Answer:
8 pieces
Step-by-step explanation:
Take 6 yds and divide by the length of each piece
6 ÷ 3/4
Copy dot flip
6 * 4/3
24/3
8
We can get 8 peices
Angle θ is in standard position and ( 4 , 4 ) is a point on the terminal side of θ. What is the exact value of sec θ sec 0 in simplest form with a rational denominator?
Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Angle θ is in standard position and (4,4) is a point on the terminal side of θ.
[tex]\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\$Using Pythagoras Theorem\\Hypotenuse^2=$Opposite^2$+Adjacent^2\\$Hypotenuse^2=4^2+4^2\\$Hypotenuse^2$=32\\Hypotenuse=\sqrt{32}=4\sqrt{2}[/tex]
Now, secant is the inverse of cosine.
Therefore:
[tex]\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}[/tex]
kojo had 1800 bags of rice in stock for sale. in January, he sold 2/3 of it. In February, he sold 3/4 of what was left.
a. what fraction of the stock of rice did he sell
(a) in February?
(b) in January and February ?
b. How many bags of rice were left unsold, by the end of February?
Answer:
Kojo had 1800 bags of rice in stock for sale.
In January, he sold 2/3 of it.
=> Number of bag he sold in January: 1800 x 2/3 = 1200
=> The number of bags of rice left: 1800 - 1200 = 600
In February, he sold 3/4 of what was left.
=> Number of bag he sold in February: 600 x 3/4 =450
=> Total number of bags he sold in January and February:
1200 + 450 = 1650
=> The number of bags of rice left at the end of February: 600 - 450 = 150
Hope this helps!
:)
Find the sum of the series 0.1+0.05+0.025+… and also find the 11 term of seq 0.1,0.05,0.025,…
A particular state's license plates have 7 characters. Each character can be a capital letter, or a digit except for 0. How many license plates are there in which no two adjacent characters are the same
Answer:
N = 35 × 34^6
N = 54,068,154,560
Step-by-step explanation:
Given;
The license plate have 7 characters.
Each character can be a capital letter, or a digit except for 0.
There are 26 capital letters
And there are 9 digits excluding 0
The total number of possible entries in each character is;
26+9 = 35
The number of license plates in which no two adjacent characters are the same are;
For no two adjacent characters of the license plate not to be the same that is no two characters that follow each other can be the same, the number of possible entries in the adjacent characters apart from the first character would be reduced by one.
N = 35 × 34 ×34×34×34×34×34
N = 35 × 34^6
N = 54,068,154,560
Therefore, there are 54,068,154,560 possible license plates
Multiply. Write your answer in simplest form. 4/9 x 2/3
Answer:
8/27
Step-by-step explanation:
4/9 * 2/3
Multiply the numerators
4*2 = 8
Multiply the denominators
9*3 = 27
Put the numerator over the denominator
8/27
This is in simplest form
Which triangle is congruence postulate can be used to prove that
Answer:
HL
Step-by-step explanation:
Both triangles are right triangles as shown by the right angle marks in the figure.
Two corresponding legs are congruent as shown.
The diagonal is congruent to itself, and it is the hypotenuse of both right triangles.
Answer: HL
Can someone simplify
Answer:
Option (2). [tex]2\frac{1}{4}[/tex]
Step-by-step explanation:
The given expression is [[tex]-5\frac{1}{4}-(-7\frac{1}{2})[/tex]]
We can rewrite the fractions as,
[tex]-5\frac{1}{4}[/tex] = [tex]-(5+\frac{1}{4})[/tex]
[tex]-7\frac{1}{2}=-(7+\frac{1}{2})[/tex]
Now we will substitute the fractions in the expression,
[tex][-(5+\frac{1}{4})]-[-(7+\frac{1}{2})][/tex]
= [tex]-(5+\frac{1}{4})+(7+\frac{1}{2})[/tex]
= (-5 + 7) + [tex](-\frac{1}{4}+\frac{1}{2})[/tex]
= 2 + [tex]\frac{2-1}{4}[/tex]
= 2 + [tex]\frac{1}{4}[/tex]
= [tex]2\frac{1}{4}[/tex]
Therefore, Option (2). will be the answer.
A light bulb is programmed to turn on when the temperature in a terrarium is 72 F or cooler
Question:
Write an inequality to represent the situation.
A light bulb is programmed to turn on
when the temperature in a terrarium is
72°F or cooler.
Answer:
t ≤ 72⁰F
Step-by-step Explanation:
Given this situation, we can write an inequality to represent the temperature in a terrarium at which the light bulb is programmed to turn on as follows:
t ≤ 72⁰F
where, t is the temperature of the terrarium, the sign "≤" implies that at a temperature of 72⁰F and below (i.e. colder would mean temperature below 72⁰F), the light bulb should turn on, as programmed.
Invariably, the inequality "t ≤ 72⁰F" mean the light bulb would turn on if the temperature of the terrarium is less than or equals 72⁰F.
Listed below are the gross amounts (in millions of dollars) earned in box office receipts for a recent movie. The amounts are listed in order for the first 14 days of the movies release. Find the range, variance, and standard deviation of the data set. If you invested in this movie, what characteristic of the data set would you care about most, and is it a measure of center or variation? 60 58 55 53 47 45 44 43 25 25 20 18 7 5
Answer:
[tex] Range = 60-5=55[/tex]
In order to find the variance and deviation we need to find the mean with this formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \bar X =36.07 [/tex]
Now we can find the variance with the following formula:
[tex]s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
And replacing we got:
[tex] s^2=357.610[/tex]
And the standard deviation would be:
[tex] s = \sqrt{357.610}= 18.911[/tex]
For this case since the range observed is large is better to use a measure of variation in order to check the spread of the values and take a decision useful
Step-by-step explanation:
For this case we have the following dataset:
60 58 55 53 47 45 44 43 25 25 20 18 7 5
We can find the range with this formula:
[tex] Range = Max-Min[/tex]
And replacing we got:
[tex] Range = 60-5=55[/tex]
In order to find the variance and deviation we need to find the mean with this formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex] \bar X =36.07 [/tex]
Now we can find the variance with the following formula:
[tex]s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
And replacing we got:
[tex] s^2=357.610[/tex]
And the standard deviation would be:
[tex] s = \sqrt{357.610}= 18.911[/tex]
For this case since the range observed is large is better to use a measure of variation in order to check the spread of the values and take a decision useful
This equation shows how the total cost of visiting the art museum as a member is related to the number of visits c= v+7. The variable v represents the number of visits to the art museum and the variable c represents the total cost of those visits. For a member of the art museum, what is the total cost of 10 visits?
Answer:
17
Step-by-step explanation:
the amount of visits given by the problem is:
[tex]v=10[/tex]
and we have that the equation that relates the number of visits with the total cost is:
[tex]c=v+7[/tex]
where [tex]c[/tex] is the total cost for [tex]v[/tex] number of visits.
We plug into this equation the known value of visitors:
[tex]c=10+7[/tex]
and we solve this expression:
[tex]c=17[/tex]
the total cost for 10 visitors is 17.
The campus bookstore knows from the past several semesters that a certain elementary statistics book has a demand that is approximated by a normal distribution with a mean of 250 and a standard deviation of 40. They buy these books for $105 each and sell them to unsuspecting undergraduates at $222 each. All demand for this book is realized by the middle of the semester, at which point the bookstore bundles them up and sells them to a vendor in another country for $40 each. What is the marginal profit for a single elementary statistics book
Answer:
$117
Step-by-step explanation:
Given that:
They buy these books for $105 each and sell them to unsuspecting undergraduates at $222 each
Marginal Profit = Marginal Revenue – Marginal Cost.
Marginal Profit = $222 - $105
Marginal Profit = $117
the marginal profit for a single elementary statistics book $117
For the remaining unsold books in the middle of the semester he bundles them up and sells to vendor in another country for $40 each for which he suffers a marginal loss of $105 - $40 = $65 each
You are a state inspector for the Division of Weights and Measures. Your responsibility is to be sure the net weight found on all containers is correctly reflected on the label (note: the label is a claim). You are inspecting ABC Company who makes dry dog food in boxes and bags. The boxes you are checking indicate a net mean weight of 32 ounces. You check a sample of 200 boxes and found the average content to be 31.7 ounces. The standard deviation allowed for this type of product is 2.2 ounces. Can you conclude at a .02 level of significance that the boxes of dog food are being under filled
Answer:
No. There is not enough evidence to support the claim that the boxes of dog food are being under filled (P-vaue=0.027).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the boxes of dog food are being under filled.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=32\\\\H_a:\mu< 32[/tex]
The significance level is 0.02.
The sample has a size n=200.
The sample mean is M=31.7.
The standard deviation of the population is known and has a value of σ=2.2.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{2.2}{\sqrt{200}}=0.156[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{31.7-32}{0.156}=\dfrac{-0.3}{0.156}=-1.928[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.928)=0.027[/tex]
As the P-value (0.027) is bigger than the significance level (0.02), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the boxes of dog food are being under filled.
What is the equation of a line , in general form, that passes through points (-1,2) and (5,2)
Answer:
y-2=0
Step-by-step explanation:
In y=mx+b
m=(y2-y1)/(x2-x1) [2]
Or another way of thinking about it is rise over run.
define point (-1,2) as x1,y1
define point (5,2) as x2,y2
substitute into formula [2]
m=(2-2)/(5-(-1))
We know that 2-2=0 therefore the slope (m) is 0
y=0x+b
Or simply
y=b
to solve for b we substitute into the formula any of the points
2=b for y1
or 2=b for y2
b=2
therefore y=2
to convert it into general form make the equation equal 0
y-2=0
Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of 40 lb and the terminal point of the vector is point P(1, 1, 0). The second force has a magnitude of 60 lb and the terminal point of its vector is point Q(0, 1, 1). Let F be the resultant force of forces F1 and F2.
(a) Find the magnitude (in pounds) of F. (Round the answer to one decimal place.)
(b) Find the direction of F.
Answer:
Step-by-step explanation:
The two force F1 and F2 are represented by vectors with initial points that are at the origin.
the terminal point of the vector is point P(1, 1, 0)
Therefore, the direction of the vector force is
[tex]v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j[/tex]
The unit vector in the direction of force will be
[tex]\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}[/tex]
The magnitude of the force is 40lb, so the force will be
[tex]F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)[/tex]
The terminal point of its vector is point Q(0, 1, 1)
Therefore, the direction of the vector force is
[tex]v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k[/tex]
[tex]\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}[/tex]
The magnitude of the force is 60lb, so the force will be
[tex]F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)[/tex]
The resultant of the two forces is
[tex]F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k[/tex]
The magnitude force will be
[tex]|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68[/tex]
to (1 decimal place)=55.7lb
b) The direction angle of force F
The angle formed by F and x axis
[tex]\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469[/tex]
The angle formed by F and y axis
[tex]\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=[/tex]
The angle formed by F and z axis
[tex]\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359[/tex]
If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem. (x + 2)(x + 60) (x – 2)(x – 60) (x – 10)(x + 2)(x + 6) (x + 10)(x – 2)(x – 6)
Answer:
Step-by-step explanation:
A
All the factors of the function f (x) = x³ - 2x² - 68x - 120 are,
⇒ (x - 10) (x + 6) (x + 2)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = x³ - 2x² - 68x - 120
Here, We have;
⇒ f (-2) = 0
Hence, This function have a factor (x + 2).
Now, After divide the function f (x) = x³ - 2x² - 68x - 120 by (x + 2), we get;
⇒ ( x³ - 2x² - 68x - 120 ) ÷ (x + 2)
⇒ x² - 4x - 60
⇒ (x - 10) (x + 6)
Hence, All the factors of the function f (x) = x³ - 2x² - 68x - 120 are,
⇒ (x - 10) (x + 6) (x + 2)
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
The complete question is this,
If f(–2) = 0, what are all the factors of the function f (x) = x cubed minus 2 x squared minus 68 x minus 120? Use the Remainder Theorem. (x + 2)(x + 60) (x – 2)(x – 60) (x – 10)(x + 2)(x + 6) (x + 10)(x – 2)(x – 6)
2.2.17
Given the function H(v) = 10v +9, find each of the following.
H(3) =
Answer:
H(3)=39
Step-by-step explanation:
H(3) =10 (3) + 9
=30 +9
=39
Hope this helps...
A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected.
Question:
For the following exercise, determine the range (possible values) of the random variable. A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected.
Answer:
Possible values are all integers from 1 to 491.
{1,2,...........491}
Step-by-step explanation:
Given:
Total number of machined parts = 500
Number that do not conform to customers requirements = 10
Number that conforms to customers requirements = 500 - 10 = 490
Since, parts are selected successively, without replacement, until a nonconforming part is obtained, the range of the random variable (number of parts selected) here will be all integers from 1 to 491 ie {1,2,...........,491}.
Here, we have a total of 490 conforming parts, and 10 non conforming parts, there must be a non-conforming part among 491 selections, considering the fact that total number of parts are 500
There will be one non-confirming part in the 491 selections and this can be determined by using the given data.
Given :
A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained.Given that the total number of parts is 500 that contains 10 that do not conform to customer requirements. So, the total number of parts that conform to customer requirements is (500 - 10) 490.
It is also given that parts are selected successively, without replacement, until a nonconforming part is obtained so, the range of the random variables is [1,491]
So, there will be one non-confirming part in the 491 selections.
For more information, refer to the link given below:
https://brainly.com/question/23044118
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.7-in and a standard deviation of 1.1-in.In what range would you expect to find the middle 50% of most head breadths
Answer:
[tex] 6.7 -0.674 *1.1 =5.96[/tex]
[tex] 6.7 +0.674 *1.1 =7.44[/tex]
Step-by-step explanation:
Let X the random variable that represent the head breadths of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(6.7,1.1)[/tex]
Where [tex]\mu=6.7[/tex] and [tex]\sigma=1.1[/tex]
We want the range of the middle 50% values on the distribution. Since the normal distribution is symmetrical we know that in the tails we need to have the other 50% and on each tail 25% by symmetry.
We can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The critical values that accumulates 0.25 of the area on each tail we got:
[tex] z_{crit}= \pm 0.674[/tex]
And if we solve x from the z score we got:
[tex] x = \mu \pm z \sigma[/tex]
And replacing we got:
[tex] 6.7 -0.674 *1.1 =5.96[/tex]
[tex] 6.7 +0.674 *1.1 =7.44[/tex]
Which line is parallel to the line that passes through the points (1, 7) and (-3, 4)? A. B. C. D.
Answer:
hope this helps you
How many arrivals were much more delayed than others (i.e., positive outliers with z-score of time difference > 3)? (e) How many flights arrived much earlier than scheduled compared to others (i.e., negative outliers with z-score of time difference < -3)?
Answer:
d) 0.135% of total arrivals were much more delayed than others.
e) 0.135% of total flights arrived much earlier than scheduled compared to others.
Step-by-step explanation:
With the question not totally complete, we will solve the available parts as well as possible.
d) How many arrivals were much more delayed than others (i.e., positive outliers with z-score of time difference > 3)?
P(z > 3)
Using the normal distribution table
P(z > 3) = 1 - P(z ≤ 3) = 1 - 0.99865 = 0.00135 = 0.135% of total arrivals were much more delayed than others.
e) How many flights arrived much earlier than scheduled compared to others (i.e., negative outliers with z-score of time difference < -3)?
P(z < -3)
Using the normal distribution table
P(z < -3) = 0.00135 = 0.135% of total flights arrived much earlier than scheduled compared to others.
Hope this Helps!!!
The ratio of the angles of a triangle is 3:8:4. What is the size of the largest angle?
Answer: 96°
Step-by-step explanation:
Sum of angles of a triangle = 180°
3 + 8 + 4 = 15
The biggest angle is 8/15 * 180 = 96°
The U.S. Department of Transportation provides the number of miles that residents of the75 largest metropolitan areas travel per day in a car. Suppose that for a simple randomsample of 50 Buffalo residents the mean is 22.5 miles a day and the standard deviation is 8.4 miles a day, and for an independent simple random sample of 40 Boston residents themean is 18.6 miles a day and the standard deviation is 7.4 miles a day.a. What is the point estimate of the difference between the mean number of miles thatBuffalo residents travel per day and the mean number of miles that Boston residentstravel per day?b. What is the 95% confidence interval for the difference between the two populationmeans?
Answer:
a. The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residentstravel per day is 88
b. The 95% confidence interval for the difference between the two population means is (0.58171,7.21829)
Step-by-step explanation:
a. According to the given data we have the following:
Buffalo residents mean=22.5
Standard deviation=8.4
n=50
Boston residents mean=18.6
Standard deviation=7.4
n=40
Hence, the point estimate is the difference of the means=22.5-18.6=3.9
The standard error=√((s1∧2/n1)+((s2∧2/n2))=√((8.4∧2/50)+(7.4∧2/40))=1.67
Therefore, the difference of miles=n1+n2-2=50+40-2=88
The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residentstravel per day is 88.
b. The critical value of t at 95% confidence level and DoF=88 is 1.987
The interval:(x1-x2)+ (critical value* std error)
=3.9-(1.987*1.67),3.9+(1.987*1.67)
Difference between mean=(0.58171,7.21829)
The 95% confidence interval for the difference between the two population means is (0.58171,7.21829)
One hundred ople were surveyed
about their favorite flower. Of these,
20 people say their favorite flower is
the tulip. What fraction of the people
say their favorite flower is NOT the
tulip? Explain your answer.
Answer:
4/5
Step-by-step explanation:
Since there are 100 people, and 20 people say their favorite flower was the tulip, we can make a fraction of the people who like tulip.
20/100=2/10=1/5
There are the people who's favorite flower is tulip. However, the question asks what fraction of the people say their favorite flower is NOT tulip.
Take 1 as the entire people surveyed, and subtract:
1-1/5= 4/5
Therefore 4/5 of the people surveyed says their favorite flower is NOT tulip.
Compare 2/6 and 5/8 using benchmark number. Which number can you use to compare these fraction
Answer:
5/8 is about 1/2. 2/6 is about 0.
Step-by-step explanation: 2/6 is about 0 because 2 is close to 0. If the numerator is close to 0 and the denominator is not close to 0 then the benchmark is going to be 0. If the numerator is about half of the denominator then the benchmark is going to be 1/2. If the numerator and denominator is close to each other than the benchmark is going to be 1.
SOLVE THIS SUPER IMPORTANT EQUATION!!! Please
Answer:
a
Step-by-step explanation:
the slope is negative bec it's going from the top left to the bottom right corner(if I was negative the line would be going from the bottom left to the too right) then your y-intercept( the point that hits y when x is zero) is 120
Answer:
The correct answer would be A, y = -4/3x + 120
Step-by-step explanation:
Let us start with the y-intercept, the y-intercept is 120. The graph shows that the y-intercept is positive, but the slope is negative. B, C, D, and E are not correct due to the mis use of signs, a wrong slope, and a wrong y-intercept.
if u want to prove me wrong, then go ahead.
A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t)=a(b)t.
Answer:
[tex] f(t) = 6000 (\frac{1}{2})^t^/^3 [/tex]
Step-by-step explanation:
Let's take the equation:
[tex] y = y_0 e^-^k^t[/tex]
Given the initial population of bacteria = 6000,
[tex] y = 6000e^-^k^t[/tex]
Population of bacteria after 3 hours is 3000.
y(3) = 3000
Thus,
[tex] 6000e^-^k^3 = 3000[/tex]
[tex] e^-^k^3 = \frac{3000}{6000}[/tex]
[tex] e^-^k^3 = \frac{1}{2}[/tex]
[tex] (e^-^k)^3 = \frac{1}{2}[/tex]
[tex] e^-^k= (\frac{1}{2})^1^/^3[/tex]
Let's substitute [tex] (\frac{1}{2})^1^/^3 [/tex] for [tex] e^-^k[/tex] in [tex] y = 6000e^-^k^t [/tex]
Therefore, we have:
[tex] 6000e^-^k^t [/tex]
[tex] = 6000 [(\frac{1}{2}) ^1^/^3]^t[/tex]
[tex] = 6000 [\frac{1}{2}] ^t^/^3 [/tex]
A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 21 newly graduated law students. Their scores give a sample standard deviation of 68 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.
(a) What is the level of significance?
(b) Find the value of the chi-square statistic for the sample. (Use 2 decimal places.) What are the degrees of freedom?
Answer:
Step-by-step explanation:
From the information given :
The null hypothesis [tex]H_o : \sigma = 60[/tex]
The alternative hypothesis [tex]Ha : \sigma \neq 60[/tex]
Given that:
the sample size n = 21
sample standard deviation s = 68
population standard deviation σ = 60
a) The level of significance [tex]\alpha =0.01[/tex]
b) The chi-square statistics can be calculated as:
[tex]\bar X = \dfrac{(n-1)s^2}{\sigma^2}[/tex]
[tex]\bar X = \dfrac{(21-1)68^2}{60^2}[/tex]
[tex]\bar X = \dfrac{(20)4624}{3600}[/tex]
[tex]\bar X = 25.69[/tex]
The degree of freedom is :
= n - 1
= 21 - 1
= 20
Suppose that, in a hypothesis test, the null hypothesis is in fact true. a. Is it possible to make a Type I error? Explain your answer. b. Is it possible to make a Type II error? Explain your answer.
Answer:
a. Yes
b. No
Step-by-step explanation:
In a hypothesis test, the null hypothesis is in fact true.
a. Is it possible to make a Type I error?
Yes, it is possible to make a type I error because a type I error typically occurs if the null is rejected when it is actually true.
b. Is it possible to make a Type II error?
It is not possible to make a type II error because the condition for a type II error is that the null is in fact not true but we fail to reject it.
In recent commercials Toyota claimed that 80% of its vehicles sold in the past 20 years are still on the road. You work for an agency that wants to test this claim. You are willing to accept Toyota's claim unless there is statistically significant evidence that it is false. You have a limited budget, but you want to get the most accurate results you can. Describe, from beginning to end, how you would run your study. Use as many concepts you learned in this course as possible to get maximum credit. HTML EditorKeyboard Shortcuts
Answer:
Step-by-step explanation:
We have to perform one sample proportion test. To do so we have to proceed through following steps.
(1) We have to collect data about vehicle sales in last 20 years.
(2) Using random number table or random number generator or otherwise we have to select sample of vehicles from the list of sale. In this step, we have to keep an eye on the fact that sample is to be selected from all years (all of 20). Using stratified random sampling by dividing vehicles sold over different years is an effective way to do so. That means, we may divide vehicles sold into 20 homogeneous strata over 20 years and select sample from each strata.
(3) After selecting sample of vehicles we have to communicate to corresponding vehicle owners to gather information about that particular vehicle.
(4) We have to note number of vehicles which are still on the road.
Suppose, we have selected n vehicles as sample and after communicating we found that \tiny r of those are still on the road.
We have to test for null hypothesis [tex]H_0:p=0.80[/tex]
against the alternative hypothesis [tex]H_1 \neq 0.80[/tex]
Our test statistic is given
[tex]z=\frac{\hat p - p_0}{\sqrt{p_0(1-p_0)/n} }[/tex]
here,
[tex]\hat p =\frac{r}{n}[/tex]
[tex]p_0 =0.80[/tex]
[tex]z=\frac{r/n-0.80\sqrt{n} }{0.40} \\\\=2.5(\frac{r}{n} -0.8)\sqrt{n}[/tex]
We then calculate corresponding p-value.
We reject our null hypothesis if [tex]\text{p-value}<\alpha[/tex] , level of significance.
According to our obtained p-value and level of significance we proceed to certain conclusion.
What’s the correct answer for this?
Answer:
first option
Step-by-step explanation:
Given 2 secants to a circle from an external point, then
The product of the external part and the whole of one secant is equal to the external part and the whole of the other secant, that is
PQ(RP) = PS(TP)