1. The two cylinders have the same height and the same cross-sectional area at every point along that height, so they have the same volume. Sue is correct.
2. The two stacks of quarters have the same height and the same cross-sectional area at every point along that height, so they have the same volume.
3. The two triangular prisms have the same height and the same cross-sectional area at every point along that height, so they have the same volume. This can also be explained using Cavalieri's principle.
How to explain the informationThe two stacks of quarters have the same height and the same cross-sectional area at every point along that height, so they have the same volume.
This can be explained using Cavalieri's principle, which states that two solids have the same volume if they have the same height and the same cross-sectional area at every point along that height.
Learn more about cylinder on
https://brainly.com/question/9554871
#SPJ1
The Drop Tower at Carowinds takes riders to the top of a tower and drops them. A function that
approximates this ride is h= -16t² + 64t + 60, where h is the height in feet and t is the time in seconds.
About how many seconds does it take for riders to drop 60 feet?
Answer: It takes riders 4 seconds to drop 60 feet on the drop tower at Carowinds.
Step-by-step explanation:To answer the question, we need to solve for t in the given function.
h = -16t^2 + 64t + 60
We know that the height dropped is 60 feet. So, we can substitute h with 60 and solve for t.
60 = -16t^2 + 64t + 60
Simplifying the equation, we get:
16t^2 - 64t = 0
Dividing both sides by 16t, we get:
t - 4 = 0
Suppose there is a regular polygon that can be decomposed into 46 triangles. The measure of one of it’s interior angles is (9.5x+26)
The value of x is equal to 15.1 units.
How to determine the value of x?In Mathematics and Geometry, the measure of each interior angle of a regular polygon can be calculated by using this mathematical equation:
Interior angle = [180 × (n - 2)]/n
Where:
n represents the number of sides of a regular polygon.
Since this regular polygon can be decomposed into 46 triangles, it ultimately implies that it has 46 x 3 = 138 sides.
Therefore, the value of each interior angle can be calculated as;
Interior angle = [180 × (n - 2)]/n
Interior angle = [180 × (138 - 2)]/138
Interior angle = 169.6⁰
For the value of x, we have:
9.5x + 26.2 = 169.6
9.5x = 143.4
x = 15.1 units.
Read more on interior angles here: brainly.com/question/13293407
#SPJ1
Complete Question:
Suppose there is a regular polygon that can be decomposed into 46 triangles. The measure of one of its interior angles is (9.5x+26.2).
What is the value of x?
The following table list two investment plans, A and B. Given this information, determine which investment is an ordinary annuity and the future value of the ordinary annuity after one year, given that both investments, A and B, compound interest monthly at the rate of 3.5%. Round to the nearest cent. B Jan. Feb. Mar. Apr. May Jun. Jul. Aug Sept. Oct. Nov. Dec. 350 350 350 350 350 350 350 350 350 350 350 350 350 O A 350 350 350 350 350 350 Investment A is an ordinary annuity with $3,918.03 in the account after 1 year. b. Investment B is an ordinary annuity with $3,918.03 in the account after 1 year. C. Investment A is an ordinary annuity with $3,906.64 in the account after 1 year. d. Investment B is an ordinary annuity with $3,906.64 in the account after 1 year Please select the best answer from the choices provided O B 350 350 350 Mark this and return Save and Exit Next Submit
(C) Investment A is an ordinary annuity with 3,906.64 in the account after 1 year is correct option.
Both Investment A and Investment B are annuities, but we need to determine which one is an ordinary annuity. An ordinary annuity is one in which payments are made at the end of each period, while in an annuity due, payments are made at the beginning of each period.
Looking at the table, we can see that Investment A and Investment B both have payments made at the end of each month, so they are both examples of ordinary annuities.
