Answer:
V=1,125.1
Step-by-step explanation:
The equation for the volume of a cylinder is (V= πr^2h)
V= π(5.25)^2(13)
V= π(27.5625)(13)
V= π(358.3125)
V=1,125.10125
Write 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 using an exponent.
Answer:
9
[tex] {9}^{8} [/tex]
MODELING EXPONENTIAL GROWTH
1. You put $3,800 dollars in a savings account. The bank will provide 1.8% interest every year. Write and solve a model that describes how much money will be in the account in 15 years.
2. Suppose you deposit $2000 into a savings account that pays an interest annual rate of 4% if no money is added or withdrawn from the account, how much will be in the account after 3 years? What about 18 years? How many years will it take for the account to contain 3000 (for this now you know the total amount, you need to find t time)?
Answer:
1. M = C*1.018^t
After 15 years: M = 4965.93
2. After 3 years: M = 2249.728
After 18 years: M = 4051.633
Time to achieve 3000: t = 10.338 years
Step-by-step explanation:
1. Since the money gets increased every year at a rate of 1.8% after one year it'll be the initial amount multiplied by 1.018, so:
After one year:
M = C*1.018
After two years:
M = C*1.018*1.018 = C*(1.018)²
After three years:
M = C*(1.018)²*1.018 = C*(1.018)³
And so on, therefore:
M = C*(1.018)^t
Where M is the final amount, C is the initial amount and t is the time elapsed in years. For this case we have:
M = 3800(1.018)^15 = 4965.92626
2. Applying the same line of thought as above, we have:
M = C*(1.04)^t
After 3 years:
M = 2000*(1.04)^3 = 2249.728
After 18 years:
M = 2000*(1.04)^18 = 4051.633
To obtain 3000:
3000 = 2000*(1.04)^t
2000*(1.04)^t = 3000
1.04^t = 3000/2000
1.04^t =1.5
log(1.04^t) = log(1.5)
t*log(1.04) = log(1.5)
t = log(1.5)/log(1.04) = 10.338 years
At time t is greater than or equal to zero, a cube has volume V(t) and edges of length x(t). If the volume of the cube decreases at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases?
A) dV/dt=-1.2x^2
B) dV/dt=-1.2x^3
C) dV/dt=-1.2x^2(t)
D) dV/dt=-1.2t^2
E) fav/dt=-1.2V^2
Answer:
A) dV/dt=-1.2x^2
Step-by-step explanation:
The rate of change of volume is given by dV/dt. Surface area is proportional to x^2. Since the volume is decreasing, the constant of proportionality between surface area and rate of volume change will be negative. Hence a possible equation might be ...
dV/dt = -1.2x^2
Answer:
C
Step-by-step explanation:
V(t) = [x(t)]³
A(t) = 6[x(t)]²
dV/dt = k × 6[x(t)]²
Where k < 0
From the options,
taking k = -0.2
dV/dt = -1.2[x(t)]²
x2 + 4x - 21 = 0 quadratic formula
Answer:
0
Step-by-step explanation:
x2 +4x-21=0. solve for x
[tex]x = \frac{7}{2} [/tex]
[tex]x = 3 \frac{1}{2} \ x = 3.5[/tex]
Frank has twice as many CDs as Vanessa. Lois has 4 less than 2 times as many CDs as Frank. If there is a total of 115 CDs for all 3 people, how many CDs does each person have?
Answer:
Frank, Vanessa, Lois have 34, 17, 64 disks respectively
Step-by-step explanation:
In this question, we are to calculate the number of disks each of the 3 has.
Let the number of disks owned by Frank be x
for vanessa, she has half of what frank has and that would be x/2
Lois has 4 less than 2 times what Frank has, that would be 2x - 4
adding the 3, we have a total of 115 disks
This means that;
x + x/2 + (2x-4) = 115
Multiply throughout by 2;
that gives;
2x + x + 4x - 8 = 230
7x -8 = 230
7x = 230+ 8
7x = 238
x = 238/7
x = 34 disks
Frank has 34
Vaness has 34/2 = 17
Lois have 2x - 4 = 2(34) - 4 = 68 - 4 = 64 disks
Answer:
So Frank has 34 CDs, Vanessa has 17 CD's and Lois has 64 CDs
Step-by-step explanation:
Let's call the amount of CDs that Frank has by 'F', that Vanessa has by 'V' and that Lois has by 'L'. Then, we can write the following equations:
F = 2*V
L = 2*F - 4
F + V + L = 115
If we use the values of F and L in the third equation, we have that:
2*V + V + 2*(2*V) - 4 = 115
7*V = 119
V = 17 CD's
Now we can find F:
F = 2*V = 34 CDs
And then we find L:
L = 2*F - 4 = 68 - 4 = 64 CDs
So Frank has 34 CDs, Vanessa has 17 CD's and Lois has 64 CDs
The graph of the function f(x) = (x+6)(x+2) is shown.
Which statements describe the graph? Check all that
apply.
The vertex is the maximum value.
The axis of symmetry is x= -4.
The domain is all real numbers.
The function is increasing over (-0, -4).
The function is negative over (-6, -2).
Intro
Done
Answer: Is 2, 3 and 5
Step-by-step explanation:
I just completed the assignment on Edge
By analyzing the quadratic function, we can see that:
1) true2) true3) true4) false5) true.Which statements are correct?
Here we have the quadratic function:
f(x) = (x + 6)*(x + 2)
Let's analyze each statement to see which ones are correct.
1) "The vertex is the maximum value."
True, the leading coefficient is positive, so the parabola opens up, meaning that the vertex is the minimum.
2) " The axis of symmetry is x= -4."
The two roots are x = -6 and x = -2, the axis of symmetry is right between these two values, so it is at x = -4, so this is true.
3) "The domain is all real numbers."
For all quadratic functions, this is true.
4) "The function is increasing over (-0, -4)"
(I don't know what -0 means, the segment (-0, -4) does not exist, so i will take this as false).
5) "The function is negative over (-6, -2)."
This is true, the two roots are at -6 and -2, so between these values the function must be negative.
If you want to learn more about quadratic functions, you can read:
https://brainly.com/question/1214333
What is the degree of the monomial?
8x
Answer:
1
Step-by-step explanation:
when a variable does not have an exponent the degree is always one. Ex: 8x is the same as 8x to the power of 1
What is 3/2 times 14
Answer:
21
Step-by-step explanation:
3/2×14=21
Answer:
21
Step-by-step explanation:
Hannah planted flowers next to the school playground. She planted 2 daisies, 3 sunflowers and 4 tulips.
What is the ratio of the number of daisies she planted to the total number of flowers she planted?
Answer:
the ratio is 2:9
Step-by-step explanation:
there are a total of 9 flowers, she planted 2 daisies
T=s+.50 T=0.25s+1.70 In the equation above t and a represent the weight in tons of a sedan and of a truck, respectively. What is the weight of a sedan in tons
Answer :
The weight of a sedans in tons is 2.1 tons.
Step-by-step explanation:
Given : Equations [tex]T=s+0.50[/tex] and [tex]T=0.25s+1.70[/tex] where T and s represents the weight in tons of a sedan and of a truck, respectively.
To find : What is the weight of a sedan in tons ?
Solution :
Solving equations,
[tex]T=s+0.50[/tex] ......(1)
[tex]T=0.25s+1.70[/tex] .....(2)
As LHS is equate we equate RHS,
[tex]s+0.50=0.25s+1.70[/tex]
[tex]s-0.25s=1.70-0.50[/tex]
[tex]0.75s=1.2[/tex]
[tex]s=\frac{1.2}{0.75}[/tex]
[tex]s=1.6[/tex]
Substitute in equation (1),
[tex]T=1.6+0.50[/tex]
[tex]T=2.1[/tex]
Therefore, the weight of a sedans in tons is 2.1 tons.
A leaf blower runs on a mixture of oil and gas. The ratio is 40 to 1. How many ounces of gas does the leaf blower need for 4 ounces oil??
Answer:
160
Step-by-step explanation:
you need to multiply the ounces of gas by 4 like you did to the oil.
Answer:
160 oz
Step-by-step explanation:
However, I personally think this does not make sense. A leaf blower should take more gas than oil, right? For this reason, I will provide an additional answer.
If the ratio of gas to oil is 40:1, then you would multiply by 4 to get 4 oz oil and 160 oz gas.
Alternate answer:
If the ratio of oil to gas is 40:1, then you divide by 10 on both sides to get 4 oz oil and .1 oz gas.
Alt answer: .1 oz
1093999 nearest to million
Answer:
1,000,000
Step-by-step explanation:
Because you are rounding down because it is not enough to round up.
what makes 2 figures congruent
Two polygons are congruent if they are the same size and shape
What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?
Answer:
there is one zero: 5/16
Step-by-step explanation:
i used photomath
An automobile dealer agrees to discount the $10,288 sticker price of a new car by 5% for a customer. What is the price of the car for the customer?
Answer: 514.4
Step-by-step explanation:
10, 288 x 5 ÷ 100
A jet departs from an airport flying east. At the same time, a second jet departs from the same airport flying west at a speed of 20 miles per hour slower than the first jet. After 1.5 hours, the planes are 1,500 miles apart. What is the speed in miles per hour of the jet traveling east?
A. 300
B. 750
C. 510
D. 490
Answer:
490mph and 510mph
Step-by-step explanation:
Let x mph and x+20 mph be the speeds of the planes. The rate at which their distance from each other increases will be the sum of their speeds which is 2x+20 mph.
Their distance from each other after three hours is ( 1.5 hours)*(2x+20 mph) = 3x+30 miles. We are given that this is 1500 miles so we can solve for x.
3x+30 = 1500
3x = 1500 - 30
3x = 1470
x = 1470/3
x = 490mph
For the second jet :
x +20 = 490+20
x = 510
Thus the speeds of the two planes are 490 mph and 510mph.
Answer:
510 miles
Step-by-step explanation:
Please kindly check the attached file for explanation.
You have 16 socks in your drawer. 4 are black, 6 are white, 4 are blue, and 2 are gray. Suppose you randomly choose a sock, replace it, and randomly choose another. What is the probability that either the first sock is blue or the second sock is gray?
Answer:
11/32
Step-by-step explanation:
4/16 + 2/16 - 1/32
simplify and solve
we started something new and I'm competely lost
Given:
Triangle ABC is similar to triangle XYZ.
The measures of the sides are AB = 6 cm, BC = 18 cm and XY = 12 cm
We need to determine the measure of side YZ.
Measure of YZ:
Since, ABC and XYZ are similar triangles, by using similar triangles property, we have;
[tex]\frac{AB}{XY}=\frac{BC}{YZ}[/tex]
Let the length of YZ be x.
Substituting the values, we get;
[tex]\frac{6}{12}=\frac{18}{x}[/tex]
Cross multiplying, we get;
[tex]6x=12 \times 18[/tex]
[tex]6x=216[/tex]
Dividing both sides by 6, we have;
[tex]x=36[/tex]
Thus, the value of x is 36.
Hence, the measure of the side YZ is 36 cm.
Una Sección, compuesta por 18 soldados y 2 suboficiales, entra en combate y gasta la quinta parte del total de la munición de dicha Sección. Si la cantidad de cartuchos gastados por los soldados excede en 424 cartuchos al número de cartuchos gastados por los suboficiales. ¿Cuántos cartuchos gastaron los soldados y cuántos los suboficiales sabiendo que la dotación completa por cada hombre es de 175 cartuchos?
The soldiers used 562 cartridges in combat, while the subofficers used 138, using the total amount of ammunition and the difference between cartridges used.
Explanation:The total amount of ammunition for the section is 175 per soldier for a total of 20 soldiers, so we have 175 * 20 = 3500 cartridges. A fifth of this ammunition is used in combat, that is, 3500/5 = 700 cartridges. According to the question, the number of cartridges used by the soldiers exceeds that of the subordinates by 424 cartridges, so we can establish a system of equations:
The total ammunition, 700, is the sum of the cartridges used by soldiers (x) and subofficers (y): x + y = 700The number of cartridges used by soldiers (x) is greater than the ammunition used by subofficers (y) by 424: x = y + 424We can then solve this system and find that the soldiers used 562 cartridges and the subofficers used 138.
Learn more about System of Equations here:https://brainly.com/question/35467992
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The math team has 11 boys, 10 girls, and 1 coach. What is the ratio of coach to students?
Group of answer choices
11/1
1/21
1/11
21/1
Answer: 1:21
Step-by-step explanation:
We know that if they say students they mean both boys and girls so we add 11 and 10 to make 21 and since its, (COACH,) and then student we do 1:21 and not 21:1!
1/21
Step-by-step explanation:
First we need to figure out how many students are in the class.
10 + 11 = 21
Then we need to make a ratio
1/21
For every 21 students there is 1 coach
If you look at the question it says from coach to students so we do 1 coach to 21 students which is why 21/1 is wrong
Hope this helps can I have brainliest
A student decided to start saving money.On the first day he saved 1 cent, on the second day an additional 2 cents, on day 3 he saved 4 cents. Each day he doubled the amount he saved the previous day. How much would he be saving on day 20?
(Hint: The first term of the geometric sequence is 0.01 and the common ratio is 2. What is the 20th term?)
Question 1 options:
A-$3.80
B-$10,485.75
C-$5,242.88
D-$10,485.76
Answer:
The correct option is option (B).
He would be saving $10,485.75.
Step-by-step explanation:
We know that,
1 cent =$ 0.01.
Geometric sequence:
The first term of the sequence be a and common ratio n, then [tex]n^{th}[/tex] term of the sequence is [tex]T_n=a(r)^{n-1}[/tex] .The sum of the sequence is[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex] where r>1
[tex]=\frac{a(1-r^n)}{1-r}[/tex] where r<1
=na where r=1
Here first term(a)= $0.01, r= 2 , n=20
[tex]S_n=\frac{0.01(2^{20}-1)}{2-1}[/tex]
=10,485.75
He would be saving $10,485.75.
What is 240,000 divided by 1962.5 ?
Answer:
122.293
Step-by-step explanation:
What is the length of BC given that CG is 2.5 inches and GB is 253 inches? Round to the nearest tenth.
3.5 inches
8.8 inches
9.1 inches
10.8 inches
Answer 3.5 inches
Step-by-step explanation:
Answer:
A. 3.5
Step-by-step explanation:
There are 12 employees at the sub shop. How many ways can the manager choose 4 for the Sunday evening shift? Permutation or combination and the answer?
Answer:
It is a combination answer
495 ways
Step-by-step explanation:
In this question, we are tasked with calculating the number of ways in which a manager can select 4 people out of 12 for the Sunday evening shift.
Firstly, the question talks about selecting a particular number from a mix, this is a combination question since the key word SELECT is mentioned.
Now, how do we go about it? To select a partial number from a mix , we use the combination formula as stated.
Mathematically, say we are selecting a number r from a total of numbers n, the number of ways we can do this is nCr = n!/(n-r)!r!
In this case however, we are simply selecting 4 out of 12
Our combinational equation thus becomes 12C4 = 12!/(12-4)!4! = 12!/8!4! = 495 ways
Final answer:
The manager can choose 4 from 12 employees in 495 different ways for the Sunday evening shift, using a combination rather than a permutation since the order of selection does not matter.
Explanation:
To determine the number of ways the manager can choose 4 out of 12 employees for the Sunday evening shift, we need to decide whether the order in which the employees are chosen matters. If the order does not matter, we will use a combination. If the order does matter, we would use a permutation. In this case, because the task is simply to choose 4 employees and the order in which they are chosen does not affect the outcome, we use a combination.
The formula for finding the number of combinations when choosing k objects out of a total of n objects without repetition is given by:
C(n, k) = n! / (k! * (n-k)!)
In this situation, we have n=12 and k=4, so we calculate:
C(12, 4) = 12! / (4! * (12-4)!) = 12! / (4! * 8!) = (12*11*10*9) / (4*3*2*1) = 495
Therefore, there are 495 different ways for the manager to choose 4 employees for the Sunday evening shift.
A bag contains white marbles and blue marbles, 65 in total. The number of white marbles is 8 more than 2 times the number of blue marbles. How many white marbles are there?
Answer:
NOTE: THIS IS AN EXAMPLE
Step-by-step explanation:
Let the Yellow Marbles be “X” and Red Marbles be “Y”
Total is 65, so X+Y = 65
Since we know that Yellow Marbles are 5 more than 4 times red marbles, let us convert that in terms of X and Y as well.
i.e, X = 4Y+5
Now replace X with (4Y+5) in the first equation we wrote above.
(4Y+5)+Y = 65
i.e, 5Y+5 = 65
5Y = (65–5),
5Y = 60
Therefore Y = 60/5 = 12
we know total is 65
So X= 65-Y
X=65–12 = 53
Therefore, the number of Yellow Marbles are 53 and the Red ones are 12.
PLEASE HELP
A circle has radius 50 cm. Which of these is closest to its area?
Captionless Image
1. A
2. B
3. C
4. D
Answer:
C.) [tex]7,854[/tex] [tex]cm^2[/tex]
Step-by-step explanation:
use the area of a circle formula:
[tex]A=\pi r^2[/tex]
Insert the radius:
[tex]A=\pi *50^2[/tex]
Simplify exponents:
[tex]A=\pi *2500[/tex]
Simplify pi:
[tex]A=3.14*2500\\A=7850[/tex]
Option C is the closest to 7850.
Finito.
If (x, y) is a solution to the system of equations, what is the value of x?
5
2
x + y = 2
x +
2
3
y = 4
A) 4
B) -4
C) 12
D) -12
Answer:
B) -4
Step-by-step explanation:
(5/2)x + y = 2
x + (2/3)y = 4
y = 2 - (5/2)x
x + (2/3)(2 - (5/2)x) = 4
x + 4/3 - (5/3)x = 4
(-2/3)x = 8/3
-2x = 8
x = -4
Solve the equation 264 = 2(x+26)
You purchased a car for $23,000 and can expect the car to depreciate at an average annual rate of 9%. What will the value of your care be 6 years after purchasing it
Answer:
$13,060.99
Step-by-step explanation:
We can use the following formula to solve:
[tex]A=P(1-r)^t[/tex]
P = principal value
r = rate (decimal)
t = time (years)
First, change 9% into a decimal:
9% -> [tex]\frac{9}{100}[/tex] -> 0.09
Now, just plug the values into the equation:
[tex]A=23,000(1-0.09)^6[/tex]
[tex]A=13,060.99[/tex]
The value of the car after 6 years will be $13,060.99
How to solve a quadrilateral
Answer:
You give it a nudge and it solves itself.
Step-by-step explanation:
Answer: Here is an example.
Step-by-step explanation:
Given: parallelogram ABCD, sides as marked.
Find AD.
Solution: 6x - 10 = 3x + 5 (opposite sides)
3x - 10 = 5; 3x = 15; x = 5
AD = 4x - 5 = 4(5) - 5 = 15
Remember:
• This is where the properties of a parallelogram are needed. You know the opposite sides of a parallelogram are congruent, so set the opposite sides equal to one another.
• Be sure to pair up the opposite sides correctly. The side labeled 4x - 5 will not be used when solving for x, but will be used to solve for AD.