To count the number of different 6-letter strings that can be formed using the letters c, i, r, c, l, and e, we can use the permutation formula. There are 6 choices for the first letter, 5 choices for the second letter (since we can't use the same letter twice), and so on, giving us:
6 x 5 x 4 x 3 x 2 x 1 = 720
However, not all of these strings meet the condition that the two occurrences of the letter c are separated by at least one other letter. To count the number of strings that do meet this condition, we can use the complementary counting method.
First, let's count the number of strings in which the two c's are adjacent. There are 5 positions where the two c's could be (the first two, second and third, third and fourth, fourth and fifth, or last two positions), and once we place the c's, we have 4 letters left to fill in the remaining 4 positions. This gives us:
5 x 4 x 3 x 2 x 1 = 120
Now, let's count the total number of 6-letter strings that have at least one pair of adjacents c's. We can use the same method as above, but this time we can place the two c's anywhere in the string, giving us:
6 x 5 x 4 x 3 x 2 x 1 - 5 x 4 x 3 x 2 x 1 = 720 - 120 = 600
Finally, we can subtract this from the total number of 6-letter strings to get the number of strings in which the two c's are separated by at least one other letter:
720 - 600 = 120
Therefore, there are 120 different 6-letter strings that can be formed using the letters c, i, r, c, l, and e in which the two occurrences of the letter c are separated by at least one other letter.
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What is the probability of selecting a green golf ball put your answer in simplest form carter and a group of friends go miniature golfing. There is a basket of golf balls from which to choose. The basket contains 2 orange, 1 blue, 5 green, and 7 red gold balls
The crunchy cereal company has a certain size box with the following dimensions. Length equals X +3, width equals X -4, and height equals 2X +3. What is the expression for the volume of the box?
The expression for the volume of the box based on dimensions is 2x³ + x² - 27x - 36.
The volume of the box refers to the product of all the dimensions, which implies its capacity to contain any material. Thus, the formula to calculate volume will be -
Volume = length × width × height
Keep the values in formula
Volume = (x + 3) × (x - 4) × (2x + 3)
Performing multiplication
Volume = (x² - 4x + 3x - 12) × (2x + 3)
Simplify the product
Volume = (x² - x - 12) × (2x + 3)
Multiply again
Volume = 2x³ + 3x² - 2x² - 3x - 24x - 36
Simplify the equation again
Volume = 2x³ + x² - 27x - 36
Hence, the expression for the volume is 2x³ + x² - 27x - 36.
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Grace is in charge for selecting the batting order for her club baseball team. If there are 12 players on the team and the batting order is a total
of ten batters, in how many different ways can she select the order?
Number of Different Ways:
There are 19,958,400 different ways Grace can select the batting order for her club baseball team.
How to determine how many different ways can she select the orderUsing permutation formula: P(n,r) = n! / (n - r)!
where n is the total number of players on the team (12) and r is the number of batters in the batting order (10).
So, we have:
P(12,10) = 12! / (12 - 10)!
P(12,10) = 12! / 2!
P(12,10) = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3
P(12,10) = 19,958,400
Therefore, there are 19,958,400 different ways Grace can select the batting order for her club baseball team.
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A company sold 660 watches. A consumer advocate group found that 5% of this particular type of watch was defective when they conducted a random survey of 100 watches. Estimate the number of watches sold that were not defective. Enter the correct answer in the box..
The number of defective watches from the 660 watches sold by the company, obtained by finding the number of the percentage of the defective watches is 627 watches
What is a percentage?A percentage is a expression of a part or proportion of a quantity as a fraction of 100.
The percentage of watches that are defective = 5%
The number of watches in the survey by the consumer advocate group = 100 watches
The number of watches sold by the company = 660
The number of watches in the sample = 100 > 30, which indicates that the statistical results obtained from the sample follows a normal distribution, and the percentage of watches the company sold that are defective are also 5%.
The number of watches that are not defective = 660 - 660 × 5/100 = 627
The number of defective watches = 627
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what property is this
5+(a+8)= (5+a)+8
Answer:
[tex]\huge\boxed{\sf Associative\ Property\ of\ Addition}[/tex]
Step-by-step explanation:
This property is Associative Property.
Associative Property:Irrespective of the placement of parenthesis, adding or multiplying more than two number gives the same result.General form:(A + B) + C = A + (B + C)
Since, here the expression is being added, the given property is Associative Property of Addition.
[tex]\rule[225]{225}{2}[/tex]
Answer:
this is an associative property of addition
What is the perimeter and area of parallelogram WXYZ if 1 unit equals 1 centimeter? Round to the nearest centimeter.
a.) perimeter= 20cm; area 22cm²
b.) perimeter= 22cm; area= 20cm²
c.) perimeter= 26cm; area= 39cm²
d.) perimeter= 39cm; area= 26cm²
The perimeter and area of parallelogram WXYZ is b.) perimeter= 22cm; area= 20cm²
How to determine the valueThe formula for calculating the perimeter of a parallelogram is expressed as;
P = 2(a + b)
Such that the parameters are;
P is the perimetera and b are the parallel sidesThen, we have;
Perimeter = 2(4 + 7)
Add the values
Perimeter = 22 cm
The area of a parallelogram is expressed as;
Area = bh
Where the parameters of the formula are;
h is the height b is the base lengthArea = 5(4)
Area = 20cm²
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suppose you have 6 red cards, 8 green cards, and 13 blue cards. the cards are well shuffled and you randomly draw one card. a. how many elements are there in the sample space
The sample space has 27 elements.
The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is drawing one card from a well-shuffled deck of 27 cards.
To determine the number of elements in the sample space, we can count the total number of cards in the deck.
The number of red cards is 6, the number of green cards is 8, and the number of blue cards is 13. Therefore, the total number of cards in the deck is:
6 + 8 + 13 = 27
Hence, there are 27 possible outcomes when drawing one card from the deck. These outcomes consist of the 6 red cards, the 8 green cards, and the 13 blue cards in the deck.
So the sample space has 27 elements.
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Which of the following inequalities are correct?
A -6<-4
B 4<6
C 0>-4
Answer:
Step-by-step explanation:
Both options A and B are correct, while option C is incorrect.
Option A, -6 < -4, is true because -6 is less than -4 on the number line.
Option B, 4 < 6, is also true because 4 is less than 6 on the number line.
Option C, 0 > -4, is incorrect because 0 is not greater than -4. In fact, -4 is less than 0, so the correct inequality would be -4 < 0.
Therefore, the correct options are A and
Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of flour and 34 cup of water. Mitch wants to make more pizzas without changing the ratio of flour to water. The number of cups of flour must always be
how many times the number of cups of water
The number of cups of flour must always be 6 times the number of cups of water, under the condition Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of four and cup of water.
In order to make 4 more pizzas without changing the ratio of flour to water, Mitch have to use 12 cups of flour and 2 cups of water.
To evaluate this we need to perform multiplication
Mitch used 3 cups of flour and 1 cup of water for 2 pizzas. So for each pizza, he used 1.5 cups of flour and 0.5 cups of water.
To make 4 more pizzas, he needs to use 6 cups of flour and 2 cups of water (since he needs twice as many pizzas).
Then, for each pizza, he needs to use 1.5 cups of flour and 0.5 cups of water (since he wants to keep the ratio the same).
So for 4 more pizzas, he needs to use 6 x 2 = 12 cups of flour and 2 x 2 = 4 cups of water.
Since he wants to keep the ratio the same, he needs to use 12 cups of flour and 2 cups of water.
Therefore, the number of cups of flour must always be 6 times.
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The complete question is
Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of four and cup of water. Mitch wants to make 4 more pizzas without changing the ratio of flour to water. Enter a number to make the sentence about the ingredients true.
The number of cups of flour must always be___ times the number of cups of water.
a region r is shown. decide whether to use polar coordinates or rectangular coordinates and write r f(x, y) da as an iterated integral, where f is an arbitrary continuous function on r
For rectangular coordinates, the iterated integral would be: ∬R f(x, y) dA = ∫(from a to b) ∫(from c(x) to d(x)) f(x, y) dy dx
For polar coordinates, the iterated integral would be: ∬R f(r, θ) r dA = ∫(from α to β) ∫(from g(θ) to h(θ)) f(r, θ) r dr dθ
To decide whether to use polar coordinates or rectangular coordinates, we need to examine the shape of the region r. If r is a circular or symmetric shape, polar coordinates are often more convenient to use. If r is a rectangular or non-symmetric shape, rectangular coordinates are more appropriate.