To calculate the future value of each annuity after one year, we can use the formula:
[tex]FV = P \times [(1 + r)^n - 1] / r[/tex]
where:
FV is the future value of the annuity
P is the payment amount
r is the interest rate per period (in this case, 3.5% per month)
n is the number of periods (12 in this case, since we're looking at one year)
For Investment A, we have P = 350, r = 0.035, and n = 12. Plugging these values into the formula, we get:
FV = 350 × [(1 + 0.035[tex])^12[/tex] - 1] / 0.035
= 3,906.64
Therefore, the answer is (C) Investment A is an ordinary annuity with 3,906.64 in the account after 1 year.
for such more question on ordinary annuity
https://brainly.com/question/25792915
#SPJ11
pls give me the right answer okay
Answer:
We have to use 3 for pi it says
Volume for cylinder:
V= pi*r²*h
Input values=
3x2²x7
=84
Volume of the cone:
pi*r²*h/3
Input values:
84/3
=28
Add them 84+28= 112
Pleaseeeeee helppppp meeeee
The probability of randomly selecting an apartment unit that has both internet and cable connection on the second floor = 0.23
Given that,
For second floor:
Total outcomes = 40
Network preference of internet & cable both = 9
Then Favorable outcomes = 9
Since we know that,
Probability is the ratio of number of favorable outcomes and total number of outcomes. It deals with finding out the likelihood of the occurrence of an event.
Therefore, to find the probability that,
P(Randomly selecting an apartment unit having internet and cable both )
= 9/40
= 0.225
≈ 0.23
Thus, the required probability = 0.23
Learn more about the probability visit:
https://brainly.com/question/13604758
#SPJ1
Rewrite the expression as a single logarithm.
The expression [tex]3log_b(8) - log_b(7)[/tex] written as a single logarithm is [tex]log_b(\frac{512}{7})[/tex].
How to turn expressions into a single logarithm?Given the logarithmetic expression in the question:
[tex]3log_b(8) - log_b(7)[/tex]
To rewrite the expression [tex]3log_b(8) - log_b(7)[/tex] as a single logarithm, we can use the properties of logarithms.
Using the quotient rule property, which states that:
logₙ(a) - logₙ(b) = logₙ(a/b)
Applying the quotient rule:
First, rewrite [tex]3log_b(8) - log_b(7)[/tex] as:
[tex]log_b(8^3) - log_b(7)[/tex]
Now, since the base of the logarithm is the same (b), we can combine the two logarithms using the power rule, which states that logₙ(aᵇ) = b × logₙ(a).
[tex]log_b(\frac{8^3}{7})[/tex]
Simplify
[tex]log_b(\frac{512}{7})[/tex]
Therefore, the single logarithm is [tex]log_b(\frac{512}{7})[/tex].
Learn more about logarithm here: https://brainly.com/question/29291192
#SPJ1
Maria’s line is represented by the equation
y
=
−
5
6
x
+
8
. Nate’s line is perpendicular to Maria’s line.
Which of the following could be an equation for Nate’s line?
A.
5
x
−
6
y
=
15
B.
5
x
+
6
y
=
15
C.
6
x
−
5
y
=
15
D.
6
x
+
5
y
=
15
The possible equation for Nate's line is C) 6x - 5y = 15.
To find the equation of the line perpendicular to Maria's line, we need to determine the slope of Maria's line first.
Maria's line is represented by the equation:
y = -5/6 x + 8
The slope of this line can be determined by comparing it to the slope-intercept form of a linear equation (y = mx + b), where m is the slope. Thus, the slope of Maria's line is -5/6.
The slope of a line perpendicular to Maria's line will be the negative reciprocal of -5/6, which is 6/5.
Therefore, the equation of Nate's line could be in the form:
y = 6/5 x + b
where b is the y-intercept of Nate's line.
To determine which of the given answer choices is the equation of Nate's line, we can substitute the equation y = 6/5 x + b into each answer choice and see which one holds true.
A) 5x - 6y = 15
Substituting y = 6/5 x + b, we get:
5x - 6(6/5 x + b) = 15
5x - 36/5 x - 6b = 15
-11/5 x - 6b = 15
This equation is not equivalent to y = 6/5 x + b, so A is not the answer.
