Answer:
[tex]\frac{3}{25\pi}[/tex] meters per minute
Step-by-step explanation:
Given:
[tex]V=\pi r^2h[/tex]
[tex]r=5[/tex]
[tex]\frac{dV}{dt}=3[/tex]
[tex]\frac{dh}{dt}=?[/tex]
Substitute r=5:
[tex]V=\pi r^2h[/tex]
[tex]V=\pi(5)^2h[/tex]
[tex]V=25\pi h[/tex]
Differentiate both sides:
[tex]\frac{d}{dt}V=\frac{d}{dt}(25\pi h)[/tex]
[tex]\frac{dV}{dt}=25\pi\frac{dh}{dt}[/tex]
Solve for dh/dt:
[tex]3=25\pi\frac{dh}{dt}[/tex]
[tex]\frac{3}{25\pi}=\frac{dh}{dt}[/tex]
Therefore, the height of the water is increasing at a rate of [tex]\frac{3}{25\pi}[/tex] meters per minute.
If the purchase price for a house is $218,500, what is the monthly payment if you put 3. 5% down for a 30 year loan with a fixed rate of 6. 5%? a. $1,332. 73 b. $1,378. 19 c. $1,247. 54 d. $646. 40.
Answer: A $1,332.73
Step-by-step explanation:
The monthly payment if you put 3. 5% down is a. $1,332. 73.
Down payment=218,500 - (218.500×3.5%)
Down payment=218.500-7,647.5
Down payment=210,852.50
Time = 12×30=360 months
rate=6.5/1,200 = 0.005416667
Using the loan payment formula
Monthly payment = (Rate + [Rate / (((1 + rate)^months) -1)] × Principal
Let plug in the formula
Monthly payment = (0.005416667 + [0.005416667 / (((1.005416667)^360)-1)] × principal
Monthly payment = (0.005416667 + [0.005416667 / (((1.005416667)^360)-1)] ×principal
Monthly payment = 0.005416667 + [(0.005416667 / 6.9917988084 -1)] ×210,852.50
Monthly payment = 0.005416667 + [(0.005416667 / 5.9917988084)] × 210,852.50
Monthly payment = 0.005416667 + [(0.005416667 / 5.9917988084)] × 210,852.50
Monthly payment = (0.005416667 + 0.0009040135) × 210,852.50
Monthly payment = 0.0063206805× 210,852.50
Monthly payment = 1,332.73
Inconclusion the monthly payment if you put 3. 5% down is a. $1,332. 73.
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A rectangular garden has a walkway around it. The area of the garden is 4(2.5x + 1.5). The combined
area of the garden and the walkway is 5.5(4x + 4). Find the area of the walkway around the garden as
the sum of two terms.
Answer:
Area of Walkway = 12x+16
Step-by-step explanation:
Area of Garden = 4(2.5x + 1.5) [Garden Area]: (10x + 6)
Area of Garden and Walkway = 5.5(4x+4) [Total Area]: (22x + 22)
Area of Walkway = [Total Area] - [Garden Area]
Area of Walkway = [5.5(4x+4)] - [4(2.5x + 1.5)]
Area of Walkway = [22x+22)] - [10x + 6)]
Area of Walkway = 12x+16
Answer:
9x+11 Its hard to explain but if you need a explanation khan academy really helps.
Need some help on this question please
[tex]2(4x+1)<3(2x-3)\\\\\implies 8x +2 < 6x -9\\\\\implies 8x <6x -9 -2\\\\\implies 8x -6x < -11\\\\\implies 2x<-11\\\\\implies x< -\dfrac{11}2\\\\\\\text{Interval,} ~ \left(-\infty, -\dfrac{11}2 \right)[/tex]
Answer:
x<3.5
Step-by-step explanation:
multiply 2 with 4x and 1 to get 8x + 2 < 3(2x-3). Then multiply 3 by 2x and -3 to get 8x + 2 < 6x- 9. Then subtract -6x on both sides to get 2x + 2< -9. Next subtract 2 from -9 so x is by itself and then you get 2x < 7. Finally divide 2 on each side so you leave x byitself completely. You get x > 3.5
I hope u get it right!
help me plsssssssssssssssssssssssss
when -3 - 2m < 0 => -2m < 3 => m > -3/2
ANSWER: C
Ok done. Thank to me :>
Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, and a distribution of relative frequencies for the values was created. Let the random variable X represent the number of days per week that a member visits. The mean of X is 3.12. Which of the following statements is the best interpretation of the mean
A. Each member visits the fitness center 3 or 4 days per week.
B. The average number of days that each member visits the fitness center is 3.12 days per week.
C. Half the members visit the fitness center 3 days per week or less, and the other half 4 days per week or more.
D. The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
E. For a random sample of members selected from the population, the average number of visits for the sample will be 3.12 days per week.
Answer: D
Step-by-step explanation:
The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. Option D is correct.
What is mean?The mean of the values is the ratio of the total sum of values to the number of values.
Here,
Let the random variable X represent the number of days per week that a member visits.
The mean of X is 3.12.
This mean describes that on an average 3.12 day in a week members visit the fitness center, it implies that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
Thus, the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. Option D is correct.
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Which equation represents the vertical line passing through (14,-16)?.
The vertical line shall have its x-coordinate equal to 14 because the points (14, -16) is on this vertical line.
Given the following data:
Points (x, y) = (14, -16)To find an equation of the vertical line that passes through the given points (14, -16):
The standard form of an equation of line is given by the formula;
[tex]y=mx+b[/tex]
Where:
x and y are the points.m is the slope.b is the intercept.For any equation of a straight line, the x-coordinate of a vertical line will always be the same irrespective of the point chosen on the vertical line. because a vertical line is perpendicular to the x-axis.
Deductively, the vertical line shall have its x-coordinate equal to 14 because the points (14, -16) is on this vertical line.
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simplify: 2x^2+15x-30
A= 2x^2
B= 15x
C= -30
(x-5)(x-6)
I dunno, its my question, just answering it for fun
Need some help with this one.
Answer:
y = -3x + 7
Step-by-step explanation:
Answer:
y = -3x + 7 (above)
Step-by-step explanation:
To add on, the person above me is correct. The equation of the line is in mx + b, where m is slope and b is the y-intercept.
We see the line intercepts the y axis at (0,7). Therefore the equation is y= mx +7
Now we look for m, the slope. If you may remember slope is also change in y over change in x, or rise/run. If you look at the graph, for each unit to the right, the line drops 3 units(it goes down, so negative). Therefore the slipe would be -3/1, or -3.
Plugging that in,
y = -3x + 7
y^2 - 19 = 0 find the sum and product
Answer: Sum of the roots: √19 - √19 = 0
Product of roots: (√19)(-√19) = -19
Step-by-step explanation:
y2 - 19 = 0
add 19 to both sides
y2 = 19
take square root of both sides
y = ±√19
So y = √19 or y = -√19
Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, l ≥ 20. He has 200 feet of fencing. The inequality that models the possible perimeter of the yard is 2l 2w ≤ 200. Which are possible dimensions for Mike’s backyard? Check all that apply. W = 50 ft; l = 10 ft w = 10 ft; l = 50 ft w = 20 ft; l = 60 ft w = 90 ft; l = 30 ft w = 50 ft; l = 40 ft.
The inequality that models the possible perimeter of the yard is 2(l + w) ≥ 200
The possible dimension of the width is 90 feet
The formula for calculating the perimeter of the fence is expressed as:
P = 2(l + w)l is the length of the fencew is the width of the fenceIf he has 200 feet of fencing, then:
2(l + w) ≥ 200
If the length of the fenced-in area to be at least 20 feet long, the equation becomes:
2(20 +w) ≥ 200
40 + 2w ≥ 200
2w ≥ 200 - 40
2w≥ 160
w≥ 80
Hence the possible dimension of the width is 90 feet
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Please help me with my math problem!! NO LINKS PLEASE!! IT IS DUE TONIGHT AT 11:59PM!! WILL GIVE BRAINLIEST!! :)
Step-by-step explanation:
Hi, i think this is how to do it. I'm sorry if I do it wrong!
2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The number 4 is outside of the circles. On the Venn diagram, which region(s) represent the intersection of Set A and Set B (Aâ©B)? II I and III I, II, and III I, II, III, and IV.
The intersection of sets is the point that represents the common point of multiple sets.
The region that represents the intersection of sets A and B is region II.
From the question, we understand that sets A and B have a common set element at II.
This means that region II is the intersection of both sets.
Hence, the region that represents the intersection of sets A and B is II.
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Answer:
II is the answer
Step-by-step explanation:
Edge 2022
when using the zero product rule you know at least one of the factors must equal *blank*
Answer:
The Principle of Zero Products states that if the product of two numbers is 0, then at least one of the factors is 0.
Step-by-step explanation:
Answer:
when using the zero product rule you know at least one of the factors must equal 0 because and most places anything that is put with zero equal zero because zero have no value
Step-by-step explanation:
bryan has some 3 cent stamps and some 4 cent stamps. what is the least number of stamps he can combine so the value of the stamps is 33 cents?
Answer:
The least number of stamps required is [tex]9[/tex]
Step-by-step explanation:
Let the number of [tex]3[/tex] cent stamps be [tex]x[/tex] and [tex]4[/tex] cent stamps be [tex]y[/tex]
We have
[tex]3x+4y=33[/tex]
The minimum number is obtained when more [tex]4[/tex] cent stamps are used
Here [tex]y[/tex] cannot be greater than [tex]8[/tex] since [tex]\frac{33}{4} <9[/tex]
Substitute [tex]y=8[/tex]
[tex]3x+4\times 8=33\\\\3x=1\\\\x=\frac{1}{3}[/tex]
Not possible since [tex]x[/tex] is not a fraction
Substitute [tex]y=7[/tex]
[tex]3x+4\times 7=33\\\\3x=5\\\\x=\frac{5}{3}[/tex]
Not possible since [tex]x[/tex] is not a fraction
Substitute [tex]y=6[/tex]
[tex]3x+4\times 6=33\\\\3x=9\\\\x=\frac{9}{3}\\\\=3[/tex]
Possible
Hence minimum number of stamps is
[tex]=x+y\\\\=3+6\\\\=9[/tex]
Which function is represented by the graph?
O f(x) = (x – 11 + 3
O f(x) = 5x + 11 – 3
O f(x) = |x – 11 – 3
Of(x) = x + 1] + 3
Answer:
b
Step-by-step explanation:i took the quiz
PLEASE HELP!!!!
ILL MARK AS BRAINIEST!!!!
ANSWER HOW MUCH U CAN!!!
Answer:
1) C
2) B
3) D
4) A
5) B
Step-by-step explanation:
Hope this helps
MAy I get braineist pls???????????
Answer:
MARK ME AS BRAINLIEST!!!
Step-by-step explanation:
1. A
2. B
3. D
4. A
5. B
HAVE A NICE DAY!!!
:)
A= 3x3x3x3x3x5x7x7x7
B= 2x2x2x3x7x7x7x7
Find the Lowest Common Multiple (LCM) of A and B.
Please help
Answer:
LCM(57624, 416745) = 23,337,720 or LCM = 23337720
Step-by-step explanation:
List all prime factors for each number.
Prime Factorization of 57624 is:
2 x 2 x 2 x 3 x 7 x 7 x 7 x 7 => 23 x 31 x 74
Prime Factorization of 416745 is:
3 x 3 x 3 x 3 x 3 x 5 x 7 x 7 x 7 => 35 x 51 x 73
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 3, 3, 3, 3, 3, 5, 7, 7, 7, 7
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 7 x 7 x 7 = 23337720
In exponential form:
LCM = 23 x 35 x 51 x 74 = 23337720
LCM = 23337720
Therefore,
LCM(57624, 416745) = 23,337,720
32 feet
8 feet
What will the new dimensions of the rectangle
be after a dilation with a scale factor of
7/8
Answer:
i do not know
Step-by-step explanation:
Which of the following expressions has a ''x'' term with a coefficient of 1?
x² + 5x + 1
3x² - x - 4
5x² + x - 9
4x²- 7x + 1
Write an equation for the graph.
Answer:
y = 3x + 2
Step-by-step explanation:
3 is the slope
2 is the y-intercept
find the volume of this figure:
Answer:
= 5l. 66 in^3
Step-by-step explanation:
Area of cross section (A) = 1/2×b×h
=1/2 ×3.5×4.1
=7.175
Volume =AXH
= 7.175× 7.2
= 5l. 66 in^3
PLEASE HELP!! :( I will mark brainliest!
Answer:
14 give me that badge :)
Step-by-step explanation:
Answer:
Step-by-step explanation:
14 faces
From the observation deck of a skyscraper, Jamal measures a 51° angle of depression
to a ship in the harbor below. If the observation deck is 1123 feet high, what is the
horizontal distance from the base of the skyscraper out to the ship? Round your
answer to the nearest hundredth of a foot if necessary.
Answer:
Your answer is 909.39 feet
Step-by-step explanation:
Is this correct check please
Answer:
its most likely CORRECT!
just have confidence that your answers are correct :)
Answer:
yes
Step-by-step explanation:
What is the best estimate for this sum?
1/8+1/6
Options here:
The sum will be close to 1/4
The sum will be close to 1/2
The sum will be close to 1
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An Ipad that costs $500 is on sale for 15% off. Then has a 6% tax. What's the final price?
Answer:
subject tooo
Step-by-step explanation:
sorry
Answer:
$450.50
Step-by-step explanation:
9. Change the given equation to the form y = mx + b. Give the values of b and m.
x + 4y = 16
B=
M=
Solve:
A.152
B.176
C.5
D.27
Answer:
Option B
176
Step-by-step explanation:
take 11 to the next side of the equation making the division multiplication getting us 16×11=176
write an algebraic expression for the word expression.
the sum of 9 and a number x
Answer:
9 + x
Step-by-step explanation:
i think this is what you meant
Answer:
Write each phrase as an algebraic expression. In Example 2, each algebraic expression consisted of one number, one operation and one variable.
...
Algebraic Expressions With Example Problems and Interactive Exercises.
Phrase Expression
the sum of nine and a number x 9 + x
Step-by-step explanation:
Hopes this helps\
Mark as brainliest
Which numbers are irrational numbers?
Select each correct answer.
Answer
Well pi is an irrational number because it can't be simplified into a fraction. And from what I can see neither can the sqaure root of 10/49. So I believe it would be both of them. But if there is only one answer than i'm not sure sorry. But it also says each so maybe there is more than one answer.
Step-by-step explanation: