Subtract the ceiling fan from the height of the room:
8.4 - 1.875 = 6.525 feet
The answer is:
Maury’s head will hit the fan because there are 6.525 feet between the floor and the fan, and 6.525 is less than 6.6.
Answer:
it is A
Step-by-step explanation:
If the price of a product is p (dollars), the number of units demanded is given by the equation q-pe-3p
(a) Find the price elasticity of demand by using the differentials definition of elasticity. Fully simplify your answer.
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.
Answer:
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%
Step-by-step explanation:
Given that:
the number of units demanded [tex]q = pe^{-3p}[/tex]
Taking differentiations ; we have,
[tex]\dfrac{dq}{dp}=e^{-3p}+p(-3e^{-3p})[/tex]
[tex]\dfrac{dq}{dp}=(1-3)e^{-3p}[/tex]
Now; the price elasticity of demand using the differentials definition of elasticity is:
[tex]E(p) = \dfrac{dq}{dp}*\dfrac{p}{q}[/tex]
[tex]E(p) =[(1-3)e^{-3p}]*[\dfrac{p}{pe^{-3p}}][/tex]
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
(b) Use your answer from part (a) to estimate the percent change in q when the price is raised from $2.00 to $2.10.
The estimate of the percentage change in price is :
[tex]=\dfrac{2.10-2.00}{2.00}*100 \%[/tex]
= 5%
From (a)
[tex]\mathbf{E(p) = 1 - 3p}[/tex]
Now at p = $2.00
E(2) = 1 - 3 (2.00)
E(2) = 1 - 6
E(2) = -5
The percentage change in q = -5 × 5%
The percentage change in q = -25%
Thus; we can conclude that the estimate the percent change in q when the price is raised from $2.00 to $2.10 decreases by 25%
Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. See Attached Excel for Data. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.
Answer:
The 99% confidence interval for the mean germination time is (12.3, 19.3).
Step-by-step explanation:
The question is incomplete:
Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.
We start calculating the sample mean M and standard deviation s:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\[/tex]
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\[/tex]
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=15.8.
The sample size is N=10.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075[/tex]
The degrees of freedom for this sample size are:
df=n-1=10-1=9
The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=3.25 \cdot 1.075=3.49[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3[/tex]
The 99% confidence interval for the mean germination time is (12.3, 19.3).
[tex]{f}^{4} = - 1[/tex]
O True
O False
?
Answer:
False.
Step-by-step explanation:
This statement is false, for any value of F because the power function with an even exponent is always positive or 0.
Find the value : 10a^2b^0 for a=−3, b=−8
In order to solve for the variable in the equation 2 (4 x + 3) + 4 = 3 x minus (2 x + 4), Giovanni first applies the distributive property. Which equation is a result of this step?
Answer:
8x + 6 + 4 = 3x - (2x + 4)
Step-by-step explanation:
When Gio applies the distributive property, the equation above is the result. Naturally, I look at the 1st parenthesis I see and start the 1st distributive property there first. The 2nd distributive property would be the other parenthesis where you multiply by -1, so you would get 8x + 6 + 4 = 3x - 2x - 4
Answer:
A or 8x + 6 + 4 = 3x - (2x + 4)
Step-by-step explanation:
Lily is cutting a piece of yarn into 3 (three) pieces. The 2nd piece is 3 times as long as the 1st piece, while the 3rd piece is 6 centimeters longer than the 1st piece. When the yarn has a total length of 211 centimeters, calculate the length of the first piece.
