[tex]_____________________________________[/tex]
[tex]\sf\huge\underline\red{SOLUTION:}[/tex]
Use formula:
[tex]\sf{V = \pi(\frac{d}{2})^2h}[/tex]
Solving for diameter:
[tex]\sf d = 2 \times \sqrt{ \frac{V}{\pi h} } \\ \sf = 2 \times \sqrt{ \frac{40}{\pi \times 1800} } \approx0.16821 \\ = \sf \large\boxed{\sf{\green{d = 0.17}}}[/tex]
[tex]\sf\huge\underline\red{FINAL \: ANSWER}[/tex]
[tex]\large\boxed{\sf{\green{d=0.17}}}[/tex]
[tex]_____________________________________[/tex]
✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ
✍︎ᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢ
Is the distance a baseball travels in the air after being hit a discrete random variable, a continuous random variable, or not a random variable?
Answer: a continuous random variable
Step-by-step explanation:
Can you count the distance it traveled? You can't, so it couldn't be discrete because you can count discrete variables.
Can you measure the distance it traveled? You sure can, that makes it a continuous random variable.
Do you know the exact distance it's going to travel? You won't, therefore it's a random variable since you don't know the value beforehand.
Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is µ = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than µ = 19 inches? Use ???? = 0.05.
Answer:
The test statistics will be "-0.876",
Step-by-step explanation:
Given:
[tex]\bar x=18.6[/tex][tex]\mu = 19[/tex][tex]s = 3.1[/tex][tex]n = 46[/tex]According to the question,
Level of significance will be:
= 0.05
Now,
The test statistics will be:
= [tex]\frac{\bar x-\mu}{\frac{s}{\sqrt{n} } }[/tex]
By substituting the values, we get
= [tex]\frac{18.6-19}{\frac{3.1}{\sqrt{46} } }[/tex]
= [tex]-\frac{2.713}{3.1}[/tex]
= [tex]-0.876[/tex]
I need at least two more sentences in regards with this assignment. Note the included photo. Please come up with two proper sentences following the assignments instructions. Ps. Don’t try to steal points from this or you will be reported
Answer:
A={x: x is a cat}
B={x: x likes climbing on trees}
My little cat Louis likes climbing on trees (Louis is in the intersection of the two sets)
A={x: x is a town in the USA}
B={x: x is a town in the UK}
To improve my English I'd like to go on holiday to a town in the USA, but a town in the UK would work too (the town shall be in the union of the two sets)
There is a high-speed rail track between London and Manchester.
The length of this track is 210 miles.
A train departs London at 11:20 and arrives in Manchester at 13:28
The train company claims
the average speed of this train is 104 miles per hour.
Is the average speed of this train 104 miles per hour?
(4)
Use the box below to show clearly how you get your answer.
Answer:
Step-by-step explanation:
this is the famous dirt formula, :P I made it up :D
D=rt ( notice it looks like Dirt , kinda, but it also means it dirt simple )
D= distance
r = rate ( think speed or how fast)
t = time ( in what ever units of time you want to use, seconds, minutes, hours )
13:28 - 11:20 = 128 minutes ( b/c the question is asking in MPH convert to hours) 2.4666667 hours
210 miles = r * 2.46666667
210 / 2.46666667 = r ( in MPH) ( does anyone else find it odd that they are saying miles in London instead of kilometers? :/ )
85.135 MPH = rate
so no, not even close to 104 MPH :/
Answer:
Average speed is 98 mph
Step-by-step explanation:
[tex]\frac{distance (miles)}{time (hours)}[/tex] = speed [tex]\frac{mile}{hours}[/tex] (miles per hour is a ratio)
The time is 2 hours and 8 minutes.
[tex]\frac{8}{60}[/tex] = .13333 ( 8 minutes / 60 minutes in a hour)
So time is 2.133333 hours .
Divide the distance 210 by the time 2.13333 and get the speed.
Its 98.437..
Round to 98 miles per hour.
a car travels 10 km southeast and 15 km in a direction 60 degrees north of east. find the magnitude and direction
Answer:
the car travels 10km then 15km 60* north of east
Step-by-step explanation:
(x-1)/(x-1)=1, what is the answer and explenation
19. In a random sample of 250 students, we found that 75 work out 4 or more times a week. Find the 95% confidence interval for the proportion of students who work out 4 or more times a week.
Answer:
The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a random sample of 250 students, we found that 75 work out 4 or more times a week.
This means that [tex]n = 250, \pi = \frac{75}{250} = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.2432[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.3568[/tex]
The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1125. What was the rate charged per hour by each mechanic if the sum of the two rates was $140 per hour?
Answer:
The first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.
Step-by-step explanation:
Given that two mechanics worked on a car, and the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours, and together they charged a total of $ 1125, to determine what was the rate charged per hour by each mechanic if the sum of the two rates was $ 140 per hour, the following calculation must be performed:
1125/15 = X
75 = X
80 x 10 + 60 x 5 = 800 + 300 = 1100
85 x 10 + 55 x 5 = 850 + 275 = 1125
Therefore, the first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.
A six sided number cube rolled once. what is the probability of landing on a multiple of 2. write the probability as a fraction, percent and decimal.
Answer:
12 is the correct answer
Mr. Clinton went to the lumber company. He bought 6 boards at a cost of $4.12 per board and 5 pounds of nails at $0.78 per pound. What was the total cost for these items (not including tax)?
Answer:
djjdjdjdjdjdjdjdjdidi
$28.62 not including tax.
You may recall that the area of a rectangle is A=L⋅W, where W is the width and L is the length.
Suppose that the length of a rectangle is 3 times the width. If the area is 300 square feet, then what is the width of the rectangle, in feet?
Do not type the units in your answer.
Answer:
The width is 10 feet.
Step-by-step explanation:
We know that the area of a rectangle is given by the formula:
[tex]\displaystyle A=L\cdot W[/tex]
Where L is the length and W is the width.
We are given that the length of the rectangle is three times the width. In other words:
[tex]L=3W[/tex]
The total area is 300 square feet. And we want to determine the width of the rectangle.
So, substitute 300 for A and 3W for L:
[tex](300)=(3W)\cdot W[/tex]
Multiply:
[tex]300=3W^2[/tex]
Divide both sides by three:
[tex]W^2=100[/tex]
And take the principal square root of both sides. So:
[tex]W=10[/tex]
Thus, the width of the rectangle is 10 feet.
solve 5x^2-2=-12 by taking the square root
Answer:
x = ±i√2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality
Algebra II
Imaginary root i
i = √-1Step-by-step explanation:
Step 1: Define
Identify
5x² - 2 = -12
Step 2: Solve for x
[Addition Property of Equality] Add 2 on both sides: 5x² = -10[Division Property of Equality] Divide 5 on both sides: x² = -2[Equality Property] Square root both sides: x = ±√-2Rewrite: x = ±√-1 · √2Simplify: x = ±i√2Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis: y=x6, y=1 about y=6.
Answer:
mehoimehoihoi
Step-by-step explanation:
4g+r=2r-2x
I need someone’s help if you can help me
Answer:
4g+2x=r
Step-by-step explanation:
4g+r=2r-2x
collecting like terms
4g+2x=2r-r
4g+2x=r
If F is the function defined by F(x)=3x−1, find the solution set for F(x)=0.
The solution for set F(x) is -1
In a survey, 24 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $2. Construct a confidence interval at a 98% confidence level.
Answer:
The 98% confidence interval for the mean amount spent on their child's last birthday gift is between $40.98 and $43.02.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 24 - 1 = 23
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 23 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.5
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.5\frac{2}{\sqrt{24}} = 1.02[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.02 = $40.98.
The upper end of the interval is the sample mean added to M. So it is 42 + 1.02 = $43.02.
The 98% confidence interval for the mean amount spent on their child's last birthday gift is between $40.98 and $43.02.
Sara is working on a Geometry problem in her Algebra class. The problem requires Sara to use the two quadrilaterals below to answer a list of questions.
Part A: For what one value of are the perimeters of the quadrilaterals the same? (Hint: The perimeter of a quadrilateral is the sum of its sides.)
Part B: For what one value of are the areas of the quadrilaterals the same? (Hint: The area of a quadrilateral is the product of its base and height.)
Answer:
For the perimeters, x must be equal to 2.
For the areas, it is either undefined, or something.
Step-by-step explanation:
You can first find the perimeters for both sides.
For the left shape, we add the two sides of 6 and x + 4 to get x + 10.
Then we multiply x + 10 by 2 because there are 4 sides, and we only got 2 sides.
The perimeter of the first shape is 2x + 20.
The second shape can be solved by doing the same thing by adding 2 and 3x + 4 to get 3x + 6.
3x + 6 times 2 is 6x + 12.
The second perimeter is 6x + 12.
If both sides are supposed to be equal, then we can write these two expressions we solved for like:
6x + 12 = 2x + 20.
Subtraction property of equality
6x + 12 - 12 = 2x + 20 - 12
Simplify
6x = 2x + 8
Again
6x - 2x = 2x - 2x + 8
Simplify
4x = 8
Division property of equality
4/4x = 8/4
Simplify
x = 2
So if x = 2, the perimeters will be the same.
You can confirm this by plugging it back into either equation.
For the areas, we just multiply the length and width for both shapes, so we get
6(x+4) = 2(3x+4)
Since they are supposed to be equal.
We simplify and get
6x + 24 = 6x + 8
We know this is false and is not possible, since we can remove the 6x because it is on both sides.
We also know that 24 is not equal to 8 (who thought!)
:D
24 ≠ 8
So it is undefined or whatever you call it.
Which property is demonstrated by this expression? 142 x 1 = 142 One Associative Commutative
Step-by-step explanation:
It is Associative property, I have seen this somewhere
An internet cafe charges a fixed amount per minute to use the internet. The cost of using the
internet in dollars is, y = 3/4x. If x is the number of minutes spent on the internet, how many
minutes will $6 buy?
er
Answer:
x = 8 minutes
Step-by-step explanation:
Given that,
An internet cafe charges a fixed amount per minute to use the internet.
The cost of using the internet in dollars is,
[tex]y=\dfrac{3}{4}x[/tex]
Where
x is the number of minutes spent on the internet
We need to find the value of x when y = $6.
So, put y = 6 in the above equation.
[tex]6=\dfrac{3}{4}x\\\\x=\dfrac{6\times 4}{3}\\\\x=8\ min[/tex]
So, 8 minutes must spent on internet.
A man had 35 goats.he sold 10 of
them.how many did he remains with.
Answer:
He remained with 25 goats.
Step-by-step explanation:
35 - 10 = 25
Hope this helps.
Answer:
He remained with 25 goats
Step-by-step explanation:
35 - 10 = 25
Convert 45 minutes to seconds. There are seconds in 45 minutes (Simplify your answer.) how many seconds are in 45 minutes
answer:2700sec
Step-by-step explanation:
if 60 sec=min
therefore;60×45
HELP PLEASE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start. Thank you for your time.
Answer:
6.09 is the answer rounded to nearest hundredths.
Step-by-step explanation:
It gives you n=150, p=0.55, and q=1-p.
If p=0.55 and q=1-p, then by substitution property we have q=1-0.55=0.45.
It ask you to evaluate the expression sqrt(npq).
So npq means find the product of 150 and 0.55 and 0.45. So that is 150(0.55)(0.45)=37.125.
The sqrt(npq) means we need to find the square root of that product. So sqrt(37.125)=6.093 approximately .
Suppose that Bag 1 contains a red (R), a blue (B) and a white (W) ball, while Bag 2 contains a red (R), a pink (P), a yellow (Y) and a green (G) ball. A game consists of you randomly drawing a ball from each of Bag 1 and Bag 2. (a) What are the 12 outcomes in the sample space S for this experiment? (b) You win the prize of baked goods if you draw at least 1 red ball. List the outcomes in the event that you win that prize, and use them to compute the probability of this event. You should assume that all outcomes in the sample spaces obtained in (a) are equally likely.
Answer:
1 /2
Step-by-step explanation:
Given :
Bag 1 : Red (R) ; Blue (B) ; White (W)
Bag 2 : Red (R) ; Pink (P) ; Yellow (Y) ; Green (G)
Total number of possible outcomes :
3C1 * 4C1 = 3 * 4 = 12 outcomes
Sample space (S) ;
_______ R ______ B _______ W
R_____ RR _____ RB ______ RW
P_____ PR _____ PB ______ PW
Y _____YR_____ YB ______ YW
G _____GR ____ GB ______ GW
To win price of baked goods ; Atleast one red ball must be drawn :
Probability of winning ; P(winning) = required outcome / Total possible outcomes
Required outcome = {RR, RB, RW, PR, YR, GR} = 6
Total possible outcomes = S = 12
P(winning) = 6/12 = 1/2
Juan and Lizette rented a car for one week to drive from Phoenix to Boise. The car rental rate was $250 per week and $0.20 per mile. By the most direct route, the drive is 926 miles. How much did they spend on the rental car?
( solution at pic)
PLEASE ANSWER MY QUESTION AND EXPLAIN RIGHT
Answer:
$ 1943
Step-by-step explanation:
You two congruent trapezoids.
Find the area of one and multiply by 2.
A = [tex]\frac{base_{1} + base_{2} }{2}[/tex] x h
= [tex]\frac{28+39}{2}[/tex] x 14.5
= [tex]\frac{67}{2}[/tex] x 14.5
= 33.5 x 14.5
= 485.75
= 485.75 x 2 (Two trapezoids)
= 971.50
= 971.50 x 2 (two dollars a square foot)
= 1943.00
An angle is bisected forming two new angles. If the origina angle a measure of degrees what is the measure of each angle
Answer:
so the measure of both angle is 24°
Step-by-step explanation:
original angle = 48°
so since its bisected the both angles are equal and let the angles be x
so,
x + x = 48°
2x = 48°
x = 48°/2
so, x = 24°
Midwest Publishing publishes textbooks. The company uses an 800 number where people can call to ask questions about the textbooks and place orders. Currently, there are 2 representatives handling inquiries. Calls occurring when both lines are in use get a busy signal. Each representative can handle 12 calls per hour. The arrival rate is 20 calls per hour.
Required:
a. How many extension lines should be used if the company wants to handle 90% of the calls immediately?
b. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used?
c. What percentage of calls receive a busy signal for the current telephone system with two extension lines?
Answer:
A. 18 calls
B. 0.9
C. 20
Step-by-step explanation:
Number of representatives=2,
Number of extension lines=2,
Average calls each representative can accommodate per hour = 15 calls,
Arrival rate per hour = 30 calls
(a) 90% of the arrival rate = 0.09 × 20 = 18 calls
To handle 18 calls immediately, 18 extension lines should be used
(b) Probability is given by number of possible outcomes ÷ number of total outcomes
Number of possible outcomes = 18, number of total outcomes = 20
Probability (call will receive busy signal) = 18/20 = 0.9
(c) For one extension line, numbers of calls to receive busy signal = 20 - 10 = 10 calls
Number of calls to receive busy signal for the current telephone system with two extension lines = 2 × 10 = 20 calls
rewrite 1/6 and 2/11 so they have a common denominator then use <, =, or > to order
Answer:
1/6 < 2/11
Step-by-step explanation:
1/6 = 2/12
2/11 >2/12
So that means 1/6 < 2/11
Answer: 1/6 < 2/11
This is the same as saying 11/66 < 12/66
===========================================================
Explanation:
1/6 is the same as 11/66 when multiplying top and bottom by 11.
2/11 is the same as 12/66 when multiplying top and bottom by 6.
The 6 and 11 multipliers are from the original denominators (just swapped).
We can see that 11/66 is smaller than 12/66, simply because 11 < 12, so that means 1/6 is smaller than 2/11
-----------------
Here's one way you could list out the steps
11 < 12
11/66 < 12/66
1/6 < 2/11
------------------
Here's another way to list out the steps. First assume that 1/6 and 2/11 are equal. Cross multiplication then leads to
1/6 = 2/11
1*11 = 6*2
11 = 12
Which is false. But we can fix this by replacing every equal sign with a less than sign
1/6 < 2/11
1*11 < 6*2
11 < 12
---------------------
Yet another way to see which is smaller is to use your calculator or long division to find the decimal form of each value
1/6 = 0.1667 approximately
2/11 = 0.1818 approximately
We see that 0.1667 is smaller than 0.1818, which must mean 1/6 is smaller than 2/11.
If the mean, median, and mode are all equal for the set (10, 80, 70, 120, x}, find the value of x.
X
(Simplify your answer. Type an integer or a decimal.)
Question Viewer
Answer:
x=70
Step-by-step explanation:
First, we know that the mode is the number that is the most common. As each value in the set so far only has one of each number, we know that x must be one of the current numbers, making that the mode.
Next, because x is the mode and has to be the median as well, and our number line so far is
(10, 70, 80, 120), x must be either 70 or 80 to make it the median. This is because if x is 10 or 120, we would end up with (10, 10, 70, 80, 120) with 70 as the median or (10, 70, 80, 120, 120) with 80 as the median.
Finally, to calculate the mean, we have
mean = sum / count
The mean must be x, as it is equal to the mode, so we have
x = (10+70+80+120 + x)/5 (as there are 5 numbers including x)
multiply both sides by 5 to remove the denominator
5 * x = 10+70+80+120+x
5 * x = 280 + x
subtract x from both sides to isolate the x and the coefficient
4 * x = 280
divide both sides by 4 to get x
x= 70
We see that x is 70 or 80 and is one of the current numbers, checking off all boxes.
In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2. The numbers of tornadoes in different weeks are mutually independent. Calculate the probability that fewer than four tornadoes occur in a three-week period.
Answer:
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2
Three weeks, so [tex]\mu = 2*3 = 6[/tex]
Calculate the probability that fewer than four tornadoes occur in a three-week period.
This is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.0025[/tex]
[tex]P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.0149[/tex]
[tex]P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.0446[/tex]
[tex]P(X = 3) = \frac{e^{-6}*6^{3}}{(3)!} = 0.0892[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0025 + 0.0149 + 0.0446 + 0.0892 = 0.1512[/tex]
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
