Answer:
See answer below
Step-by-step explanation:
In inductive reasoning we arrive to a general conclusion based on particular observations.
For example:
"My friends Peter and Mary study at XYZ University. Peter and Mary are brilliant.
Yesterday I met Joe in a party. Joe also studies at XYZ University and he happens to be brilliant, too.
I conclude that all the students of XYZ University are brilliant"
Notice that this kind of reasoning might lead to a false conclusion.
In deductive reasoning, we arrive to a particular conclusion based on general observations. So, deductive reasoning is the opposite of inductive reasoning.
An example of deductive reasoning could be the following:
"To be accepted in the XYZ University you must pass a test with a score greater than 70%.
My friend Peter studies at XYZ University, so he passed the test with a score greater than 70%"
In deductive reasoning you may arrive to a false conclusion if your general assumption is false.
Answer:
but did now am the am
Step-by-step explanation:
You have decided to invest $1000 in a savings bond that pays 4% interest, compounded semi-annually. What will the bond be worth if you cash it in 10 years from now?
N= I/Y= PV= PMT= FV= P/Y=
Answer:
$2191.12
Step-by-step explanation:
We are asked to find the value of a bond after 10 years, if you invest $1000 in a savings bond that pays 4% interest, compounded semi-annually.
[tex]FV=C_0\times (1+r)^n[/tex], where,
[tex]C_0=\text{Initial amount}[/tex],
r = Rate of return in decimal form.
n = Number of periods.
Since interest is compounded semi-annually, so 'n' will be 2 times 10 that is 20.
[tex]4\%=\frac{4}{100}=0.04[/tex]
[tex]FV=\$1,000\times (1+0.04)^{20}[/tex]
[tex]FV=\$1,000\times (1.04)^{20}[/tex]
[tex]FV=\$1,000\times 2.1911231430334194[/tex]
[tex]FV=\$2191.1231430334194[/tex]
[tex]FV\approx \$2191.12[/tex]
Therefore, the bond would be $2191.12 worth in 10 years.
What is an essential goal of a programmer and why?
Answer: A programmer is the person who is responsible for making computer programs.He/she makes sure that the program is created according to the requirement and accurate performing operations .The goals of the programmer are as follows:-
Keep progressing in the field of computer programmingLearning various new programming languages and technologiesEnhancing the skills to be in this field for long -run of timeGrabbing the opportunities as programmer for improvementProgrammer is indulged in these goals because there are always upcoming new technologies in the field of programming so, to keep theirselves updates and maintain their skill they improve theirselves time to time. Also it can affect the job of the programmer if they are not aware about programming skills quite well or might end up losing the job.
At a grocery store, Daniel wants to buy 3 lb of ham.
What decimal should the digital scale show?
Write 3 as a fraction and then divide.
The scale should read
The digital scale should display 3.0 when weighing 3 lbs of ham. This is because 3 pounds exactly can be displayed as the decimal 3.0 after converting the number into a fraction, 3/1, and dividing the numerator by the denominator.
Explanation:When Daniel wants to buy 3 lb of ham, the digital scale at the grocery store should display the decimal 3.0. This is because 3 pounds exactly translates to 3.0 in decimal terms.
The process of converting a number like 3 into a fraction would begin by writing it as 3/1 (as any number can be written over 1).
To convert that into decimal form, you would divide the top number (numerator) by the bottom number (denominator), so 3 ÷ 1 = 3.0.
Thus, the digital scale should read 3.0 when Daniel weighs out his 3 lbs of ham.
Learn more about Decimal Conversion here:https://brainly.com/question/34390573
#SPJ1
In the xy plane, a quadrilateral has vertices at (-1, 4), (7,4), (7,5), and (-1. 5). What is the perimeter of the quadrilateral? (A) 17 (B) 18 (C) 19 (1) 32 (E) 34
Answer:
(B) 18.
Step-by-step explanation:
We are asked to find the perimeter of a quadrilateral with vertices at (-1, 4), (7,4), (7,5), and (-1. 5).
First of all, we will draw vertices of quadrilateral on coordinate plane and connect the vertices as shown in the attached photo.
We can see that our quadrilateral is a parallelogram, whose parallel sides are equal.
[tex]\text{Perimeter of quadrilateral}=8+1+8+1[/tex]
[tex]\text{Perimeter of quadrilateral}=16+2[/tex]
[tex]\text{Perimeter of quadrilateral}=18[/tex]
Therefore, the perimeter of the given quadrilateral is 18 units.
