Let [tex]y = F^{-1}(x)[/tex] and [tex]F(y) = x[/tex]
[tex]4y^2 - 1 = x\\4y^2 = x + 1\\y^2 = \frac{x + 1}{4}\\y = \sqrt{\frac{x + 1}{4}}\\f^{-1} = \sqrt{\frac{x + 1}{4}}[/tex]
an ant has fallen into a bottle 60cm deep and is climbing up 8 cm everyday. As it is exhausted, the ant is slipping down 4cm every night. Then how long would it take teh ant to escape from the bottle
Answer:
It took 13 days and a half to escape
Step-by-step explanation:
This is a classic problem where the first answer that comes to one's mind is not the correct answer.
The ant climbs up 8 cm per day and slips down 4 cm every night. It means the real distance the ant goes up is 8 - 4 = 4 cm per day. Since the total distance is 60 cm, it could lead us to think the time needed to escape from the bottle is 60/4=15 days. This is wrong, as we'll prove below.
Assume the last day, the ant climbs up the final 8 cm and escapes. We don't know yet when, but we can assure that day the ant was at a height of 60 - 8 = 52 cm.
That 52 cm was the result of the 4 cm per day the ant effectively went up, thus it needed 52/4=13 days to reach that height.
At 13 days, the ant was at 52 cm, the day 14 it climbed up the final 8 cm and escaped.
Answer: It took 13 days and a half to escape
Find the 60th term of the arithmetic sequence -27, -24, -21, ...
which of these go with each other?
Write an equivalent expression for (2m+3)(m-1).
After paying 6 dollars for the pie, Melanie has 99 dollars left. How much money did she have before buying the pie ?
Answer:
105
Step-by-step explanation:
Answer:
$105
Step-by-step explanation:
x-6=99
x=105
QUESTION 9 of 10: You are considering leasing a store site that has 1,800 square feet. The landlord is asking for rent of $55 per square foot per year. How much is the rent per month?
a) $8,000
b) $8,250
c) $8,500
d) $8,750
Answer: $8,250
Step-by-step explanation:
just did the quiz
HELP DUE TODAY! Determine if the problem is done correctly AND explain your reasoning. If the problem is correct then explain the steps that were taken. If the problem is incorrect then explain what the mistake made was and what the correct solution should be.
Multiply the polynomials using the distribution method: (2x – 3)(4x + 8)
Line 2 is correct because of the distribution rule. You multiply each outer term by the inner terms in the parenthesis.
2x(4x+8) = 2x*4x + 2x*8 = 8x^2+16x
-3*(4x+8) = -3*4x-3*8 = -12x-24
---------------------------------------------------------------------------------------------
Line 3 is correct as well. The 16x and -12x combine to 4x. You can think of it like 16-12 = 4, then just tack x's onto everything getting 16x-12x = 4x
Or you can think of it like "16 boxes - 12 boxes = 4 boxes" and you replace "boxes" with "x" for shorthand.
The other terms aren't like terms so we just leave them as is.
plz plz plz, help me :(
Answer:
b = 3 in
Step-by-step explanation:
The area (A) of a rectangle is
A = lb ( l is the length and b the breadth )
Here A = 24, l = 4 and breadth = b + 3 , thus
4(b + 3) = 24 ( divide both sides by 4 )
b + 3 = 6 ( subtract 3 from both sides )
b = 3
Thus the width of the message is 3 in
When multiplying or dividing both sides of an inequality by a negative number, you need to remember to "flip" the inequality sign.
True or False
That is a true statement
Step-by-step explanation:
true................
to the nearest tenth of a unit, what is the distance on a coordinate plane between the points (-6, -9) and (5, 7)? Answer needs to be in units
Answer: 20 units
Step-by-step explanation:
Answer:
20 units
distance formula is (x-x2)^2 + (y-y2)^2 all under a square root.
The number of days each licensed driver in Marion County uses a commuter rail line annually is normally distributed with mean 66 and standard deviation 21. How many days must a driver use a commuter rail line annually to be in the top 5% of rail users? Round to the nearest integer.
Answer:
31.5 days
Step-by-step explanation:
We.solve using z score formula
z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
The 5th percentile z score = -1.645
Mean = 66
Standard deviation = 21
Hence:
-1.645 = x - 66/21
-1.645 × 21 = x - 66
-34.545 = x - 66
-34.545 + 66 = x
x = 31.455 days
Approximately to the nearest round integer
= 31.5 days
Therefore, driver use a commuter rail line 31.5 days annually to be in the top 5% of rail users
Which steps can be used in order to determine the solution to Negative 1.3 + 4.6 x = 0.3 + 4 x? Subtract 1.3 from both sides of the equation, add 4x to both sides of the equation, then divide by the coefficient of x. Subtract 1.3 from both sides of the equation, subtract 4.6x from both sides of the equation, then divide both sides by the coefficient of x. Add 1.3 to both sides of the equation, subtract 4.6x from both sides of the equation, then divide both sides by the coefficient of x. Add 1.3 to both sides of the equation, subtract 4x from both sides of the equation, then divide both sides by the coefficient of x.
