The weighted average is -5
The formula for the weighted average is
= Σwixi/Σwi (1)
Where wi = are the weights and
xi are the coordinates
We have been given that
w1 = 3 , x1 = -8 and w2 = 1 , x2 = 4
Σwixi = w1x1 + w2x2
= 3*-8 + 1*4
= -24 + 4
= -20
Σwi = w1 + w2
= 3 + 1
= 4
Now putting the required value in equation (1) we get
Weighted average = -20/4
= -5
Hence the weighted average is -5
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Part of your bathroom remodel involves you needing to repaint. the walls measure to be 150 square feet. if a gallon of paint covers 400 square feet, how many gallons do you need to buy if you need 2 coats?
I need to buy 0.75 gallons of paint 2 coats on the wall.
We are given the area of wall, which is 150 square feet. So, if I need to put double or two coats on the wall, the area of wall to be considered will be : 150 × 2
Area of wall to be considered = 300 square feet
As per the information on paint -
400 square feet is covered by amount of paint = 1 gallon
300 square feet will be covered by amount of paint = (1 ÷ 400) × 300
Amount of paint = 300 ÷ 400
Amount of paint = 0.75 gallons
Therefore, I need to buy 0.75 gallons of paint 2 coats on the wall.
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Find the exact equation of the function graphed to the right. Show your work. Vertex: (-2,4) x intercepts:(-5,0) (1,0) y intercept (0,2)
The equation for the parabola Is; y = -²/₅[(x + 5)(x - 1)]
How to Interpret a Quadratic Graph?
We are given the following;
x-intercepts = (-5,0) and (1,0)
y - intercept = (0, 2)
We know that the x-intercepts are the roots of the quadratic equation while the y-intercept is the value of y when x is zero.
Thus;
(x + 5) and (x - 1) are factors of the given quadratic equation.
f(x) = a(x + 5)(x - 1)
At y-intercept of (0,2), we have;
a(0 + 5)(0 - 1) = 2
a = -2/5
Thus we can write the equation for the parabola as;
y = -²/₅[(x + 5)(x - 1)]
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Solve the equation p + 5 = −12 for p.
Answer: 17
Explanation
P-5=12
Transpose 5 to the other side
It will become +5 after transposing becuase it was -5 before transposing
P=12+5
P=17
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Calculate the 95onfidence interval for the true population mean based on a sample with =225, =8.5, and =45. function
The true population mean is (222.52, 227.48) with a 95% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true population mean is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95
⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95
⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95
95% confidence interval for
⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))
Here, x = 225, s = 8.5, and n = 45
⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))
⇒ μ = (222.52, 227.48)
Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.
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The question seems to be incomplete the correct question would be
Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.
It takes 5.5 hours to fly from Richmond, VA to Los Angeles, CA. It takes 3 days, 3 hours, and 30 minutes to drive. How many hours does it take to drive from Richmond, VA to Los Angeles, CA? Show the work that leads to your answer.
Answer:
75.5 hours
Step-by-step explanation:
Given:
Fly: Richmond --> LA 5.5 hours
Drive: Richmond --> LA 3 days 3 hours 30 minutes
Find:
Drive: Richmond --> LA in hours
Conversions needed:
1 hour = 60 minutes
1 day = 24 hours
3 days + 3 hours + 30 minutes =
= 3 days × (24 hours/day) + 3 hours + 30 minutes × (1 hour / 60 minutes)
= 72 hours + 3 hours + 0.5 hours
= 75.5 hours
Kyrail is 12 years old and is twice as old Aiden who is 2 years younger than maya.how old is maya?
Of all of the common assumptions that we discussed in class, I think one of the most common is the idea that a children’s text should in some way teach the reader something. We of course talked about the term didactic, and how a didactic book strongly pushes a lesson onto the reader, telling them that they should believe this or that. Many times a reason for that lesson isn’t even given, as though the young person reading the book should just accept that lesson because they are told to, because the other knows better. As I was reading Cat in the Hat by Dr. Seuss, the book I selected for the assignment, I was hoping that it wouldn’t be as didactic as most other children’s books, and that it would be as playful and exciting as I remember as a child. On the last two pages of the book, however, the absent mother returns home, the cat has disappeared, the children are behaving nicely, sitting in chairs, and it is pretty obvious that even though they got into mischief they are still good children after all. Nothing really has changed at the end of the book. Although all sorts of things got played with, and the children broke the rules I am sure they know about (like, “Don’t fly kites in the house”), major boundaries were never crossed.
We talked about how the opposite of a didactic book might be an ambiguous book, or a book that encourages the reader to think about issues, to make decisions for themselves. In that kind of book, the author usually wants to the reader to think for her or himself, to understand that some things are difficult, even for adults. The author may present a problem and ask you what you think, or might just never come around to saying exactly what you are supposed to believe. The last page of Cat in the Hat ends with the narrator saying, referring to the mother, “Should we tell her about it? / Now what SHOULD we do? / Well . . . / What would YOU do / If your mother asked you?” (61). In some ways, this is probably a pretty ambiguous ending. The author asks the reader that if your mother left, if someone wanted you to do what you weren’t supposed to, if you did it anyway, and if you didn’t get caught, then would you tell your mother or father what happened? Most adults wouldn’t tell what happened themselves, but the question is there anyway, and it seems to be really asking children what they believe.
But it doesn’t seem really that ambiguous. If the book were really ambiguous it would be breaking the Typical Case Prototype of children’s books, and in almost every other way the book keeps to those prototypes. As Nodelman describes it, children’s books are typically bright, colorful, funny, entertaining, and maybe sometimes rhyming. Children’s books portray children as the way adults typically think of them, as crazy kids who aren’t serious like adults, or innocent angels who would never really do any harm when they play. Dr. Suess portrays typical kids, bored by the rain, wanting to do something wild. Although Seuss’s style is strange, the children even look like the sort of standard white children that appear in most books, the girl in a dress and ribbon in her hair. We saw in class how these children are a lot like the standard one’s in Cassie’s history textbook And although strange things happen in the book – a talking cat, a couple of strange Things, a lot of things getting thrown around – it is the kind of play we come to expect in children’s lives, especially in the sorts of standard things shown on television and in movies.
In fact, the children never quite seem to trust the Cat, and they always just sort of watch him play. The children never really do anything that crazy themselves. The Fish, who sounds a lot like an adult, is always there to warn them, and in the end everything gets cleaned up. Of course the book is fun and playful, and is obviously one of the most famous and liked picture books ever made, but it is still pretty straightforward. Cat in the Hat reinforces and demonstrates almost all of the typical assumptions about childhood, and it fulfills all of the typical case prototypes of children’s books. Examining it made me think about how the book might have changed in recent years, especially since children are rarely bored when they are at home any more (with all of the stuff they own to play with). But more than that, it made me think about why we expect all children’s books to be like this, why it is always considered one of the best books for children. Although I like typical children’s books, it makes me also interested in books that don’t do what we expect. The book was written 1957, and in so many ways children’s books have become so incredibly different since then. But in a lot of other ways, some good, some bad, they haven’t changed at all.
Answer:
Maya is 8 years old.
Step-by-step explanation:
12 = 2a
Aiden is 6 years old.
a + 2 = m
6 + 2 = 8
Maya is 8 years old.
answer the photo
please do it correctly
Answer:
65
Step-by-step explanation:
180 -( 95 + 20 )
=180 - 115
= 65
Nate and Maya are building model cars. Maya's car is 3 inches less than 2 times the length of Nate's car. The sum of the lengths of both cars is 26 inches. Write an equation to determine the lengths of Nate's and Maya's cars.
x + 3 − 2x = 26
x + 2x = 26
2x − 3 = 26
x + 2x − 3 = 26
Answer:
x + 2x - 3 = 26
Step-by-step explanation:
Define the variables:
Let x = length of Nate's car.Let y = length of Maya's car.If Maya's car is 3 inches less than 2 times the length of Nate's car, then:
⇒ y = 2x - 3
If the sum of the lengths of both cars is 26 inches, then:
⇒ x + y = 26
Substitute the found expression for y into the equation:
⇒ x + y = 26
⇒ x + (2x - 3) = 26
⇒ x + 2x - 3 = 26
Therefore, the equation to determine the lengths of Nate'a and Maya's cars is:
[tex]\boxed{x + 2x - 3 = 26}[/tex]
Solving the equation for x
⇒ x + 2x - 3 = 26
⇒ 3x - 3 = 26
⇒ 3x - 3 + 3 = 26 + 3
⇒ 3x = 29
⇒ 3x ÷ 3 = 29 ÷ 3
⇒ x = 9.7 in (nearest tenth)
Therefore, Nate's car is 9.7 in (nearest tenth).
To find the length of Maya's car, subtract the length of Nate's car from 26:
⇒ 26 - 9.7 = 16.3 in (nearest tenth).
Therefore, Maya's car is 16.3 in (nearest tenth).
Answer:
d) x + 2x - 3 = 26
Step-by-step explanation:
Given that,
→ Maya's car is 3 inches less than 2 times the length of Nate's car.
→ The sum of the lengths of both cars is 26 inches.
Now the equation will be,
→ x - 3 + 2x = 26
→ x + 2x - 3 = 26
→ 3x = 29
Hence, option (d) is correct answer.
Trying to prepare a budget, alvin has done research and found that he spends an average of $123 on his phone/internet/cable service, $213 on his electric bill, and $270 on his health insurance premium. if he earns $2600 per month, estimate the amount of money he will have after paying these bills each month.
A alvin makes 3,200 and spends 701 each month leaving 2,499.
What are average?The average can be calculated by dividing the sum of observations by the number of observations.
Average = Sum of observations/the number of observations
It is Given that alvin has done research and found that he spends an average of $123 on his phone/internet/cable service, $213 on his electric bill, and $270 on his health insurance premium.
Subtract expenditures from earnings;
= 3200 - (178 + 203 + 320)
= 3200 - 701
= 2499
Thus, Grant will have $2,499 after paying these bills each month
Therefore, alvin makes 3,200 and spends 701 each month leaving 2,499.
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What is the slope of the line that passes through the points (-4,5) and (-7,8) ? write your answr in the simplest form
A zumba instructor charges according to the number of participants. If there art 15 participants or below, the instructor charges 500.00 for each participant per month. If the number of participants is between 15 and 30 , he charge 400.00 for each paetricipants pe month . If there are 30 partricipantsor more . he charge 350.00 for each partricipas per month
The piecewise function that describes what the instructor charges is; f(x) = 500x , 0 < x ≤ 10
400x , 10 < x < 25
350x , x ≥ 25
How to create piecewise functions?
Let x represent the number of participants and let y represent the charge per participant.
Now, y depends on x, and as such we can say that;
f(x) = y
For, 0 < x ≤ 10, the total charges is 500x,
f(x) = 500x , 0 < x ≤ 10
For 10 < x < 25, total charge is 400x,
f(x) = 400x , 10 < x < 25
For x ≥ 25, the total charge is 350
f(x) = 350x x ≥ 25
Therefore, we can say that;
f(x) = 500x , 0 < x ≤ 10
400x , 10 < x < 25
350x , x ≥ 25
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Write the piecewise function that describes what the instructor charges.
What is the remainder when f(x) = x4 + 7x3 + 17x2 + 20x is divided by x2 + 4?
Answer:/
Step-by-step explanation:
Simplify 2x+x+x+2y×3y×y
Answer: 6y^3 +4x
Step-by-step explanation:
collect like terms
2x + x + x + 2y * 3y *y
so
6y^3 +4x
Answer:
6y3 + 4x ( 3 is cube)Step-by-step explanation:
2x + x + x + 2y ( 3 )yy
2x + x + x + 6y 3
Combine Like Terms:2x + x + x + 6y3
( 6y3 ) + ( 2x + x + x)
6y3 + 4x
What are the units on each side of the equation gmm/x2 = mv2/x? (m and m are two different masses.)
In the given statement is:
Gravitational Force between two bodies at a distance x is given by:-
F = GmM/ x2 ; If a body of mass ' m' is revolving around the body of mass M and it's orbit is stationary then centrifugal force must be equal to the Gravitational Force i.e. Fg = mv2/x therefore FG = Fg i.e. GmM/ x2 =mv2/x; where v is the orbit motion of the orbiting body of mass.
Now, Let us understand the :
In mechanics, gravity, often known as gravitation, is the constant force of attraction occurring on all matter. It plays no part in shaping the interior features of common stuff because it is easily the weakest force known to exist in nature.
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Identify the transformation that maps the figure onto itself. A Reflect across the line x = 3 Reflect across the line x = 3, B Rotate 180° about the point (3, -3)Rotate 180° about the point (3, -3) C Rotate 180° about the point (5, -5)Rotate 180° about the point (5, -5) D Reflect across the line y = -3
Answer:
D Reflect across the line y = -3
Step-by-step explanation:
The only way you can divide the trapezoid so that there are two congruent parts is when you draw a line on y=-3.
Find the equation of the given table in slope intercept form. Please show work, answer must be in y=mx+b format!
Answer:
y=5x+1.5
Step-by-step explanation:
First, we need to find the slope which is M
put B as 0 for now so we going to plug in 2 numbers on the same horizontal side
I'm going to use (-2 and 11.5) and (4 and -18.5), and now I'm going to do [tex]\frac{y^{2}-y^{1} }{x^{2} -x^{1} } \\[/tex] which -18.5-11.5/4-(-2)
I'm going to get 30/6 which means 5
the slope is 5 now we can find Y-intercept by plugging in a pair of Y and X and plug in M to find B
11.5=(5)-2+b
11.5=10+b now we going to separate b by subtracting 10 from both sides
1.5=b
You rent an apartment that costs \$1100$1100 per month during the first year, but the rent is set to go up 9.5% per year. What would be the rent of the apartment during the 12th year of living in the apartment? Round to the nearest tenth (if necessary).
The rent of the apartment during the 12th year of living in the apartment is $2076.30
Geometric order is a geometric series or sequence. By multiplying the terms of a geometric series, we arrive to conclusions. A geometric sequence, to put it simply, progresses from one term to the next by multiplying (or dividing) each phrase by the same constant value or number.
A mathematics series is a sum of an infinite number of terms with the objective of maintaining a constant ratio between the progressing terms.
Given:
In the n-th year, the rent will be ...
an = a1·r^(n-1) . . . . . . . . . r is the year on year ratio: 1+rate of increase
an = 1100·(1.095^(n-1))
Then the rent in the 8th year is ...
a8 = 1100·(1.095^(8-1)) ≈ 2076.30
The rent in the 8th year would be $2076.30.
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These tables of values represent continuous functions. In which table do the
values represent an exponential function?
A
X
1
2.
3
4
5
y
4
12
36
108
324 B X 1
2
3
4
5
у
9
10
11
12
13. C
X
1
2
3
4
5 7 28
49
70
91
D X 1 2 3
4
5 y 4
12
20
28. 36. Yo
Answer: Could you possibly make the question telligible via photo or better tables? I'd love to help if you would!
Step-by-step explanation:
Helpppppppppppppppppppppppppppp
Step-by-step explanation:
A yes
C no
D no
it's only a function if the X coordinate is just being used once.
Answer:
A:no C:yes D :yes
Step-by-step explanation:
A is no because one of the numbers doesn't have a line so they aren't functions
The distance from arias home to the science museum is 0.72 mile which fraction is equivalent to this distance in miles.
The fraction which is equivalent to this distance in 0.72 mile of science museum from Arias home is 18/25.
What is described as a fraction?Fractions are defined as a numerical value that represents a portion of a whole.
A fraction is a portion or section of any quantity taken from the whole, which can be any number, a constant set, or a thing.Every fraction has a numerator or a denominator divided by a horizontal bar recognized as the fractional bar.The denominator represents the number of parts into which the whole has also been subdivided. It is positioned below the fractional bar in the bottom section of the fraction.The numerator specifies how many fractional sections are depicted or selected. It is positioned above the fractional bar in the upper portion of the fraction.For the given question.
The distance from the science museum to Arias home is 0.72 mile.
As, we have to 2 significant figures on the right of the decimal.
Then, remove the decimal and divide the number by 100.
= 72/100
Now, divide the numerator and denominator by 4 , we get;
= 18/25
Therefore, the distance between the Arias home and the science museum in fraction is written as 18/25.
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help
show that x - y = 90°
y - x = 90° is represents a circle's circumference.
What is meant by a circle's circumference?
The distance along a circle's perimeter is referred to as its circumference. In other words, the circumference of a circle is equal to the length of a straight line formed by opening up the circle.
connect O and B
∵ OB = OD
∴ ∠ OBD = ∠ODB = x°
∴ ∠BOD = 180° - 2x°
∵ ∠BAD = y°
∴ ∠C = 180° - y°
∠BOD = 2∠C
180° - 2x° = 2 ( 180 - y° )
180° - 2x° = 360 - 2y°
2y - 2x = 180°
y - x = 90°
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if there are 15 cubs and 4 lionesses, what is the ratio of cubs to lionesses?
Answer:
15 : 4
Step-by-step explanation:
Given that,
→ 4 lionesses
→ 15 cubs
Then the ratio of cubs to lionesses,
→ x = No. of cubs : No. of lionesses
→ [ x = 15 : 4 ]
Hence, the ratio is 15 : 4.
So my math teacher is very specific about showing work and explaining why the answer is what it is. I'm confused quite a bit about this question.
"Given that 1 yard = 36 inches, explain how you would find the number of cubic inches in a yard"
I would assume the answer would just be 36in^3?
Answer:
There are 46,656 cubic inches in a cubic yard.
Explanation:
for an approximate result, multiply the volume value by 46660
Danae is choosing between two jobs. One job pays an annual bonus of $1,500 plus $120 per day worked. The second job pays an annual bonus of $2,500 plus $110 per day worked. Which equation can be solved to determine after how many days, d, Danae would make the same amount of money regardless of the job she chooses?
O 120d + 110d = 1,500 + 2,500
O 120 + 110 = 1,500d + 2,500d
• 120d + 1,500 = 110d + 2,500
• 120d + 2,500 = 110d + 1,500
Answer: 120d + 1500 = 110d + 2500
Solution: The first 1500 + 120d
The second 2500 + 110d
So. 120d + 1500 = 110d +2500
What are all the solutions for the inequality m> −9?
m=3
m= −20
m= −12
m= −2
Answer:
m = [-9, +infinity]
Step-by-step explanation:
13
Write the time.
-9
11 12
10
8
76
1
2
Answer:
5:45
...................................
Answer:
the time is 5:45 PM according to that watch
The lengths of the four sides of a
quadrilateral (in inches) are consecutive integers. If
the perimeter is 110 inches, find the value of the longest of the four side lengths.
The value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
According to the given question.
The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
So, let the length of the quadrilateral be x, (x + 1), (x + 2), and (x + 3).
Also, it is given that the perimeter of the quadrilateral is 110 inches.
⇒ x + x+1 + x + 2 + x + 3 = 110
⇒ 4x + 6= 110
⇒ 4x = 110 -6
⇒ 4x = 104
⇒ x = 104/4
⇒ x = 26 inches
Thereofore, the length of the sides of the quadrilaterals is given by
x = 26 inches
x + 1 = 26 + 1 = 27 inches
x + 2 = 26 + 2 = 28 inches
x + 3 = 26 + 3 = 29 inches
Hence, the value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
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Part 1: Mapping Diagrams
Look at the mapping diagrams below, which represent two different relations. The relation on the
left is a function since each value in the blue set is paired with one value in the yellow set. For
the function on the left, the domain is {0, 1, 2, 3) and the range is {0, 1.69, 3.38, 5.07).
1. Is the relation on the right a function? Explain.
20
70
-60
3
-6
2
5
Based on the definition of a function,
1. The relation on the right is not a function.
2. Domain: {20, 70, -60}
Range: {3, -6, 2, 5}
What is a Function?A relation that is defined as a function has each domain value that is assigned to only one possible range value, in such a way that, each of the domain element cannot have two different range element that corresponds to it.
1. The relation on the right has a domain element, -60, which corresponds to two different range element, -6 and 2.
Therefore, the relation on the right is not a function.
2. The domain of the relation that is not a function is: {20, 70, -60}
The range of the relation that is not a function is: {3, -6, 2, 5}
In summary, based on the definition of a function,
1. The relation on the right is not a function.
2. Domain: {20, 70, -60}
Range: {3, -6, 2, 5}
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he zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
A.
f(x) = (x + 6)(x + 4)
B.
f(x) = (x + 6)(x − 4)
C.
f(x) = (x − 6)(x + 4)
D.
f(x) = (x − 6)(x − 4)
Answer:
The answer is option C
Step-by-step explanation:
The roots of the quadratic equations are x= 6 or x= -4
X-6=0 or x+ 4=0
⇒(x-6)(x+4)
F(x)=(x-6)(x+4)
greatest to least,
7.
1
33,34,3
3 17
20' 5
3.
The numbers arranged in decreasing order from greatest to least is given by 133 , 53 ,34 ,33 ,20 ,17 ,7 .
Decremental Order When numbers (or other items) are arranged from largest to smallest, this is known as decreasing order.
This is called the sorting of numbers. When various data are given then we can sort the number s accordingly.Numbers can be sorted in the increasing order or decreasing order.Increasing order is sorting from lowest to greatest.Given numbers are 7, 133 , 34, 33 ,17, 20 , 53.
From looking at the numbers to arrange them in decreasing order we can see that 133 is the greatest of the numbers , so it will come first.
Then comes 53 which is the second highest number , then comes 34 the third highest number and so on unless we get the least number which is 7.
Hence the given numbers are arranged greatest to least:
133, 53, 34, 33, 20, 17.
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