Answer: $21,000
Step-by-step explanation:
Cleaning expense is only related to the floor space occupied by the department.
If the company spend a total of $30,00 on cleaning each year.
And Department B occupies 70% of the company floor.
Therefore, the company spends 70% of their cleaning expense on department B
Hence, the cleaning expense on department B is given as;
= 70% of $30,000
= $21,000
Department B should be allocated $21,000 for cleaning expenses, as it occupies 70% of the floor space and the total cleaning expense is $30,000.
Explanation:To determine how much cleaning expense should be allocated to Department B at Calico Company, you should consider the proportion of floor space occupied by the department. Since cleaning expenses are primarily based on vacuuming the carpet, it's reasonable to use floor space as the basis for allocation.
Department B occupies 70% of the company's floor space. With a total annual cleaning expense of $30,000, we can calculate Department B's share of the expense by multiplying the total expense by the percentage of space that Department B occupies:
Allocated expense to Department B = Total cleaning expense × Department B's percentage of floor space
Allocated expense to Department B = $30,000 × 70%
Allocated expense to Department B = $30,000 × 0.70
Allocated expense to Department B = $21,000
Therefore, $21,000 should be allocated to Department B for cleaning expenses.
The New York Knicks must win at least 3/7 of their remaining games to qualify for the NBA playoffs. If they have 15 games left qnd they win 7 of them,they feel they will 7 of them,they feel they will be eligible to compete in the playoffs. Are they correct? Explain and justify your answer.
Answer:
Step-by-step explanation:
In order to qualify for the NBA playoffs, the New York Knicks must win at least 3/7 of their remaining games. Number of games remaining to be played is 15.
3/7 × 15 = 6.43
Since it is above 6 and closest to 7,
It means that they must win at least 7 games in order to qualify for the playoffs.
So they were correct by thinking that if they won 7 games from 15, they will be eligible to compete in the playoffs.
PLEASE HELPPP WILL GIVE BRAINLIEST!!!!!
Let f(x) = 36x^5 − 44x^4 − 28x^3 and g(x) = 4x^2. Find f(x)/g(x) .
A. 9x^2 − 11x − 7
B. 9x^2 + 11x + 7
C. 9x^3 − 11x^2 − 7x
D. 9x^3 + 11x^2 + 7x
Answer:
C. 9x³ − 11x² − 7xStep-by-step explanation:
[tex]f(x)=36x^5-44x^4-28x^3\\\\g(x)=4x^2\\\\\dfrac{f(x)}{g(x)}=\dfrac{36x^5-44x^4-28x^3}{4x^2}\\\\\dfrac{f(x)}{g(x)}=\dfrac{(4x^2)(9x^3)-(4x^2)(11x^2)-(4x^2)(7x)}{4x^2}\\\\\dfrac{f(x)}{g(x)}=\dfrac{(4x^2)(9x^3-11x^2-7x)}{4x^2}\qquad\text{cancel}\ 4x^2\\\\\dfrac{f(x)}{g(x)}=9x^3-11x^2-7x[/tex]
Answer:option C is the correct answer
Step-by-step explanation:
f(x) = 36x^5 − 44x^4 − 28x^3
g(x) = 4x^2
We want to determine f(x)/g(x). It becomes
(36x^5 − 44x^4 − 28x^3) /(4x^2)
Looking at the numerator, each term in the numerator can divide the term in the denominator without remainder. it means that the term in the denominator is a common factor of the numerator and thus, 4x^2 can be factorized out of the numerator. It becomes
4x^2(9x^3 − 11x^2 − 7x) /(4x^2)
4x^2 in the numerator cancels out 4x^2 in the denominator. It becomes
9x^3 − 11x^2 − 7x
You're dealt three cards in a row at random from a standard deck of 52 cards.Now suppose that you are dealt a pair or three of a kind in the three cards. What are the odds that you had a pair on your first two cards; that is, that your first two cards were of the same denomination? A) 22,776/132,600B) 1/13C) 7,800/22,776D) 3/51
Answer:D
Step-by-step explanation:
Given
There are 52 cards out which we have to choose 3 cards
and starting 2 will have same denomination
For first card we can withdraw any card of any denomination and for second card we have to choose card of same denomination
There are total of 4 cards of same denomination and after 1 st card is drawn we need to choose 1 card out of 3 card
Probability[tex]=\frac{^3C_1}{^{51}C_1}[/tex]
[tex]=\frac{3}{51}[/tex]
While some nonsmokers do not mind being seated in a smoking section of a restaurant, about 60% of the customers demand a smoke-free area. A new restaurant with 120 seats is being planned.
How many seats should be in the nonsmoking area in order to be very sure of having enough seating there? Comment on the assumptions and conditions that support your model, and explain what "very sure" means to you.
Answer: There are 72 seats in order to be very sure of having enough seating.
Step-by-step explanation:
Since we have given that
Total number of seats is being planned = 120
Percentage of customers demand a smoke free area = 60%
So, Number of seats that should be in the non smoking area in order to be very of having enough seating would be
[tex]\dfrac{60}{100}\times 120\\\\=0.6\times 120\\\\=72[/tex]
Hence, there are 72 seats in order to be very sure of having enough seating.
Samantha has a rectangular shaped fish tank in her room. The tank has a height of 2.6 ft, a width of 2.1 ft, and a length of 3.9 ft. What is the BEST approximation of the amount of water her fish tank can hold?
Answer: the BEST approximation of the amount of water her fish tank can hold is 21ft^3
Step-by-step explanation:
The shape of Samantha's fish tank is rectangular. The volume of the rectangular fish tank would be expressed as LWH
Where
L represents length of the tank
W represents the width of the tank.
H represents the height of the tank.
The tank has a height of 2.6 ft, a width of 2.1 ft, and a length of 3.9 ft.
This means that the volume of the fish tank would be
Volume = 2.6 × 2.1 × 3.9
= 21.294 ft^3
Write the equation of the line that passes through (0,3) and (-4,-1).
Answer:
number 1
Step-by-step explanation:
if you'd look at Number One X is negative and if you look at the two number problems the x that is negative is negative for and then the one that is positive is the Y which is 3
Craig earns 5 points each time he catches a bad guy in his game.He catches 2 types of bad guys,pirates and ghosts.Craig caught 24 ghost and 36 pirates.How many points did he earn?
Answ300er:
300
24+36=60
60x5=300
Step-by-step explanation:
Answer:he would earn 300 points
Step-by-step explanation:
Let x represent the number of pirates that Craig catches.
Let y represent the number of ghosts that Craig catches.
Craig earns 5 points each time he catches a bad guy in his game. The total number of points that Craig will earn if he catches x pirates and y ghosts would be
5x + 5y
Craig caught 24 ghost and 36 pirates. Therefore, total number of points earned would be
5×36 + 5×24 = 180 + 120 = 300 points.
the graph of f(x) can be compressed vertically and shifted to the left to produce the graph of g(x). if f(x) =x^3, which of the following could be the equation of g(x)?
Answer: [tex]B.\ g(x)=\frac{1}{4}(x+3)^3[/tex]
Step-by-step explanation:
The misssing options are: [tex]A.\ g(x)=4(x-3)^3\\\\B.\ g(x)=\frac{1}{4}(x+3)^3\\\\C.\ g(x)=4(x+3)^3\\\\D.\ g(x)=\frac{1}{4}(x-3)^3[/tex]Some transformations for a function f(x) are shown below:
1. If [tex]f(x-k)[/tex], the function is shifted right "k" units.
2. If [tex]f(+k)[/tex], the function is shifted left "k" units.
3. If [tex]bf(x)[/tex] and [tex]b>1[/tex], the function is stretched vertically by a factor of "b".
4. If [tex]bf(x)[/tex] and [tex]0<b<1[/tex], the function is compressed vertically by a factor of "b".
In this case, you know that the parent function f(x) is:
[tex]f(x)=x^3[/tex]
If the graph of the function g(x) is obtained by compressing vertically and shifting the function f(x) to the left, then:
[tex]g(x)=bf(x+k)[/tex] and [tex]0<b<1[/tex]
Based on this, you can identify that the following function could be the equation of the g(x):
[tex]g(x)=\frac{1}{4}(x+3)^3[/tex]
Yrone likes to snack on his big bag of candy. He takes 8888 pieces of candy from the bag each time he snacks. After eating 181 snacks, there are only 6 pieces of candy remaining in the bag. The number c of pieces of candy remaining in the bag is a function of s, the number of snacks Tyrone eats. Write the function's formula. c=, equals
Answer:
The Function formula is given by [tex]c = 150 -8s[/tex].
