Answer:
Accuracy = Tape measurement.
Precision = Laser measurement
Step-by-step explanation:
Given that :
True height, = 70.2 inches
Laser measured height = 71.05 (nearest hundredth)
Tape measured height = 69.5 - nearest half inch.
Accuracy simply means how close a measured value is to the true value of the measurement. ;
True height - tape measurement
70.2 - 69.5 = 0.7
True measurement - laser measurement :
|70.2 - 71.05| = 0.85
Fron the difference in the values, the measurement which is closer to the true height is the tape measurement.
However, in terms of detail in the measured value, the laser measure value is expressed to the nearest hundredth, hence giving it more precision over the tape measured value.
The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sample of 20 cables is selected and tested. Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population. Assume the variable is normally distributed.
Answer:
The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.
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 normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds.
This means that [tex]\mu = 2000, \sigma = 100[/tex]
A sample of 20 cables is selected and tested.
This means that [tex]n = 20, s = \frac{100}{\sqrt{20}} = 22.361[/tex]
Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population.
This is the 100 - 95 = 5th percentile, which is X when Z has a p-value of 0.05, so X when Z = -1.645. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.645 = \frac{X - 2000}{22.361}[/tex]
[tex]X - 2000 = -1.645*22.361[/tex]
[tex]X = 1963.2[/tex]
The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.
At a hockey game, a vender sold a combined total of 192 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Find the
number of sodas and the number of hot dogs sold.
Answer:
they sold 64hotdogs and 128 sodas
Step-by-step explanation:
2x+x=192 3x=192 x=64
Consider points a, b, and c in the graph. Determine which of these points is relative maxima on the interval x = –1 and x = 2 in the graph.
Given:
The graph of a function is given.
To find:
The point that is the relative maxima on the interval x = –1 and x = 2 in the graph.
Solution:
Relative maxima: It is the maximum point of a function over a short interval.
From the given graph it is clear that the graph of the function over the interval x = –1 and x = 2 has a relative maxima at (0,0).
Clearly, (0,0) is represented by point a.
So, the point a is the relative maxima on the interval x = –1 and x = 2 in the graph.
Therefore, the correct option is A.
Graph 5 and it’s opposite on the number line
Answer:
See pic below.
Step-by-step explanation:
The opposite of 5 is -5.
Solve the inequality (help pls)
Answer:
B
Step-by-step explanation:
(-2/3x)-10<1/3
(-2/3x)<1/3+10
(-2/3x)<31/3
x>-31/2, -31/2=-15 (1/2), x> - 15 (1/2)
If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as
V=5000 (1-1/50*t)^2 0⤠t ⤠50.
1. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)
a. 5 min
b. 10 min
c. 20 min
d. 50 min
2. At what time is the water flowing out the fastest?
3. At what time is the water flowing out the slowest?
Answer: hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation
answer:
1) a) -180 gallons/minute ,
b) -160 gallons/minute
c) -120 gallons/minute
d) 0
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins
Step-by-step explanation:
Volume of tank = 5000 gallons
Time to drain = 50 minutes
Volume of water remaining after t minutes by Torricelli's law
V = 5000 ( 1 - [tex]\frac{1}{50}t[/tex] )^2 ----- ( 1 )
1) Determine the rate at which water is draining from the tank
First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank
V' = [tex]-10000[ ( 1 - \frac{1}{50}t ) (\frac{1}{50}) ][/tex]
a) After t = 5minutes
V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]
= -180 gallons/minute
b) After t = 10 minutes
V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]
= - 160 gallons/minute
c) After t = 20 minutes
V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]
= -120 gallons/minute
d) After t = 50 minutes
V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]
= 0 gallons/minute
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins because no water flows out after 50 minutes
Question 3 of 10
What is the value of p?
V140
140°
90-
A. 50°
ООО
B. 90°
C. 60°
D. 40°
Answer:
A. 50º
Step-by-step explanation:
we are given the exterior angles 140º and 90º
exterior angles + corresponding interior angles = 180º
that means the two other angles of the triangle are:
180 - 140 = 40º
and
180 - 90 = 90º
the sum of interior angles in a triangle = 180
p = 180 - (40 + 90)
p = 180 - 130
p = 50º
The scores on an entrance exam to a university are known to have an approximately normal distribution with mean 65% and standard deviation 7.1%. Using the normalcdf function on your graphing calculator, what percentage of students would score 70 or better on this entrance exam?
