Answer:
[tex]-\frac{1}{2\pi}[/tex] cm³/min
Step-by-step explanation:
Let h = height of water and r = radius of its surface
[tex]V = \frac{ 1}{ 3}\pi r^{2}h[/tex]
At all times,
[tex]\frac{r }{h } = \frac{4 }{16 } = \frac{ 1}{4 }[/tex]
So, [tex]r = \frac{h }{4 }[/tex]
[tex]V = \frac{ 1}{ 3}\pi (\frac{h }{ 4})^{2}h[/tex]
[tex]V = \frac{ 1}{ 48}\pi h^{3}[/tex]
[tex]\frac{\text{d}V}{\text{d}h} = \frac{ 1}{ 16}\pi h^{2}[/tex]
We want [tex]\frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}V}{\text{d}t} = \frac{\text{d}V}{\text{d}h} \frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}V}{\text{d}t}[/tex] = -2 cm³/min
[tex]-2 = \frac{ 1}{ 16}\pi h^{2} \frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{2}{\frac{ 1}{ 16}\pi h^{2} }[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi h^{2}}[/tex]
When h = 8 cm
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi\times8^{2}}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{64\pi}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{1}{2\pi}[/tex] cm³/min
The depth of the water is decreasing at a rate of [tex]\frac{1}{2\pi}[/tex] cm³/min
.
It is worked out that 3 ladles full of soup each will feed 160 people.
The customers have complained in the past that the portions are too small.
The cook decides to give 5 ladles full of soup to each person.
How many people can now be fed soup?
Answer:if your still on it tell me
Step-by-step explanation:
By using the ratio and proportion method, it is calculated that 5 ladles of soup can feed 96 people.
Explanation:This problem can be solved using the ratio and proportion concept in Mathematics. Given that 3 ladles of soup feed 160 people, we can set up the ratio 3 ladles : 160 people. If the cook now provides 5 ladles, we need to know how many people this amount can feed. To find this, we cross-multiply in the ratio.
Calculating: (3 ladles x X people) = (160 people x 5 ladles), after simplifying we find that X = 96 people. This calculation suggests that the soup will now feed 96 people if each person is given 5 ladles of soup.
Learn more about Ratio and Proportion here:https://brainly.com/question/26974513
#SPJ3
Problem Page
Suppose we want to choose
2 letters, without replacement, from the
4 letters A, B, C, and D.
If order matters, then there are 12 ways to do this
If order does not matter, then there are 6 ways to do this
===========================================
We have 4 choices for the first slot and 3 choices for the next (we can't reuse a letter) so that's where 4*3 = 12 comes from
If order doesn't matter, then something like AB is the same as BA. So we are doubly counting each possible combo. To fix this, we divide by 2: 12/2 = 6
To be more formal, you can use nPr and nCr to get 12 and 6 respectively (use n = 4 and r = 2)
In combinatorics, you can choose 2 letters from 4 (A, B, C, D) without replacement in 6 ways, according to the 'combination' principle in probability.
Explanation:The subject of this question is combinatorics, a topic in Mathematics, particularly probability. You are asked to choose 2 letters without replacement from a set of 4 different letters {A, B, C, D}. To do this, we can use the formula for combinations, which is denoted as nCr, where n is the total number and r is the number being chosen. In this case, we can see it as 4C2.
To execute this, the formula is ‘n! / [r!(n-r)!]’ where '!' denotes factorial, meaning you multiply all natural number up to that number. Hence, 4C2 = 4! / [2!(4-2)!]. Factorial 4 (4!) = 4 * 3 * 2 *1 = 24. Factorial 2 (2!) is simply 2 * 1 = 2. Thus the calculation becomes 24 / [2*(2!)], simplifying to 24 / 4 which equals 6. So, there are 6 ways to choose 2 letters from 4 without replacement.
Learn more about Combinations here:
https://brainly.com/question/30646507
#SPJ12
Simplify 2(a+5)−3(5a−4)
Answer:
[tex]-13a+22[/tex]
Step-by-step explanation:
we have
[tex]2(a+5)-3(5a-4)[/tex]
step 1
Apply the distributive property both terms
[tex]2a+2(5)-3(5a)+3(4)[/tex]
[tex]2a+10-15a+12[/tex]
step 2
Combine like terms
[tex](2a-15a)+(10+12)[/tex]
[tex](-13a)+(22)[/tex]
[tex]-13a+22[/tex]
Find the recursive definition of the following sequence (Remember to define the first term t, the recursive rule to find tn,and the value n will start at.) 1, 6, 36, 216, 1296…..
