Answer:
0.0438 kg
Step-by-step explanation:
We are given;
Potential energy; U = 860 J
Height; h = 2 km = 2000 m
Formula for potential energy is;
U = mgh
Where g is acceleration due to gravity = 9.81 m/s²
Thus;
860 = m × 9.81 × 2000
m = 860/(9.81 × 2000)
m = 0.0438 kg
A magazine includes a report on the energy costs per year for32-inch liquid crystal display (LCD) televisions. The article states that 14 randomly selected 32-inch LCD televisions have a sample standard deviation of $3.42 . Assume the sample is taken from a normally distributed population. Construct 98 % confidence intervals for (a) the population variance sigma squared and (b) the population standard deviation sigma .
Interpret the results. (a) The confidence interval for the population variance is (___,___ ). (Round to two decimal places as needed.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)
A. With 98 % confidence, you can say that the population variance is less than ___.
B. With 2 % confidence, you can say that the population variance is between nothing and ___ .
C. With 98 % confidence, you can say that the population variance is between ___ and ___ .
D. With 2 % confidence, you can say that the population variance is greater than ___
(b) The confidence interval for the population standard deviation is (n___,___). (Round to two decimal places asneeded.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)
A. With 98% confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
B. With 98% confidence, you can say that the population standard deviation is greater than ___ dollars per year.
C. With 2% confidence, you can say that the population standard deviation is less than ___ dollars per year.
D. With 2% confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
Answer:
a
The confidence interval for the population variance is [tex] 5.49 < \sigma^2 < 37.02 [/tex]
The correct option is C
b
The confidence interval for the population standard deviation is [tex] 2.34 < \sigma < 6.08 [/tex]
The correct option is A
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The standard deviation is [tex]s = \$3.42[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = 14 -1[/tex]
=> [tex]df = 13 [/tex]
Given that the confidence level is 98% then that level of significance is
[tex]\alpha = (100 -98) \%[/tex]
=> [tex]\alpha = 0.02[/tex]
Generally the 98% confidence interval for the variance is mathematically represented as
[tex]\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}} < \sigma^2 < \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}[/tex]
=> [tex]\frac{(14- 1) (3.42)^2}{x^2 _{[\frac{0.02 }{2} , 13]}} < \sigma^2 < \frac{(14- 1) (3.42)^2}{x^2 _{[1- \frac{0.02 }{2} , 13]}}[/tex]
From the chi -distribution table
[tex]x^2 _{[1- \frac{0.02 }{2} , 13]} = 4.107[/tex]
and
[tex]x^2 _{[\frac{0.02 }{2} , 13]} = 27.689[/tex]
So
=> [tex]\frac{(14- 1) (3.42)^2}{27.689} < \sigma^2 < \frac{(14- 1) (3.42)^2}{4.107}[/tex]
=> [tex] 5.49 < \sigma^2 < 37.02 [/tex]
Generally the 98% confidence interval for the standard deviation is mathematically represented as
[tex]\sqrt{\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}}} < \sigma <\sqrt{ \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}}[/tex]
=> [tex]\sqrt{5.49} < \sigma < \sqrt{37.02 }[/tex]
=> [tex] 2.34 < \sigma < 6.08 [/tex]
7 + 2/3x= -1 can you help me solve
[tex]7 + \dfrac{2}{3x} = - 1 \\ \implies \: \dfrac{2}{3x} = - 1 - 7 \\ \implies \: \dfrac{2}{3x} = - 8 \\ \implies \: 2 = - 24x \\ \implies \: x = - \dfrac{2}{24} \\ \implies \: x = - \dfrac{1}{12} [/tex]
Answer:
x = -12
Step-by-step explanation:
multiply all terms by 3 to get whole numbers
->21+2x=-3
subtract 21 both sides to isolate the variable
->2x=-24
divide by 2 both sides to simplify
->x=-12
x+2x+x+20=180 what is x
Answer: x=40
Step-by-step explanation:
x+2x+x+20=180
first you combine the like terms which are (x, 2x, x) and get 4x.
now you have 4x+20=180
next you subtract 20 on both sides:
4x+20=180
-20 -20
and get 4x=160
finally you divide 4 on both sides and get a final answers of x=40
Thirteen students entered the business program at Sante Fe College 2 years ago. The following table indicates what each student scored on the high school SAT math exam and their grade-point averages (GPAs) after students were in the Sante Fe program for 2 years.
Student A B C D E F G
SAT Score 421 375 585 693 608 392 418
GPA 2.93 2.87 3.03 3.42 3.66 2.91 2.12
Student H I J K L M
SAT Score 484 725 506 613 706 366
GPA 2.50 3.24 1.97 2.73 3.88 1.58
The least-squares regression equation that shows the best relationship between GPA and the SAT score is:_____.
Answer:
y=1.003009+0.003453x
or
GPA=1.003009+0.003453(SAT Score)
Step-by-step explanation:
The least square regression equation can be written as
y=a+bx
In the given scenario y is the GPA and x is SAT score because GPA depends on SAT score.
SAT score (X) GPA (Y) X² XY
421 2.93 177241 1233.53
375 2.87 140625 1076.25
585 3.03 342225 1772.55
693 3.42 480249 2370.06
608 3.66 369664 2225.28
392 2.91 153664 1140.72
418 2.12 174724 886.16
484 2.5 234256 1210
725 3.24 525625 2349
506 1.97 256036 996.82
613 2.73 375769 1673.49
706 3.88 498436 2739.28
366 1.58 133956 578.28
sumx=6892
sumy=36.84
sumx²=3862470
sumxy=20251.42
n=13
[tex]b=\frac{(nsumxy)-(sumx)(sumy)}{nsumx^{2}-(sumx)^{2} }[/tex]
b=9367.18/2712446
b=0.003453
a=ybar-b(xbar)
ybar=sum(y)/n
ybar=2.833846
xbar=sum(x)/n
xbar=530.1538
a=2.833846-0.003453*(530.1538)
a=1.003009
Thus, required regression equation is
y=1.003009+0.003453x.
The least-squares regression equation that shows the best relationship between GPA and the SAT score is
GPA=1.003009+0.003453(SAT Score)
A survey showed that 82% of kids play video games at home. What fraction of kids play video games at home?
Answer:
8.2/10
Step-by-step explanation:
Answer:
42/50
Step-by-step explanation:
What's 2 × 30 ÷12 +10
Answer:
Your answer would be 15
Step-by-step explanation:
The first step you are going to want to do is multiply 2 and 30
30×2=60
Then you are going to divide 60 by 12
60÷12=5
Last you wanna add the 5 and the 10
5+10=15
0.9 7/8 0.86 least to greatest work
Answer:
7/8, 0.86, 0.9
Step-by-step explanation:
Convert 7/8 to a decimal:
7 / 8 = .875
Solve:
.875, .86, .9
Or:
7/8, 0.86, 0.9
A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 9.8 inches, and standard deviation of 1.6 inches. If 48 items are chosen at random, what is the probability that their mean length is greater than 9.2 inches
Answer:
0.6462
Step-by-step explanation:
Given that
Mean (m) = 9.8
Standard deviation (s) = 1.6
Probability that mean length is greater than 9.2
Z = (x - m) / s
Z = (9.2 - 9.8) / 1.6
Z = - 0.6 / 1.6
Zscore = - 0.375 = - 0.375
P(Z >- 0.375) = 1 - P(Z < - 0.375) ;
P(Z < - 0.375) = 0.3538
1 - P(Z < - 0.38) = 1 - 0.3538 = 0.6462
Jill runs 3/4 of a mile, and
Amy runs 2/3 of a mile.
How far did Jill and Amy
run combined?
Answer:
1 1/5 mile
Step-by-step explanation:
3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 1/5
The changes in housing prices over short time periods are in part determined by supply and demand. A real estate company in Minnesota projected an increase in its average selling prices of homes in the first quarter of 2014 over the mean 2013 selling price of $201,800. The reason for the projection was an increase in demand due to business expansion and the subsequent increase in labor. To investigate the accuracy of the projection, a sample of homes in the first quarter of 2014 was selected and the following selling prices (in $) recorded:
235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500
Required:
a. At 5% level of significance, is there sufficient evidence to support the real estate company's projection?
b. Which statistical distribution should be applied in this situation and why? Explain carefully.
c. Discuss the consequences of Type I and Type II errors in terms of the problem.
d. Does the management at the real estate company want a small or large value of the significance level? Explain carefully.
e. Based on a 95% confidence level, estimate the actual average selling price homes in the first quarter of 2014.
Answer:
The data given is
235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500
The sample size is n = 16
The population is [tex]\mu = \$201,800[/tex]
The sample mean is mathematically represented as
[tex]\= x =\frac{\sum x_i}{n}[/tex]
=> [tex]\= x =\frac{235,000 + 271,900 + \cdots + 245,500 }{16}[/tex]
=> [tex]\= x = 218653.125[/tex]
Generally the sample standard deviation is mathematically represented as
[tex]s = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }[/tex]
=> [tex]s = \sqrt{\frac{ (235,000 - 218653.125)^2+ (271,900 - 218653.125)^2 + \cdots + (245,500 - 218653.125)^2}{16} }[/tex]
=> [tex]s = 23946.896 [/tex]
The null hypothesis is [tex]H_o : \mu = \$201,800[/tex]
The alternatively hypothesis is [tex]H_o : \mu > \$201,800 [/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{218653.125 - 201800 }{ \frac{23946.896 }{\sqrt{16} } }[/tex]
=> [tex]t = 2.82[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
=> [tex]df = 16 - 1[/tex]
=> [tex]df = 15[/tex]
Generally the probability of [tex]t = 2.82[/tex] at a degree of freedom of [tex]df = 15[/tex] from the t - distribution table is
[tex]p-value = P( t >2.82 ) =0.00646356[/tex]
The
From the values obtained we see that [tex]p-value < \alpha[/tex]
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the real estate company's projection is true
Given that the population variance is unknown then the best statistical distribution to be applied is the t -distribution
Type I Error
The type 1 error occur when the null hypothesis is wrongfully rejected
The consequence in this case is the company will assume that the average selling price has increase and this will lead the company to start expanding the business while in the real sense the average selling price is still $201,800
Type II Error
The type 11 error occur when the null hypothesis is wrongfully accepted(i.e wrongfully failed to reject the null hypothesis)
The consequence in this case is that the company will assume that the average selling price is still $201,800 and will not make plans to increase the business while in the real sense the average selling price has increased
Given that resource is scare the management of the company will want a smaller significance level in order not to commit type I error which will lead to wrongly expanding the business and wastes of resources
generally the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E =Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }[/tex]
=>[tex]E =1.96* \frac{23946.896}{\sqrt{16} }[/tex]
=>[tex]E = 11733.96[/tex]
Generally the 95% confidence interval is mathematically represented as
[tex]218653.125 - 11733.96 < \mu < 218653.125 + 11733.96[/tex]
=> [tex]206919.165 < \mu < 230387.085[/tex]
Generally there is 95% confidence that the actual average selling price is within this interval
Step-by-step explanation:
A furniture manufacturer makes two types of furniture: chairs and sofas. The production of the sofas and chairs requires three operations: carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The prfit per chair is $90 and the profit per sofa is $75. The manufacturer wants to know how many chairs and how many sofas should be produced each day to maximize the profit.
Formulate a linear programming (LP)problem you would use to find a solution.
Step-by-step explanation:
let chairs be C and sofas be S
The objective function is
Maximize
90C+75S=P
The constraints are
carpentry
3C+2S=66------1
finishing
9C+4S=180-----2
upholstery
2C+10S=200-----3
C>0, S>0
The linear programming is
3C+2S=66
9C+4S=180
2C+10S=200
Please help guys this has to be do in 10:00 please help
Answer:
1)14oz
2)28oz
Step-by-step explanation:
1) To find the amount of water is left in the bottle you want to substract 1/3 so the first thing you want to do is find what 1/3 of 42 is. So do this: (This is also 42/3)
42*1/3=14
So we now know that 14 is 1/3 of 45 which is the first answer. To find the second answer you want to substract 14 from 42 which is 28.
So that means she has 28 oz of water left when she gets there.
Eight individuals are candidates for positions of president, vice president, and treasurer of an organization. How many possibilities of selections exist
Answer:
336
Step-by-step explanation:
It is given that,
Total number of individuals are 8
They are candidates for positions of president, vice president, and treasurer of an organization.
It is a based on permutations. We need to find P(8,3). It can be calculated as follows :
[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]
So,
[tex]P(8,3)=\dfrac{8!}{(8-3)!}\\\\=\dfrac{8!}{5!}\\\\=\dfrac{8\times 7\times 6\times 5!}{5!}\ [\because n!=n(n-1)!]\\\\=8\times 7\times 6\\\\=336[/tex]
Hence, there are 336 possibilities of selections.
Solve the literal equation xy - 4xz = 5 for x.
X=
Answer:
x = 5/(-4 z + y)
Step-by-step explanation:
Solve for x:
x y - 4 x z = 5
Hint: | Write the linear polynomial on the left-hand side in standard form.
Collect in terms of x:
x (-4 z + y) = 5
Hint: | Solve for x.
Divide both sides by -4 z + y:
Answer: x = 5/(-4 z + y)
Paula walked 4.5 miles. How many kilometers did Paula walk? I mile = 1.61 kilometers
Answer:
2.79 kilometers
Step-by-step explanation:
4.5/1.61
How do I work the problem the ratio of Jane age to her daughter age is 9:2 the sum of their ages is 44... how old is jane
Answer:
Jane is 4years old......
Using the following conversions between the metric and U.S. systems, convert the measurement. Round your answer to the nearest tenth as needed
There are 8 fluid ounces in a cup, 2 cups in a pint, 2 pints in a quart,
and 4 quarts in a gallon.
1L ~ 0.26 gallons
9 fl oz _____ mL
Answer:
266.162 ml
Step-by-step explanation:
$5.97 / 2
please show your work! I'll give brainliest to whoever shows work.
Answer:
2.99
Step-by-step explanation:
1.) 2 goes into 5 2 times. So the 2 goes on top of the division sign
2.) 2x2=4
3.) Move 4 below 5
4.) Subtract 5-4=1
5.) Bring down 9
6.) 2 Goes into 19 9 times
7.) 2x9=18
8.) 19-18=1
9.) Bring down the 7
10.) 2 Goes into 17 8 times
11.) 2x8= 16
12.) 17-16=1
13.) Add a zero onto the end, bring down that zero
14.) 2 goes into 10 5 times.
15.) Round answer to 2.99 because with money you only have two decimals
A. Choudhury’s bowling ball factory in Illinois makes bowling balls of adult size and weight only. The standard deviation in the weight of a bowling ball produced at the factory is known to be 0.12 pounds. Each day for 24 days, the average weight, in pounds, of nine of the bowling balls produced that day has been assessed as follows:
Day Average (LB) Day Average (LB)
1 16.3 13 16.3
2 15.9 14 15.9
3 15.8 15 16.3
4 15.5 16 16.2
5 16.3 17 16.1
6 16.2 18 15.9
7 16.0 19 16.2
8 16.1 20 15.9
9 15.9 21 15.9
10 16.2 22 16.0
11 15.9 23 15.5
12 15.9 24 15.8
Required:
a. Establish a control chart for monitoring the average weights of the bowling balls in which the upper and lower control limits are each two standard deviations from the mean. What are the values of the control limits?
b. If three standard deviations ate used in the chart, how do these values change? Why?
Answer and explanation:
Please find attached answer and explanation
how math is used in technology
Answer:read the explanation
Step-by-step explanation:
The processors that power computers are able to perform calculations quickly, and the calculations are performed using Boolean algebra. People generally solve math problems using a base-10 number system. Boolean algebra relies on base-2 math, in which all numbers are represented using ones and zeros.
In addition to calculating basic math problems, however, computers also use Boolean logic. This logic, which is rooted in discrete mathematical principles, allows computers to solve problems that require making logical decisions. Boolean algebra and logic combine to make sophisticated devices; self-driving cars, for example, use the input calculated from digital cameras to make decisions about how to navigate.
Federico read the nutritional information on a package of gummi bears.
The points on the following coordinate plane show how many gummi bears there are in 2, 3, and 5 servings.
Answer:
80
gummi bears
Step-by-step explanation:
a: -20
b:-8
c:8
d:48
¿?
Answer:
the correct answer is -8
Step-by-step explanation:
to find this you are going to substitute 8 in for x in the equation
what is the lcm of 16 and 24
Answer:
48
Step-by-step explanation:
How does the graph of y = sec(x - 2) + 2
compare to the graph of y = sec(x)?
0 It is shifted 2 units down and 2 units left.
It is shifted 2 units down and 2 units right.
O It is shifted 2 units up and 2 units left.
It is shifted 2 units up and 2 units right.
Answer:
D
or
It is shifted 2 units up and 2 units right.
Step-by-step explanation:
The graph of y = sec(x) is shifted 2 units up and 2 units right.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given graph is y = sec(x)
After transformation it is y = sec(x - 2) + 2
We need to find the transformation applied to y=secx to get y = sec(x - 2) + 2.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
y=f(x-a) is the same graph shifted 'a' units to the right. If 'a' is negative, then, the graph is shifted to the left.
y = f(x) - a is the same graph, but shifted 'a' units downwards. If 'a' is negative, then the graph will be shifted upwards.
In this case, our main function is y=sec(x). And the function y= sec(x-2)+2 is shifted two units to the right and 2 units upwards.
Hence, the graph of y = sec(x) is shifted 2 units up and 2 units right.
To learn more on Graph click:
https://brainly.com/question/17267403
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Graph the system of linear inequalities on the coordinate plane.
y [tex]\geq[/tex] 1/2x + 2 1/2
y< 1/5 x + 6
a. Shade the solution to the system of inequalities.
b. Pick a point and show your solution is correct.
Answer: Images of Graphs are listed below. I am unsure on how to conduct the second part. but there is the first part
Step-by-step explanation:
Claire wants to determine how her math score 690 on a standardized college entrance exam compared to her mother score 680 what she took the exam 20 years earlier the year Clair took the exam the mean math score was 510 with a standard deviation of 110 points on Claires mother took the exam the mean math score was 490 with a standard deviation of 100 points who has the better relative performance
Answer:
Claires mother did better because her z score was greater than Claires
Step-by-step explanation:
I j took the quiz
Claire's mother did better because her z-score was greater than that of Claires.
What is Z -score?A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
As per the given information, the solution would be as
Here is Claire's data:
ц₁ = 510
σ₁ = 110
X₁ = 690
⇒ z-score = (X₁-ц₁ )/σ₁
Substitute the values,
⇒ z-score = (690 - 510)/110
⇒ z-score = 180/110
⇒ z-score = 1.636
Here is Claire's mother's data:
ц = 490
σ₂ = 100
X₂ = 680
⇒ z-score = (X₂-ц )/σ₂
Substitute the values,
⇒ z-score = (680 - 490)/100
⇒ z-score = 190/100
⇒ z-score = 1.9
So Claire's mother's z-score > Claire's z-score
Therefore, Claire's mother did better because her z-score was greater than that of Claires.
Learn more about the z-score here:
brainly.com/question/13793746
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Please help...
Solve using the method of your choice:
[tex]2 {x}^{2} + 3x - 2 = 0[/tex]
Answer:
x=½, -2
x= 0.5, -2
possibly im not perfect
help me please i’ll give u a cookie
Answer:
the answer is B
Step-by-step explanation:
i just did this.
What is the area of a rectangle with sides measuring 2x+3 and 3x-1 feet
Suppose n(t) = -51^2 + 10t + 3 represents the height of a
diver above the water (in meters), 1 seconds after
the diver leaves the springboard. Which of these
statements is true?
(А)
After 1 second, the diver will be 3 feet above
the water.
B
After 5 seconds, the diver will be 25 feet above
the water.
С
After 1 second, the diver will be 8 feet above
the water.
D
After 5 seconds, the diver will be 78 feet above
the water.
Answer:
The correct option is (c).
Step-by-step explanation:
The height of a diver abov the water is given by :
[tex]h(t) = -5t^2 + 10t + 3[/tex] ....(1)
Where h(t) is in meters and t is in seconds
Put t = 1 s, in equation (1) we get :
[tex]h(1) = -5(1)^2 + 10(1) + 3\\\\=8\ \text{feet}[/tex]
Put t = 5 s, in equation (1) we get :
[tex]h(1) = -5(5)^2 + 10(5) + 3\\\\=-72\ \text{feet}[/tex]
Out of the given options, "after 1 second, the diver will be 8 feet above the water is (c)". Hence, the correct option is (c).