Answer:
B. 40
Step-by-step explanation:
What do you understand by sample size; a sample size is a little portion of a large number we which to investigate. Imagine we wanted to know the electricity consumption of people in a town of 200million people sometimes we could do that be investigating that of 50million especially when you know the conditions would be no different from others. In this sense the sample size is 50 million because that's the one we are investigating.
Similarly our concern of interest for investigation is 40, so that's the sample size.
Help! Which of the following side lengths would NOT make a right triangle?
Answer:
The Answer is 10, 50, and 54
Step-by-step explanation:
You want to figure this answer out by using the Pythagorean Theorem. If 10 squared plus 50 squared does not equal 54 squared, then those side lengths can not make a triangle.
graph of y=- 3x+2 is:
Answer:
GRAPH OF 3X+2 IS 6
Step-by-step explanation:
Answer:
The graph below
Step-by-step explanation:
The average cost of producing a single bicycle based on the total number of bicycles produced, x, is represented by this function:f(x)=800+30,000/xUse the drop-down menus to complete the statements to show the difference between the mathematical and reasonable ranges. The reasonable range includes the set of A whole number, B rational numbers,C integers, D real numbers where 800 < y ≤ , A 801, B 30,000, C 30,800, D 24,000,000 while the mathematical range includes the set of A whole numbers,B rational numbers C integers D real numbers and only excludes the value . A 0, B 800, C 30,800
Answer:
The correct answers are B, C, D, B
Step-by-step explanation:
These answers complete the statements that show the difference between the mathematical and reasonable ranges. Good luck! :)
B) Rational Numbers
C) 30,800
D) Real Numbers
B) 800
Correct on edge2020!
Answer:
BCDB
Step-by-step explanation:
which choice is equivalent to the fraction below?
Answer: 2 ÷ 17
Step-by-step explanation: When you have something in this form, a/b, it means the same thing as a divided by b.
So 2/17 means the same thing as 2 ÷ 17.
The following data represent the pulse rates? (beats per? minute) of nine students enrolled in a statistics course. Treat the nine students as a population.Complete parts ?(a) through? (c). Student Pulse ??Perpectual Bempah 64 ??Megan Brooks 77 ??Jeff Honeycutt 89 ??Clarice Jefferson 69 ??Crystal Kurtenbach 89 ??Janette Lantka 65 ??Kevin McCarthy 88 ??Tammy Ohm 69 ??Kathy Wojdya 87(a) Determine the population mean pulse. The population mean pulse is approximately nothing beats per minute. ?(Round to one decimal place as? needed.)(b) Determine the sample mean pulse of the following two simple random samples of size 3. Sample? 1: StartSet Janette comma Clarice comma Megan EndSet Sample? 2: StartSet Perpectual comma Clarice comma Megan EndSet The mean pulse of sample 1 is approximately nothing beats per minute. ?(Round to one decimal place as? needed.) The mean pulse of sample? 2, is approximately nothing beats per minute. ?(Round to one decimal place as? needed.)(c) Determine if the means of samples 1 and 2? overestimate, underestimate, or are equal to the population mean. The mean pulse rate of sample 1 ? (underestimates/ is equal to/ overestimates) the population mean. The mean pulse rate of sample 2 (is equal to/ underestimates/ or overestimates) the population mean.
Answer:
(a)77.4bpm
(b)Mean of Sample 1 = 70.3 beats per minute.
Mean pulse of sample 2 = 70 beats per minute.
(c)
The mean pulse rate of sample 1 underestimates the population mean. The mean pulse rate of sample 2 underestimates the population mean.Step-by-step explanation:
(a)Population mean pulse.
The pulse of the nine students which represent the population are:
Perpectual Bempah 64Megan Brooks 77Jeff Honeycutt 89 Clarice Jefferson 69Crystal Kurtenbach 89 Janette Lantka 65Kevin McCarthy 88Tammy Ohm 69Kathy Wojdya 87[tex]\text{Population Mean} =\dfrac{64+77+89+69+89+65+88+69+87}{9} \\=\dfrac{697}{9} \\\\=77.44[/tex]
The population mean pulse is approximately 77.4 beats per minute.