Solve the Following Initial Value Problem: 2XYY'+Y^2-4X^3=0. where Y(1)=2
The answer is y= sqrt((x^4+3)/x)
[tex]2xyy'+y^2-4x^3=0[/tex]
Let [tex]z(x)=y(x)^2[/tex], so that [tex]z'(x)=2y(x)y'(x)[/tex] (which appears in the first term on the left side):
[tex]xz'+z=4x^3[/tex]
This ODE is linear in [tex]z[/tex], and we don't have to find any integrating factor because the left side is already the derivative of a product:
[tex](xz)'=4x^3\implies xz=x^4+C\implies z=\dfrac{x^4+C}x[/tex]
[tex]\implies y(x)=\sqrt{\dfrac{x^4+C}x}[/tex]
With [tex]y(1)=2[/tex], we get
[tex]2=\sqrt{1+C}\implies C=3[/tex]
so the solution is as given in your post.
An airplane flying at an altitude of 30,000 feet flies up to avoid a storm. Immediately after passing the storm, the airplane returns to its original altitude. What integer represents the airplane's change in altitude to avoid the storm? What integer represents the altitude after passing the storm?
Answer:
The integer representing the change of altitude to avoid the storm is 8,000
The integer representing the altitude after passing the storm is 30,000
Explanation:
The diagram of this question is shown in the attached image
We are given that the initial altitude of the plane was 30,000 ft
1- During the storm:
The plane flew at at altitude of 38,000 feet
To get the change in the altitude, we will subtract the final altitude from the initial one
change of altitude = final altitude - initial altitude
change of altitude = 38,000 - 30,000 = 8,000 ft
Therefore, the integer representing the change of altitude to avoid the storm is 8,000
2- After the storm:
We know that, after the storm, the plane returned to its initial altitude
Given that the initial altitude is 30,000 ft, this would mean that the integer representing the altitude after passing the storm is 30,000
Hope this helps :)
Final answer:
The integer representing the change in altitude when the airplane avoided the storm and then returned to its original altitude is zero. The altitude after passing the storm is 30,000 feet, the same as its original altitude before the ascent.
Explanation:
The integer representing the airplane's change in altitude to avoid the storm is zero because it returned to its original altitude after passing the storm. During the avoidance maneuver, the airplane would have increased in altitude (a positive change) and then decreased the same amount to return to its original altitude (a negative change). The sum of this positive and negative change is zero.
The integer representing the altitude after passing the storm is 30,000 feet, which is the same as the original altitude since the airplane returned to this altitude after avoiding the storm.
When considering aircraft performance, it's vital to take into account the rate of climb and descent, potential energy swaps from kinetic energy, and altitude effects on aircraft performance. However, in this instance, the specific figure for altitude change during the storm avoidance is not given, but the concept of returning to starting altitude implies no net change.
Consider the quadratic function f(x)=−x^2+4x+12
Determine the following:
The smallest xx-intercept is x=Incorrect
The largest xx-intercept is x=
The yy-intercept is y=
Answer:
a) -2 from (-2,0) b) 6 from (6,0) c) y-intercept: 12 from (0,12)
Step-by-step explanation:
The X intercepts in a quadratic function are the points of the x-axis crossed by the parabola. One quadratic equation may have up to two points on the X-axis. This or these points in the X-axis, the Zeros of this function, will be crossed by the parabola.
The Y-intercept is the point of the y-axis crossed by the parabola.
Solving the equation:
[tex]-x^{2} +4x+12=0\\ x'=\frac{-4+\sqrt{64}}{-2} \\ x"=\frac{-4-\sqrt{64}}{-2} \\ x'=-2\\ x"=6\\[/tex]
S={-2, 6} These values, or zeros of this quadratic function are the X, intercepts.
c) The indepent term, or c, in f(x)= ax²+bx+c in this case is 12, also is the Y coordinate for the Parabola Vertex. This point is our intercept for y.
What of the following basic rules is true about geometry?
A. Opposite angles are equal when two straight lines intersect
B. Supplementary angles total 180°
C. Complementary angles total 90°
D. A, B, and C
E. None of the above
Answer:
D. A, B, and C
Step-by-step explanation:
Option (A) is true because when two straight lines intersect to each other we get two pair of vertically opposite angles and the angles opposite to each other is always equal.