B) 5x + 6y = 15
Substituting y = 6/5 x + b, we get:
5x + 6(6/5 x + b) = 15
5x + 36/5 x + 6b = 15
46/5 x + 6b = 15
This equation is not equivalent to y = 6/5 x + b, so B is not the answer.
C) 6x - 5y = 15
Substituting y = 6/5 x + b, we get:
6x - 5(6/5 x + b) = 15
6x - 6x - 5b = 15
-5b = 15
b = -3
This equation is equivalent to y = 6/5 x - 3, so C could be the answer.
D) 6x + 5y = 15
Substituting y = 6/5 x + b, we get:
6x + 5(6/5 x + b) = 15
6x + 6x + 5b = 15
12x + 5b = 15
This equation is not equivalent to y = 6/5 x + b, so D is not the answer.
Therefore, the possible equation for Nate's line is C) 6x - 5y = 15.
for such more question on equivalent
https://brainly.com/question/2328454
#SPJ11
The heights of a certain group of adult parrots was found to be normally distributed. The mean height is 34cm with a standard deviation of 8cm. IN a group of 400 of these birds, how many would be more than 18cm tall?
The required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.
Given that the heights of adult parrots are normally distributed with a mean height of 34 cm and standard deviation of 8 cm.
The formula used to calculate the z-score for the height of 18 cm is
z = (x - mean) / standard deviation
By substituting the value of mean and standard deviation gives,
z = (18 - 34) / 8.
On simplification of numerator gives,
z= -16 / 8 = -2.
To find the proportion of parrots more than 18 cm tall by calculating the area under the standard normal curve to the right of z = -2 by the standard normal distribution table.
That implies, proportion = area to right of z = -2 is approximately equal to 0.9772.
The formula used to calculate the number of parrots that is more than 18 cm tall is proportion × total number of parrots.
That implies, the number of parrots out of 400 birds which are more than 18 cm tall is 0.9772 × 400 = 390.88 ≈ 391.
Therefore, the required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.
Learn more about standard normal deviation table click here:
https://brainly.com/question/31329054
#SPJ1
What is the domain of the exponential function?
[tex]y=2^{x}+6[/tex]
The domain of the exponential function is all real numbers.
The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.
For the exponential function y = 2ˣ + 6, the domain includes all real numbers.
This is because there are no restrictions on the input values that can be plugged into the function.
We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.
Hence, the domain of the exponential function is all real numbers.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ1
What is the solution to the equation Negative 3 (h + 5) + 2 = 4 (h + 6) minus 9?
Answer:
h = -10
Step-by-step explanation:
The solution to the equation is h = -10. To solve for h, we need to isolate h on one side of the equation. We do this by adding 9 to both sides, subtract 4h from both sides, and add 5 to both sides. This gives us:
Negative 3 (h + 5) + 2 + 9 = 4 (h + 6) - 9 + 9
Negative 3h + 14 = 4h + 15
Negative 3h - 4h = 15 - 14
-7h = 1
h = -1/7
h = -10
A coin-operated machine sells plastic rings. It contains 5 white rings, 6 orange rings, 7 purple rings, and 15 pink rings. Constance puts a coin into the machine. Find the theoretical probability she gets a orange ring. Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
The theoretical probability of Constance getting an orange ring from the coin-operated machine is 0.182. This means that out of all the possible outcomes, there is an 18.2% chance that Constance will get an orange ring.
To find the theoretical probability of Constance getting an orange ring from the coin-operated machine, we need to first understand what theoretical probability means. Theoretical probability is the likelihood or chance of an event happening based on the number of possible outcomes. In this case, the possible outcomes are the different colored rings that the machine contains.
We are given that the machine contains 5 white rings, 6 orange rings, 7 purple rings, and 15 pink rings.
Therefore, the total number of rings in the machine is 5 + 6 + 7 + 15 = 33.
The probability of Constance getting an orange ring can be calculated by dividing the number of orange rings by the total number of rings in the machine.
