Answer:
a) CI = (113,637.5 , 124,672.5)
b) CI = (112,581 , 125,729)
c) CI = (110,501.4 , 127,808.6)
Step-by-step explanation:
You have the following information:
[tex]\overline{x}[/tex]: mean annual household income = 119,155
σ: standard deviation = 30,000
n: sample = 80
The interval of confidence is given by the following expression:
[tex]\overline{x}\pm Z_{\alpha/s}(\frac{\sigma}{\sqrt{n}})[/tex]
Z_α/2: distribution density factor
where α and Z_α/2 are given by the range of the confidence interval.
a) For a 90% confidence interval you have:
α = 1 - 0.9 = 0.1
Z_0.1/2 = Z_0.05 = 1.645 (found in a table of normal distribution)
You replace in the equation (1) to obtain the confidence interval:
[tex]119,155\pm (1.645)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm5,517.5[/tex]
Then, the confidence interval is (119,155 + 5,517.5 , 119,155 - 5,517.5 )
= (113,637.5 , 124,672.5)
b) For a 95% confidence interval you have:
α = 1 - 0.95 = 0.05
Z_0.05/2 = Z_0.025 = 1.96
[tex]119,155\pm (1.96)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 6,574.0[/tex]
The confidence interval is (112,581 , 125,729)
c) For a 99% confidence interval:
α = 1 - 0.99 = 0.01
Z_0.01/2 = Z_0.005 = 2.58
[tex]119,155\pm (2.58)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 8,653.6[/tex]
The confidence interval is (110,501.4 , 127,808.6)
d) When the confidence level increases the width of the confidence increases too. This can be noticed in the normal distribution, when the confidence level is higher, the area of the tails is reduced, and so, the confidence interval is higher.
Please answer this correctly
Answer:
0
Step-by-step explanation:
No one is there which satisfies the condition
Answer:
0 or 0/9 of the club members
Step-by-step explanation:
The only part of the data of members that have logged more than 1 1/5 but less than 1 3/5 hours is the members that logged 1 2/5 hours. There are no members that have logged 1 2/5 hours so our answer is 0 or 0/9.
Two barrels are mathematically similar
The smaller barrel has a height of [tex]h[/tex]cm and a capacity of 100 Liters
The larger barrel has a height of 90cm and a capacity of 160 Liters
-Work out the value of [tex]h[/tex]
Answer:
h ≈ 77 cm
Step-by-step explanation:
Let us convert the liters to cm³.
Smaller barrel
0.001 litres = 1 cm³
100 litres = 100000 cm³
Larger barrel
0.001 litres = 1 cm³
160 litres = 160000 cm³
For a similar solid figure the cube of their corresponding sides is equal to the volume ratio.
This means
h³/90³ = 100000/160000
cube root both sides
h/90 = ∛100000 / ∛160000
h/90 = 46.4158883/54.2883523
cross multiply
54.2883523h = 46.4158883 × 90
54.2883523h = 4177.429947
divide both side by 54.2883523
h = 4177.429947/54.2883523
h = 76.9489175858
h ≈ 77 cm
A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =
Answer:
a) [tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex], b) [tex]\frac{dB}{dt}\approx 5.595[/tex]
Step-by-step explanation:
a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:
[tex]\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})[/tex]
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex]
b) The rate of increase after one day is:
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)[/tex]
[tex]\frac{dB}{dt}\approx 5.595[/tex]
find the common difference of the arithmetic sequence 4, 10, 16,...
4+6=10+6=16+6=22+6=28...
I hope it is helpful for everyone
Do you think a sequence of translations across the x- or
y-axis and/or reflections on a figure could result in the
same image as a 90-degree clockwise rotation? Explain
why or why not.
I think just two reflections would do it.
First we reflect around y = -x, the 45 degree line through the origin and the second and fourth quadrant.
Then we reflect through the y axis, x=0.
The composition of the two reflections is equivalent to a 90 degree clockwise rotation.
Answer: No, it is not possible to get the same image as a 90-degree clockwise rotation using only translations and/or reflections. In the rotation, the x- and y-coordinates are switched. There is no way to reverse the order of the coordinates using only reflections or translations.
Step-by-step explanation:
ITS CORRECT. EDGE 2020
Parallelogram L M N O is shown. Angle M is (3 x minus 55) degrees, angle N is (5 y) degrees, and angle O is (2 x) degrees. In parallelogram LMNO, what are the values of x and y?
Answer:
x=55,y=14
Step-by-step explanation:
<M = <{opposite angles of a parallelogram are congruent and equal}
Hence 3x-55 = 2x=>3x-2x= 55 =>x=55
Simarly;
M+N=180°{ sum of angles in a parallelogram is 180°}
N= 180°-M=>N=180-(3x-55)=180-(3x55-55)= 180- 110=70°
N=70°=>5y=70=>y=70/5=14
therefore x=55,y=14
Answer:
55 and 14
Step-by-step explanation:
i just took the test
How can I make the red segment less steep than the blue segment , and more steep than the green segment ?
Translate the phrase into a variable expression. Use the letter d to name the variable. If necessary use the asterisk for multiplication and the slash for division. the product of 40 and distance to the finish line
Answer:
40*d
Step-by-step explanation:
The word product means multiplication, and here it is multiplying 40 and the distance(d).
Answer:
40x5
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Volume of sphere = (4/3)πr³
= 4/3(3.14)(d/2)³
= 4/3(3.14)(7/2)³
= 4/3(3.14)(3.5)³
= 4/3(3.14)(42.875)
= (1.33)(3.14)(42.875)
= 179.5 cm³
Answer:
The answer is 179.5 cm^2
The sum of two numbers is 978. One of the numbers is 152. What is the other number?
Answer:
826
Step-by-step explanation:
a+b=978
a=152
b=978-152=826
What is the answer ?
Answer:
[tex]f = \frac{1}{ {d}^{2} } [/tex]
what is the common ratio of the geometric sequence below ?
-96,48,-24,12,-6...
Answer:
r = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The common ratio r is the ratio between consecutive terms in the sequence.
r = [tex]\frac{48}{-96}[/tex] = [tex]\frac{-24}{48}[/tex] = [tex]\frac{12}{-24}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex]
Answer:
-1/2 or b on edge
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
S ≈ 9.8
Step-by-step explanation:
Finding central angle of circle A first
S=r∅
6.5 = (4)∅
Central angle = 6.5/4
C A = 1.63(in radians)
Now finding Arc EF
S = r∅
S = (6)(1.63)
S = 9.75
S ≈ 9.8
A triangle with side lengths is 5,5,8 is what type of triangle
Answer:
isosceles triangle
Step-by-step explanation:
The volume of a triangular prism is increased by a factor of 8.
By what factor is the surface area of the figure increased?
o 2
o 4
016
o 24
Change the fraction1/5 to a percent
Answer:
Step-by-step explanation:
A study compared paired daytime and nighttime counts of sea trout, lake trout, and rainbow trout made by the same divers in six lakes during September 2015. Overall, they counted 127 trout during the day and 356 trout at night. The researchers speculate that trout counted at night were present during the daytime but were hidden from view. Biologists should consider that trout behavior and susceptibility to being seen might vary a great deal between daytime and nighttime, even during the summer. In some lakes, the majority of trout may not be seen during the daytime. Determine whether the study is an observational study or an experiment. Justify your answer with specific references to the information in the study.
Answer:
Observational Study
Step-by-step explanation:
An experimental study is a research study in which conditions are under the direct manipulation of the investigator. We use it to mainly test the efficacy of a medical, preventive, or therapeutic measure.
In an observational study, on the other hand, the researcher observes the effect without trying to influence the outcome in any way.
In this study, the researchers are trying to determine the paired daytime and nighttime counts of the species of fishes made by the same divers in six lakes during September 2015.
This is simply an Observational Study as nothing is done to influence the population count.
Please answer this correctly
Answer:
169.5 yd²
Step-by-step explanation:
See attachment.
In situations like this, ALWAYS (!) make as sketch.
Divide the areas by adding dotted lines on sensible places, and write in the missing numbers for the correct distances.
The only possible difficult one is the triangle, which is the half of a rectangle. So you are dealing with a series of areas of rectangles. That is really easy if you understand what you are doing.
Total area =
area 1 + area 2 + area 3 + area 4
10*4 + 4*7 + 3*13 + (0.5 * 7*17)
40 + 28 + 42 + 59.5
Total area = 169.5 yd²
It is believed that approximately 12% of the population of the United States is lefthanded. Suppose researchers suspect that the proportion of left-handed people is higher in certain states than the national average. The researchers conduct a sample of 200 randomly selected people in the state of Maine and find that 29 people in the sample are left-handed.
a. Write the null hypothesis and alternative hypothesis and define your parameter.
b. Show that the necessary conditions (Randomization Condition, 10% Condition, Sample Size Condition) are satisfied to perform a hypothesis test. Briefly explain how each condition is satisfied.
c. Perform the hypothesis test and find the P-value. (To show your work: Write down what values you are entering into the hypothesis testing calculator.)
d. Is there strong evidence that the left-handed rate in the state of Maine is higher than the national average? Briefly explain how you know.
Answer:
Step-by-step explanation:
a. Null hypothesis: P = p
Alternatives hypothesis: P =/ p
Where P is the hypothesized population proportion and p is the sample proportion
b. Performing a test of proportions
Randomization: the sample was randomly selected in the study
The population size is at least 20 times as big as the sample size.
The sample includes both successes and failures with 29 success and 171 failures.
c. To perform the hypothesis test: we have to find the standard deviation first
Sd = sqrt[ P * ( 1 - P ) / n ]
where P is the hypothesized value of population proportion, n is the sample size.
Sd = √[0.12*(1-0.12)/200]
Sd = √[0.12*(0.88/200]
Sd = √[0.12*(0.0044)]
Sd = √0.000528
Sd = 0.023
Then we can find the z score
z = (p - P) / σ where p = 29/200 = 0.145
z = (0.145-0.12)/ 0.023
z = 0.025/0.023
z = 1.09
Calculation the p value using 0.05 level of significance and a two waited test (p value calculator),
A p-value of 0.2757 which is greater than 0.05, thus we will fail to reject the null stating that there is not enough strong evidence that the left-handed rate in the state of Maine is higher than the national average.
A survey found that women's heights are normally distributed with mean 63.3 in. and standard deviation 2.7 in. The survey also found that men's heights are normally distributed with a mean 67.3 in. and standard deviation 2.8. Complete parts a through c below.
a) most of the live characters at an amusement park have height requirements with a minimum of 4ft 9in and a maximum of 6ft 4in find the percentage of women meeting the height requirement
the percentage of woment who meet the height requirement?
(round to two decimal places as needed)
b) find the percentage of men meeting the height requirement
the percentage of men meeting the height requirement
(round to two decimal places as needed )
c) If the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women what are the new height requirements
the new height requirements are at least ___ in. and at most ___ in.
(round to one decimal place as needed)
a) The percentage of women meeting the height requirement is approximately 99.99%.
b) The percentage of men meeting the height requirement is approximately 99.95%.
c) The new height requirements are at least 58.5 inches and at most 71.8 inches.
a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.
First, we standardize the height requirement using the formula:
Z = (X - μ) / σ
where X is the value (height), μ is the mean, and σ is the standard deviation.
For the lower limit (57 inches):
Z_lower = (57 - 63.3) / 2.7 ≈ -2.33
For the upper limit (76 inches):
Z_upper = (76 - 63.3) / 2.7 ≈ 4.70
Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.
The percentage of women meeting the height requirement is approximately 99.99%.
b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:
For the lower limit (57 inches):
Z_lower = (57 - 67.3) / 2.8 ≈ -3.68
For the upper limit (76 inches):
Z_upper = (76 - 67.3) / 2.8 ≈ 3.11
Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.
The percentage of men meeting the height requirement is approximately 99.95%.
c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.
For men:
Z_upper_men = Z(0.95) ≈ 1.645
For women:
Z_lower_women = Z(0.05) ≈ -1.645
Using these Z-scores, we can calculate the new height requirements:
For the new lower limit:
X_lower = Z_lower_women * σ + μ
For the new upper limit:
X_upper = Z_upper_men * σ + μ
Substituting the values:
X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches
X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches
Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.
For more such question on percentage visit:
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a) The percentage of women meeting the height requirement is 99.99%.
b) The percentage of men meeting the height requirement is 99.95%.
c) The new height requirements are at least 58.5 inches and at most 71.8 inches.
a) For women meeting the height requirement:
Given: Mean (μ) = 63.3 in.
Standard Deviation (σ) = 2.7 in.
So, Minimum height requirement:
= 4 ft 9 in
= 4 * 12 + 9
= 57 inches
and, Maximum height requirement:
= 6 ft 4 in
= 6 * 12 + 4
= 76 inches
We will calculate the Z-scores for these heights using the formula:
Z = (x - μ) / σ
For the minimum height requirement:
[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33
For the maximum height requirement:
[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70
So, the the area between -2.33 and 4.70.
Thus, the percentage is 99.99%.
b) For men meeting the height requirement:
Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.
Minimum height requirement: 4 ft 9 in = 57 inches
Maximum height requirement: 6 ft 4 in = 76 inches
For the minimum height requirement:
[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68
For the maximum height requirement:
[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11
So, the area between -3.68 and 3.11.
Thus, the percentage is 99.95%.
c) For the new height requirements:
For men:
[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645
For women:
[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645
For the new lower limit:
[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]
For the new upper limit:
[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]
Substituting the values:
[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]
= 58.53 inches
and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]
= 71.78 inches
Therefore, the new height at least 58.5 inches and at most 71.8 inches.
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Hello! I'm stuck on this problem. Can someone help me? Thanks!
The model below represents an equation.
2 long x tiles and 3 square 1 tiles = 3 long x tiles
Which represent like terms in the model of the equation?
2 long x tiles and 3 square 1 tiles
2 long x tiles and 3 long x tiles
3 long x tiles and 3 square 1 tiles
1 long x tile and 1 square 1 tile
Answer:
Answer is B
Step-by-step explanation:
This is because you can combine both the green tiles. With the other options, you can't combine them.
(also I did the test )
Answer:
The answer is in ur head lololol
Step-by-step explanation:
Its b
If the size of the sample to be used in a particular test of attributes has not been determined by utilizing statistical concepts, but the sample has been chosen in accordance with random selection procedures
A) No inferences can be drawn from the sample.
B) The auditor has committed a nonsampling error.
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
D) The auditor will have to evaluate the results by reference to the principles of discovery sampling.
E) The auditor may or may not achieve the desired
Answer:
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
Step-by-step explanation:
In a concept of risk sampling, if the sample size is chosen randomly in accordance with random selection procedures, the auditor may or may not achieve the desired risk of assessing risk too low. In other words the auditor may or may not achieve desired precision. This is because a samole chosen randomly may not represent the true population.
This depends largely on the sample size. If the sample size selected is too small, the allowance for sampling risk will be larger than what is required because it will lead to a large standard error of the mean
Anyone know this at all?
Answer:
24.2
Step-by-step explanation:
You are given the hypotenuse and angle, and you want to find the length of the adjacent side.
The mnemonic SOH CAH TOA reminds you that the relation between angle and sides is ...
Cos = Adjacent/Hypotenuse
cos(41°) = x/32
x = 32·cos(41°)
x ≈ 24.2
The set of whales is a proper subset of the set of mammals.
What is the value of g-1(7)
Answer:
g-7
Step-by-step explanation:
Multiply the numbers
g-(1*7)
g-7
Answer:
5
Step-by-step explanation:
We know that g is an invertible function and so it must also be a one-to-one function.
This means that each input is paired with exactly one output and that each output is paired with exactly one input.
We know that g(a)=7g and g(5)=7. If the output of 7 is to be paired with exactly one input, then a must be equal to 5.
Solve the following equation. x + 6 = x + x
Answer:
x = 6
Step-by-step explanation:
x + 6 = x + x
Combine like terms
x+6 =2x
Subtract x from each side
x+6-x = 2x-x
6 = x
please help :( really need answer
Answer:
Options (C) and (F)
Step-by-step explanation:
Polynomial function is,
f(x) = x³ - x² - 5x - 3
Possible rational roots of the given function will be = [tex]\frac{\pm1, \pm3}{\pm1}[/tex]
By putting x = -1
f(-1) = (-1)³ - (-1)² -5(-1) - 3
= -1 - 1 + 5 - 3
= 0
Therefore, x = -1 will a root of the given function.
Now we apply synthetic division to get the other roots,
-1 | 1 -1 -5 -3
↓ -1 2 3
1 -2 -3 0
Therefore, factored form of the polynomial will be (x + 1)(x² - 2x - 3).
Now we will find the roots of (x² -2x - 3).
x² - 2x - 3 = x² - 3x + x - 3
= x(x - 3) + 1(x - 3)
= (x + 1)(x - 3)
For roots of the function, f(x) = 0
(x + 1)(x - 3) = 0
x = -1, 3
Therefore, roots of the function are x = -1, 3
Options (C) and (F) are the answers.
PLEASE HELP
Which of the following is an arithmetic sequence?
A: -2, 4, -6, 8, ...
B: -8, -6, -4, -2, ...
C: 2, 4, 8, 16, ...
What role did youth play in the Civil Rights Movement?
Answer:
they played the pivotal role
Which choice is equivalent to the expression below?
root-81
A. 9i
B. i root9
C. root9i
D. -9
E. -root9
Answer: B
Step-by-step explanation:
