Answer:
The calculated value t = 1.76 < 2.131 at 0.05 level of significance
Null hypothesis is accepted
The manufacturer’s claim is greater than 560 bags per hour
Step-by-step explanation:
Explanation:-
Given sample size 'n' =16
Given the manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour.
mean of the Population 'μ' = 560
Mean of the sample Χ⁻ = 538
sample standard deviation' S' = 50
Null hypothesis:H₀:μ > 560
Alternative Hypothesis:H₁ : :μ < 560 (left tailed test)
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{538-560 }{\frac{50}{\sqrt{16} } } = -1.76[/tex]
|t| = |-1.76| = 1.76
Degrees of freedom
γ = n-1 =16-1 =15
[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } =t_{0.025} =2.131[/tex]
Conclusion:-
The calculated value t = 1.76 < 2.131 at 0.05 level of significance
Null hypothesis is accepted
The manufacturer’s claim is greater than 560 bags per hour
The factor tree below provides the factors of 18. A factor tree of 18. 18 branches to 2 and 9. 9 branches to 3 and 3. What is the prime factorization of 18? 2 times 3 2 times 9 2 times 3 times 3 2 times 3 times 9
Answer:
the prime factorization of 18 is 2 times 3 and 1 time two
Step-by-step explanation:
Factorization refers to the process by which we decompose a number in its prime factors, in other words, we express the number as a multiplication of prime numbers.
In this case we have the number 18:
18= 9 x 2, however, 9 is not a prime number so we are going to factor the 9.
18= 3 x 3 x 2.
Now we see that all our factors are prime and thus this is the factorization of 18.
Thus, the prime factorization of 18 is 2 times 3 and 1 time two
Answer:
A
enginuity2020
Antonio has a CD-player that holds six CDs. He puts six different
CDs in the player and the CD player randomly plays a song from
any of the CDs. What is the probability that the CD player will
play the first song from the first CD and the first song from the
sixth CD?
Answer:
1/6
Step-by-step explanation:
There are 6 CD
P( song from 6th ) = number of CD's that are 6th/ total
= 1/6
.I am going to buy 2 kilos of oranges. A kilo of oranges is 1,5 TL. How much will I pay
Answer:
The amount to be paid for 2 kilograms of oranges is 3.0 TL.
Step-by-step explanation:
The total amount of oranges to be bought is, Q = 2 kilograms.
The cost of 1 kilogram of oranges is, C = 1.5 TL.
Compute the cost of 2 kilograms of oranges as follows:
Total cost = Q × C
[tex]=2\times 1.5\ \text{TL}\\\\=3.0\ \text{TL}[/tex]
Thus, the amount to be paid for 2 kilograms of oranges is 3.0 TL.
I will give brainliest just please help
The equation ax2 + bx + c = 0 has no real solutions.
Which statement about the graph of f(x) = ax2 + bx + c could be true?
A. It could pass through the origin.
B. Its vertex could be at (–6, 0).
C. It could have a maximum at (–3, 2).
D. It could have a minimum at (0, 4).
Answer:
D. It could have a minimum at (0, 4).
Step-by-step explanation:
ax2 + bx + c = 0 has no real solutions, which means it does not touch the x axis
Since it points upwards, the vertex must be above the x axis
It will have a minimum since it opens upwards
A. It could pass through the origin. False
B. Its vertex could be at (–6, 0). False
C. It could have a maximum at (–3, 2). False
D. It could have a minimum at (0, 4). True
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 pile of earth removed from an excavation is a cone measuring 12 ft high and 30 ft across its base. How many trips will it take to haul away the
earth using a dump truck with a capacity of 9 cubic yards?
trips =
Answer:
12 trips
Step-by-step explanation:
Given;
Dimension of cone shapef pile of earth;
height h = 12 ft = 4 yards
diameter d = 30 ft = 10 yards
radius r = d/2 = 10/2 = 5 yards
The volume of a cone V;
V = (1/3)πr^2 h
Substituting the given values;
V = (1/3) ×π × 5^2 × 4 cubic yards
V = 104.72 cubic yards
Given that a dump truck have a capacity of 9 cubic yards.
Vc = 9 cubic yards
Number of trips it will take is;
N = Volume of earth pile/truck capacity
N = V/Vc
Substituting the values;
N = 104.72/9
N = 11.64
N ≈ 12 trips
Therefore, the truck will make 12 trips
What is the value of -2(5) + 3?
Answer:
-2 (5) + 3
- 10 + 3
= -7
Linda earns $600 each week working her full time job. Her employer has a 16% tax deduction on all monies earned each week
Answer:
$504 a week
Step-by-step explanation:
Jack has a summer job caddying at a golf course. Jack earns $120
a week. By rounding his weekly income to the nearest hundred
dollars, find a reasonable estimate for his total income during the
12 week summer.
A) $700
B) $800
C) $1200
D) $1700
Find the domain of the graphed function.
Answer:
A
Step-by-step explanation:
The number of points that Shira scored each basketball game so far this season is shown on the dot plot. A number line going from 1 to 13. 2 dots are above 2. 1 dot is above 3. 1 dot is above 5. 2 dots are above 7. 3 dots are above 9. 6 dots are above 11. 1 dot is above 12. Which statement must be true according to the dot plot?
The according to the dot plot, the true statement is: the data is left-skewed and shows Shira never scored fewer than 2 points or more than 12 points in a game
What is Left-Skewed Data Distribution?A data distribution that is left-skewed is negatively skewed. This means that the long tail goes in the negative direction of the number line, with most of the values being concentrated on the right side.
The dot plot given is left-skewed, which means it is negatively-skewed.
Therefore, the according to the dot plot, the true statement is:
The data is left-skewed and shows Shira never scored fewer than 2 points or more than 12 points in a game
Learn more about left-skewed data on:
https://brainly.com/question/3252860
Answer:
c
The data is skewed to the left and shows that she never scored fewer than 2 points or more than 12 points in a game.
Step-by-step explanation:
swag
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.
On March 1, 2022, Carla Vista Co. acquired real estate, on which it planned to construct a small office building, by paying $79,000 in cash. An old warehouse on the property was demolished at a cost of $8,000; the salvaged materials were sold for $1,660. Additional expenditures before construction began included $1,160 attorney’s fee for work concerning the land purchase, $4,400 real estate broker’s fee, $8,660 architect’s fee, and $13,800 to put in driveways and a parking lot. (a) Determine the amount to be reported as the cost of the land.
Answer:
Cost of the land = $90,900
Step-by-step explanation:
Cash Paid for the construction = $79,000
Cost of demolition of the old warehouse = $8,000
Salvage (i.e Proceeds from the salvaged materials) = $1,660
Additional Expenditure before construction began
Attorney's fee = $1,160
Real estate broker's fee = $4,400
Architect's fee = $8,660 ( Note that this will be capitalized to building cost)
Driveways and parking lot = $13,800 ( Note that this is capitalized to land improvements)
Sum of additional expenditure = Attorney's fee + Real estate broker's fee
Sum of the additional expenditure = 1160 + 4400
Sum of the additional expenditure = $5,560
Cost of the land = Cash paid + cost of demolition + Additional expenditure - salvage
Cost of the land = 79000 + 8000 + 5560 - 1660
Cost of the land = $90,900
Answer:
Amount to be reported as the cost of the land = $ 91,400
Step-by-step explanation:
Payment of Real Estate= $ 79,000
Building Demolished $ 8000
Gains on Sale of materials = ($1660)
Attorney’s fee for work concerning the land purchase, $1160
Broker's fee $4,400
Amount to be reported as the cost of the land = $ 91,400
Broker's fee is included in the purchase of land . Gains on the sale of salvaged materials is deducted from the cost of land because it is of the building demolished. Architect's fee is not also included in the cost of land but in the construction costs.
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What is the value of f(x) when X=-3?
f(x)=-2x-3
f-3)=
Answer:
f(-3)=3
Step-by-step explanation:
We know that f(x)=-2x-3. In order to find f(-3), we simply need to substitute x with -3.
Thus, we have:
=-2(-3)-3
=6-3
=3
Answer:
3
Step-by-step explanation:
f(x)=-2x-3
Let x=-3
f(-3)= -2(-3) -3
= 6-3
= 3
A company produces steel rods. The lengths of all their steel rods are normally distributed with a mean of 155.1-cm and a standard deviation of 2.2-cm. For shipment, 11 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm.
Answer:
The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm
P(155.6 < x⁻ < 156.2) = 0.174 cm
Step-by-step explanation:
Given sample size 'n' = 11 steel rods
Mean of the Population = 155.1 cm
Standard deviation of the Population = 2.2 cm
Given x⁻ be the random variable of Normal distribution
Let x₁⁻ = 155.6 cm
[tex]Z_{1} = \frac{x^{-} _{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{155.6-155.1}{\frac{2.2}{\sqrt{11} } } = 0.7541[/tex]
Let x₂⁻ = 156.2 cm
[tex]Z_{2} = \frac{x^{-} _{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{156.2-155.1}{\frac{2.2}{\sqrt{11} } } = 1.659[/tex]
The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm.
P(x⁻₁ < x⁻ <x⁻₂) = P(Z₁ < Z <Z₂)
= P(Z <Z₂) - P(Z<Z₁)
= 0.5 +A(1.629) - (0.5 +A(0.7541)
= A(1.629) - A(0.7541)
= 0.4474 - 0.2734
= 0.174
Conclusion:-
The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm = 0.174
if you have a population of 40million people and 2million of them are from out of town. what percentage of them are out of towners??
Answer:
5%
Step-by-step explanation:
There are 2000000 people out of town and 4000000 people in total.
Solution for 2000000 is what percent of 40000000:
2000000:40000000*100 =
(2000000*100):40000000 =
200000000:40000000 = 5
Now we have: 2000000 is what percent of 40000000 = 5
Question: 2000000 is what percent of 40000000?
Percentage solution with steps:
Step 1: We make the assumption that 40000000 is 100% since it is our output value.
Step 2: We next represent the value we seek with x
Step 3: From step 1, it follows that 100%= 40000000.
Step 4: In the same vein, x%=2000000.
Step 5: This gives us a pair of simple equations:
100%=40000000(1).
x%=2000000(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
100%/x%=40000000/2000000
Step 7: Taking the inverse (or reciprocal) of both sides.
⇒ x=5%
Therefore, 2000000 is 5% of 40000000.
I hope that answers your question and plz mark me brainliest!
What is the volume of the sphere in the diagram? with a diameter of 3
Answer:
Given diameter: r = d / 2 , Given area: r = √[A / (4 * π)] , Given volume: r = ³√[3 * V / (4 * π)] , Given surface to volume ratio: r = 3 / (A/V) .
Step-by-step explanation:
So, do that!
Answer:
36pi
Step-by-step explanation:
i already did it and it was correct.
Macy spent 2 hours working on homework. She spent 1/4
of that time working on math.
How much time did Macy spend on her math homework?
Answer:
1/2 h or 30 min
Step-by-step explanation:
2 h * 1/4 = 2/4 = 1/2 h or 30 min
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!!!
Boris is riding a ferris wheel at a carnival. After a time t, his height H above the ground is given by the following formula. H=a cos(bt)+c Find Boris's height above the ground when a=-15m,b=2.241 rad/s,t=3s, and c=23m
Answer:
Boris height above the ground is 9.428m
Step-by-step explanation:
Boris height above the ground is given by the formula;
H = a cos(bt) + c
Now, we are told that,
a = -15m
b = 2.241 rad/s
t = 3s
c = 23m
Plugging in the relevant values, we have;
H = -15 cos (2.241 * 3) + 23
H = -15 cos(6.723 rad) + 23
cos(6.723rad) = 0.9048
Thus,
H = (-15 × 0.9048) + 23
H = 9.428 m
So boris height above the ground is 9.428m
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)
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)
The Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. The mayor of Smart Town believes the county’s residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area. A researcher is hired to conduct a study to determine whether Smart County’s residents have, on average, higher Full Scale IQs than the population. A random sample of 100 people from Smart County were given the IQ test and were found to have an average Full Scale IQ of 105. After analyzing the data to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average, the p-value of 0.0004 was obtained. Using a 0.05 significance level, what conclusion can be drawn from the data?
Answer:
Step-by-step explanation:
Hello!
The variable "X: Full scale IQ score of an adult" follows a normal distribution with mean μ= 100 and standard deviation σ= 15
The claim is that the county's residents are smarter than the national average, symbolically: μ > 100
To test this a researcher took a sample of n=100 residents that took the test and recorded an average of X[bar]= 105
The hypotheses are:
H₀: μ ≤ 100
H₁: μ > 100
α: 0.05
p-value: 0.0004
Using the p-value approach, the decision rule is as follows:
p-value ≤ α, reject the null hypothesis.
p-value > α, do not reject the null hypothesis.
The p-value is less than the significance level so the decision is to reject the null hypothesis.
At a 5% significance level, you can conclude that the average full-scale IQ score of the Smart County residents is higher than the national average.
I hope this helps!
Joann's entire office is moving to a new location. She is helping to fill two moving vans with boxes. The large van can hold up to 15 boxes. The large van can hold up to 25 boxes. There are 800 boxes that must be moved. How many trips will the two vans need to take to transport all of the boxes to the new location?
Answer:
20 trips
Step-by-step explanation:
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)
Solve the following equation, if possible, and determine the number of solutions.
6y+4−3y−7=3(y−1)
write one answer for the number of solutions, and write at least one answer that explains your answer for the number of solutions.
6y+4−3y−7=3(y−1)
Opening the bracket we notice that it will yield same thing for both sides of the equation.
There is only one way to solve the equation because it's clear that y = 0
So it's by opening the bracket.
So the value for y is equal to zero
A certain disease only affects men 20 years of age or older. The chart shows the probability that a man with the disease falls in the given age group. What is the probability that a randomly selected man with the disease is not between the ages of 55 and 64
Answer:
0.68
Explanation:
The question is incomplete without the tables. Find attached the table used in solving the question.
group 20-24 25-34 35-44 45-54 55-64 65-74 75+ respectively
Probability 0.004 0.006 0.14 0.29 0.32 0.17 respectively
This is a probability of complementary events. The sum of the two complementary events = 1
Hence, the probability of selecting a man with the disease that is not between the ages of 55 and 64 + the probability of selecting a man with the disease that is between the ages of 55 and 64 = 1
The probability of selecting a man with the disease is not between the ages of 55 and 64 = 1- probability of selecting a man with the disease is between the ages of 55 and 64
Let Pr(between 55 and 74) = probability of selecting a man with the disease is between the ages of 55 and 64
From the table, Pr(between 55 and 74) = 0.32
The probability of selecting a man with the disease is not between the ages of 55 and 64 = 1 - 0.32
The probability of selecting a man with the disease is not between the ages of 55 and 64 = 0.68
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]
Scores on a certain IQ test are knownto have a mean of 100. A random sample of 43 students attend a series of coaching classes before taking the test. Let \small \mu be the population mean IQ score that would occur if every student took the coaching classes.The classes are successful if \small \mu > 100 . A test is made of the hypothesis \small H_{0}:\mu = 100 versus \small H_{1}:\mu > 100
Consider three possible conclusions :
(i) The classes are successful
(ii) The classes are not successful
(iii) The classes might not be successful.
Part 1
Assume that the classes are successsful but the conclusion is reached that the classes might not be successful. Which type of error is this?
Part 2
Assume that the classes are not successful. It is possible to make a type II error? Explain.
_______(Yes, No) , a type II error _____(is, is not) possible. The classes are not successful when the null hypothesis is______(true, false).
Answer:
Part 1
Type II error
Part 2
No ; is not ; true
Step-by-step explanation:
Data provided in the question
Mean = 100
The Random sample is taken = 43 students
Based on the given information, the conclusion is as follows
Part 1
Since it is mentioned that the classes are successful which is same treated as a null rejection and at the same time it also accepts the alternate hypothesis
Based on this, it is a failure to deny or reject the false null that represents type II error
Part 2
And if the classes are not successful so we can make successful by making type I error and at the same time type II error is not possible
Therefore no type II error is not possible and when the null hypothesis is true the classes are not successful
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.