Therefore, the theoretical probability of Constance getting an orange ring is:
6 / 33 = 0.181818...
To express this as a decimal, we can round it to the nearest thousandth, which is 0.182.
know more about theoretical probability here:
https://brainly.com/question/22962752
#SPJ11
Work out the minimum number of extra squares that need to be shaded so that the pattern below has rotational symmetry of order
a) 2
b) 4
The minimum number of extra squares that need to be shaded so that the pattern has rotational symmetry of order is 3
Working out the minimum number of extra squares that need to be shadedFrom the question, we have the following parameters that can be used in our computation:
The composite figure
On the extension at the left-hand side of the figure, we can see that
The shaded shape is a rectangle while other shaded shapes are squares
This means that the other shaded squares must be extended to form a rectangle
There are three of the squares that can be extended to rectangles
Hence, the minimum number of squares is 3
Read more about rotational symmetry at
https://brainly.com/question/2762589
#SPJ1
The table and graph represent the time vs elevation of a snow boarder as they come down the mountain. Time 0 5 10 15 20 25 30 40 45 50 60 Elevation 100 90 80 70 50 40 30 25 20 10 0 Which linear model best fits the data? Responses y=0.5647x+53.7117 y equals 0.5647 x plus 53.7117 y=−0.5647x−53.7117 y equals negative 0.5647 x minus 53.7117 y=1.6881x−92.571 y equals 1.6881 x minus 92.571 y=−1.6881x+92.571
A linear model that best fits the data include the following: D. y = -1.6881x + 92.571.
How to determine the line of best fit?In this scenario, the time would be plotted on the x-axis (x-coordinate) of the scatter plot while the elevation of a snow boarder would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the time and the elevation of a snow boarder, an equation for the line of best fit is given by:
y = -1.6881x + 92.571
Next, we would substitute the x-values into the equation for the line of best fit as follows;
When x = 0, we have:
y = -1.6881(0) + 92.571
y = 92.571 ≈ 93.
When x = 5, we have:
y = -1.6881(5) + 92.571
y = 84.1305 ≈ 84.
When x = 10, we have:
y = -1.6881(10) + 92.571
y = 75.69 ≈ 76.
In conclusion, we can logically conclude that the slope of this graph (line) is negative because the line decreases downward, and this is best modeled by only this equation y = -1.6881x + 92.571.
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
if a triangle has one side with a length of 20 meters and a second side with a length of 18 meters
Answer:
see attached
Step-by-step explanation:
You want the possible lengths of the third side of a triangle with side lengths 20 m and 18 m.
Triangle inequalityIf the third side is length c, the triangle inequality requires ...
18 +c > 20 ⇒ c > 2
20 +c > 18 ⇒ c > -2
18 +20 > c ⇒ c < 38
The possible lengths for the third side (c) are ...
2 < c < 38
That is, the third side must lie between the difference and the sum of the given sides.
The attachment shows the values on the list that are in this range.
Additive opposites x+4y=28 and -x+y=12 Is y equal to 8
For the additive opposites x+4y=28 and -x+y=12, yes, y is equal to 8.
How to solve the given system of equations?In order to solve the given system of equations, we would apply the substitution method. Based on the information provided above, we have the following system of equations:
x + 4y = 28 .......equation 1.
-x + y = 12 .......equation 2.
By making x the subject of formula in equation 2, we have the following:
x = y - 12 .......equation 3.
By using the substitution method to substitute equation 3 into equation 1, we have the following:
y - 12 + 4y = 28
5y = 28 + 12
5y = 40
y = 40/5
y = 8
Read more on equation here: brainly.com/question/28148072
#SPJ1
I neeeeeeed help. Pleaseeee helpppp. I dont get the last question like what am i supposed to do?
Answer:
0.1429
Step-by-step explanation:
The formula for the average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]. a = 0, b = 7, f(a) = 2, and f(b) = 3, We plus the numbers into the formula and get 0.1429 as our answer.
Find the probability of randomly choosing an ace or a club from a standard deck of cards. Remember that a standard deck consists of
52 cards, where each card is made up of a number or letter from {2, 3,4, 5, 6, 7, 8, 9, 10, J, Q, K, A} and a suit from {clubs, diamonds, hearts, spades
Answer: The probability of choosing an ace or a club is 16.
Step-by-step explanation:
Does the dollar belong inside the cash box or not? Explain your reasoning
We can see here that the dollar doesn't belong to the box.
How we arrived at the solution?We can see here that in order to known if the dollar belongs to the box or not, here is an explanation:
Let the single tickets = x
and the couples tickets = y
Note: $8 = 2 tickets (for couples),
Thus, 1 ticket = $4
5x + 4y = 200 -------(1)
x + y = 47 ----------- (2)
-4 × (2)
5x + 4y = 200 -------(1)
-4x - 4y = 188
x = 12
Substituting 12 in (2)
12 + y = 47
y = 47 - 12 = 35
y = 35
So, 5x + 4y = 200
5 (12) + 4 (35) = 200
60 + 140 = 200.
Thus, we see here that the dollar doesn't belong to the box.
Learn more about algebra on https://brainly.com/question/22399890
#SPJ1
The density of milk is 1.03g/cm^3. What is the mass of 405 cm^3 of milk?
A 393.2
B 1016.2
C 206.23
D 417.15g
please help!!
The mass of 405 cm³ of milk is 417.15 g.
To solve this problem need to use the formula:
mass = volume x density
The volume of milk given in the problem is 405 cm³ and the density of milk is 1.03 g/cm³.
Substitute these values in the formula to calculate the mass of the milk.
mass = 405 cm³ x 1.03 g/cm³
mass = 417.15 g
The mass of 405 cm³ of milk is 417.15 g.
To understand the concept behind this formula we need to understand what density is.
Density is defined as the amount of mass per unit volume of a substance.
It is expressed in units of grams per cubic centimeter (g/cm³) for solids and liquids.
The formula for calculating the mass of a substance is the product of its volume and density.
In this problem we have been given the volume and density of milk so we can easily calculate its mass using this formula.
The density of a substance can vary with changes in temperature and pressure.
For similar questions on mass
https://brainly.com/question/19385703
#SPJ11
Assume that ryan does save 10% for retirement if he allocate the remainder of his take-home pay to entertainment then what percent of the total budget will entertainment compromise how much money will the budget towards entertainment in each month
Entertainment will comprise 90% of Ryan's total budget. He will allocate 90% of his monthly income towards entertainment expenses.
How to solveAccording to the given information:
Let's assume Ryan's take-home pay is P dollars.
Assuming that Ryan puts aside 10% of his net income for his retirement plan, he will accumulate savings of 0.10P dollars.
After setting aside funds for retirement, the remaining portion of his net earnings will constitute 90% of the original amount, equating to 0.90P dollars.
Assuming that Ryan puts the remaining amount of his income towards entertainment, it is possible to determine the proportion of his overall expenses that entertainment would represent.
Percentage of entertainment budget = (Entertainment budget / Total budget) * 100
Given an overall budget of P dollars, with 0.90P dollars allotted for entertainment expenses, the proportion of the total budget that will be spent on entertainment can be calculated as a percentage.
Percentage of entertainment budget = (0.90P / P) * 100
Percentage of entertainment budget = 90%
So, entertainment will comprise 90% of Ryan's total budget.
He will allocate a monthly entertainment budget of 0.90P dollars, equivalent to 90% of his salary after taxes.
As such, the overwhelming majority of Ryan's budget will be allocated towards Entertainment. Every month, the entertainment allowance will constitute 90% of his net income as per the allocated budget.
Read more about Percentage here:
https://brainly.com/question/24877689
#SPJ1
write a paragraph of 10 lines where you explain how human actions to the surrounding cause causes health problems
Human actions and behaviors towards our surroundings can have significant implications for human health, leading to the emergence of various health problems.
