The sum of two hundred even numbers in the sequence from 0 to 398 is 39800
Sum of an APTo find the sum of two hundred even numbers from 0 to 398, we can use the formula of sum of an arithmetic progression.
[tex]S_n = \frac{n}{2}[2a(n-1)]d[/tex]
n = number of termsa = first termd = common differenceThe number of terms given here is 200, the first term is 0 and the common difference is 2
Substituting the values into the equation
[tex]S_n = \frac{n}{2}[2a+(n-1)]d\\S_n = \frac{200}{2}[2*0+(200-1)*2\\S_n = 100(0+199)*2\\S_n = 39800[/tex]
The sum of two hundred even numbers from 0 to 398 is 39800
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A function is modeled by the equation f(x) = 2x + 5.
Which function models a transformation of f (x + 3)?
f(x + 3) = 2x+8
f (x + 3) = 2x + 11
f(x + 3) = 5x + 8
f (x + 3) = 6x + 15
A
B
C
D
"y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).
f(x) = 2x + 5.
f(x+3) = 2(x+3) + 5.
f(x+3) = 2x + 11.
What is meant by function ?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The dependent variable or output value is denoted by the letter y, or f(x).To learn more about : function
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The system of equations is solved using the linear combination method.
StartLayout 1st row 1st column one-half x + 4 y = 8 right-arrow 2nd column negative 2 (one-half x + 4 y = 8) right-arrow 3rd column negative x minus 8 y = negative 16 2nd row 1st column 3 x + 24 y = 12 right-arrow 2nd column one-third (3 x + 24 y = 12) right arrow x + 8 y = 4 with Bar Underscript 3rd row 3rd column 0 = negative 12 EndLayout
What does 0 = −12 mean regarding the solution to the system?
There are no solutions to the system because the equations represent parallel lines.
There are no solutions to the system because the equations represent the same line.
There are infinitely many solutions to the system because the equations represent parallel lines.
There are infinitely many solutions to the system because the equations represent the same line.
Answer: The answer is A) There are no solutions to the system because the equations represent parallel lines.
Step-by-step explanation: got it on edge 2022
Answer:
There are no solutions to the system because the equations represent parallel lines
Step-by-step explanation:
11. What is the value of the expression below?
1-10+6|-|3²-5|
The value of the expression |-10+6|-|3²-5| = 0
The expression given is |-10+6|-|3²-5|.
This contains absolute value which needs to be evaluated.
We will go through the definition of absolute value.
Absolute value for x = x, when x is a positive integer.
i.e., |x| = x, when x >0
Absolute value of (-x) = x, when -x is a negative integer.
So absolute value always gives the positive value of the number inside it.
Now |-10+6|-|3²-5| = |-4| - |9-5|
= 4 - |4| [Since |-4| = 4]
= 4 - 4 [Since |4| = 4]
= 0.
So the value of the expression |-10+6|-|3²-5| = 0
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Rectangle 1 has an area of 60.81 square centimeters. Rectangle 2 has an area of 61.44 square centimeters. Rectangle 3 has an area of 35.52 square centimeters. Rectangle 4 has an area of 47.88 square centimeters. Part A..Which two rectangles have the greatest difference in area? Part B Look at your answer to part A what is the difference between those two rectangles areas?
The two rectangles that is R3 and R4 have the greatest difference in the area.
How to calculate the area of the rectangle?
In mathematics, the rectangle is a closed polygon shape which has four vertex as well as four sides. And the opposite side are parallel to each other. To calculate the area, multiply the length and breadth. Similarly, for the perimeter means add all the sides.
According to the question, the given data in the form of the area of the rectangle is as follows:
Area of Rectangle1 = 60.81 square centimeters
Area of Rectangle2 = 61.44 square centimeters
Area of Rectangle3 = 35.52 square centimeters
Area of Rectangle4 = 47.88 square centimeters
Now, to calculate the greatest difference in the area of the rectangles:
Difference(Rect2 - Rect1) = 61.44 - 60.81 = 0.63
Difference(Rect1 - Rect3) = 60.81 - 35.52 = 25.29
Difference(Rect1 - Rect4) = 60.81 - 47.88 = 12.93
Therefore, the two rectangles that is R3 and R4 have the greatest difference in the area.