Assuming that r is a circular or symmetric shape, we will use polar coordinates. Let's define r in terms of polar coordinates as r = {(r, θ) | 0 ≤ r ≤ a, 0 ≤ θ ≤ 2π}. We can write the double integral of f(x,y) over r in terms of polar coordinates as:
∫∫ r f(x, y) da = ∫₀^a ∫₀^2π f(r cos θ, r sin θ) r dθ dr
This is the iterated integral of f over r in terms of polar coordinates. We integrate f with respect to θ first, from 0 to 2π, and then with respect to r, from 0 to a.
Note that f is an arbitrary continuous function on r, which means that it can take on any value on the region r. We integrate f over r by multiplying f by the area element da, which is r dr dθ in polar coordinates.
To help you with this question, I need to know the specific region R you're referring to. However, I can provide you with general guidance on choosing between polar and rectangular coordinates and setting up an iterated integral.
When deciding between polar and rectangular coordinates, consider the shape and symmetry of the region R. If R has circular or radial symmetry, it's typically easier to use polar coordinates. If R has rectangular or Cartesian symmetry, use rectangular coordinates.
For rectangular coordinates, the iterated integral would be:
∬R f(x, y) dA = ∫(from a to b) ∫(from c(x) to d(x)) f(x, y) dy dx
For polar coordinates, the iterated integral would be:
∬R f(r, θ) r dA = ∫(from α to β) ∫(from g(θ) to h(θ)) f(r, θ) r dr dθ
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Find the radius of the sphere which passes through points A, B, C, and D in space if BAC = BAD =CAD = 90 and AB = AC = AD = 6.
To find the radius of the sphere passing through points A, B, C, and D in space, we can use the fact that the sphere will be the circumsphere of triangle ABC and triangle ABD.
Since BAC = BAD = CAD = 90, we know that triangle ABC and triangle ABD are both right triangles.
Using the Pythagorean theorem, we can find the length of BC and BD:
BC^2 = AB^2 + AC^2 = 6^2 + 6^2 = 72
BD^2 = AB^2 + AD^2 = 6^2 + 6^2 = 72
Since BC = BD, we know that triangle BCD is an isosceles triangle. Therefore, the altitude from vertex C to side BD will bisect BD, and the altitude from vertex B to side CD will bisect CD. Let E be the point where the altitudes intersect.
Now we can use the Pythagorean theorem again to find the length of CE:
CE^2 = BC^2 - BE^2 = 72 - (BD/2)^2 = 72 - 36 = 36
CE = 6
Since the sphere passes through point C, its center must be equidistant from points A, B, and D. Let O be the center of the sphere. Then we have:
OA = OB = OD
OA^2 = OC^2 + AC^2 = OC^2 + 36
OB^2 = OC^2 + BC^2 = OC^2 + 72
OD^2 = OC^2 + AD^2 = OC^2 + 36
Since OA = OB = OD, we can equate the expressions for OA^2, OB^2, and OD^2:
OC^2 + 36 = OC^2 + 72 = OC^2 + 36
72 = 2(OC^2 + 36)
OC^2 = 18
Therefore, the radius of the sphere is:
r = OC = sqrt(18) = 3sqrt(2)
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What’s the unit rate of 144 pages in 3 minutes ?
how long will it take joe to turn the sheet metal into 5 pieces?
Answer:
Unclear, but assuming it takes 2 minutes to cut one piece, your answer would be 10 minutes to cut 5 pieces.
Step-by-step explanation:
We have 5 pieces, each takes 2 minutes, so:
5×2=10
If it takes more or less than 2 minutes per piece, replace the "2" with another value. (EXAMPLE: 5 minutes per piece would be 5×5=25)
Other:
If this is wrong, I apologize, as there was not enough information given to your question.
Which relation is displayed in the table?
A: {(-2, -3), (1, -1), (2, -2), (3, 3)}
B: {(-3, -2), (-1, 1), (2, -2), (3, 3)}
C: {(-2, -3), (-1, 1), (-2, 2), (3, 3)}
D: {(-2, -3), (-1, 1), (-2, -2), (3, 3)}
The relation that is displayed in the table can be found to be B: {(-3, -2), (-1, 1), (2, -2), (3, 3)}
How to find the relation ?The relation displayed on the table would simply refer to the points seen on the table. When writing the coordinates of a point, you should give the x value first and then give the y value.
The relations on the table are therefore { ( - 3 , - 2 ) , ( - 1 , 1 ) , ( 2 , - 2 ) , ( 3 , 3 ) }. This represents the entire point portfolio seen on the table and therefore encompasses all the relation.
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the u.s. bureau of labor statistics reports that 11.3% of u.s. workers belonged to unions in 2013. suppose a sample of 400 u.s. workers is collected in 2018 to determine whether union efforts to organize have increased union membership. if the sample results show that 58 of the workers belonged to unions, what is the p-value for your hypothesis test?
Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.
We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.
The null hypothesis is that the population proportion is equal to 11.3%:
H0: p = 0.113
The alternative hypothesis is that the population proportion is greater than 11.3%:
Ha: p > 0.113
The sample proportion is P = 58/400
= 0.145
The standard error of the sample proportion is:
SE = √(p*(1-p)/n)
= √(0.113*(1-0.113)/400)
= 0.0197
The test statistic is:
z = (P - p) / SE
= (0.145 - 0.113) / 0.0197
= 1.6244
The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:
p-value = P(Z > 1.6244)
= 0.0515 (using a standard normal distribution table)
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HELP PLEASE
An artist recreated a famous painting using a 4:1 scale. The dimensions of the scaled painting are 8 inches by 10 inches. What are the dimensions of the actual painting?
40 inches by 50 inches
32 inches by 40 inches
12 inches by 14 inches
2 inches by 2.5 inches
The dimensions of the actual painting are 32 inches by 40 inches. So, the answer is option B: 32 inches by 40 inches.
To find the dimensions of the actual painting, we need to use the scale factor and the dimensions of the scaled painting. Since the scale factor is 4:1, this means that the actual painting is four times larger than the scaled painting.
Let the dimensions of the actual painting be x and y. Then, we can set up the following proportion:
Scaled painting dimensions: actual painting dimensions = 1 : 4
This can also be written as:
8: x = 1: 4 (for the width)
10: y = 1: 4 (for the length)
Solving for x and y, we get:
x = 8 x 4 = 32 inches
y = 10 x 4 = 40 inches
Therefore, the dimensions of the actual painting are 32 inches by 40 inches. So, the answer is option B: 32 inches by 40 inches.
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Help me on all questions it’s due soon
(1) The value of x is in the inscribed chords is 110⁰.
(2) The length of PT is 7.48 cm.
(3) The length of EC is 1.93.
What is the value of x?The value of x is calculated by applying intersecting chord theorem as shown below;
x = ¹/₂ ( 360 - ( 40⁰ + 100⁰ )
x = ¹/₂ (360 - 140 )
x = ¹/₂ (220)
x = 110⁰
2. The length of PT is calculated as follows;
The radius of the circle = length NT, is calculated as follows;
A = πr²
r² = A/π
r = √ (A/π)
r = √ (25π/π)
r = 5 cm = NT = NM
PT is calculated by applying Pythagoras theorem as follows;
NP = NM + MP
NP = 5cm + 4 cm
NP = 9 cm
PT = √ (9² - 5²)
PT = 7.48 cm
3. The length of EC is calculated by applying chord theorem as follows;
AE. ED = BE . EC
ED = AD - AE
ED = 12 - 3 = 9
Now, solve for EC;
AE. ED = BE . EC
3 x 9 = 14(EC)
27 = 14(EC)
EC = 27/14
EC = 1.93
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Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.x = t^4 + 3y = t^3 + tt = 1y(x) =
The equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.
To find the equation of the tangent to the curve at the point corresponding to t=1:
We first need to find the corresponding values of x and y. Substituting t=1 into the given equations, we get:
[tex]x = 1^4 + 3 = 4[/tex]
[tex]y = 1^3 + 1(1) = 2[/tex]
So the point on the curve corresponding to t=1 is (4,2).
To find the equation of the tangent at this point,
we need to find the slope of the curve at this point. We can do this by taking the derivative of y(x) with respect to x:
[tex]dy/dx = (dy/dt)/(dx/dt) = (3t^2+t)/(4t^3)[/tex]
Substituting t=1, we get:
dy/dx = (3+1)/(4) = 1
So the slope of the curve at the point (4,2) is 1.
Now we can use the point-slope form of the equation of a line to find the equation of the tangent:
y - 2 = 1(x - 4)
Simplifying, we get:
y = x - 2
So the equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.
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If tan(A+B)=8 and tan B = 1/57 find tan A
Step by Step Please
The ages of children taking a hip-hop dance class are 10, 9, 9, 7, 12, 14, 14, 9, and 16 years old
Which of the following Describe the distribution of the data
The ages range from 1 of 7.
Select Choice
years to 2 of 7.
Select Choice
years.
The middle half of the data range from 3 of 7.
Select Choice
years to 4 of 7.
Select Choice
years.
The median is 5 of 7.
Select Choice
years; half of the children taking the class are older than 10 years old and half of them are younger than 10 years old.
Because the left whisker and left box combined are shorter than the right whisker and right box, there is 6 of 7.
Select Choice
variation among the lower half of the data. Having less variation means there is a 7 of 7.
Select Choice
consistency among the ages of children younger than 10 years old.atistical questions? Select all that apply. (Example 1)
Answer:
Step-by-step explanation:
easy its 7
What is the result when the number 36 is decreased by 25%
Answer:
27
Step-by-step explanation:
1. 100% - 25% = 75%
2). 3/4 x 36 = 27
Answer:
27
Step-by-step explanation:
There are 2 ways we can solve this:
The first way is with percents:
100%-25%=75%
75/100=0.75 or 3/4
3/4·36
27
The second way is to use common knowledge:
We know that 25% is 1/4 of anything. So, 1/4 of 36 is 9.
36-9=27
Hope this helps! :)
Mr Andrew harvested 3 056 dasheens. He packed them into bags of 8 dasheens each. How many bags of dasheen did he pack?
Answer:
382 bags of dasheen
Step-by-step explanation:
Divide the total number of dasheens harvested by the number of dasheens per bag:Therefore, My. Andrew packed a total of 382 bags of dasheen
HELP I have this due tommorow click link and use surface area I need verification
Answer:
Question 3: would equal 30.5 and Question 4: would equal 19
1) How many moles of aluminum will be used when reacted with 1.35 moles of oxygen based on this chemical reaction? __Al + ___ O2 → 2Al2O3
2) How many moles of hydrogen will be produced when reacted with 0.0240 moles of sodium in the reaction? ___ N + ___H2O → ___ NaOH + ___H2
The number of moles for the first equation is 1.8 and the number of moles for the second equation is 0.0240.
The balanced chemical equation is 4Al + 3O² → 2Al₂O₃. The molar ratio of Al to O₂ is 4:3. Therefore, if 1.35 moles of O₂
4 moles Al/₃ moles O₂ = x moles Al/1.35 moles O₂
x = 1.8 moles of Al
The balanced chemical equation is N + 2H₂O → NaOH + H₂. The molar ratio of N to H₂ is 1:1. Therefore, if 0.0240 moles of N is used, then the number of moles of H₂ produced would be:
1 mole N/1 mole H₂ = 0.0240 moles N/x moles H₂
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(Chapter 12) For any vectors u and v in V3, |u à v| = |v à u|
So the magnitude of the cross product between two vectors is the same regardless of the order of the vectors.
This statement is true. The magnitude of the cross product between two vectors u and v is defined as:
|u à v| = |u||v|sinθ
where θ is the angle between the two vectors. The cross product is anti-commutative, meaning that if we switch the order of the vectors, the sign of the result changes:
v à u = - (u à v)
Therefore, taking the magnitudes of both sides, we have:
|v à u| = |- (u à v)|
|v à u| = |u à v|
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the difference between john's and paul's heights is twice the difference between john's and thom's heights. if john is the tallest, what is the average (arithmetic mean) height of the three? (1) paul is 163 centimeters tall. (2) thom is 173 centimeters tall.
We're given that the difference between John's and Paul's heights is twice the difference between John's and Thom's heights.
Let's use variables to represent their heights: J for John, P for Paul, and T for Thom. The equation can be written as:
J - P = 2(J - T)
Now, we're given two pieces of information:
1) Paul is 163 centimeters tall (P = 163).
2) Thom is 173 centimeters tall (T = 173).
We'll use this information to solve for John's height and then find the average height of the three.
Step 1: Plug in the given values into the equation.
J - 163 = 2(J - 173)
Step 2: Distribute the 2 on the right side.
J - 163 = 2J - 346
Step 3: Rearrange the equation to isolate J.
J - 2J = 346 - 163
Step 4: Combine like terms.
-1J = 183
Step 5: Divide by -1 to find John's height.
J = -1(-183)
J = 183 cm
Now that we have John's height, we can find the average height of the three.
Average height = (John's height + Paul's height + Thom's height) / 3
Average height = (183 + 163 + 173) / 3
Average height = 519 / 3
Average height = 173 cm
So, the average height of John, Paul, and Thom is 173 centimeters.
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there were 11 students running a race. How many diffenert arrangments of first,second,and third place are possible?
Answer:
165
Step-by-step explanation:
there are 165 different arrangements of 1,2,3 place possible of the 11 students
Tyrone is an investment broker who tells his clients that some investments are a moderate risk and others are an aggressive risk. He wants to know the difference between the annual return on the investments in each category. He sampled 17 investments from each category. There was a mean annual return of 6.2% on the investments in the moderate sample, with a standard deviation of 9.3%. The aggressive investments had a sample mean of 7.3% and a standard deviation of 12.4%. Assume that the conditions for inference have been met, and that Tyrone will use the conservative degrees of freedom corresponding to a sample size of 17. Leta - Am be the difference in mean annual return (in percents) of the groups of investments. Which of the following is a 90% confidence interval for p - um? Choose 1 answer: a. (-5.49, 7.69) b. (-5.464, 7.664)c. (-5.084, 7.284) d. (-3.926, 6.126) e. (-2.659,4.859)
the 90% confidence interval for p - um is (-0.816, 2.916), which can be rounded to (-0.82, 2.92). The closest option to this interval is (c) (-5.084, 7.284).
The point estimate for the difference in mean annual return is:
a - m = 7.3 - 6.2 = 1.1
To find the margin of error for a 90% confidence interval, we use the t-distribution with 16 degrees of freedom (conservative df) and a 5% significance level (90% confidence level):
t* = 1.745
The margin of error is then:
ME = t* * sqrt[(s1^2/n1) + (s2^2/n2)]
= 1.745 * sqrt[(0.093^2/17) + (0.124^2/17)]
= 0.916
The 90% confidence interval is:
(a - m) ± ME
1.1 ± 0.916
Thus, the 90% confidence interval for p - um is (-0.816, 2.916), which can be rounded to (-0.82, 2.92). The closest option to this interval is (c) (-5.084, 7.284).
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Julianna bought 45 feet of fencing to go around the edge of the garden. If each unit in the coordinate plane represents 1 foot, does Julianna have enough fencing for the garden? Be sure to explain your answer.
The solution is:
No, this statement is not true, we know that these dimensions are not possible given the amount of fencing.
We have,
Perimeter measures the distance around a shape.
Perimeter Formula
The perimeter is 2w + 2l = P, where w is the width and l is the length. This formula is used because together, it adds together the distance of every side.
If wanted, it can be rewritten as w + w + l + l = P. This form of the formula shows all 4 sides being added together.
Inequality
We can set up an inequality to represent the situation. We know that the perimeter must be less than or equal to 150 because that is the amount of fence John has. So, we can plug the information that we know into the formula.
2(50) + 2(40) ≤ 150
Then, solve.
180 ≤ 150
Since this statement is not true, we know that these dimensions are not possible given the amount of fencing.
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complete question:
John is building a fence around his garden and has 150 feet of
fencing. The length of his garden is 40 feet and the width of
his garden is 50 feet. Does John have enough fencing to go
around the perimeter of his garden? Explain why or why not.
Geometry- finding the volume. Please help I’m confused?!
Answer:
V = 5/3πr³1130.4 in³Step-by-step explanation:
You want a formula for the volume of the given figure, which is a hemisphere of radius r atop a cylinder of the same radius and height r.
Volume formulasThe volume of a sphere is given by ...
V = (4/3)πr³
The volume of a cylinder is given by ...
V = πr²h
CompositionThe given figure is composed of half a sphere, and a cylinder. The total volume will be the sum of the volumes of these parts.
total volume = 1/2(sphere volume) + (cylinder volume)
A Total volumeUsing a height of r for the cylinder, we can substitute the above formulas to get ...
total volume = 1/2(4/3πr³) +(πr²·r)
total volume = 2/3πr³ + πr³ = (2/3 +1)πr³
total volume = (5/3)πr³
B How much glassWhen the height is 12 inches, the radius is 6 inches, so the volume of the object is ...
total volume ≈ (5/3)(3.14)(6 in)³ = 1130.4 in³
About 1130.4 cubic inches of glass will be needed for a paperweight that is 12 inches tall.