(b)Sample 1: {Janette,Clarice,Megan}
Janette: 65bpmClarice: 69bpmMegan: 77bpmMean of Sample 1
[tex]\text{Sample 1 Mean} =\dfrac{65+69+77}{3} \\=\dfrac{211}{3} \\\\=70.3[/tex]
Sample 2: {Janette,Clarice,Megan}
Perpetual: 64bpmClarice: 69bpmMegan: 77bpmMean of Sample 2
[tex]\text{Sample 2 Mean} =\dfrac{64+69+77}{3} \\=\dfrac{210}{3} \\\\=70[/tex]
The mean pulse of sample 1 is approximately 70.3 beats per minute.
The mean pulse of sample 2 is approximately 70 beats per minute.
(c)
The mean pulse rate of sample 1 underestimates the population mean. The mean pulse rate of sample 2 underestimates the population mean.For the function, find all critical numbers and then use the second-derivative test to determine whether the function has a relative maximum or minimum at each critical number. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x) = x3 − 12x2 + 21x − 8relative maxima x=relative minima x=
Answer:
relative maximum: x = 1
relative minimum: x = 7
Step-by-step explanation:
Critical points:
Values of x for which f'(x) = 0.
Second derivative test:
For a critical point, if f''(x) > 0, the critical point is a relative minimum.
Otherwise, if f''(x) < 0, the critical point is a relative maximum.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]f(x) = x^{3} - 12x^{2} + 21x - 8[/tex]
Finding the critical points:
[tex]f'(x) = 3x^{2} - 24x + 21[/tex]
[tex]3x^{2} - 24x + 21 = 0[/tex]
Simplifying by 3
[tex]x^{2} - 8x + 7 = 0[/tex]
So [tex]a = 1, b = -8, c = 7[/tex]
[tex]\bigtriangleup = (-8)^{2} - 4*1*7 = 36[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{36}}{2} = 7[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{36}}{2} = 1[/tex]
Second derivative test:
The critical points are x = 1 and x = 7.
The second derivative is:
[tex]f''(x) = 6x - 24[/tex]
[tex]f''(1) = 6*1 - 24 = -18[/tex]
Since f''(1) < 0, at x = 1 there is a relative maximum.
[tex]f''(7) = 6*7 - 24 = 18[/tex]
Since f''(x) > 0, at x = 7 there is a relative minumum.
Suppose that in a certain sinkhole the ground dropped 69.6 ft in 24 hr. Find the unit rate representing the change in altitude per hour ..the unit rate representing the change in altitude is how many feet per hour
Answer:
2.9 per hour
Step-by-step explanation:
Divide 69.9 by 24
The dimensions of the base of Box 1 are x by 3x.
The base area of Box 1 is:
3x
3.x2
3r3
4x
Answer:
3x²
Step-by-step explanation:
The area is the product of the dimensions of the base:
area = x(3x) = 3x²
A coin is tossed twice in succession. Let A be the event that the first toss is heads and let B the event that the second toss is heads. Find: (a) P(A) (b) P(B) (c) P(A∩B) (d) P(B /A)
Answer:
Step-by-step explanation:
A coin has two faces, a head (H) or tail (T). Tossing a coin twice in succession would give the following sample size;
{HH, HT, TH, TT}
Given that: A = first toss is heads, B = second toss is heads, then:
i. P(A) = {HH, HT} = 2
ii. P(B) = {TH} = 1
iii. P(A∩B) = {HH} = 1
iv. P(B /A) = [tex]\frac{1}{2}[/tex]
On Saturday, a local hamburger shop sold a combined total of 432 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday
Answer: 268 hamburgers
What is the simplified form of this expression?
Answer:
[tex]=13x+5[/tex]
Step-by-step explanation:
[tex]\left(2x+9\right)+\left(11x-4\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=2x+9+11x-4\\\mathrm{Group\:like\:terms}\\=2x+11x+9-4\\\mathrm{Add\:similar\:elements:}\:2x+11x=13x\\=13x+9-4\\\mathrm{Add/Subtract\:the\:numbers:}\:9-4=5\\=13x+5[/tex]
f(x) = 2x - 2
Find f(3)
Step-by-step explanation:
Replace x = 3
f(3) = 2(3) - 2
= 6 - 2
= 4
Answer:
f(3) =4
Step-by-step explanation:
f(x) = 2x - 2
Let x=3
f(3) = 2*3 - 2
= 6-2
= 4
Un bosque de 2 km2 está formado por hayas y pinos. Las hayas ocupan 380.000 m2 ¿Cuántos metros cuadrados ocupan los pinos?
Answer:
Los pinos ocupan [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.
