If a baker's five helpers take five minutes to decorate five cookies, then how long do you think 100 helpers to decorate 100 cookies?
Use the Midpoint Rule with \(n=5\) to estimate the volume obtained by rotating about the y-axis the region under the curve \(y=\sqrt{1+x^3}\), \(0\leq x\leq 1\).
To estimate the volume using the Midpoint Rule with \(\displaystyle n=5\), we need to divide the interval \(\displaystyle 0\leq x\leq 1\) into \(\displaystyle n\) subintervals of equal width. Since \(\displaystyle n=5\), each subinterval will have a width of \(\displaystyle \Delta x=\frac{1-0}{5}=\frac{1}{5}\).
Now, let's calculate the volume using the Midpoint Rule. The formula for the volume obtained by rotating about the y-axis is:
\(\displaystyle V\approx 2\pi \sum _{i=1}^{n}y_{i}\Delta x\)
where \(\displaystyle y_{i}\) represents the value of the function \(\displaystyle y=\sqrt{1+x^{3}}\) evaluated at the midpoint of each subinterval.
First, let's find the midpoints of the subintervals. Since the width of each subinterval is \(\displaystyle \Delta x=\frac{1}{5}\), the midpoint of the \(\displaystyle i\)-th subinterval is given by:
\(\displaystyle x_{i}=\frac{\Delta x}{2}+\left( i-\frac{1}{2}\right) \Delta x=\frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\)
Substituting \(\displaystyle x_{i}\) into the function \(\displaystyle y=\sqrt{1+x^{3}}\), we obtain:
\(\displaystyle y_{i}=\sqrt{1+\left( \frac{1}{10}+\left( i-\frac{1}{2}\right) \frac{1}{5}\right) ^{3}}\)
Now, we can calculate the approximate volume using the Midpoint Rule:
\(\displaystyle V\approx 2\pi \sum _{i=1}^{5}y_{i}\Delta x\)
Substituting the values of \(\displaystyle y_{i}\) and \(\displaystyle \Delta x\) into the formula, we can evaluate the sum and compute the estimated volume.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
help me please this is due in 24 mins :(
Answer:
D is your answer............................................................
The ratio of rainbow butterflies to blue butterflies in the Exhibit is 3 to 4. There are 27 blue butterflies in the Exhibit. What is the total number of
butterflies in the Exhibit?
Answer:
There are 47 butterflies
Step-by-step explanation:
We can write a proportion of 3/4 = x/27 to find out how many rainbow butterflies there will be if there is 27 blue butterflies.
1. Cross Multiply 4x=81 = 20.25
Since you cannot have 20.25 butterflies you would round down to 20.
2. Add 20 to 27
Answer = 47
HELP
Match the following equation to the correct situation.
$6.50(c + 18) = $6.50c + $117.00
A. The amount of zoo admission for $6.50 more than c and $117.00.
B. The cost of a birthday package at the theater with a base cost of $117.00 plus $6.50 per child.
C. The amount for movie tickets for c adults when the cost is $6.50 more than $117.00 each.
D. The cost of attending a concert for c groups of people for $6.50 each.
Answer:
B
Step-by-step explanation:
You pay $117 no matter how many kids show up and then you pay an additional fee of 6.50 per kid.
1 kid
y = 6.50(1) + 117
y = 123.50
If 10 kids come
y = 6.50(10) + 117
y = 65 + 117
y = 182
You can use this equation to help you figure out how much it will cost you depending on how many kids you invite.
The circumference of a circular park is approximately 18 feet. What is the approximate area inside the circular park?
Answer:
25.685 square feet.
Step-by-step explanation:
Circumference = 2 * π * radius
From this, we can derive the formula for the radius:
radius = Circumference / (2 * π)
Let's substitute the value of the circumference and calculate the approximate radius:
radius = 18 / (2 * π)
radius ≈ 18 / (2 * 3.14159)
radius ≈ 2.865 feet
Now that we have the approximate radius, we can calculate the area:
Area ≈ π * radius²
Area ≈ 3.14159 * (2.865)²
Area ≈ 3.14159 * 8.193225
Area ≈ 25.685 square feet
Therefore, the approximate area inside the circular park is approximately 25.685 square feet.
Estimate the quotient by rounding the expression to relate to a one-digit fact. Explain your thinking in the space below. 432 ÷ 73 ≈ ___ *
Answer:
5.9..... there are a bunch of numbers after that but you would round it to 6.0
Step-by-step explanation:
Select the correct scientific notation form of this numeral.