Option (B) is also correct as If the sum of two angles is equal to 180°, then they are supplementary to each other.
Option (C) is also correct as If the sum of the two angles is equal to 90°, then they are Complementary to each other.
Hence, Option (D) is correct.
The local pet store surveyed 50 people about pets. Eleven of these people owned dogs, 13 owned cats, and 6 owned fish. One person owned all three types of pets, 2 people owned only fish and dogs, 3 people only fish and cats, and 5 people owned only cats and dogs. How many people owned none of these pets?
Answer: 29
Step-by-step explanation:
Let S denotes the total number of people surveyed, A denotes the event of having dog , B denotes the event of having cats and C denotes the event of having fish.
Given : n(S)=50 ;n(A)=11 ; n(B) =13 and n(C)=6
Also, n(A∩B)=5 ; n(A∩C) = 2 and n(B∩C)=3 and n(A∩B∩C)=1
We know that,
[tex]n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A \cap B)-n(A \cap C)-n(B \cap C)-n(A \cap B\cap C)\\\\=11+13+6-5-2-3+1=21[/tex]
Now, the number of people owned none of these pets :-
[tex]n(S)-n(A\cup B\cup C)\\\\=50-21=29[/tex]
Hence, the number of people owned none of these pets =29
determine the payment to amortized the debt quarterly payments on $16,500 at 3.6% for 6 years
Answer:
$767.49
Step-by-step explanation:
given,
Amount of money = $16,500
quarterly rate = 3.6/4 = 0.9 %
times = 6 × 4 = 24 quarters.
[tex]A =\dfrac{P(r(1+r)^n)}{(1+r)^n-1}\\\\A =\dfrac{16500\times(0.009(1+0.009)^{24})}{(1+0.009)^{24}-1}\\A = \$ 767.49[/tex]
hence, the payment to amortize the dept will be equal to $767.49 .
A penalty in Meteor - Mania is - 5 seconds. A penalty in Cosmic Calamity is - 7 seconds. Yolanda had penalties totaling -25 seconds in a game of meteor- Mania and -35 seconds in a game of Cosmic Calamity. In which game did Yolanda receive more penalties? Justify the answer.
Answer:
Yolanda had the same number of penalties in both games.
Step-by-step explanation:
Both of these penalties can be modeled by a first order equation.
Game of Meteor-Mania:
In a game of Meteor-Mania, each penalty is -5 seconds. So the expression for the total of penalties is:
Tp(n) = -5*n, where n is the number of penalties.
In the game of Meteor-Mania, Yolanda had penalties totaling -25 seconds. So
-25 = -5*n *(-1)
5n = 25
n = 25/5
n = 5
Yolanda had 5 penalties in the game of Meteor-Mania
Game of Cosmic Calamity
In a game of Meteor-Mania, each penalty is -7 seconds. So the expression for the total of penalties is:
Tp(n) = -7*n, where n is the number of penalties.
In the game of Cosmic Calamity, Yolanda had penalties totaling -35 seconds. So
-35 = -7n *(-1)
7n = 35
n = 35/7
n = 5
Yolanda had 5 penalties in the game of Cosmic Calamity
Yolanda had the same number of penalties in both games.
Tour players Harry, Ron, Harmione and Ginny are playing a card game. A deck of 52 cards are dealt out equally. If Harmione and Ginny have a total of 8 spades among them, what is the probability that Harry has 3 of the remaining 5 spades?
Answer: 0.339
Step-by-step explanation:
Given : Tour players Harry, Ron, Harmione and Ginny are playing a card game.
. A deck of 52 cards are dealt out equally.
Then, the number of card each person has = [tex]\dfrac{52}{4}=13[/tex]
If Harmione and Ginny have a total of 8 spades among them, then the total cards the total spades left = 13-8=5
Now, the number of ways to get 3 of 5 spades : [tex]^5C_3=\dfrac{5!}{3!2!}=10[/tex]
Number of ways to draw remaining 10 cards : [tex]^{21}C_{10}=\dfrac{21!}{10!11!}=352716[/tex]
Also, the total cards Harmione and Ginny have = 13+13=26
Then the total cards left = 26
The number of ways to get 13 cards for Harry :
[tex]^{26}C_{13}=\dfrac{26!}{13!(26-13)!}\\\\=\dfrac{26!}{13!13!}=10400600[/tex]
Now, the probability that Harry has 3 of the remaining 5 spades :_
[tex]\dfrac{^5C_3\times ^{21}C_{10}}{^{26}C_{13}}\\\\=\dfrac{10\times352716}{10400600}\\\\=0.339130434783\approx0.339[/tex]
Hence, the probability that Harry has 3 of the remaining 5 spades= 0.339 (approx)
Prove that x-1 is a factor of x^n-1 for any positive integer n.
