The algebraic expression or sigma (summation) notation is given by:
∑ = 10(-3 - 30)/2
And its value is ∑ = -165
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
(-3)+(-6)+(-9)+. . . . . . +(-30)
a1 =-3an = -30n = 10∑ = 10(-3 - 30)/2
∑ = 10(-33)/2 = 5(-33)
∑ = -165
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Write the correct messurement indicated by the arrows on the lines to the left
Answer:
Step-by-step explanation:
It is given that we need to find the correct measurement indicated by the arrows on the lines to the left.
Now, let us have a look at the figure;
6 inches5.2 inches4.6 inches4.3 inches4 inches3.6 inches3.1 inches2.6 inches2.3 inches1.7 inches1.4 inches1.2 inches1.1 inches0.5 inches0.3 inches0.2 inches0.1 cm0.7 cm1.7 cm2.3 cm3.1 cm3.4 cm4.2 cm4.7 cm5.5 cm6.4 cm7.2 cm8.2 cm8.5 cm9.1 cm9.6 cmTo know more about this topic, click here:
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It takes Amelia 45 minutes to rake her yard every Saturday during the fall. It takes Andy 1 hour to rake the same yard. If Amelia and Andy work together, how long will it take them to rake the yard? Round your answer to the nearest minute.
Determine the probability of following event, flipping a coin and not landing on heads
According to the question, to calculate the probability of an event which states that flip a coin and not landing on head. That means P = {H,T}
Therefore, the probability can be written as:
Probability of getting tail = [tex]\frac{no of favorable events}{total number of outcomes} = \frac{1}{2}[/tex]
Therefore, the probability of a coin in which head is not landing is [tex]\frac{1}{2}[/tex].
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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need help solving please
Answer: a=√3 b=√6
Step-by-step explanation:
We have a right-angled isosceles triangle
Hence, a=√3
According to the sine theorem :
[tex]\displaystyle\\\frac{b}{sin90^0} =\frac{a}{sin45^0} \\\\\frac{b}{1} =\frac{\sqrt{3} }{\frac{\sqrt{2} }{2} } \\\\b=\frac{2\sqrt{3} }{\sqrt{2} } \\\\b=\frac{2\sqrt{3}(\sqrt{2)} }{\sqrt{2} (\sqrt{2}) } \\\\b=\frac{2\sqrt{6} }{2} \\\\b=\sqrt{6}[/tex]
Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer
she would pay $2,500 down and $150 each month. At another dealer, she would pay $3,000 down and $125
each month. After how many months would the total amount paid be the same for both dealers? What
would that amount be?
Answer:
Step-by-step explanation:
2500+150x=3000+125x
150x-125x=3000-2500
25x=500
x=500/25
x=20 mo
----------------
2500+150*20=3000+125*20
5500=5500 total paid after twenty months
Hope this helps! ;0
does someone mind helping me with this? Thank you!
=======================================================
Work Shown:
A = area of the triangle on top, aka ceiling
A = 0.5*base*height = 0.5*6*8 = 24
B = area of the triangle on the bottom, aka floor
B = A = 24
C = area of the front rectangular face
C = length*width = 10*7 = 70
D = area of the face in back on the left
D = length*width = 6*7 = 42
E = area of the face in back on the right
E = length*width = 8*7 = 56
Total surface area = A+B+C+D+E = 24+24+70+42+56 = 216 square meters
------------------------
Alternative Method:
A = area of the triangle on top, aka ceiling
A = 0.5*base*height = 0.5*6*8 = 24
B = area of the triangle on the bottom, aka floor
B = A = 24
LA = lateral area = wall area
LA = (perimeter of the base)*(height)
LA = (6+8+10)*(7)
LA = 24*7
LA = 168
Total surface area = A+B+LA = 24+24+168 = 216 square meters
How many solutions does each of the following equations have?
6(x-3)+12=6x-6
Answer:
All real numbers are solutionsStep-by-step explanation:
How many solutions does each of the following equations have?
6(x-3)+12=6x-6
6x - 18 + 12 = 6x - 6
-18 + 12 = -6
-6 = -6
0 = 0
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book. With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book. For how many books produced will the costs from the two methods be the same?
The number of books published by a small publishing company is 3240.
Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of books be x.
With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.
That is, 44,714+11.50x
With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.
That is, 17,174+20x
Now, the number of books produced will the costs from the two methods be the same.
So, 44,714+11.50x=17,174+20x
⇒ 44,714-17,174=20x-11.50x
⇒ 8.5x = 27540
⇒ x=3,240
Therefore, the number of books published by a small publishing company is 3240.
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C. what does it mean when an element is written inside a circle? at the intersection of two circles? outside the circles
D. do the elements written at the intersection of both circles from a subset of the two sets? Why?
Answer:
c ) it either shows diameter or radius
d) I am not sure
C. When elements are represented in a Venn diagram (using circles), the placement of elements inside or outside the circles indicates their relationship to the sets being represented.
D. Yes, the elements written at the intersection of both circles form a subset of the two sets.
C. Place an element inside a circle to indicate that it is a member of the set indicated by the circle.
An element that is positioned at the intersection of two circles denotes an element that is a part of both sets that are symbolized by those circles.
Outside the circles: In a Venn diagram, an element that is positioned outside every circle does not belong to any of the sets being represented.
D. This is so because these components are a part of the intersection of the two sets and as such, they are a part of both sets. In set theory, all of the components that are shared by two sets are contained in their intersection. Due to their simultaneous membership in both sets, the elements at the intersection are a subset of both sets.
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I'll give brainliest
What values of x and y satisfy the system of equations {x=−2y+13x+8y=11?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution of the simultaneous equation is given by (-7 , 4) .
A pair of simultaneous equations is the most common representation of a pair of straight lines in the cartesian plane.
For solving a pair of simultaneous equation we can use various procedures such as the matrix method, substitution or the method of elimination.
The given pair of simultaneous equation is given as:
x=−2y+1
3x+8y=11
Let us solve the equations by the method of substitution:
From the first equation we take the value of x and put it in the second equation:
3x + 8y = 11
or, 3 ( -2y + 1 ) + 8y = 11
or, -6y +3 +8y = 11
or, 2y + 3 = 11
or, 2y = 8
or, y = 4
Substituting the value of y as 4 in the first equation we get:
x = − 2y + 1
or, x = - 2 × 4 +1
or, x = -8 +1
or, x = -7
Therefore the solution set of the pair of equations is given by (-7 , 4) .
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25446 to 1 significant figure
Answer: 30,000 rounded to 1 significant figure
I hope this helped!
Does the infinite series converge or diverge? If it converges, what is the sum?
a. 1/2 + 3/4 + 9/8 + . . . . .
Does the infinite series converge or diverge? The series converges.
If it converges, what is the sum?
a. 1/2 + 3/4 + 9/8 + . . . . .
The sum of the infinite series is -1
What is the sum of the infinite series?
Given:
[tex]a(\text{ the first term})=\frac{1}{2} \\\\r(\text{ thecommon ratio})=\frac{a_2}{a_1} =\frac{3}{2}[/tex]
Since ,[tex]\vert r\vert < 1[/tex], the infinite series converges.
The sum of infinite geometric series is:
[tex]S_\infty=\frac{a }{1-r} ; -1 < r < 1\\\\S_\infty=\frac{\frac{1}{2}}{1-\frac{3}{2}}=-1[/tex]
The sum of the infinite series is -1
What is an infinite geometric series?
The result of an endless geometric sequence is an infinite geometric series.There would be no conclusion to this series.The total of all finite geometric series can be determined.However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.To learn more about infinite geometric series, refer:
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A meeting room is set up with 16 rows of seats. The number of seats in a row increases by two with each successive row. The first row has 12 seats. What is the total number of seats?
a. How can you find the number of seats in each row using an explicit formula?
The most commonly used explicit of an arithmetic sequence is given as,
an = a + (n - 1) d
Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,
2nd row seat = 12+ 1x2
3rd row seat = 12 + 2 x2
nth seat = 12 + (n-1) x 2
16th row seat = 12 + (16–1) x2 = 42
Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows
Average number of seats per row = (12 +42)/2= 27
So total seats = average per row x number of rows
= 27 x 16 = 432.
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Please help!!!
For questions 10-13 use f(x)=4(1/2)^x
Identify the appropriate mixed number for the picture shown.
A. 54
B. 14
C. 114
D.45
Answer:
c
Step-by-step explanation:
its one full square and 1/4
A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate advertised as 5 cm by 3 cm must have a length within 0.25 cm of 5 cm. Use the solution to the equation |x − 5| − 0.25 = 0 to find the minimum and maximum area, in sq. cm, of the plates.
The minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2
What is area of rectangle?In mathematics, area of rectangle refers to the product of length of the rectangle and width of the rectangle. The unit is in square units. Area shows the extent a surface or a plane covers
Given data
size of rectangular plate = 5 cm by 3cm.
the length should be within = 0.25 of 5 cm
How to solve for the minimum and maximum areaThis means the length, L of the rectangular plate can be mathematically represented as
5 - 0.25 ≤ L ≤ 5 + 0.25
4.75 ≤ L ≤ 5.25
Area of rectangle = Length × Width.
Width = 3
minimum length = 4.75
maximum length = 5.25
minimum length
= 4.75 * 3
= 14.25 cm^2
maximum length
= 5.25 * 3
= 15.75 cm^2
Therefore, the minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2
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A stop sign in the shape of a regular octagon is inscribed in a circle. Find following measure.
m < LRQ
The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.
The measure of < LRQ is 112.5.
What is an Intercepted Arc?
The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.
An arc is a segment of a circle's circumference. An intercepted arc is thus one formed when one or two different chords or line segments cut across a circle and meet at a common point known as a vertex.
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
So, [tex]$m \angle L R Q=\frac{1}{2}(m \overparen{L N Q})$[/tex]
The sum of the measures of the central angles of a circle with no interior points in common is 360 .
Here, 360 is divided into 8 equal arcs and each arc measures
360/ 8 = 45.
Then, m LNQ = m LM + m MN + m NO + m OP + m PQ = 5(45) = 225.
[tex]$m \angle L R Q=\frac{1}{2}(225)=112.5$[/tex].
Therefore, the measure of < LRQ is 112.5.
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Kendra buys 5 yards of yellow fabric and 8yards of purple fabric The yellow
costs $2 more per yard than the purple fabric,
She pays a total of 62.80 what
would be the combined cost of 2 yards of yellow and yards of purple
fabric?
The combined cost of 2 yards of yellow and 1 yard of purple fabric is $17.69.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Length of yellow fabric = 5 yards
Length of purple fabric = 8 yards
Let x be the cost of per yard purple fabric.
Then, cost of per yard yellow fabric = 2 + x
Now since, Total amount paid is $62.80
Therefore,
5(2 + x) + 8x = 62.8
expanding the brackets we get,
10 + 5x + 8x = 62.8
Solving we get,
10 + 12x = 62.8
or, 12x = 52.8
⇒ x = 62.8/12
⇒ x = $5.23
Thus the cost of per yard purple fabric = $5.23
Similarly, cost of per yard yellow fabric = 2 + 5.23 = $7.23
Thus, combined cost of 2 yards of yellow and 1 yard of purple
fabric = 2*$5.23 + $7.23
= $10.46 + $7.23
= $17.69
Thus, the combined cost of 2 yards of yellow and 1 yard of purple fabric is $17.69
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A store is having a sale on jelly beans and almonds today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.
The system of equations that can be used to determine the cost for each pound of jellybeans and almonds is
5x + 3y = 16
2x + 6y = 22
The cost of one pound of jellybeans is $1.25.
The cost of one pound of almonds is $3.25.
What is the cost of one pound of jellybeans and almonds?Given this two equations:
5x + 3y = 16 equation 1
2x + 6y = 22 equation 2
Take the following steps to determine the required values:
Multiply equation 1 by 2
10x + 6y = 32 equation 3
Subtract equation 2 from equation 3
8x = 10
Divide both sides of the equation by 8: x = 10 / 8
x = 1.25
Substitute for x in equation 1:
5(1.25) + 3y = 16
6.25 + 3y = 16
3y = 16 - 6.25
3y = 9.75
y = 9.75 / 3
y = 3.25
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I will Mark BRAINLIST!!! Please Help its A Math Question!!!! Determine the approximate value of x using basic trigonometry.
hope it will help you...good luck
Find x. 24² + x² = 26²
The unknown variable's result of the equation 24² + x² = 26² is 10
To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:
What is adding goes to the other side of the equality by subtracting.What is multiplying goes to the other side of the equality by dividing.24² + x² = 26²
576 + x² = 676
x² = 676 - 576
x² = 100
x = [tex]\sqrt{}[/tex]100
x = 10
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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Find the other endpoint of the line segment with the given endpoint and midpoint.
Endpoint: (7,9), midpoint: (-4,-3)
Answer:
(-15, -15)
Hope this helps!
Simplify by combining like terms. -(3 z-5)+z
The simplification by combining like terms of -(3z -5) + z is -2z + 5.
According to the given question.
We have an expression -(3z -5) + z.
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression -(3z - 5) +z.
Here -3z and z both are the like terms.
