Answer:
Step-by-step explanation:
Hello!
To see if driving heavy equipment on wet soil compresses it causing harm to future crops, the penetrability of two types of soil were measured:
Sample 1: Compressed soil
X₁: penetrability of a plot with compressed soil.
n₁= 20 plots
X[bar]₁= 2.90
S₁= 0.14
Sample 2: Intermediate soil
X₂: penetrability of a plot with intermediate soil.
n₂= 20 (with outlier) n₂= 19 plots (without outlier)
X[bar]₂= 3.34 (with outlier) X[bar]₂= 2.29 (without outlier)
S₂= 0.32 (with outlier) S₂= 0.24 (without outlier)
Outlier: 4.26
Assuming all conditions are met and ignoring the outlier in the second sample, you have to construct a 99% CI for the difference between the average penetration in the compressed soil and the intermediate soil. To do so, you have to use a t-statistic for two independent samples:
Parámeter of interest: μ₁-μ₂
Interval:
[(X[bar]₁-X[bar]₂)±[tex]t_{n_1+n_2-2;1-\alpha/2}[/tex]*Sa[tex]\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }[/tex]]
[tex]t_{n_1+n_2-2;1-\alpha/2}= t_{20+19-2;1-(0.01/2)}= t_{37; 0.995}= 2.715[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{19*0.0196+18*0.0576}{20+19-2} }= 0.195= 0.20[/tex]
[(2.90-2.29)±2.715*0.20[tex]\sqrt{\frac{1}{20} +\frac{1}{19} }[/tex]]
[0.436; 0.784]
I hope this helps!
Using the t-distribution, it is found that the 99% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil is (-0.418, 1.182).
Using a calculator, we find that for the compressed soil, the mean and the standard deviation are given by:
[tex]\mu_C = 2.9075, s_C = 0.1427[/tex]
For the intermediate soil, omitting the high outlier of 4.26, we have that:
[tex]\mu_I = 3.2895, s_I = 0.2385[/tex]
The distribution of the decrease has mean and standard deviation given by:
[tex]\overline{x} = \mu_I - \mu_C = 3.2895 - 2.9075 = 0.382[/tex]
[tex]s = \sqrt{s_C^2 + s_I^2} = \sqrt{0.1427^2 + 0.2385^2} = 0.2779[/tex]
The interval is given by:
[tex]\overline{x} \pm ts[/tex]
By the conservative method, the amount of degrees of freedom is one less than the smaller sample size, which in this case is 19, for the intermediate soil.
Then, critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 19 - 1 = 18 df, is t = 2.8784.Then:
[tex]\overline{x} - ts = 0.382 - 2.8784(0.2779) = -0.418[/tex]
[tex]\overline{x} + ts = 0.382 + 2.8784(0.2779) = 1.182[/tex]
The 99% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil is (-0.418, 1.182).
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Petra has 12 pound and ski has nothing. They both receive the same money for doing a delivery job.
Now Petra has three times as much as ski.
How much did they get for the job?
Answer:
6 pounds
Step-by-step explanation:
Originally
Petra : 12 pounds
Ski: 0 pounds
Delivery job
Petra & Ski: Same amount.
Represent amount with 'D'
Total Amount
Petra: 12 + D pounds
Ski: D pounds.
Petra has three times as much as Ski, meaning
12 + D = 3 (D)
12 + D = 3D
12 = 3D - D
12 = 2D
Divide both sides by 2
6 = D...
0.12109375 fraction
Answer:
31/256
Step-by-step explanation:
0.12109375 = 12109375/100000000
= 31/256
Dividing numerator and denominator by 390625.. we have the simplest solution
You can start out by dividing by 5 the numerator and denominator.you would see this division by 5 goes on 8 times
Or you can start out dividing both numerator and denominator by 25, we see this division goes on 4 times
Answer:
Step-by-step explanation:
0.12109375
=[tex]=\frac{12109375}{100,000,000} \\=\frac{484375}{4,000,000} \\=\frac{19375}{160000} \\=\frac{775}{6400} \\=\frac{31}{256}[/tex]
Before 1918, approximately 55% of the wolves in a region were male, and 45% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 65% of wolves in the region are male, and 35% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.)(a) Before 1918, in a random sample of 9 wolves spotted in the region, what is the probability that 6 or more were male? What is the probability that 6 or more were female? What is the probability that fewer than 3 were female?(b) For the period from 1918 to the present, in a random sample of 9 wolves spotted in the region, what is the probability that6 or more were male? What is the probability that 6 or more were female? What is the probability that fewer than 3 were female?
Answer:
Are you being timed??
Step-by-step explanation:
y=4−2xy, equals, 4, minus, 2, x
Answer:
The slope is 2
Y-int is -4
Step-by-step explanation:
For the given equation, y=4−2x the slope and y-intercept of the line will be -2 and 4 respectively.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that the equation is"y=4−2xy"
The given equation is of a straight line, A straight line is a combination of endless points joined on both sides of the point. A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
The given in form of a standard equation can be written as,
y=4−2x
y=-2x+4
Comparing the equation we get, the slope of the line as
m= -2
The intercept of the line is,
b= 4
Thus for the given equation, y=4−2x the slope and y-intercept of the line will be -2 and 4 respectively.
The question is incomplete, "the complete question is to find the slope and intercept for the given equation y=4−2xy."
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A rectangle on a coordinate plane has vertices Q(Negative 1, 1), R(6, 1), S(6, Negative 8), and T(Negative 1, Negative 8). What are the dimensions of the rectangle?
Answer:
The base is 7 and the height is 9.
Step-by-step explanation:
Answer:
The base is 7 and the height is 9.
Step-by-step explanation:
i got it correct on edge
verified answer
Which is the graph of F(x)= sqrt 4x
The graph of f(x) = sqrt(4x) looks like this
So choose the one that looks like the image attached
The graph has been plotted.
What is a Graph?Graph is a mathematical representation of relation between two objects.
A graph is plotted between two variables that depicts the relation between them which is helpful in prediction of the pattern of the function that it is following.
A function is a relation between a dependent and an independent variable.
The domain and range of a function is always defined.
A domain is the value that can be an input to the function and a range is all the possible output value that can be obtained from the function.
The function is
F(x)= √4x
A square root is the factor of a number when multiplied by itself gives the number itself.
A square root function is also called as a radical function represented by
y = √x
the domain of f(x)=√x is x≥0 and the range is y≥0
The graph of the function is plotted and attached with the answer.
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There is also another answer and it is “nether”
Answer:
It’s only sequence A I think
Step-by-step explanation:
I hope this was helpful
Answer:
Sequence A
Step-by-step explanation:
Which number represents the country of Egypt
A) 1
B) 2
C) 3
D) 4
Answer:
2
Step-by-step explanation:
the way I remember is that Egypt is always the top right country
2 is the number represents the country of Egypt. Hence, option B is correct.
What country does Egypt belong to?In 1922, modern Egypt attained independence. Egypt and Syria formed the United Arab Republic from 1958 to 1961. The Arab Republic of Egypt, as it is officially known, has a surface area of 1 million km2, which is more than twice the size of the US State of California or roughly twice the size of France.
Egypt's history as a British colony lasted from 1882, when British troops invaded it during the Anglo-Egyptian War, to 1956, during the Suez Crisis, when the last British troops left Egypt in accordance with the 1954 Anglo-Egyptian Accord.
Modern Standard Arabic, which is used in most written documents and educational institutions, is Egypt's official language. Nevertheless, Modern Standard Arabic primarily describes Arabic's literary form, which is
Thus, option B is correct.
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8/9 Divided by 6/9 = ?