Step-by-step explanation:
Given:
Number of candies eaten each time he has snacks = 8
Number of snacks ate = 18
Now Number of candies eaten will be equal to number of snacks he ate multiplied by number of candies eaten each time he ate snacks
Hence. Number of candies he ate in 18 snacks = 18* 8 = 144 candies
Also given that 6 candies are remaining after eating 18 snacks;
Total Number of candies at the beginning will be = Number of candies he ate in 18 snacks + Number of candies remaining after 18 snacks
Total Number of candies at the beginning will be = 144 + 6 = 150 candies
Now, let The number of pieces of candy remaining in the bag be 'c'
Also Let the number of snacks Tyrone eats be 's'
Since it has been given that in number of candies in each snack is 8 candies.
Therefore,In 's' snacks , candies will be eaten by him = [tex]8s[/tex]
Total number of candies = 150
Now Remaining candies 'c' is equal to Total number of candies minus number of candies eaten in 's' snacks.
framing in equation form we get;
Remaining candies [tex]c = 150 -8s[/tex]
Hence the Function formula is given by [tex]c = 150 -8s[/tex].
In a fruit survey, children choose their favorite fruit out of apples, bananas and oranges. 29% chose oranges and 30% chose bananas. What percentage chose apples?? show me your answer plz
Following the guidelines of the Food and Drug Administration, Dale tries to eat at least 5 servings of fruit each day. For the first six days of one week, she had 4, 5, 3, 5, 4, and 4 servings. How many servings of fruit should Dale eat on Saturday to average at least 5 servings per day for the week?
Answer:
[tex] x = 35-4-5-3-5-4-4=10[/tex]
So then the value for Saturday should be equal or higher to 10 servings per day in order to have an average of 5 or higher.
Step-by-step explanation:
First we can begin finding the original average for the first 6 days of the week. We assume that the week start at Sunday, and we have data for Sunday, Monday, Tuesday, Wednesday, Thrusday, Friday. And we can find the average like this:
[tex]\bar X_i =\frac{4+5+3+5+4+4}{6}=4.167[/tex]
And for this case we have the original average under the goal of 5, so we need to find a value x, such that the final average taking in count the 7 days of the week would be 5.
[tex]\bar X_f = \frac{4+5+3+5+4+4+x}{7}=5[/tex]
So we can nultiply both sides by 7 and we got:
[tex]4+5+3+5+4+4+x = 35[/tex]
And then solving for x we got:
[tex] x = 35-4-5-3-5-4-4=10[/tex]
So then the value for Saturday should be equal or higher to 10 servings per day in order to have an average of 5 or higher.
What is the average rate of change of the function on the interval from x = 0 to x = 5?
f(x)=
1/2^(3)x
Final answer:
The average rate of change of the function on the interval from x = 0 to x = 5 is 1/8.
Explanation:
The average rate of change of a function on an interval is calculated by finding the slope of the secant line between two points on the interval. In this case, the interval is from x = 0 to x = 5.
The function is [tex]f(x) = (1/2^(3))x.[/tex]
To find the average rate of change, we need to calculate the slope between the points (0, f(0)) and (5, f(5)).
Using the formula for slope, [tex]m = (y2 - y1) / (x2 - x1)[/tex], we substitute the values from the given function and interval:
[tex]m = ((1/2^(3))(5) - (1/2^(3))(0)) / (5 - 0)[/tex]
m = (5/8 - 0) / 5 = 5/40 = 1/8
Therefore, the average rate of change of the function on the interval from x = 0 to x = 5 is 1/8.
What is the cross section shown below?
Circle
Ellipse
Parabola
Hyperbola
Explanation:
Imagine that white rectangle as a blade that cuts the cylinder as the diagram shows. If you pull the top cylinder off and examine the bottom of that upper piece, then you'll see a circle forms. It's congruent to the circular face of the original cylinder. This is because the cutting plane is parallel to both base faces of the cylinder. Any sort of tilt will make an ellipse form. Keep in mind that any circle is an ellipse, but not vice versa.
Another example of a cross section: cut an orange along its center and notice that a circle (more or less) forms showing the inner part of the orange.
Yet another example of a cross section: Imagine an egyptian pyramid cut from the top most point on downward such that you vertically slice it in half. If you pull away one half, you should see a triangular cross section forms.
Good morning,
Answer:
it’s a circleStep-by-step explanation:
Because the plane is parallel to the cylinder base.
:)
for every natural number n, n^5 + 4n is a multiple of 5 could begin with... what is the appropriate next step
Answer: The proof is done below.
Step-by-step explanation: We are given to prove that the following statement is true :
"For every natural number n, [tex]n^5+4n[/tex] is a multiple of 5."
We will prove the above statement by MATHEMATICAL INDUCTION.
Let n = 1. Then, we get
[tex]n^5+4n=1^5+4\times5=5,[/tex] a multiple of 5.
Let n = 2. Then, we get
[tex]n^5+4n=2^5+4\times2=40,[/tex] a multiple of 5.
Let the statement be true for n = m, where m is a natural number.
So,
[tex]m^5+4m=5k,[/tex] for any natural number k.
Then,
[tex](m+1)^5+4(m+1)\\\\=m^5+5m^4+10m^3+10m^2+5m+1+4m+4\\\\=(m^5+4m)+5m^4+10m^3+10m^2+5m+5\\\\=5k+5(m^4+2m^3+2m^2+m+1)\\\\=5(k+m^4+2m^3+2m^2+m+1),[/tex] which is a multiple of 5.
Therefore, if the statement is true for n = m, then it is true for n = m+1.
That is, the statement is true for all natural numbers n.
Hence proved.
An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment. For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3. For the ANOVA, what value would be obtained for SSbetween?
a. 30b. 20c. 10d. 2
Answer: c. 10
Step-by-step explanation:
Given : An independent-measures research study compares three treatment conditions using a sample of n = 5 in each treatment.
For this study, the three sample means are, M1 = 1, M2 = 2, and M3 = 3.
Grand mean = [tex]\overline{X}=\dfrac{M1+M2+M3}{3}[/tex] [All sample have equal elements]
[tex]=\dfrac{1+2+3}{3}=2[/tex]
For ANOVA,
[tex]SS_{between}=n\sum(M_i-\overline{X})^2[/tex] , where i= 1, 2 , 3
[tex]SS_{between}=5((1-2)^2+(2-2)^2+((3-2)^2)[/tex]
[tex]SS_{between}=5((-1)^2+(0)^2+((1)^2)= 5(1+1)=10[/tex]
Hence,the value would be obtained for [tex]SS_{between}=10[/tex] .
hence, the correct answer = c. 10
Final answer:
For an independent-measures research study comparing three treatment conditions with n = 5 in each treatment, the SSbetween value calculated using ANOVA is 10.
Explanation:
To calculate the SSbetween (Sum of Squares Between) for an independent-measures research study using a one-way ANOVA, we first need the mean of the group means, also known as the grand mean (GM), and then use the formula to find SSbetween: SSbetween = ∑ n(M - GM)², where n is the number of subjects in each group, M is the group mean, and GM is the grand mean.
In this case, with three sample means of M1 = 1, M2 = 2, and M3 = 3, each with n = 5, the grand mean is GM = (1+2+3) / 3 = 2. Using the formula, we have:
SSbetween = 5(1 - 2)² + 5(2 - 2)² + 5(3 - 2)²
SSbetween = 5(-1)² + 5(0)² + 5(1)²
SSbetween = 5(1) + 5(0) + 5(1)
SSbetween = 5 + 0 + 5
SSbetween = 10.