Answer:
its D
Step-by-step explanation:
got it correct on a test :)
The correct option is Option D: Adding 1.3 to both sides of the equation, subtracting 4x from both sides of the equation, then dividing both sides by the coefficient of x.
What is the linear equation?The linear equation is an equation where the highest degree of the variables used in the equation is 1.
For example 9x+5=23
Given the equation is -1.3 +4.6x= 0.3+ 4x
In order to the linear equation first, try to keep the constant and the variable part to one side by adding or subtracting the constant term.
Then divide the coefficient of the variable (if the coefficient is not equal to 1) on both sides.
Here the given equation is -1.3 +4.6x= 0.3+ 4x
Step-1: Adding 1.3 to both sides of the equation
⇒-1.3 +4.6x +1.3 = 0.3+ 4x +1.3
⇒4.6x = 4x+1.6
Step-2: subtracting 4x from both sides of the equation
⇒4.6x -4x = 4x+1.6-4x
⇒ 0.6x=1.6
Step-3: dividing both sides by the coefficient of x i.e. 0.6.
⇒0.6x/0.6 = 1.6/0.6
⇒x= 2.67
Therefore the correct option is Option D: Adding 1.3 to both sides of the equation, subtracting 4x from both sides of the equation, then dividing both sides by the coefficient of x.
Learn more about linear equation
here: https://brainly.com/question/13728326
#SPJ2
which of the following are valid for the triangle below? check all that apply A.) TAY B.)AXM C.) MAY D.) XMA E.) XMT F.) MAX
Answer:
B) XMA; C) MAX; and D) AXM
Step-by-step explanation:
A triangle is named based on its vertices. The vertices of this angle are A, M and X; this means any combination of these three letters can be used to name the triangle.
Find the slop of this linear equation y=3x -4
Answer:
3
Step-by-step explanation:
The equation [ y = 3x - 4 ] is written in slope-intercept form [ y = mx + b ].
m = slope
b = y-intercept
The variable "m" in the given equation is 3, thus makes it the slope.
Best of Luck!
Find the area and perimeter of a rectangle if
the length is 25 and the width is 8.
Answer:
area is 200 perimeter is 66
Step-by-step explanation:
Which student correctly solved their equation below?
The water level in a lake decreased by 2 1/4 inches in march and increased by 1 5/8 inches in april. Determine wether the water level increased or decreased and by how much 1. Increased by 3/8 2. Increased by 5/8 3. Increased by 5/8 4. Decreased by 5/8
Change in level is given by :
C = increase in level - decrease in level.
Now,
Decrease in level in March is 2 1/4 = 9/4 inches.
Increase in level in April is 1 5/8 = 13/8 inches.
Putting value of these in above equation, we get :
C = 13/8 - 9/4
C = 13/8 - 18/8
C = -5/8 inches
Therefore, the overall level after April will decrease by 5/8 inches.
Hence, option 4. is correct.
In Python, equations are not evaluated by following the standard order of operations when performing calculations. true or false?
Answer:
false
Step-by-step explanation:
Answer:
[tex]false.[/tex]
Step-by-step explanation:
[tex]python \: programming \: language \: is \: powerful \\ \: scientific \: coding \: language \: for \: both \\ \:high \: level \: programs \: and \: also \: for \: learners\\ its \: very \: fast \: in \: scientific \: and \: mathematical \: calculation. \\ \: for \: me \: i \: think \: python..... if \: not \: the \: best....is \: very \: easy \: to \: learn \\ [/tex]
On Saturday, 32,736 more movie tickets were sold than on
Sunday. On Sunday, only 17,295 tickets were sold.
How many people bought movie tickets over the weekend?
20 POINTS
I NEED HELP WITH THIS PLZZ HELP ME!!
Answer:
I think A
Step-by-step explanation:
Because if you change it from (43 + 60) + 40 to (60 + 40) + 43 = 143
You automatically know it is 143 because 60 + 40 is 100 + 43 = 143
And it wouldn't be D because that is already in a easy way the solve. The others looked to complicated to even attempt so it has to be A.
Did this help!!??
A Vitamin C tablet contains 1/40 of a gram of Vitamin C. You take 1 1/2 tablets every day. How many grams of vitamin C do do you take every day?
Answer:
0.0375 gram of Vitamin C
Step-by-step explanation:
Hi there !
1 1/2 tablets = (1*2 + 1)/2 = 3/2 tablets every day
How many grams of vitamin C do do you take every day?
1/40 × 3/2 = 3/80 = 0.0375 gram of Vitamin C
Good luck !
What is itttttttttttt
Answer:the second one
Step-by-step explanation:
just trust me i can't explain it on a pc
it costs $24,893.75 to repay a loan of 17,500 at 6.5% annual interest. How many years does it take to repay the loan? I saw somebody asked this question, but the answer wasn't specific.
