Let's start by finding the volume of the cistern at any given time t. Since the cistern is in the form of an inverted circular cone, its volume can be expressed as:
V = (1/3)πr^2h
where r is the radius of the circular opening, h is the height of the cone (which is also the depth of the cistern), and π is the constant pi.
We are given that the cistern is 5 meters deep, and the radius of its opening is 2 meters. Therefore, we can plug these values into the equation above to get:
V = (1/3)π(2^2)(5)
V = 20/3 π
Now, we need to find the rate at which the water level is rising in the cistern after 30 minutes. Let's call this rate dh/dt (the change in height with respect to time).
We know that the water is being added to the cistern at a rate of 65 liters per minute. Since 1 liter is equal to 0.001 cubic meters, the volume of water being added per minute is:
(65 liters/minute) × (0.001 m^3/liter) = 0.065 m^3/minute
Therefore, the rate at which the height of the water in the cistern is changing is:
dh/dt = (0.065 m^3/minute) / (20/3 π m^3) = 3.87/π meters/minute
After 30 minutes, the height of the water in the cistern will have risen by:
h = (65 liters/minute) × (0.001 m^3/liter) × (30 minutes) / (20/3 π m^3) = 0.2925 meters
Therefore, the rate at which the water level is rising in the cistern 30 minutes after the filling process began is:
dh/dt = 3.87/π meters/minute
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Find (8. 4 × 108) ÷ (1. 5 × 103). Express your answer in scientific notation
The simplified value of the given expression (8. 4 × 10^8) ÷ (1. 5 × 10^3) in scientific notation form is given by 5.6 × 10^5.
Expression is equal to ,
(8. 4 × 10^8) ÷ (1. 5 × 10^3)
To divide two numbers in scientific notation, we need to divide their coefficients and subtract their exponents.
(8.4 × 10^8) ÷ (1.5 × 10^3)
Apply law of exponents here,
When m > n
a^m ÷ a^n = a^( m - n )
Here , a = 10 , m = 8 and n = 3
= (8.4 ÷ 1.5) × 10^(8-3)
= 5.6 × 10^5
Therefore, the value of given expression is equal to 5.6 × 10^5 in scientific notation.
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The above question is incomplete , the complete question is:
Find (8. 4 × 10^8) ÷ (1. 5 × 10^3). Express your answer in scientific notation
Use differentials to estimate the value of ⁴√1.3 . Compare the answer to the exact value of ⁴√1.3 . Round your answers to six decimal places, if required. You can use a calculator, spreadsheet, browser, etc. to calculate the exact value. estimate= exact value=
Therefore, the estimate is quite close to the exact value, with an error of about 0.000450.
We can use differentials to estimate the value of ⁴√1.3 as follows:
Let y = ⁴√x, then we have:
dy/dx = 1/(4x^(3/4))
We want to estimate the value of y when x = 1.3, so we have:
Δy ≈ dy * Δx
where Δx = 0.3 - 1 = -0.7 (since we are approximating 1.3 as 1)
Substituting the values, we get:
Δy ≈ (1/(4(1)^3/4)) * (-0.7) ≈ -0.219
Hence, the estimate for ⁴√1.3 is:
y ≈ ⁴√1 + Δy ≈ 0.780
The exact value of ⁴√1.3 is approximately 0.780450255.
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Express the function graphed on the axes below as a piecewise function.
Expressing this function as a piecewise function, we get;
y = -x + 1 for x< -5
y = -1/2x + 4 for x> 4
According to the question, we can see that the graph is a line for x < -5. We will find two points on this line to find out the slope.
( - 5,6) and ( -8,9)
The slope is m= ( y2-y1)/(x2-x1)
m = ( 9-6)/(-8 - -5) = 3/ ( -8+5) = 3/-3
The slope is -1
Using point-slope form, we will find the general equation of this line
y-y1 = m(x-x1) and the point ( -8,9)
y -9 = -1(x - -8)
y -9 = -1(x +8)
y-9 = -x - 8
y = -x + 1 for x< -5
The graph is a line for x > 4
(4,2) and ( 6,1)
The slope is m= ( y2-y1)/(x2-x1)
m = ( 1 - 2)/(6 - 4) = -1/ (2) = -1/2
The slope is -1/2
Using point-slope form
y-y1 = m(x-x1) and the point (6,1)
y -1 = -1/2(x - 6)
y-1 = -1/2 x + 3
y = -1/2x + 4 for x> 4
Therefore, expressing this function as a piecewise function, we get;
y = -x + 1 for x< -5
y = -1/2x + 4 for x> 4
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at a party, seven gentlemen check their hats. in how many ways can their hats be returned so that 1. no gentleman receives his own hat? 2. at least one of the gentlemen receives his own hat? 3. at least two of the gentlemen receive their own hats?
1) There are 1854 ways to return the hats so that no gentleman receives his own hat.
2) There are 3186 ways to return the hats so that at least one of the gentlemen receives his own hat.
3) There are 865 ways to return the hats so that at least two of the gentlemen receive their own hats.
1) This problem involves the concept of permutations. A permutation is an arrangement of objects in a particular order. In this case, we need to find the number of permutations for returning the hats of the gentlemen.
To find the number of ways that no gentleman receives his own hat, we can use the principle of derangements. A derangement is a permutation of a set of objects such that no object appears in its original position.
The number of derangements of a set of n objects is denoted by !n and can be calculated using the formula:
!n = n!(1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!)
For n = 7, we have
!7 = 7!(1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!)
= 1854
Therefore, there are 1854 ways to return the hats so that no gentleman receives his own hat.
2) To find the number of ways that at least one of the gentlemen receives his own hat, we can use the complementary principle. The complementary principle states that the number of outcomes that satisfy a condition is equal to the total number of outcomes minus the number of outcomes that do not satisfy the condition.
The total number of ways to return the hats is 7!, which is 5040. The number of ways that no gentleman receives his own hat is 1854 (as we found in part 1). Therefore, the number of ways that at least one of the gentlemen receives his own hat is
5040 - 1854 = 3186
Therefore, there are 3186 ways to return the hats so that at least one of the gentlemen receives his own hat.
3) To find the number of ways that at least two of the gentlemen receive their own hats, we can use the inclusion-exclusion principle. The inclusion-exclusion principle states that the number of outcomes that satisfy at least one of several conditions is equal to the sum of the number of outcomes that satisfy each condition minus the sum of the number of outcomes that satisfy each pair of conditions, plus the number of outcomes that satisfy all of the conditions.
In this case, the conditions are that each of the seven gentlemen receives his own hat. The number of outcomes that satisfy each condition is 6!, which is 720. The number of outcomes that satisfy each pair of conditions is 5!, which is 120. The number of outcomes that satisfy all of the conditions is 4!, which is 24.
Using the inclusion-exclusion principle, the number of outcomes that satisfy at least two of the conditions is
6! - (7C₂)5! + (7C₃)4! - (7C₄)3! + (7C₅)2! - (7C₆)1! + 0!
= 720 - (21)(120) + (35)(24) - (35)(6) + (21)(2) - (7)(1) + 0
= 720 - 2520 + 840 - 210 + 42 - 7 + 0
= 865
Therefore, there are 865 ways to return the hats so that at least two of the gentlemen receive their own hats.
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The table below shows the number of students in Mr. Jang's class that are taking 1, 2, 3, or 4 AP classes. After a new student joined the class (not shown in the table), the average (arithmetic mean) number of AP classes per student became equal to the median. How many AP classes is the new student taking?
A) 2
B) 3
C) 4
D) 5
Answer:
2
Step-by-step explanation:
To solve this problem, we need to first find the current average and median number of AP classes per student, and then use that information to determine the number of AP classes the new student is taking.
To find the current average number of AP classes per student, we can use the information in the table:
(1 AP class) x 6 students = 6 AP classes
(2 AP classes) x 9 students = 18 AP classes
(3 AP classes) x 5 students = 15 AP classes
(4 AP classes) x 4 students = 16 AP classes
Total number of AP classes = 6 + 18 + 15 + 16 = 55
Total number of students = 6 + 9 + 5 + 4 = 24
Average number of AP classes per student = Total number of AP classes / Total number of students
= 55 / 24
= 2.29 (rounded to two decimal places)
To find the current median number of AP classes per student, we need to order the number of AP classes per student from least to greatest:
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4
The median is the middle value when the data is ordered in this way. Since there are 24 students, the median is the average of the 12th and 13th values:
Median = (2 + 2) / 2
= 2
Since we know that the current average and median are not equal, the new student must be taking a number of AP classes that will bring the average up to 2. We can set up an equation to represent this:
(55 + x) / (24 + 1) = 2
where x is the number of AP classes the new student is taking. Solving for x, we get:
55 + x = 50
x = -5
This is a nonsensical answer, as the number of AP classes taken by the new student cannot be negative. Therefore, our assumption that the new student is taking a number of AP classes greater than the current average is incorrect. Instead, the new student must be taking a number of AP classes less than the current average, which will bring the average down to 2.
Let y be the number of AP classes the new student is taking. We can set up a new equation to represent this:
(55 + y) / (24 + 1) = 2 - ((2.29 - 2) / 2)
where the term on the right-hand side represents the amount by which the average needs to decrease in order to reach 2. Solving for y, we get:
55 + y = 46.5
y = 46.5 - 55
y = 8.5
So the new student is taking 8.5 AP classes. However, since the number of AP classes must be a whole number, we need to round this value to the nearest integer. Since 8.5 is closer to 9 than to 8, we round up to 9. Therefore, the answer is:
The new student is taking 9 AP classes. Answer: None of the above (not given as an option).
How many different can be formed from 9 teachers and 30 students if the committee consists of 2 teachers and 2 students? if how many ways can the committee of 4 members be selected?
There are 15,660 different ways a committee consisting of 2 teachers and 2 students can be formed from 9 teachers and 30 students.
To find out how many different committees can be formed from 9 teachers and 30 students, if the committee consists of 2 teachers and 2 students, we will use the combination formula. The combination formula is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected.
First, let's find the number of ways to select 2 teachers from 9:
C(9, 2) = 9! / (2!(9-2)!) = 9! / (2! * 7!) = 36
Next, let's find the number of ways to select 2 students from 30:
C(30, 2) = 30! / (2!(30-2)!) = 30! / (2! * 28!) = 435
Now, to find the total number of ways the committee of 4 members can be selected, we simply multiply the number of ways to select teachers and students:
Total ways = 36 (ways to select teachers) * 435 (ways to select students) = 15,660
So, there are 15,660 different ways a committee consisting of 2 teachers and 2 students can be formed from 9 teachers and 30 students.
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2. Mandy is walking in the woods. She completes 70% of her walk in 3 hours. She continues walking at that same rate. How much time, in hours, will Mandy's entire walk take?
A 3 4\5
B. 5
C. 6
D. 6 1\2
Answer:
If Mandy completed 70% of her walk in 3 hours, then we can find her walking rate as follows:
Let's assume that the entire walk takes t hours. Then, 70% of the walk would take 0.7t hours. We know that Mandy completes 70% of her walk in 3 hours, so we can set up the following equation:
0.7t = 3
Solving for t, we get:
t = 3 ÷ 0.7 ≈ 4.29
So, the entire walk will take approximately 4.29 hours. Since Mandy has already walked for 3 hours, the remaining time she needs to complete her walk is:
4.29 - 3 = 1.29 hours
Therefore, the answer is closest to option A, 3 4/5 hours.
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Question 17 (5 points) ✓ saved
a patient needs to take 0.5 g po qam and 0.25 g po of a medication before sleeping.
how many 500 mg tablets must be dispensed for a 30-day supply?
90 tablets
75 tablets
25 tablets
45 tablets
The patient must be dispensed 45 tablets for a 30-day supply.
To determine how many 500 mg tablets must be dispensed for a 30-day supply given that a patient needs to take 0.5 g po and 0.25 g po before sleeping, follow these steps:
1. Convert grams to milligrams:
0.5 g = 500 mg (morning dose)
0.25 g = 250 mg (evening dose)
2. Calculate the total daily dosage:
500 mg (morning) + 250 mg (evening) = 750 mg per day
3. Calculate the number of 500 mg tablets needed per day:
750 mg / 500 mg = 1.5 tablets per day
4. Calculate the number of tablets needed for a 30-day supply:
1.5 tablets per day * 30 days = 45 tablets
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A rectangle city park measures 7/10 mile by 2/6 mile. what is the area of the park?
The area of the rectangular park is equal to 0.233 sq miles.
The measurements of the park that are given in the question are given as 7/10 mile by 2/6 mile.
The length of the rectangle park is 7/10 and the width of the park is 2/6 mile. We know that the area of the rectangle park is given as the:
= length * width of the park.
= L * W
= (7/10) * (2/6)
we can reduce the fraction even further to make the calculation easy
= (7/10) * (1/3)
Multiplying the denominators we get
= 7/30
To make the answer even simpler it can be converted into a decimal form which will be:
= 0.233 sq miles.
Therefore, The area of the rectangular park is equal to 0.233 sq miles.
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Find the volume of a hexagonal prism whose base
has area 30. 5 square centimeters and whose height is 6. 5 centimeters
The volume of the hexagonal prism is approximately 198.25 cubic centimeters.
To find the volume of a hexagonal prism, we need to know the area of the base and the height of the prism. In this case, we are given that the base has an area of 30.5 square centimeters and the height is 6.5 centimeters.
First, let's find the perimeter of the base. Since a hexagon has six sides, the perimeter will be six times the length of one side. To find the length of one side, we can use the formula for the area of a regular hexagon, which is:
Area = (3√3 / 2) × s²
where s is the length of one side.
30.5 = (3√3 / 2) × s²
s² = 30.5 × 2 / (3√3)
s² ≈ 11.13
s ≈ 3.34
So the perimeter of the base is 6 × 3.34 ≈ 20.04 centimeters.
Now we can use the formula for the volume of a prism, which is:
Volume = Base area × Height
Volume = 30.5 × 6.5 ≈ 198.25 cubic centimeters
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its due in a few minuets
Answer:
Step-by-step explanation:
If I'm wrong, write and I'll correct it. Because I don't know how to proceed
Hydrologists sometimes use Manning's equation to calculate the velocity v, in feet per second, of water flowing through a pipe. The velocity depends on the hydraulic radius R in feet, which is one-quarter of the diameter of the pipe when the pipe a flowing full; the slope S of the pipe, which gives the vertical drop in foot for each horizontal foot; and the roughness coefficient n, which depends on the material of which the pipe is made. The relationship is given by the following. v = 1.486/n R^2/3 S^1/2 For a certain brass pipe, the roughness coefficient has been measured to be n = 0.014. The pipe has a diameter of 3 feet and a slope of 0.4 foot per foot. (That is, the pipe drops 0.4 foot for each horizontal foot.) If the pipe is flowing full, find the hydraulic radius of the pipe. () Find the velocity of the water flowing through the pipe. ()
The velocity of the water flowing through the pipe is approximately 7.83 feet per second. The hydraulic radius of the pipe can be calculated as follows:
R = d/4
where d is the diameter of the pipe. In this case, the diameter is 3 feet, so the hydraulic radius is:
R = 3/4 = 0.75 feet
Now, we can use the given formula to calculate the velocity of the water:
[tex]v =[/tex][tex]1.486/n[/tex] [tex]R^(2/3) S^(1/2)[/tex]
Substituting the given values, we get:
v = 1.486/0.014 (0.75[tex])^(2/3)[/tex] (0.4[tex])^(1/2)[/tex] ≈ 7.83 feet per second
Therefore, the velocity of the water flowing through the pipe is approximately 7.83 feet per second.
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The coach of a soccer team keeps many stats on her team's performance.
For example, she records if the team was ahead, behind, or tied with the opponent at the end of each half.
Here is a summary of the data she got after games.
End of first half result End of second half result Number of games
ahead ahead
ahead behind
ahead tied
behind ahead
behind behind
behind tied
tied ahead
tied behind
tied tied
Suppose the coach will continue recording the end-of-half results for more games.
In how many of these games will the team be behind at the end of exactly one of the halves? Use the data to make a prediction
Based on the given data, the team was behind at the end of exactly one of the halves in a total of 4 games (behind ahead, behind behind, tied behind, and tied tied).
Therefore, it is likely that the team will be behind at the end of exactly one of the halves in around 4 out of every 10 games.
However, this prediction may not be accurate as it depends on various factors such as the strength of the opponent and the performance of the team in each game.
Predictions are often based on statistical data, trends, patterns, or expert knowledge, and can help individuals or organizations make informed decisions and plan for the future. However, predictions are not guarantees and can be affected by unforeseen circumstances or changes in the underlying conditions.
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Solve the initial value problem t^2 dy/dt - t=1 + y + ty, y (1) = 8.
The solution of initial value problem, y = 9/t - 1, t ≠ 0.
We can begin by rearranging the equation and separating the variables:
t^2 dy/dt - yt = t + 1
dy/(y+1) = (t+1)/t^2 dt
Integrating both sides, we get:
ln|y+1| = -1/t + t/t + C
ln|y+1| = -1/t + C
|y+1| = e^C /t
Using the initial condition y(1) = 8, we can find the value of C:
|8+1| = e^C /1
e^C = 9
C = ln 9
Substituting back into the general solution, we have:
|y+1| = 9/t
We can now solve for y in terms of t:
y+1 = ±9/t
If we take the positive sign, we get:
y = 9/t - 1
If we take the negative sign, we get:
y = -9/t - 1
Thus, the general solution to the initial value problem is:
y = 9/t - 1 or y = -9/t - 1
Using the initial condition y(1) = 8, we can see that the correct solution is:
y = 9/t - 1
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Question is attached.
Please show workings
When solved, the value of either a or b would be 0 such that we have a = 0 or b = 0. They could also both be zero.
How to solve the equation ?If the product of two numbers is zero, it necessitates that one or both of the values in question contain a value of zero. Similarly, when calculating the cross product of two given vectors and its resulting answer is equivalent to zero, then such vectors exist parallel with one another.
Alternatively, there is the possibility that only one vector holds a value of zero themselves:
( a × b ) = 0
This equation is true if either a = 0 or b = 0, or both a and b are zero.
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I have 90 kg of beef and need to add 1. 4 oz of filler to each pound. How many ounces of filler will I add
The ounces of filler will the factory need in order to make meatballs out of this shipment of beef is 56.7 oz of filler.
A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which remains almost unmodified. The avoirdupois ounce, also known as the US customary and British imperial ounce, is equal to one-sixteenth of an avoirdupois pound.
One factory obtained 90 kg of beef from overseas.
They want to add 1.4oz of filler for each pound of beef.
Given is:
0.45 kg = 1 pound
So, 90 kg = 90 x 0.45 = 40.5 pounds
The company want to add 1.4 oz of filler for each pound of beef.
So for 1 pound we have 1.4 oz of filler
So, for 40.5 pounds they will need = x oz of filler.
x = 1.4 x 40.5 = 56.7
Therefore, the company needs 56.7 oz of filler.
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Complete question;
Factories often add filler when making meatballs sold by the bag. One factory obtained 90kg of beef from overseas. They want to add 1.4oz of filler for each pound of beef. How many ounces of filler will the factory need in order to make meatballs out of this shipment of beef?
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 5. 7 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 10 samples is 6. 1 ppm with a variance of 0. 25. Does the data support the claim at the 0. 01 level? Assume the population distribution is approximately normal. Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places
If the absolute value of the calculated t-value is greater than or equal to 3.250, reject the null hypothesis.
To determine the decision rule for rejecting the null hypothesis, we need to calculate the test statistic.
First, we need to calculate the standard error of the mean:
standard error = square root of (variance/sample size)
standard error = square root of (0.25/10)
standard error = 0.158
Next, we can calculate the t-statistic:
t = (sample mean - hypothesized mean) / standard error
t = (6.1 - 5.7) / 0.158
t = 2.532
Using a two-tailed test at the 0.01 level of significance and 9 degrees of freedom (10 samples - 1), the critical t-value is ±3.250.
Since our calculated t-value of 2.532 is less than the critical t-value of ±3.250, we fail to reject the null hypothesis.
Therefore, the data does not support the claim that the current ozone level is at an excess level at the 0.01 level of significance.
Decision rule for rejecting the null hypothesis:
If the absolute value of the calculated t-value is greater than or equal to 3.250, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
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WILL GIVE BRAINLY 15 points
Michaela is making memory boxes. She wants to cover the boxes with sheets of decorative paper on all sides before filling them. This net represents a single memory box.
How much paper is needed to cover each memory box?
Enter your answer in the box
The amount of paper required to cover each memory box is 5220 square inches.
Considering the edge of the cube = L units.
Thus the area of one side of the cube will be equal to L² unit².
Now, there will be 6 such sides for a closed cube then the total surface area will be 6*(L)² unit²
The given length breadth and height of the box is 35in, 24in, and 30in.
The formula for the surface area of a rectangular prism is:
SA = 2(lw + lh + wh)
Where:
SA = surface area l = length w = width h = height
For this memory box, the given length (35 in), width (24 in), and height (30 in).
Substituting these values into the formula the SA obtained will be:
SA = 2(35 × 24 + 35 × 30 + 24 × 30) SA
= 2(840 + 1050 + 720) SA
= 2(2610) SA = 5220inches²
Therefore, the answer will be 5220 square inches.
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The radius of a bade if a cone is 8 cm. The height is 15 cm. What is the volume of the cone?
Answer: 1,004.8 or 320[tex]\pi[/tex]
Step-by-step explanation:
[tex]\frac{1}{3} \pi 8^{2} 15=1,004.8[/tex]
Given the height of the cone is 12 m, find the slant height of the cone
a) 5m
b) 13 m
c) 17m
d) 11m
The slant height of the cone is approximately 5 meters.
We can use the Pythagorean theorem to find the slant height of the cone.
The slant height, denoted by l, the height h and the radius r form a right triangle where l is the hypotenuse:
[tex]l^2 = h^2 + r^2[/tex]
In this case, we are given the height h as 12 m, but we are not given the radius r.
However, we know that the slant height is the distance from the apex of the cone to any point on its circular base.
So, we can draw a line from the apex of the cone to the center of its circular base, which will be perpendicular to the base, and we can use this line as the height of a right triangle that also includes the radius r of the circular base.
Then, we can use the Pythagorean theorem to find the slant height l.
The radius r is half the diameter of the circular base, so we need to find the diameter of the base.
Since we are not given the diameter directly, we need to find it using the height h and the slant height l.
To do this, we can draw a cross section of the cone that includes its circular base and its height, and then draw a line from the apex of the cone to a point on the base that is perpendicular to the diameter of the base.
This line will be the height of a right triangle that also includes the radius r of the base and half the diameter of the base.
Then, we can use the Pythagorean theorem to find the diameter of the base.We have:
[tex]l^2 = h^2 + r^2r = sqrt(l^2 - h^2)d/2 = sqrt(l^2 - r^2)d^2/4 = l^2 - r^2d^2 = 4(l^2 - r^2)[/tex]
Substituting the expression for r that we found above, we get:
[tex]d^2 = 4(l^2 - (l^2 - h^2))d^2 = 4h^2d = 2h[/tex]
Now we can substitute this expression for d into the formula for the volume of a cone:
[tex]V = (1/3) * pi * r^2 * hV = (1/3) * pi * ((2h)/2)^2 * hV = (1/3) * pi * h^2 * 4V = (4/3) * pi * h^3[/tex]
We can solve this formula for h:
[tex]h = (3V)/(4*pi)^(1/3)[/tex]
Substituting the given volume of the cone, which we will assume is in cubic meters:
[tex]V = (1/3) * pi * r^2 * h = (1/3) * pi * r^2 * 12V = 16pih = (3(16pi))/(4*pi)^(1/3)[/tex]
h = 4.819 m
Now we can find the slant height using the Pythagorean theorem:
[tex]l^2 = h^2 + r^2l^2 = (4.819)^2 + ((2(4.819))/2)^2l^2 = 23.187l = 4.815[/tex] [tex]m[/tex]
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Need help here guys.....
three similar bars of length 200 cm , 300cm and 360 cm are cut into equal pieces. find
the largest possible
area of square which
can be made from any of the three pieces.(3mks)
The largest possible area of a square that can be made from any of the three pieces is [tex](400 cm)^{2}[/tex]
To find the largest possible area of a square that can be made from any of the three similar bars of length 200 cm, 300 cm, and 360 cm, you need to first determine the greatest common divisor (GCD) of their lengths.
Step 1: Find the GCD of 200, 300, and 360.
The prime factorization of 200 is [tex](2^{3})(5^{2})[/tex], of 300 is [tex](2^{2})(3)(5^{2})[/tex], and of 360 is [tex](2^{3})(3^{2})(5)[/tex]. The GCD is the product of the lowest powers of common factors, which is [tex](2^{2})5=20[/tex].
Step 2: Determine the side length of the largest square.
Since the bars are cut into equal pieces with a length of 20 cm (the GCD), the largest square will have a side length of 20 cm.
Step 3: Calculate the largest possible area of the square.
The area of the square can be found by multiplying the side length by itself: [tex]Area = (side)^{2}[/tex].
[tex]Area = (20 cm)(20 cm) = (400 cm)^{2}[/tex].
So, the largest possible area of a square that can be made from any of the three pieces is [tex](400 cm)^{2}[/tex].
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Consider ABC.
What is the length of AC
A. 32units
B.48units
C.16units
D.24units
length of AC in the triangle is 32 units.
Define triangle proportionality ruleThe triangle proportionality theorem, also known as the side-splitter theorem, states that if a line is drawn parallel to one side of a triangle, then it divides the other two sides proportionally.
In mathematical terms, let ABC be a triangle with a line parallel to one side, say line DE || AB, where D lies on BC and E lies on AC. Then, the theorem states that:
BD/DC = AE/EC
In the given triangle ABC;
GH and AC are parallel
AG=BG
BH=HC
Using proportional rule
BG/AB=GH/AC
BG/2BG=16/AC
1/2=16/AC
AC=32 units
Hence, length of AC in the triangle is 32units.
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Answer:
1. 32 units
Step-by-step explanation:
sorry abt the other person but the answer is 32... i just took it
The volume of this rectangular prism is 3 cubic feet. What is the surface area?
Answer:
27
Step-by-step explanation:
What is the measure of ∠ABC?
The table below shows the number of gold, silver and bronze medals won by some
countries in the 1988 Winter Olympic Games.
Work out the ratio of gold to silver to bronze medals won by Sweden.
Give your answer in its simplest form.
Country
Canada
Finland
Soviet Union
Sweden
Gold
0
4
11
4
Silver
2
1
9
0
Bronze
3
2
9
2
Step-by-step explanation:
It looks as though ( from your post) Sweden won 4 golds and 0 silver and 2 bronze medals
4:0:2 simplifies to 2 :0 : 1
(4, 6) on a coordinate plane
Answer:
(4,6) on the coordinate plane is the 1st quadrant. You start at the origin, go 4 to the right and 6 up.
Hope this helped !!
WALK THE PATH SHOWN WHAT IS THE DISTANCE
Answer:
D. 4π
Step-by-step explanation:
Circumference: C = 2πr = 2π(8) = 16π
The distance = 1/4 circumference (angle is 90 degrees)
=> distance = 16π/4 = 4π
Assume that a procedure yields a binomial distribution with n trials and a probability of success of p. use a binomial probability table to find the probability that the number of successes x is exactly .
To find the probability that the number of successes x is exactly a certain value in a binomial distribution with n trials and a probability of success of p, we can use a binomial probability table. The table will provide us with the probability of getting x successes out of n trials, given a specific value of p.
For example, let's say we want to find the probability of getting exactly 3 successes in a binomial distribution with 10 trials and a probability of success of 0.5. We can use a binomial probability table to find the probability of getting exactly 3 successes, which is 0.117.
It is important to note that the probability of getting a specific number of successes in a binomial distribution is dependent on both the number of trials and the probability of success. Therefore, if we change either of these values, the probability of getting a certain number of successes will also change.
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Jon has 8 packets of soup in his cupboard, but all the labels are missing. he knows that there are 5 packets of tomato soup and 3 packets of mushroom soup. he opens three packets at random. work out the probability that all three packets are the same variety of soup.
Answer:
37.5%
Step-by-step explanation:
If all were the same from opening 3, it would all have to be mushroom soup. This would look like: desired outcome/total quantity: 3/8 = 0.375 = 37.5%
The Bayview community pool has a snack stand where Juan works part time he tracks his total sales during each shift last month this box plot shows the results what fraction of Juan’s shifts had a total sales of $225 or more
The fraction of Juan's shifts with a total sales of $225 or more can be found by looking at the box plot.
We can see that the top line of the box represents the third quartile (Q3) which is the value where 75% of the data falls below.
In this case, Q3 is at approximately $250. This means that 75% of Juan's shifts had total sales less than $250. To find the fraction of shifts with sales of $225 or more, we need to determine how many shifts fall within the range of $225 to $250.
Looking at the box plot, we can see that the distance between Q1 and Q3 (the interquartile range) is approximately $100. Therefore, the distance between Q1 and $225 is approximately one-third of the interquartile range or $33.33. So, any shift with total sales of $225 or more would fall within one-third of the distance between Q1 and Q3.
Therefore, the fraction of Juan's shifts with total sales of $225 or more is approximately one-third of 75%, which is 25%.
In summary, approximately 25% of Juan's shifts at the Bayview community pool had total sales of $225 or more, based on the box plot.
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