The angular speed of the wheel at its point of contact on the surface is 8 radians per second.
Given that:
A wheel is rolling on a horizontal surface.
The radius of the wheel, r = 0.5 m
The velocity of the axle of the wheel is constant.
Here, the linear velocity can be found by taking the ratio of the distance to the time taken to cover that distance.
So, the linear speed is:
[tex]\text{v}=\frac{20}{5}[/tex]
[tex]=4 \text{ m/s}[/tex]
Now, the relationship between the angular speed and the linear speed is:
[tex]\omega=\frac{v}{r}[/tex]
[tex]=\frac{4}{0.5}[/tex]
[tex]=8[/tex] rad/s
Hence, the angular speed is 8 radians per second.
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The angular speed of the wheel about its point of contact on the surface is 8 rad/s.
To find the angular speed of the wheel about its point of contact on the surface, we can use the relationship between linear and angular velocity.
The linear velocity of a point on the wheel is given by:
v = ω * r
Where:
v is the linear velocity
ω is the angular velocity (angular speed)
r is the radius of the wheel
In this case, we know that the wheel rolls without slipping, which means the linear velocity of the point of contact with the surface is equal to the velocity of the axle. Since the axle moves a distance of 20 m in 5 s, the linear velocity can be calculated as:
v = 20 m / 5 s = 4 m/s
Given that the radius of the wheel is 0.5 m, we can rearrange the equation to solve for ω:
ω = v / r
ω = 4 m/s / 0.5 m
ω = 8 rad/s
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The measures of the angles of the triangle are 32, 53, 95 based on the side lengths, what are the measure of each angle?
Answer:
angle measures are 32°, 53°, 95°.
Step-by-step explanation:
The problem statement asks you to report the angle measures after telling you what they are. The mention of side lengths (without any numbers for them) seems irrelevant.
"The measures of the angles of the triangle are 32, 53, 95."
HELP ME PLZZZ ITS PRECALC
Answer:
8
Step-by-step explanation:
We observe that the logarithm bases are ...
5√5 = √125 . . . . . 125 is the 2nd power of this
2√2 = √8 . . . . . . . 8 is the 2nd power of this; 64 is the 4th power of √8
If we define ...
[tex]p=\sqrt{125}\\q=\sqrt{8}[/tex]
Then our logarithms are ...
[tex]\log_{p}{p^2}=x=2\\\\\log_{q}{q^4}=y=4\\\\xy=2\cdot 4=8[/tex]
The product of x and y is 8.
Loren is flying round trip from Dallas, Texas, to Minneapolis, Minnesota. The fare for her ticket is $308. Each airport charges a $16 airport fee. There is also a tax of $12 on the fare. What is the total cost of Loren's ticket?
Answer:The total cost of Loren's ticket is $352
Step-by-step explanation:
Loren is flying round trip from Dallas, Texas, to Minneapolis, Minnesota. The total fare for her ticket is $308.
Each airport charges a $16 airport fee. This means that the total airport charges would be 16 × 2 = $32
There is also a tax of $12 on the fare.
The total cost of Loren's ticket would be
308 + 32 + 12 = $352
The total cost of Loren's round-trip ticket from Dallas to Minneapolis, including the fare, airport fees, and tax, is $352.
To find the total cost of Loren's round-trip ticket from Dallas to Minneapolis, we need to add the base fare, airport fees, and the tax.
The base fare for the ticket is $308.Each airport charges a $16 fee, and since she uses two airports, the total fee is $16 × 2 = $32.A tax of $12 is also applied to the fare.We then add these amounts together to find the total cost:
$308 (fare) + $32 (airport fees) + $12 (tax) = $352
Therefore, the total cost of Loren's ticket is $352.
Mia starts with a piece of paper 6 cm long she folds the paper into a dragon that is 2 1/2 cm long. How much longer was the original paper than the dragon
Answer: the original length was
3 1/2 cm longer than the length of the dragon
Step-by-step explanation:
The original length of the paper is
6 cm. Mia folds the 6 cm piece of into a dragon that is 2 1/2 cm long. Converting 2 1/2 cm to decimal, it be comes 2.5cm
To determine How much longer the original paper was than the dragon, we would determine difference in length between the original paper and the dragon. It would be
6 - 2.5 = 3.5 = 3 1/2 cm
Answer: The original paper is longer by the difference btw the length
6cm - 2½cm
3½cm
Step-by-step explanation:
The times to process orders at the service counter of a pharmacy are exponentially distributed with mean 1 0 minutes. If 100 customers visit the counter in a 2-day period, what is the probability that at least half of them need to wait more than 10 minutes?
Answer:
Therefore, the probability that at least half of them need to wait more than 10 minutes is 0.0031.
Step-by-step explanation:
The formula for the probability of an exponential distribution is:
P(x < b) = 1 - e^(b/3)
Using the complement rule, we can determine the probability of a customer having to wait more than 10 minutes, by:
p = P(x > 10)
= 1 - P(x < 10)
= 1 - (1 - e^(-10/10) )
= e⁻¹
= 0.3679
The z-score is the difference in sample size and the population mean, divided by the standard deviation:
z = (p' - p) / √[p(1 - p) / n]
= (0.5 - 0.3679) / √[0.3679(1 - 0.3679) / 100)]
= 2.7393
Therefore, using the probability table, you find that the corresponding probability is:
P(p' ≥ 0.5) = P(z > 2.7393)
P(p' ≥ 0.5) = 0.0031
Therefore, the probability that at least half of them need to wait more than 10 minutes is 0.0031.
Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively. How many times will they ring together at the same second in one hour excluding the one at the end?
Answer:
60 times will they ring together at the same second in one hour excluding the one at the end.
Step-by-step explanation:
Given : Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively.
To find : How many times will they ring together at the same second in one hour excluding the one at the end?
Solution :
First we find the LCM of 3, 6, 10, 12 and 15.
2 | 3 6 10 12 15
2 | 3 3 5 6 15
3 | 3 3 5 3 15
5 | 1 1 5 1 5
| 1 1 1 1 1
[tex]LCM(3, 6, 10, 12,15)=2\times 2\times 3\times 5[/tex]
[tex]LCM(3, 6, 10, 12,15)=60[/tex]
So, the bells will ring together after every 60 seconds i.e. 1 minutes.
i.e. in 1 minute they rand together 1 time.
We know, 1 hour = 60 minutes
So, in 60 minute they rang together 60 times.
Therefore, 60 times will they ring together at the same second in one hour excluding the one at the end.
Aaron wants to make a path to guide guest through the conservation area.He uses rolls of rope to make the path.He uses 3/4 of a roll of rope for 1/8. He has 4 rolls.How many more rolls does Aaron need to complete the path
Answer:
Aaron needs 2 more rolls to complete the path.
Step-by-step explanation:
Given:
Total rolls Aaron has = 4
Part of path covered by using [tex]\frac{3}{4}[/tex] of a roll = [tex]\frac{1}{8}[/tex]
So, in order to find the number of rolls required to cover the complete path is given using the unitary method.
Rolls used for [tex]\frac{1}{8}[/tex] of a path = [tex]\frac{3}{4}[/tex]
Therefore, rolls used to cover the whole path is given by dividing the rolls used for one-eighth of the path and the path covered. This gives,
[tex]=\frac{3}{4}\div \frac{1}{8}[/tex]
[tex]=\frac{3}{4}\times \frac{8}{1}[/tex]
[tex]=\frac{3\times 8}{4\times 1}[/tex]
[tex]=\frac{24}{4}[/tex]
[tex]=6\ rolls[/tex]
Now, rolls required to complete the path is 6. But Aaron has only 4 rolls.
So, he will need 6 - 4 = 2 rolls more to complete the path.
Aaron can cover 6 portions of the path with his 4 rolls. Since the path has 8 portions, he needs 2 more rolls of rope to complete the path.
Explanation:In this question, Aaron uses 3/4 of a roll for 1/8 of the path. Therefore, he will need one roll for (1/8) / (3/4) = 2/3 of the path. Now, we want to know how many rolls he needs for the complete path. The full path will be 1/(2/3) = 3/2 = 1.5 times bigger than the amount of path he can cover with one roll. Since he has four rolls to start with, he can cover 4 * 1.5 = 6 portions of the path. But to cover a full path, he would need 8 portions (as 1/8 of the path corresponds to one portion). So, he needs 8 - 6 = 2 more rolls.
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A merchant marks his wares 40% more than the real price and allows 20% discount. His profit is?a) 20%
b) 18%
c) 16%
d) 12%
e) None of these
Answer:
D) 12%
Step-by-step explanation:
The merchant marks his wares 40% more than the real price.
The merchant also allows 20% discount.
Let the real price = 100
After a 40% mark up, the price becomes
(40 /100) * 100
= 40
So we have 100 +40= 140
Discount of 20% = (20/100)* 140
= 28
The price is 140 - 28 = 112
Profit = 112 -100
= 12%
A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?(A) 0.8(80 – y)(B) 0.8 + 0.0025y(C) 80/y – 1.25(D) 80/1.25y(E) 80 – 0.25y
Answer:
(B) 0.8+0.0025y
Step-by-step explanation:
Total houses =80
First y houses was painted at the rate of x hours per week
Remaining houses was painted at 1.25x hours per week
Remaining houses= 80-y
Rate = quantity/ time
Time = quantity/ rate
Time for the first painting = y/x
Time for the second painting = 80-y/1.25x
Total time y/x + 80-y/1.25x
= 0.25y +80/1.25x
If it was being painted at the original rate
Time = 80/x
The time to paint in this scenario as a fraction of the time it will take to paint in the original rate.
(0.25y+80/1.25x) /(x/80)
=( 0.25y +80)/100
=0.0025y +0.8
Jill filled up the gas tank in her new hybrid car.Jill put 10.3 gallons of gas in her car and she has driven 473.8 miles. Determine how many miles per gallon her car achieved
Jill put 10.3 gallons of gas into her car. She drove for 473.8 miles.
So we have to find how many miles per gallon she drove.
473.8 into 10.3 = 46
To make sure= 10.3 x 46 = 473.8
So Jill drove 46 miles per gallon.
Sarah buys a new bike. The total cost of the bike including taxes is $349. She pays $100 down and then agrees to pay the balance in 6 equal payments.
Which of the following values is an appropriate representation of the amount of each of the 6 payments?
A
$58.17
B
$42
C
$41.50
D
$41
The amount of each of the 6 payments will be $41.50
Step-by-step explanation:
Given,
Cost of bike including taxes = $349
Down payment = $100
Amount left to pay = Cost of bike - Down payment
Amount left to pay = 349 - 100
Amount left to pay = $249
She agrees to pay in 6 equal payments, therefore, we will divide the total amount to pay by 6.
Amount to pay for one month = [tex]\frac{Amount\ left\ to\ pay}{No.\ of\ months}[/tex]
Amount to pay for one month = [tex]\frac{249}{6} = \$41.50[/tex]
The amount of each of the 6 payments will be $41.50
Keywords: division, subtraction
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Joe owns a coffee house and produces coffee drinks under the production function q = 5KL where q is the number of cups generated per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labor). What is the marginal product of labor?
Answer:
Marginal Product of Labour = 5K
Step-by-step explanation:
Marginal product of labor is the change in output when additional labor is added,
To calculate marginal product of labor you simply divide the change in total product by the change in labour.
Marginal product of labour (MPL) = Change in total products/ Change in labour
Here, change in labour = 5KL
Change in labour = L
MPL = 5KL/L
MPL = 5K
The marginal product of labor for Joe's coffee house, where the production function is q = 5KL, is found by differentiating q with respect to L, resulting in 5K, which indicates that each additional employee increases output by 5 times the number of coffee machines available.
Explanation:The marginal product of labor (MP) is the additional output generated by employing one more unit of labor while holding other factors of production constant. In Joe’s coffee house, where the production function is given by q = 5KL (with q as the number of cups produced per hour, K as the number of coffee machines, and L as the number of employees), the marginal product of labor can be found by differentiating the production function with respect to labor. As capital (K) is held constant, the marginal product of labor will be calculated as follows:
MP = d(q)/d(L) = d(5KL)/d(L) = 5K
This equation indicates that the marginal product of labor is 5 times the number of coffee machines in use because K is constant in the short run. Therefore, every additional employee hired will increase the output (q) by an amount equal to 5 times the number of coffee machines that Joe has in his coffee house.
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Use technology to find the P-value for the hypothesis test described below. The claim is that for 12 AM body temperatures, the mean is μ > 98.6°F. The sample size is n = 6 and the test statistic is t = 1.965.
Answer:
[tex]p_v =P(t_5>1.965)=0.0533[/tex]
We can use the following excel code to find it :"=1-T.DIST(1.965,5,TRUE) "
Step-by-step explanation:
Data given and notation
[tex]\bar X[/tex] represent the average score for the sample
[tex]s[/tex] represent the sample standard deviation
[tex]n=6[/tex] sample size
[tex]\mu_o =98.6[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to apply a one upper tailed test.
What are H0 and Ha for this study?
Null hypothesis: [tex]\mu \leq 98.6[/tex]
Alternative hypothesis :[tex]\mu > 98.6[/tex]
Compute the test statistic
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
The calculated value on this case is given t=1.965
Give the appropriate conclusion for the test
First we need to calculat ethe degrees of freedom given by:
[tex]df=n-1=6-1=5[/tex]
Since is a one side right tailed test the p value would be:
[tex]p_v =P(t_5>1.965)=0.0533[/tex]
We can use the following excel code to find it :"=1-T.DIST(1.965,5,TRUE) "
Conclusion
If we compare the p value and a significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significantly higher than 98.6 at 5% of significance.
Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?A. 93%B. 97%C. 100%D. 107%E. 120%
Answer:
A. 93%
Step-by-step explanation:
Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit.
So each children started with 0.2A, in which A is Arthur's fortune.
Alice
In the first year, she earned a profit of 50 percent. In the second year, she earned a profit of 10%. So her part is
0.2A*(1+0.5)*(1 + 0.1) = 0.33A
Bob
In the first year he earned a profit of 50 percent. In the second year, he earned a profit of 10%. So his part is
0.2A*(1+0.5)*(1 + 0.1) = 0.33A
Carol
In the first year, she earned a profit of 50 percent. In the second year, she lost 60 percent. So
0.2A*(1+0.5)*(1-0.6) = 0.12A
Dave
In the first year, he lost 40 percent. In the second, he earned a profit of 25%. So
0.2A*(1-0.4)*(1 + 0.25) = 0.15A
Errol
Lost all the money he had. So he has 0A.
What percentage of Arthur's fortune currently remains?
This is the sum of the results of all five of his children.
0.33A + 0.33A + 0.12A + 0.15A = 0.93A
So the correct answer is:
A. 93%
How many ways can a person toss a coin 13 times so that the number of tails is between 7 and 9 inclusive
Answer:
3718 ways
Step-by-step explanation:
How many ways can a person toss a coin 13 times so that the number of tails is between 7 and 9 inclusive
Probability is the likelihood for an event to occur or not
The formula for a combination is:
n choose r = n! / (r! x (n-r)!)
n=13
r=7 to 9
We are going to add up the cases for 7 through 9:
[tex]^{n } C_{r}[/tex]
[tex]^{13 } C_{7}[/tex]+[tex]^{13 } C_{8}[/tex]+[tex]^{13 } C_{9}[/tex]
[tex]\frac{n!}{r!(n-r)!}[/tex]
[tex]\frac{13!}{7!(13-7)!}[/tex]+[tex]\frac{13!}{8!(13-8)!}[/tex]+[tex]\frac{13!}{9!(13-9)!}[/tex]
1716+1287+715
3718 ways
The length of a rectangle is the sum of the width and 3. The area of the rectangle is 54 units. What is the width, in units, of the rectangle?
Answer:
Step-by-step explanation:
let width=x
length=x+3
x(x+3)=54
x²+3x-54=0
x²+9x-6x-54=0
x(x+9)-6(x+9)=0
(x+9)(x-6)=0
x=-9,6
x=-9 (rejected)
as width can't be negative.
hence width=6 units
Tex wants to make a lawn in the front of his house. The total yards are 30 by 30 yards he gets 20 by 10 yards. Is that enough and if so how much more does he need?
Answer:
Step-by-step explanation:
Tex wants to make a lawn in the front of his house. The total yards are 30 by 30 yards. This means that the total area of the lawn is
30 × 30 = 900 yards^2
he gets 20 by 10 yards. This means that the total area of what he got would be
20 × 10 = 200 yards^2
Since what he needs is 900 yards^2 and it is greater than what he got, 200 yards^2, then it won't be enough.
What he needs more would be
900 - 200 = 700 yards^2
A sale transaction closes on April 15th. The day oIf a lot contains 48,000 square feet and is 240’ wide, how deep is the lot? closing belongs to the seller. Real estate taxes for the year, not yet billed, are expected to be $2,110. According to the 365-day method, what is the seller's share of the tax bill?
a. $626
b. $675
c. $607
d. $721
Answer:
c =$607
200 ft deep
Step-by-step explanation:
A sale transaction closes on April 15th. The day oIf a lot contains 48,000 square feet and is 240’ wide, how deep is the lot? closing belongs to the seller. Real estate taxes for the year, not yet billed, are expected to be $2,110. According to the 365-day method, what is the seller's share of the tax bill?
a. $626
b. $675
c. $607
d. $721
Since there are 90 days between january and March, we add that to the 15 days in April. which will give us 105 days.
Applying the 365-day method,
therefore 2110/365
5.78*105
606.98
approximately=$607
b. the day golf contains 48000 square feet
then 48000 divided by how wide it is
48,000 sq ft ÷ 240' = 200'
Veronica was recently diagnosed with a heart condition. Her doctor's bill was $4,200 for the diagnostics. Her policy has a $250 deductible and a 80/20 coinsurance provision up to $10,000 and then the insurance pays 100% thereafter. In total, how much will Veronica pay for her diagnosis?
Answer:
$1040
Step-by-step explanation:
As 80/20 insurance policy is a form of coinsurance in which deductible is satisfied first and then the client would pay 20% of additional medical costs and the remaining 80% is paid by the insurance company. Under the current scenario, Veronica will bear an amount of $250 and $790(i.e. 20% of the amount after deductible), totaling to $1040.
For how many positive values of n are both n3 and 3n four-digit integers?
Answer:
No positive value of n
Step-by-step explanation:
we have to find out for how many positive values of n are both
[tex]n^3 , 3^n[/tex] our-digit integers
Let us consider first cube
we get 4digit lowest number is 1000 and it has cube root as 10.
Thus 10 is the least integer which satisfies four digits for cube.
The highest integer is 9999 and it has cube root as 21.54
or 21 the highest integer.
Considering 3^n we get,
3^10 is having 5 digits and also 3^21
Thus there is no positive value of n which satisfy that both n cube and 3 power n are four digits.
Solve this problems: a company has two office building that hold 30000 employees. Their headquarters contains 14 times as many employees as their overseas branch. Therefore, their headquarters contains employees
Their headquarters contains 28000 employees.
Step-by-step explanation:
Given,
Total number of employees = 30000
Let,
Number of employees in headquarters = x
Number of employees in overseas branch = y
According to given statement;
x+y=30000 Eqn 1
x = 14y Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]14y+y=30000\\15y=30000\\[/tex]
Dividing both sides by 15
[tex]\frac{15y}{15}=\frac{30000}{15}\\y=2000[/tex]
Putting y=2000 in Eqn 2
[tex]x=14(2000)\\x=28000[/tex]
Their headquarters contains 28000 employees.
Keywords: linear equation, division
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The overseas branch has 2,000 employees, and since the headquarters has 14 times as many employees, it contains 28,000 employees.
We need to determine the number of employees at the headquarters of a company given that the headquarters has 14 times as many employees as the overseas branch, and the total number of employees in both buildings is 30,000.
Let's denote the number of employees in the overseas branch as x. Then, the number of employees in the headquarters is 14x. According to the problem, the total number of employees in both buildings is:
x + 14x = 30,000
Combining the terms:
15x = 30,000
To find x, we divide both sides by 15:
x = 30,000 / 15
x = 2,000
This means the overseas branch has 2,000 employees.
Now, since the headquarters contains 14 times as many employees as the overseas branch, we calculate:
14x = 14 * 2,000 = 28,000
Therefore, their headquarters contains 28,000 employees.
Las Cruses, NM, is about 600 mi from Dallas, TX. One plane flies from Dallas to Las Cruses in 1 hr 12 min, and another plane with the same air speed flies from Las Cruses to Dallas in 1 hr 30 min. Find the air speed of the planes and the speed of the wind
Answer: the speed of the plane is 7.4 miles per minute.
the speed of the wind is 0.93 miles per minute.
Step-by-step explanation:
Let x represent the speed of the plane.
Let y represent the speed of the wind.
Distance of Las Cruses, NM from Dallas, TX is 600 miles.
Distance = speed × time
One plane flies from Dallas to Las Cruses in 1 hr 12 min(72 minutes). Assuming the plane flew in the same direction with the wind, then
600 = 72(x + y)
600 = 72x + 72y - - - - - - - - 1
Another plane with the same air speed flies from Las Cruses to Dallas in 1 hr 30 min(90 minutes). Assuming it flew in opposite direction to that of the wind, then
600 = 90x - 90y - - - - - - - 2
Adding equation 1 and equation 2, it becomes. 1200 = 162x
x = 1200/162 = 7.4 miles per minute.
x + y = 600/72 = 8.33
y = 8.33 - x = 8.33 - 7.4 = 0.93 miles per minute
Answer:
Hi am sitting in my post office waiting for you to come over and then I’ll come over to you
Step-by-step explanation:
Inside the post office office became offices when offices are offices
The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given:Old SeedNumber of Seeds = 11Average Length = 6.25 inchesStandard Deviation = 1.0 inchesNew SeedNumber of Seeds = 16Average Length = 5.95 inchesStandard Deviation = 0.80 inchesBased on these data, if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is:______
Answer:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{0.8^2}{1.0^2}=0.64[/tex]
[tex]p_v =P(F_{15,10}<0.64)=0.2105[/tex]
Since the [tex]p_v > \alpha[/tex] we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.
Step-by-step explanation:
Data given and notation
[tex]n_1 = 11 [/tex] represent the sampe size for the Old
[tex]n_2 =16[/tex] represent the sample size for the New
[tex]\bar X_1 =6.25[/tex] represent the sample mean for Old
[tex]\bar X_2 =5.95[/tex] represent the sample mean for the New
[tex]s_1 = 1.0[/tex] represent the sample deviation for Old
[tex]s_2 = 0.8[/tex] represent the sample deviation for New
[tex]\alpha=0.05[/tex] represent the significance level provided
Confidence =0.95 or 95%
F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:
[tex]F=\frac{s^2_2}{s^2_1}[/tex]
Solution to the problem
System of hypothesis
We want to test if the variation for New sample it's lower than the variation for the Old sample, so the system of hypothesis are:
H0: [tex] \sigma^2_2 \geq \sigma^2_1[/tex]
H1: [tex] \sigma^2_2 <\sigma^2_1[/tex]
Calculate the statistic
Now we can calculate the statistic like this:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{0.8^2}{1.0^2}=0.64[/tex]
Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_2 -1 =16-1=15[/tex] and for the denominator we have [tex]n_1 -1 =11-1=10[/tex] and the F statistic have 15 degrees of freedom for the numerator and 10 for the denominator. And the P value is given by:
P value
Since we have a left tailed test the p value is given by:
[tex]p_v =P(F_{15,10}<0.64)=0.2105[/tex]
And we can use the following excel code to find the p value:"=F.DIST(0.64,15,10,TRUE)"
Conclusion
Since the [tex]p_v > \alpha[/tex] we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.
if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is 1.56. The option (d) is correct.
To test whether the new seed results in less variability in individual potato length compared to the old seed, we can perform an F-test for comparing variances.
The F-test statistic for comparing two variances is given by:
[tex]\[ F = \frac{s_1^2}{s_2^2} \][/tex]
where [tex]\( s_1^2 \)[/tex] is the variance of the old seed and [tex]\( s_2^2 \)[/tex] is the variance of the new seed. The larger variance should be the numerator to ensure the F-value is greater than or equal to 1.
Given data:
- Old Seed:
[tex]- \( n_1 = 11 \)\\ - \( \bar{x}_1 = 6.25 \) inches\\ - \( s_1 = 1.0 \) inch[/tex]
- New Seed:
[tex]- \( n_2 = 16 \)\\ - \( \bar{x}_2 = 5.95 \) inches\\ - \( s_2 = 0.80 \) inch[/tex]
First, calculate the variances:
- Variance of old seed, [tex]\( s_1^2 = (1.0)^2 = 1.0 \)[/tex]
- Variance of new seed, [tex]\( s_2^2 = (0.80)^2 = 0.64 \)[/tex]
Since [tex]\( s_1^2 \)[/tex] (old seed) is larger than [tex]\( s_2^2 \)[/tex] (new seed), we use:
[tex]\[ F = \frac{s_1^2}{s_2^2} = \frac{1.0}{0.64} \][/tex]
Now, calculate the F-value:
[tex]\[ F = \frac{1.0}{0.64} = 1.5625 \][/tex]
The calculated test statistic is approximately 1.56. Therefore, the correct answer is (d) 1.56.
The complete question is:
The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given: Old Seed - Number of Seeds = 11, Average length = 6.25 inches , Standard Deviation = 1.0 inches New Seed - Number of Seeds = 16, Average length = 5.95 inches Standard Deviation = 0.80 inches. On this data, if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is:
(a) 1.25
(b) 0.80
(c) 0.64
(d) 1.56
For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. Hypertension is commonly defined as a systolic blood pressure above 140. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.
Answer: 0.0001
Step-by-step explanation:
Given : For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1.
i.e. [tex]\mu=114.8\ \ \ \&\ \ \sigma=13.1[/tex]
Sample size =4
Let x be the sample mean systolic blood pressure.
Then the probability that their mean systolic blood pressure is greater than 140 will be
[tex]P(x>140)=1-P(x\leq140)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{140-114.8}{\dfrac{13.1}{\sqrt{4}}})\\\\\ =1-P(z\leq3.85)\ \ [\because \ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9999\ \ \text{[By z-table]}\\\\= 0.0001[/tex]
Hence, the required probability = 0.0001
Answer:
Hence, the required probability = 0.0001
Step-by-step explanation:
Derek's math teacher put some candy in a brown paper bag. The bag contains 4 lemon, 6 lime, 8 cherry, 2 pineapple, 5 orange, and 5 grape candies. All 14 students ahead of Derek selected a candy to eat, but no one got pineapple. What is the probability that Derek will draw out a pineapple candy?
Answer:
Even though 14 candies were gone there still is a very low change of getting pineapple. out of 12 candies 2 are pineapple.
Step-by-step explanation:
Find the relative minimum of
y = 3x^3 + 14x^2 - 11x - 46
(___ , ____)
Round your answers to the nearest tenth when applicable.
Write your answer in the format (a, b).
Answer:
Step-by-step explanation:
The max and min values exist where the derivative of the function is equal to 0. So we find the derivative:
[tex]y'=9x^2+28x-11[/tex]
Setting this equal to 0 and solving for x gives you the 2 values
x = .352 and -3.464
Now we need to find where the function is increasing and decreasing. I teach ,my students to make a table. The interval "starts" at negative infinity and goes up to positive infinity. So the intervals are
-∞ < x < -3.464 -3.464 < x < .352 .352 < x < ∞
Now choose any value within the interval and evaluate the derivative at that value. I chose -5 for the first test number, 0 for the second, and 1 for the third. Evaluating the derivative at -5 gives you a positive number, so the function is increasing from negative infinity to -3.464. Evaluating the derivative at 0 gives you a negative number, so the function is decreasing from -3.464 to .352. Evaluating the derivative at 1 gives you a positive number, so the function is increasing from .352 to positive infinity. That means that there is a min at the x value of .352. I guess we could round that to the tenths place and use .4 as our x value. Plug .4 into the function to get the y value at the min point.
f(.4) = -48.0
So the relative min of the function is located at (.4, -48.0)
Charles owns a toy store and to store his inventory of toys at his home office he keeps them in plastic containers. Each container holds 12 toy boxes and he has 278 toy boxes how many containers does he need?
Answer:
He needs 23 containers
Step-by-step explanation:
1 container = 12 toy boxes
X container= 278 toy boxes
12x= 278
X= 278/12
X= 23 containers
what is the lateral area of a square pyramid with side length 11.2 and slant height 20
Answer:
The lateral surface area of square pyramid is 448 square units.
Step-by-step explanation:
We are given the following in the question:
Side length of square pyramid = 11.2 units
Slant height of square pyramid = 20 units
Lateral area of a square pyramid =
[tex]L = \dfrac{1}{2}Ph[/tex]
where P is the perimeter of square base and h is the slant height.
Perimeter of square base =
[tex]P = 4\times \text{Base edge}\\= 4\times 11.2 = 44.8\text{ units}[/tex]
Putting the values, we get:
[tex]L = \dfrac{1}{2}\times 44.8\times 20 = 448\text{ square units}[/tex]
Thus, the lateral surface area of square pyramid is 448 square units.
Answer:
[tex]448 cm^{2}[/tex]
Step-by-step explanation:
s = 11.2; l = 20
L.A. = [tex]4 (\frac{1}{2} sl)[/tex]
L.A.= [tex]\frac{1}{2}(4 * 11.2)20[/tex] Multiply 4 * 11.2 to get perimeter 44.8
L.A. = [tex]\frac{1}{2} pl[/tex]
L.A. = [tex]\frac{1}{2} (44.8)20\\[/tex] Simplify 44.8 * 20
L.A. = [tex]\frac{1}{2}(896)\\[/tex] Divide 896 by 2
L.A. = [tex]448cm^{2}[/tex]
A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded. What is the probability that one spin of the spinner will land in a shaded sector?
Answer:
2/3
Step-by-step explanation:
A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded.
Probability is the likelihood that an event will occur. Probability is a selection over the number of observation.
There are 4 shaded portion of the spinner and two unshaded portion.
The probability that when the spinner is spinned the portion will liand on four is simply
4/6, divided to its lowest term.
2/3
The probability that when the spinner is spined the portion will land on four is simply [tex]\frac{2}{3}[/tex].
Given information:
A certain spinner is divided into [tex]6[/tex] sectors of equal size, and the spinner is equally likely to land in any sector. Four of the [tex]6[/tex] sectors are shaded, and the remaining sectors are not shaded.
According to question,
[tex]P(E)=\frac{\rm{No\;of\;favourable\;outcomes}}{\rm{Total\;no\;of\;outcomes}}[/tex]
Four of the [tex]6[/tex] sectors are shaded, and the remaining sectors are not shaded.
There are [tex]4[/tex] shaded portion of the spinner and two unshaded portions.
[tex]P(E)=\frac{4}{6}=\frac{2}{3}[/tex]
Hence, The probability that when the spinner is spined the portion will land on four is simply [tex]\frac{2}{3}[/tex].
Learn more about Probability here:
https://brainly.com/question/10198002?referrer=searchResults
A circle has its center at the origin and has a diameter of 24 units.
What is the standard equation of the circle?
Answer:
B
Step-by-step explanation:
radius=24/2=12
eq. of circle is
x²+y²=12²
Answer:
b. x² + y² = 12²
Step-by-step explanation:
A circle has a general equation of:
(x + h)² + (y – k)² = r²
where h and k are the center (h,k) and r is the radius.
The circle is centered at origin (0, 0), so h=0, k=0.
The diameter is 24, but we want the radius instead. So divide the diameter by 2 to get the radius. r = 24/2 = 12
Plug it into the equation
(x + h)² + (y – k)² = r²
(x + 0)² + (y – 0)² = 12²
x² + y² = 12²