Answer:
Step-by-step explanation:
A) Demand per month= 40 cars
Annual Demand (D)= 12*40 = 480
Fixed Cost per order (K)= 15
Holding Cost= 20% of cost= 60 *0.2 = 12
a. Economic Order Quantity=
Q^{*}={\sqrt {{\frac {2DK}{h}}}}
= √(2*480*15)/12
=34.64 ~ 35
Total Cost =P*D+K(D/EOQ)+h(EOQ/2) P= Cost per unit
= 60*480+ 15(480/35) + 12(35/2)
= 28800+ 205.71+ 210
=$29215.71
B). Backorder Cost (b)= $45
Qbo= Q* × √( b+h/ h)
= 35*√(12+45/ 45)
= 35* 1.12
=39.28 ~ 39
Shortage (S)= Qbo * (K/K+b)
= 39* (15/15+45)
= 39* 0.25
= 9.75
Total Cost Minimum=( bS2/ 2Qbo) + P (Qbo- S)2/2Qbo + K(D/Qbo)
=45* 9.752 / 2* 392 + 60 (39-9.75)2/ 2* 392 + 15 ( 480/39)
= 1.40+ 21.9.+ 184.61
=$207.91
C)Length of backorder days (d) = Demand ÷ amount of working days
d = 480 ÷ 300
d = 1.6
Calculate the backorders as the maximum number of backorders divided by the demand per day
s/d = 9.75/1.6 = 6.09 days (answer)
D) Calculate the difference in total between not using backorder:
$207.85 + $207.85 - 207.91 = $207.79
The saving in using backorder is $207.79.
Therefore I would recommend using a backorder
Which term best describes a figure formed by three segments connecting three non Collin ear points
Answer:
Triangle
Step-by-step explanation:
Find the surface area of the cylinder and round to the nearest tenth and its recommended that you use pie or 3.14 also the radius is half the diameter
Diameter=d=2ft
Radius=d/2=2/2=1ftHeight=h=2ftWe know
[tex]\boxed{\sf Lateral\:Surface\:Area=2πrh}[/tex]
[tex]\\ \sf\longmapsto Lateral\: Surface\:Area=2\times 3.14\times 2\times 1[/tex]
[tex]\\ \sf\longmapsto Lateral\;Surface\:Area=4(3.14)[/tex]
[tex]\\ \sf\longmapsto Lateral\:Surface\:Area=12.56ft^3[/tex]
[tex]\begin{gathered} {\underline{\boxed{ \rm { \purple{Surface \: \: area \: = \: 2 \: \pi \: r \: h \: + \: 2 \: \pi \: {r}^{2} }}}}}\end{gathered}[/tex]
r represents radius of cylinder.h denotes height of cylinder.Solution[tex]\large{\bf{{{\color{navy}{h \: = \: 2 \: ft. }}}}}[/tex]
[tex]\bf \large \longrightarrow \: \: r \: = \: \frac{Diameter}{2} [/tex]
[tex]\bf \large \longrightarrow \: \: r \: = \: \frac{2}{2} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: r \: = \: \cancel\frac{2}{2} \: ^{1} \\ [/tex]
[tex]\large{\bf{{{\color{navy}{r \: = \: 1 \: ft. \: }}}}}[/tex]
☛ Now , Substuting the values[tex]\bf \hookrightarrow \: \: \: 2 \: \times \: 3.14 \times \: 1 \: ft \: \times \: 2 \: ft \: + \: 2 \: \times \: 3.14 \: \times \: {(1 \: ft)}^{2}[/tex]
[tex]\bf \hookrightarrow \: \: \:6.28 \: ft \: \times \: 2 \: ft\: \: + \: 6.28 \: ft[/tex]
[tex]\bf \hookrightarrow \: \: \:12.56 \: {ft}^{2} \: + \: 6.28 \: ft[/tex]
[tex]\bf \hookrightarrow \: \: \:18.84 \: {ft} \: ^{2} [/tex]
Hence , the surface area of cylinder is 18.84 ft²
Round to the nearest 10 of 18.84 is 18.8
cách tính tổng
12+25+45+65+34
12+25+45+65+34
= 181
Must click thanks and mark brainliest
n(AnB)=3 and n(AuB)=10, then find (p(A∆B))?
I assume A ∆ B denotes the symmetric difference of A and B, i.e.
A ∆ B = (B - A) U (A - B)
where - denotes the set difference or relative complement, e.g.
B - A = {b ∈ B : b ∉ A}
It can be established that
A ∆ B = (A U B) - (A ∩ B)
so that
n(A ∆ B) = n(A U B) - n(A ∩ B) = 10 - 3 = 7
Not sure what you mean by p(A ∆ B), though... Probability?
The equation of a line is (3)/(5)x+(1)/(3)y=(1)/(15) . The x-intercept of the line is , and its y-intercept is .
bxf-mgii-whr
Step-by-step explanation:
come I will teach
If 2L of solution needs to be administered through an IV over 24hours, then how many mililitres of solution needs to be provided per hour, rounded to two decimal places?
Answer:
83.33 milliliters
Step by step explanation:
2L = 2000 ml Change the liters to milliliters first
2000 ml : 24 hours
x ml : 1 hour
Next you cross multiply : 2000 × 1 hour = 2000 and 24 × x = 24x
Then you divide:
[tex]\frac{24x}{24} : \frac{2000}{24}[/tex]
x : 83.3333333...
When this is rounded off it is equal to 83.33
HOPE THIS HELPED
Before an election, combining the results of 12,625 polls with 14,491,635 samples in total, it shows that 6,413,959 responders (44.3%) say they will vote for the first candidate and 6,134,272 responders (42.3%) say they will vote for the other candidate. Assume a binomial model Binomial(n,p) of the polls for the first and second candidates, where p is the percentage of the votes to the first candidate and n is the total number of votes to the first candidate or the second candidate. Suppose we are interested in whether the first candidate wins more than half of the votes to the first and second candidates:
H0: p = 0.5 v.s. H1: p > 0.5
(a) Compute the test statistics of the generalized likelihood ratio test. Is this test a uniformly most powerful test?
(b) Use Wilks' theorem to compute the critical value of the generalized likelihood ratio test under α = 0.05 level. Make a decision.
(c) Another test has test statistics p - po/√po(1 - po)/n, where po = 0.5. Compute the p-value of this test using the central limit theorem and make a decision. Assume the significance level α = 0.05.
(d) If the second candidate wins the election, comment on possible problems in this statistical analysis.
Answer:
C
Step-by-step explanation:
Sorry if im wrong it just looks right to me.
Need help answer plz help
Answer:
BONANA MY NANA
Step-by-step explanation:
1) Sử dụng phương pháp diện tích chứng minh định lí Pitago: “Trong một tam giác vuông, bình phương cạnh huyền bằng tổng bình phương hai cạnh góc vuông”.
2) Chứng minh rằng tứ giác có một và chỉ một đường nối trung điểm hai cạnh đối chia tứ giác thành hai phần có cùng diện tích là hình thang.
Answer:
hmm i thought abt it and i think the answer is no
Step-by-step explanation:
lim ₓ→∞ (x+4/x-1)∧x+4
It looks like the limit you want to find is
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4}[/tex]
One way to compute this limit relies only on the definition of the constant e and some basic properties of limits. In particular,
[tex]e = \displaystyle\lim_{x\to\infty}\left(1+\frac1x\right)^x[/tex]
The idea is to recast the given limit to make it resemble this definition. The definition contains a fraction with x as its denominator. If we expand the fraction in the given limand, we have a denominator of x - 1. So we rewrite everything in terms of x - 1 :
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\dfrac{x-1+5}{x-1}\right)^{x-1+5} \\\\ = \left(1+\dfrac5{x-1}\right)^{x-1+5} \\\\ =\left(1+\dfrac5{x-1}\right)^{x-1} \times \left(1+\dfrac5{x-1}\right)^5[/tex]
Now in the first term of this product, we substitute y = (x - 1)/5 :
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(1+\dfrac1y\right)^{5y} \times \left(1+\dfrac5{x-1}\right)^5[/tex]
Then use a property of exponentiation to write this as
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\left(1+\dfrac1y\right)^y\right)^5 \times \left(1+\dfrac5{x-1}\right)^5[/tex]
In terms of end behavior, (x - 1)/5 and x behave the same way because they both approach ∞ at a proportional rate, so we can essentially y with x. Then by applying some limit properties, we have
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty} \left(\left(1+\dfrac1x\right)^x\right)^5 \times \left(1+\dfrac5{x-1}\right)^5 \\\\ = \lim_{x\to\infty}\left(\left(1+\dfrac1x\right)^x\right)^5 \times \lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)^5 \\\\ =\left(\lim_{x\to\infty}\left(1+\dfrac1x\right)^x\right)^5 \times \left(\lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)\right)^5[/tex]
By definition, the first limit is e and the second limit is 1, so that
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = e^5\times1^5 = \boxed{e^5}[/tex]
You can also use L'Hopital's rule to compute it. Evaluating the limit "directly" at infinity results in the indeterminate form [tex]1^\infty[/tex].
