In a study of its reservation patterns, a national hotel chain randomly sampled the records of 20 of its locations and recorded the number of days last year when the locations had no rooms available: 163, 126, 59, 47, 146, 64, 39, 75, 86, 114, 51, 68, 58, 38 66, 72, 42, 85, 40, 59
a) Construct a histogram of these data
b) Describe the distribution
Answers
Answer:
Step-by-step explanation:
a)
Class limits Frequency
38 - 63 9
64 - 89 7
90 - 115 1
116 - 141 1
142 - 167 2
Construct a histogram of these data(image attached)
b)
Frequency distribution table (also known as frequency table) consists of various components.
Classes: A large number of observations varying in a wide range are usually classified in several groups according to the size of their values. Each of these groups is defined by an interval called class interval. The class interval between 10 and 20 is defined as 10-20.
Class limits: The smallest and largest possible values in each class of a frequency distribution table are known as class limits. For the class 10-20, the class limits are 10 and 20. 10 is called the lower class limit and 20 is called the upper class limit.
Class limit: Class limit is the midmost value of the class interval. It is also known as the mid value.
Mid value of each class = (lower limit + Upper limit)2.
If the class is 38 to 63 , lower limit is 38 and upper limit is 63. So the mid value is
[tex]\frac{(38+63)}{2} =50.5[/tex]
Class width is calculated using upper and lower value
Class width = (upper - lower) value /class
[tex]=\frac{ ( 163 - 38)}{5} \\\\=25[/tex]
Magnitude of a class interval: The difference between the upper and lower limit of a class is called the magnitude of a class interval.
Class frequency: The number of observation falling within a class interval is called class frequency of that class interval.
Related Questions
simplify (3a-2b)²-2(3a-2b)(a+2b)+(a+2)²
Answers
4a - 20ab + 12b. +4a + 4
Please answer this correctly
Answers
Answer:
x = 48
Step-by-step explanation:
Since it's given that these two shapes are similar, you can set up a proportion to solve for x, like so:
[tex]\frac{27}{18} =\frac{72}{x}[/tex]
Cross multiply:
[tex]\frac{27x}{1296}[/tex]
Divide 1296 by 27:
x = 48
What’s the correct answer for this?
Answers
9.4 units.
Because,
Formula for arc length is 2times pie times radius times angle divided by 360.
Answer:
The answer is option 2.
Step-by-step explanation:
You have to use length or arc formula, Arc = θ/360×2×π×r where θ represents degrees and r is radius. Then substitute the following values into the formula :
[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]
Let θ = 45,
Let r = 12,
[tex]arc = \frac{45}{360} \times 2 \times \pi \times 12[/tex]
[tex]arc = \frac{1}{8} \times 24\pi[/tex]
[tex]arc = 9.42 \: units \: (3s.f)[/tex]
An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown. Which best describes the range of possible values for the third side of the triangle? A x 18.9 B 12.5 26 D 6 < x < 26
Answers
Solution:
12.5 < x < 18.9
Reason:
To solve this problem, we can apply Pythagorean's theorem.
To find the upper bound:
We can set the two given legs as the 2 legs of a right triangle. This allows us to keep the angle under 90 degrees. So if we set the legs to be 10 and 16, then the third side must be:
10^2 + 16^2 = x^2
x^2 = 356
x is roughly equal to 18.9
For the lower bound, this time, we set x as one of the legs, and 10 as the other let. Since we know that the longest side is 16, we can set up an equation again:
x^2 + 10^2 = 16^2
x^2 = 16^2 - 10^2
x^2 = 156
x is roughly equal to 12.5
So we have found the bounds to be 12.5 < x < 18.9
Answer:
its B
Step-by-step explanation:
A manufacturer of large appliances must decide which of two​ machines, A and​ B, they want to purchase to perform a specific task in the production process. The goal is to buy the machine that has smaller mean time required to perform the task. The plant supervisor selects 15 machine operators at​ random, and each operator performs the task on each of the two machines. The production times are paired for each worker. A paired​ t-test is to be performed to determine if there is evidence that the population mean time using machine A is less than the population mean time using machine B. The summary statistics for the differences in the times required for the task in minutes​ (machine A​ - machine​ B) for the 15 randomly selected workers are given below.
n=15; xÌ… = -10.9 and s=20.3
What must be true about the population of differences in the times required for the task between machine A and machine B for conclusions from the paired t-test to be valid for the population of differences among all workers?
a. Because of the small sample size of differences in times required between machine A and machine B, the distribution of sample means of the differences cannot be normal.
b. Because there were a total of 30 obervations (15 times from machine A and 15 times from machine B), the distribution of sample means of the differences will be approximately normal by the Central Limit Theorem.
c. Because the sample size is "large" enough, the distribution of differences for all workers will be normal.
d. Because of the small sample size of differences in times required between machine A and machine B, the distribution of differences for all workers must be normal.
Answers
Answer:
d. Because of the small sample size of differences in times required between machine A and machine B, the distribution of differences for all workers must be normal.
Step-by-step explanation:
A paired t- test conclusion is said to be valid if one of the assumptions that must be satisfied is that: the distribution of the differences must be normal in most cases for which the sample size is small.
From the given information:
the sample size n = 15 ;which is far less than 30
Therefore;we require the distribution of differences in times required between machine A and machine B for all workers to be normal.
From the first option; it is incorrect because even if the sample size is small; the distribution of sample means of the differences will be normal but in the first option ; it is stated that the differences cannot be normal. That makes the first option to be incorrect.
From the second option; is not correct because the sample size (for differences) is 15 and therefore that is a minimal sample which makes the Central Limit Theorem to be invalid and not applicable here.
From the third option; we all know that the sample size is small and not large since it is lesser than 30.
A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow. Model Price ($) Model Price ($) Retail Outlet Deluxe Standard Retail Outlet Deluxe Standard 1 39 27 5 40 30 2 39 29 6 39 35 3 46 35 7 35 29 4 38 31 The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10. a.Calculate the value of the test statistic (to 2 decimals).
b.What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)?
Answers
Answer:
Step-by-step explanation:
The data is incorrect. The correct data is:
Deluxe standard
39 27
39 28
45 35
38 30
40 30
39 34
35 29
Solution:
Deluxe standard difference
39 27 12
39 28 11
45 35 10
38 30 8
40 30 10
39 34 5
35 29 6
a) The mean difference between the selling prices of both models is
xd = (12 + 11 + 10 + 8 + 10 + 5 + 6)/7 = 8.86
Standard deviation = √(summation(x - mean)²/n
n = 7
Summation(x - mean)² = (12 - 8.86)^2 + (11 - 8.86)^2 + (10 - 8.86)^2 + (8 - 8.86)^2 + (10 - 8.86)^2 + (5 - 8.86)^2 + (6 - 8.86)^2 = 40.8572
Standard deviation = √(40.8572/7
sd = 2.42
For the null hypothesis
H0: μd = 10
For the alternative hypothesis
H1: μd ≠ 10
This is a two tailed test.
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 7 - 1 = 6
2) The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (8.86 - 10)/(2.42/√7)
t = - 1.25
We would determine the probability value by using the t test calculator.
p = 0.26
Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis.
b) Confidence interval is expressed as
Mean difference ± margin of error
Mean difference = 8.86
Margin of error = z × s/√n
z is the test score for the 95% confidence level and it is determined from the t distribution table.
df = 7 - 1 = 6
From the table, test score = 2.447
Margin of error = 2.447 × 2.42/√7 = 2.24
Confidence interval is 8.86 ± 2.24
samantha is making punch for a class picnic. there are 25 students in her class. Samantha uses 1 gallon 2 quarts of orange juice, 3 quarts of lemonade, and 1 gallon 3 quarts of sparkling water. How much punch did samantha make? will there be enough for each student to make two 1 cup servings of punch?
Answers
Answer:
4 gallonsyesStep-by-step explanation:
A quart is 1/4 gallon, so the total of liquid ingredients for the punch is ...
(1 2/4 gal) +(3/4 gal) +(1 3/4 gal) = 2 8/4 gal = 4 gal
Samantha made 4 gallons of punch.
__
1 cup is 1/16 gallon, so 2 cups each for 25 students requires ...
(1/16 gal)(2)(25) = 50/16 gal = 3 1/8 gal
Samantha made more punch than that, so there will be enough for 2 1-cup servings for each student.
A paper company produces 4,675 notebooks in 5 days. How many notebooks can it produce in 13 days?
OA. 12,155
OB. 2,431
OC. 4,473
OD. 12,100
Answers
Answer:
OA. 12,155
Step-by-step explanation:
A paper company produces 4,675 notebooks in 5 days. How many notebooks can it produce in 13 days?
--------
in 5 days= 4675
in 13 days= 4675/5*13= 12155
Answer
A OR D
Step-by-step explanation:
pls help i give brainliest
you buy a bag of crisps in an airport.After take off you take the crisps out of your ruck sack why has the bag expanded
Answers
Answer:
Step-by-step explanation:
there is a pressure difference between inside and outside the container and if the — bag, bottle, whatever — is flexible enough it will either expand as the ambient air pressure decreases when climbing or collapse when the aircraft is descending and the pressure is increasing.......
this is ur answer ....
What should the rule be for the table?
On a recent test, you were given the table displayed and
asked to write the rule that models it.
Subtract 6 from the x value to get the y value.
Multiply the x value by 1/2 to get the y value.
Multiply the x value by 1/4 to get the y value.
Add 6 to the x value to get the y value.
8
12
12
6
16
10
(look at picture) pls help
Answers
Answer: it’s A
Step-by-step explanation:
Answer:
I check the answer was a or Subtract 6 from the x value to get the y value
Solve for x.
Solve for x.
Answers
Answer:
20
Step-by-step explanation:
x is the radius of the circle. The tangent line is perpendicular to the radius line at that point. Using Pythagorean theorem:
x² + 15² = (x + 5)²
x² + 225 = x² + 10x + 25
225 = 10x + 25
200 = 10x
x = 20
Answer is:
x = 20. hope this helps
Some smells are perceived as being more feminine or more masculine. Researchers asked a random sample of 300 American adults to score quantitatively the perceived gender-orientation of lavender. Smaller scores indicate a more feminine scent and larger scores a more masculine scent. In this design, a gender-neutral scent would have a perceived gender-orientation score of 12. The participants gave the scent of lavender an average score of 10.28
a. Is this evidence that the scent of lavender is not gender-neutral, on average? State H0cap h sub zero and Hacap h sub a in the corresponding test, indicating what the parameter in your hypotheses is.
b.The researchers report that "p<.01p less than full stop 01 (2-tail)" for this test. Explain the meaning of "p<.01p less than full stop 01" and "2-tail."
c.Assuming that the conditions for inference were met, conclude in the context of this study.
Answers
Answer:
a) We are told smaller scores indicate a more feminine scent and larger scores a more masculine scent, also a score of 12 represents a gender-neutral scent.
Here the average from the sample for lavender is 10.28
To test for the evidence that lavender is not gender neutral on average, the null hypothesis H0 would take that lavender is gender-neutral, while the alternative hypothesis would take that the score of lavender is not gender neutral. We now have the null and alternative hypotheses as:
H0 : u = 12
H1 : u ≠ 12
Here, u represents the mean gender-orientation score for lavender. The alternative is two sided because we want to test if lavender is not gender neutral. Which means lavender might be more masculine of more feminine.
b) Given: p < 0.01 (2 tailed)
This means the p-value is less than level of significance 0.01.
Since the pvalue is less than the level of significance, we reject null hypothesis H0. This means there is sufficient evidence to conclude that the smell is not gender-neutral.
There is no reason to prefer a particular gender, that's why this is a two tailed hypothesis.
c) c.Assuming that the conditions for inference were met, which means the p-value is less than 0.01 so the null hypothesis H0 is rejected.
The conlusion would be that there is enough evidence to conclude that lavender is not gender-neutral
Find the value of x in the triangle shown below.
8
3
Answers
Answer:
[tex] \sqrt{55}[/tex]
Step-by-step explanation:
Given is a right angled triangle.
