Answer:
Exercise (a)
The work done in pulling the rope to the top of the building is 750 lb·ft
Exercise (b)
The work done in pulling half the rope to the top of the building is 562.5 lb·ft
Step-by-step explanation:
Exercise (a)
The given parameters of the rope are;
The length of the rope = 50 ft.
The weight of the rope = 0.6 lb/ft.
The height of the building = 120 ft.
We have;
The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;
ΔW₁ = 0.6Δx·x
The work done for the second half, ΔW₂, is given as follows;
ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375
The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375
∴ We have;
W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]
The work done in pulling the rope to the top of the building, W = 750 lb·ft
Exercise (b)
The work done in pulling half the rope is given by W₂ as follows;
[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]
The work done in pulling half the rope, W₂ = 562.5 lb·ft
Mode of certain scores is x. If each score is decreased by 3, then find the mode of the new series.
Step-by-step explanation:
It is given that mode of certain scores is x It means x is the score with highest frequency.
common difference is -3
So, the new mode of the score is
New Mode = 3
Therefore the new mode of the new series is x-3.
Georgia brought a snow cone shaped like the cone below what is the height of the snow cone
Answer:
Step-by-step explanation:
Use the Pythagorean Theorem.
h² = 5² - 3² = 4²
h = 4 in
The diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long. Any washers that do not meet this requirement must be discarded. What percentage of washers will the factory have to discard
Answer:
32%
Step-by-step explanation:
Let x be the mean of the values and σ their standard deviation.
Since the minimum value of the diameter of the washers is 1.53 mm, then
x - σ = 1.53 mm (1)
Also, the maximum value of the diameter of the washers is 1.65 mm, then
x + σ = 1.65 mm (2)
Adding (1) and (2), we have
x - σ = 1.53 mm
+
x + σ = 1.65 mm
2x = 3.18
x = 3.18/2
x = 1.59 mm
Subtracting (1) and (2), we have
x - σ = 1.53 mm
-
x + σ = 1.65 mm
-2σ = -0.12
σ = -0.12/-2
σ = 0.06 mm
Since the diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long, and x - σ = 1.53 mm to x + σ = 1.65 mm are the required values, 68% of the washers lie in this range. The other values lie outside this range. The amount that the factory would have to discard is 100% - 68% = 32%
This question is based on the percentage. Thus, 32% of washers will the factory have to discard.
Given:
The diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long.
We need to determined the percentage of washers will the factory have to discard.
According to question,
Let x be the mean and σ be their standard deviation.
The minimum value of the diameter of the washers is 1.53 mm.
Then,
x - σ = 1.53 mm (1)
Also, the maximum value of the diameter of the washers is 1.65 mm, then
x + σ = 1.65 mm (2)
Adding (1) and (2), we have
x - σ = 1.53 mm
+ x + σ = 1.65 mm
⇒ 2x = 3.18
We get,
x = 1.59 mm
Subtracting (1) and (2), we have
x - σ = 1.53 mm
- x + σ = 1.65 mm
⇒ -2σ = -0.12
We get,
σ = 0.06 mm
Therefore, the diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long, and x - σ = 1.53 mm to x + σ = 1.65 mm are the required values, 68% of the washers lie in this range.
And the other values lie outside this range. The amount that the factory would have to discard is 100% - 68% = 32%.
Thus, 32% of washers will the factory have to discard.
For more details, prefer this link:
https://brainly.com/question/13703753
Which of the following is the correct way to state the similarity between these two figures?
A.) ABCDE ~ YXVZW
B.) ABCDE ~ VWXYZ
C.) ABCDE ~ VZWYX
D.) ABCDE ~ ZWYXV
Answer:
ABCDE is similar to the ZWYXV
ANSWERRRRR????HELPP PSLSSSSS
Answer:
its sas side angle side plz mark me branliest
A dot plot titled Number of runs scored going from 0 to 5. 0 has 2 dots, 1 has 4 dots, 2 has 6 dots, 3 has 4 dots, 4 has 2 dots, and 5 has 1 dot. What is a dot plot and how do you read it? Check all that apply. A dot plot displays data values as dots above a number line. Dot plots show the frequency with which a specific item appears in a data set. There was 1 run in 5 of the games. There were 0 runs in 2 of the games. Dot plots show the distribution of the data. There were a total of 19 games.
