Answer:
Max revenue: R = $679.73
Step-by-step explanation:
total people = 100
each person orders 1 of 2 dishes
salad price = $10 - 0.04x
turkey price = $12 - 0.02*y^2
so x + y = 100
s = 10 - 0.04x
t = 12 - 0.02*y^2
Revenue = s*x + t*y
Revenue = (10 - 0.04x)*x + (12 - 0.02y^2)*y
y = 100 - x
so
Revenue = (10 - 0.04x)*x + (12 - 0.02*(100 - x)^2 )*(100 - x)
R =
R = (10 - 0.04x)*x + (12 - 0.02*(100 - x)^2 )*(100 - x)
R = 10x - 0.04x*x + (12 - 0.02*(10000 - 200x + xx) )*(100 - x)
R = 10x - 0.04x*x + (12 - 200 + 4x -0.02 xx )*(100 - x)
R = 10x - 0.04x*x + (-188 + 4x -0.02 xx )*(100 - x)
R = 10x - 0.04x*x + (-188 + 4x -0.02 xx )*100 -x (-188 + 4x -0.02 xx )
R = 10x - 0.04x*x + -18800 + 400x -2 xx -x (-188 + 4x -0.02 xx )
R = 10x - 0.04x*x + -18800 + 400x -2 xx + 188x - 4xx +0.02 xxx
R = 10x - 0.04x*x + -18800 + 588x -6 xx + 0.02 xxx
R = -18800 + 598x -6.04 xx + 0.02 xxx
dR/dx = 598 - 12.08x + 0.06 x^2
set = 0
598 - 12.08x + 0.06xx = 0
299 - 6.04x + 0.03xx = 0
x = -(-6.04)/(2*0.03) + root((-6.04)^2 - 4*0.03*299) / 2*0.03
x = 100.6667 - root(36.4816 - 35.88) / 0.06
x = 100.6667 - 12.927
x = 87.739
so that is where you get the maximum revenue, when you sell 87.7 salad plates and 12.2605 turkey dishes
Revenue = (10 - 0.04*87.739)*87.739 + (12 - 0.02(12.2605)^2)*12.2605
Revenue = 569.464715 + 110.266
R = $679.7307
R = $679.73
To find the maximum revenue, differentiate the revenue functions of salads and turkey plates with respect to the number of salads sold, considering a total of 100 guests, find critical points, and use the second derivative test or sign changes to identify the maximum revenue. Ensure that the number of meals are integers.
Explanation:To determine the maximum revenue for the food truck, we need to derive the revenue functions for salad and turkey plates and then find the total revenue function. Assuming s salads and t turkey plates are sold, the price functions are Ps(s) = 10 - 0.04s for salads and Pt(t) = 12 - 0.02t2 for turkey plates. The revenue functions would be Rs(s) = s × Ps(s) and Rt(t) = t × Pt(t). Because there are 100 guests, s + t = 100, hence t = 100 - s. We substitute t in Rt and add Rs and Rt for the total revenue R(s). To find the maximum revenue, we differentiate R(s) with respect to s, find critical points, and check these for the maximum value using the second derivative test or analyzing the sign changes of R'(s). Remember to check if the critical points result in s and t being positive integers, as per the conditions given.
Estimation is best defined as: a. both a process of inferring the values of unknown samples statistics from those of known population parameters and any procedure that views the parameter being estimated not as a constant, but, just like the estimator, as a random variable b. a sampling procedure that matches each unit from population A with a "twin" from population B so that any sample observation about a unit in population A automatically yields an associated observation about a unit in population B c. any procedure that views the parameter being estimated not as a constant, but, just like the estimator, as a random variable d. a process of inferring the values of unknown samples statistics from those of known population parameters e. a process of inferring the values of unknown population parameters from those of known sample statistics
Answer:
Option D is the correct answer - Estimation is best defined as a process of inferring the values of unknown samples statistics from those of known population parameters
Step-by-step explanation:
Estimation involves the usage of the value of a statistic derived from a sample to estimate the value of a corresponding population parameter.
The sample provides information that can be extended, through several formal or informal processes, to determine a range most suitable to describe the missing information.
