Answer:
0.3 liters
Step-by-step explanation:
Molly made 3600mL of tea for a party.
The tea was served equally in 12 cups.
We are to determine how many liters of tea Molly put in each cup.
Total Volume of Tea = 3600mL
Number of Cups=12
Volume Per Each Cup = 3600/12 = 300mL
Next, we convert our Volume Per Each Cup from mL to Liters
1000 Milliliter = 1 Liter
300 Milliliter =[tex]\frac{300}{1000}[/tex] liters =0.3 liters
Molly put 0.3 liters of tea in each cup.
Solve the system of linear equations by substitution.
−x−8=−y
9y−12+3x=0
The solution is ( , )
Answer:
The solution (x, y) = (-5, 3)
Step-by-step explanation:
-x - 8 = -y .... (1)
9y - 12 + 3x = 0 .... (2)
from equation (1)
-x = - y + 8 ... (3)
multiply equation (3) by -1
x = y - 8 ..... (4)
substituting equation (4) in equation (2)
9y - 12 + 3 ( y - 8) = 0
9y - 12 + 3y - 24 = 0
12y - 36 = 0
12y = 36
y = 36 /12
y = 3
Substitute y = 3 in equation (4)
x = y - 8
x = 3 - 8
x = -5
Sociologists want to test whether the number of homeless people in a particular urban area is increasing. In 2010, the average number of homeless people per day who sought shelter was 42.3 (σ = 6.2). Data from the current year reveal that the mean number of people seeking shelter per day is 45.3. Compute the test statistic using an alpha = .01 and n = 1000.
Answer:
The test statistic value is 15.3.
Step-by-step explanation:
The hypothesis for this test is:
H₀: The average number of homeless people is not increasing, i.e. μ = 42.3.
Hₐ: The average number of homeless people is increasing, i.e. μ > 42.3.
Given:
[tex]\bar x=45.3\\\sigma=6.2\\n=1000[/tex]
As the population standard deviation is provided use a single mean z-test for the hypothesis testing.
The test statistic is:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3[/tex]
Thus, the test statistic value is 15.3.
Using the z-distribution, it is found that the test statistic is of z = 15.3.
At the null hypothesis, it is tested if the mean number has not increased, that is, it still is of 42.3, hence:
[tex]H_0: \mu = 42.3[/tex]
At the alternative hypothesis, it is tested if it has increased, that is, the mean is greater than 42.3, hence:
[tex]H_1: \mu > 42.3[/tex]
We have the standard deviation for the population, hence, the z-distribution is used.
The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are:
[tex]\overline{x} = 45.3, \mu = 42.3, \sigma = 6.2, n = 1000[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{45.3 - 42.3}{\frac{6.2}{\sqrt{1000}}}[/tex]
[tex]z = 15.3[/tex]
The test statistic is of z = 15.3.
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Asna works on a shipping dock at a tire manufacturing plant. She load a pallet with 4 Mudslinger tires and 6 Roadripper tires. The tires on the pallet weigh 212 pounds. She loads a secong pallet with 7 Mudslinger tires and 2 Roadripper tires. The tires on the secong pallet weigh 184 pounds. How much does each Mudslinger and each Roadripper tire weigh? (9th Grade CP Math)
Answer:
A Mudslinger tire weighs 20.71 pounds and a Roadripper tire weighs 19.52 pounds
Step-by-step explanation:
Let the weight of a Mudslinger tire=m
Let the weight of a Roadripper tire=r
4 Mudslinger tires and 6 Roadripper tires weigh 200 pounds
4m+6r=200.....(i)
7 Mudslinger tires and 2 Roadripper tires weigh 184 pounds
7m+2r=184....(ii)
To find the values of m and r, we solve the two derived equations simultaneously.
4m+6r=200.....(i)
7m+2r=184....(ii)
Multiply (ii) by 3 to get (iii)
21m+6r=552....(iii)
4m+6r=200.....(i)
SUbtract (i) from (iii)
17m=352
m=352/17=20.71 pounds
Substitute m=20.71 in (i)
4(20.71)+6r=200
6r=200-82.84=117.16
r=117.16/6=19.52 pounds
PLLLLZ HELP Find the seventh partial sum of 13, 22, 31, 40, ...
