Answer:
r=$14,400
The hotel should charge $120
Step-by-step explanation:
Revenue (r)= p * n
where,
p = price per item
n = number of items sold
A change in price leads to a change in number sold
A variable to measure the change in p and n needs to be introduced
Let the variable=x
Such that
p + x means a one dollar price increase
p - x means a one dollar price decrease
n + x means a one item number-sold increase
n - x means a one item number-sold decrease
for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)
know that at $60 per room, the hotel rents 210 rooms
r = (60 + 2x) * (210 - 3x)
=12,600-180x+420x-6x^2
=12,600+240x-6x^2
r=2100+40x-x^2
= -x^2 +40x+2100=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a= -1
b=40
c=2100
x= -b +or- √b^2-4ac / 2a
= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)
= -40 +or- √1600-(-8400) / -2
= -40 +or- √ 1600+8400 / -2
= -40 +or- √10,000 / -2
= -40 +or- 100 / -2
x= -40+100/-2 OR -40-100/-2
=60/-2 OR -140/-2
= -30 OR 70
x=70
The quadratic equation has a maximum at x=70
p+2x
=60+2(30)
=60+60
=$120
r= (60 + 2x) * (210 - 3x)
={60+2(30)}*{(210-3(30)}
r=(60+60)*(210-90)
=120*120
=$14,400
1. Manuel quiere fabricar banderitas chilenas para venderlas en los partidos de la selección nacional. Si se demora 1 hora en hacer 45 banderitas y trabaja 5 horas diarias. ¿Cuántos días se demorará en fabricar 1800 banderitas?
Answer:
[tex]\large \boxed{\text{Eight days}}[/tex]
Step-by-step explanation:
1. Calculate the hours
[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]
2. Calculate the days
[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]
Using Pascal’s Theorem, expand the expression 〖(2x-y)〗^3
Answer:
(2x - y)³ = 8x³ - 12x²y + 6xy² - y³
Step-by-step explanation:
Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.
For the expansion of
(a + b)ⁿ
As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.
The coefficient of terms are obtained starting from 1 for n = 0.
- For the next coefficients of terms are 1, 1 for n = 1.
- For n = 2, it is 1, 2, 1
- For n = 3, it is 1, 3, 3, 1
The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.
So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.
The Pascal's triangle is
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ
So, for n = 3, the coefficients are 1, 3, 3, 1
Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n
So,
(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]
= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)
= 8x³ - 12x²y + 6xy² - y³
Hope this Helps!!!
What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
What point lies on the line described by the equation below? Y+3=2 (x-1
Answer:
[tex]\boxed{(1, -3)}[/tex]
Step-by-step explanation:
[tex]y+3=2 (x-1)[/tex]
Put equation in slope-intercept form.
[tex]y=mx+b[/tex]
[tex]y=2(x-1)-3[/tex]
[tex]y=2x-2-3[/tex]
[tex]y=2x-5[/tex]
Let x = 1
[tex]y=2(1)-5[/tex]
[tex]y=2-5[/tex]
[tex]y=-3[/tex]
The point (1, -3) lies on the line.
if 5x - 17 = -x +7, then x =
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
What is the slope of the line
described by -4X + 2Y = 16?
A. -2
B. -4
C. 4
D. 2
E. 16
Answer: THe slope is 2
SO answer d
Step-by-step explanation:
-4X + 2Y = 16 add 4x to the other side so equation is
2y=16+4x divided by 2
y=8+2x
when Charles eats Oreos , he likes to dunk 2 out of every 5 cookies in a cold glass of milk. if he eats a total of 15 Oreos , how many will he dunk ? how many will ge eat without dunking?
Answer: 6 with milk, 9 without
Step-by-step explanation:
2/5 of the cookies he eats are dunked. Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.
Hope it helps <3
Use Bayes' theorem to find the indicated probability 5.8% of a population is infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
a. 0.905
b. 0.585
c. 0.038
d. 0.475
Answer:
b. 0.585
Step-by-step explanation:
According to Bayes' theorem:
[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]
Let A = Person is infected, and B = Person tested positive. Then:
P(B|A) = 93.9%
P(A) = 5.8%
P(B) = P(infected and positive) + P(not infected and positive)
[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]
Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:
[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]
The probability is 0.585.
PLEASE ANSWER FAST I WILL MARK BRAINLEIST AMD 20 POINTSBased on the figure below what is the value of X
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
The two angles are complementary to each other.
That means they add up to 90 degrees.
[tex]5x+15+30=90[/tex]
[tex]5x+45=90[/tex]
[tex]5x=45[/tex]
[tex]x=9[/tex]
Answer:
x = 9
Step-by-step explanation:
So you know that the total is 90 degrees.
What you need to do is create an equation.
5x + 15 + 30 = 90
Then, solve the equation like this.