A. 28.4%
B. 18.9%
C. 24.1%
D. 22.3%
Answer:
The correct answer is - C. 24.1%
Step-by-step explanation:
Given:
mean μ = 65%
standard deviation δ = 7.1 %
solution:
Prob( X>70) = 1 - Prob(x<70)
= P (x-μ/δ ≥ 70 -65/7.1)
= 1 - Prob( (70-65)/7.1)
= 1 - Prob ( z < 0.7042553)
= 0.24065
the percentage of students scoring 70 or more in the exam
= 24.065*100
= 24.1%
A simple random sample of 27 filtered 100-mm cigarettes is obtained from a normally distributed population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.20 mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below. a. What are the null and alternative hypotheses?
Answer:
The null hypothesis is [tex]H_0: \sigma = 0.3[/tex]
The alternative hypothesis is [tex]H_1: \sigma \neq 0.3[/tex]
Step-by-step explanation:
Test if the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg.
At the null hypothesis, we test if the standard deviation is of 0.3, that is:
[tex]H_0: \sigma = 0.3[/tex]
At the alternative hypothesis, we test if the standard deviation is different of 0.3, that is:
[tex]H_1: \sigma \neq 0.3[/tex]
Find the missing side of the right triangle.
Answer:
√65
Step-by-step explanation:
you have to use the pythagoras theorem to find x which is the hypotenuse
x²=7²+4²
x²=49+16
√x²=√65
x=√65
I hope this helps
find all the missing measurement
Answer:
Hello,
|FD|=15
Step-by-step explanation:
Since the triangles are similar, the bissects are also.
k*35=21 ==> k=21/35
k*25=|FD|
|FD|=(21/35)*25=15
What are vertices of the conic 16x² - 25y² = 400 ?
Answer:
(-5, 0) and (5, 0)
Step-by-step explanation:
This equation fits the form for a hyperbola with x-intercepts. The standard form for such an equation is
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
To get the equation in the question into this standard form, divide each term by 400.
[tex]\frac{16x^2}{400}-\frac{25y^2}{400}=\frac{400}{400}\\\frac{x^2}{25}-\frac{y^2}{16}=1[/tex]
To find the x-intercepts, make y = 0.
[tex]\frac{x^2}{25}=1\\x^2=25\\x=\pm 5[/tex]
The vertices are located at the points (-5, 0) and (5, 0).
Note: There are no y-intercepts; making x = 0 produces no real solutions for y.
Solve x/4 > 2 Question 10 options: x ≥ 8 x < –8 x > 8 x ≤ –8
Answer:
x > 8
Step-by-step explanation:
You can start y multiplying both sides by 4 to cancel out the division by 4:
x/4 > 2
*4 *4
x > 8
Answer:
x > 8
Step-by-step explanation:
x/4 > 2
=> x > 2 × 4
=> x > 8
in the figure above, three congruent circles are tangent to eachother and have centers that lie on the diameter of a larger circle. if the area of each of these small circles is 9pi, what is the area of the larger circle?
a) 36pi
b) 49pi
c) 64pi
d) 81pi
The area of the larger circle is 81π square units.
Congruent circles are circles that are similar in pattern.
The formula for calculating the area of a circle is expressed as:
[tex]A = \dfrac{\pi d^2}{4}[/tex]
Given that the area of each of the small circles is 9π, then:
[tex]9 \pi =\frac{\pi d^2}{4}\\9 = \frac{d^2}{4}\\d^2=9*4\\d^2=36\\d=\sqrt{36}\\d=6units[/tex]
This shows that the diameter of one of the small circles is 6units.
Since the diameter of the three circles will be equivalent to the diameter of the larger circle, hence;
Diameter of the larger circle = 3(6) = 18units
Get the area of the larger circle:
[tex]A=\frac{\pi D^2}{4}\\A=\frac{\pi \times 18^2}{4}\\A =\frac{324\pi}{4}\\A= 81\pi[/tex]
Hence the area of the larger circle is 81π square units.