Answer:
[tex]x-1[/tex] is a factor of [tex]x^n - 1[/tex]
Step-by-step explanation:
[tex]x-1[/tex] is a factor of [tex]x^n - 1[/tex]
We will prove this with the help of principal of mathematical induction.
For n = 1, [tex]x-1[/tex] is a factor [tex]x-1[/tex], which is true.
Let the given statement be true for n = k that is [tex]x-1[/tex] is a factor of [tex]x^k - 1[/tex].
Thus, [tex]x^k - 1[/tex] can be written equal to [tex]y(x-1)[/tex], where y is an integer.
Now, we will prove that the given statement is true for n = k+1
[tex]x^{k+1} - 1\\=(x-1)x^k + x^k - 1\\=(x-1)x^k + y(x-1)\\(x-1)(x^k + y)[/tex]
Thus, [tex]x^k - 1[/tex] is divisible by [tex]x-1[/tex].
Hence, by principle of mathematical induction, the given statement is true for all natural numbers,n.
Determine whether the following possible responses should be classified as ratio, interval, nominal or ordinal data.
? Ratio Ordinal Nominal Interval 1. The college (Arts and Science, Business, etc.) you are enrolled in
? Ratio Ordinal Nominal Interval 2. The number of students in a statistics course
? Ratio Ordinal Nominal Interval 3. The age of each of your classmates
? Ratio Ordinal Nominal Interval 4. Your hometown
Answer:
1. The college (Arts and Science, Business, etc.) you are enrolled in
Nominal
2. The number of students in a statistics course Ratio
3. The age of each of your classmates Ratio
4. Your hometown Nominal
Step-by-step explanation:
Nominal, ordinal, interval, or ratio data are the four fundamental levels of measurement scales that are used to capture data.
Nominal, are used for labeling variables, without any quantitative value.
Ordinal, the order of the values is what is significant, but the differences between each one is not really known.
Interval, we know both, the order and the exact differences between the values
Ratio, they have the order, the exact value between units, and have an absolute zero
Help! BRANLIEST and 300 points!!! Plz show ALL your steps.
PB is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?
Step-by-step explanation:
(12 + -2 )/2
10/2
5 im pretty sure
What is the lenght of a diagonal of a square with sides 16feet
long ? Round to the nearest tenth.
Answer:
The length of the diagonal is 22.6 ft.
Step-by-step explanation:
To find the length of the diagonal of a square, multiply the length of one side by the square root of 2:
If the length of one side is x, [tex]length = x\sqrt{2}[/tex] as you can see in the image attached.
This fact is a consequence of applying the Pythagoras' Theorem to find the length of the diagonal if we know the side length of the square.
[tex]length^{2} = x^{2}+x^{2} \\ length=\sqrt{x^{2}+x^{2}} \\ length=\sqrt{2x^{2} } \\ length=x\sqrt{2}[/tex]
We know that the length of one side is 16 ft so [tex]length = 16\sqrt{2}=22.627[/tex] and round to the nearest tenth is 22.6 ft
As the owner of a small restaurant, you purchase 5 boxes of napkins for $75.00 every 3 months. Each box contains 525 napkins. To the nearest hundredth, what is the cost for each individual napkin?
As the owner of a small restaurant, you purchase 5 boxes of napkins for $75.00 every 3 months. Each box contains 525 napkins. To the nearest hundredth, what is the cost for each individual napkin?
A) 0.01
B) 0.02
C) 0.03
D) 0.05
Answer: 0.03
Step-by-step explanation:
Total number of napkins: 5 x 525 = 2,625
75/2626 = 0.02857, which rounds to 0.03
The cost per individual napkin, when rounded to the nearest hundredth, is $0.03.
Explanation:To begin finding the cost per napkin, we first need to find out how many napkins are purchased every 3 months. Since each box contains 525 napkins and you purchase 5 boxes every 3 months, that would be 525 * 5 = 2625 napkins. The cost of these napkins is $75.00.
