Answer:
16 ounces/minute
Step-by-step explanation:
1 pound = 16 ounce
60 pound = 960 ounce
1 hour = 60 minute
960/60 = 16
Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis.
y
=
11
−
x
,
y
=
0
,
x
=
3
,
x
=
9
Using the shell method, the volume of the solid generated when R is revolved about the y-axis is V= 324π cubic units.
The shell method refers to a method of finding volumes of the solid by decomposing a solid of revolution into cylindrical shells. It is one of the methods to find the volume of the solid. This solid is generated when region R is rotated about an axis or the y-axis. In case it is y-axis then the following formula is used:
V= ∫_a^b▒〖2πx [f(x)-g(x)]dx〗
Where y = f(x), y = g(x), and the interval is considered as [a,b].
The given curves are: y = 11 − x, y = 0, x = 3, x = 9
V= ∫_3^9▒〖2πx [11-x-0]dx〗
V= 2π∫_3^9▒〖(11x-x^2)dx〗
V= 2π[11/2 x^2- 1/3 x^3]
V= 2π[11/2 9^2- 1/3 9^3- 11/2 3^2+ 1/3 3^3]
V= 2π[891/2- 729/3- 99/2+ 27/3]
V= 2π[729/2- 702/3]
V= 2π[396-234]
V= 2π[162]
V= 324π cubic units
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Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
answer would be A because it u factor it out you will get your initial equation
Find a and b using the factor theorem.
\(f(x)=x^3+ax^2+bx-12\) has factor \((x-1), (x+1)\)
The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.
To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.
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Imagine math Item 994395
Start with the equation 0.2=0 to explain why -4-2 must equal -8.
Drag descriptions and equations to the table to complete the explanation.
In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.
1. Begin with the equation 0.2 = 0.
2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.
This simplifies to 0 = -0.2.
3. Observe that the right side of the equation, -0.2, is a negative number.
4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.
5. Rewrite the equation as 0 = +0.2.
6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.
7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.
8. Simplify the equation to 0 = +0.2.
9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.
10. As a result, the original equation 0.2 = 0 is invalid.
11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.
12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.
To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.
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In a pizza eating contest, a participant can eat 3 slices of pizza in 2 minutes. If he continues to eat at this rate, then how many slices of pizza will he eat in 10 minutes? Double number lines
Answer:
Step-by-step explanation:
15
Answer: The answer is 30
Step-by-step explanation: Just do 2 times 3. 10 times
Select all solutions to M•M•M=729
The solution to the equation given by M * M * M = 729 is 9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Given the equation:
M.M.M = 729
This gives:
M * M * M = 729
M³ = 729
Taking the cube root of both sides:
∛M³ = ∛729
M = 9
The solution to the equation is 9
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Monica had a savings account that paid her an interest rate of 4%. After she had this account for 12 years, she had received $192 in interest. How much money had she put into the account at the beginning of the 12 years?
Answer:
Money she put in her account = $400
Step-by-step explanation:
As, to find the interest the formula is PTR/100 = I
Where P = Principcal
And T = time (in years)
And R = rate
And I = interest
So here p is not present we need to find it
R = 4%
And T = 12 years
And I = $192
= p x 4 x 12 /100 = 192
P x 4 x 12 = 19200
P x 48 = 19200
P = 19200/48
P = 400
So Principcal = $400
Show/explain how to solve the formula forbhfinding the area of a triangle, A =2for h. Describe how you can use possibleunits associated with each of thevariables in this equation to guide yourthinking about solving this literalequation.
we need to solve h of the equation so
We do the oppisite operation for example, the 2 dividing is multipliying to the other side
\(2\times A=b\times h\)and the same way for b
\(\frac{2\times A}{b}=h\)Rae's unpaid credit card balance was $1,603. Her APR is 28.6%. What is her new
balance after she makes one new transaction for $51? Round answer to the
hundredths place. If answer doesn't have a hundredths place then include a zero so
that it does. Use a word not a symbol for the units.
$2010.458 is her new balance after she makes one new transaction for $51.
What does a credit balance mean?
The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.
When you return something you purchased with your credit card, you can receive an additional credit.
Credit balance = $1,603
APR = 28.6%
= 28.6% * $1,603
= 458.458
Credit balance = $1,603 + 458.458
= $2061.458
net balance = $2061.458 - 51
= $2010.458
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A survey of 100 high school students provided this frequency table on how students get to school. What is the probability that a randomly selected student is a junior who takes the bus?
The probability of selecting a junior who takes the bus is P (Junior who takes the bus) = 12/200 = 0.06Hence, the probability that a randomly selected student is a junior who takes the bus is 0.06 or 6/100.
The given frequency table on how students get to school among the high school students is represented in the below table:Transportation Walk Bike BusDriveTotalGrade 9 11 10 14 15 50Grade 10 10 7 13 20 50Grade 11 8 6 12 24 50Grade 12 5 8 8 29 50 Total 34 31 47 88 200Given data from the above frequency table, we are interested in finding the probability of a randomly selected student being a junior who takes the bus.SolutionWe know that the total number of students is 200, and the total number of junior students is 50. Hence the probability of selecting a junior is P (Junior) = 50/200 = 0.25Similarly, the number of students who take the bus is 47 and the number of junior students who take the bus is 12.
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What is the M.A.D. (mean absolute deviation) of the following data set?
8 9 9 7 8 6 9 8
The mean absolute deviation is 0.75
How to determine the mean absolute deviationTo calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set
From the information given, we have that the data set is;
8 9 9 7 8 6 9 8
Let's calculate the mean, we get;
Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8
Mean = 64 / 8
Divide the values
Mean = 8
Let's determine the absolute difference, we get;
Absolute differences=
|8 - 8| = 0
|9 - 8| = 1
|9 - 8| = 1
|7 - 8| = 1
|8 - 8| = 0
|6 - 8| = 2
|9 - 8| = 1
|8 - 8| = 0
Find the mean of the absolute differences:
Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8
Absolute difference = 6 / 8 = 0.75
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Heyyyyy<3 help me please
Answer:
90 x 78
100
= 70.2
Step-by-step explanation:
እኔ በጣም ብልህ ቢሆንም አሁን ግን ድራገንቦል እና naruto
አጓጊ መመልከት አለብዎት
Answer:
70.2
Step-by-step explanation:
Hope it helps and Have a nice day!!
please help and I will mark big brain
Solve for x. Round to the nearest tenth.
Answer:
x = 4.55
Step-by-step explanation:
Tan(75) = 17/x
3.73 = 17/x
x3.73 =17
x = 4.55
Find the missing fraction.
5/2- blank = 1/3
Answer: 13/6 (5/2 - 13/6 = 1/3)
Step-by-step explanation:
(Help please and thank you!) :)
Answer:
the answer is the 3rd one and I am 100% sure
what is the geometric mean of 8 and 18
Answer:
12.
Step-by-step explanation:
The geometric mean of two numbers a and b is sqrt(ab).
Hence, sqrt(8 * 18) = sqrt (144) = 12.
Hope this helped!
The geometric mean of 8 and 18 is 12 which is calculated as the square root of their product, which is 12.
Given two numbers are:
First number = 8
Second number = 18.
To find the geometric mean of two numbers, multiply the numbers together and then take the square root of their product.
Step 1: Find of the two numbers.
Product P: \(8 \times 18 = 144\)
Step 2: Find the square root of the product.
Geometric mean = \(\sqrt{P}\)
Plugging the value of P gives:
Geometric mean = \(\sqrt{144}\)
Take the square root of 144, gives:
Geometric mean = 12.
Therefore, the geometric mean of 8 and 18 is 12.
The geometric mean is often used to find the average growth rate or to compare quantities that vary exponentially.
In summary, the geometric mean of 8 and 18 is calculated as the square root of their product, which is 12.
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how much is the scale factor if you dilate it until its area is 36?
Answer:
1/32xp
Step-by-step explanation:
but not sure was there a picture to go with this
The product of two negative integers is a negative integer.
Answer:
False. The product of two negative integers is a positive integer.
What are all of the solutions to the equation 2y2 = 64?
