The value of the sum of the series is are 234 and 10200
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
For the first series, we have
In this series, a1=3 , an=36 , n=12
Plugging these values into the formula, we get:
Sn = 12/2 * (3 + 36)
Sn = 234
For the second series, we have
In this series, a1=3 , d = 2 , n=100
So, we have
an = a + (n - 1)d = 3 + 99 * 2 = 201
Plugging these values into the formula, we get:
Sn = 100/2 * (3 + 201)
Sn = 10200
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A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 6 in. and a base of 10 in. The area of the hexagonal base is 259.8 in².
What is the surface area of the pyramid?
Enter your answer in the box.
in²
The surface area of the pyramid, given the height and base of the triangles, and the area of the hexagonal base, is 439. 8 square inches
How to find the surface area ?Let's determine the area of the six isosceles triangles using the formula;
= 6 x 1 /2 x base x height
= 6 x 1 / 2 x 10 x 6
= 180 square inches
The surface area of the pyramid is therefore;
= Area of triangles + Area of hexagonal base
= 180square inches + 259.8 square inches.
Add the values, we get;
= 439. 8 square inches
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Answer: 439.8
Step-by-step explanation:
What is the Interquartile range of 41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75,97
Answer:
Step-by-step explanation
Sort the data: 41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75, 97
Find the median (Q2): 53
Split the data set into two parts: Q1 (25th percentile) and Q3 (75th percentile)
Q1: 41, 41, 43, 43, 45, 50, 52, 53
Q3: 54, 62, 63, 63, 67, 75, 97
Find the median (Q1) of Q1 and the median (Q3) of Q3:
Q1 = 45
Q3 = 63
Finally, calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 63 - 45 = 18
So, the interquartile range of the given data set is 18. This means that 50% of the data falls within a range of 45 + 18 = 63 and 45 - 18 = 27.
Can yall help me pls i really need it
Kevin's solution is incorrect. He found the area of the triangle as [tex]bh[/tex], not [tex]\frac{1}{2}bh[/tex].
The correct area of the triangle is [tex]\frac{1}{2}(8)(5)=20 \text{ in}^2[/tex].
i need help with this question
The exponential function from the table is f(x) = 2 [tex](0.5)^x[/tex].
The graph is given below.
Option D is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The exponential function is given as,
f(x) = m[tex]a^x[/tex]
Now,
From the table,
2 = m[tex]a^0[/tex]
m = 2
1 = m[tex]a^1[/tex]
m = 1/a ____(1)
0.5 = m[tex]a^2[/tex]
m = 0.5/[tex]a^2[/tex] _____(2)
Now,
From (1) and (2).
1/a = 0.5/[tex]a^2[/tex]
a = 0.5
Now,
f(x) = 2 [tex](0.5)^x[/tex]
Thus,
The exponential function is f(x) = 2 [tex](0.5)^x[/tex].
The graph is given below.
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Can somebody help me with this? I need it answered fast please Also, I need to show work
The length of CE in the triangle is 20.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
From the given triangle ABC
BC=CD which are congruent sides
x-5=14
x=19
AB=DE
2x+3=6
2x=3
x=3/2
Now DE 2x+3=2(3/2)+3=6
CE=CD+DE
=14+6
=20
Hence, the length of CE in the triangle is 20.
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Describe the error in finding the perimeter of the figure. And find the perimeter
Answer:
The length of 5 inches should be counted 1 time.
Step-by-step explanation:
The 5 inches between the triangle and rectangle is inside the shape. So, it doesn't count as perimeter.
please help me. {adding this so i am allowed to post this question.
Answer:
The base is 8 and the height is 3. Multiply.
8 * 3 = 24
You will then multiply your product by 1/2.
24 * 1/2 = 12
The area is 12 inches squared.
Step-by-step explanation:
Hope it helps! =D
Answer:
[tex] {12cm}^{2} [/tex]
Step-by-step explanation:
Given
[tex]a = \frac{1}{2} bh[/tex]
b= 8in
h= 3in
8x3 = 24
24 ÷ 2 (Same as multiplying by half)
Which graph shows a proportional relationship that passes through the point (2, 1)?