So, to find the cost per individual napkin, you would divide the total cost by the total number of napkins. That would be 75 / 2625 = $0.028571... When rounded to the nearest hundredth, this becomes $0.03. So, each individual napkin costs $0.03. Therefore, the correct answer is (C) 0.03.
Learn more about Cost per Napkin here:https://brainly.com/question/34904419
#SPJ3
A small restaurant has a menu with 2 appetizers, 5 main courses, and 3 desserts. (a) How many meals are possible if each includes an main course and a dessert, but may or may not include an appetizer? (b) What if the dessert is also not required?
Answer: a) 45 b) 60
Step-by-step explanation:
Given : A small restaurant has a menu with 2 appetizers, 5 main courses, and 3 desserts.
a) Number of meals includes an main course , a dessert and a appetizer, :-
[tex]2\times5\times3=30[/tex]
Number of meals includes an main course and a dessert and but not appetizer , then total possible meals:-
[tex]5\times3=15[/tex]
Then, the number of meals are possible if each includes an main course and a dessert, but may or may not include an appetizer= 30+15=45
b) Number of meals includes an main course and appetizer but not dessert:
[tex]5\times2=10[/tex]
Number of meals includes only main course =5
Now, the number of meals if dessert is also not required= 45+5+10=60
A piecewise function is shown below
g(x) = { -3x^2 -2x+8 for -4 ≦ x < 1
-2x+7p for 1 ≦ x ≦ 5
(a) for what value of p will the function be continuous
(b) Because one piece stops and the next piece starts at the point identified in part a, the pieces can be set equal to each other to find p. Fine p. Show your work. If you did everything on a calculator, explain the steps you took and include screenshots of each step.
Answer:
p = 5/7
Step-by-step explanation:
The given function is:
[tex]g(x) = -3x^{2} - 2x + 8[/tex] for -4 ≦ x < 1
[tex]g(x) = -2x + 7p[/tex] for 1 ≦ x ≦ 5
Part a)
A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5
The point where, g(x) stops during the first interval is at x = 1, which will be:
[tex]-3(1)^{2}-2(1)+8=3[/tex]
The point where g(x) starts during the second interval is:
[tex]-2(1)+7(p) = 7p - 2[/tex]
For the function to be continuous, these two points must be equal. Setting them equal, we get:
3 = 7p - 2
3 + 2 = 7p
p = [tex]\frac{5}{7}[/tex]
Thus the value of p for which g(x) will be continuous is [tex]\frac{5}{7}[/tex].
Part b)
We have to find p by setting the two pieces equal to each other. So, we get the equation as:
[tex]-3x^{2}-2x+8=-2x+7p\\\\ -3x^{2}+8=7p[/tex]
Substituting the point identified in part (a) i.e. x=1, we get:
[tex]-3(1)^{2}+8=7p\\\\ 5=7p\\\\ p=\frac{5}{7}[/tex]
This value agrees with the answer found in previous part.
A hemispherical bowl of radius 12 inches is filled to a depth of h inches, where 0less than or equalshless than or equals12. Find the volume of water in the bowl as a function of h. (Check the special cases hequals0 and hequals12.)
Answer:
Suppose the bowl is situated such that the rim of the bowl touches the x axis, and the semicircular cross section of the bowl lies below the x-axis (in (iii) and (iv) quadrant ). Then the equation of the cross section of the bowl would be [tex]x^2+y^2=144[/tex], where y≤ 0,
⇒ [tex]y=-\sqrt{144-x^2}[/tex]
Here, h represents the depth of water,
Thus, by using shell method,
The volume of the disk would be,
[tex]V(h) = \pi \int_{-12}^{-12+h} x^2 dx[/tex]
[tex]= \pi \int_{-12}^{-12+h} (144-y^2) dy[/tex]
[tex]= \pi |144y-\frac{y^3}{3}|_{-12}^{-12+h}[/tex]
[tex]=\pi [ (144(-12+h)-\frac{(-12+h)^3}{3}-144(-12)+\frac{(-12)^3}{3}}][/tex]
[tex]=\pi [ -1728 + 144h - \frac{1}{3}(-1728+h^3+432h-36h^2)+1728-\frac{1728}{3}][/tex]
[tex]=\pi [ 144h - \frac{1}{3}(h^3+432h-36h^2}{3}][/tex]
[tex]=\pi [ 144h - \frac{h^3}{3} - 144h + 12h^2][/tex]
[tex]=\pi ( 12h^2 - \frac{h^3}{3})[/tex]
Special cases :
If h = 0,
[tex]V(0) = 0[/tex]
If h = 12,
[tex]V(12) = \pi ( 1728 - 576) = 1152\pi [/tex]
Jorgensens, an Electronics
distributor, just received ashipment of 12 DVDPlayers. Shortly after arrival the
manufacturer called to saythat that he had accidentally shipped
five defective units with theshipment. Mr. Jorgensen immediately
pulled ten of the unitsand tested two of them. What is the
probability that neitherof them was defective?