So, we subtract coeffcients of z to simplify the given expression.
Therefore, the simplification of the expression -(3z - 5) +z is given by
-(3z - 5) + z
= -3z + 5 + z
= -3z + z + 5
= -2z + 5
Hence, the simplification by combining like terms of -(3z - 5) + z is -2z + 5.
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WHAT DOES C=???
QUESTION BELOW
================================================
Work Shown:
M = number of miles
L = cost to rent a luxury car = 1.15M + 16.40
E = cost to rent an economy car = 0.80M+10.95
C = difference in price
C = L - E
C = (1.15M + 16.40) - (0.80M+10.95)
C = 1.15M + 16.40 - 0.80M-10.95
C = 0.35M + 5.45
Don't forget to distribute the negative to each term in the second parenthesis.
-------------------
Optional Section:
Let's say you drove M = 100 miles as an example.
The luxury car would cost L = 1.15M+16.40 = 1.15*100+16.40 = 131.40 dollars to rent.
The economy car would cost E = 0.80M+10.95 = 0.80*100+10.95 = 90.95 dollars to rent.
The difference in rental costs is L-E = 131.40-90.95 = 40.45 dollars.
Or you could say C = 0.35M+5.45 = 0.35*100+5.45 = 40.45
This means you pay $40.45 more if you go for a luxury car instead of an economy car.
Which step in the construction of copying a line segment ensures that the new line segment has
the same length as the original line segment?
The steps 5 and 6 in the construction of a new line segment ensures the lengths are equal.
A line segment in geometry has two different points on it that define its boundaries. Alternatively, we may define a line segment as a section of a line that joins two points.
Below are the steps for copying a line segment:
1. Let's begin with a line segment we need to copy, AB.2. we take a point C at this stage. That will be one endpoint of the new line section, either below or above AB.3. Now we place the the compass pointer on the point A of line segment AB.4. We spread the compass out until point B, making sure that its breadth corresponds to the length of AB.5. We place the compass tip on the point C created in step 2 without adjusting the compass's width.6. We now draw a rough arc without adjusting the compass's settings. we add a point D oh the arc . The new line segment will be formed by this.7. From C, draw a line to D;CD thus formed is equal to AB.Hence steps 5 and 6 are the steps in the construction of a new line segment which ensures the lengths are equal.
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Draw a line representing the rise and representing the run of the line. State the slope of the line in simplest form.
Homework Yelp please
Answer:
I might be able to help. :))
Fill in the blank: The opposite of __________________ a number is finding the square root. Squared means to raise to the power of ___.
squaring, 4
squaring, 2
cubing, 3
doubling, 2
Answer:
B. Squaring, 2
Step-by-step explanation:
When you Square a number, doing the opposite is finding the square root. When squaring a number, you multiply the number by itself, the number it raises the the power of 2.
Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane to obtain line segment A′B′. What is the length of A′B′? (1 point) a 2 units b 4 units c 6 units d 8 units
Hep please T^T
The length of A'B' is 2 unit when Line segment AB has a length of 2 units. It is translated 6 units to the right on a coordinate plane.
What is Translation ?
Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size.
That is, if the measurement of segment AB is 2 unit then after translation by any factor its measurement will not change,
So, the measurement of segment A'B' would be 2 unit.
Verification :
Let the coordinates of A and B are (x₁, y₁) and (x₂, y₂) respectively,
Also, the rule of translation 6 unit right is,
(x,y) → (x + 6, y)
By the distance formula,
The measure of segment AB = √(x₂- x₁)² + (y₂ - y₁)²
Thus, if A'B' is the transformed segment of segment AB,
Then, coordinates of A' and B' are (x₁ + 6, y₁) and (x₂ + 6, y₂)
So, the measure of segment A'B' =
√(x₂ + 6 - x₁ - 6)² + (y₂ - y₁)² = √(x₂- x₁)² + (y₂ - y₁)²
Hence, the measure of AB = measure of A'B'.
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Put the following numbers in order from least to greatest
1/2, -2, √5, -7/4, -24
Answer:
-24 < -2 < -7/4 < 1/2 < √5
Step-by-step explanation:
Negative integers are always less than 0 and positive integers. More the magnitude (numerical value) of a negative integer, lesser is that number.Hence the order of negativeintegers will be -24 < -2 < -7/4. 1/2 is 0.5 and root 5 is around 2.236. Hence, 1/2 < √5. The final order is -24 < -2 < -7/4 < 1/2 < √5