Answer:
r = 1,248 in
Step-by-step explanation:
v(c) = 12 in³
The surface area of a right cylinder is:
Area of the base and top + lateral area
S(a) = 2*π*r² + 2*π*r*h (1)
v(c) = 12 in³ = π*r²*h h is the height of the cylinder, then
h = 12 / π*r²
By substitution, in equation (1) we get the Surface area as a function of r
S(r) = 2*π*r² + 2*π*r* ( 12 / π*r²)
S(r) = 2*π*r² + 24 /r
Tacking derivatives on both sides of the equation we get:
S´(r) = 4*π*r - 24 /r²
S´(r) = 0 4*π*r - 24 /r² = 0 π*r - 6/r² = 0
π*r³ - 6 = 0
r³ = 1,91
r = 1,248 in
How do we know that the value r = 1,248 makes Surface area minimum??
We get the second derivative
S´´(r) = 4*π + 48/r³ S´´(r) will be always positive therefore we have a minumum of S at the value of r = 1,248 in
A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the other three sides. Given that there are 56 meters of fencing available, determine the dimensions that would create the garden of maximum area. You may enter an exact answer or round your answer to the nearest hundredth.
Answer:
x = 28 m
y = 14 m
A(max) = 392 m²
Step-by-step explanation:
Rectangular garden A (r ) = x * y
Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.
the perimeter of the rectangle is p = 2*x + 2*y ( but in this particular case only one side x will be fencing with wire
56 = x + 2*y 56 - 2*y = x
A(r) = ( 56 - 2*y ) * y
A(y ) = 56*y - 2*y²
Tacking derivatives on both sides of the equation we get:
A´(y ) = 56 - 4 * y A´(y) = 0 56 - 4*y = 0 4*y = 56
y = 14 m
and x = 56 - 2*y = 56 - 28 = 28 m
Then dimensions of the garden:
x = 28 m
y = 14 m
A(max) = 392 m²
How do we know that the area we found is a local maximum??
We find the second derivative
A´´(y) = - 4 A´´(y) < 0 then the function A(y) has a local maximum at y = 14 m
A box is filled with 2 red carts, 3 green cards, and 8 brown cards. A card is chosen at random from the box, What is the grobability that the card is not green?
Write your answer as a fraction in simplest form.
Answer:
10/13
Step-by-step explanation:
High. Very High
The total number of cards is 8 + 3 + 2 = 13
There are 3 green ones and 10 others.
P(~G) = 10/13 = 0.769
Kelly is using a rectangular container to fill up a bucket of water. The container is 3.8 inches long, 2.5 inches wide, and 7.2 inches tall. If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket
Answer:
Kelly will have to fill the cup 20 times.
Step-by-step explanation:
Volume of the cube:
Rectangular cube, so the volume of the cube is the multiplication of its three dimensions(3.8 inches, 2.5 inches and 7.2 inches).
V = 3.8*2.5*7.2 = 68.4 cubic inches.
If the bucket holds 1,368 cubic inches of water, how many times will Kelly have to fill the cup in order to fill the bucket?
Solved by proportions, using a rule of three.
1 time - 68.4 cubic inches
x times - 1368 cubic inches
Applying cross multiplication:
[tex]68.4x = 1368[/tex]
[tex]x = \frac{1368}{68.4}[/tex]
[tex]x = 20[/tex]
Kelly will have to fill the cup 20 times.
please help (i mark brainlist)
Here is the function for the number of zombies, N, after t years, with the negative exponent expressed using the fraction ½:
N(t) = 300 • 0.5t/8
What is the half-life for the zombie population?
Answer:
The half-life for the zombie population is of 8 years.
Step-by-step explanation:
Exponential equation:
An exponential equation has the following format:
[tex]N(t) = N(0)(1-r)^t[/tex]
In which N(0) is the initial value and the part [tex](1-r)^t[/tex] is related to the decay.
In this question:
[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]
Thus N(0) = 300, that is, initial population of 300.
What is the half-life for the zombie population?
This is t for which N(t) = 0.5*300 = 150. So
[tex]N(t) = 300(0.5)^{\frac{t}{8}}[/tex]
[tex]150 = 300(0.5)^{\frac{t}{8}}[/tex]
[tex](0.5)^{\frac{t}{8}} = \frac{150}{300}[/tex]
[tex](0.5)^{\frac{t}{8}} = 0.5[/tex]
[tex](0.5)^{\frac{t}{8}} = (0.5)^1[/tex]
Equal exponents, so:
[tex]\frac{t}{8} = 1[/tex]
[tex]t = 8[/tex]
The half-life for the zombie population is of 8 years.
Which equation is written in factor form?
I need help
1−(−3)−5
answer is -1 you can check it on the calculator
pleaseeee mark me as the BRAINLIEST pleaseeee
Step-by-step explanation:
(-)(-)=+
1−(−3)−5
1+3-5
4-5
-1
A watering can contained 5 1/2 quarts water. After all the plants were watered, only 4 cups remained.
How many cups of water were used to water the plants?
Answer:
4 1/2 quarts.
Step-by-step explanation:
So 5 1/2 quarts to start. 4 left over.
Theres 4 cups in a quart.
So theres be 4 1/2 quarts used.. as 4 cups left would be a quart and 1 quart taken away from 5 1/2 quarts in 4 1/2.
please help!! 15 points i’m stressed out :/
Answer:
Since this (looks) like a homework assignment/test, I'll give you a hint.
Step-by-step explanation:
A function is where you have a input, that usually involves an equation that you have to replace the unknown with, to get the output.
Don't get it? Well, I didn't either.
What's great about this problem that you don't neccessarily have to know what the definition is.
A function can only output. So if you inputted the number 6, and got the output -3, you can't have another number that also had the output -3, and vice versa. This is my hint for the number 1.
Number 4 is a bit harder, but here's my hint:
Look for a pattern.
Given P(A) = 0.3, P(B) 0.63 and P(BA) = 0.79, find the value of
P(A and B), rounding to the nearest thousandth, if necessary.
Answer:
P(A and B) = 0.14.
Step-by-step explanation:
Venn probabilities:
Suppose we have two events, A and B. The probability P(A and B) is given by:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
In which [tex]P(A \cup B)[/tex] is P(A or B).
In this question:
P(A) = 0.3, P(B) = 0.63, P(A or B) = 0.79. So
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 + 0.63 - 0.79 = 0.93 - 0.79 = 0.14[/tex]
So
P(A and B) = 0.14.
Fat Kat's offers a special on large two topping pizzas. In how many different ways can you order a two topping pizza if you can choose from 18 toppings? NO LINKS!!!
=======================================================
Explanation:
There are 18 ways to pick the first topping and 18-1 = 17 ways to pick the next topping. Picking the same topping again doesn't make much sense (though I suppose it could mean that you just want more of that topping than usual?), so that's why we have the 18 drop to 17 when making that second selection.
If the order of toppings mattered, then we'd have 18*17 = 306 permutations. However, the order of toppings doesn't matter. All that matters is the group rather than the individual toppings. When counting out the 306 permutations, we've overcounted by a factor of 2. In other words, we've double counted.
So we must divide by 2 to fix this double count. That leads to 306/2 = 153 combinations
------------------------
The alternative method involves using the nCr combination formula
Use n = 18 and r = 2 in this formula
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
the exclamation marks indicate factorial.
What do u multiply first?
Answer:
Order of operations tells you to perform multiplication and division first, working from left to right, before doing addition and subtraction. Continue to perform multiplication and division from left to right. Next, add and subtract from left to right.
pls Mark me as brainliest trust me..
The step function f(x) is graphed
What is the value of f(-1)?
0-3
O-1
ОО
0 1
The value of f(-1) in the graph is 1.
What is Function?In mathematics, a function is an expression, rule, or law that establishes a relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The graph leads to the following finding:
The values of f(-1) for x = -1 are -1 and -3.
The function does, however, have a closed circle at f(-1) = 1.
The function has an open circle at f(-1) = -3.
A closed circle represents inclusive principles.
Hence, the graph's value for f(-1) is 1.
Learn more about functions here:
brainly.com/question/13136492
#SPJ7
The sampling distribution describes the a. long-run behavior of a statistic. b. short-term behavior of the population. c. sample size. d. population proportion.
Answer:
Option A
Step-by-step explanation:
A probability distribution of a statistic that represents a large sample derived from a certain specific population size to determine a range of possible outcomes of statistics such as Mean, Standard deviation, mode, median etc. in a way that it represents the existing entire population is known as a sampling distribution
Hence, option A is correct
READ PIC! PLEASE HELP
Answer:
B. 0< b < 1
Step-by-step explanation:
b is a fraction that less than 1, so 0 < b < 1
Help with volume all help is appreciated :)
Answer:
It would be 0.41 ft^3
Step-by-step explanation:
Alright, to start, lets get the volume of the entire cinder block and the holes within it.
1.31 * 0.66 * 0.66 ---> 0.5706...
Next with the holes, they are both 0.33 wide, 0.39 long, and just as tall at 0.66 feet.
0.33 * 0.39 * 0.66 ---> 0.0849...
Since there's two of them: 0.1698...
To finish it, subtract the hole volume from the total volume;
0.5806 - 0.1698 = 0.4108
Rounds to 0.41 ft^3
1. Points scored by a basketball player are 12, 15, 8, 12, 15, 10, 3, 14, and 15
Calculate the:
a) mean
b) median
c) mode
d) midrange
e) Use the relative location of the mean, median, and mode calculated describe the sets as
symmetric, skewed left, or skewed right.
Answer:
mean : add all of them and divide by how much they are
mode: is what repeats it self like 15 is the most repeated.
Imagine a simple process in which 5 ticket booths are selling tickets for an opera. If customers are coming at a rate of 15 / hour, and the utilization of the 5 booths is 50%, then how long does a customer spend at a booth (each customer goes to only one booth)?
Answer: The customer spends 10 minutes at a booth.
Step-by-step explanation:
Let n= number of booths, [tex]\rho[/tex] = utilization, [tex]\lambda[/tex] = arrival rate, [tex]\mu=[/tex]Service rate
We know that
[tex]\rho=\dfrac{\lambda}{\mu\times n}[/tex]
As per given,
[tex]0.5=\dfrac{15}{\mu\times5}\\\\\Rightarrow\ \mu=\dfrac{15}{5\times0.5}\\\\\Rightarrow\ \mu=6[/tex]
Service rate = 6 customers per hour.
Time taken by each customer = [tex]\frac{1}{\mu}[/tex]
[tex]=\frac{1}{6} \ hours \ or\ \dfrac{60}{6}\ minutes\\\\=10 \ minutes[/tex]
Hence, the customer spends 10 minutes at a booth.
brainliest and many poitns FAST
Answer:
you're answer is, 22
Answer:
Solution given;
[tex]11 \div \frac{1 }{2} = \frac{11}{ \frac{1}{2} } = 11 \times 2 = 22[/tex]
22 is a required answer:.
Rewrite 5ab showing the multiplication signs
Answer:
[tex]5ab = 5 \times a \times b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
5a*b
20 POINTS AND I WILL MARK YOU BRAINLIEST !!!
the london ferris wheel has a maximum height of 443 ft and a diameter of 394 ft . the wheel takes 30 mins to rotate
#1. what is the minimum height of the ferris wheel ?
94 , 85 , 49 , or 40
#2. where would the midline of the graph be ?
y=246 , y=221.5 , or y=197
#3. what is the amplitude of the graph ?
246 ft , 221.5 ft , or 197 ft
#4. what is the period of the function ?
15 , 30 , or 60 minutes
Step-by-step explanation:
#1 . the minimum height =
443 - 394 = 49 ft
#2. y = (394/2) + 49 = 197+49
=> y =246
#3. the amplitude is ½× diameter
= ½×394 = 197 ft
#4. the period of function is
the time that the wheel takes
one rotation =>30 minutes
please help what's the exact value for x?
cos(x+pi)-sin(x-pi)=0
SHOW WORK PLEASE
Step-by-step explanation:
Recall that
[tex] \cos(x + \pi) = \cos x \cos\pi - \sin x \sin\pi[/tex]
and
[tex] \sin(x - \pi) = \sin x \cos \pi - \cos x \sin \pi[/tex]
But we also know that
[tex] \cos \pi = - 1 \\ \sin \pi = 0 \: \: \: \: [/tex]
so the above relations reduce to
[tex] \cos(x + \pi) = - \cos x \\ \sin(x - \pi) = - \sin x [/tex]
Therefore,
[tex] \cos(x + \pi) - \sin(x - \pi) = - \cos x + \sin x [/tex]
If y is inversely proportional to (tan x) and y = 2
when x = 30°, find the value of y when this value
of x is doubled.
Answer:
When something is inversely proportional it can be solved by using the equation:
y = k/x
where k is the constant.
So using this we can plug in x and y to find the value of k.
3 = k/4.
Next we isolate k and find that k = 12. Now we use this to find the value of y when x = 8. Plug in x and you get y = 12/8 or y = 3/2 or 1.5.
Another way to solve this is to look at how the value of x changes. When the value of x goes up, the value of y goes down.
In other words, when x is multiplied by some number, y is divided by that number. In this equation we can see that x is multiplied by 2 to go from 4 to 8.
Thus, y must be divided by 2.
Thus, y = 3/2 or 1.5.
Answer:
Step-by-step explanation:
y is inversely proportional to tan x means
[tex]y \ \alpha \ \frac{1}{tan x}\\\\y = k \times \frac{1}{tanx}[/tex]
Given y = 2 when x =30° . So we will find k.
[tex]y =k \times \frac{1}{tanx } \\\\2 = k \times \frac{1}{tan 30}\\\\k = 2 \times tan 30 = 2 \times \frac{1}{\sqrt{3}} = \frac{2}{\sqrt{3} }[/tex]
Now x is doubled, x = 60°, find y
[tex]y = k \times \frac{1}{tanx}\\[/tex]
[tex]= \frac{2}{\sqrt{3}} \times \frac{1}{tan 60}\\\\= \frac{2}{\sqrt{3}} \times \sqrt{3}\\\\=2[/tex]
What is 0.25% of 30?
Answer:
0.075
Step-by-step explanation:
if you were to too a dice one time what is the odds of rolling a number less than three?
Answer:
1/3 or 33.33%
Step-by-step explanation:
A regular dice has 6 sides each with a single number from 1 to 6. Therefore, there are a total of 6 possible outcomes. Out of all of these only two outcomes are actually less than three and those are the numbers 1 and 2. Meaning, that if the dice were rolled only a single time then the probability of rolling a number less than 3 would be 2/6 or 1/3 (simplified). As a percentage, this probability would be 33.33%
Plzzz help as soon as possible
Answer:
Step-by-step explanation:
8 is not a function
9 is a function
10 is a function
how do I find the percent of 60% of 40
Answer: turn percentages into decimals then multiply that by the initial number
Step-by-step explanation:
60%
0.60
0.60*40= 24
another name for the positive integrets is the ___ Numbers.
Answer:
natural
Step-by-step explanation:
A salesman earns $250 per week PLUS a 10% commission on all sales over $5000. In one week, his sales totaled $14,000. What were his earnings that week?
A. $1,050
B. $1,150
C. $400
D. $2,150
Answer:
B. 1150
Step-by-step explanation:
14000-5000=9000 sales over 5000
9000 x .10=900 commission
250 (salary)+ 900 (commission)=1150 total
Lil' HydroPhil owns five pieces of precious apparel and wants to choose two to wear to the awards show. He defines his precious apparel as: platinum nose ring, diamond shirt, titanium boots, suede pants, and beryllium hat. Assuming the selection is random and each has an equally likely outcome, determine the probability HydroPhil chooses a combination that includes the suede pants.
Answer:
The probability HydroPhil chooses a combination that includes the suede pants is 0.40
Step-by-step explanation:
Given
Let
[tex]P \to Platin um\ no se\ ri ng[/tex]
[tex]D \to Diamond\ shirt[/tex]
[tex]T \to Titanium\ boots[/tex]
[tex]S\to Suede\ pants[/tex]
[tex]B\to Beryllium\ hat[/tex]
Required
Probability of selecting a combination that has S
First, list out all possible combinations (A) of 2
[tex]A = \{PD, PT, PS, PB, DT, DS, DB, TS, TB, SB\}[/tex]
The sample size is:
[tex]n(A) = 10[/tex]
The combinations that has S are:
[tex]S \to \{PS, DS, TS, SB\}[/tex]
The size is:
[tex]n(S) = 4[/tex]
So, the probability that he choose the combination that has S is:
[tex]Pr = \frac{n(S)}{n(A)}[/tex]
[tex]Pr = \frac{4}{10}[/tex]
[tex]Pr = 0.40[/tex]