Answer: 0.3399
Step-by-step explanation:
The binomial probability distribution formula to find the probability of getting success in x trial:-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where n is the number of trials and p is the probability of getting success in each trial.
Given : Jorgensens received a shipment of 12 DVD Players. Shortly after arrival the manufacturer called to say that that he had accidentally shipped five defective units with the shipment.
i.e. The proportion of the defective units : [tex]p=\dfrac{5}{12}\approx0.417[/tex]
Also, Mr. Jorgensen pulled ten of the units and tested two of them.
For n=2, the probability that neither of them was defective:-
[tex]P(x=0)=^{2}C_0(0.417)^0(1-0.417)^{2}\\\\=(1)(1)(0.583)^{2}\ \ \ [\text{ Since}^nC_0=1]\\\\=0.339889\approx0.3399[/tex]
Hence, the probability that neither of them was defective = 0.3399
Dr. Fitzgerald has graded 15 of 26 exams for Epi 501. (a) What proportion of all exams has Dr. Fitzgerald graded? (b) What was the ratio of graded to ungraded tests?
Answer: a) 15:26, and b) 15:11.
Step-by-step explanation:
Since we have given that
Number of graded tests = 15
Number of total tests = 26
Number of ungraded tests is given by
[tex]26-15\\\\=11[/tex]
a) Proportion of all exams has Dr. Fitxgerald graded is given by
15:26.
b) Ratio of graded to ungraded tests is given by 15:11
Hence, a) 15:26, and b) 15:11.
(a) The proportion of all exams graded by Dr. Fitzgerald is [tex]\(\frac{15}{26}\)[/tex].
(b) The ratio of graded to ungraded tests is [tex]\(\frac{15}{26 - 15}\) or \(\frac{15}{11}\)[/tex].
(a) To find the proportion of exams graded by Dr. Fitzgerald, we divide the number of exams graded by the total number of exams. This gives us the fraction:
[tex]\[ \text{Proportion graded} = \frac{\text{Number of exams graded}}{\text{Total number of exams}} = \frac{15}{26} \][/tex]
This fraction represents the part of the whole set of exams that has been graded.
(b) To find the ratio of graded to ungraded tests, we take the number of exams that have been graded and divide it by the number of exams that have not been graded. The number of ungraded exams is the total number of exams minus the number of graded exams:
[tex]\[ \text{Number of ungraded exams} = \text{Total number of exams} - \text{Number of exams graded} = 26 - 15 = 11 \][/tex]
Now, we can find the ratio:
[tex]\[ \text{Ratio of graded to ungraded tests} = \frac{\text{Number of exams graded}}{\text{Number of exams ungraded}} = \frac{15}{11} \][/tex]
This ratio tells us how many times greater the number of graded exams is compared to the number of ungraded exams.
The CEO of a company that sells car stereos has determined the profit of selling x number of stereos to be: P(x) = –.04x2 + 1000x – 16,500 How much profit should the company expect from selling 12,500 stereos?
Answer:
6233500
Step-by-step explanation:
We are given that CEO of a company that sells car stereos has determined the profit x number of stereos.
The profit of selling x number of stereos is given by
[tex]P(x)=-0.04x^2=100x-16500[/tex]
We have to find the value of profit when the company selling 12500 stereos.
Substitute the value of x=12500
Then, we get
[tex]P(12500)=-.04(12500)^2+1000(12500)-16500[/tex]
[tex]P(12500)=-6250000+12500000-16500=-6266500+12500000[/tex]
[tex]P(12500)=6233500[/tex]
Hence, the company should expect profit 6233500 from selling 12500 stereos.