And the differences are as follows:
Area(Rect1 - Rect3) = 60.81 - 35.52 = 25.29 square centimeters
Area(Rect1 - Rect4) = 60.81 - 47.88 = 12.93square centimeters
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Under her cell phone plan, Mayerlin pays a flat cost of $55 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine x x, the number of gigabytes Mayerlin can use while staying within her budget.
The number of gigabytes that Mayerlin can use while staying within her budget is 5.
How many gigabytes can she use?The first step is to determine the appropriate inequality sign to use. Here are the inequality signs:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The sign that would be used is <
The form of the inequality is:
flat cost + (cost per gigabyte x number of gigabytes) < total budget
$55 + $5x < $70
5x < $70 - $55
5x < 25
x < 25 / 5
x = 5
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Aryon has $20. He buys 2 cokes that each cost $1.50. He also buys a sandwich for $5.50. And a bag of chips that cost $2.25. After Aryon pays for his lunch, how much money does he have left.
Aryon is left with $9.25 of money after he has paid for his lunch.
According to the question,
We have the following details:
Total amount Aryon has = $20
The cost of 1 coke = $1.50
So, the cost of 2 cokes = $(2*1.50)
The cost of 2 cokes = $3
The cost of a sandwich = $5.50
The cost of a bag of chips = $2.25
So, the total cost of all the materials = the cost of 2 cokes + the cost of a sandwich + the cost of a bag of chips
The total cost of all materials = $(3+5.50+2.25)
The total cost of all materials = $10.75
Now, the money Aryon has = Total money he has - the total cost of all materials
The money Aryon is left with = $(20-10.75)
The money Aryon is left with = $9.25
Hence, the money Aryon is left with is $9.25.
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solve for t
275,000 = 300 1-(1 + .038/12 ) ^(-12t)/(.038/12)
In linear equation , 2,932.25 * ( 1.0316)¹²t = (1)t is value of t .
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an uncertain variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.275000 = 3001 - ( 1 + 0.38/12)⁻¹²t/0.038/12
275000 = 3001 - ( 1 + 0.38/12)⁻¹²t/0.0025
275000 * 0.0025 = 3001 - ( 1 + 0.38/12)⁻¹²t
68.75 = 3001 - ( 1 + 0.38/12)⁻¹²t
3001 - 68.75 = ( 1 + 0.38/12)⁻¹²t
2,932.25 = ( 1 + 0.0316)⁻¹²t
2,932.25 = ( 1.0316)⁻¹²t
2,932.25 = 1/ ( 1.0316)¹²t
2,932.25 * ( 1.0316)¹²t = (1)t
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The sum of 2 and b is less than or equal to -16 translate the scentence into an inequaltiy
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{G\textsf{uide:}}[/tex]
[tex]\bullet\large\textsf{ Greater than or equal to}\rightarrow\mathsf{\geq}\\\bullet\large\textsf{ Greater than}\rightarrow\mathsf{ > }\\\bullet\large\textsf{ Less than or equal to}\rightarrow\mathsf{\leq}\\\bullet\large\textsf{ Less than}\rightarrow\mathsf{ < }[/tex]
[tex]\star\large\textsf{ The word \boxed{\rm{difference}} means subtract/subtraction}\\\star\large\textsf{The word \boxed{\rm{product}} means multiply/multiplication}\\\star\textsf{The word \boxed{\rm{quotient}} means divide/division}\\\star\large\textsf{The word \boxed{\rm{sum}} means add/addition}[/tex]
[tex]\large\text{Now, let us answer your given question}[/tex]
“[tex]\large\textsf{The \underline{SUM} of 2 and b is \underline{LESS THAN or EQUAL to} }\mathsf{-}\large\textsf{16}[/tex]”
[tex]\large\text{Your equal should possibly look like this:}\large\textsf{ 2 + b }\mathsf{\leq\ -}\large\textsf{16}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{2 + b \leq -16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Translate this sentence into an equation.
78 is the product of Helena's savings and 6.
Use the variable h to represent Helena's savings.