Step-by-step explanation:
Una manera de resolver este problema es la siguiente:
[tex] \\ 1km^{2} = 1km * 1km = 1000m * 1000m = 1000000m^{2}[/tex]
[tex] \\ 2km^{2} = 2km * 1km = 2000m * 1000m = 2000000m^{2} = 2 * 10^{6}m^{2}[/tex]
En palabras, [tex] \\ 2km^{2} = 2000000m^{2}[/tex], o dos kilómetros cuadrados son iguales a 2 millones de metros cuadrados.
Sabemos que:
Estos [tex] \\ 2km^{2} = 2000000m^{2}[/tex] de bosque lo ocupan hayas y pinos, y, adicionalmente, Las hayas ocupan [tex] \\ 380000m^{2}[/tex].De esta manera, la parte que ocupan los pinos es el total del bosque menos el área ocupada por las hayas. Por lo tanto, el área ocupada por los pinos es:
[tex] \\ 2000000m^{2} - 380000m^{2}[/tex]
[tex] \\ 1620000m^{2}[/tex]
¿Cuántos metros cuadrados ocupan los pinos?
Los pinos ocupan, entonces, [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.
Data from the U.S. Department of Education indicates that 46% of business graduate students from private universities had student loans. Suppose you randomly survey a sample of graduate business students from private universities. Consider the sampling distribution (sample size n = 215) for the proportion of these students who have loans.What is the mean of this distribution?What is the standard deviation of this sampling distribution (i.e., the standard error)?
Answer:
For this case the mean is given by:
[tex] \mu = p =0.46[/tex]
And the standard deviation would be:
[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]
Step-by-step explanation:
For this case we have the following info given :
[tex] n = 215[/tex] represent the sample size
[tex]p = 0.46[/tex] represent the proportion of business graduate students from private universities had student loans
For this case we want to find the distribution for the sample proportion and we know that this distribution is given by:
[tex] \hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]
And for this case the mean is given by:
[tex] \mu = p =0.46[/tex]
And the standard deviation would be:
[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]
Answer:
The mean of this distribution is 0.46 and the standard deviation is 0.034.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For sampling distributions of samples of size n of a proportion p, the mean is [tex]\mu = p[/tex] and the standard deviation is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]n = 215, p = 0.46[/tex]
So
[tex]\mu = 0.46, s = \sqrt{\frac{0.46*0.54}{215}} = 0.0340[/tex]
The mean of this distribution is 0.46 and the standard deviation is 0.034.
Mr. Evans is considering offering a second after-school tutoring session for his math students each week. He records the number of
students who attend his current sessions each week. The results from the last twelve weeks are shown in the dot plot below.
+
1 2
+
0
+
3
4 5 6 7 8 9 10 11 12 13 14 15
Number of Students
Which statement properly describes the data?
There is not enough information to determine if the data is skewed.
O
The data is symmetric.
The data is skewed right.
The data is skewed left.
Answer:
Step-by-step explanation:
the data is skewed left
The data in the given set is skewed towards left because the mean of the data is 7.5 and the data is not distributed symmetrically in the given set. Thus, the correct option is C.
What is a Skewed data set?Skewed data is the data which creates an asymmetrical, skewed curve on the graph scale. In statistics, the graph of a data set with normal distribution is symmetrical and has a bell-like shape. However, the skewed data has a tail on either side of the graph as well.
Skewness can be demonstrated on a bell curve when the data points are not distributed symmetrically to the left and right sides of the median on the curve. If the bell curve is shifted to the left or towards the right side, it is said to be skewed curve. The two halves of the distribution are not mirror images in the skewed curve because the data are not distributed equally on both sides of the distribution peak.
Therefore, the correct option is C.
Learn more about Skewed data here:
https://brainly.com/question/3907939
#SPJ2
Find the volume of the rectangular prism in cubic centimeters.
(V2 Lowoh)
a. 30
b. 210
7 cm
c. 70
d. 280
10 cm
3 cm
WILL MARK BRAINLIEST !!! NEED HELP
Answer:
[tex] y = -\frac{1}{3}x-2[/tex]
Step-by-step explanation:
From the table it is clear that the line is passing through the points [tex] (0,\: -2)= (x_1, \:y_1) \: \&\: (-6, \:0)=(x_2,\:y_2) [/tex]
(There are many other points in the table and any two of them can chosen as per our convenience)
Equation of line in two point form is given as:
[tex] \frac{y-y_1}{y_1 - y_2} = \frac {x-x_1}{x_1 - x_2} \\\\
\therefore \frac{y-(-2)}{-2 - 0} = \frac {x-0}{0 - (-6)} \\\\
\therefore \frac{y+2}{-2} = \frac {x}{0+6)} \\\\
\therefore \frac{y+2}{-2} = \frac {x}{6)} \\\\
\therefore 6(y + 2) = - 2(x)\\
\therefore 6y + 12 = - 2x \\
\therefore 6y = - 2x - 12\\\\
\therefore y = -\frac{2}{6}x-\frac{12}{6}\\\\
\huge \red {\boxed {y = -\frac{1}{3}x-2}} \\\\[/tex]
Identify the graph of the equation. What is the angle of rotation for the equation?
