Step-by-step explanation:
Volume of Cylinder =
[tex]500 {cm}^{3} = \pi {r}^{2} h[/tex]
given d = 18
r = 1/2 x d = 9cm,
[tex]\pi( {9}^{2} )h = 500 \\ 81\pi \: h = 500 \\ h = \frac{500}{81\pi} cm[/tex]
I will leave the answer in terms of Pi as I am not sure how you want to leave your answer as.
what is the equation of the line that passes through the point (-6,-6) and has a slope of 2/3?
Answer:
-6=2/3*-6
Step-by-step explanation:
y=mx+b
slope = m b=y intercept
A certain airplane offers two types of seats, first class and economy.
There are 209 total seats on the airplane. If the difference between the
number of economy and first class seats is 153, find the number of
economy seats.
Answer:
56
Step-by-step explanation:
you do 209-153=56
Number of economy seats are 181
What is linear equation?An equation between two variables that gives a straight line when plotted on a graph
Consider,
Number of economy seats =x
Number of First class seats =y
There are 209 total seats on the airplane
Then,
x + y=209
Difference between the number of economy and first class seats is 153
x - y=153
Solve both the equation
x + y=209
x = 209-y
Substitute the value of x in second equation
(209-y) - y=153
2y=209-153=56
y=28
Then
x + y=209
x + 28=209
x=209-28
x=181
Hence, the number of economy seats are 181
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You must estimate the mean temperature (in degrees Fahrenheit)
with the following sample temperatures:
79.5
102.8
80.8
76.8
80.4
79.2
86
67.7
Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). * Answer should be obtained without any preliminary rounding.
98% C.I. =
The interval value at 98% confidence level for the given scenario is (73.51 ; 89.79)
From the data :
Mean(x) = (79.5+102.8+80.8+76.8+80.4+79.2+86+67.7)/8
Mean = 81.65
Sample standard deviation :
s = √[(x1 - mean)² + (x2 - mean)² + ... + (x(n) - mean)²] / n
Using a statistical calculator :
s = 9.98
The confidence interval is defined thus :
Mean ± Tcritical × s/√n
Tcritical at 98% = 2.306
Substituting values into the formula :
81.65 ± (2.306 × 9.98/√8)
81.65 ± 8.137
(73.51, 89.79)
Therefore, the confidence interval for the given scenario is (73.51 ; 89.79)
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Gerry conversed his sole partnership to an S corporation and transferred several assets to the corporation. The assets cost $19,570 and had an adjusted basis of $9,600. He also spent an additionally $975 to make the conversion to an S corporation. What is his beginning basis in the S corporation?
Gerry's beginning basis in the S corporation is $20,545.
To calculate Gerry's beginning basis in the S corporation, we need to consider the cost of the assets transferred and the additional expenses incurred for the conversion.
The cost of the assets transferred is given as $19,570. This represents the original cost of the assets when Gerry acquired them.
The adjusted basis of the assets is stated as $9,600. The adjusted basis takes into account any adjustments made to the original cost, such as depreciation or other deductions.
To calculate the beginning basis in the S corporation, we add the cost of the assets transferred ($19,570) to the adjusted basis ($9,600). This gives us a total of $29,170.
In addition to the assets, Gerry incurred an additional expense of $975 for the conversion to an S corporation. We include this amount in the calculation of the beginning basis.
Therefore, Gerry's beginning basis in the S corporation is $29,170 + $975 = $20,545.
This beginning basis is important for determining Gerry's tax consequences and future deductions within the S corporation structure.
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find the slope. -2,1 and 4,4
Answer:
2
Step-by-step explanation:
To find the slope of two points, we must subratct the Y values from each other and divide them from the X values
4-(-2) 6
--------- = ----- = 2
4-1 3
Answer: The slope is 1/2 as a fraction and 0.5 as a decimal
Hope it helped :D
Help Please! Find The Area Of A Circle With D=8.2
Answer:
52.81
Step-by-step explanat
PLEASE HELP!!
In a right triangle, the length of one of the sides is 13.7, while one of the other sides measures 14.3. Find the length of the hypotenuse.
The length of the hypotenuse is approximately 19.8 units.
In a right-angled triangle, the hypotenuse is the longest side, and it is opposite to the right angle. To find its length, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, we have:
h^2 = 14.3^2 + 13.7^2
h^2 = 204.49 + 187.69
h^2 = 392.18
h = sqrt(392.18)
h ≈ 19.8
We can round the answer to one decimal place, as this is the nearest level of precision to the data provided. Note that for a right-angled triangle, the hypotenuse is always the longest side, so it makes sense that the hypotenuse is longer than both of the other sides in this case.
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Your customer has found base plates that are defective, they exceed the maximum width dimension of 4.005. As a result the mating component will not fit on these base plates properly. You manufacture these base plates on four identical CNC milling machines with approximately 25% of the production coming from each machine.
Simplified drawing of base plate is shown below.
Assignment:
Your manager has requested you sample 50 pieces from the manufacturing floor that were manufactured from each machine, analyze the data and come up with recommendations to solve the problem. (The data for the 50 piece sample is attached at the end of the assignment.)
Introduction: describing the process and statement of the general problem(s)
Analysis of the data: Graphical analysis is required
Each table and graph must be briefly explained at the point of the table or graph to indicate how it relates to the study at hand.
A brief summary of the findings relating back to specific analytical tools
Cause and effect diagram(s): identifying PERTINENT possible solutions to the problem(s)
The problem at hand involves base plates that exceed the maximum width dimension, resulting in improper fitting of the mating component. To address this issue, a sample of 50 base plates manufactured from each of the four CNC milling machines was analyzed.
Graphical analysis of the data revealed insights into the problem. Recommendations for solving the problem include identifying pertinent possible solutions through cause and effect diagrams.
The analysis of the sample data from each CNC milling machine provides valuable insights into the issue of base plates exceeding the maximum width dimension. By graphically analyzing the data, patterns or variations can be identified, helping to pinpoint the specific source of the problem. This analysis may involve creating graphs or tables to visualize the measurements and compare them across the machines.
To identify possible solutions, cause and effect diagrams, such as fishbone diagrams, can be utilized. These diagrams help to identify potential causes of the issue by categorizing them into different categories such as machine factors, material factors, human factors, and environmental factors.
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1. The values, x in a sample of 15 are summarized as follows
Σ(x-c) = 72,Σ(x-c)2 = 499.6
where c is a constant. Given that the sample mean is 104.8.
(a) Find the value of constant c.
(b) Find the variance of x.
Answer:
(a) 100
(b) 10.27
Step-by-step explanation:
We are given
No of elements = 15
Σ(x-c) = 72,Σ(x-c)^2 = 499.6
,where c is a constant
and the sample mean is 104.8.
(a) lets take into account Σ(x-c) = 72
this means that we have the sum of the 15 elements of x and each element of x is subtracted by the constant c
so the equation becomes Σxi -15c = 72, ............(1)
where xi means the sum of the elements of x from 1 to 15.
we are given the mean as 104.8
this means that Σxi/15 = 104.8
Σxi = 15*104.8 = 1572 .............(2)
substituting (2) in (1)
we get
1572 - 15c = 72
15c = 1500
c = 100
(b) We will use the property that variance does not change when a constant value is added or subtracted to the elements. This we can observe in the given equation that c is a constant that has the value of 100.
so the variance is
σ^2 = Σ(x-c)^2/15 - (Σ(x-c)/15 )^2
= 499.6/15 - (72/15)^2
= 33.31 - 23.04
σ^2 = 10.27
Therefore the variance of the given problem is 10.27.
What is k^2+16k+64+89
Answer:
k²+16k+ 153
Step-by-step explanation:
k²+16k+64+89
= k²+16k+ 153
The proportion of students who fail the comprehensive statistics final had been 4%. With instruction moving completely online, instructors believe that this percentage will decrease for various reasons (the final must now be open book, some students will cheat, etc.). To test their claim, the appropriate test is
paired t test
z test for two proportions
t test for one mean
z test for one proportion
one-way ANOVA
The appropriate test to investigate whether the proportion of students failing the comprehensive statistics final has decreased with the shift to online instruction is the z test for two proportions.
Explanation:
The z test for two proportions is used when we want to compare two proportions or percentages from different populations or groups. In this case, we want to compare the proportion of students who fail the statistics final before and after the instruction moved online.
To conduct the z test for two proportions, we follow these steps:
1. Define the null hypothesis (H₀) and alternative hypothesis (H₁). In this case, the null hypothesis would be that the proportion of students failing the final is the same before and after the instruction moved online, while the alternative hypothesis would be that the proportion has decreased after the shift to online instruction.
2. Collect data on the number of students who fail the statistics final before and after the shift to online instruction.
3. Calculate the sample proportions for each group. Let's denote the proportion before the shift as p₁ and after the shift as p₂.
4. Calculate the standard error (SE) of the difference between two proportions using the formula:
SE = sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))
where n₁ and n₂ are the sample sizes for the two groups.
5. Calculate the test statistic (z) using the formula:
z = (p₁ - p₂) / SE
6. Determine the critical value for the desired significance level (e.g., 0.05) and compare it to the calculated test statistic. If the calculated test statistic falls within the critical region, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
7. Interpret the results and draw conclusions about whether there is sufficient evidence to support the claim that the proportion of students failing the statistics final has decreased after the shift to online instruction.
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A 20-inch television screen has a width of 12 inches. What is the length of the television screen?
A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution with mean μ=298ml and standard deviation σ=3ml. What is the probability that the mean contents of six randomly selected bottles are less than 295 ml?
The probability that the mean contents of six randomly selected bottles are less than 295 ml is 0.007, or 0.7%.
To find the probability that the mean contents of six randomly selected bottles are less than 295 ml, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means from a population with any distribution approaches a normal distribution as the sample size increases.
In this case, we have a normal distribution with a mean (μ) of 298 ml and a standard deviation (σ) of 3 ml. We want to find the probability of the mean contents of six bottles being less than 295 ml.
First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution of the mean. The formula for the standard error is σ / √n, where σ is the population standard deviation and n is the sample size.
In our case, σ = 3 ml and n = 6. Therefore, the standard error (SE) is:
SE = 3 / √6 ≈ 1.225 ml
Next, we need to calculate the z-score, which is the number of standard errors the sample mean is away from the population mean. The formula for the z-score is (x - μ) / SE, where x is the sample mean.
In our case, x = 295 ml, μ = 298 ml, and SE = 1.225 ml. Therefore, the z-score is:
z = (295 - 298) / 1.225 ≈ -2.449
Finally, we can use a standard normal distribution table or a calculator to find the probability corresponding to the z-score. The probability that the mean contents of six bottles are less than 295 ml is the area under the normal curve to the left of the z-score.
Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -2.449 is approximately 0.007.
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Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions
To find the first five terms of a sequence defined by a recurrence relation and initial conditions, we apply the relation repeatedly. Each term is calculated based on the previous terms in the sequence according to the given relation.
The first five terms of a sequence defined by a recurrence relation and initial conditions can be determined by applying the recurrence relation repeatedly. Each term is calculated based on the previous terms in the sequence, according to the given relation. Here are the first five terms for each recurrence relation:
1. Linear recurrence relation: If the recurrence relation is of the form an = an-1 + d, where "a" is the term and "d" is a constant, and the initial condition is a1 = c, then the first five terms can be found by adding the constant "d" repeatedly to the initial term "c". For example, if c = 2 and d = 3, the first five terms would be 2, 5, 8, 11, 14.
2. Quadratic recurrence relation: If the recurrence relation is of the form an = an-1² + c, where "a" is the term and "c" is a constant, and the initial condition is a1 = d, then the first five terms can be calculated by squaring the previous term and adding the constant "c". For instance, if d = 1 and c = 2, the first five terms would be 1, 3, 11, 123, 15187.
These examples demonstrate how to find the first five terms of a sequence by applying the given recurrence relation and initial conditions. By following the recurrence relation, each term is determined based on the previous terms in the sequence.
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Write the word sentence as an equation. Then solve the equation.
9 is the difference of a number n and 7.
An equation that represents this word sentence is
Answer: 9=n-7
Step-by-step explanation:
Answer ASAP pls pls
Answer:
67.5
Step-by-step explanation:
b times h
7.5 times 9
Answer:
A = 67.5 in²
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
Here b = 9 and h = 7.5 , then
A = 9 × 7.5 = 67.5 in²
Cindy lost 28 pounds while on a diet. She now weighs 157 pounds. Write and solve an equation to find her initial weight
Answer:
The equation is 157+28=185.
157+ 28= 185
I think that’s right
please helpppp which function h(x) results when g(x) is translated 7pi/8 units right and one unit down????
Answer:
The second option
Step-by-step explanation:
Use the Linear Approximation to estimate Δꜰ=ꜰ(3.5)−ꜰ(3) ꜰᴏʀ ꜰ(x)=41+x2 (Use decimal notation. Give your answer to five decimal places.)
Δf≈ help (decimals)
Calculate the actual change.
(Use decimal notation. Give your answer to five decimal places.)
Δf = help (decimals)
Compute the error and the percentage error in the Linear Approximation.
(Use decimal notation. Give your answer to five decimal places.)
Error = help (decimals)
Percentage error = % help (decimals)
To estimate Δf = f(3.5) - f(3) using the linear approximation, we'll use the formula:
Δf ≈ f'(a) * Δx
where f'(a) represents the derivative of f at the point a, and Δx represents the change in the x-values.
Given that f(x) = 41 + [tex]x^2[/tex], we can calculate the derivative as:
f'(x) = 2x
Now, let's calculate the values step by step:
Calculate Δf:
Δf ≈ f'(a) * Δx
Δf ≈ f'(3) * (3.5 - 3)
Δf ≈ 2(3) * (3.5 - 3)
Δf ≈ 6 * 0.5
Δf ≈ 3
Calculate the actual change:
To calculate the actual change, we need to evaluate f(3.5) and f(3) separately:
f(3.5) = 41 +[tex](3.5)^2[/tex]
f(3.5) = 41 + 12.25
f(3.5) = 53.25
f(3) = 41 + [tex](3)^2[/tex]
f(3) = 41 + 9
f(3) = 50
Δf = f(3.5) - f(3)
Δf = 53.25 - 50
Δf = 3.25
Calculate the error and the percentage error:
Error = |Δf - Δf_approx|
Error = |3.25 - 3|
Error = 0.25
Percentage error = (|Δf - Δf_approx| / Δf) * 100
Percentage error = (0.25 / 3.25) * 100
Percentage error ≈ 7.69%
So, the results are as follows:
Δf ≈ 3
Actual change (Δf) ≈ 3.25
Error ≈ 0.25
Percentage error ≈ 7.69%
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The science and technology class is studying robotics. One group builds a robot that can be controlled by entering positive and negative numbers into a control unit. Negative numbers make the robot roll backwards a specific number of inches. Positive numbers make it move forward a certain number of inches. For example, if −5 is entered, then the robot moves backwards 5 inches. The students enter the numbers −37, +22, and −16. What number do they need to enter to make the robot return to its original position of 0?
To achieve this, the students must enter +31 (forward) to bring the robot back to its starting position of 0.
The robot can move forward or backward depending on the type of number entered into the control unit. For example, entering a negative number causes the robot to roll backward a specific number of inches,
while entering a positive number makes it move forward a certain number of inches. If −5 is entered, the robot moves backwards by 5 inches. As a result, the students entered the numbers −37, +22, and −16 to move the robot.
The question asks what number needs to be entered to bring the robot back to its starting position of zero. To do so, we must first calculate how far the robot has traveled in total.
When a negative number is entered into the control unit, the robot rolls backward.
As a result, when we add the negative numbers and subtract them from the positive number,
we can determine the total distance traveled by the robot.-37 (back) + 22 (forward) - 16 (back) = -31 (inches traveled)Since the robot moved a total of 31 inches,
the students must enter the opposite number to bring the robot back to its starting position of 0.
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Write your answer in simplest form 11/12- 3/4
Answer: 1/6 is its simplest form :)
cars that are ready for shipping weigh 2 tons. a car being built weighs 1,135 pounds. how much more weight, in pounds, will be added to the car so it will be ready for shipping!?!
Please please help please please ASAP ASAP please ASAP help please please ASAP please please help ASAP ASAP please please help please please ASAP please
Answer:
7
Step-by-step explanation:
The two lengths (4x-7 and x+14) are the same. This is because if we look at the big trapezoid as a whole, the ratio of the three segments on the side (4, 4, 4) is the same as the ratio of the three lengths on the other side. Therefore the ratio of the two lengths would be the same as well, 1:1. (btw the photo that I attached is what I mean by the two sides). So, we can form the equation: 4x-7 = x+14. The steps to solve the problem:
4x-7 = x+14
3x=21
x=7
The value of x is 7!
please help please it would me me sm <3
Answer:
25
Step-by-step explanation:
4x25=100
100-25=75 degrees
Answer:
25°
Step-by-step explanation:
(4x-25)=75
4x=100
x=25
MARKING BRAINLIST ASAPP pleaseee help
Answer:38
Step-by-step explanation:I think it's 38 because it said right 8 and down 15 so it's kinda like a grid right mean stay positive but also means it goes up so I did 45 plus 8 which is 53 minus 15 which is 38. Hope this gets brainliest
[tex] \sqrt{39} [/tex]
Please help me to find the answer of square root 39
plz
Answer:
hi dear friend the answer is 6.245. hope that helps it has been a pleasure to help you can always look out for me if you have a math problem.
1. What is the domain of
f (x)= 9 - x?
Answer:
theres no answer
Step-by-step explanation:
Jim and three friends shared 2 poster boards for an art project. What part of the construction paper will each friend get? *
Answer: 1/2 of a sheet
Step-by-step explanation:
2 sheets divided by 4 people
2/4
Simplify to 1/2
find the buying price if the selling price is 240 and profit is 20 percent
Answer:
192
Step-by-step explanation:
You have to find 20% of 240.
So write 20% as 20 over 240 in fraction form.
[tex]\frac{20}{240}[/tex]
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
[tex]\frac{20}{100}[/tex] of 240 = [tex]\frac{20}{100}[/tex] × 240
Therefore, the answer is 48
If you are using a calculator, simply enter 20÷100×240 which will give you 48 as the answer.
Now since it wants to know how much you paid for the goods you do 240-48=192
So since a company is selling goods with a 20% profit
That means they bought it from somewhere else
Because they had to be manufactured
It wants how much the company paid the company that manufactured the goods
I hope this helped. Some resources that are helpful to look at in case of any more confusion are:
https://answers.everydaycalculation.com/percent-of/20-240
https://www.mathsisfun.com/
https://www.ixl.com/
Good luck young mathematician!
A scientist used a microscope to count the number of bacterial cells in a petri dish every hour.
Which function most accurately represents this data, where n is the number of bacteria and 1 is the time elapsed, in hours?
a. n=2t
b. n=2^t
c n=t^2
d. n=√t
Answer:
a. n=2t
Step-by-step explanation:
Given that
N denotes the number of bacteria
And, 1 denotes the time elasped in hours
Now based on this, the scientist used a microscope for counting the number of bacterial cells every hour
So,the function that represent correct data is
n = 2t
Therefore the correct option is A.
The same would be considered