The required graph of the equation is given by y=x/2
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: A graph proportional to the line that passes through the point.
Now one of the graph has the equation y= x/2
we can treat this line as some proportional equation with 1/2 as the constant.
And it also passes through the point (2,1)
Hence, The required graph of the equation is given by y=x/2
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The options containing the graph are attached
Double question, double points!
The potential energy increases as the charges or the poles get further apart.
Static charges does not build up by polarization.
What is a field force?A field force is a force that acts on a particle without physical contact. It arises from the presence of a field, such as an electric field, magnetic field, or gravitational field.
The field exerts a force on a particle based on its charge, mass, or other property, and the strength of the force is determined by the field intensity and the properties of the particle. For example, an electric field exerts a force on a charged particle, while a gravitational field exerts a force on a mass.
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lydia has money in two savings accounts one rate is 8% and the other is 12% if she has $350 more in 12% account and the total interest is $336 how much is invested in each savings account
The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12% and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)
Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)
Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470
Now
y = 1470 + 350
y = $1820
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Which angle measures 40 i-Ready
Answer:
<YTZ
Step-by-step explanation:
Vertical angles are congruent.
<VTW measures 40°.
<YTZ is vertical to angle VTW.
m<YTZ = m<VTW
m<YTZ = 40°
Answer: <YTZ
This rectangle represents the base of a rectangular prism. The height of the rectangular prism is 56 m.
What is the volume of the rectangular prism?
Responses
A.212 m³
B.525 m³
C.5,600 m³
D.29,400 m³
Select the phrase from the drop-down menu that
best completes the sentence.
Several values of a quadratic function are given
in the table.
X -5
y
-7
-2 -1 2
8 9
6
8 9
0 -40 -72 -91
There is a maximum between the two input values
>
Finish
Answer:
"of -1 and 2."
Step-by-step explanation:
The quadratic function has a maximum value between the two input values of -1 and 2, with a maximum output of 9.
h(9)=2x-3 evaluate the solution
The solution of the expression is, 15.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ h (9) = 2x - 3
Now, Substitute x = 9, we get;
⇒ h (9) = 2 × 9 - 3
⇒ h (9) = 18 - 3
⇒ h (9) = 15
Thus, The solution of the expression is,
⇒ h (9) = 15
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Explain what AB means and what AB/ means. How are these two meanings related?''
AB vector is a vector whereas AB bar is a line segment.
What is a vector ?
The vectors are described as an object containing both significance and course. Vector describes the motion of an item from one point to any other. Vector math may be geometrically picturised via the directed line segment.
The duration of the phase of the directed line is known as the value of a vector and the angle at which the vector is inclined shows the path of the vector. The start line of a vector is referred to as “Tail” and the finishing factor (having an arrow) is referred to as “Head.”
The difference is in their names itself.
AB vector is a vector whereas AB bar is a line segment.
A vector has a direction and a magnitude while a line segment ( scalar ) has only magnitude.
Therefore, AB vector is a vector whereas AB bar is a line segment.
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factor completely 6ax-15x
Factorization of 6ax - 15x is 3x.(2a - 5)
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given expression,
6ax - 15x
It can be written as
3×2 . a . x - 3×5 . x
Factoring out common factor
3x.(2a - 5)
Hence, 3x.(2a - 5) is the factorization of 6ax - 15x.
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If the car climbs 60 m vertically how far must the car have travelled horizontally?
The the gradient of the slope is 2/15
The horizontal distance which the car must have travelled is equal to 450 meters.
How to calculate the horizontal distance?Mathematically, the gradient (slope) of a geometric figure or line can be calculated by using this formula:
Pitch (slope) = V/H
Where:
V represents the rising vertical distance of an object.H represents the horizontal distance an object runs through.Based on the given image, we have the following distances and gradient (slope):
Rising vertical distance = 60
Horizontal distance (Run) = x
Gradient (slope) = 2/15
Substituting the given parameters into the formula, we have;
2/15 = 60/x
2x = 900
x = 450
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AB formed by (-4, 7) and (-2, 6)
CD formed by (2, -2) and (-8, 3)
Is is parallel or perpendicular?
Line AB and CD are two parallel lines
What is the slope of a line:The slope of a line is defined as the change in y- the coordinate with respect to the x-coordinate and the formula is given by
Slope (m) = [ y₂ - y₁]/[x₂ - x₁]Note:
When two lines are parallel lines then the slope two line is equal When two lines are perpendicular lines then the product of the slope of two lines will be equal to '-1'
Here we have
AB formed by (-4, 7) and (-2, 6)
Slope of AB = (6 - 7)/(-2 + 4) = -1/2
CD formed by (2, -2) and (-8, 3)
Slope of CD = (3 + 2)/(-8 - 2) = 5/-10 = -1/2
Here Slope of AB = Slope of CD
As we know the slope of parallel lines is equal
Therefore,
Line AB and CD are two parallel lines
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Which of the following pairs of numbers results in a product that is irrational? Choose a, b, c or d.
The result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.
What are irrational numbers?A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.
1. The product of the numbers are:
a. √2 (√8) = √16 = 4
b. √49 (∛ 8) = 14
c. √3 (2/ √3) = 2
d. √2(4)
Option d is the correct answer.
Similarly, taking the product:
2. Option a is correct.
3. Option d is correct.
4. Option b is correct.
Hence, the result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.
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The distance between two villages is 30km. Kadi took 45 mins to cover the distance by motorcycle. What was his speed?
Answer:
50to70
Step-by-step explanation:
Answer:
Below
Step-by-step explanation:
You are given distance (30 km) and time ( 3/4 hr) and want km/hr
soooo 30 km / ( 3/4 hr) = 40 km/hr
The following equation has an error in one of the operations.
2(x−4y)+3y=2x+11y
Which answer would correct the error?
1. Change 2(x−4y)+3y to 2(x+4y)−3y.
2. Change (x−4y) to (x+4y).
3. Change 2x+11y to 2x−11y.
4. Change 2(x−4y)+3y to 2(x−4y)−3y.
answer is 2 because if we expand the bracket we get 2x–8y+3y which is 2x–5y but if it was 2(x+4y) it would be equal to 2x+8y+3y therefore being 2x+11y
PLEASE HURRY This figure consists of a rectangle and semicircle.
What is the area of this figure?
Use 3.14 for π.
Enter your answer as a decimal in the box.
(Image: A shape made up of a rectangle and a semicircle, with the semicircle on top of the rectangle. The rectangle has a width of 6 centimeters and a height of 4 centimeters.)
cm²
A shape made up of a rectangle and a semicircle, with the semicircle on top of the rectangle. The rectangle has a width of 6 centimeters and a height of 4 centimeters.
The area for this figure is given as follows:
38.13 cm².
How to obtain the area of the figure?The composite area of the figure is obtained by the sum of the areas of each component of the figure.
The figure is composed as follows:
Rectangle of width 6 centimeters and height of 4 centimeters.Semi-circle of diameter = 6 centimeters = radius of 3 centimers.The area of the rectangle is given by the multiplication of the dimensions, hence:
Ar = 6 x 4 = 24 cm².
The area of the semicircle is given by half the multiplication of π = 3.14 by the radius square, hence:
As = 0.5 x 3.14 x 3² = 14.13 cm².
Hence the total area is given as follows:
A = Ar + As
A = 24 + 14.13
A = 38.13 cm².
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It costs 9 dollars for 4 hot dogs.
What is the price of one hot dog?
The cost of 1 hot dog is $2.25
What is proportion?Proportion is a mathematical comparison between two numbers.
Given that, the cost of 4 hot dogs are $9, we need to find the cost of 1 hot dog,
Let the cost of 1 hot dog be x, therefore, setting the proportion,
4 / 9 = 1 / x
x = 9/4
x = 2.25
Hence, the cost of 1 hot dog is $2.25
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if f(x)= log(x^2 + 3x) 2^3x, find f'(2)=?
Answer:
f'(2)=64
Step-by-step explanation:
After plugging in 2 for x our equation would look like
log(2^2+(3×2))×2^(3x2)
Now just follow PEMDAS, starting with the left.
1: 2^2=4, 3×2=6, 4+6= 10
2: 3×2=6, 2^6=64
3: log(10)=1
4: 1×64=64
5: f'(2)=64
The graph shows the time it takes Jacey to print T-shirts for her school’s math club.
The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.
What is a Proportional Quantities?If two variables of two quantities, x and y, are represented on a graph to show their relationship, they are proportional quantities if for every ratio of y to x, the value we get is the same, which means they have a constant of proportionality, k.
Using the points on the graph in the image attached below, the table can be completed as follows:
Part A:
Number of T-shirts (x): 1 2 3 4
Time in minutes (y): 5 10 15 20
Part B: Find the ratio of y to x for each of the points on the graph.
5/1 = 5
10/2 = 5
15/3 = 5
20/4 = 5
The table derived from the graph is:
Number of T-shirts (x): 1 2 3 4
Time in minutes (y): 5 10 15 20
B. The quantities are proportional.
The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.
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"Your question is incomplete, probably the complete question/missing part is:"
The missing information are in the attachment below.
Find the equation of the line passing through the point (8,−2) that is perpendicular to the line y=4/5x+4.
Answer: pls braiinliest :D
To find the equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4, we can use the concept of the slope of a line. The slope of a line perpendicular to another line has a negative reciprocal slope.
The slope of the line y = 4/5x + 4 is 4/5. The negative reciprocal of 4/5 is -5/4.
So, the slope of the line passing through (8, -2) and perpendicular to y = 4/5x + 4 is -5/4.
Next, we can use the point-slope form of a line to find the equation of the line:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the values, we get:
y - (-2) = -5/4 (x - 8)
Expanding and solving for y, we get:
y = -5/4x + 26/2
y = -5/4x + 13
The equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4 is y = -5/4x + 13.
Step-by-step explanation:
Cincinnati’s budget is $1,130,000,000 and it’s population is 302,605. How many dollars per person are provided by the budget?
Answer:
3734.24100725
Step-by-step explanation:
This is related for all problems like this, not just this one:
When you see the key words below, this is what it means, and you can craft an equation from it:
Per = division
Of = multiplication
Using this above, we can replace the words with an equation:
The question is asking the amount of money per person.
Remember above, per means division:
Money/person
We know the amount of money and the number of people, so let's plug it in:
1,130,000,000/302,605
After division:
3734.24100725, final answer.
Hope this helps :D
5. Jill drew 4 rectangles 3
triangles, 2 pentagons, and
3 trapezoids. How many
angles are on the
quadrilaterals she drew?
The angles on the quadrilaterals she drew are 47 in number.
What is Quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles
As there are four rectangles, The total number of angles in a rectangle are 4 × 4 = 16 angles.
The number of triangles is 3, the total number of angles is 3 × 3 = 9 angles.
Number of pentagons are 2, the total number of angles is 2 × 5 = 10 angles.
The number of trapezoids are 3, the total number of angles is 3 × 4 = 12 angles.
Total number of angles on the quadrilaterals she drew is 16 + 9 + 10 + 12 = 47 angles.
Hence, the angles on the quadrilaterals she drew 47.
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PLEASE HELP ME I WILL GIVE YOU 5 STAR RATING A THANKS AND BRAINLIEST RATINGGGGG
The set of pairs for which x and y vary inversely is given as follows:
{(-1, -2/7), (4, 1/14), (6, 1/21)}.
(third set).
What is a proportional relationship?A direct proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
For an inverse relation, the relation is modeled as follows:
y = k/x.
Meaning that when x increases, y decreases at a constant rate.
The constant is then obtained as follows:
k = yx.
Hence the third relation is then the relation for which x and y vary inversely, as:
k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.
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Reflecting Graph Math Question
Answer:
Step-by-step explanation:
The reflection of point A will be at (3, -4) - that is 2 units directly below the red X.