An estimate that turns out to be incorrect would either be termed as over-estimation or under-estimation. If the estimate exceeds the actual result, it is termed as an over-estimation, and as an under-estimation, if the estimate came short of the actual result.
Thus, option D is correct.
The best definition of estimation will be E. process of inferring the values of unknown population parameters from those of known sample statistics.
It should be noted that estimation doesn't automatically yield an associated observation about a unit in population. Rather, estimation is the process of inferring the values of unknown population parameters from those of known sample statistics.In conclusion, the best option is E.
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A new kind of rocket takes off along an exponential trajectory, with height, in miles, represented by 3x, where x is the time, in seconds. Find the time when the height of the rocket is 8 miles.
What is the exact solution written as a logarithm?
What is an approximate solution rounded to the nearest thousandth?
We have been given that a new kind of rocket takes off along an exponential trajectory, with height, in miles, represented by [tex]3^x[/tex], where x is the time, in seconds. We are asked to find the time when the height of the rocket id 8 miles.
To find the time, we will equate height function with 8 and solve for x as:
[tex]3^x=8[/tex]
To solve for x, we will take natural log on both sides as:
[tex]\ln(3^x)=\ln (8)[/tex]
We can rewrite 8 as [tex]2^3[/tex].
[tex]\ln(3^x)=\ln (2^3)[/tex]
Using natural log property [tex]\ln(a^b)=b\cdot \ln(a)[/tex], we will get:
[tex]x\cdot \ln(3)=3\cdot\ln (2)[/tex]
[tex]\frac{x\cdot \ln(3)}{ \ln(3)}=\frac{3\cdot\ln (2)}{ \ln(3)}[/tex]
[tex]x=\frac{3\cdot\ln (2)}{ \ln(3)}[/tex]
Therefore, exact solution will be [tex]\frac{3\cdot\ln (2)}{ \ln(3)}[/tex].
[tex]x=\frac{2.0794415416798359}{1.0986122886681097}[/tex]
[tex]x=1.892789260714[/tex]
Upon rounding to nearest thousandth, we will get:
[tex]x\approx 1.89[/tex]
Therefore, the height of the rocket will be 8 miles after approximately 1.89 seconds.
Graph the system of equations on your graph paper to answer the question. {y=−x+3 y=x+5 What is the solution for this system of equations? Enter your answer in the boxes.
Answer:
(x,y) = (-1,4)
Step-by-step explanation:
y = y right? So all you have to do is replace both of the equations.
[tex]-x+3=x+5\\-x-x=5-3\\-2x=2\\x=-1[/tex]
after you've found the value of x just substitute it into ANY of these two equations!
For example if we get the first one we have
[tex]y=-(-1)+3\\y=1+3\\y=4[/tex]
And there you have it. Hope it helps!
what is the meaning of range in the subject mathematics
range
Answer:
explanation
Step-by-step explanation:
The Range (Statistics) The Range is the difference between the lowest and highest values. Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9. So the range is 9 − 3 = 6.
Answer:
The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.
We need to compare volatility of multiple assets. As the assets have different variation ranges, e.g. a big stock versus a penny stock, it is useful to look at the coefficient of variation, not the standard deviation, as a measure of volatility. We have the following population data: Mean ($) 0.48 175.93 286.47 Standard deviation ($) 0.09 34.72 63.08 (a)[2] Give an equation for the coefficient of variation in percentage terms. (b)[6] Find volatility of the three assets. Use two decimals for percentages, e.g. 23.76%. (c)[2] Which asset is the least volatile? Which asset is the most volatile?
Answer:
Check the explanation
Step-by-step explanation:
a)
the formula is given by,
c.v.=[tex]\frac{\sigma}{\mu}\times 100[/tex]
where is standard deviation and is mean of the given data.
b)for asse A,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 0.03 5 , 100 0,30 x 0.30 = 10%
for asse B,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 1.50 x 100 26005 × 100 =8.27 %
for asset C,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 18.70 × 100 =10.71%
c)since, c.v. of asset B is least, it is least volatile and c.v. of asset is most, it is most volatile.
Choose the correct answer.
1. What selid figure has a shape
like a box of cereal?
A rectangular prism
B cylinder
C sphere
Dcone
Answer:
A
Step-by-step explanation:
the solid figure that has the shape like a cereal box is a rectangular prism
Suppose two players are playing a game, Even and Odd. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), then Even keeps both pennies, so wins one from Odd ( 1 for Even, -1 for Odd). If the pennies do not match (one heads and one tails) Odd keeps both pennies, so receives one from Even (-1 for Even, 1 for Odd).
1. Please draw the payoff matrix for this game.
2. Does Even have a dominant strategy?
Answer:
1.
E(down) / Odd(Across) H T
H (1,-1) (-1,1)
T (-1,1) (1,-1)
2. Even doesn't have a dominant strategy as both the strategies are providing equal payoffs for pure strategy.
Add the following numbers together: 80, 85, 90, 65, 80, 60
Answer:
Adding all the numbers together results in 460
Answer:
460 is the answer
Step-by-step explanation:
What factor is used to convert miles per minute to
miles per hour?
Answer:
The factor which is used to convert feet per minute into miles per minute is:
1 ft per minute=0.000189 miles per minute.
( since, 1 ft.= 0.000189 miles )
Step-by-step explanation:
A psychologist wants to know whether memory performance is reduced by old age. She randomly selects 67 elderly individuals and finds that their mean score on a standardized memory test equals 514. Scores on the standardized memory test in the general population are distributed normally with a mean equal to 600 and a standard deviation equal to 112. Is there sufficient evidence at the 0.1 significance level to conclude that memory performance is reduced by old age
Answer:
[tex]z=\frac{514-600}{\frac{112}{\sqrt{67}}}=-6.285[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-6.285)=1.64x10^{-10}[/tex]
Since the p value is very low than the significance level given we have enough evidence to conclude that the true mean for the scores on a standardized memory is significantly lower than 600 and then we can conclude that memory performance is reduced by old age
Step-by-step explanation:
Information given
[tex]\bar X=514[/tex] represent the sample mean for the scores on a standardized memory
[tex]\sigma=112[/tex] represent the population standard deviation
[tex]n=67[/tex] sample size
[tex]\mu_o =600[/tex] represent the value that we want to verify
[tex]\alpha=0.1[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to check if the true mean for this case is less than 600, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 600[/tex]
Alternative hypothesis:[tex]\mu < 600[/tex]
Since we know the population deviation the statistic for this case is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{514-600}{\frac{112}{\sqrt{67}}}=-6.285[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-6.285)=1.64x10^{-10}[/tex]
Since the p value is very low than the significance level given we have enough evidence to conclude that the true mean for the scores on a standardized memory is significantly lower than 600 and then we can conclude that memory performance is reduced by old age
A survey was taken of randomly selected Americans, age 65 and older, which found that 401 of 1020 men and 536 of 1059 women suffered from some form of arthritis. a) Are the assumptions and conditions necessary for inference satisfied? Explain. b) Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease. c) Interpret your interval in this context. d) Does this suggest that arthritis is more likely to afflict women than men? Explain.
Final answer:
The assumptions and conditions necessary for inference are satisfied, and a 95% confidence interval can be created to estimate the difference in proportions of senior men and women with arthritis. The interval provides a measure of precision, and the results do not suggest that arthritis is more likely to afflict women than men.
Explanation:
a) The assumptions and conditions necessary for inference are satisfied. Random sampling was used to select Americans age 65 and older, which helps ensure representativeness. The sample sizes are also large enough for accurate analysis.
b) To create a 95% confidence interval for the difference in proportions, we can use the formula:
CI = (p1 - p2) ± Z * sqrt((p1(1-p1)/n1) + (p2(1-p2)/n2))
c) The 95% confidence interval indicates that we are 95% confident that the true difference in proportions falls within the given range. It provides a measure of the precision of our estimate.
d) The survey results do not suggest that arthritis is more likely to afflict women than men. The confidence interval encompasses a range of values, indicating that the difference in proportions could be quite small or even favor men.
Yes, it was a random sample less than 10% of the population was sampled the groups were independent, and there were more than 10 successes and failures in each group option(D). The confidence interval for the difference in proportions (p₁ - p₂) is approximately (4.8%, 13.2%) after rounding to three decimal places as needed. The proportion of American women, age 65 and older, who suffer from arthritis is between 4.8% and 13.2% higher than the proportion of American men of the same age who suffer from arthritis. Therefore, arthritis is more likely to afflict women than men.
Yes, the entire interval lies above 0 option(C).
The assumptions and conditions necessary for inference in parts (a), (b), (c), and (d) can be evaluated as follows:
(a) The conditions for inference include:
The sample must be random.The sample size must be less than 10% of the population.The groups must be independent.There must be at least 10 successes and 10 failures in each group.Given the survey data:
It is a random sample.Both samples are less than 10% of their respective populations.The groups are independent.There are more than 10 successes and 10 failures in each group.Therefore, the correct answer is D. Yes, it was a random sample less than 10% of the population was sampled the groups were independent, and there were more than 10 successes and failures in each group.
(b) To create a 95% confidence interval for the difference in proportions of senior men and women who have arthritis, we follow these steps:
Calculate the sample proportions:⇒ p₁ = 532 ÷ 1065 and
⇒ p₂ = 418 ÷ 1019.
Find the standard error (SE) of the difference between proportions:⇒ SE = √((p₁(1 - p₁) ÷ n₁) + (p₂(1 - p₂) ÷ n₂))
Calculate the margin of error (ME) using the Z-score for a 95% confidence level (Z = 1.96):⇒ ME = Z × SE
Determine the confidence interval:= (p₁ - p₂) ± ME
The confidence interval for the difference in proportions (p₁ - p₂) is approximately (4.8%, 13.2%) after rounding to three decimal places as needed.
(c)There is 95% confidence, based on these samples, that the proportion of American women, age 65 and older, who suffer from arthritis is between 4.8% and 13.2% higher than the proportion of American men of the same age who suffer from arthritis.
(d) Since the entire confidence interval lies above 0, it suggests that senior women are more likely to suffer from arthritis. The correct answer is C. Yes, the entire interval lies above 0.
Complete question:
A survey was taken of randomly selected Americans, age 65 and older, which found that 418 of 1019 men and 532 of 1065 women suffered from some form of arthritis.
a) Are the assumptions and conditions necessary for inference satisfied? Explain.
A. No, more than 10% of the population was sampled. ?
B. No, the groups were not independent.
C. No, it was not a random sample.
D. Yes, it was a random sample less than 10% of the population was sampled the groups were independent, and there were more than 10 successes and failures in each group.
b) Let p₁ be the sample proportion of senior women suffering from some form of arthritis, and let p₂ be the sample proportion of senior men suffering from some form of arthritis. Create a 95% confidence interval for the difference in proportions of senior men and women who have this disease, p₁ - p₂.
The confidence interval is
( Round to three decimal places as needed.)
c) There is 95% confidence, based on these samples, that the proportion of American women, age 65 and older, who suffer from arthritis is between % and % than the proportion of American men of the same age who suffer from arthritis.
(Round to one decimal place as needed.)
d) Does this suggest that arthritis is more likely to afflict women than men? Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
A. No, the interval is too close to 0.
B. Yes, there is 95% confidence, based on these samples that about % of senior women suffer from arthritis, while only % of senior men suffer from arthritis.
(Round to one decimal place as needed.)
C. Yes, the entire interval lies above 0.
D. No, a conclusion cannot be made based on the confidence interval.
is {(4, 8), (8, 4), (4, 12), (20, 16), (12, 16)} a function
Answer:
no
Step-by-step explanation:
Look at the first numbers of each ordered pair:
4, 8, 4, 20, 12
If any are repeated, the relation is NOT a function. Here, 4 is repeated.
The relation is not a function.
The amount of gas consumed by a car varies directly with the miles driven. The car traveled 180 miles and used 6 gallons of gas. If the car traveled 1,,260 miles, how many gallons of gas would be used?
A 7 gallon
B 30 gallon
C 42 gallon
D 210 gallon
Answer:
The correct answer is A
Step-by-step explanation:
1,260 divided by 180 = 7
180 times 6 = 1,080
180 times 7 = 1,260
If the car traveled 1260 miles, then 42 gallons of gas would be used.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have the amount of gas consumed by a car varies directly with the miles driven.
Using the formula for direct proportionality -
y₁/x₁ = y₂/x₂
180/6 = 1260/x₂
x₂ = (1260 x 6)/180
x₂ = (126 x 6)/18
x₂ = (21 x 2)
x₂ = 42
Therefore, If the car traveled 1260 miles, then 42 gallons of gas would be used.
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In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch?
Answer:
16.16 or 16 inch
Step-by-step explanation:
you can use the pythagoras theorem,
h = 19
so, width = [tex]\sqrt{19^2 - 10^2}[/tex]
Answer:
16.16 or 16 inch
Convert 65L into quarts
Answer:
68.68
Step-by-step explanation:
for an approximate result, multiply the volume value by 1.057
what is the volume of a square pyramid with base edges 24 feet and slant height 37
7140 ft^3
6950 ft^3
6720 ft^3
7268 ft^3
The volume of a square pyramid with base edges of 24 feet and a slant height of 377268 feet is 74,182,973,440 cubic feet.
Explanation:The volume of a square pyramid can be found using the formula: volume = (1/3) * base area * height. In this case, the base of the pyramid is a square with edges measuring 24 feet, so the base area is
= 24 * 24
= 576 square feet.
The slant height of the pyramid is given as 377268 ft^3, but the units should be in feet, not ft^3, as ft^3 represents volume. Therefore, it is likely a typo.
Assuming the slant height is actually 377268 feet, we can use the Pythagorean theorem to find the height of the pyramid.
The height is given by
[tex]h = \sqrt{(slant height^2 - (base edge/2)^2)[/tex]
[tex]= \sqrt{(377268^2 - (24/2)^2)[/tex]
[tex]= \sqrt{(142288127824 - 144)[/tex]
= 377268 feet.
Now we can calculate the volume using the formula: volume
= (1/3) * 576 * 377268
= 74,182,973,440 cubic feet.
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what is the length of bc in the right triangle below
Answer:
20
Step-by-step explanation:
We can use the Pythagorean theorem to solve
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
12^2+16^2 = c^2
144+256 = c^2
400 = c^2
Take the square root of each side
sqrt(400) = sqrt(c^2)
20 = c
A machine randomly dispenses a pink, orange, blue, or yellow golf ball to each customer at a miniature golf course. If is the probability of receiving a blue golf ball from the machine, what are the odds in favor of receiving a blue golf ball?
A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 15 students, he found the average time was 4.29 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.01 level of significance. Assume normality.a) What are the appropriate null and alternative hypotheses?H0: ? = 5 versus Ha: ? ? 5H0: x = 5 versus Ha: x ? 5 H0: ? = 5 versus Ha: ? < 5H0: ? = 5 versus Ha: ? > 5b) What is the test statistic? Give your answer to four decimal places. c) What is the P-value for the test? Give your answer to four decimal places. d) What is the appropriate conclusion?
Answer:
(a) H₀: μ = 5 vs. Hₐ: μ ≠ 5.
(b) The test statistic value is -3.67.
(c) The p-value of the test is 0.0025.
(d) The mean amount of time spent in the shower by an adult is different from 5 minutes.
Step-by-step explanation:
In this case we need to test whether the mean amount of time that college students spend in the shower is significantly different from 5 minutes.
The information provided is:
[tex]n=15\\\bar x=4.29\\s=0.75\\\alpha =0.01[/tex]
(a)
The hypothesis for the test can be defined as follows:
H₀: The mean amount of time spent in the shower by an adult is 5 minutes, i.e. μ = 5.
Hₐ: The mean amount of time spent in the shower by an adult is different from 5 minutes, i.e. μ ≠ 5.
(b)
As the population standard deviation is not known we will use a t-test for single mean.
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}\\\\=\frac{4.29-5}{0.75/\sqrt{15}}\\\\=-3.67[/tex]
Thus, the test statistic value is -3.67.
(c)
Compute the p-value of the test as follows:
[tex]p-value=2\times P(t_{\alpha/2, (n-1)}<-3.67)\\ =2\times P(t_{0.005, 14}<-3.67)\\=0.0025[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.0025.
(d)
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.0025 < α = 0.01
The null hypothesis will be rejected at 1% level of significance.
Thus, concluding that the mean amount of time spent in the shower by an adult is different from 5 minutes.
Gabriella drives her car 320 miles and averages a certain speed. If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time. What is her average speed?
Answer:
Her average speed is 48 miles per hour.
Step-by-step explanation:
We solve this question using a system of equations.
The speed equation is:
[tex]s = \frac{d}{t}[/tex]
In which s is the speed, d is the distance, and t is the time.
Gabriella drives her car 320 miles and averages a certain speed.
So [tex]d = 320[/tex]
Then
[tex]s = \frac{320}{t}[/tex]
If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time.
So, which s - 6, d = 280.
[tex]s - 6 = \frac{280}{t}[/tex]
From the first equation:
[tex]s = \frac{320}{t}[/tex]
[tex]st = 320[/tex]
[tex]t = \frac{320}{s}[/tex]
Replacing:
[tex]s - 6 = \frac{280}{t}[/tex]
[tex]s - 6 = \frac{280}{\frac{320}{s}}[/tex]
[tex]320(s - 6) = 280s[/tex]
[tex]320s - 1920 = 280s[/tex]
[tex]40s = 1920[/tex]
[tex]s = \frac{1920}{40}[/tex]
[tex]s = 48[/tex]
Her average speed is 48 miles per hour.
a, = - 9n - 7.
What’s the first five terms
Answer:
-16, -25, -34, -43, and -52
Step-by-step explanation:
a, = - 9n - 7.
Sequence given by
a_n, = - 9n - 7.
a_1 = -9*1 - 7 = -16
a_2 = -9*2 - 7 = -18 - 7 = -25
a_3 = -9*3 - 7 = -27 - 7 = -34
a_4 = -9*4 - 7 = -36 - 7 = -43
a_5 = -9*5 - 7 = -45 - 7 = -52
An article predicts that "spit," spam that is delivered via internet phone lines and cell phones, will be a growing problem as more people turn to web-based phone services. In a poll of 5500 cell phone users, 19% indicated that they had received commercial messages and ads on their cell phones. Is there sufficient evidence that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year? (Use α = 0.05. Round your test statistic to two decimal places and your P-value to four decimal places.)z =
P =There is evidence to suggest that the proportion cell phone users who have received commercial messages or ads in 2004 is greater than the proportion of 0.13 reported for the previous year.
Answer:
We conclude that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year.
Step-by-step explanation:
We are given that in a poll of 5500 cell phone users, 19% indicated that they had received commercial messages and ads on their cell phones.
We have to test the claim that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year.
Let p = proportion of cell phone users who have received commercial messages or ads in 2004.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 0.13 {means that the proportion of cell phone users who have received commercial messages or ads in 2004 was smaller than or equal to the proportion of 0.13 reported for the previous year}
Alternate Hypothesis, [tex]H_A[/tex] : p > 0.13 {means that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of cell phone users who have received commercial messages or ads in 2004 = 19%
n = sample of cell phone users = 5500
So, test statistics = [tex]\frac{0.19-0.13}{\sqrt{\frac{0.19(1-01.9)}{5500}} }[/tex]
= 11.34
The value of z test statistics is 11.34.
Also, P-value of the test statistics is given by;
P-value = P(Z > 11.34) = 1 - P(Z [tex]\leq[/tex] 11.34)
= 1 - 0.9999 = 0.0001
Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.
Since our test statistics is way more than the critical value of z as 11.34 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year.
a=40 c=41 what does b equal
considering this is a pythagorean theorem question (a^2+b^2=c^2)
then we can plug this in.
40^2+b^2=41^2
1600+b^2=1681 (subtract 1600 from both sides to isolate b)
b^2=81 (square root)
b=9
What is the degree and the polynomial term?
Answer:
choice A is the best 2nd degree, trinomial
Step-by-step explanation:
-x^2 +3x - 4
has 3 unique terms which make it a trinomial
The highest degree is 2 since the the highest valued exponent is 2
A software company decided to conduct a survey on customer satisfaction. Out of 564 customers who participated in the online survey, 51 rated the overall services as poor. Test, at level , the null hypothesis that the proportion of customers who would rate the overall car rental services as poor is 0.1 versus a two-sided alternative. Find the value of the test statistic (round off to first decimal place).
Answer:
[tex]z=\frac{0.0904 -0.1}{\sqrt{\frac{0.1(1-0.1)}{564}}}=-0.760 \approx -0.8[/tex]
[tex]p_v =2*P(z<-0.760)=0.447[/tex]
Step-by-step explanation:
Information given
n=564 represent the sample selected
X=51 represent the number of people who rated the overall services as poor
[tex]\hat p=\frac{51}{564}=0.0904[/tex] estimated proportion of people who rated the overall services as poor
[tex]p_o=0.1[/tex] is the value to compare
z would represent the statistic
Hypothsis to analyze
We want to analyze if the proportion of customers who would rate the overall car rental services as poor is 0.1, so then the system of hypothesis are:
Null hypothesis:[tex]p=0.1[/tex]
Alternative hypothesis:[tex]p \neq 0.1[/tex]
The statistic for a one z test for a proportion is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.0904 -0.1}{\sqrt{\frac{0.1(1-0.1)}{564}}}=-0.760 \approx -0.8[/tex]
And the p value since we have a bilateral test is given b:
[tex]p_v =2*P(z<-0.760)=0.447[/tex]
The question is about testing a null hypothesis in a customer satisfaction survey for a software company. The null hypothesis is that 10% of customers would rate the services as poor. The calculated test statistic was approximately -1.3.
Explanation:
The question involves testing a null hypothesis regarding the proportion of customers who would rate the software company's services as poor. We are given that a total of 564 customers took part in the survey, out of which 51 rated the services as poor. Here, the null hypothesis is that 10% (or 0.1) of customers would rate the services as poor.
To test the null hypothesis, we compare the sample proportion to the claimed proportion (0.1). The sample proportion in this case is 51/564 = 0.0904. We can calculate the test statistic using the formula for sample proportion, which is (p' - p) / sqrt [ p * (1 - p) / n ], where p is the claimed proportion, p' is the sample proportion, and n is the sample size. In this case, the test statistic would be approximately (0.0904 - 0.1) / sqrt [0.1 * (1 - 0.1) / 564] = -1.3 (rounded to the first decimal).
The p-value corresponds to the test statistic under the null hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis. But here, we didn't calculate the p-value as it wasn't part of the question, so we won't make a decision on the null hypothesis.
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Ri’Hanna has n nickels. Shania has 4 times as many nickels as Ri’Hanna has. Write an expression for the total number of nickels Ri’Hanna and Shania have. SImplify the Expression.
Answer:
5n
Step-by-step explanation:
i think
To find the total number of nickels Ri’Hanna and Shania have together, add the number of nickels Ri’Hanna has (n) and the number of nickels Shania has (4n). The simplified expression is 5n.
Explanation:Ri’Hanna has n nickels, and Shania has 4 times that amount. This could be represented by the expression 4n. To calculate the total number of nickels they have together, you add the amount of nickels Ri’Hanna has (n) and the amount Shania has (4n). So, the expression representing the total nickels is n + 4n. When you add n + 4n, it simplifies to 5n.
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A bookstore marks up the price of a book by 25% of the cost from the publisher. Therefore, the
bookstore's price to the student, P(x) (in $) after a 5.3% sales tax, is given by P(x) = 1.053(x+0.25x),
where x is the cost from the publisher. Evaluate P(60) and interpret the meaning in context of this
problem. (Round to the nearest cent.)