Answer:
The length of the first piece = 41 cm
Step-by-step explanation:
Let the length of the first piece = a
Let the length of the second piece = b
Let the length of the third piece = c
we are given the following:
b = 3a . . . . . (1) (The 2nd piece is 3 times as long as the 1st piece)
c = 6 + a . . . . (2) (the 3rd piece is 6 centimeters longer than the 1st piece)
a + b + c = 211 . . . . . (3) ( the yarn has a total length of 211 centimeters)
Next, let us eliminate two variables, and this can easily be done by substituting the values of b and c in equations 1 and 2 into equation 3. this is done as follows:
a + b + c = 211
a + (3a) + (6 + a) = 211 ( remember that b = 3a; c = 6 + a)
a + 3a + 6 + a = 211
5a + 6 = 211
5a = 211 - 6 = 205
5a = 205
∴ a = 205 ÷ 5 = 41 cm
a = 41 cm
Therefore the length of the first piece (a) = 41 cm
now finding b and c
substituting a into equation 1 and 2
b = 3a
b = 3 × 41 = 123
∴ b = 123 cm
c = 6 + a
c = 6 + 41 = 47
∴ c = 47 cm
Evaluate the expression. 8! − 5!
Answer:
40200
Step-by-step explanation:
(8x7x6x5x4x3x2x1) - (5x4x3x2x1)
Or simply plug 8! - 5! into the calc.
Answer:
Step-by-step explanation:
40200
Please answer this correctly
Answer:
Median
Step-by-step explanation:
I believe this is median, as the mode and median stay the same numbers with and without 26, Mean 26, Mode 45, so the median would change the most as it goes from 23 to 26
Answer:
Median
Step-by-step explanation:
Mean of 10 numbers = 260/10 = 26
Mean of 11 numbers = 286/11 = 26
No change
Median:
Median for 10 numbers
12 , 14, 15 , 17 , 19 , 27, 29 ,37 , 45, 45
Median = 19+27/2 = 46/2 = 23
Median of 11 numbers
12 , 14, 15 , 17 , 19 , 26, 27, 29 ,37 , 45, 45
Median = 26
Median changes the most
The owner of Limp Pines Resort wanted to know the average age of its clients. A random sample of 25 tourists is taken. It shows a mean age of 46 years with a standard deviation of 5 years. The width of a 98 percent confidence interval for the true mean client age is approximately:_______.
A. ± 2.492 years.
B. ± 1.711 years.
C. ± 2.326 years.
D. ± 2.797 years.
Answer:
C. ± 2.326 years.
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.01 = 0.99[/tex], so [tex]z = 2.326/tex]
Now, find the width of the interval
[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]\sigma = 5, n = 25[/tex]
So
[tex]W = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]W = 2.326*\frac{5}{\sqrt{25}}[/tex]
The correct answer is:
C. ± 2.326 years.
An account with $250 balance accrues 2% annually. If no deposits or withdrawals are made, which graphs can be used to determine approximately how many years will it take for the balance to be $282?
An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made so, to take the balance to $282 requires 6.4 years and this can be determined by using the simple interest formula.
Given :
An account with a $250 balance accrues 2% annually.No deposits or withdrawals are made.Final amount = $282SImple interest formula can be used to determine the total number of years will it take for the balance to be $282.
The formula of simple interest is given by:
[tex]\rm A = P(1+rt)[/tex]
where A is the final amount, P is the initial principal balance, r is the annual interest rate and t is the time in years.
Now, put the known values in equation (1).
[tex]\rm 282 = 250(1+0.02t)[/tex]
[tex]\rm 282=250+5t[/tex]
32 = 5t
t = 6.4 years
So, 6.4 years will it take for the balance to be $282.
So, the graph correct graph is shown by option D).
For more information, refer to the link given below:
https://brainly.com/question/24432090
Answer:
D
Step-by-step explanation:
The city planning commission has been given a budget of 300,000 if the density of concrete is 150 lbs/ft3 determine if the cpc can afford to buy the bridge. The cost of concrete is 0.80/lb
Answer:
Check Explanation
Step-by-step explanation:
The volume of concrete required to build the bridge is missing and should be provided.
In its absence, let us assign a letter to it.
Let the volume of concrete required to build the bridge be V ft³.
And we further assume that the concrete is the only major material needed to build the bridge for the sake of our question.
Density = (mass/volume)
Density = 150 lb/ft³
Mass = ?
Volume = V ft³
Mass = (Density) × (Volume)
Mass of concrete required = 150 × V = (150V) lb
Cost of concrete is 0.80 per lb
1 lb of concrete costs 0.80
150V of concrete will cost 150V × 0.80 = (120V) currency amount.
Now, depending on the value of V, we can now determine if the city planning commission (cpc) can afford the bridge.
If 120V > 300,000 budget, the cpc cannot afford the bridge, but if 300,000 budget > 120V, then the cpc can afford the bridge.
Hope this Helps!!!
The 3 by 3 grid below shows nine 1 cm x 1 cm squares and uses 24 cm of wire.
What length of wire is required for a similar 20 by 20 grid?
Answer:
840 cm
Step-by-step explanation:
From the diagram attached, the 3 by 3 grid is made up of nine 1 cm x 1 cm squares. The the length of wire needed to make this grid consist of four rows each row having a length of 3 cm and four columns with each column having a length of 3 cm.
The length of wire required by the 3 by 3 grid = 4 column (3 cm / column) + 4 row (3 cm / row) = 12 cm + 12 cm = 24 cm
The 20 by 20 grid is made up of twenty 1 cm x 1 cm squares. The the length of wire needed to make this grid consist of twenty one rows each row having a length of 20 cm and twenty columns with each column having a length of 20 cm.
The length of wire required by the 20 by 20 grid = 21 column (20 cm / column) + 21 row (20 cm / row) = 420 cm + 420 cm = 840 cm
The moon is 2.4 X 10^5 miles from Earth. Assume the speed of the fastest spacecraft is 3.6 X 10^4 miles per hour. How many hours would it take this spacecraft to fly to the moon from Earth? Write your answer in standard form, rounded to the nearest hour. The solution is
Answer: . x 10^5 miles from the earth. How long does it take light to from a source on earth to reach a reflector on the moon and then return to earth? The speed of light is 3.0 x 10^8 m/s. ... sec. to give us our final answer of 1.28 seconds (the time required for light to travel 2.4 x 105 miles). and the fastest spaceship goes 153,454 miles per hour
Step-by-step explanation:
The number of hours that should be taken to fly to the moon from Earth is 7 hours.
Given that
Distance between earth and moon is [tex]2.4 \times 10^5\ miles[/tex]The speed is [tex]3.6 \times 10^4\ miles\ per\ hour[/tex]Now we know that
[tex]Time = \frac{Distance}{Speed} \\\\= \frac{2.4 \times 10^5 }{3.6 \times 10^4} \\\\= \frac{240}{36}[/tex]
= 6.66 hours
= 7 hours
Therefore we can conclude that The number of hours that should be taken to fly to the moon from Earth is 7 hours.
Learn more about the speed here: brainly.com/question/20131441
Im stuck on this question
Answer:
well the shape is acute so it will be quite low work out the opposite angles and you will find out that the lines are parallels there for meaning the answer is the lowest angle
Step-by-step explanation:
The royal fruit company produces two types of fruit drinks. the first type is 20% pure fruit juice, and the second is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 35% pure fruit juice. How many pints of each of the two existing types of drinks must be used to make 60 pints of a mixture that is 35% pure fruit juice?
Answer:
We have 20% fruit juice and 70% fruit juice.
We need 60 pints of 35% fruit juice.
We set up 2 equations where t is 20% and s is 70%
t + s = 60 pints
.20t + .70s = (.35 * 60)
We solve for both unknowns
t = 42 s = 18
We need 42 pints of 20% and 18 pints of 70 %
**** DOUBLE CHECK *******************************
42 pints of 20% = 8.40 pints of juice 33.6 pints water
18 pints of 70% = 12.60 pints of juice 5.40 pints water
TOTAL mixture = 21 pints juice 39 pints water = 60 total pints
21 pints juice / 60 = .35 (or 35% fruit juice)
Correct !!!
Step-by-step explanation:
What is the density of a material with a mass of 512 kilograms and a volume of 4 cubic meters?
Answer:
128 kg/m^3
[tex]solution \\ \: mass = 512 \: kg \\ volume = 4 {m}^{3} \\ now \\ density = \frac{m}{v} \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{512}{4} \\ \: \: \: \: \: \: \: \: \: = 128 \: kg/ {m}^{3} [/tex]
hope this helps...
