Answer: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]
Step-by-step explanation:
[tex]f(x)=10x^{3}\\y=10x^{3}[/tex]
switch the x and y:
[tex]x=10y^{3}[/tex]
Now solve for y:
[tex]x=10y^{3} \\\frac{x}{10} =y^{3} \\\sqrt[3]{\frac{x}{10} } =y\\[/tex]
Therefore, the inverse of that function is: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]
Please help no links.Mr. Longley is buying a $15 box of trail mix at Whole Foods, where tax is 6%. If Mr. Longley has
a coupon for 10% off the price of any item, how much does he end up paying?
I
Answer:
$14.40
Step-by-step explanation:
my way of doing things:
15/100=0.15=1%of total amount
0.15 x 6=0.9= the 6% which is the tax
0.15 x 10 = 1.5=the coupon
Take the coupon amount $1.50 minus the tax amount $0.90 =$0.60. Because the coupon amount is greater than the tax the 60 cents gets taken away from the original 15 dollars leaving Mr. Longely only having to pay $14.40.
2065 Q.No. 2 a A firm produced 100 calculator sets during its first year. The total number of calculator sets produced at the end of five years is 4,500. Assume that the production increases uniformly each year. Estimate the increase in production each year. [3] Ans: 400
Answer:
400
Step-by-step explanation:
First, the firm produces 100 sets its first year. This means that our equation starts at 100. Next, the total number of calculator sets in 5 years is 4500. With y₁ representing the amount of calculator sets produced during year 1, y₂ representing the amount of sets during year 2, and so on, we can say that
y₁+y₂+y₃+y₄+y₅ = 4500
100 + y₂+y₃+y₄+y₅ = 4500
Next, we are given that the production increases uniformly by an amount each year. Representing that amount as a, we can say that
y₁+a = y₂
y₂+a = y₃
y₁+a+a = y₃
y₁+ 2 * a = y₃
and so on, so we have
100 + y₂+y₃+y₄+y₅ = 4500
100 + (100+a) + (100+2a) + (100+3a) + (100+4a) = 4500
500 + 10a = 4500
subtract 500 from both sides to isolate the a and its coefficient
4000 = 10a
divide both sides by 15 to isolate a
a = 400
trigonometric identities
Without knowing what Juan's exact steps were, it's hard to say what he did wrong. The least you could say is that his solution is simply not correct.
4 sin²(θ) - 1 = 0
==> sin²(θ) = 1/4
==> sin(θ) = ±1/√2
==> θ = π/4, 3π/4, 5π/4, 7π/4
Write the degree of [tex] {x}^{2} + 2x + 3 {x}^{5} + 4 {x}^{3} + 9[/tex].
Answer:-
5
Explanation:-The highest degree included in the polynomial is known as degree of polynomial
[tex]\sf \checkmark[/tex] Polynomial with degree 1=monomial
[tex]\sf \checkmark[/tex] Polynomial with degree 2 =binomial
[tex]\sf \checkmark[/tex] Polynomial with degree 3=Trinomial
if logx27 + logy4 =5
and logx27 - logy4 =1
find x and y
Answer:
Hello,
I have reply too quick in comments (sorry)
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}log_x (27)+log_y (4)=5\\log_x (27)-log_y (4)=1\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}2*log_x (27)=6\\2*log_y (4)=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}log_x (27)=3\\log_y (4)=2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x^{log_x (27)}=x^3\\y^{log_y (4)}=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}27=x^3\\4=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x=3\\y=2\\\end{array}\right.\\\\[/tex]
An empty freight train traveled 60 miles from an auto assembly plant to an oil refinery. There, its tank cars were filled with petroleum products, and it returned on the same route to the plant. The total travel time for the train was 4 1 2 hours. If the train traveled 20 mph slower with the tank cars full, how fast did the train travel in each direction
Answer:
On the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.
Step-by-step explanation:
Since an empty freight train traveled 60 miles from an auto assembly plant to an oil refinery, and there, its tank cars were filled with petroleum products, and it returned on the same route to the plant, and the total travel time for the train was 4.5 hours, if the train traveled 20 mph slower with the tank cars full, to determine how fast did the train travel in each direction the following calculation must be performed:
60/20 = 3
60/40 = 1.5
60/20 = 3
3 + 1.5 = 4.5
Therefore, on the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.
first person to coment on this gets a brainliest
Answer:
..?.
Step-by-step explanation:
Kelly said that 97/1000 can be written as 0.97 is correct? Explain.
Answer:
No
97/1000 is the same as 97 divided by 1000
the decimal would be .097, not .97
What is the area of the polygon given below?
Answer:
diện tích đa giác trong hình là :
186 cm2
Step-by-step explanation:
hãy tách hình đa giác trên thành 4 hình chữ nhật và tính diện tích từng hình chữ nhật
use different method of depreciation for each of the assests and explain why u used the method (ex : straight line method, double declining method, unit of production method)
Step-by-step explanation:
sorry but I don't know this answerI need help answering this question
Answer:
the correct answer is B) 10 + 10 + x = 50
Is 43,093 less than 43,903
Answer: yes
Step-by-step explanation:
43093 is less than 43903
If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as
V=5000 (1-1/50*t)^2 0⤠t ⤠50.
1. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)
a. 5 min
b. 10 min
c. 20 min
d. 50 min
2. At what time is the water flowing out the fastest?
3. At what time is the water flowing out the slowest?
Answer: hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation
answer:
1) a) -180 gallons/minute ,
b) -160 gallons/minute
c) -120 gallons/minute
d) 0
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins
Step-by-step explanation:
Volume of tank = 5000 gallons
Time to drain = 50 minutes
Volume of water remaining after t minutes by Torricelli's law
V = 5000 ( 1 - [tex]\frac{1}{50}t[/tex] )^2 ----- ( 1 )
1) Determine the rate at which water is draining from the tank
First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank
V' = [tex]-10000[ ( 1 - \frac{1}{50}t ) (\frac{1}{50}) ][/tex]
a) After t = 5minutes
V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]
= -180 gallons/minute
b) After t = 10 minutes
V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]
= - 160 gallons/minute
c) After t = 20 minutes
V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]
= -120 gallons/minute
d) After t = 50 minutes
V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]
= 0 gallons/minute
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins because no water flows out after 50 minutes
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. Use the equation P(AUB)=P(A) + P(B) - P(ANB), where A and B are any events, to compute the probability that the number drawn is prime or greater than 12.
The probability that the number drawn is prime or greater than 12 is : ___________
Answer:
17/25
Step-by-step explanation:
The equation for the probability of two events that are not mutually exclusive is:
p(A ∨ B) = p(A) + p(B) - p(A ∧ B)
A = the number is prime
B = the number is prime
The numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Here are the 8 prime numbers that satisfy event A:
3, 5, 7, 11, 13, 17, 19, 23
p(A) = 8/25
Here are the 13 numbers that are greater than 12 that satisfy event B:
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
p(B) = 13/25
Here are the 4 numbers that satisfy both event A and event B:
13, 17, 19, 23
p(A ∧ B) = 4/25
p(A ∨ B) = p(A) + p(B) - p(A ∧ B)
p(A ∨ B) = 8/25 + 13/25 - 4/25
p(A ∨ B) = 17/25
The probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
For given question,
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25.
n(S) = 25
Let event A: the number drawn is prime
The prime numbers from 1 to 25 are:
2, 3, 5, 7, 11, 13, 17, 19, 23
So, n(A) = 9
The probability that the number drawn is prime,
[tex]P(A)=\frac{n(A)}{n(S)}\\\\ P(A)=\frac{9}{25}[/tex]
Let event B: the number drawn is greater than 12
So, n(B) = 13
The probability that the number drawn is greater than 12,
[tex]P(B)=\frac{n(B)}{n(S)}\\\\ P(B)=\frac{13}{25}[/tex]
The number drawn is prime as well as greater than 12.