The answer is composed of the following two equations
[tex]t_1 = 1[/tex] and [tex]t_n = 6*t_{n-1}[/tex]
both of these two equations combine to help form the full recursive definition
=================================================
Further explanation:
The terms are represented by the letter 't' for short. Since we have more than one term, and because we have only so many letters, this means we stick a number onto the 't' to help label multiple terms. We have t1 as the first term, t2 as the second, etc. The numbers are often show as subscripts like so [tex]t_1, t_2, t_3, \ldots[/tex]
The first term of the list of numbers is 1, so [tex]t_1 = 1[/tex] is what we start with to help set up the recursive definition.
Once we have this starting point, we use it to get to the next term which is 6. This value is 6 times the first value. Therefore, the recursive step is [tex]t_n = 6*t_{n-1}[/tex] basically saying "multiply the (n-1)st term by 6 to get the nth term. Translation: "whatever the current term is, multiply by 6 to get the next term".
Solve using substitution
y=3x-5
2x+5y=-42
Answer:
Solution point is (-1,-9)
Step-by-step explanation:
Put the value of y in the first equation into the second equation.
2x + 5(3x - 5) = - 42 Remove the brackets on the left2x + 15x - 25 = - 42 Combine like terms on the left17x - 25 = - 42 Add 25 to both sides17x - 25 + 25 = - 42 + 25 Do the addition17x = - 17 Divide by 1717x/17 = -17/17 Do the divisionx = - 1=======
Solve for y
y = 3x - 6x = -1y = 3(-1) - 6y = -3 - 6y = - 9Please help please !!!!!!!!!
Answer:
C
Step-by-step explanation:
Arrange them from smallest x value to largest x value, but keep the values the same.
Please help and show work!!
Answer:
- 2 -2.5 and neither. For the left Panel
A or 40.5 for the right panel
Step-by-step explanation:
Slope AB
Givens
(3,5) (2,7)
y2 = 7y1 = 5x2 = 2x1 = 3Formula
m = (y2 - y1)/(x2 - x1)
Solution
m = (7 - 5)/(2 - 3)m = 2/-1 m= -2Slope CD
Givens
(10,5) (6,15)
y2 = 15y1 = 5x2 = 6x1 = 10Formula
m = (y2 - y1)/(x2 - x1)
Solution
m = (15 - 5)/(6 - 10)m = 10/-4 m= - 2.5What are they?
They are not parallel. m1 must equal m2 exactly. - 2 does not equal - 2.5They are not perpendicular m1 * m2 must = -1 -2 * -2.5= 5 They so not = -1 when multiplied together.Answer: Neither.
Right Panel
The best way to start this is to plot the triangle. I use Desmos for this. See diagram below
The base is between (-6,8) and (3,8)
The 8s are the same for both points. The distance between -6 and 3 is abs(-6) + abs(3) = 9
That is the base of the triangle.
The height is between (-6,17) and (-6,8)
17 - 8 = 9
Notice I did not have to use the absolute values. Why not?
Area = 1/2 * b * hbase = 9height = 9Area = 1/2 * 9 * 9Area = 40.5 Answerd (e-f) =g how to solve f
[tex]d(e-f)=g\\e-f=\frac{g}{d} \\e-\frac{g}{d}=f[/tex]
Steps:
Divide by D
Add F
Subtract g/d
Answer:
f = -g/d +e
Step-by-step explanation:
d (e-f) =g
Divide each side by d
d/d (e-f) =g /d
(e-f) =g /d
Subtract e from each side
e-e-f = g/d -e
-f = g/d -e
Multiply by -1
*-1 (-f) = -1(g/d -e)
f = -g/d +e
Below is the graph of f(x)=2In(x). How would you describe the graph of g(x)=4In(x)?
The statement which best describes the graph of g(x) is:
Option: A
A. g(x) stretches f(x) vertically by a factor of 2.
Step-by-step explanation:We are given a original function f(x) as:
[tex]f(x)=2\ln x[/tex]
and a transformed function g(x) as:
[tex]g(x)=4\ln x[/tex]
We know that any transformation of the type:
f(x) to a f(x) is a vertical stretch by a factor of a if a>1
and a vertical compression if a<1
Here we have:
[tex]g(x)=2\times (2\ln x)\\\\i.e.\\\\g(x)=2f(x)[/tex]
i.e. g(x) is a vertical stretch of f(x) by a factor of 2.
