Answer: 52.5
Step-by-step explanation: We can divide 50 by 20 to find what the number is. In this problem, the number is 2.5. Since we know this, we can multiply 2.5 and 21 to get 52.5.
hope this helps!
please give brainliest!
Answer:
21st term = 52.5
Step-by-step explanation:
Given that,
→ 20th term of a sequence is 50.
The common difference is,
→ 50 ÷ 20
→ 50/20
→ 2.5
Now the 21st term will be,
→ n × 2.5
→ 21 × 2.5
→ 52.5
Hence, the answer is 52.5.
33575 rounded to the nearest 1000
Answer:
just count 3 digit and round it off then the answer would be 34000
A spherical balloon is being inflated. Find the rate of increase of the surface area
(S = 4?r2)
with respect to the radius r when r is each of the following.
(a) 1 ft
ft2/ft
(b) 8 ft
ft2/ft
(c) 9 ft
ft2/ft
The rate of increase of the surface area of a spherical balloon is 8π square feet when r is 1 ft, 64π square feet when r is 8 ft, 72π square feet when r is 9ft and 16π square feet when r is 2 ft.
According to the question,
We have the following information:
A spherical balloon is being inflated. We need to find the rate of increase of the surface area of a spherical balloon with respect to r.
Surface area = [tex]4\pi r^{2}[/tex]
Differentiating with respect to r:
ds/dr = 8πr
Now, we will put all the values of r in this formula.
(a) r = 1 ft
Rate of increase = 8π*1
Rate of increase = 8π square feet
(b) Radius = 8 ft
Rate of increase = 8π*8
Rate of increase of area = 64π square feet
(c) Radius = 9 ft
Rate of increase of area = 8π*9
Rate of increase of area = 72π square feet
(d) Radius = 2 ft
Rate of increase of surface area = 8π*2
Rate of increase = 16π square feet
Hence, the rate of increase of the surface area of a spherical balloon is 8π square feet when r is 1 ft, 64π square feet when r is 8 ft, 72π square feet when r is 9ft and 16π square feet when r is 2 ft.
To know more about rate of increase here
https://brainly.com/question/15400336
#SPJ4
A cone with a radius of 3 feet and a height of 5 feet is placed on top of a cylinder as shown. Find the volume of the total figure in terms of
A) 69pi ft^3
B) 76pi ft^3
C) 96pi ft^3
D) 106pi ft^3
The volume of the composite figure is A) 69[tex]\pi ft^3[/tex].
What is volume?
The area occupied within an object's three-dimensional bounds is referred to as its volume. Another name for it is an object's capacity. The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Volumes vary depending on the shape.
Here the given figure contains cone and cylinder.
In cone height = 5f , radius r = 3 ft.
Then Volume of the cone is ,
=> V = 1/3 ([tex]\pi r^2[/tex]h) cubic unit
=> V = 1/3 (3.14*9*5)
=> V = 15[tex]\pi ft^3[/tex]
Now In cylinder Height = 6ft and radius = 3ft.
Then Volume of cylinder is ,
=> V=[tex]\pi r^2h[/tex] cubic unit.
=> V= [tex]\pi[/tex]*9*6
=> V=54 [tex]\pi[/tex][tex]ft^3[/tex]
Then Total volume of the figure is ,
=> Volume of cone+ volume of cylinder
=> 15[tex]\pi[/tex]+54[tex]\pi[/tex]
=> 69[tex]\pi ft^3[/tex].
Therefore the volume of the composite figure is 69[tex]\pi ft^3[/tex].
To learn more about volume refer the below link
https://brainly.com/question/463363
#SPJ1
4(x - 7)= 0.3(x + 2) + 2.11, the solution to the equation is: a)8.7 b)8.3 c)3 d)-3
The solution to the given linear equation, 4(x - 7)= 0.3(x + 2) + 2.11, is x = 8.3. The correct option is b) 8.3
Solving linear equationsFrom the questions, we are to determine the solution to the given linear equation.
The given linear equation is
4(x - 7)= 0.3(x + 2) + 2.11
To solve the equation, we will determine the value of x
Solving the equation
4(x - 7)= 0.3(x + 2) + 2.11
Clear the parentheses by applying the distributive property
4x - 28 = 0.3x + 0.6 + 2.11
Add 28 to both sides of the equation
4x - 28 + 28 = 0.3x + 0.6 + 2.11 + 28
4x = 0.3x + 30.71
Subtract 0.3x from both sides of the equation
4x - 0.3x = 0.3x - 0.3x + 30.71
3.7x = 30.71
Divide both sides by 3.7
3.7x/3.7 = 30.71/3.7
x = 8.3
Hence, the solution to the equation is x = 8.3
Learn more on Solving linear equations here: https://brainly.com/question/27882730
#SPJ1
How do you find the relationship between zeros and the coefficients of a cubic polynomial?.
A cubic polynomial is a polynomial of degree 3. That is, it is a polynomial with three terms. The relationship between the zeros and the coefficients of a cubic polynomial can be found by using the factoring theorem.
This theorem states that if a polynomial has a factor of (x-a), then a is a zero of the polynomial. In other words, the zeros of a polynomial are the values of x that make the polynomial equal to zero.
To find the zeros of a cubic polynomial, we can use the factoring theorem to factor the polynomial into factors of the form (x-a). For example, if we have the cubic polynomial x³+ax²+bx+c, we can factor it as (x-a)(x²+px+q), where a, p, and q are constants. We can then use the factoring theorem to find the values of a, p, and q that make the polynomial equal to zero.
The coefficients of a cubic polynomial are the values of a, p, and q in the factored form of the polynomial. In other words, the coefficients of a cubic polynomial are the values that determine the zeros of the polynomial.
Learn more about factor theorem at : https://brainly.com/question/24545336
#SPJ4
The school year book had 50 ads placed last year. This year there was a 20% increase in the number of ads. What was the increase in the number of ads placed?
A: 20
B: 30
C: 40
D: 10
Show your work
Answer:
10
Step-by-step explanation:
20% of 50 ads
=20/100*50 ads
=10 ads
For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
X: 5, 8, 9
Y: 3, 5, 7
Does y vary directly with x?
Write an equation for the direct variation:
The equation for the direct variation will be 5y-3x=0.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, For the data in the table, does y vary directly with x
X: 5, 8, 9
Y: 3, 5, 7
y ∝ x
y=kx
3=k5
k=3/5
For x as 5 and y as 3, the obtained equation is,
y=kx
y=3/5x
5y=3x
5y-3x=0
Thus, the equation for the direct variation will be 5y-3x=0.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ1
What is the vertex angle of an isosceles triangle?.
The vertex angle is defined as the angle opposite the base. It can be calculated by formula, 180° - 2B = A where, B=base angle and A=vertex angle.
The two sides of an isosceles triangle are congruent, which means they are the same length. The third side of an isosceles triangle is larger than the other two and is known as the base.
Every triangle has three angles that add up to a total of 180°. The base angles are the two angles located along the base of isosceles triangles. In isosceles triangles, the base angles are always congruent, or equal.
The vertex angle is defined as the angle opposite the base. The vertex angle is always greater than the sum of the two base angles. The vertex angle is always calculated by subtracting the base angles from 180°, using the general formula: 180° - 2B = A, where B represents the base angle and A represents the vertex angle.
Thus, vertex angle is defined as the angle opposite the base.
To learn more about isosceles triangle refer here
https://brainly.com/question/18933031
#SPJ4
simplify ((x-3)(x-3))/((3-x)(3+x))
Answer:
[tex]\frac{(x-3)^2}{(3-x)(3+x)}[/tex]
Step-by-step explanation:
1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]\frac{(x-3)^2}{(3-x)(3+x)}[/tex]
Thanks.
Which of the number's below are potential Rootsof the function p x x 4 22x 2 16x 12?.
The potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.
What is function?
In arithmetic, a perform from a collection X to a collection Y assigns to every part of X specifically one part of Y.
Main body:
p(x) = x⁴+ 22x² - 16x - 12
From the rational root theorem,
All the possible roots of the function are in the form of a rational number.
x = ± p/q
x = ± (Factors of the constant term)/ (Factors of leading coefficient)
In the given polynomial,
The constant term is - 12
The leading coefficient is 1
The factors of - 12 are ±1, ±2, ±3, ±4, ±6, ±12
Factors of 1 are ±1.
From the rational root theorem, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.
Therefore, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.
To know more about function click on the link below
https://brainly.com/question/11624077
#SPJ4
mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.
Scaffold instruction mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.
What is scaffold instruction?
A teacher can improve learning and help students master tasks by adding supports for them through a technique called instructional scaffolding. The teacher accomplishes this by methodically constructing on the experiences and knowledge of the pupils as they pick up new abilities. These supports are movable and temporary, just like the scaffold in the image on the left. The supports are gradually taken away as students complete the tasks they have been given by teacher.Structuring can be better understood by using the example of a kid learning to walk. A parent raises the child first. He pretends to walk, but his feet are barely on the ground. The infant is gradually given more and more freedom to bear his own weight. Then, while his parents are present, he might support himself by holding on to a piece of furniture like a coffee table. The child is now prepared to move, even if his parent's hand may still be mere centimetres away.Hence, Scaffold instruction mean(s) that teachers model strategies step-by-step and explicitly demonstrate the process of thinking before, during, and after one reads.
To know more about Scaffold instruction check the below link:
https://brainly.com/question/3706018
#SPJ4
We expect that students who do well on the midterm exam in a course will usually do well on the final exam. Gary smith of pomona college looked at the exam scores of all 346 students who took his statistics class over a 10-year period. Assume that both the midterm and final exam were scored out of 100 points. State the equation of the least-squares regression line if each student scored the same on the midterm and the final.
If each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].
What are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, Gary Smith of Pomona College reviewed the test results of all 346 students who took his statistics course over a ten-year period.
Take into account that both the midterm and final tests were rated out of 100.
Let the midterm score (x) and the final score (y) be the same.
The data for the explanatory variable x and the response variable y will be the same if each student receives the same grade on the midterm and final.
The linear model will predict that the two variables are equal if the data for the two variables are the same, and as a result, the linear model will assume that the expected y-variable is equal to the predicted x-variable.
Thus, the following is how the least-square regression line appears:
[tex]\hat{y}=x[/tex]
Therefore, if each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].
Know more about equations here:
https://brainly.com/question/28937794
#SPJ4
problem 7.2. cox-ross-rubinstein (crr) the cox-ross-rubinstein model is a binomial tree in which the up and down factors are given as u
The Cox-Ross-Rubinstein (CRR) model is a mathematical model used in finance to evaluate the potential future value of an asset or portfolio. The model is based on the concept of a binomial tree.
What is a binomial tree?A binomial tree is a mathematical model used in finance to estimate the probable future value of an asset or portfolio. The notion of a binomial, a mathematical expression with two potential outcomes, forms the foundation of the model. In a binomial tree, the future value of the asset is defined by two potential outcomes at each time step: a "upper" element and a down factor. The underlying variables that affect the asset, such as interest rates and market circumstances, dictate the up and down components. Reflecting This enables investors to assess the advantages and dangers of a possible investment and come to wise judgments.
To learn more about binomial tree, visit:
https://brainly.com/question/15901549
#SPJ4
Given: AB=AC, AD=AE and DC=EB
Prove: <1 is equal to <2
PLEASE HELP! Thank you!
The prove of ∠1 equal to ∠2 is shown below.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
⇒ AB = AC, AD = AE and DC = EB
Now,
In ΔDBC and ΔEBC;
⇒ DC = EB (Given) ..(i)
Since, AB = AC
So, the ΔABC is a isosceles triangle.
Hence, ∠DBC = ∠ ECB ..(ii)
Here, AB = AC and AD = AE
So, BD = EC ..(iii)
Hence, By the condition (i), (ii) and (iii);
By SAS condition,
⇒ ΔDBC ≅ ΔEBC
Hence, We get;
⇒ ∠1 = ∠2
Learn more about the triangle visit:
https://brainly.com/question/1058720
#SPJ1
Determine which of the following relations is a function.
To be a relation to a function there must be single output for single input thus tables (1) and (3) represent the function.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
In a function for every single input (x), there must be one output(y).
In the given second table,
For x = 0 → y =2 and y = 1 thus it will not be a function.
In the fourth table,
For x = 2 → y =2 and y = 6 thus it will not be a function.
Hence "To be a relation to a function there must be single output for single input thus tables (1) and (3) represent the function".
For more about the function,
brainly.com/question/23712366
#SPJ1
If you multiply two decimal le than 1, can you predict whether the product will be le than or greater than either of the factor? Explain
When we multiply two decimal numbers less than 1 then their product will be less than 1.
What do you mean by fraction?
A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. It is known as an improper fraction if the numerator is bigger and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder. By dividing the numerator by the denominator, any fraction can be expressed in decimal form. One or more digits may repeat indefinitely or the result may come to an end at some point.
If we multiply two decimal numbers less than 1 then their product will also be less than 1. Because we are determining a fractional portion of a quantity, this is the case.
Decimals are frequently multiplied by treating them as whole numbers before placing the decimal point in the result. Where the decimal point is placed in the solution depends on how many digits are present in the factors following the decimal points.
Therefore, when we multiply two decimal numbers less than 1 then their product will be less than 1.
To learn more about the fraction from the given link.
https://brainly.com/question/78672
#SPJ4
volume of naoh dispensed (ml) check circle highlight off highlight off mass of acid in sample (g) highlight off highlight off highlight off percentage by mass in sample
Percentage by mass in sample will be 67.8%.
We know that volume of NaOH dispensed is 24.68 ml.
And mass of the NaOH is 39.997 g/mol.
Also mass of acid is 58.94 g/mol.
We have to find percentage by mass in sample.
To calculate the mass percent of an element in a compound, we divide the mass of the element in 1 mole of the compound by the compound's molar mass and multiply the result by 100.
Therefore
Mass percent = (mass of chemical / total mass of compound) × 100
= (mass of NaOH/ mass of acid) × 100
= (39.997/58.94) × 100
= 0.678 × 100
Mass percent = 67.8
Hence percentage by mass in sample is 67.8%
To know more about molar mass here
https://brainly.com/question/17161943
#SPJ4
suppose you lift a laptop that weighs 4.1 pounds off the floor onto a shelf that is 2 feet high. how much work have you done?
The required work done in lifting the laptop to a height of 2 feet will be 263.79 foot-poundal.
Total weight of the laptop is 4.1 pounds
Acceleration due to gravity = 32.17 ft/[tex]s^{2}[/tex]
Now the height to which the laptop has been lifted = 2 feet
Since, there is no mentioned velocity of the laptop, therefore the kinetic energy will be zero
Therefore, the total work in lifting the laptop will be equal to the change in potential energy.
Potential energy is the energy that comes by virtue of its position with reference to other
Therefore, potential energy = mgh
Where, m = mass of the laptop = 4.1 pounds
g = acceleration due to gravity = 32.17 ft/[tex]s^{2}[/tex]
h = height to which the laptop is lifted = 2 feet
Therefore potential energy = (4.1)(32.17)(2) = 263.79 foot-poundal
263.79 foot-poundal is the required work done.
To know more about the potential energy, visit here:
https://brainly.com/question/8664733
#SPJ4
What accountants and auditors do?.
Accountants and auditors create and review financial records, spot possible risk and opportunity areas, and provide individuals and organisations solutions. They guarantee the accuracy of financial records, the assessment of data and financial risks, and the correct payment of taxes.
Accountants;-
An accountant is a specialist who manages bookkeeping and organises the financial records you use to run your company, including balance sheets, profit and loss statements, and more. They simplify all the financial jargon associated with running a business, audit your records, create reports for tax purposes, and more.
Auditors;-
An organization's audit is to be conducted by an auditor, who may be an individual or a company. An audit is a planned, methodical procedure that involves looking over books, records, accounts, or other documentation.
Learn more about accountants and auditors here;
https://brainly.com/question/15164491
#SPJ4
What factors are of 15?.
Answer:
factors : 1, 3, 5 and 15
Step-by-step explanation:
1 x 15 = 15
5 x 3 = 15
so those are the only factors of 15
question a sports team won twice as many games as they lost. the sum of games won and games lost was 42 games. how many games did they win?
Using the solution of Algebraic expression,
we get that total 28 games won by sports team.
We have given that,
let a sports team lost be x games .
then, total number of games won by sports team
= 2x
total number of games played by sports team
= 42
i.e , 2x + x = 42
=> 3x = 42
=> x = 42/3
=> x = 14
so, number of games lost by sports team is 14
but we have to calculate the total number of games won by spots team .
using the value of x , we get 2x = 2×14
=> 28 games
Hence, total 28 games out of 42 games are won by sports team.
To learn more about Algebraic expression, refer:
https://brainly.com/question/4344214
#SPJ4
Identify how long a player would have to practice batting to have 27 hits.
TIME (Hrs) 1 5 9 13 17
HITS 2 11 18 25 34
13.5 Hrs long a player would have to practice batting to have 27 hits.
Given:
TIME (Hrs) 1 5 9 13 17
HITS 2 11 18 25 34
To have 27 hits :
= 13 + 1 + 17 + 5 - 9 / 2
= 14 + 22 - 9 / 2
= 36 - 9 / 2
= 27 / 2
= 13.5 hours
Therefore 13.5 Hrs long a player would have to practice batting to have 27 hits.
Learn more about the times and hits here:
https://brainly.com/question/7161991
#SPJ1
Which equation represents the line that passes
through the points (-3,7) and (3,3)?