How can human actions cause health problems ?Our choices and activities encompassing lifestyle, pollution, and resource utilization exert direct impacts on our overall well-being. For instance, our exposure to environmental pollutants, encompassing air and water contaminants, toxic substances, and hazardous waste, can engender respiratory ailments, cancer, and an array of severe health conditions.
Similarly, the degradation of natural habitats, deforestation, and unsustainable practices contribute to the proliferation of infectious diseases, disrupt ecological balance, and undermine the stability of our food systems.
Moreover, unhealthy dietary patterns, sedentary behaviors, and limited access to healthcare services compound the complexities of prevailing health issues.
Find out more on health problems at https://brainly.com/question/753908
#SPJ9
Which is the graph of linear inequality 2y > x-2?
543241
X
54321.
-2.
3
O
3 4 5 x
5432
S
25
es
4
4₁
25
n
C
The graph of the inequality is attached in the solution.
Given is an inequality, 2y > x-2, we need to graph it,
So, considering this as, 2y = x-2
Solving like a linear equation to get the points to plot,
So,
Put y = 0,
0 = x - 2
x = 2
(2, 0)
Put x = 0,
2y = 0-2
y = -1
(0, -1)
Hence the two points from which the graph will pass are (2, 0) and (0, -1).
Now, since the inequality has a > sign so the shaded area will be above the line and the line will be dotted.
Learn more about inequality click;
https://brainly.com/question/30231190
#SPJ1
Question 4 Dennis purchases a new bicycle from the bike shop. Using the output expenditure model, the purchase of the bicycle would be an example of business investment government spending consumer spending net exports
Using the output expenditure model, the purchase of the bicycle would be an example of C) consumer spending.
What is consumer spending?Consumer spending is the expenditure made for the purchase of final goods and services by individuals and households.
In this situation, Dennis as a consumer is not a business organization, government institution, or an exporter, but an individual.
The expenditure for the purchase of a new bicycle is an expense for a final good.
Thus, under the output expenditure model, the purchase of a new bicycle is not a business investment, government spending, or a net export, but it is a consumer spending.
Learn more about consumer spending at https://brainly.com/question/13282888.
#SPJ1
De 2. A barbeque shop sells sausage and brisket by the pound. The first customer
orders 2 pounds of sausage and 3 pounds of brisket for $21. The second
customer orders 10 pounds of sausage and 14 pounds of brisket for $100.50.
Which two equations can be used to create a system of equations in order to
find the cost per pound of sausage, s, and brisket, b?
Select TWO correct answers.
< PREVIOUS
(02)
8
De
8
8
8
2b + 3s = 21
25+ 3b 100.5
10s+ 14b 100.5
10b+ 14s 100.5
2s + 3b = 21
NEXT >
The cost per pound of sausage, s, and brisket, b is 10s + 14b = 100.5
We are given that;
First customer order= $21
Second customer order= $100.50
Now,
The two equations that can be used to create a system of equations are:
2s + 3b = 21 10s + 14b = 100.5
These equations are obtained by multiplying the cost per pound of sausage and brisket by the number of pounds ordered by each customer and setting them equal to the total cost for each customer. The variables s and b represent the cost per pound of sausage and brisket, respectively.
Therefore, by the equation the answer will be 10s + 14b = 100.5
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ1
pls help!!!!!!!!!!!!!!!!!!!!!!!!!!
The area of the regular polygon, given the apothem and the side length, would be 52. 5 in².
How to find the area ?To find the area of a regular pentagon with a given apothem (a) and side length (s), we can use the formula:
Area = ( Perimeter × Apothem ) / 2
Perimeter would be :
= 5 x sides
= 5 x 6
= 30 inch
The area is therefore :
= ( Perimeter × Apothem ) / 2
= ( 30 in x 3. 5 in ) / 2
= 105 / 2
= 52. 5 in²
Find out more on area at https://brainly.com/question/20110859
#SPJ1
Halla el menor de tres enteros impares consecutivos tales que 4 veces el entero del medio sea 14 más que la suma del primero y tercer enteros. Hecho
Solving a linear equation we can see that the smallest number is 5.
How to find the odd number?A set of 3 consecutive odd numbers can be written as:
x, x + 2, and x + 4
the middle one is x + 2, and we know that 4 times the second must be equal to the sum of the other two plus 14, then we can write the linear equation:
4*(x + 2) = x + x + 4 + 14
Solving this linear equation we will get:
4x + 8 = 2x + 18
4x -2 x= 18 - 8
2x = 10
dividing both sides by 2, we will get:
x = 10/2
x = 5
That is the smalles odd number.
Learn more about odd numbers at:
https://brainly.com/question/543861
#SPJ1
The revenue generated by a company manufacturing lawn mowers is R= -0.5x^2+91x, where x represents the number of mowers produced. The cost to produce the mowers is C= 38x+300,where x is the number of mowers produced.
Find the profit polynomial (Hint: Profit = Revenue - Cost) that describes the total profit generated by the company manufacturing lawn mowers based on the number of mowers produced.
--------------------------.
Give the profit earned if 53 mowers are sold. ------------
add work please
The profit generated by the company manufacturing lawnmowers is given by the polynomial -0.5x²+ 53x - 300, where x is the number of mowers produced.
The profit generated by the company manufacturing lawn mowers is the difference between the revenue and the cost, so we can subtract the cost polynomial C= 38x+300 from the revenue polynomial R= -0.5x²+91x to obtain the profit polynomial:
P(x) = R(x) - C(x)
P(x) = (-0.5x²+91x) - (38x+300)
P(x) = -0.5x² + 53x - 300
Therefore, the profit generated by the company manufacturing lawnmowers is given by the polynomial -0.5x²+ 53x - 300, where x is the number of mowers produced.
To know more about expression follow
https://brainly.com/question/27267719
#SPJ1
What is the meaning of "when [tex] x_{1}, ..., x_{n}[/tex] are permuted in all possible ways, the number of different values of [tex]f (x_{1}, ..., x_{n})[/tex] is a divisor of n!"?
The meaning of the statement is if you take n distinct numbers, x₁, ..., xₙ, and permute them in all possible ways, the number of different values that the function f(x₁, ..., xₙ) can take on will be a divisor of n!.
How to explain the concept ?This assertion is a specific instance of a broader concept known as the Principle of Inclusion-Exclusion in the field of combinatorics. The Principle of Inclusion-Exclusion asserts that when dealing with a set comprising n elements and aiming to determine the number of possible subsets that can be selected, one can arrive at this figure by summing up the number of options for choosing 0, 1, 2, and up to n elements from the set.
Regarding the aforementioned assertion, the collection of components comprises every potential arrangement of the numerical values x₁, ..., xₙ. There is only one possible way to choose 0 elements, there are n options for choosing 1 element, selecting 2 elements can be done in n(n-1)/2 ways, and the pattern continues.
Find out more on the Principle of Inclusion-Exclusion at https://brainly.com/question/30995367
#SPJ1
Given that events A and B are independent with P(A) = 0.68 and
P(A and B) = 0.544, determine the value of P(B), rounding to the nearest
thousandth, if necessary.
The value of P (B) = 0.8
The probability of event A, P (A) = 0.68
The probability of events A and B, P (A ∩ B) = 0.544
The probability of event B, P (B) = ?
We know that Independent events are those where the probability of A event occurring doesn't affect the probability of B event. In other words, they don't depend upon each other and are independent.
By formula;
P (A ∩ B) = P (A) . P (B)
By substituting the values to the above equation, we get;
0.544= 0.68 * P (B)
P (B) = 0.8
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ1
Consider a circle whose equation is x2 + y2 -2x -8 =0. Which statements are true? Select three options
The three statements which are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² .......equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
Based on the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
By comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x - 0)² + (y - 0)² = 3²
x² + y² = 9.
Read more on equation of a circle here: brainly.com/question/17028215
#SPJ1
Complete Question:
Consider a circle whose equation is x² + y² – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.