Answer:
69.50%
Step-by-step explanation:
Given:
Ayrshire cows:
E(X) =μ = 47
SD(X) = σ = 6 Var (X) = 6^2 = 36
Jersey cows:
E(Y) = μ = 43
SD(Y) = σ = 5 Var(Y) = 52 = 25
Properties mean, variance and standard deviation:
E(X +Y) = E(X) E(Y)
V ar(X +Y) = Var(X) + Var(Y)
SD(X +Y) = √Var(X)+Var(Y)
X — Y represents the difference between Ayrshire and Jersey cows.
E(X — Y) = E(X) — E(Y). 47 — 43 = 4
SD(X — Y) = √Var(X)+ Var(Y) =√36+ 25 = √61 = 7.8102
The z-score is the value decreased by the mean, divided by the standard deviation:
z = x-μ /σ = 0-4/ 7.8102 = -0.51
Determine the corresponding probability using table Z in appendix F.
P(X—Y [tex]\geq[/tex] 0) = P(Z > —0.51) = 1—P(Z < —0.51) = 1-0.3050 = 0.6950 = 69.50%
Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 3x3, [1, 2] Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f '(c) = f(b) − f(a) b − a . (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.) c = 27
The values of c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a) are approximately ±√(7/3).
Based on the given information, the Mean Value Theorem can be applied to function f on the closed interval [a, b].
[tex]f(x) = 3x^3[/tex] is continuous on the closed interval [1, 2], and it is also differentiable in the open interval (1, 2).
To find the values of c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a), we need to find the derivative of f(x) and solve the equation.
The derivative of [tex]f(x) = 3x^3[/tex] can be found by applying the power rule, which states that the derivative of [tex]x^n[/tex] is [tex]nx^{n-1}[/tex].
So, the derivative of [tex]f(x) = 3x^3[/tex] is [tex]f'(x) = 9x^2[/tex].
Now, we can solve the equation f'(c) = (f(b) - f(a))/(b - a) using the given values for a and b.
Plugging in a = 1 and b = 2, we have:
[tex]f'(c) = (f(2) - f(1))/(2 - 1)\\= (3(2)^3 - 3(1)^3)/(2 - 1)\\= (3(8) - 3(1))/(2 - 1)= (24 - 3)/(2 - 1)= 21/1= 21[/tex]
Setting f'(x) = 21, we have:
[tex]9x^2 = 21[/tex]
[tex]x^2 = 21/9\\x^2 = 7/3[/tex]
x = ±√(7/3)
Therefore, the values of c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a) are approximately ±√(7/3).
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The Mean Value Theorem can be applied to the function f(x) = [tex]3x^3[/tex] on the interval [1,2] as it is continuous and differentiable on this interval. According to the theorem, a value 'c' exists in the interval (1, 2) that complies with the equation derived from the theorem.
Explanation:The Mean Value Theorem can indeed be applied for the function f(x) = [tex]3x^3[/tex] on the interval [1,2]. Mean Value Theorem can be applied if the function satisfies two conditions: it has to be continuous on the closed interval [a, b], and it has to be differentiable on the open interval (a, b).
The function f(x) = [tex]3x^3[/tex] is both continuous and differentiable for all real numbers, which includes the interval from 1 to 2. Therefore, we can apply the Mean Value theorem.
According to the theorem, there exists a number 'c' in the open interval (a, b) such that f '(c) = (f(b) − f(a)) / (b − a). Our given function f(x) = [tex]3x^3[/tex] differentiates to f '(x) = 9x. Setting f '(c) equal to (f(b) − f(a)) / (b − a), we can solve for the value of 'c'.
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A study by M. Chen et al. titled "Heat Stress Evaluation and Worker Fatigue in a "Steel Plant" (American Industrial Hygiene Association, Vol. 64, pp.352-359) assesses fatigue in steelplant workers due to heat stress. Among other things, the researchers monitored the heart rates of a random sample of 29 casting workers. A hypothesis test is to be conducted to decide whether the mean post-work heart rate of casting workers exceeds the normal resting heart rate of 72 beats per minute (bpm)
Answer:
a. Type I error (rejecting a null hypothesis when it is true).
b. Correct conclusion (reject a null hypothesis when it is false).
Step-by-step explanation:
The question is incomplete:
Now suppose that the results of carrying out the hypothesis test lead to rejection of the null hypothesis.
Classify that conclusion by error type or as a correct decision if in fact:
a. the mean post-work heart rate of casting workers equals the normal resting heart rate of 72 bpm.
b. exceeds the normal resting heart rate of 72 bpm.
In case a, the conclusion is wrong and we have rejected a null hypothesis that is true. This is a Type I error, and it has a probability equal to the level of significance α.
In case b, the conclusion is correct, as the mean post-work heart rate indeed exceeds the normal resting heart rate of 72 bpm.
A mechanic had 4 and one half gallons of motor oil at the start of the day. At the end of the day, only 5 pints remained.
How many pints of motor oil did the mechanic use during the day?
Answer:
Step-by-step explanation:
I believe that it's 19pints I've had a problem with this question also but I believe I have the answer HOPE THIS HELPS
Final answer:
The mechanic used 31 pints of motor oil during the day.
Explanation:
Question: The mechanic started with 4 and one-half gallons of motor oil and ended the day with 5 pints remaining. How many pints of motor oil did the mechanic use during the day?
Step-by-step explanation:
Convert 4 and one-half gallons to pints: 4.5 gallons x 8 pints/gallon = 36 pints.
Subtract the remaining 5 pints from the initial 36 pints: 36 pints - 5 pints = 31 pints.
Therefore, the mechanic used 31 pints of motor oil during the day.
Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 300, are selected, and 15 defective parts are found in the sample from machine 1 while 8 defective parts are found in the sample from machine 2. You want to test if it is reasonable to conclude that machine 2 produces less (difference is positive) fraction of defective parts, using α= 0.03.
Let's assume you found a test statistic value less than critical value. What would be your conclusion?
Answer:
Step-by-step explanation:
Hello!
The objective of this exercise is to compare the proportion of defective parts produced by machine 1 and machine 2.
The parameter of study is the difference between the population proportion of defective parts produced by machine 1 and the population proportion of defective parts produced by machine 2, symbolically: p₁ - p₂
The hypotheses are:
H₀: p₁ - p₂ ≤ 0
H₁: p₁ - p₂ > 0
α: 0.03
This hypothesis test is one-tailed to the right, which means that you will reject the null hypothesis with high values of the statistic.
To test the difference of proportions you have to use a standard normal distribution, the critical value will be:
[tex]Z_{1-\alpha }= Z_{1-0.03}= Z_{0.97}= 1.881[/tex]
The decision rule using the critical value approach is:
If [tex]Z_{H_0}[/tex] ≥ 1.881, the decision is to reject the null hypothesis.
If [tex]Z_{H_0}[/tex] < 1.881, the decision is to not reject the null hypothesis.
Considering the calculated [tex]Z_{H_0}[/tex] < 1.881, the decision is to not reject the null hypothesis. Using a significance level of 3%, you can conclude that the difference between the population proportion of defective plastic parts produced by machine 1 and the population proportion of defective plastic parts produced by machine 2 is at most zero.
I hope this helps!
Answer:
There is evidence to conclude that both machines produce the same fraction of defective parts
Step-by-step explanation:
Attached is the solution
Solve For X
(4x + 58)+67=180
Answer:
x=55/4
Step-by-step explanation:
M plus the product of 6 and n
Answer:
6n + M
Step-by-step explanation:
6 * n = 6n, 6n + M would be the answer
The expression is M +6n.
What is Algebra?
Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
given statement:
M plus the product of 6 and n
So, first product of 6 and n
=6n
Now, M is added to the result
=M +6n
Hence, the expression is M + 6n
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Build a generating function for ar, the number of distributions of r identical objects into (a) Five different boxes with at most three objects in each box (b) Three different boxes with between three and six objects in each box (c) Six different boxes with at least one object in each box (d) Three different boxes with at most five objects in the first box
Answer:
a) (1 + x + x^2 + x^3) ^5
b) (x^3 + x^4 + x^5 +x^6) ^3
c) ( x + x^2 + x^3 + x^4..........) ^6
d) ( 1 + x + x^2 + x^3 + x^4 + x^5) ^3
Step-by-step explanation:
A generating function is a process of encoding an infinite sequence of numbers (ar) by giving them a treatment as the coefficients of a power series. This formal power series is the generating function. As opposed to an ordinary series, this formal series is allowed to diverge, implying that the generating function is not always a true function and the "variable" is typically an indeterminate.
From the information above, build a generating function for ar, the number of distribution of r identical objects into:
(a) 5 different boxes with at most three objects in each boxes, this would be done as follows:
Answer = (1 + x + x^2 + x^3) ^5
(b) Three different boxes with between three and six objects in each boxes.
The answer is:
Answer= (x^3 + x^4 + x^5 +x^6) ^3
(c) Six different boxes with at least one object in each box.
The answer is:
Answer= ( x + x^2 + x^3 + x^4..........) ^6
(d) Three different boxes with at most five objects
The answer is:
Answer = ( 1 + x + x^2 + x^3 + x^4 + x^5) ^3
Answer:
a) ar = ( 1 + x + x^2 + x^3)^5
b) ar = ( x^3 + x^4 + x^5 + x^6 )^3
c) ar = ( x^1 + x^2 + x^3 + x^4 + ....)^6
d) ar = ( 5 + x^1 + x^2 + x^3 + x^4 + x^5 )^3
Step-by-step explanation:
Solution:-
- The generating function (ar), where the number of (r) identical objects.
- The number of identical boxes = r
- The function parameter, the number of different boxes = n
- The number of objects in each box = k
- The general generating function (ar) is of the form:
ar = (x^0 + x^1 + x^2 + x^3 + x^4 + ....+ x^k)^n
part a)
- We have 5 different boxes, n = 5.
- We are to place at most 3 objects in each box, k ≤ 3
- The generating function would be:
ar = ( 1 + x + x^2 + x^3)^5
part b)
- We have 3 different boxes, n = 3.
- We are to place 3 to 6 objects in each box, (3 ≤ k ≤ 6)
- The generating function would be:
ar = ( x^3 + x^4 + x^5 + x^6 )^3
part c)
- We have 6 different boxes, n = 6.
- We are place at-least 1 objects in each box, k ≥ 1
- The generating function would be:
ar = ( x^1 + x^2 + x^3 + x^4 + ....)^6
part d)
- We have 3 different boxes, n = 3.
- We are place at-most 5 objects in each box, k ≤ 5
- The generating function would be:
ar = ( 5 + x^1 + x^2 + x^3 + x^4 + x^5 )^3
:
A principal wants to know if students at a particular high school are in favor of a new dress code at their school. The principal is not able to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students to represent the high school.
Select which sample of students the principal should choose.
Answer:
students selected by teachers
Step-by-step explanation:
Final answer:
The principal should use a stratified random sample, selecting an equal number of students from each class year, to accurately represent the student body when surveying opinions on a new dress code. This method ensures each subgroup is proportionally represented and can provide an accurate estimate of the student population's opinion.
Explanation:
The principal should choose a sample that accurately represents the diverse student body at the high school when evaluating opinions on a new dress code. As such, the principal might select a stratified random sample where students are divided by classification (freshman, sophomore, junior, or senior) to ensure that each group is represented in the sample. For instance, by organizing the students' names by classification and then selecting 25 students from each group, we would obtain a total sample of 100 students (a). This resembles the stratified sampling method similar to the one used in the hypothetical polling in question Try It Σ 1.13. This approach as outlined in example 13, which involves drawing a proportionate random sample from each class, ensures that all groups are proportionately sampled, thereby allowing the sample to more accurately reflect the student population's opinion on the new dress code.