Such numbers are : 13, 17, 19, 23
n(A ∩ B) = 4
So, the probability that the number drawn is prime as well as greater than 12,
[tex]P(A\cap B)=\frac{n(A\cap B)}{n(s)}\\\\ P(A\cap B)=\frac{4}{25}[/tex]
Using the equation P(AUB) = P(A) + P(B) - P(A ∩ B) to find the probability that the number drawn is prime or greater than 12,
[tex]\Rightarrow P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow P(A\cup B)=\frac{9}{25}+ \frac{13}{25} -\frac{4}{25} \\\\\Rightarrow P(A\cup B)=\frac{9+13-4}{25}\\\\ \Rightarrow P(A\cup B)=\frac{18}{25}[/tex]
Therefore, the probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
Please help I need the answer ASAP!!
The hypotenuse will always be the longest side of the triangle. Option C is correct: AB > DC.
AB is the hypotenuse of triangle ABC. Therefore, it is greater than leg AC. AC is the hypotenuse of triangle ACD. If AC is less than AB, then DC must also be less than AB because DC is less than AC.
Hope this helps!
Find the volume of the figure round your answer to the nearest tenth if necessary
Answer:
56.5
I think this is right
Does the point (7,34) satisfy the equation y = 2x + 8
Answer:
no
Step-by-step explanation:
Substitute the point into the equation and see if it is true
34 = 2(7) +8
34 = 14+8
34 = 22
Since this is not true, the point does not satisfy the equation
Answer:
No
Step-by-step explanation:
because 7 is X and 34 is Y
So its 2 *7 +8=22
so no
Suppose the following data represent the ratings (on a scale from 1 to 5) for a certain smart phone game, with 1 representing a poor rating. The discrete probability distribution for the random variable x is given below:
Star Frequency
1 2140
2 2853
3 4734
4 4880
5 10,715
Required:
Construct a discrete probability distribution for the random variable X
Answer:
[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]
Step-by-step explanation:
Given
The above table
Required
The discrete probability distribution
The probability of each is calculated as:
[tex]Pr = \frac{Frequency}{Total}[/tex]
Where:
[tex]Total = 2140+ 2853 + 4734 + 4880 + 10715[/tex]
[tex]Total = 25322[/tex]
So, we have:
[tex]P(1) = \frac{2140}{25322} = 0.0845[/tex]
[tex]P(2) = \frac{2853}{25322} = 0.1127[/tex]
[tex]P(3) = \frac{4734}{25322} = 0.1870[/tex]
[tex]P(4) = \frac{4880}{25322} = 0.1927[/tex]
[tex]P(5) = \frac{10715}{25322} = 0.4231[/tex]
So, the discrete probability distribution is:
[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]
Evaluate u + xy, if u = 18, x = 10, and y = 8.
Hi there!
[tex]\large\boxed{u + xy = 98}[/tex]
We can do substitution to solve.
We are given the values of all of the letters, so:
u = 18
x = 10
y = 8
Substitute:
(18) + (10)(8)
Use the order of operations:
18 + 80 = 98
Step-by-step explanation:
u + xy
make u = 18
x = 10
y = 8
18 + 10 × 8
18 + 80
= 98
I hope this answers your question
Help !!!!!!!!!!!!!!!
Answer:
9/4 = 2 1/4
Hope this Helps!?
Find the product and simplify your answer 6w(5w^2-5w+5)
In how many different ways can the letter of word
CORPORATION" be
arranged. So that the vowel always
come together"
Answer:
= 6 ways = Required number of ways = (120×6)=720
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
The zeros of the polynomial 3x^4 - 5x^3 - 62x^2 - 92x - 24 are x = {-2, -1/3, 6}. Determine the intervals where the value of f(x) is a negative value. Check all that apply.
a. -∞ < x < -2
b. -2 < x < -1/3
c. -1/3 < x < 6
d. 6 < x < ∞
Answer:
c. -1/3 < x < 6Step-by-step explanation:
There are 3 zero's but we see the polynomial is of degree 4.