y2 + 8x = 0
hyperbola; 30°
b. parabola; 90°
a.
C.
d.
hyperbola; 180°
parabola; 0°
Answer:
D. Parabola; 0°
Step-by-step explanation:
Choose the correct answer below. A. The mean MPG of this type of vehicle for 95% of all samples of the same size is contained in the interval. B. 95% of the sample data fall between the limits of the confidence interval. C. We have 95% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval. D. We have 95% confidence that the population mean MPG of this type of vehicle is contained in the interval.
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is
The table below contains the overall miles per gallon (MPG) of a type of vehicle. Complete parts a and b below.
28, 34, 28, 20, 21, 31, 28, 24, 34, 35 , 36, 26, 25, 20
a. Construct a 95% confidence interval estimate for the population mean MPG for this type of vehicle, assuming a normal distribution.
b. Choose the correct answer below.
A. We have 95% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval.
B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval. This is the correct answer.
C.95 % of the sample data fall between the limits of the confidence interval.Your answer is not correct.
D. The mean MPG of this type of vehicle for 95?% of all samples of the same size is contained in the interval.
Solution:
a) Mean = (28 + 34 + 28 + 20 + 21 + 31 + 28 + 24 + 34 + 35 + 36 + 26 + 25 + 20)/14 = 27.86
Standard deviation = √(summation(x - mean)²/n
n = 14
Summation(x - mean)² = (28 - 27.86)^2 + (34 - 27.86)^2 + (28 - 27.86)^2 + (20 - 27.86)^2 + (21 - 27.86)^2+ (31 - 27.86)^2 + (28 - 27.86)^2 + (24 - 27.86)^2 + (34 - 27.86)^2 + (35 - 27.86)^2 + (36 - 27.86)^2 + (26 - 27.86)^2 + (25 - 27.86)^2 + (20 - 27.86)^2 = 399.7144
Standard deviation = √(399.7144/14) = 5.34
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 5.34
n = number of samples = 14
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 14 - 1 = 13
Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05
α/2 = 0.05/2 = 0.025
the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975
Looking at the t distribution table,
z = 2.16
Margin of error = 2.16 × 5.34/√14
= 3.08
The confidence interval is 27.86 ± 3.08
b) B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval.
Choose the best answer to explain whether the question is statistical or not statistical. How far from work do all the employees live?
Answer: statistical
Step-by-step explanation: A statistical – is a question that can be answered by collecting data and that anticipates variability in those data • Statistics – the science of collecting, reviewing, and analyzing data
Sky and Natalia shared some money in the ratio 6:5.
Sky gets £3 more than Natalia.
How much does Natalia receive?
Let the amount that Sky receives be S, and the amount that Natalia recieves be N.
[tex] \dfrac{s}{n} = \dfrac{6}{5} [/tex]
[tex]s = n + 3 \\ \\ \dfrac{n + 3}{n} = \frac{6}{5} \\ \\ 5n + 15 = 6n \\ \\ n = 15[/tex]
15 euros
if a quadratic equation with real coefficients has a discriminant of -36 then what type of roots does it have
Step-by-step explanation:
We have,
If a quadratic equation with real coefficients has a discriminant of -36.
The general form of quadratic equation is :
[tex]ax^2+bx+c=0[/tex]
The discriminant of this equation is : [tex]D=b^2-4ac[/tex]
If D=0, it will have 1 real roots
If D>0, it will have 2 real roots
If D<0, it will have no real roots
We have,
D = -36 < 0, so, the quadratic equation will have no real roots.
plss help bring up my grade
Answer:
117 units cubed.
Step-by-step explanation:
I have attached the work to your problem.
Please see the attachment below.
I hope this helps!
Answer:
117
Step-by-step explanation:
find all the shown surface area
The 10th grade class at Central high school was surveyed about whether they liked running or swimming. Of those surveyed, 58% said they liked to swim and 36% said they liked to run. If 18% said they liked both swimming and running, what percent of those surveyed liked neither?
Answer:
24% of those surveyed liked neither
Step-by-step explanation:
Set concepts:
We use set concepts to solve this question.
I am going to say that:
P(A) is the percentage of people that liked to swim.
P(B) is the the percentage of people that liked to run.
The percentage of people that liked at least one of these activities is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In which [tex]P(A \cap B)[/tex] is the probability that a person liked both these activities.
The percentage of people that liked neither is:
[tex]P = 1 - P(A \cup B)[/tex]
Of those surveyed, 58% said they liked to swim and 36% said they liked to run.
This means that [tex]P(A) = 0.58, P(B) = 0.36[/tex]
18% said they liked both swimming and running
This means that [tex]P(A \cap B) = 0.18[/tex]
What percent of those surveyed liked neither?
At least one:
[tex]P(A \cup B) = 0.58 + 0.36 - 0.18 = 0.76[/tex]
Neither:
[tex]P = 1 - P(A \cup B) = 1 - 0.76 = 0.24[/tex]
24% of those surveyed liked neither
Question 1:Lauren wants to buy 3 shirts at $15.00 each. At home, she calculates the total cost as $46.20, using the sales tax of 8%. At the store, Lisa (the cashier) tells Lauren the total cost is $48.60. Which person is wrong, Lauren or Lisa
Question 2:What’s the cost of the shirts before tax
Question 3:How much is the sales tax for all shirts
Question 4:What is the total cost of the shirts, including tax?
Answer:
Lauren is wrong
Step-by-step explanation:
1. Lauren is wrong
2. What’s the cost of the shirts before tax
Each shirt cost $15 and the total = $15 x 3 = $45
3. How much is the sales tax for all shirts
Sale tax for all shirts is $45 x 0.08 = $3.6
4. What is the total cost of the shirts, including tax?
Total cost = $45 + $3.6 = $48.60
can the square root of a rational number be irrational?
Answer:
Yes. Some examples are √2, √3, √5.
You better believe it ! In fact, if you don't count an infinite number of examples, you'll find that MOST of their square roots are irrational.
Let's examine the smallest 1,000 integers . . .
-- They're all rational numbers, but ...
-- only 31 of them have rational square roots !
On the dietitians beverage tray are 16 filled six ounce glasses. Four glasses contain prune juice and two glasses contain apple juice. What fractional part of the glasses contain some other beverage?( perhaps, H2O) than prune juice and apple juice?
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
Given:
Total number of glasses = 16
Number of glasses containing prune juice = 4
Number of glasses containing apple juice = 2
To find: fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice
Solution:
A fraction refers to the parts of a whole. In a fraction, a top number is the numerator, and a bottom number is the denominator.
Number of glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = 16 - 4 - 2 = 10
Total number of glasses = 16
So,
Fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = [tex]\frac{10}{16}=\frac{5}{8}[/tex]
If the average ago of retirement for a random sample of 87 retired persons is 66 years with a standard deviation of 2 years.a. b. c. d.e.f.g. Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more. Find all values to 3 decimal places.
Answer:
0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 66, \sigma = 2, n = 87, s = \frac{2}{\sqrt{87}} = 0.214[/tex]
Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
This probability is 1 subtracted by the pvalue of Z when X = 66.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{66.5 - 66}{0.214}[/tex]
[tex]Z = 2.336[/tex]
[tex]Z = 2.336[/tex] has a pvalue of 0.99.
1 - 0.99 = 0.01
0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
A cylindrical tank with a cross-sectional area of 441 cm squared is filled to a depth of 441 cm with water. At tequals0, a drain in the bottom of the tank with an area of 21 cm squared is opened, allowing water to flow out of the tank. The depth of water in the tank at time tgreater than or equals0 is d(t)equals(21 minus 1.1 t )squared.
At what time is the tank empty?
Hurry please! I really need help For what value of the variable is the value of 3−5c one less than the value of 1−c?
Answer:
Any values that is greater than 1/2.
Step-by-step explanation:
You have to form an inequality. Given that what values is added to c will satisfy that 3 - 5c is less than 1 - c :
[tex]3 - 5c < 1 - c[/tex]
Next, you have to solve :
[tex] - 5c + c < 1 - 3[/tex]
[tex] - 4c < - 2[/tex]
[tex]c > \frac{ - 2}{ - 4} [/tex]
[tex]c > \frac{1}{2} [/tex]
