} \).[/tex]
Lauren describes a parabola where the focus has a positive, nonzero x coordinate. Which parabola(s) could Lauren be describing? Check all that apply.
x2 = 4y
x2 = –6y
y2 = x
y2 = 10x
y2 = –3x
y2 = 5x
it answer is c ,d and f
The correct equations are [tex]y^2 = x[/tex], [tex]y^2 = 10x[/tex] and [tex]y^2 = 5x[/tex] respectively
What is a Parabola?A parabola is symmetrical open plane curve that is created by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.
In the given question, Lauren describes a parabola that has positive non zero coordinate value on
focusThe equation of focus of a parabola is given as
[tex]y = a(x - h)^2 + k[/tex]
In the options given,
[tex]y^2 = x[/tex] is correct
[tex]y^2 = 10x[/tex] is also correct and
[tex]y^2 = 5x[/tex] is correct
This shows that only option c, d and f are the right answers.
The correct equations are [tex]y^2 = x[/tex], [tex]y^2 = 10x[/tex] and [tex]y^2 = 5x[/tex] respectively
Learn more on focus of a parabola here;
https://brainly.com/question/4061870
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 2 units, the value of k is ________. Numerical Answers Expected!
Answer: The value of k is 2.
Step-by-step explanation:
Given : The graph of [tex]f(x)=(0.5)x[/tex] is replaced by the graph of [tex]g(x)=0.5)x-k.[/tex]
If g(x) is obtained by shifting f(x) down by 2 units, then [tex]g(x)=(0.5)-2[/tex]
[since f(x)shifted down down by 2 , so only the value of dependent variable effect]
When we compare both functions of g(x), we found that k=2.
Hence, the value of k is 2.
The value of [tex]k[/tex] is 2.
The following information should be considered:
when [tex]g(x)[/tex] is obtained by shifting f(x) fall by 2 units so [tex]g(x) = (0.5) - 2.[/tex]Since [tex]f(x)[/tex] shifted down by 2 so there is the effect on the dependent variable. Now at the time of comparing both functions of g(x) the k should be 2.Learn more: brainly.com/question/17429689
Twice a number decreased by 15 is equal to -27 . What is the number ?
Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have?
6 ounces
12 ounces
18 ounces
27 ounces
Answer:
The answer is C. 18 ounces
Step-by-step explanation:
Answer:
c on egde
Step-by-step explanation:
simplify square root of 1.69
In the given problem, the square root of 1.69 is 1.3.
The square root of a non-negative real number is a value that, when multiplied by itself, results in the original number. In mathematical notation, the square root of the number "x" is represented by the symbol "√x."
The square root is an inverse operation of squaring, which means that if one squares a number and then take its square root, he or she gets back to the original value. The concept of the square root is nearly related to obtaining the side length of a square with a given area or obtaining the magnitude of a vector in mathematics.
1.69 also can be written as [tex]\dfrac{169}{100}[/tex] in fraction form.
[tex]\sqrt{\dfrac{169}{100}} = \sqrt{\dfrac{13^2}{10^2} }[/tex]
[tex]= \sqrt{(\dfrac{13}{10} )^2}\\= \dfrac{13}{10} \\= 1.3[/tex]
Thus, 1.3 is the square root of 1.69.
Learn more about square roots here:
https://brainly.com/question/29286039
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is √2/3 a rational or irrational
sqrt(2/3) = 0.816496
since it is a decimal with no repeating numbers it would be irrational
A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle?
A quadratic equation is shown below: 2x2 − 10x − 8 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 4x2 − 12x + 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
A dogs weight increased by 50% in 3 years . By the end of the 3years , the dog weighed 45 pounds . How much did the dog weigh 3 years ago
Final answer:
To calculate the dog's weight from three years ago, we take the current weight and divide it by 1.50 since the weight increased by 50%. The equation 1.50 * x = 45 pounds results in x = 30 pounds, indicating the dog weighed 30 pounds three years ago.
Explanation:
The question concerns the original weight of a dog whose weight increased by 50% over a period of three years, bringing its weight to 45 pounds at the end of that period. To determine the dog's weight from three years ago, we use the following steps:
Understand that a 50% increase implies that the final weight is 150% of the original weight (100% + 50%).
Represent the original weight as 'x'.
Set up the equation: 1.50 * x = 45 pounds.
Divide both sides by 1.50 to solve for 'x': x = 45 / 1.50.
Calculate 'x' to find that 'x' equals 30 pounds.
Therefore, the dog weighed 30 pounds three years ago.
One integer is 7 times another. If the product of the two integers is 28, then find the integers
What is the least common denominator of the equation ? 2/9x+2/3x=7
Create a set of data that contains 11 test scores and satisfies each condition below:
Mean: 83
Median: 81
Mode: 80
Range: 26
Answer:
An example of a data set that satisfies each of these conditions is:
[72, 75, 79, 80, 80, 81, 82, 84, 88, 94, 98]
Step-by-step explanation:
Let's start by defining the terms:
Mean: Average of all numbers
Median: Middle score in a set of given numbers
Mode: Most frequently occuring number
Range: Difference between the lowest and highest number
There are many possible data sets for these conditions, but these are the numbers I found work. I'm sure there is a simpler way to figure this out, but this way makes the most sense to me. This was my process.
We know that all of our numbers need to add up to 913. We know this because our mean is 83 and there are 11 numbers (83X11=913). We can check this by taking 913/11 (the number of scores)=83 (mean)
We know that the median needs to be 81. When the numbers are in order lowest to highest, we would need to have 5 numbers below 81 and 5 numbers above 81. The sixth number in the set should be 81.
We know the mode is 80, so 80 has to be in our data set at least twice with all other numbers appearing less often. This is why I put two 80s and one of every other number in my data set.
I then picked the lowest number in my data set, ensuring that a range of 26 would allow me enough space on both sides of the median. Since I have my lowest number, I can add 26 and get the highest number in my data set.
Once I have the main numbers, I just need to put other numbers before and after the median that would give me a sum of 913 (see the section about the mean). These can be any numbers that go in the right order as long as they don't change any of the numbers we've already established and they total 913.
Which expression is equal to x + (f + g)?
xf + g
x + fg
(x + f) ⋅ g
(x + f) + g
The answer is (x + f) + g
x/9=4/y=y/36 solve for x
answer both questions to get brain ( if u cant see all the answers its fine all u need is the question)
Answer:
a and c
Step-by-step explanation:
a polynomial of degree zero is constant term. true or false
Find the circumference of a circle whose area is 24pi ft^2
Answer:
30.76 [tex]ft^{2}[/tex]
Step-by-step explanation:
To calculate the circumference of a circle you just have to multiply the diameter by pi.
C= D*[tex]\pi[/tex]
And in order to calculate the value of the diameter you have to clear the formula for the area.
A= [tex]r^{2} *\pi[/tex]
r=[tex]\sqrt{\frac{24 \pi }{\pi } }[/tex]
r=[tex]\sqrt{24}[/tex]
r=4,89
Once we get the radius, we only have to calculate the diameter:
D=2r=9,79
now we just calculate the circumference:
C=D*[tex]\pi[/tex]= (9.79)(3.14)= 30.76
If 3a+4b = 4a-4b = 21 find the value of a
How do you tell if the shape on a data distribution is symmetric or not symmetric?