Rewrite
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \exp\left((x+4)\ln\dfrac{x+4}{x-1}\right)[/tex]
so that
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty}\exp\left((x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ = \exp\left(\lim_{x\to\infty}(x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ =\exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right)[/tex]
and now evaluating "directly" at infinity gives the indeterminate form 0/0, making the limit ready for L'Hopital's rule.
We have
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\ln\dfrac{x+4}{x-1}\right] = -\dfrac5{(x-1)^2}\times\dfrac{1}{\frac{x+4}{x-1}} = -\dfrac5{(x-1)(x+4)}[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{x+4}\right]=-\dfrac1{(x+4)^2}[/tex]
and so
[tex]\displaystyle \exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right) = \exp\left(\lim_{x\to\infty}\frac{-\dfrac5{(x-1)(x+4)}}{-\dfrac1{(x+4)^2}}\right) \\\\ = \exp\left(5\lim_{x\to\infty}\frac{x+4}{x-1}\right) \\\\ = \exp(5) = \boxed{e^5}[/tex]
What is the answer to it
No question?
Why not add one!
Question 1 of 10
What is the value of n?
144
O A. 36
O B. 23
O C. 95°
D. 590
Answer:
Option C, 95°
Step-by-step explanation:
180-121 = 59
180-144 = 36
third angle of the triangle is, 180-59-36 = 85,
missing angle n = 180-85 = 95°
Answered by GAUTHMATH
Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.
Car 1 Car 2
214 220
245 221
239 244
224 225
220 258
295 259
Describe each data set, that is determine the shape, center, and spread
i. Sample mean for Car 1
ii. Sample mean for Car 2
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
Car 1 Car 2
214 220
245 221
239 244
224 225
220 258
295 259
Ordered data:
Car 1 : 214, 220, 224, 239, 245, 295
Sample mean = ΣX/ n ; n = sample size = 6
Sample mean = 1437 / 6 = 239.5
Median = 1/2(n+1)th term = 1/2(7) = 3.5th term
Median = (3rd + 4th) /2 = (224 + 239) /2 = 231.5
Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 29.60 (using calculator)
Car 2 : 220, 221, 225, 244, 258, 259
Sample mean = ΣX/ n ; n = sample size = 6
Sample mean = 1427 / 6 = 237.833
Median = 1/2(n+1)th term = 1/2(7) = 3.5th term
Median = (3rd + 4th) /2 = (225 + 244) /2 = 234.5
Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 18.21 (using calculator)
Ell takes the 17 apples home, and the bakes as many apple pies
as he can. He uses 7 apples in each ple. How many apple pies does
El bake? How many apples are left?