Good luck on your assignment
Please answer this correctly
Answer:
14.3%
Step-by-step explanation:
There is only one four out of 7 total numbers.
1/7 = 0.142857 = 14.29%
We are given 7 numbers.
4 is only one card in that 7 card set so, 1/7.
1/7 = 0.1428
0.1428 * 100% = 14.28%
Therefore, the answer is roughly 14.3%
Best of Luck!
The average adult gets 7.45 hours of sleep each night, with a standard deviation of 0.65 hours. A pharmaceutical company developing a sleep aid is researching how much sleep the top 1% of adults get each night, on average. Use a calculator to find how many hours of sleep must an adult get each night to be in the top 1% if the company is only basing their initial research on the sleep habits of 30 adults.
Answer:
At least 8.96 hours of sleep to be in the top 1%.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 7.45, \sigma = 0.65[/tex]
How many hours of sleep to be on the top 1%?
The top 1% is the 100 - 1 = 99th percentile, which is X when Z has a pvalue of 0.99. So X when Z = 2.327. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{X - 7.45}{0.65}[/tex]
[tex]X - 7.45 = 0.65*2.327[/tex]
[tex]X = 8.96[/tex]
At least 8.96 hours of sleep to be in the top 1%.
Answer:
2.31
.12
7.73
Step-by-step explanation:
σx¯=0.653–√0=0.12
By plugging all the numbers into the formula z=x¯−μσx¯ we find that
2.31=x¯−7.450.12
0.28=x¯−7.45
7.73=x¯
What is the repeating digit in the decimal equivalent of 49?
Answer:
49/99
Step-by-step explanation:
I'm assuming you want to find the fraction that gives the decimal 0.494949...
If that is the case, the 49/99 is your answer.
Answer:
4
Step-by-step explanation:
There are five faculty members in a certain academic department. These individuals have 4, 6, 7, 10, and 15 years of teaching experience. Two of these individuals are randomly selected to serve on a personnel review committee. What is the probability that the chosen representatives have a total of at least 16 years of teaching experience
Answer:
3/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given 5 individuals with 4, 6, 7, 10, and 15 years of teaching experience.
Since two of these 5 individuals are randomly selected to serve on a personnel review committee, total possible outcome = 5C2 (randomly selecting 2 personnel out of 5 )
5C2 = [tex]\frac{5!}{(5-2)!2!}[/tex]
[tex]= \frac{5!}{3!2!}\\ = \frac{5*4*3!}{3!*2} \\= 10\ possible\ selections\ can\ be\ done[/tex]
To get the probability that the chosen representatives have a total of at least 16 years of teaching experience, first we need to find the two values that will give a sum of years greater that or equal to 16 years. The possible combination are as shown;
4+15 = 19years (first reps)
6+10 = 16years (second reps)
6+15 = 21years (third reps)
7+10 = 17 years (fourth reps)
7+15 = 22 years (fifth reps)
10+15 = 25 years (sixth reps)
This shows that there are 6 possible ways to choose the representatives that have a total of at least 16 years of teaching experience
Total outcome = 10
expected outcome = 6
Probability that the chosen representatives have a total of at least 16 years of teaching experience = [tex]\frac{6}{10} = \frac{3}{5}[/tex]
Check all of the points that are solutions to the system of inequalities.
x + y<4+3
y > 4
Someone please help ASAP
Answer:
B and E
Step-by-step explanation:
A: 3 + 6 < 4 + 3 and 6 > 4
9 < 7 is false so A is not the answer.
B: 1 + 5 < 4 + 3 and 5 > 4
6 < 7 and 5 > 4 are true so B is an answer.
C: 2 + (-1) < 4 + 3 and -1 > 4
-1 > 4 is false so C is not an answer.
D: 1 + 1 < 4 + 3 and 1 > 4
1 > 4 is false so D is not an answer.
E: 2 + 8 > 4 + 3 and 8 > 4
10 > 7 and 8 > 4 are both true so E is an answer.
F: -1 + 8 > 4 + 3 and 8 > 4
7 > 7 is false so F is not an answer.
last one haha ill give 20 points
The type of triangle drawn is an isosceles triangle.
Base angles ∠ACB and ∠CAB are equal.
What is an isosceles triangle?This is a type of triangle with base angles and opposite sides equal.
Analysis:
∠DCA = ∠CAB ( alternate angles are equal)
∠CAB + ∠ACB + ∠CBA = 180°( sum of angles in a triangle)
50 + ∠ACB + 80 = 180
130 + ∠ACB = 180
∠ACB = 180 - 130 = 50°
Since ∠ACB = ∠CAB = 50°. The triangle drawn is an isosceles triangle.
In conclusion, the triangle is isosceles because the base angles are equal.
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A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, then what is the computed value of the test statistic?
Answer:
Th computed value of the test statistic is 3.597
Step-by-step explanation:
The null and the alternative hypothesis is as follows:
Null Hypothesis:
[tex]\mathbf{H_o:}[/tex] the population correlation coefficient is equal to zero
[tex]\mathbf{H_a:}[/tex] the population correlation coefficient is not equal to zero
The test statistics for Pearson correlation coefficient is thus computed as :
[tex]t =\dfrac{r \sqrt{(n-2)}} { \sqrt{(1-(r)^2)} }[/tex]
where;
r = correlation coefficient = 0.60
n = sample size = 25
So;
[tex]t =\dfrac{0.60 \sqrt{(25-2)}} { \sqrt{(1-(0.60)^2)} }[/tex]
[tex]t =\dfrac{0.60 \sqrt{(23)}} { \sqrt{(1-0.36} }[/tex]
[tex]t =\dfrac{0.60 *4.796} {0.8}[/tex]
t = 3.597
Comparing to a critical value of t (23 degrees of freedom two-tailed value) = 2.069
Decision Rule:
Since computed value of t is greater than the critical value of t; We reject the null hypothesis and accept the alternative hypothesis.
Conclusion:
We conclude that the population correlation coefficient significantly differs from 0 at 5% (0.05) level of significance.
Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that of the respondents did not provide a response, said that their experience fell short of expectations, and of the respondents said that their experience met expectations.A. If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations?B. If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations. The results showed that 4% of respondents did not provide a response, 26% said that their experience fell short of expectations, 65% of the respondents said that their experience met expectations (Clarkson Magazine, Summer, 2001). If we chose an alumnus at random, what is the probability that the alumnus would say their experience surpassed expectations? If we chose an alumnus at random, what is the probability that the alumnus would say their experience met or surpassed expectations?
Solution:
Probability = number of favorable outcomes/number of total outcomes
From the information given,
The probability that respondents did not provide a response, P(A) is 4/100 = 0.04
The probability that a respondent said that their experience fell short of expectations, P(B) is 26/100 = 0.26
The probability that a respondent said that their experience met expectations, P(C) is 65/100 = 0.65
A) Adding all the probabilities, it becomes 0.04 + 0.26 + 0.65 = 0.95
Therefore, the probability,P(D) that a respondent said that their experience surpassed expectations is 1 - 0.95 = 0.05
B) The event of a randomly chosen respondent saying that their experience met expectations and that their experience surpassed expectations are mutually exclusive because they cannot occur together. It means that P(C) × P(D) = 0
Therefore, the probability of P(C) or P(D) is 0.65 + 0.05 = 0.7
g Your underground used-book business is booming. Your policy is to sell all used versions of Calculus and You at the same price (regardless of condition). When you set the price at $10, sales amounted to 100 volumes during the first week of classes. The following semester, you set the price at $30 and sales dropped to zero. Assuming that the demand for books depends linearly on the price, what price gives you the maximum revenue?
Answer:
The price that maximizes the revenue is $15 per book.
Step-by-step explanation:
We have a demand that has a linear relation to price.
The two points we will use to calculate the demand function are:
Price p=10, Demand q=100Price p=30, Demand q=0We have the equation:
[tex]q=m\cdot p+b[/tex]
Then, we replace:
[tex]q(30)=0=m(30)+b\\\\q(10)=100=m(10)+b\\\\\\b=-30m\\\\100=10m+(-30m)=-20m\\\\m=-100/20=-5\\\\b=-30(-5)=150\\\\\\q(p)=-5p+150[/tex]
The revenue R can be calculated as the multiplication of price and quantity.
We can maximize R by deriving and equal that to 0:
[tex]R=p\cdot q=p(-5p+150)=-5p^2+150p\\\\\\\dfrac{dP}{dp}=-5(2p)+150=0\\\\\\-10p+150=0\\\\p=150/10=15[/tex]
The price that maximizes the revenue is $15 per book.
The price that will offer the maximum revenue would be as follows:
$15
Find the priceWhat information do we have,
When Price = $10, Q = 100 Units
When Price = $ 30, Q = 0 units
With the above information, we can take the equation:
Q = Maximum (p + b)
by putting the values in both the above situations,
30 = 0 = m30 + b
10 = 0 = m10 + b
we get b = -30m. by putting this, we get
100 = 10m + (-30m) = -20m
∵ q(p) = -5p + 150
Through the equation and putting the above values, we get:
[tex]R = p.q.[/tex]
[tex]= p(-5p + 150)[/tex]
[tex]= -5p^2 + 150p[/tex]
$15 as the maximum price.
Thus, $ 15 is the correct answer.
Learn more about "Price" here:
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If a company's cost function is C(x) = 15x + 100. What price should the company sell each unit, x, to break even after selling 10 units.
2/3 divided by 3/4 and for answer of 8/9. Which statement is true
Answer: true
Step-by-step explanation: reciprocal of 3/4 is 4/3
Hence, 2/3 × 4/3 = 8/9
One kind of plant has only blue flowers and white flowers. According to a genetic model, the offsprings of a certain cross have a 0.75 chance to be blue-flowering, and a 0.25 chance to be white-flowering, independently of one another. Two hundred seeds of such a cross are raised, and 142 turn out to be blue-flowering. We are interested in determining whether the data are consistent with the model or, alternatively, the chance to be blue-flowering is smaller than 0.75. For this question, find the appropriate test statistic.
Answer:
There is not enough evidence to support the claim that the chance of this cross to be blue-flowering is significantly smaller than 0.75 (P-value = 0.11).
Test statistic z=-1.225.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the chance to be blue-flowering is significantly smaller than 0.75.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.75\\\\H_a:\pi<0.75[/tex]
The significance level is 0.05.
The sample has a size n=200.
The sample proportion is p=0.71.
[tex]p=X/n=142/200=0.71[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.75*0.25}{200}}\\\\\\ \sigma_p=\sqrt{0.000938}=0.031[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.71-0.75+0.5/200}{0.031}=\dfrac{-0.038}{0.031}=-1.225[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.225)=0.11[/tex]
As the P-value (0.11) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the chance to be blue-flowering is significantly smaller than 0.75.
a line has an x-intercept of (4,0) and a y-intercept of (0,12).Find the slope of the line
Answer:
m = -3
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2 - x1}[/tex]
All you have to do is plug in 4 for x1, 0 for x2, 0 for y1, and 12 for y2 and you should be able to calculate your answer!
Answer:
-3
Step-by-step explanation:
→ Utilise the gradient formula
[tex]\frac{y2-y1}{x2-x1}[/tex]
→ Substitute in the values from the coordinates (4,0) and (0,12)
[tex]\frac{12-0}{0-4}=\frac{12}{-4} =-3[/tex]
→ The gradient of the line is -3
What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?
y = 2 x + 33
y= *x+36
y = 4x - 16
y = 4x + 16
Answer:
y = 4x +16
Step-by-step explanation:
The given equation is in "point-slope" form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
The slope of the given line is m=4. This is the same slope as any parallel line.
__
The line you want can be written in the same point-slope form as ...
y -32 = 4(x -4)
Rearranging, we have ...
y = 4x -16 +32 . . . . . add 32, eliminate parentheses
y = 4x +16 . . . . . . . . collect terms