Answer:
20
Step-by-step explanation:
n=20 it is that answer
Answer:
20
Step-by-step explanation:
20 is equal to n
The mean and standard deviation of a random sample of n measurements are equal to 34.5 and 3.4, respectively.A. Find a 95 % confidence interval for μ if n=49.B. Find a 95% confidence interval for μ if n=196.C. Find the widths of the confidence intervals found in parts a and b.D. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?1. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4.2. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2.3. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the on confidence interval by a factor of 4.4. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval.5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Answer:
a. The 95% confidence interval for the mean is (33.52, 35.48).
b. The 95% confidence interval for the mean is (34.02, 34.98).
c. n=49 ⇒ Width = 1.95
n=196 ⇒ Width = 0.96
Note: it should be a factor of 2 between the widths, but the different degrees of freedom affects the critical value for each interval, as the sample size is different. It the population standard deviation had been used, the factor would have been exactly 2.
d. 5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Step-by-step explanation:
a. We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=34.5.
The sample size is N=49.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{49}}=\dfrac{3.4}{7}=0.486[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=49-1=48[/tex]
The t-value for a 95% confidence interval and 48 degrees of freedom is t=2.011.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.011 \cdot 0.486=0.98[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 34.5-0.98=33.52\\\\UL=M+t \cdot s_M = 34.5+0.98=35.48[/tex]
The 95% confidence interval for the mean is (33.52, 35.48).
b. We have to calculate a 95% confidence interval for the mean.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{196}}=\dfrac{3.4}{14}=0.243[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=196-1=195[/tex]
The t-value for a 95% confidence interval and 195 degrees of freedom is t=1.972.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.972 \cdot 0.243=0.48[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 34.5-0.48=34.02\\\\UL=M+t \cdot s_M = 34.5+0.48=34.98[/tex]
The 95% confidence interval for the mean is (34.02, 34.98).
c. The width of the intervals is:
[tex]n=49\rightarrow UL-LL=33.52-35.48=1.95\\\\n=196\rightarrow UL-LL=34.02-34.98=0.96[/tex]
d. The width of the intervals is decreased by a factor of √4=2 when the sample size is quadrupled, while the others factors are fixed.
The U.S. Department of Agriculture (USDA) uses sample surveys to obtain important economic estimates. One USDA pilot study estimated the price received by farmers for corn sold in January from a sample of 20 farms. The mean price was reported as $3.64 per bushel with a standard deviation of $0.0835 per bushel. Give a 95% confidence interval for the mean price received by farmers for corn sold in January.
Answer:
{$3.60; $3.68}
Step-by-step explanation:
The confidence interval for a sample of size 'n', with mean price 'X' and standard deviation 's' is determined by:
[tex]X\pm z*\frac{s}{\sqrt n}[/tex]
The z-score for a 95% confidence interval is 1.96.
Applying the given data, the lower and upper bounds of the confidence interval are:
[tex]3.64\pm 1.96*\frac{0.0835}{\sqrt 20} \\L=\$3.60\\U=\$3.68[/tex]
The confidence interval for the mean price received by farmers for corn sold in January is:
CI : {$3.60; $3.68}
Eruptions of the Old Faithful geyser have duration times with a mean of 245.0 sec and a standard deviation of 36.4 sec (based on sample data). One eruption had a duration time of 110 sec.Eruptions of the Old Faithful geyser have duration times with a mean of 245.0 sec and a standard deviation of 36.4 sec (based on sample data). One eruption had a duration time of 110 sec.
a. What is the difference between a duration time of 110 sec and the mean? Answer
135
b. How many standard deviations is that (the difference found in part (a))? Answer
c. Convert the duration time of 110 sec to a z score. Answer
d. If we consider "usual" duration times to be those that convert to z scores between -2 and 2, is a duration time of 110 sec usual or unusual?
Answer:
a) 135 seconds
b) 3.71 standard deviations below the mean
c) Z = -3.71
d) Unusual
Step-by-step explanation:
Z-score:
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.
In this question:
[tex]\mu = 245, \sigma = 36.4[/tex]
a. What is the difference between a duration time of 110 sec and the mean?
Duration of 110 seconds.
Mean of 245
245 - 110 = 135 seconds
b. How many standard deviations is that (the difference found in part (a))?
This is |Z|
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 245}{36.4}[/tex]
[tex]Z = -3.71[/tex]
[tex]|Z| = 3.71[/tex]
3.71 standard deviations below the mean
c. Convert the duration time of 110 sec to a z score
From b, Z = -3.71
d. If we consider "usual" duration times to be those that convert to z scores between -2 and 2, is a duration time of 110 sec usual or unusual?
Z is not in the interval of -2 and 2, so a duration time of 110 sec is unusual
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer: m=0.5 or m=1/2
Step-by-step explanation:
To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Since we are given the coordinate points, we can directly plug them in.
[tex]m=\frac{0.25-0}{0.5-0} =\frac{0.25}{0.5} =0.5[/tex]
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is: Temperature = 110 ‑ 2(Latitude). How does the estimated temperature change when latitude is increased by one?
Answer:
Decreases by 2 degrees
Step-by-step explanation:
The expression that describes temperature as a function of latitude is:
[tex]T=110-2(Latitude)[/tex]
This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer:
m = 0.5
Step-by-step explanation:
m = (y2 - y1) / (x2 - x1)
= (0.25 - 0) / (0.5 - 0)
= 0.25/0.5
= 0.5
empt 1
Find the equation in slope-intercept form of a line with slope - 2 and y-intercept 4.
a) y = -2x
Ob) y - 2x-4
c) y = -2x+4
d) y - 4x -2
Question 12 (5 points)
Answer:
y = -2x +4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -2x +4
Find the area of the figure to the nearest square unit.
Answer:
357 mi²
Step-by-step explanation:
The shape is made of a triangle and a half-square
we will calculate the area of each one
The half square:let A1 be the area of the half-circle:
A1= (10²*π)/2 = 50π mi²
The rectangle:Let A2 be the area of the triangle:
A2= 10*20=200 mi²
The whole shape:let At be the total area:
At =A1+A2= 200+50π =357.07≈ 357 mi²
Plz solve this question, it's very urgent.
i think it is ur required ans..
Recall the equation that modeled the volume of the raised flower bed, y, in terms of the width of the box, y = x3 + 11x2 − 312x. Now, open the graphing tool and graph the equation. Remember, this equation represents the volume of a flower box, so neither the width nor the volume can be negative. Using the pointer, determine the x-intercept where the width is positive and the volume will change to positive as x increases.
Answer:
x = 17.349
Step-by-step explanation:
The right-most x-intercept is 17.349, where the curve continues upward to the right.
The number of rooms in hotel G is 10 less than twice the number of rooms in hotel H .The total number of rooms in both hotels is 425 .Find the number of rooms in each of the hotels.
Answer:
No of rooms in Hotel G = 280
No of rooms in Hotel H = 145
Step-by-step explanation:
I solved the question using Elimination Method.
write down 3 numbers that have a range of 5 and a mode of 8
Answer:
8, 8, 13
Step-by-step explanation:
The three numbers 8, 8, 13 have a range of 5.
13 - 8 = 5
The mode is 8, the repeated number.
Answer:
need pls
Step-by-step explanation:
A population of monkeys' tail lengths is normally distributed with a mean of 25 cm with a standard deviation of 8 cm. I am preparing to take a sample of size 256 from this population, and record the tail length of each monkey in my sample. What is the probability that the mean of my sample will be between 24 and 25 cm?
Answer:
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
Step-by-step explanation:
Step(i):-
Given mean of the Population 'μ'= 25c.m
Given standard deviation of the Population 'σ' = 8c.m
Given sample size 'n' = 256
Let X₁ = 24
[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]
Let X₂ = 25
[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]
Step(ii):-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)
= P( Z≤0) - P(Z≤-2)
= 0.5 + A(0) - (0.5- A(-2))
= A(0) + A(2) ( ∵A(-2) =A(2)
= 0.000+ 0.4772
= 0.4772
Final answer:-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
What is the value of p?
Answer:
Step-by-step explanation:
The angle next to 90 degrees is also 90 degrees and it's supplementary
the angle next to 133 degrees is 47 degrees and it's also supplementary
p + 90 + 47 = 180
p + 137 = 180
p = 43 degrees
the solution is d
Which best compares the volumes of the two cylinders? Geometry
Answer:
The correct answer would be C
Step-by-step explanation:
please mark brainliest
The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.
Which best compares the volumes of the two cylinders?From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.
Read more on cylinders;
https://brainly.com/question/9554871
#SPJ2
find the greatest number that divides 36 and 60 without leaving a remainder
Answer:
12
Step-by-step explanation:
36= 2 × 2 × 3 × 3
60= 2 × 2 × 3 × 5
HCF(36, 60)= 2 × 2 × 3 = 12
12 is the greatest number that divides 36 and 60 without leaving a remainder
Please answer this question now in two minutes
Answer:
the slope equation is y2 - y1 divided by x2 - x1
Step-by-step explanation:
so the answer would be 3 over 2 because of this method
Answer:
3/2
Step-by-step explanation:
Use the easy rise over run method.
start at the point (50,20) then go up 3 units and 2 units to the right to get the next point.
3/2 should be the slope.
Hope I helped you!
Identify the statement as true or false.
New Jersey is a state if and only if Florida is not a state.
Is the statement true or false?
O true
O false
The decay constant for 14C is 0.00012. A 4050-year-old wooden chest is found by archaeologists. What percentage of the original 14C would you expect to find in the wooden chest? (Express your answer as a percentage rounded to one decimal place.)
Answer:
The radioactive decay constant or k = ln (.5) / Half-Life
Half-Life = -.693147 / .00012
Half-Life = -5,776.225 years
We'll call beginning amount as 100%
Ending Amount = Beginning Amount / 2^n (where n = # of half-lives)
n = 4,050 / 5,776.225 = 0.7011499725
Ending Amount = 100% / 2^0.7011499725
Ending Amount = 100% / 1.625800202
Ending Amount = 61.5081729452%
Ending Amount = 61.5 % (rounded)
Step-by-step explanation:
Please find the missing side of the triangle and round the answer to the nearest tenth. Thanks.
Answer:
x = 74.3
Step-by-step explanation:
Using the trigonometric ratio formula, the missing side, x, of the right angled triangle, can be found as follows:
Ѳ = 22°,
adjacent side length = x
Opposite side length = 30
Thus, we would apply the formula:
tan Ѳ = opposite length/adjacent length
[tex] tan 22 = \frac{30}{x} [/tex]
Multiply both sides by x
[tex] tan 22*x = \frac{30}{x}*x [/tex]
[tex] tan 22*x = 30 [/tex]
[tex] 0.4040*x = 30 [/tex]
Divide both sides by 0.4040 to make x the subject of the formula
[tex] \frac{0.4040*x}{0.4040} = \frac{30}{0.4040} [/tex]
[tex] x = \frac{30}{0.4040} [/tex]
[tex] x = 74.26 [/tex]
x ≈ 74.3 (to the nearest tenth)
Help pls urgent!!!!!!!!!!
Answer:
d
Step-by-step explanation:
A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below.
Before: 74, 83, 75, 88, 84, 63, 93, 84, 91, 77
After: 73, 77, 70, 77, 74, 67, 95, 83, 84, 75
Required:
a. Is there evidence to suggest the logic course improves abstract reasoning?
b. Construct a 95% confidence interval for the mean difference between the before and after scores.
Answer:
don't know
Step-by-step explanation:
sorry buddy
What is the height of the triangle?
Triangle MNO is an equilateral triangle with sides
measuring 16V3 units.
O 12 units
N
0 24 units
VX
0 36 units
16/3
16/3
O 72 units
M
O
R
16/3
->
Answer:
(B)24 Units
Step-by-step explanation:
Triangle MNO is an equilateral triangle with sides measuring [tex]16\sqrt{3}[/tex] units.
The height divides the base into two equal parts of lengths [tex]8\sqrt{3}[/tex] units.
As seen in the diagram, we have a right triangle where the:
Hypotenuse = [tex]16\sqrt{3}[/tex] units.Base = [tex]8\sqrt{3}[/tex] units.Using Pythagoras Theorem
[tex](16\sqrt{3})^2=(8\sqrt{3})^2+h^2\\16^2*3-8^2*3=h^2\\h^2=576\\h=\sqrt{576}\\ h=24$ units[/tex]
The height of the triangle is 24 Units.
The height of the given equilateral triangle is gotten as;
B: 24 units
Equilateral Triangles
The height of an equilateral triangle starts from the mid - point of the base to the ap ex.
Now, if the sides of the equilateral triangle are 16√3 units, then it means we can use pythagorean theorem to find the height h.
Half of the base will be; ¹/₂ * 16√3 = 8√3
Thus, the height h can be calculated from;
h²= ((16√3)² - (8√3)²)
h² = 3(256 - 64)
h² = 576
h = √576
h = 24 units
Read more about equilateral triangles at; https://brainly.com/question/4293152
solve each question by graphing. round to the nearest tenth
2x^2 + 5 = 11x
Answer: x=5 and 1/2
Step-by-step explanation:
You have to go to a graph and put it simply it, makes it a lot easier, hope this helps!
Steps to solve:
2x^2 + 5 = 11x
~Subtract 11x to both sides
2x^2 - 11x + 5 = 0
~Factor
(2x - 1)(x - 5) = 0
~Solve each factor
2x - 1 = 0
2x = 1
x = 1/2
x - 5 = 0
x = 5
Best of Luck!
what is the slope of a line of duty hat is parallel to the line whose equation is 5y+2x=12
Answer:
-2/5
Step-by-step explanation:
The slope of two parallel lines will be the same.
Here, our equation is 5y + 2x = 12. Let's find the slope by isolating y:
5y + 2x = 12
5y = -2x + 12
y = (-2/5)x + 12/5
So, the slope is -2/5.
Thus, the slope of the line parallel to the given one will be -2/5.
~ an aesthetics lover
Answer:
-2/5
Step-by-step explanation:
5y+2x=12
Solve for y
Subtract 2x
5y = -2x+12
Divide by 5
5y/5 = -2/5 x +12/5
y = -2/5x +12/5
The slope is -2/5
Parallel lines have the same slope
Perform the indicated operation and simplify the result.
Answer:
7/ (3a-1)
Step-by-step explanation:
3a^2 -13a +4 28+7a
------------------ * --------------------
9a^2 -6a+1 a^2 -16
Factor
(3a-1)(a-4) 7(4+a)
------------------ * --------------------
(3a-1) (3a-1) (a-4)(a+4)
Cancel like terms
1 7
------------------ * --------------------
(3a-1) 1
Leaving
7/ (3a-1)
Find the length of ST to the nearest meter.
Answer:
42 m
Step-by-step explanation:
First, find <S
<S = 180 - (41+113) [ sum of angles in a triangle)
<S = 180 - 154 = 26°
Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C
Let a = RT = 28m
A = <S = 26°
b = ST
B = <R = 41°
Thus, we have:
28/sin(26°) = b/sin(41°)
Cross multiply
28*sin(41°) = b*sin(26°)
28*0.6561 = b*0.4384
18.3708 = b*0.4384
Divide both sides by 0.4384 to make b the subject of formula
18.3708/0.4384 = b
41.9041971 = b
b ≈ 42m (rounded to nearest meter)
Length of ST to nearest meter = 42 meters
Jaleel and Lisa are simplifying the expression 2 (x minus 2) + 2 as shown. Jaleel’s Method 2 (x minus 2) + 2 = 2 x minus 4 + 2 = 2 x minus 2 Lisa’s Method 2 (x minus 2) + 2 = 2 x minus 2 + 2 = 2 x Whose method is correct and why? Lisa’s method is correct because 2 (x minus 2) equals 2 x minus 2. Lisa’s method is correct because 2 (x minus 2) equals 2 x. Jaleel is correct because 2 (x minus 2) equals 2 x minus 2. Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
Answer:
(D)Jaleel's method is correct because 2(x-2)=2x-4.
Step-by-step explanation:
Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.
[tex]J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right[/tex]
[tex]L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right[/tex]
We can see that Jaleel's method is correct because:
2(x-2)=2x-4.
When you expand, you must multiply the term outside by all the terms inside the bracket.
The correct option is D.
Answer:
Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
D is correct
Step-by-step explanation:
i just took the quiz.
7. Look at the figure below.
Which theorem can be used to show that triangles QSN and LEJ are congruent?
A. HL
B. ASA
C. SAS
D. SSA
I'm pretty sure that ' HL ' stands for "hypotenuse and leg". That's the one.
-- We see the little boxes in the lower left corners, so we know that these are right triangles, and we can use the rules we know about for right triangles.
-- The hypotenuses of both triangles are marked with the same length.
-- The base legs of both triangles are marked with the same length.
-- So we have (the hypotenuse and one leg of one right triangle) equal to (the hypotenuse and corresponding leg of another right triangle). That's exactly the description of the HL conguence theorem, so we know that these two triangles are congruent.
drag the tiles to the correct boxes to complete the pears. Match the values based on parallelogram ABCD, shown in the figure.
length of BC
value of y
m
value of x
56–>
4–>
44–>
2–>
Answer:
[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]
Step-by-step explanation:
In parallelogram ABCD, BC=AD
Given:
BC=(6-x) units
AD =(x+2) units
Therefore:
6-x=x+2
x+x=6-2
2x=4
x=2
BC=(6-x) units
=(6-2) units
BC=4 units
The opposite angles of a parallelogram are equal. Therefore:
[tex]m\angle BCD=m\angle BAD\\12^\circ+y^\circ=100^\circ-y^\circ\\y^\circ+y^\circ=100^\circ-12^\circ\\2y^\circ=88^\circ\\y=44^\circ[/tex]
[tex]m\angle DAB=100^\circ-y^\circ\\=100^\circ-44^\circ\\m\angle DAB=56^\circ[/tex]
Therefore, the match is:
[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]
Answer:
Step-by-step explanation:
plato i guess