P(60) = 78.98
When the bookstore spends $60 on a textbook, the student pays $78.98
P(60) = 78.98
When the bookstore pays $78.98 on a textbook, the student pays $60
P(60) = 47.39
When the bookstore pays $47.39 on a textbook, the student pays $60
P(60) = $47.39
The sales tax on a $60 textbook is $47.39
P(60) = 78.98
The sales tax on a $60 textbook is $78.98
P(60) = 47.39
When the bookstore pays $60 on a textbook, the student pays $47.39
Answer:
(A)
P(60) = 78.98 When the bookstore spends $60 on a textbook, the student pays $78.98Step-by-step explanation:
Given:
P(x) = 1.053(x+0.25x)
P(60) = 1.053(60+0.25*60)
=1.053(60+15)
=1.053(75)
P(60)=$78.98
Since x is the cost from the publisher, when the bookstore spends $60 on a textbook, the student pays $78.98.
The correct option is A.
The price of the book to the student is $78.98 when the bookstore spends $60 on the textbook.
Explanation:The subject of this question is Mathematics and it is suitable for High School students.
The problem involves calculating the price of a book after a markup and sales tax.
To evaluate P(60), we substitute x = 60 into the given expression P(x) = 1.053(x+0.25x).
P(60) = 1.053(60 + 0.25*60) = 1.053(60 + 15) = 1.053(75) = 78.975.
The bookstore's price to the student would be $78.98 when the bookstore spends $60 on a textbook.
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Connor earned $85 at his job when he worked for 10 hours. What was his hourly pay rate in dollars per hour?
Answer:
8.5$
Step-by-step explanation:
85 diveded by 10 is 8.5$.
Answer:
Connor's hourly pay rate is $8.50
Step-by-step explanation:
Think of it as finding the unit rate.
hours : dollars
10 : 85
1 : ?
Since you must divide by 10 to get from 10 to 1, you must do the same for the other side, so you do 85 divided by 10.
85 / 10 = 8.5
Therefore, Connor's hourly pay rate is $8.50.
A decorative steel frame is shown below
It is made of a circular section ad 6 stems
The lenght of each stem is 45cm
work out the total lenght of steel used in the frame
Answer:
552.78
Step-by-step explanation:
45 x 6 =270
2πr = r x 2 x 3.142 = 45 x 2 x 3.142 = 282.78
270 + 282.78
The total length of the steel when both the circular section is added would be = 552.6cm.
How to calculate the total length of the given steel?The total length of the steel can be calculated following the steps below:
The total length of the 6 stems with 45cm = 45×6 = 270cm
The length of circular section = 2πr
where r = 45cm
C = 2× 3.14×45
= 282.6
The total length = 270+ 282.6
= 552.6cm
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A certain ambulance service wants its average time to transport a patient to the hospital to be 10 minutes. A random sample of 12 transports yielded a 95 percent confidence interval of 11.8±1.6 minutes. Is the claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital plausible based on the interval?
The claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital is false.
Given to us,average time to transport a patient = 10 minutes,sample of 12 transports yielded at 95% confidence interval is 11.8±1.6 minutes.SolutionWe know that, the confidence interval for any event shows as the interval with lower and upper bounds. Meaning it gives as the mean interval with a maximum and minimum possible values for that interval as well for unknown variables.
[tex]CI = \bar{x} \pm z \dfrac{s}{\sqrt{n}}[/tex]
where,
CI = confidence interval
[tex]\bar{x}[/tex] = sample mean
z = confidence level value
s = sample standard deviation
n = sample size
Similarly, given in sample of 12 transports yielded at 95% confidence interval is 11.8±1.6 minutes.
So, the mean interval is 11.8 minutes, with a lower bound as 10.2 minutes(11.8-1.6) while upper bound as 13.4 minutes(11.8+1.6).
Hence, the claim that the ambulance service takes an average of 10 minutes to transport a patient to the hospital is false.
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Final answer:
The ambulance service's claim that their average transport time is 10 minutes is plausible since 10 minutes is within the provided 95% confidence interval of 11.8±1.6 minutes.
Explanation:
The question asks if the ambulance service's claim that their average time to transport a patient to the hospital is 10 minutes is plausible based on the provided 95% confidence interval. The confidence interval is given as 11.8±1.6 minutes, which means the interval ranges from 10.2 minutes to 13.4 minutes. Since 10 minutes is within this range, it is plausible that the true average transport time could be 10 minutes, although the intervals suggest that it is on the lower end of the sample's confidence interval.