Answer:
x + y = 4,000
0.1x + 0.04y = 352
Step-by-step explanation:
Product A represents x and product B represents y. The first equation is the total number of items the store owner buys. The second equation is cost per item for both products. The above system of equations can be used to determine how much product A and product B the store owner bought.
Answer:
C. [tex]\left \{ {{x+y=4,000} \atop {0.1x+0.04y=352}} \right.[/tex]
Step-by-step explanation:
Edge 2020
Which functions have a maximum value greater than the maximum of the function g(x) = –(x + 3)2 – 4? Check all that apply. f(x) = –(x + 1)2 – 2 f(x) = –|x + 4| – 5 f(x) = –|2x| + 3
Answer:
A
C
D
Step-by-step explanation:
Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Select two options
The vertex form of the function is f(x) = (x - 2)2 + 2.
The vertex of the function is (-3, -13).
The axis of symmetry for the function is x = 3.
The graph increases over the interval (-3,
).
The function does not cross the x-axis.
Answer:
2 and 4
Step-by-step explanation:
A function assigns the values. The statements that are true about the given function are B and D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
To know the correct statements about the graph of the function f(x)=6x-4+x², we need to plot the graph, as shown below.
A.) The vertex form of the function is f(x)=(x-2)²+2.
To know if the vertex form of the function is f(x)=(x-2)²+2, solve the equation and check if it is of the form f(x)=6x-4+x².
[tex]f(x)=(x-2)^2+2\\\\ f(x)=x^2+4-4x+2\\\\f(x) = x^2-4x+6[/tex]
Since the two functions are not equal this is not the vertex form of the function is f(x)=6x-4+x².
B.) The vertex of the function is (-3, -13).
As can be seen in the image below, the vertex of the function lies at (-3,-13.) Therefore, the statement is true.
C.) The axis of symmetry for the function is x = 3.
As the vertex is at -3, therefore, the function symmetry will be about x=-3.
Hence, the given statement is false.
D.) The graph increases over the interval (-3).
The given statement is true since the graph will be showing a positive slope in the interval (-3, +∞).
E.) The function does not cross the x-axis.
It can be observed that the function intersects the x-axis exactly at two points, therefore, the given statement is false.
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Sera sells t-shirts at the beach. She believes the price of a t-shirt and the number of t-shirts sold are related. She has been experimenting with different prices for the
t-shirts. She has collected a data set with five pairs of
data: each consists of the price of a t-shirt and the
number of shirts sold.
The independent variable which will on on the x-axis is the price of a t-shirt.
The dependent variable which will on on the x-axis is the number of t-shirts sold.
The independent variable can be described as the variable that is used to determine the dependent variable. It is the variable that the researcher manipulates in the experiment.
The dependent variable is the variable whose value is determined in the experiment. The value of the dependent variable depends on the independent variable.
For example, assume that if the price of a shirt is $1. A person purchases 10 t shirts. If the price increases to $10, only one shirt would be sold. This means that the amount of shirts bought is dependent on the price of the t-shirt. The price of the shirt is the independent variable while the amount of shirts bought is the dependent variable.
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If you are driving at the speed of 90 km/hour. What is your speed in meter/second
Answer:
speed = 25 m/s
Step-by-step explanation:
Driving at a speed of 90 km / hour . what is the speed in meters per seconds.
converting from km to meter one have to multiply by 1000. This means 1 km is equal to 1000 meter. Converting 90 km to meter we have to multiply 90 by 1000.
90 × 1000 = 90000 meters
The time is in hours so we have to convert to seconds as required by the question.
60 minutes = 1 hour
Therefore,
1 minutes = 60 seconds
60 minutes = 3600 seconds
This means 1 hour = 3600 seconds
speed = 90000/3600
speed = 25 m/s
QUESTION 1 of 10: Which of the following is NOT a true statement?
a) Knowing the diferent food groups and how many servings from each group will allow you to have a balanced diet.
b) All work and no relaxation can compromise your health.
C) Technology benefits people by allowing them to avoid sore muscles.
d) Lack of sleep leads to increased risk for motor vehicle accidents.
Answer:
c
Step-by-step explanation:
cuzz im right
which function does this graph represent
A. f(x) = 3(x + 1)^2 + 2
B. f(x) = -3(x + 1)^2 + 2
C. f(x) = -3(x + 1)^2 - 2
D. f(x) = 3(x - 1)^2 + 2
The equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.
What is parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Here, general equation of parabola in downward direction is
(y-y₁) = -4a(x-x₁)²
vertex of parabola (-1, 2)
(y-2) = -4a(x-(-1))²
(y - 2) = -4a(x + 1)²
put the value of x = 0 and y = -1
so we get, a = 3/4
put in equation of parabola
( y - 2 ) = -3 ( x + 1 ) ²
y = -3 (x + 1)² + 2
f(x) = -3 (x + 1)² + 2
Thus, the equation of parabola which represents the graph is f(x) = -3 (x + 1)² + 2.
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Suppose the number of prisoners held in a certain type of prison, measured in thousands, can be described by the polynomial - 2.02x + 78.47x + 744. The variable x represents the number of years since 1990, According to the polynomial, by how much did the prison population increase from 2002 to 2007?
You are thinking about the things that can go wrong on your trip home over the Thanksgiving break. You have booked a flight with US-Scareways. You know that in 28 percent of the cases the company has canceled the flight you were on. Should such a thing occur, there would be no other air travel option home for you. As a backup, your friend Walter has offered you a ride back. However, you know that Walter only has a seat in his car for you with 84 percent probability. What is the Probability of you making it home for the holidays
Answer:
0.9552
Step-by-step explanation:
Probability of making home can be made by either of the options :-
Prob (Reach through flight) : 1 - prob (flight not cancelled) = 1 - 0.28 = 0.72Prob (Reach through car) : prob (flight cancelled & car seat is available) = 0.28 x 0.84 = 0.2352So, probability of making out at home : Reach through flight or car = 0.72 + 0.2352 = 9.9552
Final answer:
The probability of making it home for the holidays can be calculated using conditional probability. The probability of the flight being canceled is 28 percent, and the probability of Walter having a seat in his car is 84 percent. The probability of making it home is approximately 60.48 percent.
Explanation:
The probability of making it home for the holidays can be calculated using the concept of conditional probability. The probability of the flight being canceled is given as 28 percent, which means there is a 72 percent chance that the flight is not canceled. The probability of Walter having a seat in his car is given as 84 percent. To calculate the probability of making it home, we need to calculate the probability of both events happening.
The probability of the flight not being canceled is 72 percent (0.72) and the probability of Walter having a seat is 84 percent (0.84). To find the probability of both events happening, we multiply the probabilities: 0.72 * 0.84 = 0.6048 or approximately 60.48 percent. So, there is a 60.48 percent probability of making it home for the holidays.
Large Sample Proportion Problem. Surveys were conducted in multiple countries and respondents were asked if they felt political news was reported fairly. The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly. Suppose we want to determine if the proportion for the U.S. is below .50 for an alpha level of .05. What is conclusion of my test
Answer:
[tex]z=\frac{0.47-0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-1.897[/tex]
We have aleft tailed test the p value would be:
[tex]p_v =P(z<-1.897)=0.0289[/tex]
The p value obtained is less compared to the significance level so then we have enough evidence to conclude that the true proportion is significantly lower than 0.5.
Step-by-step explanation:
Information given
n=1000 represent the random sample selected
X=470 represent the number of people who felt political news was reported fairly
[tex]\hat p=\frac{470}{1000}=0.470[/tex] estimated proportion of people who felt political news was reported fairly
[tex]p_o=0.5[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
For this case we want to test if proportion for the U.S. is below .50 so then the system of hypothesis for this case are:
Null hypothesis:[tex]p \geq 0.5[/tex]
Alternative hypothesis:[tex]p < 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info provided we got:
[tex]z=\frac{0.47-0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=-1.897[/tex]
We have aleft tailed test the p value would be:
[tex]p_v =P(z<-1.897)=0.0289[/tex]
The p value obtained is less compared to the significance level so then we have enough evidence to conclude that the true proportion is significantly lower than 0.5.
A survey was taken among a group of people. The probability that a person chosen likes Italian food is 0.75, the probability that a person likes Chinese food is 0.28,
and the probability that a person likes both foods is 0.21.