Answer:
abdef (those are the answers)
Step-by-step explanation:
Answer:
all but C
Step-by-step explanation:
Anthony bought a new rectangular table for his living room. The length of the table is 4 feet and the perimeter of the table is 14 feet. What is the width of the table?
Answer:
3 feet
Step-by-step explanation:
If the length is 4 feet, there are two lengths so you get 8
14-8= 6
Because there are two widths, you do 6 divided 2 and you get 3 feet
The points (-1,-3, -1,7) Is located in which quadrant
Answer:
-1,-3 is on quadrant 3
-1,7 is on quadrant 2
Step-by-step explanation:
Find the measure of 61.
{
839
41
{ K
41 = [?]
Enter
Answer:
m<1 = 97°
Step-by-step explanation:
<1 and 83° are same-side interior angles. Same-side interior angles are supplementary. This implies that:
m<1 + 83° = 180°
Therefore:
m<1 + 83° - 83° = 180° - 83° (subtraction property of equality)
m<1 = 97°
Answer:
<1=97°
steps:
<1+83=180 co interior angle
<1=180-83=97°
Enter the value of b when the expression 9x + b is equivalent to
3(3x + 1).
BE
ker notes
Answer:
b = 3
Step-by-step explanation:
Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other:
First, distribute 3 to all terms within the parenthesis:
3(3x + 1) =
3 * 3x = 9x
3 * 1 = 3
9x + b = 9x + 3
Isolate the variable, b. Subtract 9x from both sides:
9x (-9x) + b = 9x (-9x) + 3
b = 3
3 is your value for b.
~
What's 9+7
Please help
Answer:
9 + 7 = 16
9 - 7 = 2
9/7 = 1.28571429
9 x 7 = 63
Step-by-step explanation:
have a good day
Answer:
16
Step-by-step explanation:
because if you add the 9 and 7 together it will get you to 16
for Example:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 2 3 4 5 6/7 8 9 10 11 12 13 14 15 16
you just add 9 and 7 and you will get 16
so that answers your question
What's 9+7 Please help
answer: 16
Hope this helps
A box of ceral contains 10 cups . if each bowl holds 1 1/4 cups of cearal. how many bowls of ceral will you get out of the box
Answer:
8 bowls
Step-by-step explanation:
10=40/4
1 1/4=5/4
40/4 divided by 5/4=160/20
160/20=8/1
Answer: the answer is 8
Step-by-step explanation:
Moriah studied for 3 hours to prepare for her history exam. How many minutes did she study?
Answer:
180
Step-by-step explanation:
Every hour is 60 minutes. To find the total number of minutes she studied, you would have to multiply 3 x 60.
3 x 60 = 180
Answer: 180 minutes.
Step-by-step explanation: 3 hours is equal to 60+60+60 because there is 60 minutes in 1 hour so 60+60 is 120+60=180 therefore, she studied for 180 minutes.
2.
Select the correct answer.
The national apple growers organization recently released its first crop of a new apple variety. It gathered data on the weight of the new apples.
It found a population mean of 4.85 ounces and a standard deviation of 0.92. Each sample size was 500 apples. By the central limit theorem,
which interval do 99.7% of the sample means fall within?
OA.
4.81 and 4.89
OB.
4.73 and 4.97
Ос. .
4.84 and 4.86
OD
4.77 and 4.93
Answer:
B. 4.73 and 4.97
Step-by-step explanation:
To solve this question, we need to understand the Empirical Rule and the Central Limit Theorem.
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
Standard deviation of 0.92, sample of 500:
This means that [tex]\sigma = 0.92, n = 500, s = \frac{0.92}{\sqrt{500}} = 0.04[/tex]
By the central limit theorem, which interval do 99.7% of the sample means fall within?
Within 3 standard deviations of the mean. So
4.85 - 3*0.04 = 4.85 - 0.12 = 4.73
4.85 + 3*0.04 = 4.85 + 0.12 = 4.97
So, option B.
Answer:
4.73 and 4.97
Please give me brainliest, I really need it.
What is the y value in solution the following system?
4x+3y=7
X+2y=-2
(Worth 10 points)
I need help what's the answer anyone?
Answer:
B
Step-by-step explanation:
In a recent survey in a Statistics class, it was determined that only 70% of the students attend class on Fridays. From past data it was noted that 88% of those who went to class on Fridays pass the course, while only 20% of those who did not go to class on Fridays passed the course. a. What percentage of students is expected to pass the course? b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays? (Hint: the above problem is based on conditional probability concept and the Bayes theorem)
Answer:
a) 67.6% of students is expected to pass the course
b) 0.9112 = 91.12% probability that he/she attended classes on Fridays
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. What percentage of students is expected to pass the course?
88% of 70%(attended class)
20% of 100 - 70 = 30%(did not attend class). So
[tex]p = 0.88*0.7 + 0.2*0.3 = 0.676[/tex]
0.676*100% = 67.6%
67.6% of students is expected to pass the course.
b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays?
Here, we use conditional probability:
Event A: Passed the course
Event B: Attended classes on Fridays.
67.6% of students is expected to pass the course.
This means that [tex]P(A) = 0.676[/tex]
Probability that passed and attended classes on Friday.
88% of 70%
This means that:
[tex]P(A \cap B) = 0.88*0.7 = 0.616[/tex]
Then
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.616}{0.676} = 0.9112[/tex]
0.9112 = 91.12% probability that he/she attended classes on Fridays
Here are five statements.
For each statement, say whether it is TRUE or FALSE.
The first one has been done for you.
Note: Please make sure you follow the format of the answers, e.g.
2) ....
3) ...
Answer:
Step-by-step explanation:
2) False.
3) True. It could be 50°-65°-65°.
4) True. It could be 35°-35°-110°.
5) True. It could be 40°-50°-90°.
Chandler, Jamal, Allison, and Qi are given the following problem. In 1982, Wayne Gretsky set a record for the greatest number of hockey goals in one season with 92 goals. If a player has scored 60 goals this season and averages 2 goals per game, how many additional games must he play to break the record? Each student writes an inequality to represent the situation. Chandler wrote 60 + 2g ≥ 92 Jamal wrote 60 + 2g > 92 Allison wrote 60 + 2g < 92 Qi wrote 60 + 2g ≤ 92 Whose inequality is CORRECT? A. Qi B. Chandler C. Allison D. Jamal
Answer:
The correct answer is B.
Step-by-step explanation:
Since Chandler, Jamal, Allison, and Qi are given the following problem: "In 1982, Wayne Gretsky set a record for the greatest number of hockey goals in one season with 92 goals. If a player has scored 60 goals this season and averages 2 goals per game, how many additional games must he play to break the record? ", And each student writes an inequality to represent the situation:
Chandler wrote 60 + 2g ≥ 92
Jamal wrote 60 + 2g> 92
Allison wrote 60 + 2g <92
Qi wrote 60 + 2g ≤ 92
To determine whose inequality is correct, the following calculation must be performed:
92 - 60 = 32
32/2 = 16
Chandler: 60 + 2x16 ≥ 92
Thus, Chandler wrote the correct option.
Shiro and Tatiana weighed some pebbles in
science class. They made a line plot to display
their data. Use the line plot to answer
Answer:
The answer is below
Step-by-step explanation:
a) Of the pebbles that were measured, which weight occurs the least?
Soln.: From the line plot, we can see that 3 ounce occurred once, 3 1/2 ounce occurred 4 times, 4 ounce occurred 3 times, 4 1/2 ounce occurred 5 times, 5 ounce occurred 2 times, 5 1/2 ounce occurred 3 times, 6 ounce occurred 2 times.
Therefore 3 ounce occurred the least.
b) What is the total weight of the pebbles represented by the data?
Soln.: The total weight is:
Total weight = (3*1) + (3 1/2 * 4) + (4 * 3) + (4 1/2 * 5) + (5 * 2) + (5 1/2 * 3) + (6 * 2) = 90 ounce
c) Is there an outlier in the data set? If so what number is the outlier?
Soln.: There is no outlier in the data set because all the data are close to each other.
what is an outlier number?
Answer:
an outlier is a number that is at least 2 standard deviations away from the mean for example in the set 1,1,1,1,1,1,1,1,1,7,7,7 would be the outlier
Step-by-step explanation:
watashi wa sore ga tadashī koto o negatte imasu
arigatozaimasu!!
Step-by-step explanation:
i have noooo idea but ayyeee
Name the first three numbers in this sequence
_ _ _ 80, 160,320,640,1280
Answer:
10, 20, 40
Step-by-step explanation:
Answer and Step-by-step explanation:
The first three numbers are 10, 20 and 40.
This is because the sequence is being increased by twice the previous number.
To get from 10 to 20, you multiply by 2, to get from 20 to 40, we multiply by 2, to get from 40 to 80, we multiply by 2, to get to 80 to 160, we multiply by 2, and so on.
#teamtrees #PAW (Plant And Water)
Find the value of x.
Plsss help
Answer:
x=6
Step-by-step explanation:
7x+5+13x-8+11x-3=180
31x-6=180
31x=186
x=186÷31
x=6
I wrote the wrong answer so I erased it
If PQRS is a rhombus, find m
Answer:
m<PQR = 82°
Step-by-step explanation:
In a Rhombus, the diagonals bisect its angles. This means that they divide each the four angles into two equal parts.
Therefore:
(4x - 27)° = (2x + 7)°
Solve for x
4x - 27 = 2x + 7
Collect like terms
4x - 2x = 27 + 7
2x = 34
Divide both sides by 2
2x/2 = 34/2
x = 17
✔️m<PQR = (4x - 27) + (2x + 7)
Plug in the value of x
m<PQR = (4*17 - 27) + (2*17 + 7)
m<PQR = 41 + 41
m<PQR = 82°
I need help with this
Answer:
1/5
Step-by-step explanation:
because u divied
In a pre-election poll, 58% of a large random sample of voters responded as planning to vote for the school enhancement millage. A 95% confidence interval was computed for the proportion of all such voters who plan to vote for the school enhancement millage. Review each of the following statements regarding the meaning of the 95% confidence level. Determine if it is a correct (true) meaning or incorrect (false).
Answer: Hello the statement related to your question is missing attached below is the statement
answer : The statement is false
Step-by-step explanation:
The statement is false
This is because a confidence interval gives a range of values for an unknown parameter.
A 95% confidence interval is calculated and it gives a lower and upper limit in which the 58% of the voters can fall into i.e. The 58% of voters can fall within the upper and lower limit of the 95% confidence interval and not exactly 95% . Hence the statement is false.
PLS HELP ME
The smallest hummingbird is the Bee hummingbird. It has a mass of about 1
1
4
grams. The mass of a larger type of hummingbird is about 6 times the mass of the Bee hummingbird.
What is the mass of the larger hummingbird?
Answer:
The mass of the larger hummingbird is 7 1/2 or 15/2.
Step-by-step explanation:
Bee hummingbird = 1 1/4g
Larger hummingbird = 6x that
So,
1 1/4 x 6 = 7.5
7.5 as fraction = 7 1/2 or 15/2
Branliest to correct answer no guessing explain how you solved it
Answer:
5,040 play list arrangements. its very complexe and will hurt to type srry
Step-by-step explanation:
1. Alice invests $1000 at 2% interest compounded monthly over a 5 year period. Assuming no other money is deposited or withdrawn, what is the total amount of money in her account after 5 years? (Round to the nearest cent)
Answer:
$1,105.08.
Step-by-step explanation:
Given that Alice invests $ 1000 at 2% interest compounded monthly over a 5 year period, assuming no other money is deposited or withdrawn, to determine what is the total amount of money in her account after 5 years, the following calculation must be performed:
X = 1,000 (1 + 0.02 / 12) ^ 5x12
X = 1,105.08
Thus, the amount of money in her account after 5 years would be $ 1,105.08.
what is the value of k if - 2/3(k - 6) = 3/2(k+6)
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: -30/13
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
