The estimate expected mean time for the given activity E from the give table data is equal to 101days.
As given in the question,
Let optimistic time be represented by [tex]T_{o}[/tex]
Most like time be represented by [tex]T_{m}[/tex]
And Pessimistic time be represented by [tex]T_{p}[/tex]
Optimistic time for activity E is equal to [tex]T_{o}[/tex] = 91
Most likely time for activity E is [tex]T_{m}[/tex] = 100
Ans Pessimistic time for activity E is [tex]T_{p}[/tex] = 115
Estimated expected mean time
= [tex]( T_{o} + 4T_{m} + T_{p} ) / 6[/tex]
= [ 91 + 4(100) + 115 ] / 6
= 606/6
= 101
Therefore, option d. 101days represents the estimated expected mean time for the given activity E.
The complete question is:
From the given table:
{ Time estimates (days)}
Activity Predecessor Optimistic Most likely Pessimistic
A A, B, C 30 50 62
B D 90 99 108
C E 85 105 115
D End 19 25 31
E F 91 100 115
F End 62 65 68
What is the estimated expected (mean) time for activity E?
Multiple choice
a. 91 days b. 100 days c. 99 days d. 101 days e.115 days
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Complete the quadratic polynomial by filling in the number that makes it a perfect-square.
\mathrm{x}^{2} + 18 \mathrm{x} +x
2
+18x+
To make the quadratic polynomial x² + 18x into a perfect square, we add 81 to it.
What is a quadratic polynomial?A quadratic polynomial is a polynomial in which the highest power of the unknown is 2.
What is a perfect square?A perfect square is a number suvh that it is equal to another number multiplied by itself
How to make the quadratic polynomial a perfect square?Since we have the quadratic polynomial x² + 18x, and we wnat to convert it to a perfect square.
To be a perfect square, we want it in the form (x + a)² = x² + 2ax + a² (1)
Compring the quadratic polynomial with equation (1), we have that
2a = 18
a = 18/2
a = 9
⇒ a² = 9² = 81
So, substituting a = 9 into equation (1), we have
(x + a)² = x² + 2ax + a²
(x + 9)² = x² + 2(9)x + 9²
= x² + 18x + 81
Thus we see that to make x² + 18x into a perfect square, we add 81 to it.
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based on the angle measures list the sides (AB,BC, and AC). In order from shortest to longest:
Order of Sides from smallest to largest is AC, BC , AB.
What is the order of Angles and Sides in a Triangle ?Finding the Triangle's Angles and/or Sides in Order of Largest to Smallest
Step 1: As stated in the issue, sort the supplied angles or sides in the order of smallest to greatest or largest to smallest.
If the sides are supplied in the issue and we are requested to arrange the angles, step 2 is to find the angles that are opposite the given sides.
If the problem specifies the angles and asks us to arrange the sides, find the sides that are perpendicular to the provided angles.
The sides opposing the angles will be listed in the same sequence as step 1's first-identified sides. Therefore, the side across from the biggest angle will be the largest, and the side across from the smallest angle will be the smallest. The angles opposing the sides will also be in the same sequence as those found in step 1 for the angles. As a result, the angle opposite the side with the greatest length will be the largest, while the angle opposite the side with the lowest length will be the smallest.
angle B is smallest , so the smallest side is opposite side of angle B i.e AC.
Again angle C is largest so similarly AB is the largest.
Order of Sides from smallest to largest is AC, BC , AB
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Variable costs of producing widgets include the cost of gas required to deliver the widgets to retailers. A widget producer finds the average cost of gas per widget. The expense equation was recently adjusted from E = 4.55q + 69,000 to E = 4.98q + 69,000 in response to the increase in gas prices.
a. Find the increase in the average cost per widget. Round to the nearest cent.
b. If the widgets are sold to retailers for $8.00 each, find the breakeven point prior to the adjustment in the expense function.
(unit)
($) (do not use commas in numbers over 1,000)
c. After the gas increase, the company raised its wholesale cost from $8 to $8.50. Find the breakeven point after the adjustment in the expense function. Round to the nearest integer.
(unit)
($) (do not use commas in numbers over 1,000)
The breakeven point after the adjustment in the expense function.
What is the revenue?
Revenue is the total amount producers receive after selling a good. Profit is the total amount producers earn after subtracting the production costs.
Revenue is the product of the number of units and the price per unit. It is given by:
Revenue = number of units * price per unit
Revenue = x * p(x)
Revenue = 8q Expense = 4.55q + 69,000
To find the breakeven point Revenue = Expense
8q = 4.55q + 69,000 3.3.45q = 69,000 q = 20,000
Equate both and find q
E = 4.55(20,000) + 69,000 = 160,000
E at q = 20,000
(20,000, 160,000)
Hence, the breakeven point after the adjustment in the expense function.
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i need help in this asap✋✋✋✋✋
By using the property of congruency of triangles,
[tex]\angle V \cong \angle S[/tex] has been proved
What is congruency of triangles?
Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.
There are different axioms of congruency. They are
SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom
UV [tex]\cong[/tex] ST [Given]
QR [tex]\cong[/tex] PQ [Given]
QT [tex]\cong[/tex] QU [Given]
PV [tex]\cong[/tex] RS [Given]
PT = PQ + QT [Additive Property of Length]
RU = QR + QU [Additive Property of Length]
PT = QR + QU [Substitution]
PT = RU [Transitive Property of Equality]
TV = UV + TU [Additive Property of Length]
SU = ST + TU [Additive Property of Length]
TV = ST + TU [Substitution]
SU = TV [Transitive Property of Equality]
[tex]\angle[/tex]SUR [tex]\cong[/tex] [tex]\angle[/tex]VTP [QT = QU]
[tex]\Delta USR \cong \Delta TVP[/tex] [SAS axiom]
[tex]\angle V \cong \angle S[/tex] [Corrosponding parts of congruent triangles are congruent]
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The number of rooms in a house is a function of the number of people who live in the house.
Which of the following statements must be true?
A. The domain of the function is the population of the town.
B. If there are four rooms in the house, then there are four people living in the house.
C. The domain of the function is the number of rooms in a house.
D. The domain of the function is the number of people who live in the house.
The domain of the function described in the problem is given as the number of people living in the house. The correct option is (D).
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
Suppose the number of rooms in the house be y.
And, the number of people is x.
As per the question, the function can be written as,
y = f(x)
From the definition of the function it is clear that all the possible values of x are domain and all values of y are range.
Thus, the domain of the function is number of people living in the house.
Hence, the domain of the function for the given case is the number of people living in house.
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Madelyn is throwing a pizza party. She has 6 pounds of cheese available and she
needs 1/2 pound of cheese to make each pizza. How many pizzas can she make?
Answer:
She can make 12 pizzas
Step-by-step explanation:
There are 2 halves in a pound, so you'll need to do 6 × 2 = 12.
the base of a parallelogram is 3 times that of the height. the area of the parallelogram is 48. find the height of the parallelogram.
Answer:
height = 4
Step-by-step explanation:
b = 3h
b * h = 48
3h * h = 48
3h² = 48
3/3 h² = 48/3
h² = 16
h = √16
h = 4
b = 4 * 3
b = 12
Question is attached
Answer:
Question 62. B) 8Question 63. D) 4/3--------------------
Question 62From the series we can observe:
The first term of the GP is t = 1/2, The common ratio is r = - 1/2,The nth term is - 1/256.Use the nth term equation to find the value of n:
[tex]t_n=t*r^{n-1}[/tex]Apply this to the last term and solve for n:
[tex]-1/256=1/2*(-1/2)^{n-1}[/tex][tex]-1/128= (-1/2)^{n-1}[/tex][tex](-1/2)^7=(-1/2)^{n-1}[/tex][tex]n-1=7[/tex][tex]n=8[/tex]--------------------------------------------------------------------
Question 62Given
Infinite sequence:
2, - 1, 1/2, - 1/4, 1/8, ...It has:
t = 2, r = - 1/2Find the sum of terms:
S = t / ( 1 - r)S = 2 /( 1 + 1/2) = 2 / (3/2) = 4/3Correct choice is D.
Mrs. Jones makes scented candles and wax warmers. The table shows the ratio of the number of candles to the number of wax warmers she makes. Candles 7 14 21 28 77 OC. 55 OD. 75 Wax Warmers 5 10 15 20 ? How many wax warmers will she make when she makes 77 candles? O A. 69 O B. 40
Mrs. Jones will make 55 wax warmers when she produces 77 candles.
The given table shows the ratio of the number of candles to the number of wax warmers she makes.
Let's assume that "x" wax warmers will she make when she makes 77 candles
According to the given question, we can write the ratio would be as:
7 Candles : 5 Wax Warmers = 77 Candles : x Wax Warmers
⇒ 7/5 = 77/x
⇒ 7x = (77)(5)
Divided by 7 on both sides of the above equation,
⇒ x = (77)(5)/7
⇒ x = 11 × 5
Apply the multiplication operation, we get
⇒ x = 55
Thus, when she makes 77 candles, she will also produce 55 wax warmers.
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Hi Can some solve this with steps please
Answer:
- 51
Step-by-step explanation:
substitute x = - 2 into the expression
2x³ - 4x² + 8x - 3
= 2(- 2)³ - 4(- 2)² + 8(- 2) - 3
= 2(- 8) - 4(4) - 16 - 3
= - 16 - 16 - 19
= - 32 - 19
= - 51
A relation i plotted a a linear function on the coordinate plane tarting at point A (0, 3)and ending at point B (2, 7). What i the rate of change for the linear function and what i it initial value? Select from the drop-down menu to correctly complete the tatement. The rate of change i Chooe. And the initial value i Chooe.
The rate of change is 2 and initial value is 3.
Given points A (0,3) B(2,7)
What is the slope of line joining between point A and point B
if let's suppose A(x1,y1) B(x2,y2)
then slope(m) = y2-y1/x2-x1
x1=0,y1=3
x2=2 y2= 7
slope(m) = 4/2 = 2
The ratio between the change in the values of the y variables and the change in the values of the x variables is known as the rate of change. The rate of change is the slope of the line if the rate of change is linear and constant.
Rate of change of linear function is also know as slope of that linear function.
So here slope itself is the rate of change.
Initial value is 3 as Coordinate of A is (0,3).
Given Question is incomplete Complete Question here
A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3)and ending at point B (2, 7) .
What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
The rate of change is____ and the initial value is___ .
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stella opens her bank account with $500. She deposits $40 each month into the account. What function shows the amount in Stella's bank account after m months?
Answer:
f(x) = 500+40m
Step-by-step explanation:
500 = initial
40m because she deposits 40 each month
Bernard was going on an 3.5 kilometre bushwalk. He needs 1.2 litres of water for every 1.4 kilometres he walks. He only has 500 mL water bottles. How many water bottles will he need to take to make sure he has enough water for his walk?
The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL
The number of water bottles = 6
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of water bottles required be = A
Now , the equation will be
The total distance of the bush walk = 3.5 km
Bernard's requirement of water for every 1.4 km = 1.2 L of water
So , Bernard's requirement of water for every 3.5 km = ( total distance of the bush walk / 1.4 ) x 1.2 L
Substituting the values in the equation , we get
Bernard's requirement of water for every 3.5 km = ( 3.5 / 1.4 ) x 1.2 L
Bernard's requirement of water for every 3.5 km = 2.5 x 1.2 L
Bernard's requirement of water for every 3.5 km = 3 L
Now , the amount of water one water bottle can hold = 500 mL
The value of 3 L = 3000 mL
So , the number of water bottles required to hold 3 L = 3000 / amount of water one water bottle can hold
Substituting the values in the equation , we get
The number of water bottles required to hold 3 L = 3000 / 500
The number of water bottles required to hold 3 L = 6 water bottles
Therefore , the value of A is 6 water bottles
Hence , The number of water bottles Bernard needs to complete a 3.5 kilometer bush walk is 6 bottles of 500 mL
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Kelli walk no more than 25 dog on Monday. M. Lincoln ha 5 dog that Kelli walk. The inequality hown can be ued to find x, the number of dog Kelli can walk on Monday in addition to M. Lincoln' dog. X 5 25 Which inequality repreent all poible value of x?
All potential values of x are represented by the inequality x≤20.
What is inequality?A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.
An inequality displays the difference between two variables, whereas an equation displays the equivalence of two variables.
So, the inequality that also represents all the possible values of x is:
On Mondays, Kelli walks no more than 25 dogs.
Also, Ms. Lincoln's five dogs are walked by Kelli.
Along with Ms. Lincoln's dogs, the inequality to determine how many additional dogs Kelli walks on Monday is written as:
x+5 ≤ 25
Take 5 away from both sides.
x + 5 - 5 ≤ 25 - 5
x ≤ 20
Therefore, all potential values of x are represented by the inequality x≤20.
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Complete question:
Kelli walks no more than 25 dogs on Mondays. Ms. Lincoln has 5 dogs that Kelli walks. The inequality shown can be used to find x, the number of dogs Kelli can walk on Monday in addition to Ms. Lincoln's dogs. x + 5 25 Which inequality represents all possible values of x?
HELP THIS IS MY LAST QUESTION
Answer:
associative property of multiplication
Step-by-step explanation:
Mrs. Rao pays the same amount each month for Internet service.She is making a graph to show the amount that she pays over time.
Given graph will be a line parallel to [x] axis.
What is the equation of a straight line? What do you mean by domain and range of a linear function?The general equation of a straight line is -
y = mx + c
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have Mrs. Rao pays the same amount each month for Internet service.
Assume that he pays amount [k], each month. Then, we can write the equation representing the graph as -
y = k
The graph will be a line parallel to [x] axis.
Therefore, the given graph will be a line parallel to [x] axis.
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If we randomly select a U.S. female, is (pregnant and over 55) = (0.06)(0.27) = 0.0162? Why or why not?
No, because being older than 55 and being pregnant are not independent events.
If we randomly select a U.S. female, is (pregnant and over 55) = (0.06)(0.27) = 0.0162 because being older than 55 and being pregnant are not independent events.
A random number is one that is selected by chance, or randomly, from a set of numbers, as the name suggests. There is an equal chance that any one of the numbers in a given distribution will be chosen at random.
The concepts of randomness are formally defined in the fields of mathematics, probability, and statistics. A random variable in statistics is the process of assigning a numerical value to each potential result of an event space. The identification of the events and the estimation of their probabilities are made easier by this association.
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The Transportation Security Administration (TSA) is responsible for airport security. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such flight has 76 passengers (12 in first class and 64 in coach). TSA officers selected an SRS of 10 passengers for screening. Let p-hat be the proportion of first class passengers in this sample. So, assuming that you are checking for the probability of choosing a first class passenger out of all passengers on the flight. Is the 10% condition met in this case? Justify your answer. (POS 447#31)
- Yes, 10 passengers out of 76 is less than 10% of the population of the flight.
- yes, 10 passengers out of all passengers on all flights is less than 10% of the population
- No, 10 passengers is the population being studied and is not less than 10% of the 10 total
- No, 10 passengers out of 76 is more than 10% of the population of the flight.
A runner runs 2 miles in 9.56 minutes. How many meters per second is this? Explanation please
Thank you!
Answer: 2 miles
Step-by-step explanation:
It takes Sandra 1 hour to word process 4.5 pages. At this rate, how long will she take to complete 29
pages?
It takes Sandra 6.44 hour to word process 29 pages.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
It takes Sandra 1 hour to word process 4.5 pages.
Now,
Since, It takes Sandra 1 hour to word process 4.5 pages.
Hence, The time to make 29 pages = 29/4.5
= 290/45
= 58/9 hours
Thus, It takes 6.44 hours to complete 29 pages.
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how would this two triangles be called
The triangles ΔUST and ΔVRQ are congruent to each other by the SSS postulates.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles ΔUST and ΔVRQ, then we have
TU = QV (Given)
ST = QR (Given)
UV = SR
Add RU on both sides, then we have
UV + RU = SR + RU
RV = SU
The triangles ΔUST and ΔVRQ are congruent to each other by the SSS postulates.
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A figure i made up of a emicircle and triangle. The diameter of the emicircle i 10ft, the bae of the triangle i 8 ft and the height i 6 ft. What i the area of the figure
The area of the figure that is made up of a semicircle and a triangle is 63.25 square feet .
In the question ,
it is given that ,
a figure is made up of a semicircle and a triangle ,
the diameter of the given semicircle is = 10 ft ,
So , the radius of the given semicircle is = 10/2 = 5 ft .
hence the area of the semicircle will be = (πr²/2)
= 3.14×(5)²/2
= 39.25 square feet
the base of the triangle is given to be = 8 ft ,
the height of the triangle is given to be = 6 ft ,
So , the area of the triangle is = (1/2)×b×h = (1/2)×8×6 .
= 4 × 6
= 24 square feet .
So , the area of the figure = area of semicircle + area of triangle
= 39.25 + 24
= 63.25 .
Therefore , the area of the figure is = 63.25 square feet .
The given question is incomplete , the complete question is
A figure is made up of a semicircle and triangle. The diameter of the semicircle is 10ft, the base of the triangle is 8 ft and the height is 6 ft. What is the area of the figure ?
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A andwich hop erve 4 ounce of meat and 3 ounce of cheee on each andwich. After making andwiche for an hour the hop owner ha ued 91 combined ounce of meat and cheee
How many combined ounce of meat and cheee are ued on each andwich?
The combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.
We have the following information:
A sandwich hop serve 4 ounce of meat and 3 ounce of cheese on each sandwich. After making sandwiches for an hour the hop owner has used 91 combined ounce of meat and cheese.
Now, we know the combined ounces of meat and cheese for 1 sandwich will be given as follows:
Ounces of meat + ounces of cheese
4+3
7 ounces
Now, in an hour 91 ounces of combined cheese and meat are used.
So, we have the following expression:
Number of sandwiches made in 1 hour = Total ounces used/ounces used in 1 sandwich
Number of sandwiches = 91/7
Number of sandwiches = 13
Ounces of meat used in 13 sandwiches = 13*4
Ounces of meat used in 13 sandwiches = 52 ounces
Ounces of cheese used in 13 sandwiches = 13*3
Ounces of cheese used in 13 sandwiches = 39 ounces
Hence, the combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.
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Select all of the following functions that are quadratic. □ y=2x² 3=2x²-8 y=-2+2x-8 y + 3x = 2x² - 8 Oy+3x²= 2x + 3x²-8
If the degree of the equation is two, then the result leads to the quadratic equation. The following equations are entitled to the quadratic equations.
[tex]- $\mathrm{y}=2 \mathrm{x}^2$- $\mathrm{y}=2 \mathrm{x}^2-8$- $y=2 x^2-3 x-8$[/tex]
What is a quadratic equation?
In the quadratic equation, the maximum power of the variable is 2 . It consists of [tex]$x^2, x$,[/tex] and the constant term.
Given
1 .[tex]$y=2 x^2$[/tex]
2. [tex]$y=2 x^2-8$[/tex]
3. [tex]$\mathrm{y}=-2+2 \mathrm{x}-8$[/tex]
4.[tex]$\mathrm{y}+3 \mathrm{x}=2 \mathrm{x}^2-8$[/tex]
5. [tex]$\mathrm{y}+3 \mathrm{x}^2=2 \mathrm{x}+3 \mathrm{x}^2-8$[/tex]
If the power of x is 2 , then it is said to be a quadratic equation.[tex]y=2 x^2[/tex]
The above expression is a quadratic equation.
2.
[tex]y=2 x^2-8[/tex]
The above expression is a quadratic equation.
3.
[tex]y=2 x-10[/tex]
The above expression is not a quadratic equation.
4.
[tex]\begin{aligned}\mathrm{y}+3 \mathrm{x} & =2 x^2-8 \\\mathrm{y} & =2 x^2-3 x-8\end{aligned}[/tex]
The above expression is a quadratic equation.
5.
[tex]\begin{aligned}\mathrm{y}+3 \mathrm{x}^2 & =2 x+3 x^2-8 \\\mathrm{y} & =2 x-8\end{aligned}[/tex]
The above expression is not a quadratic equation.
Thus, the third and fifth are not quadratic equations and the first, second, and fourth are quadratic equations.
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A parent function is a linear function of the form y=b.
True false question.
True
False
Answer: True
Step-by-step explanation:
If I remember not to mistake y=x is the parent functions. So y=b is the parent function! So this question is true.
The question is in the image
Answer:
The length of side B is 6.25, The length of side A is 8.75, The scale factor is 0.25
Step-by-step explanation:
Divide the left side of the first model by the left side of the scaled version
60 / 15 = 4
divide side A and B by the result
35 / 4 = 8.75
25 / 4 = 6.25
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
-2-
Oy=-2² +4
O y= 2²
Oy-log₂ (x+2)+1
Oy-log₂ (x+2)
Answer:
A
Step-by-step explanation:
y = - 2² + 4
y = - 4 + 4
y = 0
(2,0)
The equation that has a real zero at x = 2 is y = -[tex]2^x[/tex] + 4.
Option A is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The graph shows an x-intercept at x = 2, which means that the function has a real zero at x = 2.
Now,
We can check which of the given equations has this property by plugging in x = 2 and seeing if the corresponding y-value is zero.
For y = [tex]-2^x[/tex] + 4,
y = -2² + 4 = 0
This equation has a real zero at x = 2.
For y = 2^x,
y = 2² = 4,
This equation does not have a real zero at x = 2.
For y = log₂(x + 2) + 1,
y = log₂(2 + 2) + 1 = log₂4 + 1 = 3
This equation does not have a real zero at x = 2.
For y = log₂(-x + 2),
-x + 2 < 0, which means that x > 2.
This equation does not have a real zero at x = 2.
Therefore,
The equation that has a real zero at x = 2 is y = -[tex]2^x[/tex] + 4.
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A cone has a radius of 8 m and a height of 30 m. What is the volume of the cone in terms of pi?
Answer:
640[tex]\pi[/tex]
Step-by-step explanation:
The formula for a cone is [tex]\pi r^2*h/3[/tex].r meaning Radius and h meaning Height.Your looking for the answer in terms of [tex]\pi[/tex] so you would take the [tex]\pi[/tex] out of the equation making it [tex]r^2*h/3[/tex].Insert your values in their respective locations, r becoming 8, and h becoming 30.Solve your equation of [tex]8^2*30[/tex]/3 getting 640.Add [tex]\pi[/tex] to the end.Answer:
640π
Step-by-step explanation:
The formula for a cone volume is
[tex]V = \pi r^{2} \frac{h}{3} \\\\V = \pi 8^{2} \frac{30}{3} \\\\V = \pi 64 * 10 \\\\V = 640\pi[/tex]
The sum of two numbers is 20, and
the sum of their squares is 218. Find
the numbers.
The two numbers whose sum is 20 and sum of their squares is 218 are
13 and 7 respectively.
What is a numerical expression?A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
Let, The two numbers be a and b.
Given, The sum of two numbers is 20 which is, a + b = 20...(1) and the sum of their squares is 218 which is, a² + b² = 218...(2)
We know, (a + b)² = a² + 2ab + b².
Therefore, 20² = 218 + 2ab.
2ab = 400 - 218,
2ab = 182.
ab = 91...(3)
Now, (a - b)² = a² + b² - 2ab.
(a - b)² = 218 - 182.
(a - b)² = 36.
a - b = 6...(4).
Adding (1) and (4) we get,
2a = 26.
a = 13 and hence b = 7.
learn more about numerical expressions here :
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What is the surface area of the cylinder with height 7 mi and radius 5 mi? Round your answer to the nearest thousandth.