Determine the probability that a person likes Italian, but not Chinese
Determine the probaility that a person likes at least one of these foods
Determine the proability that a person likes at most one of these foods -
Answer:
54% probability that a person likes Italian food, but not Chinese food.
82% probaility that a person likes at least one of these foods
79% proability that a person likes at most one of these foods
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that a person likes Italian food.
B is the probability that a person likes Chinese food.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a person likes Italian food but not Chinese and [tex]A \cap B[/tex] is the probability that a person likes both Italian and Chinese food.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
The probability that a person likes both foods is 0.21.
This means that [tex]A \cap B = 0.21[/tex]
The probability that a person likes Chinese food is 0.28
This means that [tex]B = 0.28[/tex]
So
[tex]B = b + (A \cap B)[/tex]
[tex]0.28 = b + 0.21[/tex]
[tex]b = 0.07[/tex]
The probability that a person likes Italian food is 0.75
This means that [tex]A = 0.75[/tex]
So
[tex]A = a + (A \cap B)[/tex]
[tex]0.75 = a + 0.21[/tex]
[tex]a = 0.54[/tex]
Determine the probability that a person likes Italian, but not Chinese
This is a.
54% probability that a person likes Italian food, but not Chinese food.
Determine the probaility that a person likes at least one of these foods
[tex]P = a + b + (A \cap B) = 0.54 + 0.07 + 0.21 = 0.82[/tex]
82% probaility that a person likes at least one of these foods
Determine the proability that a person likes at most one of these foods
Either a person likes at most one of these foods, or it likes both. The sum of the probabilities of these events is decimal 1.
0.21 probability it likes both.
Then
0.21 + p = 1
p = 0.79
79% proability that a person likes at most one of these foods
An author argued that more basketball players have birthdates in the months immediately following July 31, because that was the age cutoff date for nonschool basketball leagues. Here is a sample of frequency counts of months of birthdates of randomly selected professional basketball players starting with January: 390, 392, 360, 318, 344, 330, 322, 496, 486, 486, 381, 331 . Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency? Do the sample values appear to support the author's claim?
Answer:
There is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
Step-by-step explanation:
In this case we need to test whether there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum{\frac{(O-E)^{2}}{E}}[/tex]
The values are computed in the table.
The test statistic value is [tex]\chi^{2}=128.12[/tex].
The degrees of freedom of the test is:
n - 1 = 12 - 1 = 11
Compute the p-value of the test as follows:
p-value < 0.00001
*Use a Chi-square table.
p-value < 0.00001 < α = 0.05.
So, the null hypothesis will be rejected at any significance level.
Thus, there is sufficient evidence to warrant rejection of the claim that professional basketball players are born in different months with the same frequency.
Final answer:
To test the claim that professional basketball players are born in different months with the same frequency, a chi-square test for goodness of fit can be used. Calculations involve comparing the actual birthdate frequencies of the players against the expected frequencies if the distribution were uniform. A statistically significant result would support the author's claim, while a non-significant result would not.
Explanation:
Chi-Square Test for Uniform Distribution
To determine if there is sufficient evidence to support the author's claim that professional basketball players are born in different months with the same frequency, we can perform a chi-square test for goodness of fit. Given the frequency counts of the birthdates of professional basketball players for each month, we will compare them to the expected frequencies if births were uniformly distributed throughout the year.
Steps to Perform the Test
Firstly, calculate the total number of players in the sample by summing up the frequency counts for each month.
Determine the expected frequency for each month, which would be the total number of players divided by 12, assuming a uniform distribution.
Calculate the chi-square statistic using the formula: χ² = ∑((observed - expected)² / expected), where 'observed' is the frequency count for each month, and 'expected' is the expected frequency.
Compare the calculated chi-square value with the critical value from the chi-square distribution table with 11 degrees of freedom (since there are 12 months - 1) and a significance level of 0.05.
If the chi-square value is greater than the critical value, reject the null hypothesis (that the birth months are uniformly distributed), which supports the author's claim. Otherwise, do not reject the null hypothesis.
Interpretation
By performing the calculations, if the chi-square test statistic is greater than the critical value, it suggests that there is a statistically significant difference in the distribution of birth months among professional basketball players. This would support the author's claim that there may be more players born in the months immediately following July 31, which is the age cutoff date for nonschool basketball leagues. If the test statistic is not greater than the critical value, there is not enough evidence to support the claim.
helphelphelphelphelphelphelphelphelphelp
Answer:
Angle A equals Angle B so 6x-2=4x+48 ---> 2x=50 ---> x=25. From this we find that both Angles A and B are equal to 148 degrees. :)
Sharif's portfolio generated returns of 12 percent, 15 percent, −15 percent, 19 percent, and −12 percent over five years. What was his average return over this period?
3.8 percent
2.1 percent
17 percent
19 percent
Answer:
3.8 percent
Step-by-step explanation:
To find his average return over n years, we sum all of his returns, and divide by n.
In this problem:
5 years.
The sum is (12 + 15 - 15 + 19 - 12) = 19
19/5 = 3.8
So the correct answer is:
3.8 percent
Answer:
The answer is 3.82
Step-by-step explanation:
(12 + 15− 15− 12 + 19)/5 = 3.8 3.
Yooo I need help right now
Answer:
The answer would be 2924. 82
What is the complete factorization of 8x^2 - 8x + 2?
Step-by-step explanation:
8x² − 8x + 2
2 (4x² − 4x + 1)
2 (2x − 1)²
What is the volume of a box that is 7cm by 11cm by 13cm?
Answer:
V = 1001
Step-by-step explanation:
This is rather simple question, but I can understand not knowing how to find volume.
The volume of a rectangular prism(as specified by the way the dimensions were given) is whl, when w is width, h is height, and l is length. It does not actually matter the order, due to the Commutative Property of Multiplication, which states that is does not matter what order you multiply things.
Plugging in the numbers, we end up with 1001.
Hope this helps!
You work for a company in the marketing department. Your manager has tasked you with forecasting sales by month for the next year. You notice that over the past 12 months sales have consistently gone up in a linear fashion, so you decide to run a regression the company's sales history. You find that the regression equation for the data is (sales) = 128.329*(time) + 115.362. In August (time = 8) you see the actual sales quantity was 322.492. The residual is -819.502. Interpret this residual in terms of the problem.
01) The month is 819.502 months less than what we would expect.
02) The month is 819.502 months larger than what we would expect.
03) The sales is 819.502 units greater than what we would expect.
04) The sales is 819.502 units less than what we would expect.
05) The sales is 322.492 units less than what we would expect.
3Answer:
Step-by-step explanation:
Toxic Pollution: In the first year of a study, health officials discovered toxic pollutants in the soil surrounding a factory. The initial measurement was 65 parts per million (ppm) of pollutant. They returned to take similar measurements for several years afterward, and uncovered a disturbing trend. The pollutant levels in the soil surrounding the factory were growing exponentially, at a rate of 4.5% each year. Which exponential model predicts the amount of pollutant in the soil t years from the first measurement?
Answer:
The model for the pollutant levels in the soil t years from the first measurement is:
[tex]Y(t)=65e^{0.044}[/tex]
Step-by-step explanation:
We have a first measurement of 65 parts per million (ppm) of pollutant.
We also know that the pollutant levels were growing exponentially at a rate of 4.5% a year.
We can model this as:
[tex]Y(t)=Y_0e^{kt}[/tex]
The value of Y0 is the first measurement, that correspond to t=0.
[tex]Y_0=65[/tex]
The ratio for the pollutant levels for two consecutive years is 1+0.045=1.045. This can be expressed as the division between Y(t+1) and Y(t), and gives us this equation:
[tex]\dfrac{Y(t+1)}{Y(t)}=\dfrac{Y_0e^{k(t+1)}}{Y_0e^{kt}} =\dfrac{e^{k(t+1)}}{e^{kt}}=e^{k(t+1-t)}=e^k=1.045\\\\\\k=ln(1.045)\approx 0.044[/tex]
Then, we have the model for the pollutant levels in the soil t years from the first measurement:
[tex]Y(t)=65e^{0.044}[/tex]
What is the following quotient 3 square root 8 4 square root 6
Answer: √3/2
Step-by-step explanation: Ok...so it would look like this:
(3√8)/(4√6)
I hope this helps!
$100 is invested at 12% per year. If the amount is compounded annually, write the total amount after 2 years in exponential function form.
Answer:
A = $100(1.12)^2
Step-by-step explanation:
The standard formula for compound interest is given as;
A = P(1+r/n)^(nt) .....1
Where;
A = final amount/value
P = initial amount/value (principal)
r = rate yearly
n = number of times compounded yearly.
t = time of investment in years
For this case;
P = $100
t = 2years
n = 1
r = 12% = 0.12
Substituting the values, we have;
A = $100(1+0.12)^(2)
A = $100(1.12)^2
A car travels at an average speed of 52 miles per hour. How many miles does it travel in 5 hours and 45 minutes?
Answer:
299
Step-by-step explanation:
On average, it travels 52 miles in each hour. In 5 3/4 hours, it travels 5 3/4 times 52 miles.
(5 3/4)(52 miles) = 299 miles
It travels 299 miles in the given time.
Answer:
The car will travel 195 miles.
Step-by-step explanation:
(3.75 hrs)(52 mph)=195 miles
The distance between sides of a polygon is always the same
Answer:
yes
Step-by-step explanation:
By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides.
Since it is true that the distance between sides of a polygon are always the same.
What is a polygon?A polygon is defined as a closed figure made up of three or more line segments connected end to end
For a regular polygon of any number of sides, then the sum of its exterior angle is 360° .
Exterior angle is an measure of rotation between one extended side of the polygon with its adjacent side which is not extended. Also, regular having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.
When a polygon is four sided (a quadrilateral), the sum of its angles is 360°
Based on the definition, all sides are the same length, thus the perimeter is simply the length of a side times the number of sides.
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Exclude leap years from the following calculations. (a) Compute the probability that a randomly selected person does not have a birthday on March 14. (b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month. (c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month. (d) Compute the probability that a randomly selected person was not born in February.
Answer:
a) 99.73% probability that a randomly selected person does not have a birthday on March 14.
b) 96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
c) 98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.
d) 92.33% probability that a randomly selected person was not born in February.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
A non-leap year has 365 days.
(a) Compute the probability that a randomly selected person does not have a birthday on March 14.
There are 365-1 = 364 days that are not March 14. So
364/365 = 0.9973
99.73% probability that a randomly selected person does not have a birthday on March 14.
(b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
There are 12 months, so there are 12 2nds of a month.
So
(365-12)/365 = 0.9671
96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
(c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month.
The following months have 31 days: January, March, May, July, August, October, December.
So there are 7 31st days of a month during a year.
Then
(365-7)/365 = 0.9808
98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.
(d) Compute the probability that a randomly selected person was not born in February.
During a non-leap year, February has 28 days. So
(365-28)/365 = 0.9233
92.33% probability that a randomly selected person was not born in February.
The probability that a person does not have a birthday on March 14, on the 2nd day of a month, on the 31st day of a month, or is not born in February is approximately 0.9973, 0.9671, 0.9808, and 0.9233 respectively. These probabilities were computed by subtracting the fraction of the year representing the specific days or month from 1. These solutions are based on a standard non-leap year of 365 days.
To solve the probability questions, we will assume a non-leap year with 365 days.
(a) Probability that a randomly selected person does not have a birthday on March 14:
There is only one day out of the year that is March 14. Therefore, the probability that a person does have a birthday on March 14 is:
P(March 14) = 1/365
Consequently, the probability that a person does not have a birthday on March 14 is:
P(Not March 14) = 1 - 1/365 = 364/365 ≈ 0.9973
(b) Probability that a randomly selected person does not have a birthday on the 2nd day of a month:
Since there are 12 months in a year, there are 12 days which fall on the 2nd day of each month.
P(2nd day) = 12/365
Therefore, the probability that a person does not have a birthday on the 2nd day of any month is:
P(Not 2nd day) = 1 - 12/365 = 353/365 ≈ 0.9671
(c) Probability that a randomly selected person does not have a birthday on the 31st day of a month:
There are only 7 months with 31 days (January, March, May, July, August, October, December).
P(31st day) = 7/365
Therefore, the probability that a person does not have a birthday on the 31st day of any month is:
P(Not 31st day) = 1 - 7/365 = 358/365 ≈ 0.9808
(d) Probability that a randomly selected person was not born in February:
February has 28 days out of the year.
P(February birthday) = 28/365
Therefore, the probability that a person was not born in February is:
P(Not February) = 1 - 28/365 = 337/365 ≈ 0.9233
The radius of a sphere is 6 units. A sphere has a radius of 6 units. Which expression represents the volume of the sphere, in cubic units?
Answer:
The volume of the sphere is 678.24 u³
V = ⁴⁄₃ * π * (6u)³
Step-by-step explanation:
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 6 units
π = 3.14
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * 3.14 * (6u)³
V = 4.187 * 216 u³
V = 678.24 u³
The volume of the sphere is 678.24 u³
What is the mode of the following numbers?
9,10,6,5,6
Answer:
6
Step-by-step explanation:
The mode is the number which appears most often in a set of numbers in this case that would be 6 because it appears twice
The mode of a set of values is the one that appears most frequently. In your list: 9, 10, 6, 5, 6 - the number 6 appears twice, more than any other number, making 6 the mode.
Explanation:In statistics, the mode of a set of values is the value that appears most frequently. An easy way to find the mode is to count the frequency of each number. Looking at your list of numbers: 9, 10, 6, 5, 6. The number 6 is the only number that appears more than once.
So, the mode of the given set of numbers is 6 because it appears more frequently than the other numbers.
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Lauren's dog jumped 4 times as high as Cheyenne's dog. The two dogs jumped 10 feet. How high dod Lauren's dog jump
Answer:
Laurens dog: 8 feet
Cheyenne's dog: 2 feet
Step-by-step explanation:
The first step is to evaluate the question, we know that you need to find the height each dog jumped, given the sum of both combined
next, you do simple math:
4x2= 8
10-8= 2
hope this helps
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Consider the recursively defined set S: Basis Step: The unit circle is in S. Recursive Step: if x is in S, then x with a line through any diameter is in S. (a) (4 points) Prove that: is in S. (b) ( 6 points) For an element x ∈ S, define V (x) be the number of vertices (i.e. the number of intersections of lines and arcs and lines with lines), let E(x) to be the number of edges (line segments or arcs between vertices), and let F(x) be the number of faces. Prove that for any x ∈ S that F + V = E + 1. (Please use structural induction.)
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images for the step by step explanation to the question
The Census Bureau reports the average commute time for citizens of Cleveland, Ohio is 33 minutes. To see if the commute time is different in the winter, a random sample of 40 drivers were surveyed. The average commute time for the month of January was calculated to be 34.2 minutes and the population standard deviation is assumed to be 7.5 minutes. At the 0.05 level of significance, can it be concluded that the commuting times are different in the winter? What is the p-value? Use the rounded test statistic from the previous problem and round to 4 decimal places.
Answer:
We conclude that the commuting times are same in the winter.
Step-by-step explanation:
We are given that the Census Bureau reports the average commute time for citizens of Cleveland, Ohio is 33 minutes. To see if the commute time is different in the winter, a random sample of 40 drivers were surveyed.
The average commute time for the month of January was calculated to be 34.2 minutes and the population standard deviation is assumed to be 7.5 minutes.
Let [tex]\mu[/tex] = average commute time in winter.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 33 minutes {means that the commuting times are same in the winter}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 33 minutes {means that the commuting times are different in the winter}
The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean commute time for the month of January = 34.2
[tex]\sigma[/tex] = population standard deviation = 7.5 minutes
n = sample of drivers = 40
So, test statistics = [tex]\frac{34.2-33}{\frac{7.5}{\sqrt{40}}}[/tex]
= 1.012
The value of z test statistics is 1.012.
Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the commuting times are same in the winter.
Also, P-value of the test statistics is given by;
P-value = P(Z > 1.012) = 1 - P(Z [tex]\leq[/tex] 1.012)
= 1 - 0.84423 = 0.1558
Please answer this correctly
Answer:
easy peasy lemon squeezy
Step-by-step explanation:
Which is similar to this quadrilateral?
Answer:
D
Step-by-step explanation:
D has the most similarities than others
The option B is correct.
Definition of similarity :Two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same and two adjacent sides have equal ratios.The option B quadrilateral is similar to the given quadrilateral.
Because the three corresponding angles are the same.
Therefore, option B is correct.
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