Answer:
786
Step-by-step explanation:
Answer:
Helena',s savings... h=78+6
jared bought a table and 12 chairs for $2,400. each chair cost $ 165. find the cost of the table?
Answer:
Answer down below!
Step-by-step explanation:
Since we do have the value of the chairs, we can do 12 * 165 to get a total of 1,980
Now, with this, to find the price of the table, you do 2,400 - 1,980
That will give you your answer of 420.
Convert to slope-intercept form to graph:
2x + 4y = 8
By converting to slope-intercept form to graph and solving this equation we are get -x/2 +2
What is slope intercept ?
The slope indicates the steepness of a line and the intercept indicates to the location where it intersects are in an axis. The slope and that the intercept define to the linear relationship between the two variables, and can be the used to the estimate an average rate of change.
The slope, m, represents the steepness of a line. The slope of the line is also the termed as gradient, sometimes .and the y-intercept, b, of a line, represents the y-coordinate of the point to where the graph of the line intersects the y-axis.
Sol-
Re write 2x+4y=8 in slope intercept form we are get-
y= -x/2+2
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The countdown before a rocket launch is described as –10, –9, –8, . . . After the countdown, the time is described as 1, 2, 3, . . . What is the meaning of zero in this situation?
Answer:dsa
Step-by-step explanation:
sadfdfsaf
Rafael is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 16 feet and its width is 13 feet. Suppose each bag of fertilizer covers 26 square feet. How many bags will he need to cover the garden?
Rafael is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 16 feet and its width is 13 feet. Suppose each bag of fertilizer covers 26 square feet. How many bags will he need to cover the garden?
step 1
Find the area of the garden
Remember that the area of a rectangle is equal to
A=L*W
we have
L=16 ft
W=13 ft
substitute
A=16*13
A=208 ft^2
step 2
we know that
each bag of fertilizer covers 26 square feet
so
Applying proportion
1/26=x/208
solve for x
x ----> number of bags
x=(1/26)*208
x=8 bags
therefore
the answer is 8 bagsI need help with this question.
Answer:the 2nd choice
Step-by-step explanation:
7th grade math please help a girl out
The tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h, where h represents the number of credit hours taken. The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h.
How many credit hours will a student have to take for the two tuition costs to be equal? Round the answer to the nearest tenth of an hour.
250 + 200h = 300 + 180h
250 + 200h = 300 + 180h
− 180h − 180h
250 + 20h = 300
The credit hours that a student has to take for the two tuition costs to be equal is A. 250 + 200h = 300 + 180h
How to illustrate the information?From the information, the tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h
h = the number of credit hours taken.
The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h.
Therefore, the credit hours that a student have to take for the two tuition costs to be equal will be:
250 + 200h = 300 + 180h
200h - 180h = 300 - 250
20h = 250
h = 250/20
h = 12.5 hours.
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Subject: geometry btopic: Chords and arcs a. 7.1 inb. 7.8 inc. 6.7 ind. 8.3 in
Chords and arcs
YM is the chord of the circle and it has a length of 12 in
The perpendicular VL bisects the chord in V.
To prove the above statement, please note that triangles VYL and VLM are similar because they have one side in common and the second side of the same length (the radius of the circle).
Let's work with any of those triangles, for example, VLY. It's a right triangle in V. The hypotenuse of the triangle is the radius, one leg is the given distance of 5 in and the other leg is half the length of the chord (6 in).
Thus, applying Pythagora's Theorem:
[tex]r^2=5^2+6^2=25+36=61[/tex]Thus, the radius is
[tex]r=\sqrt{61}[/tex]r=7.8 in
Option b.
Jessica wants to have a square garden plot in her backyard. She has enough compost to cover an area of 116 ft². Use the
formula s = A to find the length of each side of her garden. Round your answer to the nearest tenth of a foot.
The length of the each side of the square garden of Jessica is found as 10.77 ft.
What is termed as the square?A quadrilateral with 4 equal sides is known as a square. There are numerous objects in our environment that are square in shape. Each square shape is distinguished by it's own equal sides as well as interior angles of 90°.For the given question,
Jessica is making a square garden in her backyard.
The compost bought is to cover the area of the 116 ft².
The formula for the area is given as;
A = s² , where s is the length of the side of the square.
Put the values.
116 = s²
Taking square root both side.
s = √116
s = 10.77
Thus, the length of the each side of the square garden of Jessica is found as 10.77 ft.
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really need helppp plsssss asap
Answer:
Step-by-step explanation:
Please answer me this as soon as possible i need it urgently.
Note: This is grade 6 maths.
Answer:
1a. 4/6
1b. 6/9
1c. 8/12
2. [tex] \frac{6}{12} [/tex]
3. 8/16
Step-by-step explanation:
1a. Multiply top and bottom value by 2
1b.multiply top and bottom value by 3
1c. multiply top and bottom value by 4
2.To get your denominator to twelve you multiply it by 2. and if you multiply by two at the bottom you also multiply by two on top.
3.to get your denominator to 16 multiply the denominator by 8. If you multiply the bottom you should multiply the top with the same value as well.
12 > w + 3 solve the inequality for w and simplify your answer as much as possible
The solution to given inequality 12 > w + 3 is w < 9
In this question, we have been given an inequality 12 > w + 3
We need to solve the inequality for w.
Consider given inequality,
12 > w + 3 ............(Given)
12 - 3 > w + 3 - 3 ...........(Subtract 3 from each side)
9 > w
This means, w is less than 9.
Therefore, the solution to given inequality 12 > w + 3 is w < 9
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What other pair of angles or sides do you know are congruent?
1. QS = SQ
2. PS = RQ
3. angle QSP = angle SQR
4. angle P = angle R
(Look at attached files)
Based on the reflexive property of congruency, the other pair of sides that we know are congruent is: 1. QS = SQ.
What is the Reflexive Property of Congruency?The reflexive property of congruency states that a line will always be a congruent to itself. This means it will always be equal in measure to itself.
In the diagram given showing triangle QSP and triangle SQR, we are given that sides PQ and RS are congruent so also are angles PQS and RSQ.
However, we can also see that both triangles share a common side, side QS. Therefore, side QS is congruent to side SQ by the reflexive property of congruency.
This implies that another pair of sides would be: 1. QS = SQ.
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Kelyse's preschool tuition is $180 per week. She
receives a small discount for honor roll, $50 per
month. Her grandparents help out and pays
20% of her tuition. How much do her
grandparents pay?
$134 is the amount paid by grandparents every month.
What is the percentage?Percentage as the name suggests is a ratio of some particles to 100. In order to get the value of the required amount one has to divide the value by 100.
It is given that the tuition fee is $180 per week = $720 per month
It is also provided that she receives an honour rule of $50 per month.
So, her fees per month is $720- $50= $670.
It is given that 20% of the fees is paid by grandparents.
So, percentage share = 20% of $670 =20/100 x $ 670 = $134
So, $134 is paid by the grandparents every month.
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On a literature exam, there are 6 vocabulary questions for every 7 questions about
a book. If there are 12 vocabulary questions on the test, how many total questions
are on the test?
Answer:
26 total questions
Step-by-step explanation:
6 * 2 = 12
7 * 2 = 14
14 + 12 = 26
i need help with this problem i’m struggling with
4. tumbleweed, commonly found in the western united states, is the dried structure of certain plants that are blown by the wind. kochia, a type of plant that turns into tumbleweed at the end of the summer, is a problem for farmers because it takes nutrients away from soil that would otherwise go to more beneficial plants. scientists are concerned that kochia plants are becoming resistant to the most commonly used herbicide, glyphosate. the us department of the interior claims that 20 percent of kochia plants are resistant to glyphosate. in 2017 another study by researchers at university of new mexico, 38.5 percent of 52 randomly selected kochia plants were resistant to glyphosate.
Using the z-distribution, as we are working with a proportion, it is found that since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate.
What are the hypothesis tested?In null hypothesis, we test if there has been no increase, that is, the subtraction is of 0.
In this problem, we consider that:
p₁ is the proportion in 2014.
p₂ is the proportion is 2017.