9
67
106
280
Just got the test and answered 67...was absolutely sure it is correct answer...Most likely the answer is 9 ....Since to get every next sum is +9.. Well, at least 67 is a wrong answer..:(
The seventh partial sum is 280
Option D is the correct answer.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
The sequence has a common difference of 9, so it is an arithmetic sequence.
The first term is 13.
To find the seventh partial sum, we need to add up the first seven terms of the sequence:
= 13 + 22 + 31 + 40 + 49 + 58 + 67
= 280
Therefore,
The seventh partial sum is 280
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Please help!!! ASAP someone please
Answer:
0.31 yr
Step-by-step explanation:
The formula for interest compounded continuously is
[tex]FV = PVe^{rt}[/tex]
FV = future value, and
PV = present value
If FV is twice the PV, we can calculate the doubling time, t
[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]
1. Brianna's doubling time
[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.065}\\\\& = & \textbf{10.663 yr}\\\end{array}[/tex]
2. Adam's doubling time
The formula for interest compounded periodically is
[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]
where
n = the number of payments per year
If FV is twice the PV, we can calculate the doubling time.
[tex]\begin{array}{rcl}2 & = & \left (1 + \dfrac{0.0675}{4} \right )^{4t}\\\\&= & (1 + 0.016875 )^{4t}\\& = & 1.016875^{4t}\\\ln 2& = & 4 (\ln 1.01688)\times t \\& = & 0.066937t\\t& = & \dfrac{\ln 2}{0.066937}\\\\& = & \textbf{10.355 yr}\\\end{array}[/tex]
3. Brianna's doubling time vs Adam's
10.663 - 10.355 = 0.31 yr
It would take 0.31 yr longer for Brianna's money to double than Adam's.
Look at the system of equations below.
{y = − 2 x + 3
4 x − 3y = 11
What is the solution to the system? Show your work.
Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=-1[/tex]
Step-by-step explanation:
Considering the system of the equation
[tex]\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=-2x+3[/tex]
[tex]\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11[/tex]
[tex]4x-3\left(-2x+3\right)=11[/tex]
[tex]4x+6x-9=11[/tex]
[tex]10x-9=11[/tex]
[tex]10x-9+9=11+9[/tex]
[tex]10x=20[/tex]
[tex]x=2[/tex]
[tex]\mathrm{For\:}y=-2x+3[/tex]
[tex]\mathrm{Subsititute\:}x=2[/tex]
[tex]y=-2\cdot \:2+3[/tex]
[tex]y=-1[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=-1[/tex]
8. Mr. Mercado bought a bond with a face value of $5000 and a coupon rate of 7.5%. The bond will mature in 15 years. How much interest will he receive semiannually?
Answer: $187.5
Step-by-step explanation:
The interest = 5000× ( 7.5/100 )÷2
=5000 × 0.075 ÷2
= 5000 ×0.0375
= 187.5 has interest semiannually
Hence, he gets 187.5
Two companies charge differently for canoe rentals, as shown below. What is the rate of change for each function? What is the cost to rent a canoe for 4 hours for each company? Company A: c = 8h + 10, where c = totals cost (in dollars) and h = number of hours Company B: $15 per hour
The rate of change for company A is $8 an hour and it would cost $42 to rent a canoe for four hours from company A.
The rate of change for company B is $15 an hour and it would cost $60 to rent a canoe for four hours from company B.
Step-by-step explanation:
Step 1:
For company A, [tex]c = 8h + 10,[/tex] where c is the cost after h hours.
When [tex]h=1,[/tex] [tex]c = 8(1) + 10 = 18.[/tex]
When [tex]h=2,[/tex] [tex]c = 8(2) + 10 = 26.[/tex]
The rate of change for company A [tex]= 26 - 18 = 8.[/tex]
The rate of change for company A is $8 an hour.
When [tex]h=4,[/tex] [tex]c = 8(4) + 10 = 42.[/tex]
So it would cost $42 to rent a canoe for four hours from company A.
Step 2:
For company A, the cost is $15 per hour so [tex]c = 15h,[/tex] where c is the cost after h hours.
When [tex]h=1,[/tex] [tex]c =1(15) =15.[/tex]
When [tex]h=2,[/tex] [tex]c = 2(15)= 30.[/tex]
The rate of change for company B [tex]= 30 - 15 = 15.[/tex]
The rate of change for company B is $15 an hour.
When [tex]h=4,[/tex] [tex]c = 4(15) = 60.[/tex]
So it would cost $60 to rent a canoe for four hours from company B.
When Brandon was told that he correctly answered 80 percent of the items on a math achievement test, he asked how his performance compared with that of the average test-taker. Brandon's concern was directly related to the issue of Group of answer choices content validity. predictive validity. standardization. factor analysis. reliability.
Answer:
The answer is standardization.
Step-by-step explanation:
Achievement tests are used in describing students’ learning abilities and academic accomplishments.
Since standardized achievement tests can give a better indication of students’ weaknesses, the test results will corroborate what can be seen on a daily basis, and the results can give insight into how a student's achievement compares to the average national student.
So, Brandon's concern was directly related to the issue of standardization because he wanted to make sure the test fulfilled the requirements of a standardized test ( i.e the questions, conditions for administering, scoring procedures, and interpretations) were consistent, and if so his score would not deviate greatly from the average test taker, and he wouldn't be an exception in obtaining such a high score.
Brynn ate 4/10 funnel cakes and 37/100 of the food was cotton candy. The rest of the food was popcorn. What fraction of the food brynn are was funnel cakes or cotton candy?
Answer:
?
Step-by-step explanation:
Convert 4/10 into 40/100(so you can have same denominator as other fraction) and then add 40/100 and 37/100 and you will get the answer!
In which survey was a parameter reported? Select two answers.
A. “Of the 100 teenagers surveyed from Jill’s middle school, 2 out of 3 of them own a bicycle.
B. “Of the 1000 seventh grade boys surveyed across the U.S., 5 out of 6 of them want to go to college.
C. “Of the 120 sixth graders at Jill’s middle school, 3 out of 5 of them bring their lunch.
D. “Of the 50 students surveyed across the city who take the bus, 1 out of 2 of them said they would prefer another mode of transportation.
E. “Of the 92 teachers at Jill’s middle school, 3 out of 4 do not like working late.
Answer:
C and E
Step-by-step explanation:
A parameter is a percentage of a population.
A, B, and D are percentages from surveys (samples).
C and E are percentages from populations.
The number is less than one has two decimal place The digit is the hundredths place has a value of 5/100 The digit in the tenths place has a value of 2/10
Answer:
Therefore the required number is 0.25.
Step-by-step explanation:
Given that, the number is less than 1 has two decimal place.
The digit is the hundredths place has value of [tex]\frac{5}{100}[/tex]
=0.05
If a number divides with 100, then the point of the number shifts precede of two digits.
The digit in tenth place has a value of [tex]\frac2 {10}[/tex]
=0.2
The number is = tenth place value + hundredths place value
= 0.2+0.05
=0.25
Therefore the required number is 0.25.
Specifically looking at a number less than one with two decimal places: 2/10 in the tenths place and 5/100 in the hundredths place, resulting in the number 0.25.
The tenths place value, 2/10, means that there is a 2 in the tenths place. The hundredths place value, 5/100, means there is a 5 in the hundredths place. Therefore, combining these values, we get the number 0.25.
This demonstrates how decimal place values work, with each position to the right of the decimal point representing a fraction of ten (tenths, hundredths, etc.). The given values fit precisely into the decimal system, illustrating the concept of decimal place values clearly.
Triangle ABC is reflected across the line y = x. What are the coordinates of the vertex B' of the resulting triangle A'B'C'?
A. (2, -5)
B. (-2, 5)
C. (5, -2)
D. (-5, -2)
A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. The term paper counts as 20% of the course grade. The final examination counts as 20% of the course grade. Alan has test scores of 79, 95, 89, and 81. Alan received an 81 on his term paper. His final examination score was 85. Use the weighted mean formula to find Alan's average for the course.
Answer:
The Alan's average for course is 72.65.
Step-by-step explanation:
Given that,
Each test counts as 15% of the course grade. 20% of course grade is counted term test paper. Alan has test scores of 79, 95, 89, and 81. Alan got 81 score on his term paper . Alan's final examination score = 85.
[tex]\sum w=1[/tex]
Let n number x₁,x₂,.......,[tex]x_n[/tex] with respect to assigned weight[tex]w_1[/tex],[tex]w_2[/tex],.......,[tex]w_n[/tex] is
[tex]{\textrm{weighted mean}}= \frac{\sum w.x}{\sum w}[/tex]
Where [tex]\sum w.x[/tex] is the sum of the products the number with the relevant weight.
weighted mean [tex]=\frac{79\times 15\%+95 \times 15\%+89\times 15\%+81\times 20\%+85\times20\%}{1}[/tex]
=72.65
The Alan's average for course is 72.65.
Consider the statement that the product of two of the numbers 651000 − 82001 + 3177, 791212 − 92399 + 22001, and 244493 − 58192 + 71777 is nonnegative (for the purpose of this agreement, we will think of 0 as carrying a positive sign).Identify the correct proof of the given statement.(You must provide an answer before moving to the next part.)NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the statement that the product of two of the numbers 651000 - 82001 - 3177791212-92399 22001, and 244493_58192+71777 is nonnegative (for the purpose of this agreement, we will think of O as carrying a positive sign). Identify the correct proof of the given statement. (You must provide an answer before moving to the next part.) A) Of these three numbers, at least two numbers must be negative, since there are only two signs. The product of these two numbers is nonnegative. B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative. C) Of these three numbers, all three must have the same sign. Thus, the product of any two numbers is nonnegative. D) Of these three numbers, at least two must have the same sign, since there are only two signs. The product of two with the same sign is nonnegative. E) Of these three numbers, at least two must have the same sign. The product of one of these numbers and the third number is nonnegative.
Answer:
a c
Step-by-step explanation:
Final answer:
All three calculated numbers are positive, and therefore, the product of any two of them will also be positive. Option B is correct, which states that at least two numbers must be positive, making the resulting product nonnegative.
Explanation:
The statement that the product of two of the numbers 651000 - 82001 + 3177, 791212 - 92399 + 22001, and 244493 - 58192 + 71777 is nonnegative relies on the principles of arithmetic involving the addition and multiplication of numbers with different signs. Calculating the given numbers:
651000 - 82001 + 3177 = 573176 (positive)
791212 - 92399 + 22001 = 710814 (positive)
244493 - 58192 + 71777 = 255078 (positive)
All three numbers are positive, so the product of any two would also be positive, according to the multiplication rules that state the product of two positive numbers is always positive.
Therefore, the correct answer to the statement is:
B) Of these three numbers, at least two must be positive. The product of these two numbers is nonnegative.
In the following set, the mode is the most effective measure of central tendency if you want to emphasize how small the values are. 32, 21, 68, 21 True False
Answer:
FALSE
Step-by-step explanation:
The mode is a measure of the number with the highest frequency in a group of data. In the set of values (32, 21, 68, 21), the number that appears most is 21 and this is the mode.
If a set of data has two modes, it is bi-modal. If it has several modes, it is multi-modal
Consider the set of data below
2,2,3,3,5,7,8
The numbers 2 and 3 appears with the same frequency, therefore this set of data is bi-modal.
Math-The park department wants to have new tree planted. They agreed that 1/10 of the tree will be oak,3/10 will be pine, and 2/10 will be willow. They are undecided about the rest. What fraction of trees will be oak, or pine?
Someone has 240$ for a road trip this is 2/5of the coast of the trip how much dose the trip coat
Answer:
$600
Step-by-step explanation:
Divide 240 by 2/5
On a river you must release any fish that you catch ifvit measures less than 12 inches. Define a variable and then write an algebraic inequality for each senario. can you keep a fish that is 11.99 inches?
Let f = fish
If f < 12, let the fish go.
We cannot catch a fish measuring 11.99 inches.
If f = fish, then f < 11.99. It must be released.
What is a key purpose of using simulation when comparing two populations?
A) Calculating theoretical probability
B) Observing how probability works with real items
C) Checking that the correct test statistics were used
D) Finding a precise answer to a question
Answer:
B) Observing how probability works with real items
Step-by-step explanation:
Just took the quiz
A defunct website listed the "average" annual income for Florida as $35,031. What is the role of the term average in statistics? Should another term be used in place of average?
Answer:
For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]
And the average is calculated with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
Where n represent the sample size
N represent the population size, and X the observations for this case the annual income.
This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]
After calculate the average they got:
[tex] \bar X= 35031[/tex]
And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data
Step-by-step explanation:
For this case the average is an statistic unbiased for the population parameter [tex] \mu[/tex]
And the average is calculated with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
Where n represent the sample size
N represent the population size, and X the observations for this case the annual income.
This statistic is an unbiased estimator of the population mean since [tex] E(\bar X) = \mu [/tex]
After calculate the average they got:
[tex] \bar X= 35031[/tex]
And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data
If a member variable is declared , all objects of that class share that variable. A(n) function is not a member of a class, but has access to the private members of the class. A(n) tells the compiler that a specific class will be declared later in the program. When the operator is overloaded, its function must have a dummy parameter. The class Stuff has both a copy constructor and an overloaded = operator. Assume that blob and clump are both instances of the Stuff class. For each of the statements, indicate whether the copy constructor or the overloaded = operator will be called: Staff blob = clump ; clump = blob ; blob.operator =(clump) ; showValues(blob) ; // blob is passed by value Consider the following class declaration: class Thing { private: int x ; int y ; static int z ; public: Thing() { x = y = z ; } static void putThing(int a) { z = a ; } } ; int Thing:: z = 0 ; Assume a program containing the class declaration defines three Thing objects with the following statement: Thing one, two, three ; How many separate instances of the x member exist? How many separate instances of the y member exist ? How many separate instances of the z member exist? What value will be stored in the x and y members of each object? Write a statement that will call the putThing member function before the Thing objects are defined. Explain why the parameter of a copy constructor must be a reference.
Answer:
a shs s s s ss bsbsbsbs s s s s s s s s s s s s s
1) Bronson is an action and horror movie junkie. He started a movie review vlog and needs to keep
up with his movie viewing at a high pace. It has been a total of 50 weeks since he has stated his
vlog and he has watched 1250 movies. He has watched twice as many horror movies as action
movies. Write two equations that can model this situation.
two equations which can model this situation is : [tex]y=2x[/tex] and [tex]x+y=1250[/tex]
Step-by-step explanation:
Here we have , Bronson is an action and horror movie junkie. He started a movie review vlog and needs to keep up with his movie viewing at a high pace. It has been a total of 50 weeks since he has stated his vlog and he has watched 1250 movies. He has watched twice as many horror movies a action movies. We need to Write two equations that can model this situation. Let's find out:
Let Bronson watched x action movies and y horror movies , than according to question horror movies he watched is twice that of action movies i.e.
⇒ [tex]y=2x[/tex] ........(1)
Now , he has watched 1250 movies i.e.
⇒ [tex]x+y=1250[/tex] .......(2)
⇒ [tex]x+2x=1250[/tex]
⇒ [tex]3x=1250[/tex]
Therefore , two equations which can model this situation is : [tex]y=2x[/tex] and [tex]x+y=1250[/tex] .
HELP ASAP!! Write the inverse variation function given that y varies inversely with x, and y = 2 when x = 8.
Answer: y= 16/x
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 8.8 cm and a base with a diameter of 18.6 cm. Round your answer to the nearest tenth of a cubic centimeter.
Final answer:
The volume of the cone is approximately 860.6 cm³.
Explanation:
To find the volume of a right circular cone, we can use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. In this case, the diameter of the base is 18.6 cm, so the radius is half of that, which is 9.3 cm. The height of the cone is 8.8 cm. Plugging these values into the formula, we get V = (1/3)π(9.3 cm)²(8.8 cm). Calculating this, we find that the volume of the cone is approximately 860.6 cm³.
HELP PLEASEEEEEEE
can you help me find the period of the function from this table?
Answer: It’s either 6, or 2, though the answer is most likely 6, because of the way the table is created.
Step-by-step explanation:
Period is 12.
We can see the pattern 50, 33, 50, 67 that keeps repeating every m=12 points.
A gas station stores its gasoline in a tank underground. The tank is a cylinder lying horizontally on its side. The radius is 5 ft, the length is 15 ft, and the top of the tank is 10 feet under the ground. Assume the tank is full and all of the gasoline will be pumped to the surface of the ground. The density of gasoline is 42 lb/ ft3. Consider a slice of gasoline that is delta y ft thick and located y ft above the center of the cylinder. Use delta or the CalcPad for delta . Leave pi in your answer. Volume of slice : ft3 Displacement of slice : ft Find the endpoints of the integral needed to find the exact work required to pump all the gasoline to the surface of the ground. Lower endpoint = Upper endpoint =
Answer:
The exact work required to pump all the gasoline to the surface of the ground is π × 5.094 × 10⁶ j
Step-by-step explanation:
Here, we note that volume of a slice is given by
Length × Width × Height
Length of slice = Length of cylinder = 15 ft
Since the slice height is Δy ft thick and located y ft above the center of the cylinder, then
Width of slice = 2 × √(r² - y²)
Where:
r = Radius of the cylinder =5 ft
∴ Width of slice = 2 × √(25 - y²)
∴Volume of slice = 15 ×2 × √(25 - y²)×Δy
Mass of slice then = 42 × 15 ×2 × √(25 - y²)×Δy = 1260 × √(25 - y²)×Δy
The force required to lift the slice is the weight of the slice, which is given by
32.2 × 1260 × √(25 - y²)×Δy = 40572 × √(25 - y²)×Δy N (Newtons)
The work done by the force is the product of the force and the distsnce through which the force acts.
Work done = 40752×(10-y) × √(25 - y²)×Δy
Therefore total work done is given by
[tex]W = \int\limits^5_{-5} {40752\times (10-y) \times \sqrt{ (25 - y^{2} )} } \, dy[/tex]
= 5094000·π J = π × 5.094 × 10⁶ j
The exact work required to pump all the gasoline to the surface of the ground = π × 5.094 × 10⁶ j
The calculation requires determining the volume and displacement of each slice of gasoline in the tank and then integrating over these from the bottom to the top of the tank (from -5 to 5 feet).
Explanation:
To calculate the exact work required to pump all the gasoline to the surface, we need to first determine the displacement of each slice of gasoline and then integrate over the total volume. The displacement of a slice at height y is the distance it needs to be moved to the surface, which is (10 - y) feet. The volume of a cylindrical slice of thickness delta y is given by the area of the cylinder's cross section times the slice's thickness, i.e., volume = pi * r^2 * delta y. Here, r = 5ft and delta y is the thickness of the slice. Therefore, the volume of the slice is 25*pi*delta y ft3. The endpoints of the integral are defined by the top and bottom of the tank relative to the center, which in this case are -5 and 5 feet. Therefore, the lower endpoint is -5 and the upper endpoint is 5.
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Which of the following is a series ? Check all that apply . 1/2 + 1/4 + 1/6 + 1/16 + 3.14159 B. 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 20 2 3k D. 25 - 5 - 10 - 15 - - 125
Answer:
A Series is always a periodic sum of terms, so only A and D will apply to that definition
(where A= 1/2 + 1/4 + 1/6 + 1/16 + 3.14159 and B=25 - 5 - 10 - 15 - - 125
A rectangular parcel of land is 100 ft wide. The length of a diagonal between opposite corners is 20 ft more than the length of the parcel. What is the length of the parcel
Final answer:
Using the Pythagorean theorem, the length of the parcel of land was calculated to be 240 feet, given that its width is 100 feet and the diagonal is 20 feet longer than the length.
Explanation:
To solve for the length of the parcel of land, given that it has a width of 100 feet and a diagonal that is 20 feet longer than the length, we can use the Pythagorean theorem. The Pythagorean theorem 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. In this situation, let's denote the length of the parcel as 'L' and the diagonal as 'D'. We then have the relationship:
D = L + 20 feet
We can establish the equation L2 + 1002 = (L + 20)2.
Expanding the right side of the equation gives us L2 + 10,000 = L2 + 40L + 400. Simplifying the equation by subtracting L2 from both sides, we get 10,000 = 40L + 400. Subtracting 400 from both sides gives us 9,600 = 40L, which simplifies to L = 240 feet when we divide both sides by 40.
Therefore, the length of the parcel is 240 feet.
At what points on the graph of f(x)=2x^3-6x^2-27x is the slope of the tangent line -9?
Answer:
(-1, 19) and (3, -81)
Step-by-step explanation:
f(x) = 2x³ − 6x² − 27x
f'(x) = 6x² − 12x − 27
-9 = 6x² − 12x − 27
0 = 6x² − 12x − 18
0 = x² − 2x − 3
0 = (x + 1) (x − 3)
x = -1 or 3
f(-1) = 19
f(3) = -81
The points are (-1, 19) and (3, -81).