A. 17/54
B. 16/27
C. 4/3
D. 24/5
Answer:
4/3
Step-by-step explanation:
[tex] \frac{8}{9} \div \frac{6}{9} \\ \\ \implies \: \frac{8}{9} \times \frac{9}{6} \\ \\ \implies \: \frac{8}{1} \times \frac{1}{6} \\ \\ \implies \: {\boxed {\purple{\frac{4}{3} }}}[/tex]
I need help with this question, I attached a file, so it’s easier to read.
Hello there!
The median is the middle of the data set. Since we only have 7 numbers, we can arrange it from greatest to least, however the program has already done that. So, to find the median for this data set, all we have to do is simply find the middle number. The median would be 9 for this data set.
Answer:
9
Step-by-step explanation:
The median is the middle number of the set when ordered from least to greatest. We don't have to worry about that because it's already ordered like that. In this case, since there are 7 numbers, the median must be the 4th one, which is 9.
What is the first step in evaluating this expression?
15 + 20 ÷ (10 – 7) + 12
Answer:
The first step to solve the expression is to solve () i.e. (10-7) will be solved first.
Step-by-step explanation:
Any algebraic expression is solved as per BODMAS rule i.e. in the following sequential order (one after the other).
B - Bracket i.e. ()
O - Of
D - Division
M - Multiplication
A - Addition
S - Subtraction
So, as per BODMAS rule, the bracket i.e. () expression will be solved at first.
Solving the expression:
15 + 20 ÷ (10 – 7) + 12
[tex]\Rightarrow[/tex] 15 + 20 ÷ 3 + 12
[tex]\Rightarrow[/tex] 15 + 6.67 + 12
[tex]\Rightarrow[/tex] 21.67 + 12
[tex]\Rightarrow[/tex] 33.67
Hence, (10-7) will be evaluated first.
Answer:
10-7 will be done first.
Step-by-step explanation:
What is the difference when 3x2 − 2x + 7 is subtracted from 5x3 - 4x2 +10
A) 5x3-7x2+2x+3
B). 5x3+x2+2x-3
C) 5x3-7x2+2x +17
D) 5x3+x2+2x+17
Answer:
[tex]f(x) -g(x) =(5x^3) +(-4x^2- 3x^2) + (0+2x) +(10-7)[/tex]
And if we simplify we got:
[tex]f(x) -g(x) =5x^3 -7x^2 +2x+ 3[/tex]
And the best option for this case is:
A) 5x3-7x2+2x+3
Step-by-step explanation:
For this case we have this function given:
[tex] f(x) = 5x^3 -4x^2 +10[/tex]
And we want to subracr from the last function this one:
[tex] g(x) =3x^2 -2x+7[/tex]
So we want to find [tex] f(x)-g(x)[/tex] and replacing we got:
[tex]f(x) -g(x) =(5x^3 -4x^2 +10) -(3x^2 -2x +7)[/tex]
And if we aggrupate the terms we got:
[tex]f(x) -g(x) =(5x^3) +(-4x^2- 3x^2) + (0+2x) +(10-7)[/tex]
And if we simplify we got:
[tex]f(x) -g(x) =5x^3 -7x^2 +2x+ 3[/tex]
And the best option for this case is:
A) 5x3-7x2+2x+3
Rob's boss gave him $100 to buy 7 lunches for a team meeting, After buying the lunches he had $14.25 leftover, How
much did each lunch cost?
A)
$11.75
B)
$12.25
C)
$12.50
D)
$12.75
Answer:
Each lunch cost $12.25
Step-by-step explanation:
Subtract 14.25 from 100 and then divide that by 7
Imagine that there are 100 different researchers each studying the sleeping habit of a college freshman. Each researcher takes a random sample size of 50 from the same population of freshman. Each researcher is trying to estimate the population mean hour of sleep freshman get at night, and each one construct a 95% confidence interval for the mean. Approximately how many of these 100 confidence will not capture the true mean
Answer:
Approximately 5 intervals will not capture the true mean hour of sleep freshman get at night.
Step-by-step explanation:
The (1 - α)% confidence interval for population mean implies that there is a (1 - α) probability that the true value of the mean is included in the interval.
Or, the (1 - α)% confidence interval for the mean implies that there is (1 - α)% confidence or certainty that the true mean value is contained in the interval.
And, if 100 such (1 - α)% confidence interval for the mean are computed then 95 of these 100 interval will consist of the true mean value.
In this case it is provided that 100 researchers estimate the population mean hour of sleep freshman get at night, and each one construct a 95% confidence interval for the mean.
Then approximately 95 of these 100 confidence intervals will capture the true mean hour of sleep freshman get at night. And approximately 5 intervals will not capture the true mean hour of sleep freshman get at night.
Karen bought 4⁄5 pound of broccoli and 2⁄10 pound of cauliflower. How many more pounds of broccoli did she buy?
Answer:
6/10 or 3/5
Step-by-step explanation:
4/5 = 8/10
8/10 - 2/10 = 6/10 or 3/5
⅗ or 6/10
Step-by-step explanation:
4/5=8/10
8/10-2/10=6/10 or ⅗
What is the area of trapezoid ABCD in square centimeters?
Answer:
99
Step-by-step explanation:
Area of trapezium = 1/2 × (sum of parallel sides × height)
The parallel sides of the trapezium are the left and right edge.
( 9 + 13) = 22
The height is the vertical distance between the parallel sides and when you turn the shape 90degrees towards the left, we would have the parallel sides been the bottom and top edge and the vertical height between will be 9
Hence the area = 1/2 × 22 × 9
= 11 ×9 = 99
You would add the unit if measure.
Define a function f that determines the amount that Nicole pays (in dollars) for gas to drive m miles, given that Nicole's car gets 25 miles per gallon and gas costs $3.20 per gallon.
Answer:
f(m) = 0.128m
Step-by-step explanation:
cost per mile = (cost per gallon)/(miles per gallon) = $3.20/25 = $0.128
Then the desired function is ...
f(m) = 0.128m
plz help Marshmello i have 15 more
Answer:
53
Step-by-step explanation:
so you would subtract 30 from 401 to get 372 then divide it by the number of buses in this case it's 7 to get 53
Evaluate 5x3 - 2 + 7 when x= -2.
Answer:
-995
Step-by-step explanation:
5(-2)^3 - 2 + 7
first you would multiply the 5 by -2
(-10)^3 - 2 + 7
then the exponents
-1000 - 2 + 7
then you would subtract -1000 by 2
-1002 + 7
then add the 7
-995
Rewrite the function by completing the square.
g(x) = 2x^2 – 7x + 5
g(x) =...(x+...)^2+...
Answer:
2(x - [tex]\frac{7}{4}[/tex] )² - [tex]\frac{9}{8}[/tex]
Step-by-step explanation:
Given
2x² - 7x + 5
The coefficient of the x² term must be 1, thus factor out 2 from 2x² - 7x
= 2(x² - [tex]\frac{7}{2}[/tex] x ) + 5
To complete the square
add/ subtract ( half the coefficient of the x- term )² to x² - [tex]\frac{7}{2}[/tex] x
= 2(x² + 2(- [tex]\frac{7}{4}[/tex] )x + [tex]\frac{49}{16}[/tex] - [tex]\frac{49}{16}[/tex] ) + 5
= 2(x - [tex]\frac{7}{4}[/tex] )² - [tex]\frac{98}{16}[/tex] + 5
= 2(x - [tex]\frac{7}{4}[/tex] )² - [tex]\frac{18}{16}[/tex]
= 2(x - [tex]\frac{7}{4}[/tex] )² - [tex]\frac{9}{8}[/tex]
Answer:
g(x) = 2(x - 1.75)^2 - 1.125.
