Answer:
b. The engineer who weighed the rod 25 times.
Step-by-step explanation:
Hello!
Full text:
Length of a rod: Engineers on the Bay Bridge are measuring tower rods to find out if any rods have been corroded from salt water. There are rods on the east and west sides of the bridge span. One engineer plans to measure the length of an eastern rod 25 times and then calculate the average of the 25 measurements to estimate the true length of the eastern rod. A different engineer plans to measure the length of a western rod 20 times and then calculate the average of the 20 measurements to estimate the true length of the western rod.
Suppose the engineers construct a 90% confidence interval for the true length of their rods. Whose interval do you expect to be more precise (narrower)?
a. Both confidence intervals would be equally precise.
b. The engineer who weighed the rod 25 times.
c. The engineer who weighed the rod 20 times.
X₁: Length of an eastern rod of the Bay Bridge
n₁= 25
X₂: Length of a western rod of the Bay Bridge
n₂= 20
Both Engineers will use their samples to estimate the population average length of the rods using a 90% CI.
Assuming the standard normal distribution, the confidence interval will be centered in the estimated mean.
X[bar] ± [tex]Z_{1-\alpha /2}[/tex]*(σ/√n)
And the width is determined by the semi amplitude:
↓d= [tex]Z_{1-\alpha /2}[/tex]*(σ/√↑n)
As you can see the sample size has an indirect relationship with the semi amplitude of the interval. This means, when the sample size increases, the semi amplitude decreases, and if the sample size decreases, the semi amplitude increases. Naturally this is leaving all other elements of the equation constant, this means, using the same confidence level and the same population standard deviation.
Since the first engineer took the larger sample, he's confidence interval will be narrower and more accurate.
Hope this helps!
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A
Step-by-step explanation:
It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.
Answer:
A. G(x) = [tex]x^2+7[/tex]
Step-by-step explanation:
→For the function to shift upwards 7 units, 7 must be added to the function, like so:
G(x) = [tex]x^2+7[/tex]
→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.
This means the correct answer is A.
Which of the following best describes the slope of the line below?
PLSSS HELP
The slope is zero. Slope formula is Y=mx+b and since B is 1.5 and it is a straight line, Y=mx+1.5. What plus 1.5 is 1.5? 0. Hope this helps.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
96
Step-by-step explanation:
Rectangle area:
(8)(10)=80
Triangle area:
(1/2)(4)(8)=16
Total area:
16+80=96
Answer:
[tex]96 {ft}^{2} [/tex]
Step-by-step explanation:
[tex]area = \frac{1}{2} (a + b)h \\ = \frac{1}{2} \times (10 + 14) \times 8 \\ = \frac{1}{2} \times 24 \times 8 \\ = 96 {ft}^{2} [/tex]
A group of neighbors are constructing a community garden that is 80 m wide and 40 m long the top to vertex are plotted below at 10, 70 and 90, 70 what are the coordinates from the bottom to vertex of the garden
Question Correction
A group of neighbors are constructing a community garden that is 80 meters wide and 40 meters long. The top two vertices are plotted below at (10, 70) and (90, 70). What are the coordinates for the bottom two vertices of the garden?
Answer:
(10,30) and (90,30)
Step-by-step explanation:
The community garden is 80 m wide and 40 m long.
The top two vertex are plotted at: (10, 70) and (90, 70).
Horizontal Distance =90-10=80
This serves as the Width of the garden.
Since the length is 40m, the bottom two vertex can be derived by the transformation: (x,y-40).
(x,y-40)-->(10, 70)=(10,30); and
(x,y-40)-->(90, 70)=(90,30)
The coordinates for the two bottom vertices are (10,30) and (90,30).
A completely randomized design Group of answer choices has one factor and one block. has one factor and one block and multiple values. can have more than one factor, each with several treatment groups. has only one factor with several treatment groups.
Answer:
C. can have more than one factor, each with several treatment groups.
Step-by-step explanation:
A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.
Completely randomized design has found application in agricultural and environmental researches.
Solve for x. e^x - e ^ -x / e^x + e ^-x = t
Answer:
D
Step-by-step explanation:
(eˣ − e⁻ˣ) / (eˣ + e⁻ˣ) = t
Multiply by eˣ/eˣ.
(e²ˣ − 1) / (e²ˣ + 1) = t
Solve for e²ˣ.
e²ˣ − 1 = (e²ˣ + 1) t
e²ˣ − 1 = e²ˣ t + t
e²ˣ = 1 + e²ˣ t + t
e²ˣ − e²ˣ t = 1 + t
e²ˣ (1 − t) = 1 + t
e²ˣ = (1 + t) / (1 − t)
Solve for x.
2x = ln[(1 + t) / (1 − t)]
x = ½ ln[(1 + t) / (1 − t)]
Use log rule.
x = ln(√[(1 + t) / (1 − t)])
Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 10 percent are returned. If eight rings are sold today, what is the probability that fewer than three will be returned
Answer:
[tex]P(X<3) =[/tex] [tex]0.9619[/tex]
Step-by-step explanation:
From the given information;
the probability of getting returned p = 0.1
If eight rings are sold today, what is the probability that fewer than three will be returned;
According to binomial distribution
Binomial distribution is the probability of success or failure of an outcome of an experiment under observation which is usually repeated several trials. Binomial experiments are random experiment with fixed number of repeated experiment. If we cannot predict before head, the outcome of an experiment , the experiment is called a random experiment.
So , using binomial distribution to determine the probability that fewer than three will be returned;
i.e
[tex]P(X<3) =[/tex] [tex]\sum_{x=0}^{2}\binom{8}{x}(0.1)^{x}(1-0.1)^{8-x}[/tex]
[tex]P(X<3) =[/tex] [tex]0.9619[/tex]
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 5% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employee will experience a lost-time accident in both years (to 1 decimal)?
Answer:
The percentage of the employee will experience a lost-time accident in both years is 0.0%
Step-by-step explanation:
Let A denote events that employees suffered lost-time accidents during the last year
Let B denote events that employees suffered lost-time accidents during the current year
P(A) = 5% = 0.05
P(B) = 4% = 0.04
P(B | A) = 15% = 0.15
(a) P (A ∩ B) = P(B | A) × P(A)
= 0.15 × 0.05
= 0.0075
= 0.0 (1 decimal place)
The probability that an employee will experience a lost- time accident in both years is 0.0
WILL GIVE BRAINLIEST ANSWER ASAP
Answer:
x = -6
Step-by-step explanation:
-2/3x + 9 = 4/3x - 3
First we need to simplify to where we have x on one side and a constant (number not connected to a variable) on the other side.
Subtract 4/3x from both sides:
-2/3x + 9 - 4/3x = -3
-6/3x + 9 = -3
Now subtract 9 from both sides:
-6/3x + 9 - 9 = -3 - 9
-6/3x = -12
Now turn -6/3 into a whole number to make things more simple:
-6/3 = -2
-2x = -12
Now divide both sides by -2 to get x by itself
-2x/-2 = -12/-2
x = -6
help ,, I need help with this one ,, i’m soo confused
As the x values go up, the y values go down which means the line is higher on the left side than it is on the right side.
The 4th graph would be the correct one
The following data values represent a population. What is the variance of the
values?
8, 10, 14,4
A. 14
B. 10
C. 9
D. 13
Answer:
D: 13
So first you write down your equation ( its on the picture I posted) Then you need to find the mean which is the sum of all the values over the number of values you have (n) After finding your mean, you subtract it from every value you have. To check if what you have done is correct you add all the values you got after subtracting, if you get 0 your answer is correct. Then you square each of those answers you get after you subtract. You get the total which you then divide by the number of values you have (n)
I hope you understand, I am not that good at explaining. And I am not completely sure with my answer, but I think it's correct.
two lines intersect is more than one point
Answer:
FALSE
Step-by-step explanation:
two lines can be parallel- no intersectstwo lines intersect- one pointa^3b^2 divided by a^-1b^-3
Answer:
[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]
And simplifying we got:
[tex] a^3 b^2 a b^3[/tex]
[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]
Step-by-step explanation:
We want to simplify the following expression:
[tex] \frac{a^3 b^2}{a^{-1} b^{-3}}[/tex]
And we can rewrite this expression using this property for any number a:
[tex] a^{-1}= \frac{1}{a}[/tex]
And using this property we have:
[tex]\frac{a^3 b^2}{\frac{1}{a} \frac{1}{b^3}}[/tex]
And simplifying we got:
[tex] a^3 b^2 a b^3[/tex]
[tex] a^3 a b^2 b^3 = a^{3+1} b^{2+3} = a^4 b^5[/tex]
Please help me with this problem
Answer:
I think it is -2
Step-by-step explanation:
I think but I do not know
build the greatest and the smallest number using the digit 7,2,6
greatest _____ and smallest ____
What letter completes the puzzle? The answer is probably easy for you guys but I don't understand how the letters go along with the puzzle. Thank you!
Answer:
the answer is E the number at the top tells you which position it falls under in the alphabet
Solve for x
A) 36
B) 54
C) 72
D) 84
Ayo help a girl out
Answer:
72°
Step-by-step explanation:
This is called an isosceles triangle. This means that the 2 angles related to the equal sides, are also equal. Hence, the answer is 72°
Answer:
A
Step-by-step explanation:
Since it is isosceles triangle (two equal sides) therefore, there are 2 equal angles too which at the base (72°)
The total angle of triange is 180°
So 180-72-72=36°
A(x) = -0.015x^3+1.05xA ( x ) = − 0.015 x 3 + 1.05 x gives the alcohol level in an average person's blood x hrs after drinking 8 oz of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk.
Would an average person be legally drunk after 4 hours?
Answer:
Yes
Step-by-step explanation:
the function that gives the alcohol level is:
[tex]A ( x ) = - 0.015 x^3 + 1.05 x[/tex]
where x is the number of hours.
we need to know if after 4 hours an average person is legally drunk, thus:
[tex]x=4[/tex]
and we substitute this in the function:
[tex]A ( 4 ) = - 0.015 (4)^ 3 + 1.05(4)[/tex]
solving these operations we obtain:
[tex]A(4)=-0.015(64)+4.2\\A(4)=-0.96+4.2[/tex]
[tex]A(4)=3.24[/tex]
the alcohol level after 4 hours is 3.24.
Since a person is considered to be legally drunk if the level exceeds 1.5, and we obtained 3.24 which is greater than 1.5, a person who has been drinking for 4 hours under the conditions indicated by the problem would be considered legally drunk.
The lifespan of a car battery averages six years. Suppose the batterylifespan follows an exponential distribution.(a) Find the probability that a randomly selected car battery will lastmore than four years.(b) Find the variance and the 95th percentile of the battery lifespan.(c) Suppose a three-year-old battery is still going strong. (i) Find theprobability the battery will last an additional five years. (ii) Howmuch longer is this battery expected to last
Answer:
Step-by-step explanation:
Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.
Thus , the parameter of the exponential distribution is calculated as,
μ = 6
[tex]\frac{1}{\lambda} =6[/tex]
[tex]\lambda = \frac{1}{6}[/tex]
a) The required probability is
[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]
= 0.513
Hence, the probability that a randomly selected car battery will last more than four years is 0.513
b) The variance of the battery span is calculated as
[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]
The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated
[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]
c)
Let [tex]X_r[/tex] denote the remaining life time of a car battery
i)the probability the battery will last an additional five years is calculated below
[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]
ii) The average time that the battery is expected to last is calculated
[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]
A 10 foot tree create a shadow that is 15 feet long. Find the angle of elevation of the sun
The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long is 33.69 degrees
To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.
Given that:
The tree's height is 10 feet.
The length of the shadow is 15 feet.
Let's assume that the tree's height is "h" feet.
Length of its shadow is represented by "s" feet
The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.
The angle can be determined using the tangent function.
[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]
Now, substitute the given values:
[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]
[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]
The angle of elevation can be obtained by taking the inverse tangent of 2/3
angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]
angle of elevation ≈ 33.66 degrees
So, the angle of elevation of the sun is approximately 33.69 degrees.
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A) Divide 160km in the ratio 10:9:13
B) divide 66 in the ratio 6:15:1
Answer:
A) 50 km : 45 km : 65 km
B) 18:45:3
Step-by-step explanation:
A) 160 km in the ratio 10:9:13
10x+9x+13x= 16032x= 160x= 510:9:3 ⇔ 50 km : 45 km : 65 km
B) 66 in the ratio 6:15:1
6x+15x+x= 6622x=66x=36:15:1 ⇔ 18:45:3
express the measure in standard notation 5 gal 6qt 48 oz
Answer: 880 oz
Step-by-step explanation:
We want to write it in the same units, let's use oz as our common unit.
1 gal = 128 oz
then 5 gal = 5*128 oz = 640 oz
1 qt = 32 oz
then 6 qt = 6*32 oz = 192 oz
Then we have:
640 oz + 192 oz + 48 oz = 880 oz
The value of standard notation is,
⇒ 880 oz
We have to given that,
Measures are,
⇒ 5 gal 6qt 48 oz
We have to change it into standard notation as,
We want to write it in the same units, let's use oz as our common unit.
1 gal = 128 oz
then 5 gal = 5 x 128 oz = 640 oz
1 qt = 32 oz
then 6 qt = 6 x 32 oz = 192 oz
Then we have:
⇒ 5 gal 6qt 48 oz
⇒ 640 oz + 192 oz + 48 oz
⇒ 880 oz
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|x+12| =-9
Pls help!!!!
Answer:
x=-21
Step-by-step explanation:
x+12=-9
minus twelve on both sides
-9-12 equals -21
x=-21
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
15 m
12 m
0
9 m
11 m
Thanks for anyone that answers
Which decimal is closest in value to 9/20
Answer:
0.45
Step-by-step explanation:
9/20 is the same as 0.45
Answer:
0.45
Step-by-step explanation:
9/20= 9*5/20*5= 45/100= 0.45
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
In the attached file
Find the missing side. Round to
the nearest tenth.
x
9
28°
x = [?]
Answer:
19.2
Step-by-step explanation:
It's right on Acellus.
The required value of x nearest to tenth is 19.17
What is hypotenuse?The longest side of the right angled triangle is called hypotenuse
By the Pythagoras theorem in the right angled triangle
h^2 = b^2 + p^2
where h = hypotenuse, b = base, p = perpendicular
How to calculate hypotenuse?Here we have given perpendicular p = 9
and an angle = 28°
Using sin for the given angle we have
sin 28° = [tex]\frac{perpendicular}{hypotenuse}[/tex]
0.46947 = [tex]\frac{9}{x}[/tex]
x = [tex]\frac{9}{0.46947}[/tex]
x = 19.17
Hence the required length of the side hypotenuse = x = 19.17
This is the conclusion to the answer.
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Daisy has 1/8 tank of gas remaining when she pulls into a gas station. After she puts 15 gallons of gas in her car, the gas gauge reads 3/4 full. How many gallons of gas does Daisy’s tank hold?
*Please Show Work*
Answer:
24
Step-by-step explanation:
Let t represent the volume of the tank in gallons. Then we have ...
(1/8)t + 15 = (3/4)t . . . . . . . . . . . adding 15 gallons fills the tank to 3/4
15 = (6/8 -1/8)t = (5/8)t . . . . . . . subtract 1/8t
15(8/5) = (8/5)(5/8)t . . . . . . . . . multiply by 8/5 (the inverse of 5/8)
24 = t
The tank holds 24 gallons.
Outcome
0
1
5
10
1000
Probability
0.33
0.32
0.24
0.10
0.01
Which is the expected value of the random variable with the given probability distribution?
a.
5.65
c.
12.52
b.
100.44
d.
5
Answer:
The expected value of the random variable with the given probability distribution = 12 .52
Step-by-step explanation:
Given data
x : 0 1 5 10 1000
p(x) : 0.33 0.32 0.24 0.10 0.01
The expected value of the given random variable of given probability distribution
E(X) = ∑ x p ( X = x)
E(X) = 0 × 0.33 + 1 × 0.32 + 5 × 0.24 + 10× 0.10 + 1000×0.01
E (X) = 12.52
The luxury Swiss Chalet hotel general manager (GM) reported to her owner that the hotel's Occupancy Index for the calendar year 2019 was 1.25. Based upon only this information alone, what MUST be correct?
Answer:
the Swiss Chalet had higher occupancy than its competitive set in 2019
Step-by-step explanation: