Using the t-distribution, it is found that since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.
At the null hypothesis, it is tested if the average box of cereal does not contain more than 368 grams, that is:
[tex]H_0: \mu \leq 368[/tex]
At the alternative hypothesis, it is tested if it contains, that is:
[tex]H_1: \mu > 368[/tex]
We have the standard deviation for the sample, hence, the t-distribution is used to solve this question.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.In this problem, the values of the parameters are: [tex]\overline{x} = 372.5, \mu = 368, s = 15, n = 25[/tex].
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{372.5 - 368}{\frac{15}{\sqrt{25}}}[/tex]
[tex]t = 1.5[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05, with 25 -1 = 24 df, is of [tex]t^{\ast} = 1.71[/tex].
Since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.
You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/13873630
What is 7C3? Thanks.
Answer:
C7,3=7!( 3!)( 7−3)!= 7! I think tell me if I'm wrong?
Answer:
7C3 = 7! / (7 - 3)! 3! = 7 x 6 x 5 x 4! / 4!
List all the factors of 42 from least to greatest. Enter your answer below,
using a comma to separate each factor.
Answer Here
SUBMIT
Answer:
Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42.
Step-by-step explanation:
:)
At Cheesecake Factory, the cost of your meal before the tip is $77.23. You leave a 15% tip. How much
money did you leave for tip? What is the total cost of your meal?
Answer:
$88.81
Step-by-step explanation:
to find tip, multiply 77.23 and .15 to get $11.58
total cost = meal + tip
total cost = 77.23 + 11.58 which equals $88.81
The volume (V) of a rectangular pyramid can be determined by using the following
formula.
Iwi
V
Where l= the length of the rectangle, w = the width of the rectangle, and h = the heigh
of the pyramid, what is the result of solving this equation for w?
Ow=3V-th
O2 - V +3 - th
V3
th
3V
O w=
Answer:
[tex]{ \rm{V = \frac{lwh}{3} }} \\ \\ { \rm{3V = lwh}} \\ \\ { \boxed{ \rm{ \: w = \frac{3V}{lh } \: }}}[/tex]
3. West Fremont is a community consisting of 3,000 homes. A small coal-burning power plant currently supplies electricity for the town. The capacity of the power plant is 12 megawatts
(MW) and the average household consumes 8,000 kilowatt hours (kWh) of electrical energy each year. The price paid to the electric utility by West Fremont residents for this energy is $0.10 per kWh. The town leaders are considering a plan, the West Fremont Wind Project (WFWP), to generate their own electricity using 10 wind turbines that would be located on the wooded ridges surrounds the town. Each wind turbine would have a capacity of 1.2 MW and each would cost the town $3 million to purchase, finance, and operate for 25 years.
(a) Assuming that the existing power plant can operate at full capacity for 8,000 hrs/yr, how many kWh of electricity can be produced by the plant in a year?
(b) At the current rate of electrical energy use per household, how many kWh of electrical energy does the community consume in one year?
(c) Assuming that the electrical energy needs of the community do not change during the 25-year lifetime of the wind turbines, what would be the cost to the community of the electricity supplied by the WFEP over 25 years? Express your answer in dollars/kWh.
Power is the rate of doing work, and the power of the generating plant or
turbine and the duration of generation, gives the energy generated.
The correct responses are;
(a) 96 × 10⁶ kWh(b) 24 × 10⁶ kWh(c) 0.05 dollars/kWhReasons:
Number of homes in the town = 3,000 homes
The given capacity of the power plant = 12 MW = 12,000 kW
Power consumed by a household = 8,000 kWh per year
The price for electrical energy = $0.10 per kWh
Number of wind turbines = 10
WFWP = The West Fremont Wind Project
Capacity of each wind turbine = 1.2 MW
Cost of each wind turbine for 25 years = $3 million
(a) Number of hours of operation of the power plant = 8,000 hrs/yr
Required:
The amount of kWh of electricity produced in a year by the plant.
Solution:
The energy produced = Power × Time
∴ The energy produced = 12,000 kW × 8000 hr = 96,000,000 kWh
Therefore;
The energy produced by the plant in a year, E = 96 × 10⁶ kWh
(b) Energy consumed = Energy consumed per home × Number of homes
Therefore;
Energy consumed = 8,000 kWh/home × 3,000 homes = 24,000,000 kWh
The energy the community consumes in one year = 24 × 10⁶ kWh
(c) The cost per kWh = $0.10
The cost, C, of the energy per year is therefore
C = 24,000,000 kWh × $0.10/kWh = $2,400,000
The cost for 25 years = 25 × C = 25 × $2,400,000 = $60,000,000
The number of wind turbines = 10
Cost per wind turbine = $3 million
Total cost to operate the 10 wind turbine = $3 million × 10 = $30 million
Energy consumed = 24,000,000 kWh
Therefore;
24,000,000 kWh × 25 = $30 million
[tex]\displaystyle 1 \ kWh = \frac{\$ 30 \ million}{25 \times 24,000,000 \ kWh} = \mathbf{\$0.05/kWh}[/tex]
The cost to the community of the electricity supplied by WFWP over 25 years is $0.05/kWh.
Learn more about energy and power here:
https://brainly.com/question/24592300
evaluate f(2) and lim f(x) where f(x)=5x^3+3x+1
pls answer pls plsplspls pls
πr²/2
22×7×7/7×2
77cm²
πr²/2×2
πr²
22/7×3.5×3.5
38.5cm²
77-38.5=38.5cm²
whats 2077-210?
its for a thing im doing.
Answer:
1867
Step-by-step explanation:
What do you need it for?
Here is an encoded message, a message that has been converted into a code.
WRGDB LYD JRRG GDB.
Can you figure out what it says in English? How was the original message encoded?
Determine if the data below represents a function. Explain your reasoning. (3, 2), (4,7), (8, 12). (10, 15)
Answer:
the data that is shown represents a function
Step-by-step explanation:
the easiest way to know is by looking at the x-variable. Each y-variable needs one x-variable. the x-variable should not be seen paired with another y-variable.
A box contains 2 red marbles, 3 white marbles, 4 green marbles, and 1 blue marble. Two marbles are drawn at random without replacement. Find the probability of selecting a white marble, then a red marble.
1 What is the universe made of? ...
2 How did life begin? ...
3 Are we alone in the universe? ...
4 What makes us human? ...
5 What is consciousness? ...
6 Why do we dream? ...
7 Why is there stuff? ...
8 Are there other universes?
1. big planets and carbon dioxide
2. when god sent adam (the first human being) to earth and had a female with him they got married and gave birth to children and the children marry each other and so on.
3. yes we're the only alive humans within this universe, but outside the universe are god and his worshippers.
4. our human-shaped bodies are the way we feel, hear, look, and do lots more things!
5. when someone feels unlike normal.
6. to feel there's a side of u that can do the impossible.
7. things were passed down from generations so it's possible that "stuff" can be made back when adam came to earth but other than that there was "stuff" even before humanity.
8. yes
other than that, hope u got ur questions solved
Given the following polynomials
x = (a + b + c)^2
y= a^2 + b^ 2 + C^2
z = ab + bc + ac
Which identity is true?
A. x=y-z
B. x=y+z
C. x=y-2z
D. x=y+2z
Answer:
D. x=y+2z
Step-by-step explanation:
if you expand out the first equation (x) you will get: a^2+b^2+c^2+2ab+2bc+2ac
then looking at all of the choices, it can be seen that the third equation (z) needs to be multiplied by to get 2ab+2bc+2ac and then added to the second equation (y) which would result in D being the correct answer.
D. x=y+2z
A tree of unknown height casts a shadow that is 18 feet long. If a person that is 5 ft 7 in casts a shadow that is 4 ft long, then how tall is the tree in feet?
Round your answer to the nearest integer. Do not include feet in your answer.
Answer:
25.
Step-by-step explanation:
5 ft 7 in = 5.583 ft.
We have 2 similar triangles here.
If h is the height of the tree, then:
h / 5.583 = 18/4
h = 18*5.583/4
h = 25.12 ft
The height of the tree is approximately 25.12 feet.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The ratio of the shadow lengths is equal to the ratio of the object heights.
In other words, if we let H be the height of the tree in feet and h be the height of the person in feet, we have:
H/h = 18/4
We can find h by converting the person's height to feet. Since 1 inch is equal to 1/12 foot, the person's height in feet is 5 + 7/12 = 5.58 feet.
Substituting this value into the equation above and solving for H, we get:
H = (18/4) x 5.58 feet
= 25.12 feet
Therefore, the tree is around 25.12 feet tall.
Learn more about the Ratio here:
brainly.com/question/1504221
#SPJ2
here is a list of numbers: 8 7 12 7 11 10 7 12
a) find the median
b) the range
c) the mode
Answer:
Ascending order = 7,7,7,8,10,11,12,12
a) n = 8
= median = (n/2+(n/2+1)/2
= (4th term + 5th term)/2
= 8+10/2
= 9
b) range = 12-7 = 5
c) the mode = 7 (highest occuring value)
The median of the given list of numbers is 9.
The range of the given list of numbers is 5.
The mode of the given list of numbers is 7.
We have,
a) To find the median of a set of numbers, we arrange them in ascending order and determine the middle value.
If there is an odd number of values, the median is the middle number.
If there is an even number of values, the median is the average of the two middle numbers.
Arranging the numbers in ascending order: 7 7 7 8 10 11 12 12
There are eight numbers in this set, so the middle two numbers are 8 and 10.
Taking their average, the median is (8 + 10) / 2 = 9.
b) The range is the difference between the highest and lowest values in the set.
The lowest value is 7, and the highest value is 12.
So the range is 12 - 7 = 5.
c) The mode is the value that appears most frequently in the set.
In the given list, the number 7 appears three times.
Therefore,
The median of the given list of numbers is 9.
The range of the given list of numbers is 5.
The mode of the given list of numbers is 7.
Learn more about the median here:
https://brainly.com/question/28060453
#SPJ2
If I have a 1/4 chance of winning a bet, but lose it 40 times in a row, what percentage chance is that?
WILL GIVE BRAINLIEST
Answer:
the y intercept is 5/3
the y intercept is 3/5
I NEED HELP!!!!!
4. Three bags of Skittles and two bags of M&M's
weigh 3 pounds. Four bags of Skittles weigh 3
pounds. All bags of skittles weigh the same, and
all bags of M&M's weigh the same. What is the
ratio of the weight of a bag of Skittles to a bag of
M&M's?
Answer:
Step-by-step explanation:
How many Skittles is in a 4 pound bag?
Fun-size packages are perfect for parties, party favors, trick-or-treaters, gift baskets, lunch treats and on-the-go snacks. Approximately 20 individual packs per lb.
...
Skittles Fun-Size Packs, 4-Lb Box.
What is x, the distance between points S' and S? x = 2.25 units x = 2.5 units x = 4.25 units x = 4.5 units
Answer:
2.5 units
Step-by-step explanation:
I took the test and got this question right
I forgot how I did it but test your luck if you believe me
Answer:
b
Step-by-step explanation:
in the actual room, the distance between the front and back walls is 8 feet. what is the actual length of the front wall, in feet?
Answer:
8 feet
Step-by-step explanation:
it actually will be 8 feet
Yosef typed a 36 word paragraph in 2/3 minute. What is his typing speed, in words per minute?
Answer:
the answer is:
Yousef typing speed, in words per minute is
equal to
54 words
minute
Pls help stuck on it
Answer:
4,-1
Step-by-step explanation:
Please like!♥
can anyone slove this question pls
we have: -10/4 = -2.5 ⇒ -2 > -2.5 > -3
ANSWER : -2 and -3
ok done. Thank to me :>
Which statement best describes π?
A:Pi is the result of dividing a circle’s circumference by its radius.
B: Pi is the result of dividing a circle’s diameter by its circumference.
C: Pi is the result of dividing a circle’s circumference by its diameter.
D: Pi is the result of dividing a circle’s radius by its circumference.
Answer:
C.
Step-by-step explanation:
Pi = circumference / diameter.
- The width of a rectangle is 4x – 1 feet and the length is 2x + 6 feet. Find the perimeter of the rectangle.
Answer:
12x + 10 feet
Step-by-step explanation:
Perimeter = 2( length + width)
= 2[ 2x + 6 + (4x -1)]
= 2( 2x + 6 + 4x - 1)
= 2( 6x + 5)
= 12x + 10
what is the eight term of the arithmetic sequence defined by the rule A(n)=-12+2(n-1) RIGHT ANSWER ONLY
Answer:
a₈ = 2
Step-by-step explanation:
Substitute n = 8 into the nth term rule
A(8) = - 12 + 2(8 - 1) = - 12 + 2(7) = - 12 + 14 = 2
What is m<9 = 130 degrees, What is m<4
Answer:
50 degrees
Step-by-step explanation:
They are alternate exterior angles, so they add up to 180 degrees.
Activity 3.
Direction. Name the ratio as a fraction in simplest form.
1. P5.00 to P60.00
2. 1 hour to 40 minutes
3. 2 weeks to 4 days
4. Eight out of 30 passengers are tourist. Give the ratio of tourist to passengers.
5. For every 45 passengers, 9 are foreigners. Write the ratio of foreigners to
passengers.
Please answer please help me
Answer:
see explanation
Step-by-step explanation:
(1)
[tex]\frac{5}{60}[/tex] ( divide numerator/ denominator by 5 )
= [tex]\frac{1}{12}[/tex] ( in simplest form )
(2)
both quantities must have the same units
1 hour = 60 minutes , then
[tex]\frac{60}{40}[/tex] ( divide numerator/ denominator by 20 )
= [tex]\frac{3}{2}[/tex] ( in simplest form )
(3)
1 week = 7 days then 2 weeks = 2 × 7 = 14 days , so
[tex]\frac{14}{4}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{7}{2}[/tex] ( in simplest form )
(4)
[tex]\frac{8}{30}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{4}{15}[/tex] ( in simplest form )
(5)
[tex]\frac{9}{45}[/tex] ( divide numerator/ denominator by 9 )
= [tex]\frac{1}{5}[/tex] ( in simplest form )
The length of one ramp is 16 feet. The vertical rise is 5 feet. Use pythagorean theorem to estimate the ramp’s horizontal distance. (round to the nearest tenth of a foot) *
Answer:
The ramp's horizontal distance is the distance in the x-axis. So the ramp's vertical distance I.e y-axis is 14 inches. And its length which is actually the hypotenuse ofthe right angled triangle 16 feet. But let's convert feet to inches first. 1 feet makes 12 inches Hence 16 feet makes 192 inches. From pythagoras a^2 =b^2 + c^2 where a the hypotenuse is 192 and b is 14. C is the ramp's horizontal distance. So we have (192)^2 = (14)^2 + c^2 C^2 = 192^2 - 14^2 = 36668 C = 191.48 From SOHCAHTOA. We have to use Sin So sin theta = (14/192) Theta = sin^(-1) (14/192) = 4.1815. Yes, it meets the FAC standard since the ramp's angle is less than 4.78
Step-by-step explanation:
what is linear spline?
9Linear splines
The linear spline represents a set of line segments between the two adjacent data points (Vk,Ik) and (Vk+1,Ik+1). ... The linear spline is constructed for each interval V = [Vk,Vk+1] independently and it matches the data values (Vk,Ik) for k=0,1,...,n.