Are the points (-4,-1), (2,1) and (11,4) collinear? Justify your answer.
Answer: Yes , the points (-4,-1), (2,1) and (11,4) are collinear.
Step-by-step explanation:
We know that if three points [tex](x_1,y_1),(x_2,y_2)[/tex] and [tex](x_3,y_3)[/tex] are collinear, then their area must be zero.
The area of triangle passes through points[tex](x_1,y_1),(x_2,y_2)[/tex] and [tex](x_3,y_3)[/tex] is given by :-
[tex]\text{Area}=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Given points : (-4,-1), (2,1) and (11,4)
Then, the area of ΔABC will be :-
[tex]\text{Area}=\dfrac{1}{2}|-4(1-4)+(2)(4-(-1))+(11)(-1-1)|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|-4(-3)+(2)(5)+(11)(-2)||\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|12+10-22|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|0|=0 [/tex]
Hence, the points (-4,-1), (2,1) and (11,4) are collinear.
Find the length of the median of a trapezoid if the length
ofthe shorter base is 16cm and the length of the longer base
is24cm.
Answer:
20 cm
Step-by-step explanation:
We are given a trapezoid, where the length of shorter base or on of the parllel line is 16 cm and the length of other parallel side is 24 cm.
Let the two parallel sides be x and y that is x = 16 cm and y = 24 cm.
A median of a trapezoid is a line segment that divides the non parallel sides of a trapezoid equally or a line segment that passes through the mid points of non-parallel sides of a trapezoid.
The length of median of a trapezoid = [tex]\frac{\text{Sum of parallel sides}}{2}[/tex] = [tex]\frac{16+24}{2}[/tex] = 20 cm.
Thus, the length of median of trapezoid is 20 cm.
Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units, two-bedroom townhouses, and three-bedroom townhouses. A total of 216 units is planned. The total number of two- and three-bedroom townhouses will equal the number of one-bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom townhouses, find how many units of each type will be in the complex. one-bedroom units units two-bedroom townhouses units three-bedroom townhouses units
Answer:
108 one-bedroom units
72 two-bedroom units
36 three-bedroom units
Step-by-step explanation:
Let x, y, z the number of one-bedroom, two-bedroom and three-bedroom units respectively. Then
1) x+y+z = 216
2) y+z = x
3) x = 3z
Multiplying equation 1) by -1 and adding it to 2), we get
-x = x-216 so, x = 216/2 = 108
x = 108
Replacing this value in 3) we get
z = 108/3 = 36
z = 36
Replacing now in 2)
y+36 = 108, y = 108-36 and
y = 72
In the planned apartment complex, there will be 0 one-bedroom units, 216 two-bedroom townhouses, and 0 three-bedroom townhouses.
Explanation:Let x be the number of one-bedroom units. Since the number of two- and three-bedroom townhouses equals the number of one-bedroom units, let y be the number of two-bedroom townhouses and z be the number of three-bedroom townhouses. We know that x + y + z = 216. Additionally, x = 3z because the number of one-bedroom units will be 3 times the number of three-bedroom townhouses. Substituting x = 3z into the first equation gives 3z + y + z = 216. Simplifying this equation, we get 4z + y = 216.
Now, we can solve this system of equations to find the values of x, y, and z. Subtracting y from both sides of the equation 4z + y = 216 gives 4z = 216 - y. Let's call this equation (1). Substituting x = 3z and y = 216 - 4z into the equation x + y + z = 216 gives 3z + (216 - 4z) + z = 216. Simplifying this equation, we get 4z + 216 = 216. Subtracting 216 from both sides of the equation gives 4z = 0. Let's call this equation (2).
Since equation (1) and equation (2) both have 4z on the left side, we can equate the right sides of the equations. This gives 216 - y = 0. Solving for y, we find y = 216. Plugging this value of y into equation (1), we get 4z = 216 - 216, which simplifies to 4z = 0. Solving for z, we find z = 0. Finally, plugging the value of z into the equation x = 3z, we get x = 3(0), which simplifies to x = 0.
Therefore, there are 0 one-bedroom units, 216 two-bedroom townhouses, and 0 three-bedroom townhouses in the complex.
Suppose that f is a differentiable function of one variable. Show that all the tangent Planes to the the surface z = xf (y / x) intersect in a common point.
Answer:
If [tex]P_0 (x_0,y_0,z_0)[/tex] is a point on the surface, then the cartesian equation of the tangent plane at [tex]P_0 (x_0,y_0,z_0)[/tex] is
[tex](\ast)z = z_0 + \frac{\partial z}{ \partial x}(x_0,y_0)\cdot (x -x_0) + \frac{\partial z}{\partial y} (x_0, y_0) (y -y_0)[/tex],
where [tex]z_0 = x_0 f \left ( \frac{y_0}{x_0}\right )[/tex].
Given that
[tex]\frac{\partial z}{\partial x} (x_0 , y_0) = f \left( \frac{y_0}{x_0}\right ) - \frac{y_0}{x_0} \cdot \frac{\partial f}{\partial x}(x_0,y_0) \ , \ \frac{\partial z}{\partial y} (x_0 , y_0)=\frac{\partial f}{\partial y} (x_0,y_0)[/tex], then
[tex](\ast)[/tex] becomes
[tex](\ast \ast) z=x_0 f \left ( \frac{y_0}{x_0}\right ) + f \left( \frac{y_0}{x_0}\right ) - \frac{y_0}{x_0}\cdot \frac{\partial f}{\partial x} (x_0,y_0)\cdot (x -x_0)+\frac{\partial f}{\partial y} (x_0,y_0)\cdot (y -y_0)[/tex].
Finally, replacing [tex] (x,y,z)=(0,0,0)[/tex] in [tex](\ast \ast)[/tex] you have that the equality is true for all [tex]P_0[/tex]. This means that [tex]O(0,0,0)[/tex]
belongs to all tangent planes and therefore, the result follows.
Calculate:
3 pounds (lbs) =——grams (g)
Answer:
1360.78 g
Step-by-step explanation:
1 lb = 453.592 g
3 lbs = 3 * 453.592 g = 1360.78 g
Total departmental sales in the Housewares Department were $513000.00. A salesperson made 14% of the total departmental sales of that month and earns 6.5% commission on his sales. Find the dollar amount of commission.
a.
$33345.00
b.
$4691.95
c.
$4668.30
d.
$71820.00
e.
$4683.19
f.
None of the above.
Answer: c. $4668.30
Explanation:
Given:
Sales = $513000
Sales made by an individual = 14% of $513000
Sales made by an individual = [tex]\frac{14}{100}\times 513000[/tex]
Sales made by an individual = $71280
Commission made on this sales = 6.5% of $71280
Commission made on this sales = [tex]\frac{6.5}{100}\times 71280[/tex]
Commission made on this sales = $4668.30
In experiment two, I measured a block to be 4.45 cm by 3.35 em by 6.15 cm and a mass of 155.147g. What is the density of this block in kg/L? 3.
Answer:
1.69224581396 Kg/L
Step-by-step explanation:
We are given the measure of the block as 4.45 cm × 3.35 cm × 6.15 cm.
Volume of block = 4.45 cm × 3.35 cm × 6.15 cm = 91.681125 cm cube = 91.681125 × 0.001 L = 0.091681125 L
We did the above step to convert the volume of block into Liter.
Mass of block is given as 155.147 gram = 155.147 × 0.001 kg = 0.155147 kg
We converted the mass of block into kilograms because we need density in Kg/L.
Density is defined as mass per unit volume
Density = [tex]\frac{Mass}{Volume}[/tex]
= [tex]\frac{0.155147 }{0.091681125}[/tex]]
= 1.69224581396 Kg/L
The density is found to be approximately 1.688 kg/L.
To find the density of the block, we need to use the density formula:
Density = Mass / Volume
The given dimensions of the block are:
Length = 4.45 cmWidth = 3.35 cmHeight = 6.15 cmFirst, calculate the volume:
Volume = Length × Width × Height
Volume = 4.45 cm × 3.35 cm × 6.15 cm
Volume ≈ 91.88925 cubic centimeters (cm)
Next, convert mass to kilograms and volume to liters:
Mass = 155.147 g = 0.155147 kg (since 1 kg = 1000 g)Volume = 91.88925 cm³ × 0.001 L/cm³ ≈ 0.09188925 L (since 1 cm³ = 0.001 L)Finally, calculate the density in kg/L:
Density = Mass / Volume
Density ≈ 0.155147 kg / 0.09188925 L
Density ≈ 1.688 kg/L
Thus, the density of the block is approximately 1.688 kg/L.