Therefore, the value obtained for SSbetween in this study would be 10.
square root of 225 divided by 13 minus 8 plus 3 to the second power plus square root of 81 minus square root of 1 to the second power
Answer:
uo
Step-by-step explanation:
Jariah volunteers at the hospital during the week. She volunteers 3 hours on monday and thursday, 4 hours on saturday and sunday, and 2 hours on tuesday. How many hours does jariah volunteer at the hospital during the week?
Answer:
16
Step-by-step explanation:
Monday: 3
Thursday:3
Saturday:4
Sunday: 4
Tuesday:2
3+3+4+4 + 2 = 16
I need help plz
1. The range of the following relation R {(3,-5),(1,2),(-1,-4),(-1,2)} is
A. {-1,1,3}
B. {-5,-4,2)
C. {-1,-1,1,3}
D. {-4,-5,2,2}
2. The domain of the following relation R {(3,-2), (1,2), (-1,-4),(-1,2)
A. {-1,1,3}
B. {-1,-1,1,3}
C. {-4,-2,2,2}
D. {-4,-2,2}
Answer:
1 ) B. {-5 , -4 , 2}
2 ) A. {-1 , 1 , 3}
Step-by-step explanation:
1. The range of a relation is an ordered pair of real numbers to which all the real numbers in the domain relate to.
Given the Relation R: { ( 3, -5 ) , ( 1 , 2 ) , ( -1 , -4 ) , ( -1 , 2 ) }
Here The Range is the ordered pair of number towards the right in each relation.
Range = { -5 , 2 , -4 }
2. The domain of a relation is an ordered pair of real numbers which are related to any one of the element in the range of the relation.
Given the Relation R: { ( 3 , -2 ) , ( 1 , 2 ) , ( -1 , -4 ) , ( -1 , 2 ) }
Here the domain is the ordered pair of numbers towards the left in each relation.
Domain = { -1 , 1 , 3 }
On a cross-country.The anderson family planned to average 500 miles and 10 hours of drivind each day. On average,how many miles per hour did the anderson planhto drive?
Answer:
50 miles per hour
Step-by-step explanation:
Given:
Distance planned to travel each day is, [tex]D=500\ mi[/tex]
Hours of driving for covering the above distance is, [tex]t=10\ h[/tex]
The question asks to find the number of miles per hour Anderson plan to drive.
In other words, we need to calculate the average speed with which Anderson has to drive in order to cover 500 miles in 10 hours daily.
Therefore, the formula to calculate speed when distance covered and time taken are known is given as:
Average speed = [tex]\frac{Distance}{Time}[/tex]
Average speed = [tex]\frac{D}{t}[/tex]
Plug in 500 miles for 'D', 10 h for 't' and solve for speed. This gives,
[tex]\textrm{Average speed}=\frac{500}{10}\ mi/h\\\textrm{Average speed}=50\ mi/h[/tex]
Therefore, Anderson need to drive at an average of 50 miles per hour to cover the distance of 500 miles in 10 hours.
Jackson and kate jones do not pay their credit care in full, the average daily balance is $$875 and the monthly periodic rate is 2.25%, what should be the fiance charge on the statement?
Answer:
The finance charge is $19.68
Step-by-step explanation:
The finance charge on a credit card is given by the formula:
Finance Charge = The Average Daily Balance x Monthly Periodic Rate
We know that:
Average Daily Balance = $875
Monthly Periodic Rate = 2.25% = 0.0225
Using in Formula:
Finance Charge = $875 x 0.0225
Finance Charge = $19.68
To calculate the finance charge on the statement, multiply the average daily balance by the monthly periodic rate.
Explanation:To calculate the finance charge on the statement, we can use the formula:
Finance Charge = Average Daily Balance × Monthly Periodic Rate
First, convert the percentage rate to decimal form:
2.25% = 0.0225
Then, substitute the given values into the formula:
Finance Charge = $875 × 0.0225
Using a calculator, multiply $875 by 0.0225:
Finance Charge = $19.69
Therefore, the finance charge on the statement should be $19.69.
Learn more about Finance Charge Calculation here:https://brainly.com/question/15720230
#SPJ11
what time will it be eight minutes and twenty five seconds after eleven fifty one and thirty five seconds?
Answer:
After 8 minutes and 25 sec time will be 12:00
Step-by-step explanation:
We have given initial time is 11:51:35
And we have to find the time after 8 minute and 25 second
After 8 minutes time will be 51+8 = 59 minutes
So after 8 minutes time will be 11:59:35
And after 25 second time will 25 +35 = 60 sec
60 sec = 1 minute
So after 8 minutes and 25 sec time will be 11:59:35 plus 25 sec = 12:00
Answer will be 12:00
Annie gets a loan from her bank .She agrees yo borrow 8000 pounds at a fixed annual simple interest rate of 6%. She also agrees to pay the loan back over a 10 year period. How much money in total will she have paid back at the end of 10 years
Annie paid 12800 pounds at end of 10 years
Solution:
Given that Annie borrows 8000 pounds at simple interest rate of 6 %
She also agrees to pay the loan back over a 10 year period
To find: total money paid back at the end of 10 years
The total amount paid is given as:
Total amount = simple interest + principal amount borrowed
The simple interest is given as:
[tex]S.I = \frac{pnr}{100}[/tex]
Where, "p" is the principal sum
"n" is the number of years
"r" is the rate of interest
Here, p = 8000 ; r = 6 % ; n = 10 years
[tex]S.I = \frac{8000 \times 10 \times 6}{100}\\\\S.I = 4800[/tex]
Therefore total amount paid at end of 10 years is:
Total amount = 4800 + 8000 = 12800
Thus Annie paid 12800 pounds at end of 10 years
Final answer:
Annie will pay a total of 12800 pounds at the end of 10 years for her loan of 8000 pounds with an annual simple interest rate of 6%.
Explanation:
To calculate the total amount of money Annie will have paid back at the end of 10 years on her loan of 8000 pounds with an annual simple interest rate of 6%, we first need to find the total interest she will pay over the period. Simple interest can be calculated using the formula: Interest = Principal × Rate × Time. In this case, the Principal (P) is 8000 pounds, the Rate (r) is 6% or 0.06 as a decimal, and the Time (t) is 10 years.
Interest = P × r × t = 8000 × 0.06 × 10 = 4800 pounds
The total amount of interest Annie will pay over 10 years is 4800 pounds. To find the total repayment amount, we add this interest to the original loan amount.
Total repayment = Principal + Interest = 8000 pounds + 4800 pounds = 12800 pounds
At the end of 10 years, Annie will have paid back a total of 12800 pounds.
Ishaan is 727272 years old and William is 444 years old. How many years will it take until Ishaan is only 555 times as old as William?
Answer:
It will take 13 years to Ishaan age will be 5 times William age.
Step-by-step explanation:
Given : Ishaan is 72 years old and William is 4 years old.
To find : How many years will it take until Ishaan is only 5 times as old as William?
Solution :
Let x be years since today.
According to question,
Ishaan's age is I=72+x
William's age is W=4+x
Now, We want the time for Ishaan age will be 5 times William's age:
i.e. [tex]I=5W[/tex]
[tex]72+x=5(4+x)[/tex]
[tex]72+x=20+5x[/tex]
[tex]72-20=5x-x[/tex]
[tex]52=4x[/tex]
[tex]x=13[/tex]
It will take 13 years to Ishaan age will be 5 times William age.
By this time William will be 17 years old and Ishaan will be 85 years old.
It will take 13 years to Ishaan age will be 5 times William age.
Given that,
Ishaan is 72 years old and William is 4 years old.Based on the above information, the calculation is as follows:
Let x be years since today.
So,
Ishaan's age is I=72+x
William's age is W=4+x
Now
I = 5W
72 +x = 5(4 + x)
72 + x = 20 + 5x
52 = 4x
x = 13
Learn more: https://brainly.com/question/24908711?referrer=searchResults
Which Of the following represnt the range of the function y=-1/2(x+10)^2+14?
1) y>=-5 2)y>=10 3) y<=7 4) y<=14, Explain pls
Answer: the second one
Step-by-step explanation:
cuz i say so
Answer:
4). But the more correct answer is; y is less than or equal to 14.
Step-by-step explanation:
Graphing this function shows a downward facing parabola with the vertex at (-10,14). The domain must be less than or equal to 14 because it's all values including and below the vertex since there is negative a value (-1/2).
Devaughn's age is two times Sydney's age. The sum of their ages is 72 What is Sydney's age?
Answer: Devaughn's age is 48 and Sydney's age is 24
Step-by-step explanation:
72 divided by 3 gives you 24.
24+24 is 48 which is Devaughn's age.48-72 gives you 24 which is Sydney's age
Sydney is 24 and Devaughn is 48
The length of a rectangular room is 7 less than
three times the width, w, of the room. Which
expression represents the area of the room?
1 3w-4
2 3w-7
3 3w2 – 4w
4 3w²–7w
how many more days until 04-20-2069? For... school reasons....
Answer:
The answer is 18,019 days.
Step-by-step explanation:
Perform an operation on the given system that eliminates the indicated variable. Write the new equivalent system.
2x + y − 4z = 4, 2x + 4y + z = 15, 6x − 5y − z = 7
Eliminate the x-term from the third equation.
Answer:
8y-11z=5
Step-by-step explanation:
2x + y − 4z = 4, -----------A
2x + 4y + z = 15,-----------B
6x − 5y − z = 7------------C
Solving A to find the value of x
2x= 4-y+4z
x=4-y+4z/2------------------D
Putting D in C
6(4-y+4z/2) -5y -z=7
3(4-y+4z) -5y-z=7
12-3y+12z-5y-z=7
12-8y + 11z=7
-8y +11z= 7-12
-8y +11z= -5
8y-11z=5--------------E
Define g(n):=f(n!). We want to find a closed formula for g(n)g(n). First of all, we want to find a recurrence for g(n)g(n). If nn is odd, then it is pretty easy to see that g(n) = g(n-1)g(n)=g(n−1). If nn is even, try to write g(n)g(n) in terms of g(n/2)g(n/2).
Answer:
[tex]g(n)=g(n/2)+n/2[/tex]
Step-by-step explanation:
[tex](2k+1)!=1*3*5*7*...*(2k-1)*(2k+1)*2*4*6*8*...*(2k-2)*(2k)[/tex]
Notice that the odd factors of above equality don't contribute to the largest power of 2 that divides (2k+1)!
Therefore, we can conclude that [tex]g(2n+1)=g(2n)[/tex].
[tex](2k)!=1*3*5*7*...*(2k-3)*(2k-1)*2*4*6*8*...*(2k-2)*(2k)=\\= (1*3*5*...*(2k-3)*(2k-1))*((2*1)*(2*2)*(2*3)*...*(2*(k-1))*(2*k))=\\= (1*3*5*...*(2k-3)*(2k-1))*2^k*k![/tex]
Notice that the odd factors of above equality don't contribute to the largest power of 2 that divides (2k)!
Hence, [tex]g(2k)-g(k)=k[/tex]
So for [tex]k = n/2[/tex],
[tex]g(n)-g(n/2)=n/2\\g(n)=g(n/2)+n/2[/tex]
In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.). Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country. We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll. Which of the following are the appropriate hypotheses in this case?a. H0: p = .19 vs. Ha: p < .19
b. H0: p = .19 vs. Ha: p > .19
c. H0: p < .25 vs. Ha: p = .25
d. H0: p = .25 vs. Ha: p < .25
e. H0: p = .25 vs. Ha: p not equal to .25
Answer:
d. H0: p = .25 vs. Ha: p < .25
Step-by-step explanation:
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
On this case the claim that they want to test is: "If the proportion of 2005 has decreased from the info of 2004". So we want to check if the population proportion for 2005 is less than 0.25 (the value for 2004), so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.
Null hypothesis:[tex]p \geq 0.25[/tex]
The null hypothesis can be on this way: [tex]p=0.078[/tex], but is better put the complement of the alternative hypothesis.
Alternative hypothesis:[tex]p > 0.25/tex]
And the correct option would be:
d. H0: p = .25 vs. Ha: p < .25