Learn more on the area of circles here: https://brainly.com/question/12298717
Which equation does the graph of the systems of equations solve?
two linear functions intersecting at 3, negative 2
−one thirdx + 3 = x − 1
one thirdx − 3 = −x + 1
−one thirdx + 3 = −x − 1
one thirdx + 3 = x − 1
Answer:
-1/3x+3 = x-1
Step-by-step explanation:
The solution is (3,-2)
Check and see if the point solves the equation
-1/3x+3 = x-1
-1/3(3) +3 = 3-1
-1+3 = 3-1
2=2 yes
Answer:
C
Step-by-step explanation:
What is the distance from point N to LM in the figure below?
N
8.4
8.1
7.8
O
O A. 3.11
B. 0.8
C. 8.1
D. 2.18
E. 7.8
F. 8.4
Answer:
the answer to your question is 7.8 (E)
The distance from point N to LM is 7.8, 8.1 and 8.4 unit.
What is perpendicular?Perpendicular lines are those that cross at a straight angle to one another. Examples include the opposite sides of a rectangle and the steps of a straight staircase. the icon used to represent two parallel lines.
Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle.
Given:
In ΔNOM
The Perpendicular distance is 7.8 unit
and, Hypotenuse distance id 8.1 unit
Now, In ΔNOL
The Perpendicular distance is 7.8 unit
and, Hypotenuse distance id 8.4 unit
Learn more about perpendicular here:
https://brainly.com/question/29268451
#SPJ2
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use α = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?
Answer:
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
The possible proportion of patrons that do borrow books from the Owensboro Library is 0.82.
Step-by-step explanation:
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. Test if the proportion is higher in Owensboro, KY.
At the null hypothesis, we test if the proportion is of at most 0.67, that is:
[tex]H_0: p \leq 0.67[/tex]
At the alternative hypothesis, we test if the proportion is of more than 0.67, that is:
[tex]H_1: p > 0.67[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.67 is tested at the null hypothesis:
This means that [tex]\mu = 0.67, \sigma = \sqrt{0.67*0.33}[/tex]
The class randomly selected 100 patrons and found that 82 borrowed books.
This means that [tex]n = 100, X = \frac{82}{100} = 0.82[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.82 - 0.67}{\frac{\sqrt{0.67*0.33}}{\sqrt{100}}}[/tex]
[tex]z = 3.19[/tex]
P-value of the test and decision:
The p-value of the test is the probability of a finding a sample proportion of 0.82 or above, which is 1 subtracted by the p-value of z = 3.19.
Looking at the z-table, z = 3.19 has a p-value of 0.9993.
1 - 0.9993 = 0.0007
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
What is the possible proportion of patrons that do borrow books from the Owensboro Library?
The sample proportion of 0.82.
Volunteering: The General Social Survey asked 1309 people whether they performed any volunteer work during the past year. A total of 518 people said they did. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the population proportion of people who performed volunteer work in the past year. Round the answer to at least three decimal places. The point estimate for the proportion of people who performed volunteer work in the past year is .
Answer:
The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.
Step-by-step explanation:
Point estimate of a proportion:
Proportion is the number of desired outcomes divided by the number of total outcomes.
518 out of 1309 people performed volunteer work:
This means that:
[tex]p = \frac{518}{1309} = 0.396[/tex]
The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.
Using the following information to answer the questions.
- A survey asked 75 people if they wanted a later school day start time.
- 45 people were students, and the rest were teachers.
- 50 people voted yes for the later start
- 30 students voted yes for the later start
Use this information to complete the frequency table.
Use the completed table from Part a. What percentage of the people surveyed were teachers?
Use the completed table from Part a. What percentage of the people surveyed were teachers who wanted a later start time?
What does the number in the bolded cell represent?
Answer:
Hi! I'll provide the answers in the explanation.
Step-by-step explanation:
a) The table is in the attachment.
b) The percentage is 40%. Looking at the table, we can see that the total of teachers who voted is 30. You'll be able to find the percentage if you divide 30/75, since 75 is the total people who took the survey.
c) The percentage is 40%. For this situation, we have to divide the total of the people who voted for NO by the teachers who voted NO. So it'll be 20/50, which is 0.4. We can simplify that and the solution is 40%.
d) It represents the students who took the survey voted NO for a later start.
Hope this helps! :D
Answer:
5. Use the following information to answer the questions.
A survey asked 75 people if they wanted a later school day start time.
45 people were students, and the rest were teachers.
50 people voted yes for the later start.
30 students voted yes for the later start.
a) Use this information to complete the frequency table. (5 points: 1 point for each cell that was not given above)
Vote YES for later start
Vote NO for later start
Total
Students
30
15
45
Teachers
20
10
30
Total
50
25
75
b) Use the completed table from Part a. What percentage of the people surveyed were teachers? (2 points)
40%
c) Use the completed table from Part a. What percentage of the people surveyed were teachers who wanted a later start time? (2 points)
40%
d) What does the number in the bolded cell represent? (1 point)
The number of students that said no to a later start.
Step-by-step explanation:
A p E x
How many numbers multiple of 3 are in the range [2,2000]?
Answer: so there are 666 multiples of 3 between 2 and 2000.
Step-by-step explanation:
the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666
multiples of 3 between {2,2000} = 666-1+1 = 666
Find the missing ? Step by step need it
Answer:
30 degrees
Step-by-step explanation:
Use the Tan formula.
In a scatter plot, each ____. Group of answer choices individual is represented by a single point group mean is represented by a single point individual is represented by two data points group mean is represented by two data points
Answer:
Individual is represented by a single point
Step-by-step explanation:
Which of the following rational functions is graphed below?
o
A. F(x) = 1/2x
B. AX) = 1/x-2
C. F(x) = 1/x+2
Answer:
Option B.
Step-by-step explanation:
We can see that we have an asymptote at x = 2
Remember that in a rational function, the asymptote is at the x-value such that the denominator is equal to zero.
So, the denominator is something like:
(x + a)
we have that the denominator is zero when x = 2
Then:
(2 + a) = 0
solving that for a, we get:
a = -2
Then the denominator of the rational function is:
(x - 2)
For the given options, the only one with this denominator is option B, then the correct option is B.
Answer:
B. f(x) = 1/x-2
Step-by-step explanation:
Math is ez bro.
The correlation coefficient, r, between the ages of employees, x, and the number of sick days taken per year, y, equals 0.81.
Complete the statement based on the information provided.
The value of r is
✔ positive
and is relatively close to
✔ 1
, so the variables are
✔ closely
associated. It appears that, as the age of an employee increases, the number of sick days taken
✔ increases
.
Answer:
✔ positive
✔ 1
✔ closely
✔ increases
ED2021
which polygon will NOT tessellate a plane?
Answer:
pentagons
Step-by-step explanation:
In fact, there are pentagons which do not tessellate the plane. The house pentagon has two right angles. Because those two angles sum to 180° they can fit along a line, and the other three angles sum to 360° (= 540° - 180°) and fit around a vertex.
Answer:
The Regular Pentagon.
Explanation
I got a 100 % on the quiz
I need to know the answer ASAP please
By observing the points you can learn a lot about a function. Concretely [tex]f(x)[/tex] passes through [tex](1,1)[/tex] but [tex]g(x)[/tex] passes through [tex](1,-\frac{1}{2})[/tex] that should give you a hint that [tex]g(x)=-\frac{1}{2}x^2[/tex].
Hope this helps :)
Please,look at this one.
9514 1404 393
Answer:
x = √2
Step-by-step explanation:
A graph indicates the only solution is near x=√2.
__
Square both sides, separate the radical and do it again.
[tex]\displaystyle(2-x)\sqrt{\frac{x+2}{x-1}}=\sqrt{x}+\sqrt{3x-4}\qquad\text{given}\\\\(2-x)^2\cdot\frac{x+2}{x-1}=x+(3x-4)+2\sqrt{x(3x-4)}\qquad\text{square}\\\\\frac{(2-x)^2(x+2)}{x-1}-4x+4=2\sqrt{x(3x-4)}\qquad\text{isolate radical}\\\\\left(\frac{(2-x)^2(x+2)-4(x-1)^2}{x-1}\right)^2=x(3x-4)\qquad\text{square}\\\\(x^3-6x^2+4x+4)^2=4(x-1)^2(3x^2-4x)\qquad\text{multiply by $(x-1)^2$}[/tex]
Now, we can put this polynomial equation into standard form and factor it.
[tex]x^6 -12x^5+32x^4-76x^2+48x+16=0\\\\(x-2)^2(x^2-2)(x^2-8x-2)=0\qquad\text{factor it}\\\\x\in \{2,\pm\sqrt{2},4\pm3\sqrt{2}\}[/tex]
The original equation requires that we restrict the domain of possible solutions. In order for the radicals to be non-negative, we must have x ≥ 4/3. In order for the left side of the equation to be non-negative, we must have x ≤ 2. So, the only potential solutions will be in the interval [4/3, 2].
The only values in the above list that match this requirement are {√2, 2}. We know that the right side of the equation cannot be zero, so the value x=2 is also an extraneous solution.
The only solution is x = √2.
_____
Additional comment
For solving higher-degree polynomials, I like to use a graphing calculator to help me find the roots. The second attachment shows the roots of the 6th-degree polynomial. They can help us factor the equation. (There are also various machine solvers available that will show factors and roots.)
The sum of the two numbers is 66. The larger number is 10 more than the smaller number. What are the numbers?
Answer:
28 and 38
Step-by-step explanation:
a+b = 66
a + 10 = b
using substitution, a + (a+10) = 66
2a = 56
a = 28
28 + 10 = 38
b = 38
When a teacher in a private school points out to her high school principal that since there are empty seats in all classrooms, the cost of additional students is really zero, she is using the
Answer:
The answer is "Principal of marginal analysis".
Step-by-step explanation:
To determine unless the benefits of even an aggressive resource would outweigh its costs, and therefore increase utility, individuals and businesses can use a valuation model to compare the risks versus the benefits of more activities, like whether to create or consuming more. It's the amount during which net value is greater than or equal to marginal cost that's the optimal quantity in this situation. The amount where the marginal social cost curve and consumer surplus line connect.
Given the following data from a repeated-measures design study examining the effect of a treatment by measuring a group of 9 participants before and after they received treatment:
Participant Before After
A 8 7
B 7 5
C 6 6
D 7 6
E 9 7
F 8 5
G 5 4
H 9 4
I 7 4
a. Calculate the difference scores and MD.
b. Compute SS, sample variance, and estimated standard error.
c. Is there a significant treatment effect?
Answer:
MD = 2
SS = 18
SAMPLE VARIANCE = 2.25
STANDARD ERROR = 0.5
Step-by-step explanation:
Given :
A 8 7
B 7 5
C 6 6
D 7 6
E 9 7
F 8 5
G 5 4
H 9 4
I 7 4
Difference, d = Before - After
______ d
A 8 7 __ 1
B 7 5 __ 2
C 6 6 __ 0
D 7 6 __ 1
E 9 7 __ 2
F 8 5 __ 3
G 5 4 __ 1
H 9 4 __5
I 7 4 ___3
The mean of difference, MD ;
MD = Σd/ n = (1+2+0+1+2+3+1+5+3) / 9 = 18 / 9 = 2
The sum of square, SS ;
(1 - 2)^2 + (2 - 2)^2 + (0 - 2)^2 + (1 - 2)^2 + (2 - 2)^2 + (3 - 2)^2 + (1 - 2)^2 + (5 - 2)^2 + (3 - 2)^2 = 18
Sample variance, S² = SS/(N-1) = 18 / (9 - 1) = 18 / 8 = 2.25
Sample standard deviation, S = √Variance = √2.25 = 1.5
Standard Error, S.E = S / √n = 1.5 / √9 = 0.5
Test statistic : MD / S.E = 2 / 0.5 = 4
We test at α = 0.05 since no α - value is stated in the question.
Critical value at 0.05, df = 8 ;
Critical value = 2.306
Since; Test statistic > Critical value, then result is significant at α = 0.05