±32
±√ 2
±4√ 2
±8
Answer:
y=16
Step-by-step explanation:
1 Simplify 2y\times 22y×2 to 4y4y.
4y=644y=64
2 Divide both sides by 44.
y=\frac{64}{4}y=
4
64
3 Simplify \frac{64}{4}
4
64
to 1616.
y=16y=16
Done
Question 1(Multiple Choice Worth 2 points) (Proportions MC) The table shows the length and width of proportional rectangles. Length (in inches) 8 12 24 32 Width (in inches) 10 15 30 40 Using the table, find the width of a rectangle that has a length of 72. 80 90 100 105
The width of a rectangle with a length of 72 is 90 inches.
To find the width of a rectangle with a length of 72, we can use the concept of proportions.
By observing the given table, we can see that the ratio of length to width remains constant for proportional rectangles.
Let's calculate the common ratio:
\(\( \text{Ratio} = \frac{\text{Length}}{\text{Width}} = \frac{8}{10} = \frac{12}{15} = \frac{24}{30} = \frac{32}{40} \)\)
Now, we can set up a proportion to find the width for a length of 72:
\(\( \frac{72}{\text{Width}} = \frac{8}{10} \)\)
Cross-multiplying, we have:
\(\( 72 \times 10 = 8 \times \text{Width} \)\)
Simplifying, we get:
\(\( 720 = 8 \times \text{Width} \)\)
Dividing both sides by 8, we find:
\(\( \text{Width} = \frac{720}{8} = 90 \)\)
Therefore, the width of a rectangle with a length of 72 is 90 inches.
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Identify as an increase or decrease. Then find the percent of increase or decrease. If necessary, round to the nearest tenth of a percent. Original: 90 New: 160
Answer:
Since the quantity started at 90 and then changed to 160, there was clearly an increase in its value.
Step-by-step explanation:
What is the approximate volume of this cylinder? 3,140 cm³ 7,850 cm³ 10,000 cm³ 31,400 cm -20 cm 25 cm
Answer: 28055
Step-by-step explanation:
HELP PLZ IT would mean a lot
Answer:
Since this is a proportional relationship,
We know that the number which are proportional are a multiple of each other
the number which we can multiply one of the numbers to get the other number is the constant of proportionality
we could check for proportionality by using the following formula:
p1 / s1 = p2/s2 = p3/s3 = p4/s4 if they were equal, we can say that the relation is proportional
The value of any of the above values, p1/s1 , p2/s2 , p3/s3 , p4/s4 is the constant of proportionality
Therefore, the constant of proportionality = 20 / 5 = 4
What’s the square root of √125
Answer: \(5\sqrt 5\)
Step-by-step explanation:
Sol \(\sqrt 125\) = \(\sqrt{25.5}\)
= \(\sqrt{25}\) x \(\sqrt{5}\)
\(5 \sqrt{5}\)
Which shows the best estimate of the quotient of 4,346 ÷ 82?
between 50 and 60
between 60 and 70
between 500 and 600
between 600 and 700
Answer:
Between 50 and 60
Step-by-step explanation:
4,346/82 is 53 which is between 50 and 60.
Hope this helps!
robert drove at an 72 miles per hour. find this in miles per minute
Answer:
1.2 miles per minute
Explanation:
We know that 1 hour has 60 minutes, so if we want to convert 72 miles per hour into miles per minutes, we need to divide by 60 minutes as:
\(72\text{ miles per hour }\times\frac{1\text{ hour}}{60\text{ minutes}}=1.2\text{ miles per minute}\)Therefore, Robert drove at 1.2 miles per minute.
Subtract 4/15 - 1/6. Simplify the answer.
Answer:
Find the smallest multiple the denominators have in common
30
Expand each fraction so that the denominators are 30
\(\frac{8}{30} + \frac{- 5}{30}\)
Add or subtract the numerators and keep the same denominator
\(\frac{8- 5}{30}\)
Simplify
\(\frac{1}{10}\)
I need this please help me
Answer:
C. Reflection over x- axis, down 6 right 3
Step-by-step explanation:
can somebody help me with this?
Answer:
x=11
Step-by-step explanation:
Since this is a 90º angle, 46º+(4x)º has to equal 90º, and you can make and solve an equation for this:
46+4x=90
4x=44
x=11
Check:
46+4x=90
46+4(11)=90
46+44=90
90=90