Answer:
1. 2550
2. 1600
Step-by-step explanation:
Question 1Even Integer: A whole number that can be positive, negative, or zero, and that can be divided exactly by 2.
Even integers between 1 and 101:
2, 4, 6, 8, 10, ... , 100This forms an arithmetic sequence with:
first term (a) = 2common difference (r) = 2Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]
There are 50 even integers between 1 and 101.
Therefore, to find the sum of the even integers between 1 and 101, substitute n = 50 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_{50} & =\dfrac{1}{2}(50)[2(2)+(50-1)2]\\\\& =25[4+(49)2]\\\\& =25[4+98]\\\\& =25[102]\\\\& = 2550\end{aligned}[/tex]
Therefore, the sum of the even integers between 1 and 100 is 2550.
Question 2Given arithmetic sequence:
4, 9, 14, 19, 24, ...From inspection of the given arithmetic sequence:
first term (a) = 4common difference (r) = 9 - 4 = 5Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]
To find the sum of the first 25 terms of the given arithmetic sequence, substitute n = 25 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_{25} & =\dfrac{1}{2}(25)[2(4)+(25-1)5]\\\\& =\dfrac{25}{2}[8+(24)5]\\\\& =\dfrac{25}{2}[8+120]\\\\& =\dfrac{25}{2}[128]\\\\& = \dfrac{3200}{2}\\\\& = 1600\end{aligned}[/tex]
Therefore, the sum of the first 25 terms of the given arithmetic sequence is 1600.
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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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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
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
answer the photo
please do it correctly
Answer:
65
Step-by-step explanation:
180 -( 95 + 20 )
=180 - 115
= 65
Mia is building a fence using nails 2.5 in
long. She drives a nail through a board
that is 75 in. thick into a 4 in. square
fencepost. How much of the nail goes
into the post?
Answer:
jjajdawasdaw
Step-by-step explanation:
wsadwdasdawasdawdas
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:
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
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:
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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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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I need serious helpppppp!!!!!!
Answer:
Step-by-step explanation:
So we know that 22000+(-480t)
And we know that T is the minutes so we just gonna apply the number of minutes into that
if 5 minutes we going to write 22000+(-480 x 5)
and so on
Good luck :)
A student club started a fundraising effort to support animal rescue organizations. The club sent an information flyer home to the n students in the school. It says, "We welcome donations of any amount, including any change you could spare!" Their goal is to raise T dollars, and to donate to a cat shelter and a dog shelter.
Match each quantity to an expression, an equation, or an inequality that describes it.
The dollar amount the club would have if every student at the school donated a quarter to the cause.
The dollar amount the school will raise is given by the expression 0.25n, where n is the number of students.
A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression).
A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics.
The dollar amount the club would have if they reached one-fourth of their goal= [tex]\frac{1}{4} T[/tex]The dollar amount the club would have if every student at the school donated a quarter to the cause =[tex]\frac{1}{4} n[/tex]The dollar amount the club could donate to the cat shelter if they reached their goal and gave a quarter of the total donation to a dog shelter= [tex]\frac{3}{4} T[/tex]Therefore the dollar amount the school will raise is given by the expression 0.25n or [tex]\frac{1}{4} n[/tex] , where n is the number of students.
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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.
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
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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w is proportional to square root of y. y is inversely proportional to x. When x = 4, y = 16 and w = 8.
Find w in terms of x
The value of w in terms of x is w = 16/√x
VariationFrom the question, we are to find w in terms of x
From the given information,
w is proportional to square root of y
That is,
w ∝ √y
∴ w = k√y
Where k is the proportionality constant
and
y is inversely proportional to x
That is,
y ∝ 1/x
y = c/x
Where c is the constant of proportionality
From the information, we have that
When x = 4, y = 16 and w = 8
From w = k√y
8 = k√16
8 = k×4
k = 8/4
k = 2
Also,
y = c/x
16 = c/4
c = 16 × 4
c = 64
Now, we are to write w in terms of x
w = k√y and y = c/x
∴ w = k√(c/x)
w = 2√(64/x)
w = 2 × √64 / √x
w = 2 × 8/√x
w = 16/√x
Hence, the value of w in terms of x is w = 16/√x
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2x+3=7
this equation has multiplication and addition in it. to solve this equation you need to get x by itself which means you need to get 2x by itself first. how can you do this?
Answer:
Subtract 3 from both sides.
Step-by-step explanation:
Doing this will leave 2x by itself.
Answer:
read below
Step-by-step explanation:
2x + 3 = 7
To isolate 2x, subtract 3 from both sides of the equation.
[tex]2x + \frac{3}{-3} = \frac{7}{-3}[/tex]
3 - 3 = 0
7 - 3 = 4
[tex]2x = 4[/tex]
divide both sides by 2
[tex]x = 2[/tex]
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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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.
Solve #5, which algebraic proof is it
If angle 1 = 30° and angle 1 and angle 2 are equal, then angle 2 = 30°. This illustrates vertically opposite angles.
What are vertically opposite angles?When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles.
A pair of angles that are vertically opposed to one another are always equal. When two lines join to form an angle, say X=45°, the opposite angle is also 45°, for instance.
In this case, the angles are vertically opposite angles.
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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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What is the slope of the line that passes through the points (-4,5) and (-7,8) ? write your answr in the simplest form
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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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.
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)
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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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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-6 ≤ x + 3 < 10 solve x
Answer:
-6 ≤ x + 3 < 10
-6 - 3 ≤ x + 3 - 3 < 10 -3
-9 ≤ x < 7
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