Answer:
Step-by-step explanation:
First get the slope of the line. This is (7-3)/(-3-3)=4/-6=-4/6=-2/3
Using slope intercept form, we get the equation
(-2/3)x+5=y
Identify the domain and range for the relation. {(1, 3), (2, 5), (3, 7), (4, 9), (5, 9)}
Answer:
See below
Step-by-step explanation:
Given relation:= {(1, 3), (2, 5), (3, 7), (4, 9), (5, 9)}
Domain:
All the x-values of the relation are domain.
So,
Domain = {1, 2, 3, 4, 5}Range:
All the y-values of the relation are range.
So,
Range = {3, 5, 7, 9, 9}[tex]\rule[225]{225}{2}[/tex]
What triangles are congruent to ABC?.
Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D.
Congruent triangles;-
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.
Here,
Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D. In other words, if a triangle's third side matches the third side of another triangle's third side, the triangles are said to be congruent.
Learn more about congruent triangles here;
https://brainly.com/question/5499257
#SPJ4
Ahley buy a hamter wheel during the ale(25% off). If Ahley pay $6, what wa the original price?
Answer:
original price was $8
Step-by-step explanation:
Ashley buy a hamster wheel during the sale (25% off). If Ashley pay $6, what was the original price?
$6 = 75% of price
75% = 0.75
6 = 0.75x
divide both sides by 0.75:
6/0.75 = 0.75x/0.75
x = 8
original price was $8
What are the most important activities performed by accountants?.
The main activity that is performed by accountant include the safe keeping of financial records and preparation of financial statements that are helpful in order to represent the current financial positions of a company.
An accountant is a qualified personnel who is the responsibility of maintenance of accounting records and safe keeping of the books of accounts of a firm. apart from maintenance of the accounting records and accountant also has to ensure that the financial statements are true and fair.
Learn more about an accountant here:
https://brainly.com/question/29250368
#SPJ4
If there are 15 red, 15 blue, and 15 yellow marbles in a bag, if you draw two marbles out of the bag without replacement, what is the probability that the second marble is a different color than the first marble
Answer:
15/22
Step-by-step explanation:
15 red, 15 blue, 15 yellow
You draw a marble of any color.
Now the marbles left in the bag are 14 of the same color, and a total of 30 of different colors for a total of 44 marbles.
Your desired outcome is a marble of a different color.
There are 30 desired outcomes.
The total number of possible outcomes is all the marbles left in the bag: 44.
p(2 marbles of different colors) = 30/44 = 15/22
What is the range of f(x) = sin(x)? the set of all real numbers the set of all real numbers the set of all real numbers the set of all real numbers.
The range of function f(x) = sin(x) is the set of all real numbers lying between [-1, 1].
Define the function sin(x)?Although they can sometimes be written as functions, the sine, cosine, and tangent of such an angle really are defined on the basis of trigonometry.
All real numbers fall inside the domain of the function f(x) = sin x, but its range equals −1 ≤ sin x ≤ 1. If the angle is measured in degrees versus radians will affect the sine function's values. The periodicity of the function is 360 degrees, or 2π radians. As a result, sin x is just an odd function, and its algebraic expression is sin(x) = − sin x. Using the aforementioned numerical tables, you can verify this truth. When it comes to cos x, we could see that the graph has a symmetry axis along the y-axis, indicating that it's an even function that can be expressed algebraically; cos(−x) = cos x.Thus, range of function f(x) = sin(x) is the set of all real numbers lying between [-1, 1].
To know more about the function sin(x), here
https://brainly.com/question/21902442
#SPJ4
9) customers arrive at a grocery store following a poisson distribution at an average rate of 70 per hour. on average, how many customers arrive per minute? a) 1.2 customers per minute b) 7 customers per minute c) 0.86 customers per minute d) 0.02 customers per minute e) 0.7 customers per minute
On average number of customers arrives at a grocery shop per minute is equal to 1.2 customers per minute.
As given in the question,
Following a Poisson distribution:
Number of customers arrives at grocery store
= Average rate of 70 per hours
Conversion hours to minutes
1 hour = 60 minutes
λ = average rate of 70 per hours
= average rate of 70 per 60 minutes
= average rate of ( 7 / 6 ) per minute
= average rate of 1.1666...per minute
= average rate of 1.2 per minute
Therefore, on average 1.2 number of customers arrives per minute.
Learn more about average here
brainly.com/question/24057012
#SPJ4