Step-by-step explanation:
g(x) = 2x^2 – 7x + 5
First take the 2 out of the first terms:
g(x) = 2(x^2 - 3.5x) + 5
Now complete the square on the expression in the parentheses:
g(x) = 2 [ (x - 1.75)^2 - 1.75^2] + 5
g(x) = 2 [ (x - 1.75)^2 - 3.0625] + 5
g(x) = 2(x - 1.75)^2 - 6.125 + 5
g(x) = 2(x - 1.75)^2 - 1.125.
The net of a triangular prism is shown. Use the ruler provided to measure the dimension of the net to the nearest half centimeter.
Which measurement is closest to the total surface area of the triangular prism in square centimeters?
A.20cm2
B.14cm2
C.8cm2
D.6cm2
Answer:
408cm
Step-by-step explanation:
U got this
The total surface area of the triangular prism is 14 cm². Then the correct option is B.
What is a triangular prism?A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangular surface.
The total surface area of the triangular prism will be
[tex]\rm Total\ area = 3(area \ of\ rectangle) + 2(area\ of \ triangle)[/tex]
The area of the triangle will be
[tex]\rm area\ of \ triangle = \dfrac{1}{2} * 2 * 4\\\\area\ of \ triangle = 4[/tex]
The area of the rectangle will be
[tex]\rm area\ of \ rectangle = 2 *1\\\\area\ of \ rectangle = 2[/tex]
Then the total area will be
[tex]\rm Total\ area = 2*4 + 3*2\\\\Total\ area = 8 + 6 \\\\Total\ area = 14[/tex]
The total surface area of the triangular prism is 14 cm². Then the correct option is B.
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(N) Northeast
(M) Midwest
(T) South
(W) West
(N) (M) (T) (W) Total
2009 (A) 0.9 1.2 1.9 1.2 5.2
2010 (B) 0.8 1.1 1.9 1.2 5.0
2011 (C) 0.8 1.1 1.9 1.1 4.9
Total 2.5 3.4 5.7 3.5 15.1
Use symbols to describe the given set.
The set of sales of existing homes in 2010 in the West and Midwest
Which one?
W ∩ (B ∪ M)
B ∪ (W ∪ M)
B ∩ (W ∪ M)
B ∩ (W ∩ M)
W ∪ (B ∪ M)
Compute its cardinality.
? million
Answer:
B ∩ (W ∪ M)2.3 millionStep-by-step explanation:
Apparently, these sets represent sales of existing homes. Then (values of) the homes sold in 2010 are those listed in set B.
The English wording "West and Midwest" doesn't actually mean homes that are categorized as both West and Midwest. There aren't any such homes, because these sets are mutually exclusive. That wording logically means "West or Midwest", so would represent the union W ∪ M.
Then the homes in W∪M that were sold in 2010 will be ...
B ∩ (W ∪ M) . . . . . matches the 3rd choice on the list
_____
The "cardinality" of a set is the number of elements in the set. Since the sets B and W and M are not shown, we cannot tell the cardinality.
Here, that word is apparently intended to mean the sum of the numbers designated as W and as M. For 2010, we have W=1.2, M=1.1, so ...
for 2010, W +M = 1.2 +1.1 = 2.3 . . . million
Which of the following could be the equation of the function below?
On a coordinate plane, a curve crosses the y-axis at y = negative 3. It has a maximum at y = 1 and a minimum at y = negative 3. It goes through 1 cycle at pi.
y = negative 2 cosine (4 (x + pi)) minus 1
y = 2 cosine (x + pi) + 1
y = negative 2 cosine (2 (x + pi)) minus 1
y = 2 cosine (4 (x + pi)) + 2
Answer:
y = negative 2 cosine (2 (x + pi)) minus 1
Step-by-step explanation:
The amplitude of the trig function will be half the difference of the minimum and maximum, so is ...
A = (1 -(-3))/2 = 2
The coefficient of x is 2π divided by the period, so is ...
B = (2π)/π = 2
The vertical offset is the average of the maximum and minimum:
C = (1 +(-3))/2 = -1
Since the extreme negative value is at x=0, this can be the opposite of the cosine function:
y = -A·cos(Bx) +C
The answer choices have a horizontal offset of pi, which does nothing, since the period is pi.
y = -2cos(2(x+π)) -1
Answer:
C on E2020.
Step-by-step explanation:
What are the coordinates of point B on AC Such that the ratio of AB to AC is 5:6
[tex](-3\frac{1}{6}, \frac{2}{3} )[/tex]
Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11
What is the section formula in co-ordinate geometry?When the line segment is divided internally in the ration m:n, we use this formula. That is when the point C lies somewhere between the points A and B. p= (mx₂+nx₁)/(m+n) & q= (my₂+ny₁)/(m+n)
Given here, point B on AC Such that the ratio of AB to AC is 5:6
Let the point B(p,q) internally divide the line joining points A(x₁, y₁) and C(x₂, y₂) in the ratio m : n , then,
p= (mx₂+nx₁)/(m+n)
q= (my₂+ny₁)/(m+n)
Here. m=5 and n=6
p=(5x₂+6x₁)/11 , q=(5y₂+6y₁)/11
Hence, Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11
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Toby is buying apples. Red delicious apples, x, cost $2 per pound. Braeburn apples, y, cost $3 per pound. He wants to buy at least 10 pounds of apples, but spend no more than $24. Which graph represents this situation?
Answer:
I graphed all of the equations on the graph below.
Step-by-step explanation:
At the point (6,4), the equation [tex]x+y\ge10[/tex] uses 6 + 4 ≥ 10. Also, the equation [tex]2x+3y\le24[/tex] uses 2(6) + 3(4) ≤ 24.
If this answer is correct, please make me Brainliest!
Answer:
its A !!
Step-by-step explanation:
In the year 2001 Youth Risk Behavior survey done by the U.S. Centers for Disease Control, 747 out of 1168 female 12th graders said they always use a seatbelt when driving. Please construct a 98% confidence interval for the proportion of 12th-grade females in the population who always use a seatbelt when driving. 1) Use R to find the score CI for the proportion of 12th-grade females in the population who always use a seatbelt when driving (please round to 4 decimals).
Answer:
98% of confidence interval of Population proportion is determined by
(0.60683 ,0.67217)
Step-by-step explanation:
Given the sample size n = 1168
Given 747 out of 1168 female 12th graders said they always use a seatbelt when driving
The sample proportion 'p' = [tex]\frac{x}{n} = \frac{747}{1168} = 0.6395[/tex]
98% of confidence interval of Population proportion is determined by
[tex]p^{-} -Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^-)}{n} }, p^- +Z_{\frac{\alpha }{2} } \sqrt{\frac{p^-(1-p^-)}{n} } }[/tex]
The tabulated value Z₀.₀₂ score = 2.326
[tex](0.6395 -2.326 \sqrt{\frac{0.6395(1-0.6395)}{1168} }, 0.6395 +2.326 \sqrt{\frac{0.6395(1-0.6395)}{1168} } })[/tex]
on calculation , we get
(0.6395 -0.03267 , 0.6395 +0.03267)
(0.60683 ,0.67217)
help me Help Marshmello i wasn't born yesterday.
Answer:
I THINK ITS B
Step-by-step explanation:
help asap !! will get branliest.
Answer:
4096 horses, or 4 to the power of 6
Step-by-step explanation:
(4²)³×4 to the power of 0
We simplify the equation,
(16)³×4 to the power of 0
4096×1 (Since 4 to the power of 0 is 1)
= 4096 horses on the farm which is 4 to the power of 6
- Hope this helps!
The volume of a _________ is equal to ___ the volume of a cylinder that has the same base and height. The formula for the volume of a cone is ___________________. ___ stands for the area of the _____ and ___ is the __________ of the cone. Knowing this, we could quickly find the volume of a cone that has the _______ base and height as a cylinder with a volume of 9 cubic cm. Since the volume of a cone is ____ the volume of a cylinder (with the same base and height), we would multiply 9*__ to obtain a volume of ____ cubic cm.
What do I fill into the blanks?
Answer:
cone, [tex]\frac{1}{3}[/tex] , [tex]\frac{1}{3} \pi r^{2}h[/tex] , [tex]\pi r^{2}[/tex], base, h, height, same, [tex]\frac{1}{3}[/tex] , [tex]\frac{1}{3}[/tex] , 3
Step-by-step explanation:
The volume of a cone is equal to [tex]\frac{1}{3}[/tex] the volume of a cylinder that has the same base and height. The formula for the volume of a cone is [tex]\frac{1}{3}\pi r^{2}h[/tex]. stands for the area of the base and h is the height of the cone. Knowing this, we could quickly find the volume of a cone that has the same base and height as a cylinder with a volume of 9 cubic cm. Since the volume of a cone is [tex]\frac{1}{3}[/tex] the volume of a cylinder (with the same base and height), we would multiply 9*[tex]\frac{1}{3}[/tex] to obtain a volume of 3 cubic cm.
Suppose that you are in charge of evaluating teacher performance at a large elementary school. One tool you have for this evaluation is reports of the average student reading test score in each classroom. You also know that across the whole school, the average student reading score was 80 points and the standard deviation in scores was 10 points.
Determine:
(a) If each class has 25 students in it, what is the standard error of the classroom average score?
(b) In what range do you expect the average classroom test score to fall 95% of the time?
(c) What is the approximate probability that a classroom will have an average test score of 79 or higher?
(d) Do you think the probability that a classroom has an average test score of 79 or higher would be greater or smaller if there were only 15 students in a class? Explain your answer in 2-3 sentences.
(e) Do you think the probability that a classroom has an average test score of 79 or higher would be greater or smaller if the standard deviation of individual student reading scores was only 5 points (instead of 10)?
Answer:
a) Standard error = 2
b) Range = (76.08, 83.92)
c) P=0.69
d) Smaller
e) Greater
Step-by-step explanation:
a) When we have a sample taken out of the population, the standard error of the mean is calculated as:
[tex]\sigma_m=\dfrac{\sigma}{\sqrt{n}}=\dfrac{10}{\sqrt{25}}=\dfrac{10}{5}=2[/tex]
where n is te sample size (n=25) and σ is the population standard deviation (σ=10).
Then, the standard error of the classroom average score is 2.
b) The calculations for this range are the same that for the confidence interval, with the difference that we know the population mean.
The population standard deviation is know and is σ=10.
The population mean is M=80.
The sample size is N=25.
The standard error of the mean is σM=2.
The z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_M=1.96 \cdot 2=3.92[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 80-3.92=76.08\\\\UL=M+t \cdot s_M = 80+3.92=83.92[/tex]
The range that we expect the average classroom test score to fall 95% of the time is (76.08, 83.92).
c) We can calculate this by calculating the z-score of X=79.
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{79-80}{2}=\dfrac{-1}{2}=-0.5[/tex]
Then, the probability of getting a average score of 79 or higher is:
[tex]P(X>79)=P(z>-0.5)=0.69146[/tex]
The approximate probability that a classroom will have an average test score of 79 or higher is 0.69.
d) If the sample is smaller, the standard error is bigger (as the square root of the sample size is in the denominator), so the spread of the probability distribution is more. This results then in a smaller probability for any range.
e) If the population standard deviation is smaller, the standard error for the sample (the classroom) become smaller too. This means that the values are more concentrated around the mean (less spread). This results in a higher probability for every range that include the mean.