Rotating the area bounded by the given curves around the designated line yields the solid's volume as \(V = \frac{9}{22}\pi\)
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Different forms have various volumes.
The amount
of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. The capacity of an object to hold matter is generally thought of as its volume in three dimensions.
The functions provided are,
\(`y = f(x) = \sqrt{x}``y = g(x) = x^5`\)
By rotating the area around the x-axis, the solid's volume is given by (using washer method)
\(V = \pi int_a^b [f^2(x)-g^2(x)]dx\)
evaluate the integral, limit the plugins, and
\(V = \pi int_0^1 [(\sqrt{x})^2-(x^5)^2]dx\\\\V= \pi int_0^1 [x-x^10]dx V = \pi [\frac{x^2}{2}-\frac{x^11}{11}]_0^1 V = \pi [\frac{1^2}{2}-\frac{1^11}{11}]. V = \pi [\frac{1}{2}-\frac{1}{11}] = \frac{9}{22}\pi\)
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Use the terms quality of life, poverty, equality, and inequality to write a statement that describes your living conditions.
Promoting equality and addressing poverty and inequality are crucial for creating a society that values the wellbeing of all inequality and supports their pursuit of a good quality of life.
Description of our living conditions:
The general statement that highlights the importance of quality of life, poverty, equality, and inequality for individuals and societies.
Access to basic needs such as food, shelter, healthcare, education, and opportunities for personal and professional growth are fundamental aspects of a good quality of life. Poverty, on the other hand, restricts access to these resources and can negatively impact physical and mental health, social mobility, and overall wellbeing.
Equality means that everyone has an equal opportunity to achieve their potential and enjoy a good quality of life, regardless of their background or circumstances. In contrast, inequality can lead to disparities in access to resources, opportunities, and power, creating a system that benefits some while disadvantaging others.
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Given triangle MAT is an isosceles triangle and point H is the midpoint if MT. Prove triangle MHA is congruent to triangle THA
Answer:
There is everything in the image
The Side-Angle-Side postulate is satisfied. Then the triangle ΔMHA and ΔTHA are congruent with each other.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.
A triangle MAT is an isosceles triangle and point H is the midpoint of MT.
In triangle ΔMHA and ΔTHA, we have
AH = AH (Common sides)
MH = HT (H is the midpoint of MT)
∠AMH = ∠ATH (Isosceles angles)
The Side-Angle-Side postulate is satisfied. Then the triangle ΔMHA and ΔTHA are congruent with each other.
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In January 2020 oil price was $1283 but in April 2020 the price was $1351. What is the percent increase or decrease
Answer:
5.3%
Step-by-step explanation:
% Increase = Increase / Original Number × 100.
68/1283 * 100
= 5.3%
Which value is a solution to the inequality x < 4?
A. 3
B. 6
C. 5
D. 4.5
Please help me with this :)
Last question I need help with an answer not a link
Answer:
it's toooo complicated
y=mx+b
answer fast, please!
Answer: y = -1x + 3
Step-by-step explanation:
it's going through the y intercept ( 3 )
and down ( negative by 1 )
you can also write the answer as y = -x + 3
either one, its the same.
Ming bought 40 pencils and Catherine bought 24. If each package of pencils sold at the store contain the same number of pencils, what is the largest possible number of pencils in a package?
Answer:
8 pencils.
Step-by-step explanation:
This is a common, GCF question and the question becomes, what number is the GCF of 40 and 24.
40= 2x2x2x5
24=2x2x2x3
Both share 2x2x2, which is 8 so the largest number of pencils in each pack is 8.
Answer:
8
Step-by-step explanation:
To solve this you need to find the largest common factor. The way I did it was by listing out all of the factors of each number, then going through all of them and finding the largest common factor which was 8.
the product of 9 and the sum of a number x and 12
Answer:
X * 12 = 9
Step-by-step explanation:
The required model of the given situation is given as y = 9 (x + 12).
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
the product of 9 and the sum of the number x and 12 is given as
Let the product is equal to y
y = 9 (x + 12)
Thus, the required model of the given situation is given as y = 9 (x + 12).
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can yall help me??? it would be awsome and i will give brainleist
Answer:
Its eather 2a or -18
Step-by-step explanation:
I think its one of those two
Could i have a heart and branliest please.
Can I please get some help I’ve been stuck on this question for a while!
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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I need help please look at the picture and tell me what x equals thank you.
Answer:
X= 72
Step-by-step explanation:
(x-2)+ (x-2)+(x-2) = 180°
or, 3x - 36 = 180°
or, 3x = 180+36
or, 3x = 216
or, x =216/3
or, x = 72°
which of the following demonstrates how the first 21 on the left side of the triangle is calculated using the combination pattern?
Answer:
d
Step-by-step explanation:
In two half-lives, how much of a 400-gram sample of a radioactive element will remain un-decayed?
Answer:
100 grams
Step-by-step explanation:
1/2 * 1/2 = (1/2)² = 1/4
1/4 * 400 = 100
Round nine in 7,297 please do it fast
Answer:
7300 is the write answer
The ratio of dogs to cats at the
pet store is 2:5. If there are 6 more
cats than dogs, how many dogs are
at the pet store?
The ratio of dogs to cats at the
pet store is 2:5. If there are 6 more
cats than dogs, how many dogs are
at the pet store?
Dogs : 2
Cats : 5
Answer :-1
5 - 2 = 3,
-1, 0, 1, 2, 3, 4, 5
1 - 5 will give us a 6
d i need help on this
Step-by-step explanation:
Yes, they are similar because if you convert both of the measurements to fractions, which will be 2/3 and 8/12, you can see that if you simplify 8/12, you will get 2/3. That is why they are similar.
Every evening for the months of September and October, the following eight Gry ndor students, Harry, Ron, Hermione, Ginny, Fred, George, Seamus, and Dean will play a game of Exploding Snap. Let's suppose that each night, exactly three of them play one game. Can there be a game of Exploding Snap every evening throughout September and October without having the same three Gry ndors play a game twice
Answer:
Yes. There can be 56 games (92%) of Exploding Snap every evening throughout September and October that can be played without having the same three Gry ndors play a game twice.
Step-by-step explanation:
This is a combination game without repetition.
The formula for combination without repetition is:
n! /r! (n - r)!
where n = 8 and r = 3
Therefore, n! /r! (n - r)!
= 8! / 3! (8 -3)!
= 40,320 / 6 (120)
= 40,320 / 720
= 56
There are 30 nights in September and 31 nights in October, totaling 61 nights
This implies that 56/61 games can be played in these two months without repeating the same three gamers.
56/61 = 0.918
= 92%
Divide: 7 5/6 ÷ 2/3 need help
To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.
Step 1: Convert the mixed number to an improper fraction:
7 5/6 = (6 * 7 + 5) / 6 = 47/6
Step 2: Multiply the improper fraction by the reciprocal of the fraction:
47/6 ÷ 2/3 = 47/6 * 3/2
Step 3: Simplify the fraction if possible:
47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12
Step 4: Simplify the fraction further, if necessary:
141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4
Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.
If I earn $15/hour and work for 20 hours/week, how much would I earn in one
week?
A.) $35
B.)$300
C.)$150
D.)$30
Answer:
B.) $300
Step-by-step explanation:
just multiply 15 by how many hours you have
On average, Nathaniel drinks
4/5 of a 10-ounce glass of water in
2 2/5
hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Nathaniel drinks 3 glasses of water in one hour.
To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.
In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.
Let's convert the mixed number of hours to an improper fraction:
\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)
\(=\frac{12}{5}\)
Now, we can set up a proportion to find his drinking rate per hour.
We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.
Let's assign "x" as the number of glasses he drinks in one hour.
The proportion is then
\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)
Cross-multiplying gives us
\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)
Simplifying, we get
\(\frac{12}{5} =\frac{4}{5}\times x\)
Dividing both sides by \(\frac{4}{5}\), we find x:
\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)
\(x=\frac{12}{4}\)
\(x = 3.\)
Therefore, Nathaniel drinks 3 glasses of water in one hour.
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elect all equations that represent the number of subscribers, , in terms of months since the beginning of the year (when she had 150 subscribers).
Ken jumps 1 1/5 metres and Steve jumps 1.5 metres. How much more does Steve jump?
Answer: 0.3 meters.
Step-by-step explanation:
First we need to turn one of those into a fraction or decimal to make things easier for us. Lets turn \(1 \frac{1}{5}\) into a decimal.
1 1/5 as a decimal is 1.2.
Now we compare the two
\(1.5 > 1.2\)
Now we need to subtract 1.5 by 1.2 to see how much more he jumps by.
\(1.5 - 1.2 = 0.3\)
Steve jumps more by 0.3 meters.
Answer:
3/10 or .3 meters
Step-by-step explanation:
1 1/5 = 1.2
1.5 - 1.2 = 0.3
3. What percentage of an average household's expenses would you consider needs as compared to
wants?
According to the 50-30-20 budget rule shown in the image, an average household should aim to allocate 50% of their income towards needs, 30% towards wants, and 20% towards savings.
A broad rule of thumb that may be used to gauge the proportion of necessities to desires in the average household budget is included in the image you provided. A typical household should seek to allocate 50% of its income towards requirements, 30% towards desires, and 20% towards savings, according to the 50-30-20 budget guideline seen in the graphic. Of fact, given that everyone's circumstances and objectives are unique, this rule might not apply to everyone.
But for those who want to make a budget or better control their spending, it can be a helpful place to start. In the end, a multitude of variables, such as income, family size, geography, and personal preferences, will determine how much of an average household's costs are spent on necessities vs desires. It's crucial to create a budget that works for your specific situation and allows you to achieve your financial goals.
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Your question is incomplete. The complete question is:
What percentage of an average household's expenses would you consider needs as compared to wants in the image attached?
ill give brainiest if ur correct :)
Answer:
Step-by-step explanation:
rate of car per minutes = 39/60 = 13/20 = 0.65 mil/min
distance travelled in 2 minutes = 13/20*2 = 1.3 miles
Hope you will give brainliest to reach genius
Marco wants to know how much the other students in his mathematics class study. He recorded the data he collected in
the following table.
Time spent studying per week (in hours)
2.0
5.0
1.0
2.5
2.5
3.5
0.0
4.5
2.5
4.0
3.5
3.0
2.0
1.5
4.0
2.0
0.5
3.0
1.0
3.0
3.5
1.5
1. Construct a histogram for the data.
Answer:
Step-by-step explanation:
This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.
7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table
Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)
The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%
a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.
b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).
Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).
Now, let's calculate the real interest rate.
Real interest rate in base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)
= 19.22%.
The real interest rate has moved in the direction to move inflation rate towards its target.
c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.
Inflation gap is 0% in both the scenarios
Inflation rate is 3.14% and in scenario C, inflation rate is 2%.
Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)
= 20.15%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.
The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.
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Find the value of n for which the division of x^2n-1 by x+3 leave remainder of -80.
The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.
To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:
Write the dividend and divisor in polynomial long division format:
_________________________
x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...
Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).
Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).
Subtract the result obtained in step 3 from the original dividend:
x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...
Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.
Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.
-3x^(2n-2) + 0x^(2n-3) + ... = -80
Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.
This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:
2n-2 = 0
2n = 2
n = 1
Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.
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the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes
The standard deviation of the response time is 1.53 minutes.
What is the standard deviation of the response time?To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.
Z-score = z = (x - μ) / σ
For the lower bound of 10 minutes:
z = (10 - 13) / σ
For the upper bound of 16 minutes:
z = (16 - 13) / σ
As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.
Using z-scores, we set up equations:
(10 - 13) / σ = -1.96
(16 - 13) / σ = 1.96
Solving the first equation:
-3 / σ = -1.96
σ = -3 / -1.96
Solving the second equation:
3 / σ = 1.96
σ = 3 / 1.96
Dividing both sides by 1.96:
-3 / 1.96 = σ
1.53 = σ
Full question:
The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.
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15 is what percentage of 30?
Answer:
50%
Step-by-step explanation:
It is half of 30
Hey there!
QUESTION:
“15 is what percentage of 30?”
SIDE NOTE(S):
We will label “x” as the unknown number until we find what the actual number is.
⚠️Remember⚠️
PERCENTAGES RUNS OUT OF 100
SOLVING YOUR QUESTION:
15 = x% of 30
x% of 30 = 15
x% * 30 = 15
x/100 * 30 = 15
3/10 * x = 15
x * 3/10 = 15
MULTIPLY 10/3 to BOTH SIDES
x * 3/10 * 10/3 = 15 * 10/3
CANCEL out: 3/10 * 10/3 because it gives you 1
KEEP: 15 * 10/3 because it helps solve for the x-value (to find out what the actual percentage number is)
NEW EQUATION: x = 10/3 * 15
SIMPLIFY IT!
x = 50
ANSWER:
Therefore, your answer should be about [50%]
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)