Sampling large populations as mentioned, like all algebra students in a city or public opinion in presidential elections, is a common practice and random sampling is critical to avoid bias and ensure that the survey sample represents the larger population effectively. The success of the survey depends on how well the survey targets and represents the specific population without bias, as indicated by the overall description of how surveys operate. If conducted correctly, no matter the sample size, the survey can provide accurate estimates, as seen in the case of the Gallup Poll survey effectiveness discussed.
Therefore, using a stratified random sampling technique where a proportionate number of students from each classification is selected would be the most appropriate choice for the principal to get a representative sample of the high school students' opinions on the dress code.
mags wants to know what is the hottest hairstyle trend is in her town. Which is the best group to survey
A.Get a list of salons in her town and use a deck of cards to pick 5 of them to visit. Survey all hairstylists that work in each salon.
B.Get a list of salons in her town and circle the 5 salons that are close to her house. Survey all the hairstylists that work at each salon
C.Go to all the salons where Luna and her friends go. Survey all the hair stylists that work at each salon
D. Ask her clients that are celebrities which salons they go to. Survey all the hair stylists that work at each salon
Answer: A
Step-by-step explanation:
The best group to survey is option A. A.Get a list of salons in her town and use a deck of cards to pick 5 of them to visit. Survey all hairstylists that work in each salon.
What is the survey?Surveys represent the list of questions that should be focused on for extracting particular data from the people. It could be conducted via the phone, mail, internet, malls, etc.
Since mags want to know the hottest hairstyle trend so here he should get the list of towns and then use the deck of cards so that she should pick 5 for visiting them. Therefore, the correct option is a.
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When rounded to the nearest 100 I am the smallest whole number that becomes 5,000 what number am I
Step-by-step explanation:
Let the number to be identified be represented as x
Given, when rounded to the nearest 100 I am the smallest whole number that becomes 5,000
Therefore, the number is above 4000 and it is a whole number.
When rounded to the nearest 100, I am the smallest whole number that becomes 5,000
The smallest whole number must be 4950 when ronded to 100,it becomes 5000.
The number is 4950
a nutrition major at wright state was studying the relationship between carbohydrates (x) and calories (y). for example, a serving of a particular brand of wheat pasta yielded 42 carbohydrates and 210 calories. after collecting x and y data on many kinds of foods, the student determined the slope of the regression line to be 4.0 and the y intercept to be 3.0. if a new food is tested, and the number of carbohydrates (x) is 100, what would be the predicted calories (y’)?
Answer:
The predicted calories would be 403 calories.
Step-by-step explanation:
We have a linear regression model relating y: calories with x: carbohydrates, which has a slope of 4.0 and a y-intercept of 3.0.
Then, the model equation is:
[tex]y=4.0x+3.0[/tex]
With these model we can predict the calories values for any amount of carbohydrates, within the interval within which this model is valid.
If a new food is tested, and the number of carbohydrates (x) is 100, the predicted value will be:
[tex]y(100)=4.0(100)+3.0=400+3=403[/tex]
The predicted calories would be 403 calories.
what is the m?
-8 + 4m = 2
A study was carried out to investigate the relationship between the hardness of molded plastic (y, in Brinell units) and the amount of time elapsed since termination of the molding process (x, in hours). Summary quantities include n = 15, SSResid = 1236.046, and SSTo = 25460.897. Calculate the coefficient of determination. (Give the answer to four decimal places.)
Using the given values of SSResid and SSTo, we can calculate the coefficient of determination as 0.9518 or 95.18 percent.
Explanation:The coefficient of determination, denoted as r², represents the percentage of variation in the dependent variable that can be explained by the variation in the independent variable using the regression line. To calculate the coefficient of determination, divide the sum of squares of the residuals (SSResid) by the total sum of squares (SSTo), and then subtract the result from 1. In this case, the coefficient of determination can be calculated as follows:
r² = 1 - (SSResid / SSTo)
Substituting the given values, we get:
r² = 1 - (1236.046 / 25460.897)
Calculating this expression gives an answer of approximately 0.9518. Therefore, the coefficient of determination is approximately 0.9518 or 95.18 percent.