5x + 15 + 30 = 90
5x + 45 = 90
5x = 90 - 45
5x = 45
x = 45 ÷ 5
x = 9
Hope this helps! :)
PLLZZZZ help me find x you are AWSOME!! I need this ASAP
Answer:
27°
Step-by-step explanation:
D is 72° because it alternates with B, alternate angles are equal.
2x+72°+2x= 180° because it is a straight line.
4x+72°=180°
4x=108°
x=27°
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A double-blind experiment is used to increase the placebo effect. Choose the correct answer below. A. The statement is false. Double blinding has no effect on the placebo effect. B. The statement is false. Double blinding is used to increase the randomization. C. The statement is true. D. The statement is false. Double blinding is used to decrease the placebo effect.
Answer:
D. The statement is false. Double blinding is used to decrease the placebo effect.
Step-by-step explanation:
In a double blind study, neither researchers nor the participants know which group is receiving the placebo. If the researchers do not know which group took the medication, they cannot influence the behavior of this group, knowingly or nor, by suggesting how they should behave.
Therefore, a double-blind experiment is used to decrease the placebo effect.
The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Answer:
after 6 half lives: 210(1/2)^6= 3.28125
Step-by-step explanation:
isotope to be reduced to half its initial mass at first:
210(1/2)=105 half it is original weight
after second life: 210(1/2)^2=105(1/2)=52.5
after third : 210(1/2)^3=52.5/2=26.25
after fourth : 26.25/2=12.125
after fifth : 13.125/2
after 6 half lives: 210(1/2)^6= 3.28125
√9m^2n^2 + 2√m^2n^2 - 3mn
Answer:
I think it is
Step-by-step explanation:
Answer:
5n√2m^ - 3mn
Step-by-step explanation:
Section 8
Find the mean of these numbers:
24 18
37
82 17
26
Answer:
[tex]\boxed{Mean = 34.33}[/tex]
Step-by-step explanation:
Mean = Sum of Observations / No. Of Observations
Mean = (24+18+37+82+17+26)/6
Mean = 206 / 6
Mean = 34.33
A restaurant gat an average of 14 calls in a 2 hr time period. What is the probability that at most 2 calls in 45 min period
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
Con proceso por favor
Answer:se
Step-by-step explanation:
In the equation, the value of a is:
Answer:
Please check if the answer is a = 4 or not
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))
The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time. When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year. By how much does the machine depreciate during the fifth year
Answer: The machine depreciates during the fifth year by $4000.
Step-by-step explanation:
Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.
When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.
Then, the machine depreciates A(x) during the fifth year as
[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]
Hence, the machine depreciates during the fifth year by $4000.
A catering company is catering a large wedding reception. The host of the reception has
asked the company to spend a total of $454 on two types of meat: chicken and beef. The
chicken costs $5 per pound, and the beef costs $ 7 per pound. If the catering company
buys 25 pounds of chicken, how many pounds of beef can they buy?
The answer is 47 pounds
Explanation:
1. First, let's calculate the amount of money that was spent on chicken
$5 per pound of chicken x 25 pounds = $125
2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.
$454 (total) - $125 (chicken) = $329
3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.
$329 / $7 = 47 pounds
At noon a passenger train leaves the Dupont Railway station and travels due east for 2 hours. At 12:45 pm the same day a second passenger train leaves the same railway station and travels due west for 1 hour and 15 minutes at a speed 10 kilometers per hour slower than the first passenger train. At 2pm the two trains were 215 kilometers apart. How fast had each train been traveling
Answer:
The speed of the first train is 70 km/hr
The speed of the second train is 60 km/hr
Step-by-step explanation:
For the first train:
Travel time = 2 hours
The speed = ?
we designate the speed as V
For the second train:
The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)
speed = 10 km/hr slower than that of the first train, we can then say
the speed = V - 10
The total distance traveled by both trains in the opposite direction of one another is 215 km
we can put this problem into an equation involving the distance covered by the trains.
we know that distance = speed x time
the distance traveled by the first train will be
==> 2 hrs x V = 2V
the distance traveled by the second train will be
==> 1.25 hrs x (V - 10) = 1.25(V - 10)
Equating the above distances to the total distance between the trains, we'll have
2V + 1.25(V - 10) = 215
2V + 1.25V - 12.5 = 215
3.25V = 215 + 12.5
3.25V = 227.5
V = 227.5/3.25 = 70 km/hr this is the speed of the first train
Recall that the speed of the second train is 10 km/hr slower, therefore
speed of the second train = 70 - 10 = 60 km/hr
The speed of the trains are 70km/hr and 60km/hr respectively.
The distance of the first train will be represented by: = 2 × D = 2D
The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).
Based on the information given in the question, the equation to solve the question will be:
2D + 1.25(D - 10) = 215
Collect like terms
2D + 1.25D - 12.5 = 215
3.25D = 215 + 12.5
3.25D = 227.5
D = 227.5/3.25
D = 70km/hour
The speed of the second train will be:
= 70 - 10 = 60km per hour.
Read related link on:
https://brainly.com/question/24720712
4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7
Answer:
[tex]1 \frac{1}{4} [/tex]Step-by-step explanation:
[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]
To divide by a fraction, multiply the reciprocal of that fraction
[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]
Reduce the number with the G.C.F 7
[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]
Reduce the numbers with the G.C.F 17
[tex] \frac{5}{6} \times \frac{3}{2} [/tex]
Reduce the numbers with the G.C.F 3
[tex] \frac{5}{2} \times \frac{1}{2} [/tex]
Multiply the fraction
[tex] \frac{5}{4} [/tex]
In mixed fraction:
[tex]1 \frac{1}{4} [/tex]
Hope this helps..
Good luck on your assignment...
In a random sample of 40 refrigerators, the mean repair cost was $150. Assume the population standard deviation is $15.50. Construct a 99% confidence interval for the population mean repair cost. Then change the sample size to n = 60. Which confidence interval has the better estimate?
Answer: ($143.69, $156.31)
Step-by-step explanation:
Confidence interval to estimate population mean :
[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = population standard deviation
n= sample size
[tex]\overline{x}=[/tex] Sample mean
z= critical value.
As per given,
n= 40
[tex]\sigma[/tex] = $15.50
[tex]\overline{x}=[/tex] $150
Critical value for 99% confidence level = 2.576
Then, 99% confidence interval for the population mean:
[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]
Hence, the required confidence interval : ($143.69, $156.31)
Look at the number pattern shown below:3 × 17 = 5133 × 167 = 5511333 × 1667 = 555111What will be 33333 × 166667?
Answer:
33333 x 166667 = 5555511111
I think that is the answer you wanted
Step-by-step explanation:
166667
x 33333
5555511111
Use the minimum and maximum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 14, max = 121, 8 classes
Answer:
The class width is [tex]C_w \approx 13[/tex]
Step-by-step explanation:
From the question we are told that
The upper class limits is [tex]max = 121[/tex]
The lower class limits is [tex]min = 14[/tex]
The number of classes is [tex]n = 8 \ classes[/tex]
The class width is mathematically represented as
[tex]C_w = \frac{max - min}{n }[/tex]
substituting values
[tex]C_w = \frac{121 - 14}{8 }[/tex]
[tex]C_w = 13.38[/tex]
[tex]C_w \approx 13[/tex]
Since
Find the mean, median, and mode of the data, if possible. f any of these measures cannot be found or a measure does not represent the center of the data, explain why.
A sample of seven admission test scores for a professional school are listed below
11.3 10.6 11.7 9.7 11.7 9.5 11.7
What is the mean score? Select the correct choice below and fill in any answer box to complete your choice
A. The mean score is Round to one decimal place as needed.)
B. There is no mean score. Does the mean represent the center of the data?
A. The mean represents the center
B. The mean does not represent the center because it is the smallest data value.
C. The mean does not represent the center because it is not a data value.
D. The mean does not represent the center because it is the largest data value.
What is the median score? Select the correct choice below and fill in any answer box to complete your choice.
A. The median score is 0
B. There is no median score.
Does the median represent the center of the data? (Round to one decimal place as needed.)
A. The median represents the center.
B. The median does not represent the center because it is not a data value. °
C. The median does not represent the center because it is the largest data value.
D. The median does not represent the center because it is the smallest data value.
What is the mode of the scores? Select the correct choice below and fill in any answer box to complete your choice
A. The mode(s) of the scores is (are)
B. There is no mode. Does (Do) the mode(s) represent the center of the data?
(Use a comma to separate answers as needed.)
A. The mode(s) represent(s) the center
B. The mode(s) can't represent the center because it (they) is (are) not a data value.
C. The mode(s) does (do) not represent the center because it (one) is the largest data value.
D. The mode(s) does (do) not represent the center because it (one) is the smallest data value.
Answer:
Step-by-step explanation:
Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.
Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7
Mean = 76.2/7
Mean = 10.9
The mean score is 10.9 to 1 decimal place.
Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.
b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;
9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7
After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.
The median represents the center
c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.
The mode(s) does (do) not represent the center because it (one) is the largest data value.
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
angle JKL = 120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.
Consider quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
angle JKL = 360 - 90 - 60 -90 = 120 degrees
Answer:
120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.
look at quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
solve the rational equation 5/x = 4x+1/x^2
Answer:
x = 1
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
Since the expression on each side of the equation has the same denominator, the numerators must be equal
5x =4x+1
Move all terms containing x to the left side of the equation.
Hope this can help you
144 + h^2 = 225 WHAT THE HECK DOES ^ MEAN!???
Answer:
h^2 means h²
(h squared)
Step-by-step explanation:
Step 1: Write equation
144 + h² = 225
Step 2: Subtract 144 on both sides
h² = 81
Step 3: Take square root
√h² = √81
h = 9