Therefore, by Pythagoras theorem:
[tex] {x}^{2} = {8}^{2} - {3}^{2} \\ = 64 - 9 \\ = 55 \\ x = \sqrt{55} [/tex]
If f(x)= 6x squared - 4 and g(x)= 2x + 2 find (f-g)(x)
Answers
Answer:
[tex]6x^2-2x-6[/tex]
Step-by-step explanation:
[tex]f(x)=6x^2-4 \\\\g(x)=2x+2 \\\\(f-g)(x)= (6x^2-4)-(2x+2)=6x^2-2x-6[/tex]
Hope this helps!
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Frequency Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100 Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the critical value is:
Answers
Answer:
The degrees of freedom are given by;
[tex] df =n-1= 5-1=4[/tex]
The significance level is 0.1 so then the critical value would be given by:
[tex] F_{cric}= 7.779[/tex]
If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays
Step-by-step explanation:
For this case we have the following observed values:
Mon 25 Tue 22 Wed 19 Thu 18 Fri 16 Total 100
For this case the expected values for each day are assumed:
[tex] E_i = \frac{100}{5}= 20[/tex]
The statsitic would be given by:
[tex] \chi^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i}[/tex]
Where O represent the observed values and E the expected values
The degrees of freedom are given by;
[tex] df =n-1= 5-1=4[/tex]
The significance level is 0.1 so then the critical value would be given by:
[tex] F_{cric}= 7.779[/tex]
If the calculated value is higher than this value we can reject the null hypothesis that the arrivals are uniformly distributed over weekdays
In a given year, 94 cities in the world had populations of 1 million or more. Fifty years later, 530 cities had populations of 1 million or more. What was the percent increase?
Answers
Answer:
The percent increase was of 464%.
Step-by-step explanation:
To find the percent increase, first we find how much the current amount is of the original amount. Then, we subtract the current amount from the original amount.
Percentage of current amount:
We solve this using a rule of three.
The original amount(94 cities), was 100% = 1.
The current amount(530 cities) is x. So
94 cities - 1
530 cities - x
94x = 530
x = 530/94
x = 5.64
5.64 = 564% of the original amount
What was the percent increase?
The current amount is 564%
The original amount is 100%
564 - 100 = 464
The percent increase was of 464%.
The owner of a senior living facility examines data on the age of the residents at the facility. She finds that the distribution of ages of residents is approximately normal with a mean of 73.5 years and a standard deviation of 6.5 years. Which interval below estimates the middle 99.7% of ages of residents living at the facility?
a. (52,95)
b. (54,93)
c. (60.5, 86,5)
d. (67,80)
Answers
The interval of the data if, The mean of 73.5 years and the standard deviation of 6.5 years, is (67,80) so, option D is correct.
What is mean?Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Given:
The mean of 73.5 years and the standard deviation of 6.5 years,
the middle 99.7% of ages of residents living at the facility,
Calculate the interval as shown below,
The coordinates of x in the interval = Mean - Standard deviation
The coordinates of x in the interval = 73.5 - 6.5
The coordinates of x in the interval = 67
The coordinates of y in the interval = Mean + Standard deviation
The coordinates of y in the interval = 73.5 + 6.5
The coordinates of y in the interval = 80
Thus, the interval will be (67, 80).
To know more about mean:
https://brainly.com/question/2810871
#SPJ5
Five times the sum of 8u and eight gives one hundred sixty
Answers
Answer:
u=3
Step-by-step explanation:
(8u + 8)5 = 160
40u + 40 = 160
40u = 120
u = 3
A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling. (a) Choose the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line. H0: - Select your answer - Ha: - Select your answer - (b) Comment on the conclusion and the decision when H0 cannot be rejected. The input in the box below will not be graded, but may be reviewed and considered by your instructor. (c) Comment on the conclusion and the decision when H0 can
Answers
Answer:
See explanation below
Step-by-step explanation:
Given a mean of 32. The claim here is that the mean is 32.
Therefore, the null hypothesis and alternative hypothesis, would be:
H0 : u = 32
Ha: u ≠ 32
b) When we fail to reject null hypothesis, H0. This means that the mean weight, u = 32
Conclusion: There is not enough evidence to conclude that there is overfilling or underfilling.
c) When null hypothesis, H0 is rejected. This means the mean weight, u ≠ 32.
Conclusion: There is enough evidence to conclude that overfilling or underfilling exists
The null hypothesis in the sampling is u = 32 and the alternative is that u isn't equal to 32.
How is the null hypothesis depicted?It should be noted that based on the information, when the null hypothesis is rejected, it implies that the weight is 32.
Also, there's no enough evidence to conclude that there's either overfilling or underfilling. When the null hypothesis is rejected, it means that the mean weight is not equal to 32.
Learn more about sampling on:
https://brainly.com/question/17831271
An engineering school reports that 52% of its students are male (M), 33% of its students are between the ages of 18 and 20 (A), and that 27% are both male and between the ages of 18 and 20. What is the probability of a random student being chosen who is a female and is not between the ages of 18 and 20?
Answers
Answer:
42%
Step-by-step explanation:
Given: P(M) = 0.52, P(A) = 0.33, and P(M and A) = 0.27.
Find: P(not M and not A).
P(not M and not A) = 1 − P(M or A)
P(not M and not A) = 1 − (P(M) + P(A) − P(M and A))
P(not M and not A) = 1 − (0.52 + 0.33 − 0.27)
P(not M and not A) = 1 − 0.58
P(not M and not A) = 0.42
Treating these probabilities as Venn probabilities, it is found that there is a 0.42 = 42% probability of a random student being chosen who is a female and is not between the ages of 18 and 20.
-------------------------
The events are:
Event A: Female.Event B: Not between the ages of 18 and 20.-------------------------
52% of the students are male, thus, 48% are female, and [tex]P(A) = 0.48[/tex].33% are between the ages of 18 and 20, thus, 67% are not between these ages, which means that [tex]P(B) = 0.67[/tex]27% are both male and between these ages, which means that 73% are either female or not between these ages, thus [tex]P(A \cup B) = 0.73[/tex].-------------------------
The probability of a random student being chosen who is a female and is not between the ages of 18 and 20 is given by:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
Inserting the probabilities we found:
[tex]P(A \cap B) = 0.48 + 0.67 - 0.73 = 0.42[/tex]
0.42 = 42% probability of a random student being chosen who is a female and is not between the ages of 18 and 20.
A similar problem is given at https://brainly.com/question/21421475
2. A 175g sample of radioactive kryptonite-344 has a half-life of 122 days.
a) Write the exponential equation that gives the amount of kryptonite that remains after t days.
Write equation in the form M(t)= ab* where x=
elapsed time
half-life time
Answers
Answer:
[tex]M(t) = 175(0.9943)^{t}[/tex]
Step-by-step explanation:
The amount of kryptonite-344 after t days is given by the following equation:
[tex]M(t) = ab^{t}[/tex]
In which a is the initial amount.
175g sample:
This means that [tex]a = 175[/tex]
So
[tex]M(t) = 175b^{t}[/tex]
Half-life of 122 days.
This means that [tex]M(122) = 0.5*175 = 87.5[/tex]
So
[tex]M(t) = 175b^{t}[/tex]
[tex]87.5 = 175b^{122}[/tex]
[tex]b^{122} = 0.5[/tex]
[tex]\sqrt[122]{b^{122}} = \sqrt[122]{0.5}[/tex]
[tex]b = 0.9943[/tex]
So
[tex]M(t) = 175(0.9943)^{t}[/tex]
Sophie Ruth is eating a 50-gram chocolate bar which contains 30 percent cocoa.
How many grams of cocoa are in the chocolate bar?
grams
Answers
hope it helps :] !!!!!!
Answer:
15 grams hope this helps
Hal has 24 video games 6 if his games are sports related and the rest are role playing games which ratio represent the number of his role playing games
Answers
Answer:
It would be 18;24 or simplified it would be 3;4
Step-by-step explanation:
24-6=18 so there are 18 role playing games. So the ratio could be 18;24 but if it needs to be simplified you can divide both numbers by 6. 18/6=3 and 24/6=4
An account with a $250 balance accrues 2% annually.
Answers
Students are designing a new town as part of a social studies project on urban planning. ey want to place the town’s high school at point A and the middle school at point B. they also plan to build roads that run directly from point A to the mall and from point B to the mall. the average cost to build a road in this area is $550,000 per mile. a. Find the measure of each acute angle of the right triangle shown. b. Find the length of the hypotenuse. Also nd the length of each of the three congruent segments forming the hypotenuse.
Answers
Answer:
The downtown angle measures about 22.62° and the town pool angle measures about 67.38°.
The hypotenuse measures 13 miles. Each third measures 4 1/3 miles.
Step-by-step explanation:
Use trigonometric ratios to solve this problem.
a. Find the measure of each acute angle of the right triangle shown.
Let's start with the acute angle that's marked near downtown. We can use the trigonometric ratio tangent to find the measure of this angle. (Remember, tangent = opposite/adjacent!)
We can divide the opposite side from the angle by the adjacent side to find the tangent:
5/12
= 0.4166666...
Now, we do the inverse tangent to find the measure of the angle:
≈ 22.62°
Now, we can find the angle near the town pool. This time, we can use tangent again, but the 12 mi side is the opposite and the 5 mi side is the adjacent:
12/5
= 2.4
Now, calculate the inverse tangent:
≈ 67.38°
b. Find the length of the hypotenuse. Also find the length of each of the three congruent segments forming the hypotenuse.
We can use the Pythagorean theorem to find the length of the hypotenuse. Remember, given legs a and b and hypotenuse c, the Pythagorean theorem states:
a² + b² = c²
Plug the values in this triangle into this equation:
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c
The hypotenuse measures 13 miles.
Now, we find the length of the three congruent segments that form the hypotenuse. (to be honest, I'm not sure that there are three congruent segments, but oh well, I'll just go with what it says there).
Since all the segments are the same length, we can just divide 13 by 3 to find the length of each of them:
13/3 = 4 1/3.
Each of the segments measures 4 1/3 miles.
Simplify: 19w5+ (-3075)
Enter the original expression if it cannot be
simplified.
Enter the correct answer.
ODA
DONE
Answers
The temperature at noon was 10 degrees. For the next 3 hours it dropped at a rate of 3 degrees an hour. Express this change in temperature as an integer.
Answers
Answer:
Change in temperature = -9 degrees
Step-by-step explanation:
Given
[tex]Start Temperature = 10 deg[/tex]
[tex]Change = 3 deg/hr[/tex]
[tex]Time= 3hr[/tex]
Required
Change in temperature;
First, the total change in 3 hours has to be solved for. This is done as follows:
[tex]Total Change = Change* Time[/tex]
[tex]Total Change = 3 deg/hr * 3 hr[/tex]
[tex]Total Change = 9 deg[/tex]
From the question, we understand that the temperature dropped.
So, we can conclude that the temperature changed by -9 degrees;
This means that at the end of the third hour is temperature is 1 degrees
A soft drink machine outputs a mean of 24 ounces per cup. The machine's output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 21 and 28 ounces? Round your answer to four decimal places.
Answers
Answer:
[tex]P(21<X<28)=P(\frac{21-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{28-\mu}{\sigma})=P(\frac{21-24}{3}<Z<\frac{28-24}{3})=P(-1<z<1.33)[/tex]
And we can find the probability with this difference
[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)[/tex]
And using the normal standard distribution or excel we got:
[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)=0.908-0.159=0.749[/tex]
Step-by-step explanation:
Let X the random variable that represent the soft drink machine outputs of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(24,3)[/tex]
Where [tex]\mu=24[/tex] and [tex]\sigma=3[/tex]
We want to find this probability:
[tex]P(21<X<28)[/tex]
The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(21<X<28)=P(\frac{21-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{28-\mu}{\sigma})=P(\frac{21-24}{3}<Z<\frac{28-24}{3})=P(-1<z<1.33)[/tex]
And we can find the probability with this difference
[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)[/tex]
And using the normal standard distribution or excel we got:
[tex]P(-1<z<1.33)=P(z<1.33)-P(z<-1)=0.908-0.159=0.749[/tex]
The table shows input and output values of the function y = x2 + 12x – 2. What is an approximate solution of the equation x2 + 12x – 2 = 0?
Answers
Answer:
The solutions for the equations are x = 0.1644 and x = -12.1644
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]x^{2} + 12x - 2 = 0[/tex]
So
[tex]a = 1, b = 12, c = -2[/tex]
[tex]\bigtriangleup = 12^{2} - 4*1*(-2) = 152[/tex]
[tex]x_{1} = \frac{-12 + \sqrt{152}}{2} = 0.1644[/tex]
[tex]x_{2} = \frac{-12 - \sqrt{152}}{2} = -12.1644[/tex]
The solutions for the equations are x = 0.1644 and x = -12.1644
A man claims that his lot is triangular, with one side 450 m long and the adjacent side 200 m long. The
angle opposite one side is 28º. Determine the other side length of this lot to the nearest metre.
Answers
Given information:
Side a = 450 m (opposite angle A)Side b = 200 m (opposite angle B)Angle A = 28°We can use the Law of Sines to find angle B:
[tex]$\frac{a}{\sin{A}} = \frac{b}{\sin{B}}[/tex]Substitute the given values:
[tex]$\frac{450}{\sin{28^\circ}} = \frac{200}{\sin{B}}[/tex]Now, solve for angle B:
[tex]$\sin{B} = \frac{200 \times \sin{28^\circ}}{450}[/tex][tex]$\sin{B} \approx 0.208654[/tex][tex]$B \approx \arcsin{0.208654} \approx 12.0435^\circ[/tex]Now that we have angle B, we can find angle C using the fact that the sum of the interior angles in a triangle is always 180°:
Angle C = 180° - 28° - 12.0435° Angle C = 139.9565°Now, we can use the Law of Sines again to find the length of the other side (side c) opposite angle C:
[tex]$\frac{a}{\sin{A}} = \frac{c}{\sin{C}}[/tex]Substitute the given values:
[tex]$\frac{450}{\sin{28^\circ}} = \frac{c}{\sin{139.9565^\circ}}[/tex]Now, solve for side c:
[tex]$c = \frac{450 \times \sin{139.9565^\circ}}{\sin{28^\circ}}[/tex][tex]$c \approx 616.685[/tex]To the nearest meter, the other side length of the triangular lot is approximately 617 m. But, since there is not an option for the answer, the closest option is C. 616 m.
________________________________________________________
Full QuestionAnswer:
289 m or 617 m
Step-by-step explanation:
You want the third side length of a triangle with side lengths 450 m and 200 m, with an angle of 28°.
Solution 1The man's claim does not say which side the given angle is opposite. There are two possibilities. (1) It is opposite the unknown side; (2) it is opposite the side of length 450 m. (No triangle is possible having an angle of 28° opposite the shorter given side.)
If the angle is opposite the unknown side, the law of cosines can be used to find the third side length:
c² = a² + b² - 2ab·cos(C)
c² = 450² +200² -2·450·200·cos(28°) ≈ 83569.43
c ≈ √83569.43 ≈ 289 . . . . meters
The other side length could be 289 meters.
Solution 2The third side could also be figured using the law of sines.
a/sin(A) = b/sin(B) = c/sin(C)
450/sin(28°) = 200/sin(B)
B = arcsin(200/450·sin(28°)) ≈ 12.043°
Then angle C is ...
C = 180° -28° -12.043° = 139.957°
and side 'c' is ...
c = 450·sin(139.957°)/sin(28°) ≈ 617 . . . . meters
The other side length could be 617 meters.
__
Additional comment
The problem tells us "one side" is 450 m, and it tells us the angle opposite "one side" is 28°. If both of the descriptors "one side" are referring to the same side, then Solution 2 is the intended one.
The description can be written in a less ambiguous way. As is, we are not sure that the second use of "one side" is referring to any side in particular. Hence the two possibilities.
<95141404393>