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25. One of the silos pictured below holds corn, and the other holds hay. Chopped corn and hay are blown into the tops of the silos through pipes running up from the ground. a. The silos have a radius of 3 meters and a height of 18 meters. What is the volume, to the nearest cubic meter, of one of these silos? b. If a blower can load 1 cubic meter of hay in 3 minutes, how many hours (to the nearest .1 hour) will it take to fill one of these silos?
Answer:
a. 509 m³
Step-by-step explanation:
a. Assume that the silos are cylinders with a circular base. The volume of a silo is given by:
[tex]V = \pi *r^2*h[/tex]
If the radius (r) is 3 meters, and the height (h) is 18 meters, the volume is:
[tex]V = \pi *3^2*18\\V=509\ m^3[/tex]
Total volume is 509 m³
b. If the flow rate is 1 m³ per 3 minutes, the time required to fill the whole 509 m³ is:
[tex]t=509\ m^3*\frac{3\ min}{1\ m^3}*\frac{1\ h}{60\ min}\\t=25.45\ h[/tex]
It will take 25.45 or roughly 25.5 h to fill one of these silos.
What is the area of the figure
Answer: 35 square feet
Step-by-step explanation:
Name the property that justifies the statement. 17 = 17
Step-by-step explanation:
I think when you will multiply 17 by 1 the answer is 17 so 17 = 17
Below are two parallel lines with a third line intersecting them. What is X
x = 105°
Here is why:
The alternate exterior angle theorem states that alternate exterior angles are congruent.
Below I have attached a photo that will help you, the highlighted part of the image is the interior, while the parts that are not highlighted are the exterior. Inside of the two parallel lines will always be the interior.
They are alternate because they are alternating, or diagonal, across the middle line, which is the transversal.
Suppose you take a random sample of one score from this bucket. The probability that this score shows a 3 is p(X = 3) =0.09 . The probability that this score shows a number less than 3 is p(X < 3) = . The probability that this score shows a number greater than 3 is p(X > 3) = .
Answer:
P(X=3) = (1/11) = 0.09
P(X < 3) = (5/11) = 0.45
P(X > 3) = (5/11) = 0.45
Step-by-step explanation:
The complete, correct question is shown in the attached image to this solution.
From the graph and the table,
P(X=3) = (1/11) = 0.09 (as shown in the question)
The probability that this score shows a number less than 3 is p(X < 3)
P(X < 3) = P(X=1) + P(X=2)
= (3/11) + (2/11) = (5/11) = 0.45
The probability that this score shows a number greater than 3 is p(X > 3)
P(X < 3) = P(X=4) + P(X=5)
= (2/11) + (3/11) = (5/11) = 0.45
Hope this Helps!!!
Angle BCD is a circumscribed angle of circle A. Angle BCA measures 40°.
Circle A is shown. Line segments B A and D A are radii. Tangents B C and D C intersect at point C outside of the circle. A line is drawn to connect points A and C. Angle B C A is 40 degrees.
What is the measure of minor arc BD?
40°
50°
80°
100°
Answer:
D. 100
Step-by-step explanation:
correct on edu2020
Based on the calculations, the measure of minor arc BD is equal to 100°.
Given the following data:
Angle BCA = 40°.What is a line segment?A line segment can be defined as a part of a line that is bounded by two (2) distinct points and has a fixed length.
Based on the information given, we can deduce the following:
Angle BAD = 2(BCA)
Angle BAD = [tex]2\times 40[/tex]
Angle BAD = 80°.
Also, angle ABC and ADC both have a measure of 90 degrees because angle BCD is a circumscribed angle.
Note: The sum of the interior angles in a quadrilateral is equal to 360°.
[tex]ABC + ADC + BAD + BCD = 360\\\\90+90+ BAD + BCD = 360\\\\180+ BAD + BCD = 360\\\\BAD + BCD = 360-180\\\\BAD + BCD = 180[/tex]
For the minor arc BD:
[tex]BCD =180-BAD\\\\BCD =180-80[/tex]
Angle BCD = 100°.