Counters
17:7
10
10
c
Boles
pies
apples are en
Answer:
Tedyxhcj eydyfhxrstetdhsawe
Find the equation of the line passing through the point (-1,2)
and the points of intersections of the line 2x - 3y + 11 = 0 and
5x + y + 3 = 0
Answer:
[tex]y=-5x-3[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
To solve for the equation of the line, we would need to:
Find the point of intersection between the two given linesUse the point of intersection and the given point (-1,2) to solve for the slope of the lineUse a point and the slope in [tex]y=mx+b[/tex] to solve for the y-interceptPlug the slope and the y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation1) Find the point of intersection between the two given lines
[tex]2x - 3y + 11 = 0[/tex]
[tex]5x + y + 3 = 0[/tex]
Isolate y in the second equation:
[tex]y=-5x-3[/tex]
Plug y into the first equation:
[tex]2x - 3(-5x-3) + 11 = 0\\2x +15x+9 + 11 = 0\\17x+20 = 0\\17x =-20\\\\x=\displaystyle-\frac{20}{17}[/tex]
Plug x into the second equation to solve for y:
[tex]5x + y + 3 = 0\\\\5(\displaystyle-\frac{20}{17}) + y + 3 = 0\\\\\displaystyle-\frac{100}{17} + y + 3 = 0[/tex]
Isolate y:
[tex]y = -3+\displaystyle\frac{100}{17}\\y = \frac{49}{17}[/tex]
Therefore, the point of intersection between the two given lines is [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex].
2) Determine the slope (m)
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the two points [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex] and (-1,2):
[tex]m=\displaystyle \frac{\displaystyle\frac{49}{17}-2}{\displaystyle-\frac{20}{17}-(-1)}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{20}{17}+1}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{3}{17} }\\\\\\m=-5[/tex]
Therefore, the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-5x+b[/tex]
Plug in the point (-1,2) and solve for b:
[tex]2=-5(-1)+b\\2=5+b\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=-5x+b[/tex]:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
I hope this helps!
Find the midpoint of the segment with the given endpoints.
(7,10) and (-1,- 8)
Answer:
(3,1) is the midpoint
Step-by-step explanation:
To find the x coordinate of the midpoint, average the x coordinates of the endpoints
(7+-1)/2 = 6/2 =3
To find the y coordinate of the midpoint, average the y coordinates of the endpoints
(10+-8)/2 = 2/2 = 1
(3,1) is the midpoint
Answer:
(3, 1)
Step-by-step explanation:
We can use the formula [ (x1+x2)/2, (y1+y2/2) ] to solve for the midpoint.
7+(-1)/2, 10+(-8)/2
6/2, 2/2
3, 1
Best of Luck!
On January 2, 2008, the American Idol website (www .americanidol) conducted an online poll that asked respondents which contestant they liked best among six former contestants. To become part of the sample, respondents simply clicked on a response. Of the 941,434 responses to this poll, 55% voted for Clay Aiken. We can conclude that _________________________________ .
a. the sample is too small.
b. a fraction of the millions of people who watched the TV show to draw any conclusion.
c. most Americans prefer Clay Aiken out of those former contestants.
d. the poll uses voluntary response, so the results tell us little about the population of all adults.
Answer:
Online Poll
We can conclude that
c. most Americans prefer Clay Aiken out of those former contestants.
Step-by-step explanation:
Sample responses received from the poll = 941,434
Proportion of voters for Clay Aiken = 55%
Computed proportion of voters for the other 5 contestants = 45% (100% - 55%)
This gives an average of 7.5% (45%/5) for the other 5 contestants.
Therefore, the conclusion is that "most Americans prefer Clay Aiken out of those former contestants" in the American Idol contest.
Is this a function help
The area of rectangle is 36 cm2 and breadth is one fourth of the length.Find length and breadth of rectangle.
We know
[tex]\boxed{\sf Area=Length\times Breadth}[/tex]
[tex]\\ \sf\longmapsto x(4x)=36[/tex]
[tex]\\ \sf\longmapsto 4x^2=36[/tex]
[tex]\\ \sf\longmapsto x^2=\dfrac{36}{4}[/tex]
[tex]\\ \sf\longmapsto x^2=9[/tex]
[tex]\\ \sf\longmapsto x=\sqrt{9}[/tex]
[tex]\\ \sf\longmapsto x=3[/tex]
Breadth=3mLength=4(3)=12mMax has 3 fiction books and 6 nonfiction books to donate to the community center. He wants to package them so that there is an equal number of fiction and nonfiction books in each group. He also wants to have as many packages as possible. How many books are in each group?
Answer:
Each group has 1 fiction book and 2 nonfiction book(s).
SCALCET8 4.7.011. Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens
Answer:
For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.
However, the dividers change the process to find this maximum somewhat.
Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.
Letting y represent the other two sides of the rectangle, we have 2y.
We know that 2y + 5x = 750.
Solving for y, we first subtract 5x from each side:
2y + 5x - 5x = 750 - 5x
2y = - 5x + 750
Next we divide both sides by 2:
2y/2 = - 5x/2 + 750/2
y = - 2.5x + 375
We know that the area of a rectangle is given by
A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area
A = xy
Substituting the expression for y we just found above, we have
A = x (-2.5x+375)
A = - 2.5x² + 375x
This is a quadratic equation, with values a = - 2.5, b = 375 and c = 0.
To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation
x = - b/2a
x = - 375/2 (-2.5) = - 375/-5 = 75
Substituting this back in place of every x in our area equation, we have
A = - 2.5x² + 375x
A = - 2.5 (75) ² + 375 (75) = - 2.5 (5625) + 28125 = - 14062.5 + 28125 = 14062.5
Step-by-step explanation:
I want to know the distance
here's the answer to your question
5
Select the correct answer.
What is this expression in simplified form?
5/2 . 9/6
Answer:
Bro 1st expression is in simplest form and 2nd in simplest is 3/2
Step-by-step explanation:
If you like my answer than please mark me brainliest
Answer:
(5/2)*(9/6)
three can go into the fraction(9/6) giving(3/2)
(5/2)*(3/2)=15/4
mark as brainliest
Which power does this expression simplify to?
[(7)(7)
1
- -
ооо
74
O
Step-by-step explanation:
Answer is in attached image...
hope it helps
Answer:
its a
Step-by-step explanation:
just did it
Nadia is ordering cheesecake at a restaurant, and the server tells her that she can have up to five toppings: caramel, whipped cream, butterscotch sauce, strawberries, and hot fudge. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge
Answer:
The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P = 1/32 = 0.03125
Step-by-step explanation:
There are up to 5 toppings, such that the toppings are:
caramel
whipped cream
butterscotch sauce
strawberries
hot fudge
We want to find the probability that, If the server randomly chooses which toppings to add, she gets just caramel, butterscotch sauce, strawberries, and hot fudge.
First, we need to find the total number of possible combinations.
let's separate them in number of toppings.
0 toppins:
Here is one combination.
1 topping:
here we have one topping and 5 options, so there are 5 different combinations of 1 topping.
2 toppings.
Assuming that each topping can be used only once, for the first topping we have 5 options.
And for the second topping we have 4 options (because one is already used)
The total number of combinations is equal to the product between the number of options for each topping, so here we have:
c = 4*5 = 20 combinations.
But we are counting the permutations, which is equal to n! (where n is the number of toppings, in this case is n = 2), this means that we are differentiating in the case where the first topping is caramel and the second is whipped cream, and the case where the first topping is whipped cream and the second is caramel, to avoid this, we should divide by the number of permutations.
Then the number of different combinations is:
c' = 20/2! = 10
3 toppings.
similarly to the previous case.
for the first topping there are 5 options
for the second there are 4 options
for the third there are 3 options
the total number of different combinations is:
c' = (5*4*3)/(3!) = (5*4*3)/(3*2) = 10
4 toppings:
We can think of this as "the topping that we do not use", so there are only 5 possible toppings to not use, then there are 5 different combinations with 4 toppings.
5 toppings:
Similar to the first case, here is only one combination with 5 toppings.
So the total number of different combinations is:
C = 1 + 5 + 10 + 10 + 5 + 1 = 32
There are 32 different combinations.
And we want to find the probability of getting one particular combination (all of them have the same probability)
Then the probability is the quotient between one and the total number of different combinations.
p = 1/32
The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P = 1/32 = 0.03125
write your answer in simplest radical form
Answer:
z = √3
Step-by-step explanation:
sin (30°) = z / 2√3
z = sin (30°) 2√3
z = √3
Match each division expression to its quotient
[tex]\frac{122}{10}*(-\frac{10}{61} )[/tex]Let's start by calculating their values one by one, and then we can match them.
Starting with [tex]-2\frac{2}{5} \div\frac{4}{5}[/tex], we can simplify this more by adding [tex]2*5[/tex] to the nominator. That gives us [tex]-\frac{12}{5} \div\frac{4}{5}[/tex]. Now we can apply the Keep-Change-Flip rule. Keep the first fraction as it is, change the division sign into multiplication, flip the second fraction. [tex]-\frac{12}{5} *\frac{5}{4}[/tex]. We apply fraction multiplication which is simply multiplying the first nominator by the first nominator and the same for the dominator. and the result is [tex]-\frac{60}{20}[/tex] or simply -3.
[tex]-2\frac{2}{5} \div\frac{4}{5} = -3[/tex]
Now, we calculate the second one, [tex]-12.2\div(-6.1)[/tex]. This can be re-written as [tex]-\frac{122}{10}\div(-\frac{61}{10} )[/tex]. As we did in the previous part we apply the Keep-Change-Flip, this will give us [tex]-\frac{122}{10}*(-\frac{10}{61} )[/tex]. Do the multiplication and the result will be [tex]\frac{1220}{610}[/tex], we can divide both the nominator and dominator by 10 which will result [tex]\frac{122}{61}[/tex] and finally we know that [tex]61*2=122[/tex] and we can divide both of them again by 61 which will result [tex]\frac{2}{1} =2[/tex]
[tex]-12.2\div(-6.1)=2[/tex]
You can try solving the rest by yourself but here's is the final answer for them both:
[tex]16\div(-8)=-2\\3\frac{3}{7} \div1\frac{1}{7} =3[/tex]
The average weight of a professional football player in 2009 was pounds. Assume the population standard deviation is pounds. A random sample of professional football players was selected.
Required:
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will be less than 230 pounds?
c. What is the probability that the sample mean will be more than 231 pounds?
d. What is the probability that the sample mean will be between 248 pounds and 255 pounds?
Answer:
6.286;
0.0165
0.976
0.1995
Step-by-step explanation:
Given that :
Mean, μ = 243. 4
Standard deviation, σ = 35
Sample size, n = 31
1.)
Standard Error
S. E = σ / √n = 35/√31 = 6.286
2.)
P(x < 230) ;
Z = (x - μ) / S.E
P(Z < (230 - 243.4) / 6.286))
P(Z < - 2.132) = 0.0165
3.)
P(x > 231)
P(Z > (231 - 243.4) / 6.286))
P(Z > - 1.973) = 0.976 (area to the right)
4)
P(x < 248)
P(Z < (248 - 243.4) / 6.286))
P(Z < 0.732) = 0.7679
P(x < 255)
P(Z < (255 - 243.4) / 6.286))
P(Z < 1.845) = 0.9674
0.9674 - 0.7679 = 0.1995
To win at LOTTO in one state, one must correctly select numbers from a collection of numbers (1 through ). The order in which the selection is made does not matter. How many different selections are possible?
Answer: If order does not matter then we can use following formula to find different combinations of 6 numbers out of 46 numbers
Step-by-step explanation: Use following Combination formula
nCr = n! / r!(n-r)!
n=46
r=6
=46!/6!(46-6)!
=46!/[6!(40)!]
=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)
Cancel out 40!
=46*45*44*43*42*41/(6*5*4*3*2*1)
=6744109680/720
=9366819
Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))
Probably a simple answer, but I'm completely lost at what I'm being asked here.
Answer:
[tex]\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}[/tex]
Step-by-step explanation:
We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:
[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]
So, we can let j be the inverse function of h.
Function h is given by:
[tex]\displaystyle h(x) = y = 3x-2[/tex]
Find its inverse. Flip variables:
[tex]x = 3y - 2[/tex]
Solve for y. Add:
[tex]\displaystyle x + 2 = 3y[/tex]
Hence:
[tex]\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}[/tex]
Therefore, a = 1/3 and b = 2/3.
We can verify our solution:
[tex]\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]