2,000,004
2.400 000 × 10 6
2.4 × 10 6
2 × 10 6
2.000 004 × 10 6
Find −3 1/5 ÷ 1 3/4. Write your answer as a mixed number in simplest form.
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Mountain View School Seaside School
0 5, 8
9, 8, 2, 0 1 0, 1, 2, 5, 6, 8
8, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 5, 5, 7, 7, 8
0 3 0, 6
Key: 2 | 1 | 0 means 12 for Mountain View and 10 for Seaside
Part A: Calculate the measures of center. Show all work. (2 points)
Part B: Calculate the measures of variability. Show all work. (1 point)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
Can someone figre this one out for me too plss with work shown and explanation NO LINKS AND NO DOING IT JUST FOR POINTS will give brainliest
Answer:
3 right and 1 up
Step-by-step explanation:
hope this helps!
Answer:
Figure ABCD is translated 3 unit(s) right and 1 unit(s) up.
Step-by-step explanation:
Lets take the point C from the original figure and watch how it translates to it's prime point C' on the other figure. Start at point C and see how many units does it move right until it aligns with the point C', then from there how many points do you need to go up to reach exactly on the point C'. If done correctly, the answer would be: 3 units to the right and 1 unit up
Hope this helps, Good Luck!
Please help i’ll give brainliest!
For which set of data are the median and mode the same number?
A. 4, 5, 7, 7, 8, 10
B. 3, 5, 6, 8, 8, 9
C. 5, 5, 6, 8, 9, 10
D. 4, 5, 7, 8, 9, 9
Answer: A
Step-by-step explanation:
median: 7+7=14
14/2=7✅
mode: 7 shows up the most (twice)
Marsha reads for 3 hours each day. There are 24 hours a day. What decimal represents the part of each day that Tyler spends reading?
Answer:0.125
Step-by-step explanation:
Which expressions are equivalent to 78 • 7? Select all that apply. HINT: There are 3 correct answers.
a
73 • 73
b
7^18/7^9
c
(73)3
d
74 + 75
e
74 • 75
Answer:
None because 78 * 7 = 546
Step-by-step explanation:
Helppppp
what are the answers
Answer:
A. 24 lap/hour.
B. r = 24h
To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem. Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
Answer:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem,
WY ≅ WY by the reflexive property
WZ ≅ XY by the given.
Step-by-step explanation:
The option:
WX ≅ ZY by definition of a parallelogramcan't be used because we want to prove that WXYZ is a parallelogram
The Alternate Interior Angles Theorem states that, when two parallel lines (here XY and WZ) are cut by a transversal (here WY), the resulting alternate interior angles (here ∠ZWY and ∠XYW ) are congruent.
The reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself. Here, WY ≅ WY.
Answer:
[A] ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.[B] WY ≅ WY by the reflexive property.[E] WZ ≅ XY by the given.Explanation:
Which scenario can be modeled by the linear function
y = -15x + 500?
A. The temperature on Jupiter is
15℉ and increases by 500℉ every day.
B. There is a population of 500 giraffes in Western Africa that decreases by 15 giraffes each year.
C. A carpet cleaning service charges $500 plus an additional $15 for every hour.
D. A membership fee for a movie streaming service is free, but each rental costs $15.
Semaj is reading Harry Potter and the Chamber of Secrets. He is currently on page 319. After reading for 40 minutes he is on page 339.
Slope:
Y-intercept:
What does the variable y represent?
What does the variable x represent?
Answer:
Y Represents Pages read. X represents time passed.
Step-by-step explanation:
X and Y have a direct relationship because the more time passed, the more Semaj reads
PLEASE HELP!!!
Lee can type 1 1/3 pages every 15 minutes. How many hours does it take him to type 10 2/3 pages? Complete the rate table to solve the proportion.
pages---> 4/3=32/3
hours---> 1/4 = x
Lee can type 10 2/3 pages in _________ hours.
a. 1 3/4
b. 2
c. 2 1/4
d. 2 1/2
Answer:
First, we know that:
1 1/3 = 4/3
10 2/3 = 32/3
15 minutes = 0.25 hours
Let's imagine that x (hours) is the time it takes Lee to type 32/3 pages.
From the information, we can tell that:
Lee can type:
4/3 pages in 0.25 hours
32/4 pages in x hours
So x should be:
x = (32/4 . 0.25)/4/3 = 2 (hours)
So it takes Lee 2 hours ro type 10 2/3 pages
Step-by-step explanation:
in a survey of 3,100 people who owned a certain type of car, 2,015 said they would buy that type of car again. What percent of people of the people surveyed were satisfied with the car?