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Which proportion can you use to find the value of a?
Given:
The given triangle is a similar triangle.
The length of the hypotenuse is 18 units.
The length of the leg is a.
The length of the part of the hypotenuse is 16 units.
We need to determine the proportion used to find the value of a.
Proportion to find the value of a:
We shall find the proportion to determine the value of a using the geometric mean leg rule.
Applying the leg rule, we have;
[tex]$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$[/tex]
Substituting the values of hypotenuse, leg and part, we get;
[tex]\frac{18}{a}=\frac{a}{16}[/tex]
Thus, the proportion used to find the value of a is [tex]\frac{18}{a}=\frac{a}{16}[/tex]
Hence, Option D is the correct answer.
To find the value of 'a', set up a proportion where the ratios are equivalent. Determine the missing dimensions by cross-multiplying and solving for 'a'. Make sure ratios are in consistent units when setting up the proportions.
Explanation:To find the value of a, we can use the concept of proportions, which involves setting two ratios equal to one another. The provided ratios are related to scale drawings or conversions between units, a common topic in mathematics, especially in geometry and measurement units.
For example, if we have the proportion Length=1/50=0.5/5, we can cross multiply to find that 5 * 1 = 50 * 0.5, which simplifies to 5 = 25, indicating an error as the units must be consistent. Instead, it seems we are meant to find a when we have Length=w/30=0.5/, where w represents the width and should be calculated accordingly.
Another example is using scale to determine area. If we know the scale factor, we can find missing dimensions by setting up the appropriate proportion, such as in Example 4.8.4.2, where a scale measurement is given alongside a scale factor. Writing the proportion would involve equating the scale measurement with the actual measurement times the scale factor.
Write a rule for a transformation
that maps ASTU to ASTU.
Answer:
Horizontal Stretch by Scale Factor 1/2.
Employee I has a higher productivity rating than employee II and a measure of the total productivity of the pair of employees is 40Y1 20Y2. Find the variance of this measure of productivity. (Round your answer to two decimal places.)
Answer:
The variance of the measure of productivity = 141.67(to 2 d.p)
Step-by-step explanation:
The complete question and the step-by step explanation are contained in the files attached to this solution.
Create a row vector vA=1:3:34 that has 12 elements. Then, create a new nine-element vector vB from the elements of vA such that the first five elements are the first five elements of the vector vA, and the last four are the last four elements of the vector vA. Use the colon symbol to address a range of elements. (Do not type the elements of the vector vA explicitly.)
Step-by-step explanation:
Create a row vector vA=1:3:34 that has 12 elements.
Matlab Code:
vA = [1:3:34]
Where vA = [starting element:difference:ending element]
Ouput:
vA = 1 4 7 10 13 16 19 22 25 28 31 34
Create a new nine-element vector vB from the elements of vA such that the first five elements are the first five elements of the vector vA, and the last four are the last four elements of the vector vA
Matlab Code:
% get first five elements from vector vA
vB1 = vA(1:5)
% get last four elements from vector vA
vB2 = vA(9:12)
% combine them together to form row vector vB
vB = [vB1, vB2] (comma or space both are fine)
Ouput:
vB1 = 1 4 7 10 13
vB2 = 25 28 31 34
vB = 1 4 7 10 13 25 28 31 34
x³ + y³ = z³
z³ s value can be anywhere from 1 to 100. Good luck.
Answer:
z = 1,2,3,4
Step-by-step explanation:
0³ + 1³ = 1³ = 1
0³ + 2³ = 2³ = 8
.
.
.
0³ + 4³ = 4³ = 64
what is the horizontal asymptote of the function given?
Answer:
y=2
Step-by-step explanation: horizon shows where the dotted line crosses the y axis
The horizontal asymptotes is [tex]y=2[/tex]
Horizontal asymptotes :Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞.
Horizontal asymptotes are parallel to the x-axis. Vertical asymptotes are vertical lines (perpendicular to the x-axis) near which the function grows without bound.From given figure it is observed that,
at [tex]y=2[/tex] the graph of the function approaches as x tends to +∞ or −∞.
Thus, the horizontal asymptotes is [tex]y=2[/tex]
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Amanda wants to sell her old car. she will open a classified ad in the Sacramento Bee. the newspaper charges $42 for the first two lines and $11 dollars each additional line. she buys a three week ad that has four lines. What is Amanda's cost?
Write this number:
7 thousands, 4 tens, 8 ones, 5
hundreds
Answer:
7,548
Step-by-step explanation:
Answer:
7548
Step-by-step explanation:
7×1000 +4×10 +8×1 +5×100
= 7000 +40 +8 +500
= 7548
A Parks and Recreation official surveyed 200 people at random who have used one of the city's parks. The survey revealed that 26 resided outside the city limits. If she had to arrive at one single value to estimate the true proportion of park users who are residents outside of the city, it would be 0.13. Group of answer choices True False
Answer:
True
Step-by-step explanation:
The estimate of the true proportion of park users who are residents outside of the city is the number of park users in the sample who are residents outside of the city divided by the size of the sample.
In this problem:
26 park users resided outside the city, in a sample of 200 park users.
So
p = 26/200 = 0.13
So the answer is True
Dorothy Wagner is currently selling 80 "I ♥ Calculus" T-shirts per day, but sales are dropping at a rate of 2 per day. She is currently charging $7 per T-shirt, but to compensate for dwindling sales, she is increasing the unit price by $1 per day. How fast, and in what direction, is her daily revenue currently changing?
Answer:
Increasing by $66 per day
Step-by-step explanation:
If sales are dropping at a rate of 2 per day, the sales function is:
[tex]S = -2t +80[/tex]
If price is increasing by $1 per day, the daily price function is:
[tex]P=1t+7[/tex]
Revenue is given by daily sales multiplied by daily price:
[tex]R = S(t)*P(t) = (-2t+80)*(t+7)\\R(t) = -2t^2+66t+560[/tex]
The derivate of the revenue function gives us the daily rate of change in revenue:
[tex]R(t) = -2t^2+66t+560\\R'(t) = -4t+66[/tex]
Currently (t=0) her daily revenue is changing by:
[tex]R'(0) = -4*0+66\\R'(0) = \$66[/tex]
Her revenue is increasing by $66 per day.
Final answer:
Dorothy Wagner's daily revenue is increasing at a rate of $64 per day due to the combined effect of a decrease in quantity sold and an increase in unit price.
Explanation:
The question pertains to how Dorothy Wagner's daily revenue is changing due to a decrease in quantity sold and an increase in unit price. To calculate the rate of change of her revenue, we need to consider both the rate of decrease in quantity and the rate of increase in price.
Dorothy is selling 80 T-shirts per day at $7 each, so her current daily revenue is 80 T-shirts × $7/T-shirt = $560. If her sales are dropping at 2 T-shirts per day and she's increasing the price by $1 per day, then for the next day her projected sales would be 78 T-shirts (80 - 2) at $8 each (7 + 1).
So, the projected revenue for the next day would be 78 T-shirts × $8/T-shirt = $624. To find out how fast her daily revenue is currently changing, we subtract her original revenue from her projected revenue: $624 - $560 = $64. Dorothy's daily revenue is increasing at a rate of $64 per day.
If a Cell Phone Company Z charges a flat fee of $15 plus $0.50 per minute,the equation would be y=0.50x + 15, where y represents total amount of money and x represents minutes,how much would it cost for 20 minutes?
Step-by-step explanation:
f a Cell Phone Company Z charges a flat fee of $15 plus $0.50 per minute,
the equation would be y = 0.50x + 15 ..(1)
where y represents total amount of money and x represents minutes
The cell phone charge for 20 minutes = ?
substitute x = 20 in eq(1)
y = 0.50(20) + 15
y = 10 + 15
y = $25
It costs $20 dollars for 20 minutes.