Paul took 42 mile bicycle trip. he bicycle 1 1/2 hours in the morning and two hours in the afternoon what is his average speed in miles per hour
Answer:
Paul's average speed for his bicycle trip is 12 miles/hour.
Step-by-step explanation:
Since Paul rode a total of 42 miles, we need to add up the total time it took him to complete all 42 miles. Since her rode 1.5 hours in the morning and another 2 hours in the afternoon, he rode a total of 3.5 hours. Speed is calculated by dividing distance by time. Since his total distance is 42 and his total time is 3.5, we divide 42 by 3.5 to get 12. Since our calculations included miles and hours, then our final answer would be 12 miles per hour.
Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay.
f(x) = 3.6 ⋅ 1.04x
Answer:
Exponential growth; percentage rate of growth is 4%.
Step-by-step explanation:
The function,
[tex]f(x)=3.6.(1.04)^x[/tex]
represents an exponential growth function because the growth factor is greater than 1.
The general form of an exponential growth function is,
[tex]y=a(1+r)^t=(a).(ar)^t[/tex], where 'r' is the percentage rate of growth.
If we compare the given equation with the standard form of the equation we can see that, we have,
[tex]f(x)=3.6(1+0.04)^x[/tex]
Therefore, the percentage rate of growth is = [tex]0.04 \times 100=4\%[/tex] .
Transformation that produces an image that is the same shape but different size?
Answer:
Transformation that produces an image that is the same shape but different size is known as Dilation.
Step-by-step explanation:
There are many types of translations.
1. Rotation
2. Reflection
3. Translation
4. Dilation
We know that rotation, reflection and translation are rigid transformation. It means these transformation can not effect the size of the preimage.
Dilation represents the enlargement and compression of the figure according to the scale factor k.
If |k|>1, then it represent enlargement and if |k|<1, then it represent compression.
Therefore the transformation that produces an image that is the same shape but different size is known as Dilation.
What happened to Japanese-Americans during this time in WWII?
Answer:
During WWII, 120,000 Japanese-Americans were forced into camps, a government action that still haunts victims and their descendants. ... The roundups began quietly within 48 hours after the Japanese attacked Pearl Harbor, on December 7, 1941. The announced purpose was to protect the West Coast.
hope this helps.
Step-by-step explanation:
Patrick saved $500. He received 25% of the money for his birthday, saved 30% of the remainder for his allowance, and earned the rest of it by mowing laws. How much of his savings did he earn by mowing laws?
Answer:
Patrick earned $262.50 by mowing lawns
Step-by-step explanation:
500*0.75=375
375*.7=262.5
Answer:
$262.50
Step-by-step explanation:
It is a poorly worded question.
25 Percent of the 500 was from his birthday money.
500 * .25 = 125
That leaves 500-125 = 375
He saved 30 % of the 375 from his allowance
375 * .3 =112.50
375-112.50 =262.50
The rest is from mowing lawns.
Show how 7000÷1000 is the same as 7000÷10÷10÷10
Answer:
it is because 10 times 100 is 1000 so it would be the same thing
Step-by-step explanation:
Please help need answer please
Answer:
There is one solution
Step-by-step explanation:
You can tell by looking at it that 2x and 3x are different. Both are obtained once the brackets have been removed. So you will get just one answer.
2(x -1) = 3(x - 4) Remove the brackets.
2x - 2 = 3x - 12 Subtract 2x from both sides.
2x - 2x - 2 = 3x - 2x - 12 Combine
-2 = x -12 Add 12 to both sides.
-2 + 12 = x -12 +12 Combine
10 = x
Can anyone walk me through this?
Answer:
n = - 6
Step-by-step explanation:
divide both sides by 2
n + 5 = - 1 ( subtract 5 from both sides )
n = - 6
OR
distribute the parenthesis by the 2 outside
2n + 10 = - 2 ( subtract 10 from both sides )
2n = - 12 ( divide both sides by 2 )
n = - 6
write a real world problem that involves determining the distance between two points on a coordinate plane that have the same x coordinate
Answer: sir or ms your anwser would be C 98. hope this helps ;)
Step-by-step explanation:
A used-droid dealership buys a droid for $2900 and then sells it for $3900. What is the percent increase?
Answer:
The percent increase is 34.48276%
Step-by-step explanation:
we are given
original price =$2900
new price =$3900
now, we can find change in price
change in price = (new price)-(original price)
change in price =3900-2900
change in price =1000
percent increase = (change in price)/(original price) *100
percent increase is
[tex]=\frac{1000}{2900}\times 100[/tex]
[tex]=34.48276[/tex]
which is the slope of the line shown? )
Answer:
slope = [tex]\frac{9}{7}[/tex]
Step-by-step explanation:
to calculate the slope m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 6, - 3) and (x₂, y₂ ) = (1,6) ← 2 points on the line
m = [tex]\frac{6+3}{1+6}[/tex] = [tex]\frac{9}{7}[/tex]
Divide. Round to the nearest tenth if necessary.
65.2 ÷ 26
Please show procedure.
Final answer:
To divide 65.2 by 26, you perform the division to find that 26 goes into 65.2 exactly 2.5 times. Therefore, the answer, when rounded to the nearest tenth, is 2.5.
Explanation:
To divide 65.2 by 26, start with the division process. Place a decimal point directly above the decimal point in the dividend within the answer area. Since 26 does not go into 6, but goes into 65 twice, write 2 above the 5 in the dividend. Multiply 2 by 26 to get 52, and subtract this from 65, which leaves a remainder of 13. Bring down the 2 from the dividend to get 132.
Now, divide 26 into 132, which goes exactly 5 times. Multiplying 5 by 26 gives 130, subtract this from 132 to get a remainder of 2. Because we are left with no more numbers to bring down and our remainder is less than 26, we stop. The answer to 65.2 divided by 26 when rounded to the nearest tenth is 2.5.
Write the equation 2x-3y=6 in slope intercept form
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation in standard form.
[tex]2x-3y=6[/tex] subtract 2x from both sides
[tex]-3y=-2x+6[/tex] divide both sides by (-3)
[tex]y=\dfrac{2}{3}x-2[/tex]
if the correlation coefficient is 0.96, how confident can you be that your predicted value for the cost of a call at 70 minutes is close to the exact value for the cost of a call at 70 minutes?
Pick one of the options below and explain your answer?
Very confident
Somewhat confident
Not confident
Answer:
Very confident
Step-by-step explanation:
The closer the correlation coefficient is to 1, the stronger the correlation. Anything above .4 is relatively strong. So I would be very confident.
Kate uses 2 packets of milk powder per day how many days will 1/3 of a packet of milk powder last.
To find out how many days 1/3 of a packet of milk powder will last, divide 1/3 by 2 to get 1/6 of a day.
Explanation:To find out how many days 1/3 of a packet of milk powder will last, we can use the information given. Kate uses 2 packets of milk powder per day. This means in one day, she uses 2 packets. So, in order to calculate how many days 1/3 of a packet will last, we need to divide 1/3 by 2. This gives us 1/6.
Therefore, 1/3 of a packet will last 1/6 of a day.
Learn more about Milk powder consumption here:https://brainly.com/question/35713710
#SPJ3
1/3 of a packet of milk powder will last 1/6 of a day, or 4 hours, for Kate who uses 2 packets of milk powder per day.
If Kate uses 2 packets of milk powder per day, to determine how many days 1/3 of a packet of milk powder will last, you can perform a simple division. Since she uses 2 packets per day, you would divide the amount she has, 1/3 of a packet, by her daily usage, which is 2 packets. Therefore:
1/3 packets / (2 packets/day) = (1/3) / 2 days = 1/6 days
Thus, 1/3 of a packet of milk powder would last for 1/6 of a day. To determine the number of hours this represents, you can multiply 1/6 of a day by the number of hours in a day:
(1/6 day) times (24 hours/day) = 4 hours
Therefore, 1/3 of a packet of milk powder will last for 4 hours based on her current usage.
Angeline bought s yards of satin fabric priced at $8.09 per yard, and c yards of cotton fabric priced at $3.79 per yard. What expression could you use to determine the total cost of the fabric? If she bought 5 yards of satin fabric and 8 yards of cotton fabric, how much did Angeline spend in all?
Answer: 11.88
Step-by-step explanation: First You Add 8.09 then you add 3.79 Therefore your answer is 11.88
Hope This Helps You Ace Your Test
Answer:
$70.77
Step-by-step explanation:
Let represents the total cost. We know for our problem that each yard of satin fabric costs $8.09, so yards will cost . similarly, each yard of cotton fabric costs $3.79, so yards will cost . We can also infer that the total cost, , will be the sum of the yards of satin fabric and the yards of cotton fabric, so:
Now, to determine the amount that Angeline would spend in all if she bought 5 yards of satin fabric and 8 yards of cotton fabric, we just need to replace and in our expression:
We can conclude that if Angeline would spend in all if she bought 5 yards of satin fabric and 8 yards of cotton fabric, she would spend $70.77
Lucia tried to solve the system below. Lucia’s Work. What error did Lucia make? When Lucia solved for the value of x, she subtracted 2y from both sides. When Lucia solved for the value of y, she treated –2y as 2y. When Lucia solved for the value of x, she added 18 to both sides. When Lucia solved for the value of x, she treated –2(–9) as 18 instead of –18.
Final answer:
The question hints at possible arithmetic or sign operation errors Lucia made while solving a system of equations. Pinpointing her exact mistake involves understanding common errors like incorrect handling of negative numbers or arithmetic operations.
Explanation:
The question involves identifying the mistake Lucia made when solving a system of equations. When solving for the value of x, there are various potential errors one could make, such as incorrect addition, subtraction, or misinterpretation of the operation sign. For instance, treating − 2( − 9) as 18 instead of − 18 is a common mistake due to misunderstanding how to handle double negatives in algebra. Similarly, when solving for the value of y, mistaking − 2y for 2y shifts the equation's balance, leading to incorrect solutions.
Lucia's error could stem from a few different places described in the question, but without the specific steps Lucia took, it's challenging to pinpoint the exact mistake. However, common errors to watch out for when solving for x and y in systems of equations include incorrect operations with negative numbers, improper handling of variables, or erroneous arithmetic operations.
Correctly solving a system of equations requires careful attention to each algebraic step, ensuring that operations on both sides of an equation are correctly applied and that signs are properly managed. Seeking to correct mistakes like treating negative signs improperly or misapplying arithmetic operations is essential for accurate solutions.
Lee needed to make Drapes the length from the floor to the top of the window the wall beneath the window had the height of 2 2/3 feet and the height of just the window measured 2 3/4 feet how long do the Drapes have to be
Answer: 5 feet 5 inches
Step-by-step explanation:
2 2/3 + 2 3/4 is equal to 5 5/12 so the drapes will be 5 5/12 feet long (or 5 feet 5 inches)
Answer:
The length of the drapes have to be [tex]5\frac{5}{12}\ ft[/tex]
Step-by-step explanation:
Given : Lee needed to make Drapes the length from the floor to the top of the window the wall beneath the window had the height of [tex]2\frac{2}{3}[/tex] feet and the height of just the window measured [tex]2\frac{3}{4}[/tex] feet.
To find : How long do the Drapes have to be?
Solution :
The height of the wall beneath the window is [tex]2\frac{2}{3}=\frac{8}{3}\ ft[/tex]
The height of the window is [tex]2\frac{3}{4}=\frac{11}{4}\ ft[/tex]
The total height from the floor to the top of the window is
[tex]H=\frac{8}{3}+\frac{11}{4}[/tex]
[tex]H=\frac{32+33}{12}[/tex]
[tex]H=\frac{65}{12}[/tex]
[tex]H=5\frac{5}{12}\ ft[/tex]
Therefore, The length of the drapes have to be [tex]5\frac{5}{12}\ ft[/tex]
What is the slope of the line that passes through the points? (-4,4), (3,2)?
Hi there!
Step-by-step explanation:
[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{2-4}{3-(-4)}=\frac{-2}{7}[/tex]
Slope is -2/7
Final answer is -2/7.
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thank you! :)
:D
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-4, 4) and (3, 2). Substitute:
[tex]m=\dfrac{2-4}{3-(-4)}=\dfrac{-2}{3+4}=-\dfrac{2}{7}[/tex]
Answer: The slope is - 2/7.HELP!!!!!!!
The total sale price for purchase at one store is $268.97. The total sale price at another store is $240.95. You have an additional 10% off coupon for the second store for purchases over $200.00. How much more would you save by shopping at the second store
Answer:
you save $52.11 by shopping at the second store
Step-by-step explanation:
The total sale price at the second store is $240.95.
additional 10% off coupon for the second store for purchases over $200.00
10% discount on sale price is 240.95 * 10%
[tex]240.95 * \frac{10}{100} = 24.095[/tex]
Total sale price after 10% discount =240.95 - 24.095=$216.86
First store sale price = $268.97
second store sale price = $216.86
Difference = 268.97 - 216.86 = 52.11
you save $52.11 by shopping at the second store
Can someone help me find the value of x?
Answer:
x=71
Step-by-step explanation:
Since this is an isosceles triangle the bottom 2 angles are equal.
The three angles of the triangle are x, x, and 38. They must add to 180 degrees
x+x+38 = 180
Combine like terms
2x+38=180
Subtract 38 from each side
2x+38-38 = 180-38
2x = 142
Divide each side by 2
2x/2 =142/2
x =71