The percent of people of the people surveyed were satisfied with the car is the percent of people of the people would buy that type of car again, so we have: 2015 ÷ 3100 × 100% = 65%
ANSWER: 65%
Ok done. Thank to me :3
Answer:
2015 / 3100%= 65%
Step-by-step explanation:
You could never tell how many people there are in this world. So that is why the 3100 should have a percentage which is divided by 2015, equals 65%.
A group of students attend a math club. Half of the students are boys and 4/9 of the boys have brown eyes. What fraction of the group are boys brown eyes?
5/9
Step-by-step explanation:
Blood that enters the left side of the heart has just left the lungs and contains ___ to be delivered to the body’s cells.
Please help I will reward brainliest
Answer:
The answer is oxygen
Step-by-step explanation:
I took the test and got this correct. Here were the options:
capillaries
oxygen
carbon dioxide
waste products
Help me please il give 20 points!
Answer: 1. a. 15 b. 11 c. 2 d. 7 e. 5.5
2. Stem: Leaf:
1 9
2 5, 9
3 3, 3, 8
4 0, 7, 9
5 4, 5
6 1, 5
7 2, 7
8 1
3. a. 13 inches b. I'm pretty sure that it is the second quarter because there is more snow. c. The first quarter because it's section is more spread out among the numbers.
Step-by-step explanation:
f(x) is a cubic function whose roots are 2, 3, and 4. Find f(x) and also find the value of f(2).
Please give an explanation so I know how to do it next time :) Thank you!
Adoes thi involve coding?
Step-by-step explanation:
Keira said that if 6 tickets are sold, there should be 2 tickets left. Is Keira correct?
Jane's height to Max's height is in the ratio 4:7. If Max's height is 210cm, what is Jane's height? *
120
4=?
7=210 then cris cross the answer is 120
Suppose that Jane's height is x cm thus we have :
\( \frac{x}{210} = \frac{4}{7} \\ \)
\(x = \frac{210 \times 4}{7} \\ \)
\(x = 120\)
So Jane is 120 cm .
Jade is painting on top of a table. She needs to buy enough paint to cover the top. a) Is she finding the circumference or the area of the table? b) How many square inches are there on top of this table? (round to the nearest whole number) Please leave an explanation of how you got your answer! Brainliest for the best! (Photo below) Thank You! Peace XOXO
Answer:
a) Area
b) 3,848 in. cubed
Step-by-step explanation:
Since we need to find the area of a circle, we have to insert the value of the radius (diameter ÷ 2) into the equation:
\(A = \pi r^{2}\\A = \pi (70/2)^{2} \\A = 35^{2} \pi \\A = 3,848.451\\A = 3,848\)
Answer this question and write a paragraph that explains how u got it (a paragraph is 5-6 sentences)
Question: (10-2)+(5x293)+(82x90)-2938
Answer:
5915
Step-by-step explanation:
Ok, so in 5th grade, we were taught to use PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction), to get a long question correct. It has to be in that order, so start with parentheses. Here is the whole equation simplified: 8+1465+7380-2938. Now you will go from left to right. So, you have 1473+4442. And last, simplify, 1473+4442=5915. Hopefully this helped and if it did please mark it brainliest.
Answer:
5,915
Step-by-step explanation:
PEMDAS
P= Paranthesis:
(10-2)= 8
(5x293)=1,465
(82X90)=7,380
Then: AS add and subtract
8+1,465+7,380-2938=
5,915
If I animated 4 frames in 6 minutes how many frames will I animate in 12? (Will give branliest for whoever explains it the best!)
Answer:
8 frames
Step-by-step explanation:
6*2=12, so
4*2=8
Sergio divided his strawberries equally among 3 friends. If each friend received 9 strawberries, how many strawberries did Sergio have? Select all the apply.
The correct equation is StartFraction x Over 3 EndFraction = 9.
The correct equation is 3x = 9.
Solve by dividing.
Solve by multiplying.
x = 27.
x = 3.
Answer:
a,d,e on edg
Step-by-step explanation:
hope it helps :)
The correct equation for this given situation is,
⇒ 3x = 9
Where, x is number of students.
And, There are 27 strawberries did Sergio have.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Sergio divided his strawberries equally among 3 friends.
And, each friend received 9 strawberries,
Let Number of strawberries did Sergio have = a
Hence, We get;
⇒ a = 3 × 9
⇒ a = 27
Thus, There are 27 strawberries did Sergio have.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
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