Jackson weighed all of his pet guinea pigs and found the average weight to be 2.4 pounds. If the standard error of the sample mean was 0.2227 and the sample standard deviation was 0.63 pounds, how many guinea pigs does Jackson have
Using the Central Limit Theorem, it is found that Jackson has 8 guinea pigs.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], in which [tex]\sigma[/tex] is the standard deviation of the population.
In this problem, we have that [tex]s = 0.2227, \sigma = 0.63[/tex], hence we solve for n to find the number of guinea pigs that he has.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.2227 = \frac{0.63}{\sqrt{n}}[/tex]
[tex]0.2227\sqrt{n} = 0.63[/tex]
[tex]\sqrt{n} = \frac{0.63}{0.2227}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{0.63}{0.2227}\right)^2[/tex]
[tex]n = 8[/tex]
Jackson has 8 guinea pigs.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
(The following information applies to the questions displayed below.
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Saskatewan Can Company manufactures recyclable soft-drink cans. A
unit of production is a case of 12 dozen cans. The following standards
have been set by the production-engineering staff and the controller.
ook
Len
en W
rint
Direct Labor:
Quantity, 0.16 hour
Rate, $8.00 per hour
Direct Material:
Quantity, 9 kilograms
Price $0.42 per kilogram
erences
du. C
owth
sines
Actual material purchases amounted to 233,200 kilograms at $0.475
per kilogram. Actual costs incurred in the production of 22,000 units
were as follows:
arkets
pwth
Direct Labor:
Direct material:
$33,264 for 3,960 hours
$98,230 for 206,800 kilograms
onge
innov
sign,
Required:
The direct material price variance of Saskatewan Can Company will be $6552.
How to calculate the direct material price variance?From the information given, it should be noted that the direct material price variance will be calculated thus.
Firstly, the actual materials cost will be:
= Actual quantity × Actual price
= 218400 × $0.65
= $141960
The projected materials cost will be:
= 218400 × $0.62
= $135408
Therefore, the price variance will be:
= $141960 - $135408
= $6552
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Let f be the continuous function defined on [-6,6]. Let g be the function given by g(x) = [tex]\int\limits^x_{-1} {f(t)} \, dt[/tex] . Write an equation for the tangent to the graph of g at x=4
Answer:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle g(x) = \int_{-1}^x f(t)\, dt[/tex]
And we want to write the equation for the tangent to the graph of g at x = 4.
First, determine g(4):
[tex]\displaystyle \begin{aligned} g(4) & = \int_{-1}^{(4)} f(t)\, dt \end{aligned}[/tex]
This is equivalent to the area of f from -1 to 4:
[tex]\displaystyle \begin{aligned} g(4) & = \frac{1}{2}(2)(3) + \frac{1}{2}(2)(-3)+\frac{1}{2}(-3+(-2))(1) \\ \\ & = \frac{1}{2}(6-6-5) \\ \\ & = -\frac{5}{2}\end{aligned}[/tex]
Note that areas under the x-axis are negative.
Find g'(4):
[tex]\displaystyle \begin{aligned} g'(x) = \frac{d}{dx}\left[ \int_{-1}^x f(t)\, dt\right]\end{aligned}[/tex]
By the Fundamental Theorem of Calculus:
[tex]\displaystyle \begin{aligned} g'(x) & = f'(x) \\ \\ g'(4) & = f'(4) \\ \\ & =1 \end{aligned}[/tex]
Note f is a line for 3 < x < 6 with a slope of 1.
Therefore:
[tex]\displaystyle \begin{aligned} h(x) -g(x_1) & = g'(x_1)(x-x_1) \\ \\ h(x) - \left(-\frac{5}{2}\right) & = (1)(x-(4)) \\ \\ h(x)& = (x-4) - \frac{5}{2} \\ \\ & = x - \frac{13}{2}\end{aligned}[/tex]
In conclusion, the equation of the tangent line is:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
What is the measure of DE ? Would the correct answer be 5in
Answer:
I think it would be 5 I'm honestly not 100% sure though!
A hypothesis test in which rejection of the null hypothesis occurs for values of the
point estimator in either tail of the sampling distribution is called
a. The null hypothesis
b. The alternative hypothesis
c. A one-tailed test
d. A two-tailed test
If the probability of an event is
23
96
, what is the probability of the event not happening?
Answer:
73/96
Step-by-step explanation:
I hope you meant 23/96
the probability of not happening would be 1-23/96
73/96
A box is 36 inches long
18 inches wide
And 6 inches deep
How many cubic feet are in the box
3,888 ft³
Step-by-step explanation:
Multiply the dimensions together.
Therefore, the box is 3,888 ft³.
PLEASE HELP IM BEGGING YOU!!!
Find the value of x. Round angle measures to the nearest degree.
Answer:
61°Step-by-step explanation:
sin x = 29/33sin x =0.8787x = arcsin(0.8787)arcsin (0.8787) = 61.5°Correct choice is 61°
Please help with the attached file! Thank you
9514 1404 393
Answer:
see attached
Step-by-step explanation:
There is no 'y'. Your problem statement has a typo.
Pick any values of x you like. I find small integers are usually convenient. I also find a spreadsheet does repetitive evaluation very nicely. See the attached for an appropriate table.
Triangle EFG has vertices E(–3, 4), F(–5, –1), and G(1, 1). The triangle is translated so that the coordinates of the image are E’(–1, 0), F’(–3, –5), and G’(3, –3).
Which rule was used to translate the image?
T4, –4(x, y)
T–4, –4(x, y)
T2, –4(x, y)
T–2, –4(x, y)
Answer:
T2, –4(x, y)
Step-by-step explanation:
Pre image has taken place ⇒ 2 units Horizontally right and 4 unit vertically down to obtain vertices of Image.
Hence, Answer = T2, –4(x, y)
~Lenvy~
Answer: T2, –4(x, y)
Step-by-step explanation:
right on edge 2023
how many more grains of rice are in a fifty-pound bag of valencia rice than in a fifty pound bag of basmati rice
Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A fifty pound bag of basmati rice has 1.1 * 10³ grains in each ounce of 8 * 10² ounce and fifty pound bag of valencia rice has 1.2 * 10⁶ grains
Difference in number of grains = 1.2 * 10⁶ grains - (1.1 * 10³ grains * 8 * 10² ounce) = 3.2 * 10⁵ grains
Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice
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Ok what is the time and how do I actually get this free trial lol
the time is only 9:30 and fine in it lol
What is the measure of BAC. Degree of 53
Answer:
37
Step-by-step explanation:
y – 3(2y – 7) = 76
solve for Y!!
Answer:
y=-11
Step-by-step explanation:
Answer:
y = -11
Step-by-step explanation:
y – 3(2y – 7) = 76
y - 6y + 21 = 76
-5y + 21 = 76
-5y = 55
y = -11
Find the interest on 2180 for one year at simple interest 4%
please mark me as brainlest
Please click on this picture and explain why I got this answer wrong
Answer: $79.12
Step-by-step explanation:
We have to find total amount that was paid for dinner
5 people each order was worth $12.80
Therefore, total bill = 12.80*5
= $64
Tax: 7.5%
Therefore, the bill after tax was:
[tex]=64(\frac{100+7.5}{100})\\= 64(1.075)\\[/tex]
Bill with tax = $68.8
Gratuity = 15.0% of bill with tax
Therefore, gratuity = 0.15 * 68.8
= $10.32
Ended up paying in total = Gratuity + Bill with tax
= $68.8 + $10.32
= $79.12
A worker in the USA is paid $22,000 per year as a gross salary. The worker is asked to reduce her salary to $19,000 per annum. What is the percentage decrease? Round you answer to the nearest whole percent.
by name and label all inputs. 1: Saving for Retirement Devon is young and has just graduated college with her associate's degree. She plans to start saving money for retirement as soon as she starts her new job. By taking 10% of her monthly gross income, Devon is able to contribute (a) $ $587 each month to a retirement plan. The account is expected to earn interest with an APR of 5.25% compounded monthly. Round answers to two decimal places. a. How much money will be in Devon's retirement account if she continues to make the same monthly investment for 40 years? (3 pt) I b. Overall, Devon contributed how much of her own money into the retirement account? (4 pt)
The amount of money in Devon's retirement account if she saves $587 each month for 40 years is $956,488.14.
The total amount of her money contributed is $956,488.14.
What is the value of th retirement account?The formula that can be used to determine the future value of the retirement account is:
Future value = monthly contribution x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 5.25% / 12 = 0.4375%n = number of years = 40 x 12 = 480{[(1.004375^480) - 1] / 0.004375} x $587 = $956,488.14
Total contributions = $587 x 12 x 40 = $281,760
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8. An adult male elephant can weigh up to 15,000 pounds. How many tons is this?
show your work.
Answer:
this is 7.5 tons.
Step-by-step explanation:
Simply divide 15,000lbs by 2,000lbs (how many lbs in a ton), and you get 7.5!
what is -5½×2¾ ????
Answer:
Mixed fraction: -15 1/8
Improper fraction: 121/8
what is the magnitude of an account of -218 Dollars
Hey there!
The magnitude of 218 will always be 218 because the absolute value of a positive number is always itself. The magnitude of -218 will be 218 as well because the absolute value of a negative number is the positive version of the number without the negative sign. You are essentially dropping or ignoring the negative sign.
Therefore, the magnitude of an account of -218 Dollars is 218 dollars
Help ! What do we know about the slopes of two lines if we are told that the lines are parallel?
Answer:
they have the same slope
Step-by-step explanation:
because if they are parallel they have the same slope
Find a third degree polynomial with the given zeros and a leading coefficient of 4. 1/2, 3/2, 2
Answer:
[tex]4x^3-16x^2+19x-6[/tex]
Step-by-step explanation:
P(x)=a(x-r1)(x-r2)(x-r3)
This is a third degree polynomial of leading coefficient a, where r1, r2 and r3 are the roots.
So just replace it with the values you are asked for :
[tex]4\left(x-\frac{3}{2}\right)\left(x-\frac{1}{2}\right)\left(x-2\right)\\[/tex]
Then expand and you will find the answer : [tex]4x^3-16x^2+19x-6\\[/tex]
1. The full Renegade dance Jalaiah created is 56 seconds long. For a 15-second-long TikTok, what percent of Renegade is used?
Answer:
3.7
Step-by-step explanation:
You have to divide
Answer:
i do not know tbh .
Step-by-step explanation:
A rectangular table top has length 1.8 m and width 1.2 m.
A force of 600 N is applied to the whole table top.
Calculate the pressure in N/m2 to the nearest integer.
The equation of pressure is given by:
[tex]p = \frac{f}{s} [/tex]
where p is the pressure.
f is the applied force.
s is the surface area to which the force is applied.
I will start off by calculating the surface area of the table top given by:
[tex]s = l \times w = 1.8 \times 1.2 = 2.16[/tex]
s=2.16 m²
We know that f=400 N, that is given.
[tex]p = \frac{400 \: n}{2.16 \: m {}^{2} } [/tex]
Plug this on your calculator (excluding the units lol)
[tex]p = 185.185 \frac{n}{m {}^{2} } [/tex]
[tex]p = 185 \frac{n}{m {}^{2} } [/tex]
A study was conducted investigating the long-term prognosis of children who have suffered an acute episode of bacterial meningitis, an inflammation of the membranes enclosing the brain and spinal cord. Listed below are the times to the onset of seizure for 13 children who took part in the study [10]. In months, the measurements are: 0.10 0.25 0.50 4 12 12 24 24 31 36 42 55 96 60 Chapter 3 Numerical Summary Measures
(a) Find the following numerical summary measures of the data.
i. mean
ii. range
iii. median
iv. interquartile range
v. mode
vi. standard deviation
(b) Show that L.~,: 1 (x;- X) is equal to 0.
Answer:
I'll help you
Step-by-step explanation:
In the given set of data, mean is 0.352, range is 0.86, median is 0.31, interquartile range is 0.28, mode is 0.12 and 0.24, and standard deviation is 0.81.
What is a data set?A data set is a certain number of data given in any order.
Given, the measurements for 13 children are: 0.10, 0.25, 0.50, 0.4, 0.12, 0.12, 0.24, 0.24, 0.31, 0.36, 0.42, 0.55, 0.96.
By rearranging the data set in ascending order we get:
(0.10, 0.12, 0.12, 0.24, 0.24, 0.25, 0.31, 0.36, 0.4, 0.42, 0.50, 0.55, 0.96.)
1. Therefore, mean
= (0.10 + 0.25 + 0.50 + 0.4 + 0.12 + 0.12 + 0.24 + 0.24 + 0.31 + 0.36 + 0.42 + 0.55 + 0.96)/13
= 4.57/13
= 0.352
2. Therefore, range
= (0.96 - 0.10)
= 0.86
3. Therefore, median = 0.31
4. Here, median of the first half of the data set is
= Q₁
= (0.12 + 0.24)/2
= 0.18
Again, median of the second half of the data set is
= Q₃
= (0.42 + 0.50)/2
= 0.46
Therefore, the interquartile range
= (Q₃ - Q₁)
= (0.46 - 0.18)
= 0.28
5. Therefore, mode = 0.12, 0.24
6. Therefore, standard deviation is
= √[(x₁ - X)² + (x₂ - X)² + (x₃ - X)² + (x₄ - X)² + (x₅ - X)² + (x₆ - X)² + (x₇ - X)² + (x₈ - X)² + (x₉ - X)² + (x₁₀ - X)² + (x₁₁ - X)² + (x₁₂ - X)² + (x₁₃ - X)²]
Here, x₁, x₂,......, x₁₃ are given data set in ascending order.
X = mean of the given data set.
Therefore, standard deviation is
= √[(0.10 - 0.352)² + (0.12 - 0.352)² + (0.12 - 0.352)² + (0.24 - 0.352)² + (0.24 - 0.352)² + (0.25 - 0.352)² + (0.31 - 0.352)² + (0.36 - 0.352)² + (0.40 - 0.352)² + (0.42 - 0.352)² + (0.50 - 0.352)² + (0.55 - 0.352)² + (0.96 - 0.352)²]
= √[.064 + 0.054 + 0.054 + 0.013 + 0.013 + 0.01 + 0.0018 + 0.00006 + 0.0023 + 0.0046 + 0.023 + 0.039 + 0.37]
= √(.6488)
= 0.81
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three notebooks and 4 binders are $9.00. two notebooks and 4 binders cost $8.00. how much does a binder cost?
A 50 foot rope weighing a total of 32 lbs extended over a cliff that is 35 feet to the ground. A large 8 pound bucket with 19 gallons of water was tied to the end of the rope at the ground. A group of hikers at the top of the cliff lifted the bucket by pulling up the rope, but when the bucket reached the top, only 12 gallons of water remained (the water spilled out steadily on the way up). If water weighs 8.3 lbs. / gallon. write a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground, and use it to find the work to get the bucket to the top of the cliff.
Answer:
A function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is [tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex] and the work to get the bucket to the top of the cliff is 3726 foot-lbs
Step-by-step explanation:
Work done to lift the rope by distance x feet:
[tex]W_1=32(\frac{50-x}{2})[/tex]
Work done to lift the bucket by distance x feet:
[tex]W_2=(19-\frac{x}{5})(8.3)x[/tex]
On reaching top 7 gallons of water spilled out so , on going up by x feet [tex]\frac{7x}{35}=\frac{x}{5}[/tex] gallons of water spilled out.
a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground:
[tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex]
Now the work to get the bucket to the top of the cliff i.e. x =35
[tex]W=16(50-35)+(19-\frac{35}{5})(8.3)(35)[/tex]
W=3726
Hence, a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is [tex]W=16(50-x)+(19-\frac{x}{5})(8.3)x[/tex] and the work to get the bucket to the top of the cliff is 3726 foot-lbs
help is needed here please and thank you!
A news organization interested in chronicling winter holiday travel trends conducted a survey. Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays. Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays. Construct a 99% confidence interval for the difference in population proportions of people in the eastern half of a country who fly to visit family members for the winter holidays and people in the western half of a country who fly to visit family members for the winter holidays. Assume that random samples are obtained and the samples are independent. (Round your answers to three decimal places.) z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576
Answer:
(-0.481 , -0.144)
Step-by-step explanation:
Confidence Interval for difference is proportion formula is given as:
p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]
For p1
Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays.
n1 = 96 people
p1 = x/n
x = 42 people
p1 = 42/96
= 0.4375
1 - p1 = 0.5625
For p2
Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays.
n2 = 108 people
p2 = x/n
x = 81 people
p2 = 81/108
= 0.75
1 - p2 = 0.25
99% confidence interval = 2.576
p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]
= 0.4375 - 0.75 ± 2.576 ×√[0.4375(1 -0.4375)/96 +0.75 (1 - 0.75)/108]
= -0.3125 ± 2.576 × √0.4375× 0.5625/96 + 0.75 × 0.25 /108
= -0.3125 ± 2.576 × √0.0025634766 + 0.0017361111
= -0.3125 ± 2.576 × √0.0042995877
= -0.3125 ±2.576 × 0.0655712414
= -0.3125 ± 0.1689115178464
Confidence Interval
-0.3125 - 0.1689115178464
= -0.4814115178
Approximately to 3 decimal places = -0.481
= -0.3125 + 0.1689115178464
= -0.1435884822
Approximately to 3 decimal places = -0.144
Therefore, the 99% confidence interval for difference in proportion = (-0.481 , -0.144)