Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 10+7+4+ . . . ; n=5
The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.
The given arithmetic series is 10+7+4+ . . .
The summation notion of given series is ∑10-3n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=5, [tex]a_{1}[/tex] = 10
To calculate sum of arithmetic series, we need to find [tex]a_{5}[/tex] .
[tex]a_{5} = a_{1} + (n-1)d[/tex]
d = -3 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{5}[/tex] = 10 + (5-1)(-3)
[tex]a_{5}[/tex] = 10-12 =-2
On substituting values in sum of arithmetic series formula, we get
[tex]S_{5}[/tex] = (5(10 + (-2)))/2 = 20
The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.
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1 orange tree grows 3 oranges. How many oranges trees will grow 15 oranges? (its for my cousin ;-;)
Answer:
Step-by-step explanation:
t = number of trees per 3 oranges
3t = 15
3t/3 = 15/3
t = 5 trees
Which angles are obtuse?
D
AB
C
Check all that apply.
A. ZMLK
B. ZGFE
C. ZDBC
D. ZOBA
K
G
24
H
PREVIOUS
M
SUBMIT
Answer:
dbc
Step-by-step explanation:
thats the only one that is obtuse
Round 1.602 to the nearest
whole number.
Answer:
2
Since the numbers after the decimal are above 500 , thereby rounding it to nearest whole number is 2.
A shipping box is in the shape of a cube. What is the volume of the shipping box if the length of one side of the box is 4m24n4
Answer:
A shipping box is in the shape of a cube. What is the volume of the shipping box if the length of one side of the box is 4m24n4
A seamstress is designing a triangular scarf so that the length of the base is 7 less than twice the height h, express the height of the scarf as a function of the height
Using algebraic expression, For the given expression, the height of the scarf will be 2h - 7
What is an Algebraic expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given the height = h
length of the base = 2h - 7
The area will be - 1/2 . B . H
= 1/2 . (2h - 7) . (h)
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The graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9). What is the value of y in the equation y= f(2)
The answer is 4. The generalized equation is y = f(x). So when the coordinate of x is 4, value of y is 2
Graph of the equation y= f(x) passes through the points (0,2), (2,4), (4,6), and (7,9).
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
The coordinate plane comprises a horizontal line (x-axis) and a vertical line (y-axis), and it is divided into four quadrants named using roman numbers (I, II, III and IV).
The different points in a graph have coordinates written as ordered pairs (pairs of numbers within parentheses separated by a comma). The first number in an ordered pair (x, y) represents the value of x, and the second one represents the value of y for a given point.
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Part A
BOOKLETS A digital media company is ordering booklets to promote their business. The manufacturer charges $0.50 for each booklet when 50
or fewer are ordered, $0.45 for each booklet when 51 to 100 booklets are ordered, $0.40 for each booklet when 101 to 250 booklets are ordered,
and $0.35 for each booklet when 251 or more booklets are ordered. Each order consists of a $10 shipping charge, no matter the size of the order.
Answer:
Step-by-step explanation:
Which of the following functions is graphed below?
Answer:
The answer is A because both equations are true
[tex] a) \: {x}^{3} - 2 = {1}^{3} - 2 \\ = 1 - 2 \\ = - 1 \\ \\ b) \: {x}^{2} + 4 = {1}^{2} + 4 \\ = 1 + 4 \\ = 5 \\ \\ [/tex]
Find the future value and interest earned if $8704.56 is invested for 9 years at 5% compounded (a) semiannually and (b) continuously.
The future value and interest earned when compounded semiannually are $13,576.14 and $4,871.58 respectively.
The future value and interest earned when compounded continuously are $13,651.47 and $4,946.91 respectively.
What is the future value and interest earned compounded semiannually and continuously?Compound interest is mathematically expressed as;
A = P(1 + r/n)^nt
Given the data in the question;
Principal P = $8704.56Annual rate r = 5% = 5/100 = 0.05Time t = 9 yearsCompounded n = (a) semiannually and (b) continuouslyAccrued amount and interest = ?a) Determine the accrued amount and interest when compounded semiannually ( n = 2 )
A = P(1 + r/n)^nt
A = 8704.56(1 + 0.05/2)^( 2× 9 )
A = 8704.56(1 + 0.025)¹⁸
A = 8704.56(1.025)¹⁸
A = 8704.56(1.025)¹⁸
A = $13,576.14
Note that; A = Principal + Interest.
Interest = $13,576.14 - $8704.56 = $4,871.58
b) Determine the accrued amount and interest when compounded continuously.
A = P × e^(r × t)
A = 8704.56 × e^(0.05 × 9)
A = 8704.56 × e^0.45
A = $13,651.47
Note that; A = Principal + Interest.
Interest = $13,651.47 - $8704.56 = $4,946.91
The future value and interest earned when compounded semiannually are $13,576.14 and $4,871.58 respectively.
The future value and interest earned when compounded continuously are $13,651.47 and $4,946.91 respectively.
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28-6x+4=30-3x what is the answer ?
Answer: x=2/3
Step-by-step explanation:
Determine whether the events are independent or dependent. Then find the probability. In a bag of 3 green and 4 blue marbles, a blue marble is drawn and not replaced. Then, a second blue marble is drawn.
The probability. In a bag of 3 green and 4 blue marbles, a blue marble is drawn and not replaced. Then, a second blue marble is drawn is 3/7.
What is probability?Total number of marbles is 7.
Number of blue marbles are 4.
the probability that a second blue marble is drawn is 3/7.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics.
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117 divided by 9 step by step
The quotient of 117 divided by 9 is 13.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
The answer thus got is called the quotient.
We have to divide 117 by 9.
Division algorithm states that,
Dividend = (Divisor × quotient) + Remainder
Remainder will be 0 if divisor is a factor of dividend.
Here dividend = 117 and divisor = 9
We know that 90 is a multiple of 9, where 90 = 9 × 10.
Remainder is 117 - 90 = 27
27 = 9 × 3
Hence 117 = 90 + 27 = (9 × 10 ) + (9 × 3) = 9 (10 + 3) = 9 × 13
So 117 / 9 = 13
Hence the quotient is 13.
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3b+2≤8
Help me please
Work Shown:
3b+2 ≤ 8
3b+2-2 ≤ 8-2
3b ≤ 6
3b/3 ≤ 6/3
b ≤ 2
Explanation: In the 2nd step, I subtracted 2 from both sides. In step 4, I divided both sides by 3. The inequality sign stays the same. It would flip if we multiplied or divided both sides by a negative number.
If you want to graph this on a number line, then plot a closed filled in circle at 2. Then shade to the left. This visually represents numbers that are 2 or smaller.
The depth and the corresponding pressure form an arithmetic sequence, where the depth
represents the number of the term and the corresponding distance represents the value of
the term. What is the pressure, in pounds per square inch, that a scuba diver will
experience when they are 130 feet underwater?
Answer:
40 psi
Step-by-step explanation:
We can see that the relationship is linear with pressure increasing by 5 psi for every extra 15 feet depth
The data is given from depth of 40 feet
At 40 feet, pressure = 10 psi
At 55 feet, pressure = 15 psi
At 70 feet pressure = 20 psi
We have to use 40 as the base depth since there are no measurements less than that value. So relative depth is d - 40 and since for every 15', there is an increase of 5psi, the relative increase in pressure per 15' is [tex]= \dfrac{d-40}{15}\cdot 5[/tex]
But the base pressure is 10psi not 0 so we have to add 10 to this equation to get the absolute psi
So the equation that connects depth (d) and pressure (p) is:
[tex]p = \dfrac{d - 40}{15}\cdot 5 + 10\\\\\textrm{At 130' depth},\\p = \dfrac{130-40}{15}\cdot 5 + 10\\= \dfrac{90}{15}\cdot 5 + 10\\\\= 30 + 10 = 40 psi\\[/tex]
If we plot these values, we can see they fit a straight line with slope = 1/3 and y-intercept = -10/3
Hope that helps
⠀I
R={(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
-3
-2
-1
0
1
2
Answer:
-3, -1, 1
Step-by-step explanation:
Answer: -3,-1, and 1.
Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.
Kelly is designing a new quilt. It will be made of squares that are sewn together at the sides with a circle sewn on top of each square. a. Kelly decides that the quilt will be a rectangle 7ft 4in by 6ft 5in. How many squares will she need to make for the quilt? Round the answer to the nearest tenth, if necessary.
Answer:
14ft 8in by 12ft 10in
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
The given statement is False. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
Euclidean geometry a mathematical system in which we study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid.
Parallel Postulate is one of the five postulates of Euclidean geometry. It is Euclid's fifth postulate which states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. Non-Euclidean geometry refers to geometrical systems that are not in accordance with the Parallel Postulate.
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Cameron works at an electronics store as a salesperson. Cameron earns a 4% commission on the total dollar amount of all phone sales he makes, and earns a 6% commission on all computer sales. Cameron made a total of $3600 in sales and earned $178 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Cameron made and the dollar amount of computer sales he made. Define the variables that you use to write the system.
Step-by-step explanation:(4/100x)+(6/100y)=178---------(i)
2х+3y=8900-----------(i)
x+y=3600---------(ii)
where x is phone
y is pen
The system of equations that describes the situation are 4x + 6y = 17800 and x + y = 3600.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Let the cost of 1 phone is x dollars and cost of 1 computer is y dollars.
Cameron earns a 4% commission on the total dollar amount of all phone sales he makes and earns a 6% commission on all computer sales.
∴ (4/100)x + (6/100)y = 178
4x + 6y = 17800...(i)
Cameron made a total of $3600 in sales.
∴ x + y = 3600...(ii)
Now to solve the equations we'll multiply eqn(ii) by 4 or 6 to cancel out x or y, and then we'll substitute the numerical value of x or y in any of these equations.
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Find the sum: 435,098 + 37,987
Answer:
473085 is the answer
Step-by-step explanation:
Hope it helps you
Paisley took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.70 plus $1.75 per mile. The total fare was $17.45, not including the tip. Which equation or tape diagram could be used to represent the context if a represents the number of miles in the taxi ride?
An equation that could be used to represent the context if a represents the number of miles in the taxi ride is 1.70 + 1.75a = 17.45
How to solve equation word problems?
We are given;
Base pick up fee = $1.70
Additional taxi fee per mile covered = $1.75
Total taxi fare = $17.45
Now, if we assume that a represents the number of miles in the taxi ride, then we can form the equation to represent the given scenario above as;
1.70 + 1.75a = 17.45
We conclude that an equation that could be used to represent the context if a represents the number of miles in the taxi ride is 1.70 + 1.75a = 17.45
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Please help!! ;-; I cannot figure this out
to get the equation of any straight line, we simply need two points off of it, let's use the points from the table in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 3 }\implies -1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-4=-x+2\implies {\LARGE \begin{array}{llll} y=-x+6 \end{array}}[/tex]
Simplify each rational expression. State any restrictions on the variable. x²+4 x+3 / x²-3 x-4
Just like polynomials and other expressions, you can perform basic arithmetic operations on rational expressions: addition, subtraction, multiplication, and division. A rational expression is a fraction whose numerator and the denominator is a polynomial. If f is a logical expression, then we can write f in the form of p/q, where p and q are polynomials.
Solution:
To find the restriction on a variable in the denominator, we Set the denominator equal to zero. Then we solve for X
So,
X+1 = 0
X = -1
X-4 = 0
X = 4
When we put the X= -1 or X= 4, we get 0 in the denominator, so these are restrictions variables
= (x2+4x+3)/(x2-3x-4)
= (x+1) (x+3)/(x+1) (x-4)
Now cancel the common factor (x+1)
= x+3x-4
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Square each of the binomials and place them into perfect square trinomial form, then subtract the trinomial‘s
Answer: #11? y^2-14 #12 m^2-64
Step-by-step explanation:
Factor each of the binomials: (2y-5)^2 -> 2 (y-5) (y+5) and (y+6)^2 -> (y+6) (y-6) Multiply the each factored binomial into perfect squares: (since the second numbers are opposites it will be binomials since they cancel out) 2 (y-5) (y+5) would be 2y^2-10y+10y-50 or 2y^2-50 and (y+6) (y-6) will become y^2-6y+6y-36 or y^2-36 Subtract the binomials: Remember when you are subtracting polynomials you are changed the sign to addition and invert the operations of the second polynomial (so if the term was positive it would be negative and vice versa) so it would be 2y^2-50 + ‐y^2+36 and that would equal y^2-14- For the second question you apply the same steps to #12 to get m^2-64
Type in one, none or infinite
What is 4x -2 = -12
[tex]4x-2=-12\\\\4x=-10\\\\\frac{4x}{4} =\frac{-10}{4} \\\\x=\boxed{-\frac{5}{2} }[/tex]
An angle is a figure formed by two rays with a common initial point called a
of the angle.
An angle is a figure formed by two rays with a common initial point called a of the angle.
What does a math angle mean?
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.What is type of angle ?
There are three different types of angles in geometry: acute angles, which range from 0 to 90 degrees. Right angle, or a 90° angle. A 90–180 degree angle is referred to as an obtuse angle. a 180 degree angle, or a straight angle.What is acute angle?
Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.Learn more about acute angle
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Determine the smallest integer value of x in the solution of the
Following inequality.
2x - 82 -11
The smallest integer is 1 and solution is (₋1)
Given, the inequality is 2x ₋ 8 ≥ ₋11
The mathematical expressions with inequalities are those with unequal sides on both sides. Unlike equations, we compare two values when we work with inequality. A statement that two things are not equal is what is meant by the word "inequality." It's possible for one of the items to be more than, smaller than, equal to, or equal to the other things.
now add 8 on both sides.
2x ₋ 8 ₊ 8 ≥ ₋11 ₊ 8
2x ≥ ₋3
dividing both sides by 2.
2x/2 ≥ ₋3/2
⇒ x ≥ ₋3/2
₋3/2 is not an integer.
hence the smallest integer value of x is 1, and solution is (₋1)
Hence we get the integer value as 1.
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A triangle has vertex coordinates (0,0) and (a, 0) . If the coordinates of the third vertex are in terms of at, and the triangle is isosceles, identify the coordinates and position the triangle on the coordinate plane.
The coordinate of another point will be (a/2,y) where y can be any value.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
An isosceles triangle is a triangle whose two sides are equal.
Let's say AB = AC
So,
Distance associate to AB = Distance associate to AC
(x- 0)² + (y - 0)² = (x - a)² + (y - 0)²
x² + y² = (x - a)² + y²
x = a/2
So the coordinate of the third vertex is (a/2,y)
Hence "The coordinate of another point will be (a/2,y) where y can be any value".
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question in the picture
Answers:
14 rides: 52
and
r rides: 3r + 10
Step-by-step explanation:
3(14) + 10
52
HELP ME WITH THIS QUESTION PLS
Answer:
49π in²
Step-by-step explanation:
Formula for Area of a Circle: A = πr²
The image shows the radius (r) = 7in
A = πr² → A = π(7)²→ A = π(49)
A = 153.94 in²
Step-by-step explanation:
Area of circle with radius of r is given by:
[tex] a = \pi {r}^{2} \\ a = 49\pi {(in)}^{2} \\ or \: \: a = 153.9 \: {(in)}^{2} [/tex]
