0.70 ft
Step-by-step explanation:
The volume V of a cone is given by
[tex]V = \dfrac{\pi}{3}r^2h[/tex]
where r is the radius of the base and h is the height of the cone. Since the radius is half the diameter D, we can rewrite V as
[tex]V = \dfrac{\pi}{3}\left(\dfrac{D}{2}\right)^2h = \dfrac{\pi}{12}D^2h[/tex]
But since the base diameter D is always equal to the cone's height, we can write the volume in terms of the height h as
[tex]V = \dfrac{\pi}{12}h^3[/tex]
Now gravel is being added to the conical pile at a rate of 35 cubic ft per minute so to find the rate at which the height of the pile is increasing, we are going to take the derivative of V with respect to time:
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}\left(\dfrac{\pi}{12}h^3\right)[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{\pi}{12}\cdot 3h^2\dfrac{dh}{dt} = \dfrac{\pi}{4}h^2\dfrac{dh}{dt}[/tex]
Rearranging the variables and solving for dh/dt, we get
[tex]\dfrac{dh}{dt} = \dfrac{4}{\pi h^2}\dfrac{dV}{dt}[/tex]
[tex]\:\:\:\:\:\:\:\:= \dfrac{4}{\pi(8\:\text{ft})^2}(35\:\text{ft}^3\text{min})[/tex]
[tex]\:\:\:\:\:\:\:=0.70\:\text{ft/min}[/tex]
painter has a 24-foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder safely reach?
Answer:
this is a pythagorean theorem problem. 24 is the whole ladder, and if you draw it out, is a hypotenuse. 8 is a leg. . so 8^2 + b^2 = 24^2
b^2 = 512, so b = sqrt(512) = 22.6
i inserted a picture of the question could you please make it short.
Answer
B) 6²
E) 36
Step-by-step explanation:
[tex]6^{7}[/tex] / [tex]6^5[/tex] = 6^(7-5) = 6²
6² = 36
A definition of a statistical question is given below.
Statistical question:
Any question whose answer could involve working with more than one data value.
In each situation below, determine whether the question is a statistical question.
Answer:
I dont know
Step-by-step explanation:
Question 2 (Essay Worth 10 points)
(07.02 MC)
An equation is shown below:
3(2x - 7) = 3
Part A: How many solutions does this equation have? (4 points)
Part B: What are the solutions to this equation? Show your work. (6 points)
Answer:
Part A: 1 solution
Part B:
3(2x-7)=3
6x-21=3
+21 +21
6x=24
/6 /6
x=4
Step-by-step explanation:
First you distribute 3(2x-7)=3 to 6x-21=3. Next you do inverse operations by adding 21 to both sides of the equation to get 6x=24. Finally you divide both sides by 6 to get x=4
Suppose carpet for a 12 ft by 10 ft room costs $400. Find the cost to carpet a room 36 ft by 30 ft
Answer:
About $3600
Step-by-step explanation:
10 x 12 =120 square feet - area of the first room
$400 / 120 =$3.33 - cost of carpet per square foot.
36 x 30 = 1080 square feet - the area of the second room
1080 x $3.33 = (about) $3600 cost of carpeting the second room.
The probability that homework is assigned in Ethan's computer science class is 7/10 From a randomly chosen class, find the probability that Ethan does NOT have computer science homework.
The probability that Ethan does NOT have computer science homework is 0.3
From the information given:
Let the probability that homework is assigned in Ethan's computer science be P(A) = 7/10However, in probability, the sum of all event outcomes is always equal to 1.
∴
[tex]\mathbf{P(A) + P(A^c) = 1}[/tex]
where;
[tex]\mathbf{ P(A^c) = }[/tex] the probability that Ethan does NOT have computer science homeworkThus;
[tex]\mathbf{ P(A^c) = 1- P(A)}[/tex]
[tex]\mathbf{ P(A^c) = 1- \dfrac{7}{10}}[/tex]
[tex]\mathbf{ P(A^c) =\dfrac{10 -7}{10}}[/tex]
[tex]\mathbf{ P(A^c) =\dfrac{3}{10}}[/tex]
[tex]\mathbf{ P(A^c) =0.3}[/tex]
Therefore, we can conclude that the probability that Ethan does NOT have computer science homework is 0.3
Learn more about probability here:
https://brainly.com/question/11234923?referrer=searchResults
Which expression is equivalent to [(4^5/4•4^1/4)/4^1/2]^1/2
Answer:
2
Step-by-step explanation:
[(4^5/4•4^1/4)/4^1/2]^1/2
= [(4^(5/4) • 4^(1/4))/4^(1/2)]^1/2
= [(4^(3/2))/4^(1/2)]^1/2
= 4^(1/2)
= sqrt(4)
= 2
Answer:
2Step-by-step explanation:
[tex][(4^{5/4}*4^{1/4})/4^{1/2}]^{1/2}=[/tex][tex](4^{5/4+1/4-2/4})}^{1/2}=[/tex][tex](4^1)^{1/2}=[/tex][tex]2[/tex]Josh runs 6 miles in 44 minutes. At the same rate, how many minutes would he take to run 9 miles?
Answer:
66 minutes
Step-by-step explanation:
Method I - proportion
x/44 = 9/6
multiply both sides by 44
x = 9 / 6 * 44
x = 66 minutes
--------------------------
Method II - rate
44/6 = 7.3333333 minutes / mile
9 * 7.3333333 = 66 minutes
Which inequality is true when the value of d is 14?
−d−9>−1.5
−d−9<1.5
−d−9>1.5
d−9<−1.5
Answer:
-d - 9 < 1.5
Step-by-step explanation:
In this problem, my reasoning is shown below for each individual inequality. We can test each one to see if it is true or not.
[tex]-(14)-9>1.5?\\-14-9>1.5?\\-23>1.5?\\[/tex]
-23 is not greater than 1.5, so it can't be the first one. Let's try the next one.
[tex]-(14)-9<1.5?\\-14-9<1.5?\\-23<1.5?[/tex]
Yes! -23 is smaller than 1.5. So we can say that the second option is correct. But just for good measure, we can try the other two.
[tex]-(14)-9>1.5?\\-14-9>1.5?\\-23>1.5?[/tex]
Nope! -23 is not greater than 1.5. Let's try the last one.
[tex]14-9<-1.5?\\5<-1.5?[/tex]
And again... nope. 5 is not smaller than -1.5. So our reigning option is -d - 9 < 1.5. Hopefully this was helpful! If you have any more questions, let me know.
−d−9<1.5 inequality is true when the value of d is 14.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
We have to check the inequality which is true for d when it is 14.
−d−9>−1.5
-14-9>-1.5
-23>-1.5
The first option is false.
−d−9<1.5
-23<-1.5
So the inequality −d−9<1.5 is true for d=14.
−d−9>1.5
-23>1.5
The inequality is false.
d−9<−1.5
14-9<-1.5
5<-1.5
The inequality is false.
Hence, −d−9<1.5 inequality is true when the value of d is 14.
To learn more on Inequality click:
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Determine the inverse of the function f(x) = 3(x - 4)^2 + 5.
f(x) as given has no inverse. We see that, for instance, f(1) = f(7) = 32; that is, two different values of x give the same value of f(x), so f is not one-to-one.
We can however restrict the domain over which f is defined to extract an invertible function. One such choice would be to restrict to the interval x ≥ 4, which I'll demonstrate below.
Recall the definition of function inverse:
f(f^(-1)(x)) = x
Then for this function, we have
3 (f^(-1)(x) - 4)² + 5 = x
3 (f^(-1)(x) - 4)² = x - 5
(f^(-1)(x) - 4)² = (x - 5)/3
√((f^(-1)(x) - 4)²)= √((x - 5)/3)
For all x, √(x²) = |x|. Then √((f^(-1)(x) - 4)²) = |f^(-1)(x) - 4|, but by restricting x ≥ 4, or x - 4 ≥ 0, we have the condition that f^(-1)(x) - 4 ≥ 0, and so by definition (of the absolute value function) the absolute value reduces to the positive case. In short, we end up with
f^(-1)(x) - 4 = √((x - 5)/3)
and hence the inverse
f^(-1)(x) = √((x - 5)/3) + 4
The science club sponsor is ordering caps and shirts for the boys and girls in the science club. There are 45 science club members. If the caps come in packages of 3 and the shirts come in packages of 5, what is the least number of packages of caps and shirts that will need to be ordered? Explain.
Answer:
The least number of packages of caps and shirts that will need to be ordered would be 9 Boxes of shirts and 15 boxes of hats .
Step-by-step explanation:
9(boxes) x 5(shirts) = 45
45(members) divided by 3(hats) = 15(boxes)
Write an exponential equation, given initial population of 2500 and doubling time of 2 years
A population of 32,000 with a 5% annual growth rate would be modeled by the equation:
y=32000(1.05)t
with t in years.
i'll mark brainliest thanks in advance
Answer:
x = 2
Step-by-step explanation:
These are known as alternate exterior angles. These types of angles are equal to each other.
[tex]8x-7=2x+5\\6x-7=5\\6x=12\\x=2[/tex]
The table below represents which equation?
Answer:
the third answer is correct
Step-by-step explanation:
the starting point is 2 and it goes up by 3
I think of a number subtract 5 then double the result
Answer:
Step-by-step explanation:
choose a number for example 20
20-5=15
15x2=30
if each of the following quadrilaterals are trapezoids find the missing measures. show your work.
A line has a slope of 3/7 . Through which two points could this line pass?
Answer:
(0,0) and (7,3) and (14,6) and (-7,-3)
Just graph it.
Answer:
the correct answer is (-8,-2) and (6,4)
Step-by-step explanation:
hope this helps
Simplify the expression
Answer:
it would equal 12x + 12
:)))
V is the midpoint of UW. If UV = x + 2 and VW = 2x, what is VW?
Answer:
8 units
Step-by-step explanation:
x + 2 = 2x
2 = 2x - x
x = 2
uW = 2(2+2) = 8
Answer:
VW = 4
Step-by-step explanation:
Since V is the midpoint of line UW, we can say that the measure of UV is equal to VW (see def. of midpoint). Thus, we can generate the equation using the statements provided, leading us to this equation: x+2 = 2x. We can then subtract x on both sides, leading us to 2 = x, or x = 2.
We were given that VW = 2x, thus the measure of VW is equal to 2(2) or 4.
(BONUS: since we know that VW ≅ UV, then the measure of UV is also equal to 4, which when applied to the formula for UV (x+2) we get the equation for UV, x+2=4. This is a way to prove that x=2, as 2+2=4. We can also use this knowledge to find the total length of this line segment, which would be 8, as 4+4=8)
PLEASE NOT BOTS OR LINKS
THIS IS THE THIRD TIME I HAVE HAD TO POST THIS QUESTION
Answer: C
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63% to fraction
[tex] \frac{63}{?100} [/tex]
Follow the steps mentioned below to write 0.63 as a fraction.
Step 1: Determine the number of digits after the decimal point in the decimal number. Here, there are 2 digits after the decimal point.
Step 2: Remove the decimal point and write the number by the power of 10 which is equal to the number of digits after the decimal point. So, here we will divide 63 by 102
Step 3: Express the fraction in simplified form.
So, 0.63 as a fraction is,
0.63 = 63/100
(3)a train travel 252 km in 42 hours. what amount of time will it take to complete a journey of 350km. (4) calculate the cost of 15 article at $1.95 each cost. (5) if 25 article cost 43.75 how much does each cost. (6) A car travel 240km on 20 liter of petrol. how many liters of petrol is needed to travel 600km
Answer:
(3)
Distance the train can travel=252km
Distance the train can travel in 1 hour=252÷42=6km
The time needed to cover 350km= 350÷6=58.4 hours.
(4)
The cost of 1 articles=$1.95
The cost of 15 articles= 15(1.95)=$29.25
(5)
Cost of 25 articles= 43.75
Cost of 1 article= 43.75/25=1.75
(6)
Liters of petrol needed when a car travels 240km=20litre
liters of petrol needed when a car travels 600km= 20/240 x600
20/24x60
20/4x10
5x10=50liter
There are about 3 × 1020 gallons of salt water on the earth, while there are about 6 × 1018 gallons of fresh water. About how many times the amount of fresh water is the amount of salt water? 200 times the amount 500 times the amount 2 times the amount 50 times the amount
Answer C
Step-by-step explanation:
22 is 32% of what number?
Answer:
68.75
Step-by-step explanation:
x is the number we are looking for, so 32% of x is 22.
First, we have to find the number that is equivalent to 1% of x.
To do this we simply do 22/32 which is 0.6875.
Now we know that 1% of x is 0.6875, so we can find 100% of 0.6875 (0.6875*100) to find x.
x is 68.75
The Shah family uses up 1/2-gallon jug of milk every 3 days. At what rate do they drink milk?
Answer:
1 Gallon per 6 days
Step-by-step explanation:
1/2 *2 = 1
3*2 =6
Answer:
1/6 Gallons of Milk per Day
Step-by-step explanation:
1/2 / 3 = 1/6
Brainiest for answer as always
Answer:
X=33
Step-by-step explanation:
Hope this helps!!!
Hi, someone else asked this question and I know that the answer is 6, but don’t know why. Could someone explain this for me, please? If you can make me understand I’ll give you brainliest…
Answer:
6
Step-by-step explanation:
I'm not exactly sure, but since 6 is the only number missing from this pattern, wouldn't it make sense for the answer to be 6?
I need it asap!!! Help a struggling geometry student out!!
9514 1404 393
Answer:
6. A
7. 80°
8. 20°
Step-by-step explanation:
6.It is helpful to read the question and identify the particular parts of the diagram it is asking about.
The corresponding hash marks mean the marked segments are congruent. These show you that ΔMQT is isosceles, so angles QMT and QTM are congruent. The sets of hash marks on NT and SM mean those segments are congruent. Of course MT is congruent to itself.
These facts let you conclude that triangles NTM and SMT are congruent by the SAS theorem. (The base angles of ΔMQT are between the pairs of congruent sides.)
The only answer choice referencing SAS is the first one, choice A.
__
7.Based on the previous question, it is a simple matter to show ΔMPT ≅ ΔTRM by SAS. Then angles MPT and TRM are congruent. Angle MPT is supplementary to angle MPN, so is 180° -100° = 80°.
Angle TRM is congruent to angle MPT, so is 80°.
__
8.With reference to ΔMQN, angle MQT is an external angle. Its measure is equal to the sum of the opposite internal angles QNM and QMN:
∠MQT = ∠NMQ + ∠QNM
95° = 75° + ∠QNM
20° = ∠QNM
From problem 6, we know that angle N is congruent to angle S, so, ...
∠TSR = ∠QNM = 20°
1 out of 5 apple were rotten . If 284 were edible, how many apples were harvested?
Answer:
200 apple yet to go byhfhhf
plz help with this will mark as brinliest
Answer:
it’s c
Step-by-step explanation:
