She would offer to split the cookies evenly, so they each get 4.
If she offered Max less than 4, he would not accept and their dad would eat half, so each person would only get 2 cookies each.
If she offered Max more than 4, then she doesn't maximize the amount she would get.
PLEASE HELP I ONLY NEED THIS ONE TO FINISH THE SECTION
The functions r and s are defined as follows.
r(x) = -2x + 1
s(x) = -x^2 + 2
Find the value of .
r(s(3))
Answer:
The value of r(s(3)) = -21
Step-by-step explanation:
It is given that,
r(x) = -2x + 1
s(x) = -x^2 + 2
To find the value of r(s(3))
s(x) = -x^2 + 2
s(3) = (-3)^2 + 2 [Substitute 3 instead of x]
= 9 + 2
= 11
Therefore s(3) = 11
r(x) = -2x + 1
r(s(3)) = r(11) [Substitute 11 instead of x]
= -2(11) + 1
= -22 + 1
= -21
Therefore the value of r(s(3)) = -21
The answer is:
[tex]r(s(3))=15[/tex]
Why?To solve the problem, first, we need to compose the functions, and then evaluate the obtained function. Composing function means evaluating a function into another function.
We have that:
[tex]f(g(x))=f(x)\circ g(x)[/tex]
From the statement we know the functions:
[tex]r(x)=-2x+1\\s(x)=-x^{2}+2[/tex]
We need to evaluate the function "s" into the function "r", so:
[tex]r(s(x))=-2(-x^2+2)+1\\\\r(s(x))=2x^{2}-4+1=2x^{2}-3[/tex]
Now, evaluating the function, we have:
[tex]r(s(3))=2(3)^{2}-3=2*9-2=18-3=15[/tex]
Have a nice day!
The amount of sales tax on a new car is directly proportional to the purchase price of the car. Victor bought a new car for $30,000 and paid $1,500 in sales tax. Rita bought a new car from the same dealer and paid $2,375 sales tax. How much did Rita pay for her car?
Answer:
Rita paid 47,500 dollars for the purchase price.
Step-by-step explanation:
We are given the sales tax on a new car is directly proportional to the purchase price of the car which means there is is something k such that
when you multiply it to the sales tax you get the purchase price.
Let's set this equation:
y=kx
Let y represent the purchase price and x the sales tax.
The second sentence tells us that (x,y)=(1500,30000).
We can plug this into y=kx to find the constant k. (Constant means it stays the same no matter what the input and output is).
So we have:
30000=k(1500)
300 =k(15) I went ahead and divided previous equation by 100.
Now divide both sides by 15:
300/15=k
Simplify:
20=k
So the equation to use the answer the question is
y=20x
where y is purchase price and x is sales tax.
So we want to know the purchase price on a car if the sales tax is 2375.
So replace x with 2375:
y=20(2375)
y=47500
Answer:
$47500
Step-by-step explanation:
If the amount of sales tax on a new car is directly proportional to the purchase price of the car and Victor bought a new car for $30,000 and paid $1,500 in sales tax and Rita bought a new car from the same dealer and paid $2,375 sales tax, Rita payed $47,500 for her car.
y=20(2375)
y=47500
A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 3. f(t) = 10 + 20 / (t + 1).
Answer:
Step-by-step explanation:Find the slope of the line that passes through the points shown in the table.
The slope of the line that passes through the points in the table is
.
Suppose that 9 female and 6 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 15 ?finalists, what is the probability of selecting no? females?
Answer: [tex]\dfrac{2}{1001}[/tex]
Step-by-step explanation:
Given : The number of female applicants = 9
The number of male applicants = 6
Total applicants = 15
The number of ways to select 5 applicants from 15 applicants :-
[tex]^{15}C_5=\dfrac{15!}{5!(15-5)!}=3003[/tex]
The number to select 5 applicants from 15 applicants such that no female applicant is selected:-
[tex]^{9}C_0\times^6C_5=1\times\dfrac{6!}{5!(6-5)!}=6[/tex]
Now, the required probability :-
[tex]\dfrac{6}{3003}=\dfrac{2}{1001}[/tex]
Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $5. If Kyd selects any other type of card, he pays North $2. a) What is Kyd's expected value for this game? b) What is North's expected value for this game? c) Who has the advantage in this game?
Step-by-step explanation:
In a 52 deck, there are 12 face cards (4 Jacks, 4 Queens, and 4 Kings). The remaining 40 cards are non-face cards.
The probability that Kyd draws a face card is 12/52, and the probability that he draws a non-face card is 40/52.
a) Kyd's expected value is:
K = (12/52)(5) + (40/52)(-2)
K = -5/13
K ≈ -$0.38
b) North's expected value is:
N = (12/52)(-5) + (40/52)(2)
N = 5/13
N ≈ $0.38
c) Kyd is expected to lose money, and North is expected to gain money. North has the advantage.
Kyd's expected value for this game is -$0.38.
North's expected value for this game is $0.38.Kyd is expected to lose money, and North is expected to gain money.
North has the advantage.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given
In a 52 deck, there are 12 face cards (4 Jacks, 4 Queens, and 4 Kings). The remaining 40 cards are non-face cards.
The probability that Kyd draws a face card is 12/52, and the probability that he draws a non-face card is 40/52.
a) Kyd's expected value is:
K = (12/52)(5) + (40/52)(-2)
K = -5/13
K ≈ -$0.38
b) North's expected value is:
N = (12/52)(-5) + (40/52)(2)
N = 5/13
N ≈ $0.38
c) Kyd is expected to lose money, and North is expected to gain money. North has the advantage.
To know more about probability refer to :
https://brainly.com/question/13604758
#SPJ2
rain gutter is 36 feet long, 8 inches in height,3 inches across base, 12 inches across top..how many gallons of water will it hold when full?
Answer:
112.77 gallons of water
Step-by-step explanation:
We will calculate the area by Trapezoid formula :
[tex]A=\frac{a+b}{2}\times h\times l[/tex]
Given Base a = 12 inches = 1 feet
Base b = 3 inches = 0.25 feet
height = 8 inches = 0.67 feet
length = 36 feet = 36 feet
[tex]Area=\frac{1+2.5}{2}\times 0.67\times 36[/tex]
= 0.625 × 0.67 × 36
= 15.075 cubic feet.
As we know 1 cubic feet = 7.48052 per liquid gallon
Therefore, 15.075 cubic feet = 15.075 × 7.48052
= 112.768839 ≈ 112.77 liquid gallon
When full it will hold 112.77 gallons of water
A bookmark has a perimeter of 46 centimeters and an area of 102 square centimeters. What are the dimensions of the bookmark?
Answer:
6 cm by 17 cm
Step-by-step explanation:
The area is the product of the dimensions; the perimeter is double the sum of the dimensions.
So, we want to find two numbers whose product is 102 and whose sum is 23.
102 = 1·102 = 2·51 = 3·34 = 6·17
The last of these factor pairs has a sum of 23.
The dimensions are 6 cm by 17 cm.
The distribution of the amount of money spent on book purchases for a semester by college students has a mean of $280 and a standard deviation of $40. If the distribution is bell-shaped and symmetric, what proportion of students will spend between $200 and $280 this semester? Round your answer to four decimal places.
Answer: 0.4772
Step-by-step explanation:
Given : The distribution is bell shaped , then the distribution must be normal distribution.
Mean : [tex]\mu=\$280[/tex]
Standard deviation :[tex]\sigma= \$40[/tex]
The formula to calculate the z-score :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = $200
[tex]z=\dfrac{200-280}{40}=-2[/tex]
For x = $280
[tex]z=\dfrac{280-280}{40}=0[/tex]
The p-value = [tex]P(-2<z<0)=P(z<0)-P(z<-2)[/tex]
[tex]0.5-0.0227501=0.4772499\approx0.4772[/tex]
Hence, the proportion of students will spend between $200 and $280 this semester = 0.4772
Approximately 34% of the college students will spend between $200 and $280 on book purchases for a semester according to the empirical rule for a bell-shaped and symmetric distribution.
Explanation:The distribution of the amount of money spent on book purchases for a semester by college students is described as bell-shaped and symmetric with a mean of $280 and a standard deviation of $40. To find the proportion of students that will spend between $200 and $280, we can use the empirical rule (68-95-99.7 rule) which indicates that approximately 68% of the data fall within one standard deviation from the mean. Since we are concerned with the range from $200 (which is 2 standard deviations below the mean) to $280 (the mean), we are effectively looking at half of this 68% range. Therefore, approximately 34% of the students are expected to spend between $200 and $280 on books for a semester.
To calculate the proportion, we take 68% of the range (which covers -1 to +1 standard deviation from the mean) and divide it by 2:
68% / 2 = 34%Thus, the proportion of students spending between $200 and $280 is 0.34, which when rounded to four decimal places, gives us 0.3400.
A pig farmer owns a 20-arce farm and started business with 16 pigs. After one year, he has 421 pigs. Assuming a constant growth rate, how many pigs would he have after a total of 5.1 years?
Answer:
The correct answer is 206550 pigs.
Step-by-step explanation:
First of all you need to calculate the constant growth rate, which is given by the formula [tex]p=((\frac{f}{s} )^{\frac{1}{y} } -1)*100[/tex] where f is the value at the end of the year, s is the start value of that year, and y is the number of years.
From the excercise facts, we know that for 1 year (y=1), the final value is 421 (f=421), and the start value is 16 (s=16). Replacing them in the formula we get : [tex]((\frac{421}{16}) ^{\frac{1}{1} } -1)*100 = 2531.25[/tex] So, the constant growth rate equals 2531.25.
Next, we have to multiply the starting amount of pigs times the constant growth rate times the amount of time that passed to get the final quantity of pigs. This would be [tex]16*2531.25*5.1[/tex] and this gives us a total amount of 206550 pigs.
Have a nice day.
To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 48 numbers (1 through 48). The order in which the selection matter. How many different selections are possible? made does not There are different LOTTO selections.
The number of different possible 7-number selections from a pool of 48, where order does not matter, can be calculated using the mathematical concept of combinations. The formula to calculate the total number of combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of options and k is the number of options selected.
Explanation:In the LOTTO game you described, you must select 7 numbers from a pool of 48, and the order of the numbers does not matter. This is a problem of combinations in mathematics. The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of options, k is the number of options selected, and '!' denotes a factorial. In this case, n=48 (the numbers 1 through 48) and k=7 (the seven numbers you select).
By plugging these values into the formula, we can calculate the total number of different selections possible: C(48, 7) = 48! / [7!(48-7)!]. This calculation would give us the total number of combinations of 7 numbers that can be selected from a pool of 48, which represents all the different possible LOTTO selections. It should be remembered that factorials such as 48! or 7! represent a product of an integer and all the integers below it, down to 1.
Learn more about Combinations here:https://brainly.com/question/39347572
#SPJ12
There are 85,900,584 different selections possible in the LOTTO game.
Explanation:To calculate the number of different selections possible in the LOTTO game, we need to focus on the concept of permutations.
With 48 numbers to choose from and 7 numbers to be selected, the number of permutations can be calculated using the formula P(n, r) = n! / (n-r)!, where n is the total number of items and r is the number of items to be selected.
In this case, n = 48 and r = 7.
Using the formula, we have P(48, 7) = 48! / (48-7)! = (48 * 47 * 46 * 45 * 44 * 43 * 42) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
= 85,900,584 different selections possible.
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ2
You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing texts should be purchased from students for resale. Due to budget limitations, you cannot purchase more than 700 of these textbooks each semester. There are also shelf-space limitations: Calculus texts occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 4 units each, and you can spare at most 1,200 units of shelf space for the texts. If the used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, how many of each type of text should you purchase to maximize profit? HINT [See Example 3.]
calculus text(s) =
history text(s) =
marketing text(s) =
What is the maximum profit the program can make in a semester?
Answer:
Calculus texts: 600History texts: 0Marketing texts: 0Step-by-step explanation:
Each Calculus text returns $10/2 = $5 per unit of shelf space. For History and Marketing texts, the respective numbers are $4/1 = $4 per unit, and $8/4 = $2 per unit. Using 1200 units of shelf space for 600 Calculus texts returns ...
$5/unit × 1200 units = $6000 . . . profit
Any other use of units of shelf space will reduce profit.
The College should purchase only 600 Calculus textbooks to maximize College profits.
Data and Calculations:
Budget limit on the number of textbooks per semester = 700
Shelf space for the purchased textbooks = 1,200 units
Calculus History Marketing
Shelf-space occupied
by each textbook 2 1 4
Profit per textbook $10 $4 $8
Profit per shelf-space $5 ($10/2) $4 ($4/1) $2 ($8/4)
The highest profit per shelf space is $5 generated by Calculus.
The highest profit that the College can make over the purchase of used Calculus textbooks = $6,000 ($5 x 1,200) or ($10 x 600).
Thus, for the College to maximize its profits, it should purchase 600 Calculus textbooks, which will not exceed the textbook limit for the semester, and at the same time maximally utilize the shelf space available.
Related link: https://brainly.com/question/14293956
Your Co. collects 50% of its sales in the month of the sales, 30% of the follow month, and 20% the second month after the sale.
Calculate budgeted cash receipts for March and April.
January=50
February=40
March=60
April=30
May=70
June=50
Answer:
March 52April 41Step-by-step explanation:
In March, Your Co. will collect 20% of January's sales, 30% of February's sales, and 50% of March's sales:
.20×50 +.30×40 +.50×60 = 10 +12 +30 = 52
Similarly, in April, collections will be ...
.20×40 + .30×60 + .50×30 = 8 +18 +15 = 41
Answer:Am nevoie de Puncte
Step-by-step explanation:
Write y = 2x^2 + 8x + 3 in vertex form.
y = 2(x – 2)^2 – 5
y = (x – 4)^2 + 3
y = 2(x + 2)^2 – 5
y = (x + 4)^2 + 3
Answer:
y = 2(x + 2)^2 – 5
Step-by-step explanation:
When y = ax^2 +bx +c is written in vertex form, it becomes ...
y = a(x +b/(2a))^2 +(c -b^2/(4a))
The constant term in the squared binomial is b/(2a) = 8/(2(2)) = +2. Only one answer choice matches:
y = 2(x +2)^2 -5
Find x.
A. 124
B.56
C.62
D.28
Answer:
C. 62 degrees
Step-by-step explanation:
Alright I see a circle and a half a rotation where the diameter is at. A half of 360 degrees is 180 degrees.
So the arc measure in degrees for EG is 180 degrees (both the left piece and right piece have this measure).
Since EG is 180 then FG=EG-EF=180-56=124.
To find x we have to half 124 since it is the arc measure where x is but x is the inscribed angle.
x=124/2=62
C.
62 degrees ! All the rest wouldn’t make sense (:
what is the solution if the inequality shown below? a+2<-10
Answer:
a < -12
Step-by-step explanation:
Isolate the variable, a. Treat the < as a equal sign, what you do to one side, you do to the other. Subtract 2 from both sides:
a + 2 < -10
a + 2 (-2) < -10 (-2)
Simplify:
a < -10 - 2
a < -12
a < -12 is your answer.
~
Answer:
[tex]\huge \boxed{a<-12}\checkmark[/tex]
Step-by-step explanation:
Subtract by 2 both sides of equation.
[tex]\displaystyle a+2-2<-10-2[/tex]
Simplify, to find the answer.
[tex]-10-2=-12[/tex]
[tex]\displaystyle a<-12[/tex], which is our answer.
The mean length of six-year-old rainbow trout in the Arolik River in Alaska is 481 millimeters with a standard deviation of 41 millimeters. Assume these lengths are normally distributed. What proportion of six-year-old rainbow trout are less than 516 millimeters long?
Answer: 0.8023
Step-by-step explanation:
Given : [tex]\text{Mean}=\mu=481 \text{ millimeters}[/tex]
[tex]\text{Standard deviation}=41 \text{ millimeters}[/tex]
Assuming these lengths are normally distributed.
The formula to calculate the z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= [tex]516 \text{ millimeters}[/tex]
[tex]z=\dfrac{516-481}{41}=0.853658536585\approx0.85[/tex]
The p-value = [tex]P(z\leq0.85)=0.8023374\approx0.8023[/tex]
Hence, the required probability : 0.8023
a. Find dy/dx if y^2 + x^2 = 16 b. Find the equation of the tangent line that contains the point (2, 2 squareroot 3).
Answer:
[tex]x+\sqrt{3}y=8[/tex]
Step-by-step explanation:
Given equation of curve,
[tex]y^2+x^2=16[/tex]
[tex]\implies y^2=16-x^2[/tex]
Differentiating with respect to x,
[tex]2y\frac{dy}{dx}=-2x[/tex]
[tex]\implies \frac{dy}{dx}=-\frac{x}{y}[/tex]
Since, the tangent line of the curve contains the point (2, 2√3),
Thus, the slope of the tangent line,
[tex]m=\left [ \frac{dy}{dx} \right ]_{(2, 2\sqrt{3})}=-\frac{1}{\sqrt{3}}[/tex]
Hence, the equation of tangent line would be,
[tex]y-2\sqrt{3}=-\frac{1}{\sqrt{3}}(x-2)[/tex]
[tex]\sqrt{3}y-6=-x+2[/tex]
[tex]\implies x+\sqrt{3}y=8[/tex]
If $9,400 is invested at an interest rate of 8% per year, find the value of the investment at the end of 5 years if interested is compounded annually (once a year), semiannually (twice a year), monthly (12 times a year), daily (assume 365 days a year), or continuously. Round to the nearest cent. For each, use the correct compound interest formula from the following. A = P ( 1 + r n ) n t or A = P e r t
(a) Annual:
(b) Semiannual:
(c) Monthly:
(d) Daily:
(e) Continuously:
Answer:
(a) $13811.68
(b) $13914.30
(c) $14004.55
(d) $14022.54
(e) $14023.15
Step-by-step explanation:
Since, the amount formula in compound interest,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where,
P = Principal amount,
r = annual rate,
n = number of periods,
t = number of years,
Here, P = $ 9,400, r = 8% = 0.08, t = 5 years,
If the amount is compounded annually,
n = 1,
Hence, the amount of investment would be,
[tex]A=9400(1+\frac{0.08}{1})^5=9400(1.08)^5=\$ 13811.6839219\approx \$ 13811.68[/tex]
(a) If the amount is compounded annually,
n = 1,
The amount of investment would be,
[tex]A=9400(1+\frac{0.08}{1})^5=9400(1.08)^5=\$ 13811.6839219\approx \$ 13811.68[/tex]
(b) If the amount is compounded semiannually,
n = 2,
The amount of investment would be,
[tex]A=9400(1+\frac{0.08}{2})^{10}=9400(1.04)^{10}=\$13914.2962782\approx \$ 13914.30[/tex]
(c) If the amount is compounded Monthly,
n = 12,
The amount of investment would be,
[tex]A=9400(1+\frac{0.08}{12})^{60}=9400(1+\frac{1}{150})^{60}=\$ 14004.549658\approx \$ 14004.55[/tex]
(d) If the amount is compounded Daily,
n = 365,
The amount of investment would be,
[tex]A=9400(1+\frac{0.08}{365})^{365\times 5}=9400(1+\frac{2}{9125})^{1825}=\$ 14022.5375476\approx \$ 14022.54[/tex]
(e) Now, the amount in compound continuously,
[tex]A=Pe^{rt}[/tex]
Where, P = principal amount,
r = annual rate,
t = number of years,
So, the investment would be,
[tex]A=9400 e^{0.08\times 5}=9400 e^{0.4}=\$14023.1521578\approx \$14023.15[/tex]
PLEASE HELP
Identify the radius and center
x^2 +y^2 -6x -2y + 1 = 0
Answer:
The center is the point (3,1) and the radius is 3 units
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
we have
[tex]x^{2}+y^{2}-6x-2y+1=0[/tex]
Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-6x)+(y^{2}-2y)=-1[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex](x^{2}-6x+9)+(y^{2}-2y+1)=-1+9+1[/tex]
[tex](x^{2}-6x+9)+(y^{2}-2y+1)=9[/tex]
Rewrite as perfect squares
[tex](x-3)^{2}+(y-1)^{2}=9[/tex]
The center is the point (3,1) and the radius is 3 units
Use Gauss's approach to find the following sum
4+10+16+22+...+70
The sum of the sequence is
Each consecutive term in the sum is separated by a difference of 6, so the [tex]n[/tex]-th term is [tex]4+6(n-1)=6n-2[/tex] for [tex]n\ge1[/tex]. The last term is 70, so there are [tex]6n-2=70\implies n=12[/tex] terms in the sum.
Now,
[tex]S=4+10+\cdots+64+70[/tex]
but also
[tex]S=70+64+\cdots+10+4[/tex]
Doubling the sum and grouping terms in the same position gives
[tex]2S=(4+70)+(10+64)+\cdots+(64+10)+(70+4)=12\cdot74[/tex]
[tex]\implies\boxed{S=444}[/tex]
1) Let A = {1, 2, 3, 4} and R be a relation on the set A defined by: R = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (4, 1), (4, 4)} Determine whether R is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. For each property, either explain why R has that property or give an example showing why it does not. (30 points)
Answer:
R is not reflexive,not irreflexive ,symmetric,not asymmetric,not antisymmetric and transitive.
Step-by-step explanation:
1.Reflexive : Relation R is not reflexive because it does not contain identity relation on A.
Identity relation on A:{(1,1),(2,2),(3,3),(4,4)}
If we take a relation R on A :{(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)}
The relation R is reflexive on set A because it contain identity relation.
2.Irreflexive: Given relation R is not reflexive because it contain some elements of identity relation .If a relation is irreflexive then it does not contain any element of identity relation. We can say the intersection of R with identity relation is empty.
[tex]R\cap I=\left\{(1,1),(2,2),(4,4)\right\} \neq \phi[/tex]
If we take a relation on A R:{(1,2),(2,1)}
Then relation is irreflexive because it does not contain any element of identity relation
[tex]R\cap I=\phi[/tex]
3.Symmetric : The given relation R is symmetric because it satisfied the property of symmetric relation.
(1,2)belongs to relation (2,1) also belongs to relation ,(1,4) belongs to relation and (4,1) also belongs to given relation Hence we can say it is symmetric relation.
4.Asymmetric: The given relation is not asymmetric relation.Because it does not satisfied the property of asymmetric relation
Asymmetric relation: If (a,b) belongs to relation then (b,a) does not belongs to given relation.
Here (1,2) belongs to given relation and (2,1) also belongs to given relation Therefore, it is not asymmetric.
If we take a relation R on A
R:{(1,2),(1,3)}
It is asymmetric relation because it does not contain (2,1) and (3,1).
5.Antisymmetric: The given relation is not antisymmetric because it does not satisfied the property of antisymmetric relation.
Antisymmetric relation: If (a,b) and (b,a) belongs to relation then a=b
If we take a relation R
R;{(1,2) (1,1)}
It is antisymmetric because it contain (1,1) where 1=1 .Hence , it is antisymmetric.
6.Transitive: The given relation is transitive because it satisfied the property of transitive relation
Transitive relation: If (a,b) and (b,c) both belongs to relation R then (a,c) belongs to R.
Here, we have (1,2) and (2,1)belongs to relation then (1,1) and (2,2) are also belongs to relation.
(1,4) and (4,1) then (1,1) and (4,4) are also belongs to the relation.
A simple random sample of size nequals15 is drawn from a population that is normally distributed. The sample mean is found to be x overbarequals31.1 and the sample standard deviation is found to be sequals6.3. Determine if the population mean is different from 25 at the alpha equals 0.01 level of significance.
Answer with explanation:
To test the Significance of the population which is Normally Distributed we will use the following Formula Called Z test
[tex]z=\frac{\Bar X - \mu}{\frac{\sigma}{n}}[/tex]
[tex]\Bar X =31.1\\\\ \sigma=6.3\\\\ \mu=25\\\\n=15\\\\z=\frac{31.1-25}{\frac{6.3}{\sqrt{15}}}\\\\z=\frac{6.1\times\sqrt{15}}{6.3}\\\\z=\frac{6.1 \times 3.88}{6.3}\\\\z=3.756[/tex]
→p(Probability) Value when ,z=3.756 is equal to= 0.99992=0.9999
⇒Significance Level (α)=0.01
We will do Hypothesis testing to check whether population mean is different from 25 at the alpha equals 0.01 level of significance.
→0.9999 > 0.01
→p value > α
With a z value of 3.75, it is only 3.75% chance that ,mean will be different from 25.
So,we conclude that results are not significant.So,at 0.01 level of significance population mean will not be different from 25.
With a short time remaining in the day, a delivery driver has time to make deliveries at 7 locations among the 9 locations remaining. How many different routes are possible?
There are 9,072 different routes possible for the delivery driver.
Explanation:To find the number of different routes possible, we can use the concept of permutations. Since the driver has to deliver to 7 out of the 9 remaining locations, we can calculate the number of ways to choose 7 out of 9 and then multiply it by the number of ways to arrange those 7 locations. The formula for permutations is P(n, r) = n! / (n - r)!. In this case, n = 9 and r = 7.
P(9, 7) = 9! / (9 - 7)! = 9! / 2! = 9 × 8 × 7 × 6 × 5 × 4 × 3 = 9,072
Therefore, there are 9,072 different routes possible for the delivery driver.
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ12
To find the number of different routes possible, we can use the combination formula: C(n, k) = n! / (k!(n-k)!). Plugging in the values, we get C(9, 7) = 36. Therefore, there are 36 different routes possible.
Explanation:To find the number of different routes possible, we can use the combination formula:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of locations remaining (9) and k is the number of locations the driver can make deliveries to (7).
Plugging in the values, we get:
C(9, 7) = 9! / (7!(9-7)!)
= 9! / (7!2!)
= (9 * 8 * 7!)/(7! * 2!)
= (9 * 8)/(2 * 1)
= 36
Therefore, there are 36 different routes possible.
Marla Opper currently earns $95,000 a year and is offered a job in another city for $118,000. The city she would move to has 11 percent higher living expenses than her current city.
What amount must Marla earn in the new city to maintain her current buying power?
Answer:
Since living expenses are 11% higher in the new city. Marla would need an 11% increase in her current income to maintain her current buying power when moving. We can solve this by simply multiplying her current income by 11%.
Step-by-step explanation:
[tex]95,000*1.11 = 105,450[/tex]
If we multiply her current income of $95,000 by 11% we see that Marla would need an income of $105,450 in order to maintain her buying power in the new city. Since her new job offer is paying $118,000 she will have more buying power in the new city.
Answer: Marla must earn an Income of $105,450 to maintain her buying power.
Marla would need to earn $105,450 in the new city to maintain her current buying power after taking into account an 11 percent increase in living expenses.
Explanation:The student has asked how much Marla Opper must earn at the new job in another city to maintain her current buying power, considering that the new city has living expenses that are 11 percent higher. To calculate this, we first need to figure out what amount of income in the new city would be equivalent to Marla's current income of $95,000, given the increase in living expenses.
Firstly, we find 11 percent of Marla's current income:
11% of $95,000 = 0.11 × $95,000 = $10,450This means Marla needs an additional $10,450 on top of her current income to maintain the same buying power in the new city. So, the amount Marla needs to earn in the new city is:
$95,000 + $10,450 = $105,450Thus, Marla would need to earn $105,450 in the new city to keep her current buying power.
What is the mode for the set of data?
Ages
Stem Leaves
1 0, 3, 6
2 0, 1, 3, 7, 7, 8, 9
3 0, 2, 3, 3, 3, 3, 8, 9
4 6, 6, 6, 8
1|0 = 10 years old
3
33
38
46
Answer:
33
Step-by-step explanation:
The mode is the number that sets up the most in an answer.
Remember, the stem is the number that is in the "tens" place value, while the leaves is the number in the "ones" place value.
Expand the stem-leaves:
10, 13, 16, 20, 21, 23, 27, 27, 28, 29, 30, 32, 33, 33, 33, 33, 38, 39, 46, 46, 46, 48
The number that shows up the most is 33, and is your answer.
~
Analyze the diagram below and complete the instructions that follow.
Find the value of x.
A.√3
B. 3√2/2
C. 3√2
D. 3√3
Answer:
B. 3√2/2
Step-by-step explanation:
The value of x can be found with the tan rule.
Step 1: Identify the sides as opposite, adjacent and hypotenuse to apply the formula
Opposite = (opposite from angle 45 degrees)
Adjacent = x (between angle 45 degrees and 90 degrees)
Hypotenuse = 3 (opposite from 90 degrees)
Step 2: Apply the tan formula
Cos (angle) = adjacent/hypotenuse
Cos (45) = x/3
√2/2 = x/3
x = √2/2 x 3
x = 3√2/2
Therefore, the correct answer is B; x = 3√2/2
!!
Use spherical coordinates to find the volume of the region that lies outside the cone z = p x 2 + y 2 but inside the sphere x 2 + y 2 + z 2 = 2. Write the answer as an exact answer, which should involve π and √ 2. Do not round or use a calculator.
I assume the cone has equation [tex]z=\sqrt{x^2+y^2}[/tex] (i.e. the upper half of the infinite cone given by [tex]z^2=x^2+y^2[/tex]). Take
[tex]\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
The volume of the described region (call it [tex]R[/tex]) is
[tex]\displaystyle\iiint_R\mathrm dx\,\mathrm dy\,\mathrm dz=\int_0^{2\pi}\int_0^{\sqrt2}\int_{\pi/4}^\pi\rho^2\sin\varphi\,\mathrm d\varphi\,\mathrm d\rho\,\mathrm d\theta[/tex]
The limits on [tex]\theta[/tex] and [tex]\rho[/tex] should be obvious. The lower limit on [tex]\varphi[/tex] is obtained by first determining the intersection of the cone and sphere lies in the cylinder [tex]x^2+y^2=1[/tex]. The distance between the central axis of the cone and this intersection is 1. The sphere has radius [tex]\sqrt2[/tex]. Then [tex]\varphi[/tex] satisfies
[tex]\sin\varphi=\dfrac1{\sqrt2}\implies\varphi=\dfrac\pi4[/tex]
(I've added a picture to better demonstrate this)
Computing the integral is trivial. We have
[tex]\displaystyle2\pi\left(\int_0^{\sqrt2}\rho^2\,\mathrm d\rho\right)\left(\int_{\pi/4}^\pi\sin\varphi\,\mathrm d\varphi\right)=\boxed{\frac43(1+\sqrt2)\pi}[/tex]
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
A. x=9, y=18√2
B.x=18, y=18
C.x=9√2, y=18√2
D. x=9√3, y=18
Answer:
D. x = 9√3 and y = 18
Step-by-step explanation:
This is an isosceles triangle divided into two equal parts.
Step 1: 18 can be divided into 2 parts which makes the base of both triangles 9.
Step 2: Find the value of x
The value of x can be found through the tan rule.
tan (angle) = opposite/adjacent
tan (60) = x/9
√3 = x/9
x = √3 x 9
x = 9√3
Step 3: Find the value of y
The value of y can be found through the cos rule.
Cos (angle) = adjacent/hypotenuse
Cos (60) = 9/y
1/2 = 9/y
y = 18
Therefore, the correct answer is D; x = 9√3 and y = 18
!!
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x) = x^2 - 400x + 45,377 . What is the minimum unit cost?
Do not round your answer.
Answer:
5377
Step-by-step explanation:
C(x) = x^2 - 400x + 45,377
To find the location of the minimum, we take the derivative of the function
We know that is a minimum since the parabola opens upward
dC/dx = 2x - 400
We set that equal to zero
2x-400 =0
Solving for x
2x-400+400=400
2x=400
Dividing by2
2x/2=400/2
x=200
The location of the minimum is at x=200
The value is found by substituting x back into the equation
C(200) = (200)^2 - 400(200) + 45,377
=40000 - 80000+45377
=5377
Answer:
The minimum unit cost is 5377
Step-by-step explanation:
Note that we have a cudratic function of negative principal coefficient.
The minimum value reached by this function is found in its vertex.
For a quadratic function of the form
[tex]ax ^ 2 + bx + c[/tex]
the x coordinate of the vertex is given by the following expression
[tex]x=-\frac{b}{2a}[/tex]
In this case the function is:
[tex]C(x) = x^2 - 400x + 45,377[/tex]
So:
[tex]a=1\\b=-400\\c=45,377[/tex]
Then the x coordinate of the vertex is:
[tex]x=-\frac{-400}{2(1)}[/tex]
[tex]x=200\ cars[/tex]
So the minimum unit cost is:
[tex]C(200) = (200)^2 - 400(200) + 45,377[/tex]
[tex]C(200) = 5377[/tex]
could someone give me an answer and explain how you got it ?
Answer:
A (9, 3)
Step-by-step explanation:
First the point is rotated 90° counterclockwise about the origin. To do that transformation: (x, y) → (-y, x).
So S(-3, -5) becomes S'(5, -3).
Next, the point is translated +4 units in the x direction and +6 units in the y direction.
So S'(5, -3) becomes S"(9, 3).