H₀=p₂-p₁
By alternative hypothesis,
H₁=p₂-p₁≠0,
we test if there has been an increase
The proportions and standard errors are given by:
p₁=0.97, s₁=√0.97(0.803)/61=0.0509
p₂=0.385, s₁=√0.385(0.615)/52=0.0675
Hence, the distribution has mean and standard error given by:
p=p₂-p₁=0.0675-0.0509
s=√s₁²+s₂²=0.0845
Test static z=p bar-p/s
at p = 0 is the value tested at the null hypothesis,
z=0.0166/0.0845
z=0.2
By a right-tailed test, we are testing is the proportion is greater than a value, with a significance level of 0.05, the critical value is of
z=1.645
0.2<1.645 there is not enough evidence to conclude that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate.
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x^2-y=7 and y-5x=-11 The system of equations above has two solutions. The solution in Quadrant 1 is (A,B) and the solution in Quadrant 4 is (C,D) . Find the values of (A,B), (C,D)
By solving the system of equations, we can see that the solutions are:
(A, B) = (4, 9)
(C, D) = (1, -6).
How to solve the system of equations?Here we have the following system of equations:
x^2 - y = 7
y - 5x = -11
If we isolate the variable y in both equations, we get:
y = x^2 - 7
y = -11 + 5x
Now we can equate these two to get:
x^2 - 7 = -11 + 5x
now we have a quadratic equation, this can be rewritten as:
x^2 - 7 + 11 - 5x = 0
x^2 - 5x + 4 = 0
Using the quadratic formula, we will see that the solutions are:
[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*(4)} }{2*1}[/tex]
Solving that we get:
[tex]x = \frac{5 \pm \sqrt{(9} }{2} \\\\x = \frac{5 \pm 3}{2}[/tex]
So the two solutions for x are:
x = (5 + 3)/2 = 4
x = (5 - 3)/2 = 1
Evaluating the second equation in these x-values we get:
y = -11 + 5*4 = -11 + 20 = 9
y = -11 + 5*1 = -6
Then we have the coordinate pairs: (4, 9) (on the first quadrant) and (1, -6) on the fourth quadrant.
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The cost of 3 pounds of grapes is $6.57. What is the constant of proportionality that relates the cost in dollars, y, to the number of pounds of grapes, x?
PLEASE I NEED HELP ME PLEASE
I WILL GIVE 40 POINTS FOR THE NEXT QUESTION
The value of the Constant of Proportionality will be $2.19.
In the given question, it is stated that 3 pounds of grapes cost $6.57. We have to calculate and find out the Constant of Proportionality.
The constant of Proportionality is a constant term in the equation that does not vary and has a fixed value that represents a certain quantity in a given situation.
Here, we know that 3pounds cost $6.57. Taking:
y = Total Cost
x = Number of Pounds
c = Constant of Proportionality
We get the equation to represent the Total cost with respect to the number of pounds where c will be the proportionality constant which defines the unit price of a pound. The equation will be:
=> y = c*x
=> 6.57 = 3c
=> c = 2.19
Hence, we get the Constant of Proportionality $2.19
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A store has two types of animal feed available. Type A contains 3 pounds of oats and 2 pounds of corn per bag. Type B contains 1 poun
of corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least 16 pounds of oats and at least 52
only has 15 bags of type A feed and 13 bags of type B feed in stock. Type A costs $4 per bag, and type B costs $1 per bag. How many
the farmer buy to minimize his cost?
Note that the ALEKS graphing calculator can be used to make computations easier.
OO EXPLANATION
Answer : type A feed : 1 bag(s)
Type B feed : 13 bag(s)
(Worksheet typo.. Use this question) On the same map, the dining hall is located at (-12, 6) and the stables are located at (20, 6). How far apart is the dining hall from the stables? (Just type in the number)
If the dining hall is located at (-12,6) and the stables are located at (20,6), then the dining hall is 32 units apart from the stables
The location of the dining hall = (-12,6)
The location of the stables = (20,6)
The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Where d is the distance between the two points
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
d = [tex]\sqrt{20-(12))^2+(6-6)^2}[/tex]
= [tex]\sqrt{1024}[/tex]
= 32 units
Hence, if the dining hall is located at (-12,6) and the stables are located at (20,6), then the dining hall is 32 units apart from the stables
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