It means it has 2 same zero's. We can verify it is -2. Since -2 is doubled, it reflects the local minimum and it is on the x-axis.
In reality we need to consider the other two zero's.
It is obvious the negative interval is between -1/3 and 6 since the polynomial is of even degree and has positive leading coefficient.
Correct choice is c.
The graph is attached to confirm the theory.
3(8a - 5b) – 2(a + b); use a = 3 and b = 2
Answer:
32
Step-by-step explanation:
3(8(3)-5(2))-2((3)+(2))
3(24-10) -2(5)
3(14) -10
42-10
32
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{3(8a - 5b) - 2(a + b)}\\\\\huge\textsf{= 3(8(3) - 5(2)) - 2(3 + 2)}\\\\\huge\textsf{= 3(24 - 10) - 2(3 + 2)}\\\\\huge\textsf{= (3)(14) - 2(3 + 2)}\\\\\huge\textsf{= 42 - 2(3 + 2)}\\\\\huge\textsf{= 42 - 2(5)}\\\\\huge\textsf{= 42 - 10}\\\\\huge\textsf{= 32}}[/tex]
[tex]\huge\boxed{\textsf{Answer: 32}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
Please help——- Geometry problem
Thank you.
Answer:
b
Step-by-step explanation:
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{s\sqrt{3} }{2s}[/tex] ( cancel s on numerator/ denominator ), then
sinA = [tex]\frac{\sqrt{3} }{2}[/tex] → b
If f(x) = 5x squared -3 and g(x) = x squared - 4x -8, find (f-g)(x)
Answer:
[tex]4x^2+4x+5[/tex]
Step-by-step explanation:
[tex]f(x)=5x^2-3\\g(x)=x^2-4x-8[/tex]
Set up an expression.
[tex]5x^2-3-(x^2-4x-8)[/tex]
Distribute the negative (-1)
[tex]5x^2-3-x^2+4x+8[/tex]
Solve / Simplify
[tex]4x^2+4x+5[/tex]
I'm late, but I hope this helps!
A circular water fountain in the town square has a 112-foot circumference. How far is the center of the fountain from the outer edge? Round to the nearest whole number.
Answer:
18 feet
Step-by-step explanation:
The distance of the center of the fountain from the enter edge is equal to the radius of the circular fountain.
Use the circumference formula, c = 2[tex]\pi[/tex]r, to find the radius.
c = 2[tex]\pi[/tex]r
112 = 2[tex]\pi[/tex]r
18 = r
So, to the nearest whole number, the distance between the center of the fountain and outer edge is 18 feet.
Simplify the following by removing parentheses and combining terms
- (2x + 8) + 3(2x + 8) - 2x
Answer:
2x+16
Step-by-step explanation:
PEMDAS
what principle will amount to Rs. 4000 in 20 yrs at 2.5%?
Answer:
3200Step-by-step explanation:
Consider principle =Rs.P, Time (T)=4 years
Consider principle =Rs.P, Time (T)=4 yearsRate =6
Consider principle =Rs.P, Time (T)=4 yearsRate =6 4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 =
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest =
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R =
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P×
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 =
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P =
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P =
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P = 4
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P = 45P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P = 45P
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P = 45P =4000
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P = 45P =40005P=4×4000
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P = 45P =40005P=4×4000P=Rs.3200
Consider principle =Rs.P, Time (T)=4 yearsRate =6 41 = 425 %Simple interest = 100P×T×R = 100P× 425 ×4 = 4P =∴ Amount =P+ 4P = 45P = 45P =40005P=4×4000P=Rs.3200Therefore, Principle =Rs.3200
Which expression is the best estimate of the product of 7/8and 8 1/10?
Answer:
7 7/80 or 7.0875
Step-by-step explanation:
product is the result of multiplication
7/8 * 81/10 = 567/80 = 7 7/80 or 7.0875