Answer:
11.5 years
Step-by-step explanation:
The formula for the monthly payment of a loan is:
[tex] A = P\dfrac{r(1 + r)^n}{(1 + r)^n - 1} [/tex]
where
A = monthly payment
r = interest rate per period
n = number of periods
Assuming a monthly payment, we have
P = 17500
r = 0.065/12
The total amount of payments is the monthly payment times the number of payments, so
An = 24893.75
We can try 10 years. n = 10 * 12 = 120
[tex] A = 17500\dfrac{\frac{0.065}{12}(1 + \frac{0.065}{12})^{120}}{(1 + \frac{0.065}{12})^{120} - 1} = 198.71 [/tex]
An = 198.71 * 120 = 23845.08
The total amount of payments is too low.
Let's try 11 years.
n = 11 * 12 = 132
[tex] A = 17500\dfrac{\frac{0.065}{12}(1 + \frac{0.065}{12})^{132}}{(1 + \frac{0.065}{12})^{132} - 1} = 185.92 [/tex]
An = 185.92 * 132 = 24540.90
The total amount of payments is still too low.
Let's try 12 years.
n = 12 * 12 = 144
[tex] A = 17500\dfrac{\frac{0.065}{12}(1 + \frac{0.065}{12})^{144}}{(1 + \frac{0.065}{12})^{144} - 1} = 175.34 [/tex]
An = 185.92 * 144 = 25248.41
The total amount of payments is too high.
11 years is too little, and 12 years is too much.
Let's try 11.5 years.
n = 11.5 * 12 = 138
[tex] A = 17500\dfrac{\frac{0.065}{12}(1 + \frac{0.065}{12})^{138}}{(1 + \frac{0.065}{12})^{138} - 1} = 180.39 [/tex]
An = 180.39 * 138 = 24893.20
11.5 gives a total of payments of $24,893.20 which is very close to $23.893.75.
Answer: 11.5 years
The total amount of payments is too high.
Which pair of circles have equivalent areas shaded?
Answer:
A
Step-by-step explanation:
They both have 2 areas shaded, have the same amount of parts and are the same size
Slope = -1; y-intercept = 7
Written in slope intercept form
Answer:
Find the Equation of a Line Given That You Know Its Slope and Y-Intercept. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know the slope (m) any y-intercept (b) of a line, this page will show you how to find the equation of the line.
Step-by-step explanation:
9514 1404 393
Answer:
y = -x +7
Step-by-step explanation:
The slope-intercept form of the equation for a line is ...
y = mx +b
where m is the slope and b is the y-intercept.
Put the given values in the corresponding places:
y = (-1)x +7
y = -x +7
HELP!!!!!!
Which of the following is a true statement?
4/5 x 4/5=1
3/10 ÷ 7/9=3/10 x 9/7
9/12 x 12/9= 0
1/2 ÷1/2= 1/4
Answer:
3/10 ÷ 7/9=3/10 x 9/7 is the true one
Step-by-step explanation:
4/5 x 4/5 = 16/25 not 1 so this statement is wrong.
3/10 ÷ 7/9=3/10 x 9/7, this is the true statement and it equals 27/70
9/12 x 12/9= 1 not 0
1/2 ÷1/2= 1 not 1/4
Johnny's electric bill is a variable expense. What is the average amount he pays for electricity If he paid $235 in December, $119 in January, $109 in February, $1 22 in March and $135 in April?
PLEASE HELP!!!!!!!!!!!!! Solve for the following question. SHOW ALL STEPS! 8x-6/2=x+12
Answer: 15/7
Step-by-step explanation: Simplify 6/2 to 3
8x-3=x+12
Add 3 to both sides
8x=x+15
Subtract x from both sides
7x=15
Divide both sides by 7
x=15/7
Answer:
x = 2.14
Step-by-step explanation:
8x - 3 = x + 12 (6/2 = 3)
7x - 3 = 12 (subtracted 1x from both sides)
7x = 15 (added 3 to both sides)
x = 2.14 (divided 15 by 7)
Hope this helps :)
I need help, please I have until 9 p.m. to finish it number 3 homework
Answer: 1/3
Step-by-step explanation:
When adding or subtracting fractions, they must have the same denominator.
[tex]\dfrac{5}{9}-\boxed{\dfrac{?}{?}}=\dfrac{12}{54}\\\\\\\dfrac{5}{9}\bigg(\dfrac{6}{6}\bigg)-\boxed{\dfrac{?}{?}}=\dfrac{12}{54}\\\\\\\dfrac{30}{54}-\boxed{\dfrac{?}{?}}=\dfrac{12}{54}\\\\\\\dfrac{30}{54}-\boxed{\dfrac{18}{54}}=\dfrac{12}{54}\\\\\\\text{Simplify}\quad \dfrac{18}{54}\div \dfrac{18}{18}\quad =\large\boxed{\dfrac{1}{3}}[/tex]
I need help please
ew=p ,solve for e
Answer:
e=p/w
Step-by-step explanation:
Take w and move it to the left by dividing both sides by w to get the answer