Answers
Most folks like to eliminate fractions first. To do that, you can multiply by 12.
9(x -3) < 4(x -4)
Now, eliminate parentheses.
9x -27 < 4x -16
Subtract 4x to put the variable on one side only. Add 27 to put the constant on the other side only.
5x < 11
Divide by the coefficient of x to get x by itself.
x < 11/5
39. You can actually work these without eliminating fractions. Just do the arithmetic in the usual way.
Eliminate parentheses.
(2/5)(3 -2n) ≥ (3/8)(2 -3n)
6/5 -(4/5)n ≥ 3/4 -(9/8)n
Add (9/8)n -6/5
n(9/8 -4/5) ≥ 3/4 -6/5
(13/40)n ≥ -9/20
Multiply by the inverse of the coefficient of n
n ≥ (-9/20)*(40/13)
n ≥ -18/13
Related Questions
If the rules for the lottery game powerball required participants to choose 5 unique numbers (ranging from 1 to 59) in any order along with one "powerball" (ranging from 1 to 35), what is the probability of winning the jackpot under these game rules?
Answers
5,006,386 x 35 = 175,223,510
probability 1: 175,223,510
To calculate the probability of winning the Powerball, you need to identify all possible combinations for drawing 5 unique numbers from a set of 59, then multiply that with the separate 35 options for the 'powerball'. Your chance of winning equals one (the exact match to your ticket) divided by the total possible combinations.
Explanation:The probability of winning the Powerball jackpot can be determined using the concept of combination in probability theory. Probabilities are calculated by taking the total number of successful outcomes or combinations and dividing it by the total number of possible outcomes or combinations.
In the case of Powerball, there are 5 unique numbers to be drawn from a pool of 59 (ignoring order), and 1 'powerball' from a pool of 35. For the 5 unique numbers, there are C(59,5) combinations where C(n,r) = n! / [r!(n-r)!], n being the total number of options available and r being the number of options chosen at a time.
For the 'powerball', since it is a separate pool of 35 numbers and only 1 is chosen, the number of combinations is simply 35. As such, you multiply the two outcomes for total possible combinations: C(59,5)*35.
For the probability of winning, you want to know combinations that match exactly your selection, of which there is only one. Therefore the probability is 1 / [C(59,5)*35], resulting in extremely low chances of winning.
Learn more about Powerball Probability here:
https://brainly.com/question/33176496
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Solve log2 ( x - 1 ) + log2 ( x + 1 ) = 3
check answers are in domain
Answers
For ΔABC, the measure in degrees of angles A, B, and C are 60, 55, and x + 20 respectively. What is the value of x?
Answers
135 + x = 180
x = 180 - 135 = 45 degrees Answer.
Answer:
45
Step-by-step explanation:
60 + 55 + x + 20 = 180
135 + x = 180
x = 180 - 135 = 45
Answer: 45
1/3 equivalent first 2 fractions
Answers
1/3 is equivalent to 2/6
Here is why:
1 x 2 = 2
3 x 2 = 6
You can do this by cross multiplying 1/3 and 2/6
That's how you get 2/6 as an equivalent fraction.
1/3 is also equivalent to 3/9
Here is why:
3 x 1 = 3
3 x 3 =9
You can also do this by cross multiplying 1/3 and 3/9
That's how you get 3/9 as an equivalent fraction.
There are also many other fractions that are equal to 1/3, but these are the first two.
Hope this helps you.
Have a great day!
Please help with the question. For some reason, I find it confusing and I need some assisstance. Thank you!
Answers
C=4x5+2.
C=20+2
C=22
You need 22 chairs.
Answer: i think it is 22
Step-by-step explanation:
Lydia drove 302 miles in 10 hours. on average, how fast did she drive in miles per hour? express your answer in simplest form.
Answers
Answer:
30.2 mph
Step-by-step explanation:
Hello, I think I can help you with this
the speed average is the is the quotient of the distance traveled and the time used to do it, mathematical speaking
[tex]Average\ speed =\frac{distance}{time}\\[/tex]
Step 1
Put the values into the equation
Let
Distance:302 miles
Time:10 hours
[tex]Average\ speed =\frac{distance}{time}\\\\Average\ speed =\frac{302\ miles}{10\ hours}\\Average\ speed =30.2 \frac{miles}{hour} \\[/tex]
Average speed=30.2 mph
Have a great day.
The circumference of a circle is 31.4 inches. What is the circle's diameter? C=31.4 in Use 3.14 for .
Answers
C = 2πr
31.4 = (2)(3.14)(r)
31.4 = 6.28r
5 = r
So our radius is 5 in.
We can multiply it by 2 to get the diameter.
5*2 = 10
So the diameter is 10 inches
this can be calc for a form
What is the area of this triangle?
Picture below, will give brainliest!!!! please help
can you give it to me in a decimal? Thank you
Answers
[tex]\text {Area = } \dfrac{1}{2} (3.2)(4.7)sin (62 \textdegree)[/tex]
[tex]\text {Area = } 6.64 \ yd^2[/tex]
The expression 52x – 169 is equivalent to 13
Answers
The length of a rectangle is 7 m less than triple the width. if w represents the width, write an expression for the length, l. question 13 options:
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what is the correct answer to this question?
a
b
c
d
Answers
.. from 275/6.58 = $41.79
.. to 275/6.25 = $44.00
which is a change of $2.21.
Based on each applicant’s median credit score, to which client is Rachel likely to offer the best interest rates? a. Leslie b. Pat c. Sam d. Alex
Answers
Just got this question in a practice test on Edge. The answer is definitely Alex, or D.
A pond is freshly stocked with 6 brown trout and 18 lake trout. The first fisherman in the area catches and releases a trout. He catches another trout a while later. What is the probability that the fisherman caught brown trout each time?
Answers
24÷6= 4 so probability of 1 out of 4. times 2 because he caught 2 fish. so then that would be 1 out of 8. :)
Evaluate. 134 × -7
A)-2,158
B)-828
C)-938
D)938
Answers
Because you are multiplying a positive and a negative your answer should be negative
Simplify (SecX-TanX)(1+sinX) X stands for theta
Answers
[tex]\bf [sec(\theta )-tan(\theta )][1+sin(\theta )]\implies \left[ \frac{1}{cos(\theta )}-\frac{sin(\theta )}{cos(\theta )} \right][1+sin(\theta )] \\\\\\\ \left[\frac{1-sin(\theta )}{cos(\theta )} \right][1+sin(\theta )]\implies \cfrac{\stackrel{\textit{difference of squares}}{[1-sin(\theta )][1+sin(\theta )]}}{cos(\theta )} \\\\\\ \cfrac{1^2-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )}\implies cos(\theta )[/tex]
hello, Can someone please help me with this math problem? thanks!
Answers
Nacir is buying school supplies. He purchases 8 notebooks for $12.48. How much does Nacir pay for 1 notebook?
Answers
Assume you have a poker chip set containing blue, red, and white chips, all of the same size. you place 15 blue chips, 10 red chips, and 25 white chips in a bag. as you are about to randomly draw a chip from the bag, you bet your friend you will pick a red chip from the bag because you feel that red is your lucky color.
Answers
Jean adds 35 and 9.how can she solve using only equations to model her thinking?
Answers
Hope this helps! ;)
Answer:
Step-by-step explanation: 35+(5+4)=35+5+4=40+4=44
is 7/8×6/6 greater then, equal to, or less than 7/8
Answers
6/6 simplified equals 1.
7/8 times 1 would equal 7/8.
Therefore, 7/8 times 6/6 is equal to 7/8.
Find a linear differential operator that annihilates the given function. (use d for the differential operator.) e−x + 8xex − x2ex
Answers
Explanation:
Let
[tex]f(x) = e^{-x} + 8xe^x - x^2 e^x[/tex].
[tex]d^n (f(x))[/tex] = nth derivative of f
Note that
[tex](d + 1) (e^{-x}) = d (e^{-x}) + e^{-x} = -e^{-x} + e^{-x} = 0 \\ \boxed{\Rightarrow (d + 1)e^{-x} = 0} [/tex]
So, (d + 1) annihilates [tex]e^{-x}[/tex].
Note that
[tex](d + 1) (8x e^x - x^2 e^x) = d(8x e^x - x^2 e^x) + (8x e^x - x^2 e^x) \\ = (8e^x + 8x e^x - 2x e^x - x^2 e^x) + (8x e^x - x^2 e^x) \\ \boxed{(d + 1) (8x e^x - x^2 e^x) = 8e^x + 14x e^x - x^2 e^x}[/tex]
Let [tex]g(x) = 8e^x + 14x e^x - x^2 e^x[/tex]
For any real number [tex]\alpha[/tex] and positive integer n,
[tex](d - \alpha)^n (c_1 e^{\alpha x} + c_2 xe^{\alpha x} + c_3 x^2 e^{\alpha x} + ... + c_n x^{n - 1} e^{\alpha x}) = 0 [/tex] (1)
So, for g(x), [tex]\alpha = 1, n = 3[/tex]. Thus, using equation (1),
[tex](d - 1)^3 (8e^x + 14x e^x - x^2 e^x) = 0[/tex] (2)
Since, [tex]8e^x + 14x e^x - x^2 e^x = (d + 1) (8x e^x - x^2 e^x)[/tex] ,
[tex](d - 1)^3 ((d + 1) (8x e^x - x^2 e^x)) = (d - 1)^3 (8e^x + 14x e^x - x^2 e^x) = 0[/tex]
Moreover, since [tex](d + 1) (e^{-x}) = 0[/tex]
[tex](d - 1)^3(d + 1) (e^{-x}) = (d - 1)^3 (0) [/tex]
[tex]\\ \boxed{(d - 1)^3(d + 1) (e^{-x}) = 0 }[/tex] (3)
Hence based on equations (2) and (3),
[tex](d - 1)^3(d + 1) (e^{-x} + 8xe^x - x^2e^x) \\ = (d - 1)^3(d + 1)(e^{-x}) + (d - 1)^3(d + 1)(8xe^x - x^2e^x) \\ = 0 + 0 \\ \boxed{(d - 1)^3(d + 1) (e^{-x} + 8xe^x - x^2e^x) = 0}[/tex]
Therefore, the linear operator [tex](d - 1)^3(d + 1)[/tex] annihilates [tex]e^{-x} + 8xe^x - x^2e^x[/tex].
To find the differential operator that annihilates the given function e^(-x) + 8xe^x - x^2e^x, we individually find differential operators for each term. The operators d^2, d^3, and d^4 annihilate e^(-x), 8xe^x, and x^2e^x respectively. The least common multiple of these operators is d^4, which is the common operator that annihilates the entire function.
Explanation:To find a linear differential operator that annihilates the function e−x + 8xex − x2ex, we must apply an operator that, when used on these functions, yields zero. For simplicity, we can use d to represent the differential operator d/dx. We annihilate each term independently and find a differential operator common to all terms.
Starting with the first term e−x, we note that d(e−x) = −e−x. Applying d again gives us d(d(e−x)) which is e−x. Thus, applying d2 annihilates e−x.
Annihilating 8xex and x2exNext, consider the second term 8xex. Applying the operator d3 to 8(xex) would be: d3(8xex) = d3(8(ex + xex))= d3(8ex) + d3(8xex) which results in zero.
For the third term x2ex, applying d4 annihilates the term, following the pattern: d4(x2ex) = d(d(d(d(x2ex)))) = 0.
The common differential operator that annihilates all three terms is the least common multiple of the individual operators for each term, in this case, d4.
delia spent 45 minutes working on her book report she finished at 6:10 p.m. at what time did delia start working on her paper
Answers
6:10 - 10 = 6:00
6:00 - 35 =5:25
When she finished the work, the time was 6:10 p.m. In other words, 6 hours and 10 minutes.
It says that she took 45 minutes to complete the work.
We need to find the time when she started working on it.
Start Time = Finish Time - time taken to complete work.
Start Time = (6 hours and 10 minutes) - 45 minutes
(Hint:- 1 hour = 60 minutes)
Start Time = (5 hours and 70 minutes) - 45 minutes
Start Time = 5 hours and 25 minutes i.e. 5:25 p.m.
It means that she started the work at 5:25 p.m.
write a whole number as a fraction the number 5
Answers
5/1, as 5 divided by 1 = 5
Hope this helps
Hope this helped!
The graph below shows the solution set to which system of inequalities?
Answers
using a graph tool
I proceed to verify each case to get the answer
see the attached figure
case A)
y> 2x-4 y>=-x y<=3
case B)
y> 2x-4 y>=-x y<3
case C)
y< 2x-4 y>=-x y<=3
the answer is the option A)
y> 2x-4 y>=-x y<=3
which of the following expressions is equivalent to the expression below ?
Answers
What is the approximate volume of the come 8cm and 12cm use 3.14 for pie
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A fleet of vehicles is comprised of 60 vans, 20 limos, and X sedans. If 10% of all vehicles are limos, how many sedans are in the fleet?
Answers
Answer:
120 sedans are in the fleet.
Step-by-step explanation:
A fleet of vehicles is comprised of 60 vans, 20 limos and X sedans.
It is given that 10% of all vehicles are limos.
Let all vehicles be n
10% × n = 20
0.10n = 20
n = [tex]\frac{20}{0.10}[/tex]
n = 200
Now we have to calculate the number of sedans.
So 60 vans + 20 limos + x sedans = 200
80 + x = 200
x = 200 - 80
x = 120
Therefore, 120 sedans are in the fleet.
Final answer:
By knowing that 10% of the fleet are limos and that there are 20 limos, we determine that the fleet has 200 vehicles. Subtracting the known number of vans and limos from the total, we find there are 120 sedans in the fleet.
Explanation:
To solve the problem, we need to determine the total number of vehicles in the fleet and use the information that 10% of all vehicles are limos. We know there are 60 vans and 20 limos already, and we want to find the number of sedans, denoted as X.
Since 10% of the vehicles are limos and there are 20 limos, that means there must be 200 vehicles in total (because 20 is 10% of 200).
So the equation to find the total number of vehicles is: 60 vans + 20 limos + X sedans = 200 vehicles. We already know that there are 60 vans and 20 limos, so we can say: 60 + 20 + X = 200. Solving for X, we subtract 60 and 20 from 200: X = 200 - 80 = 120.
Therefore, there are 120 sedans in the fleet.
a taxi ride costs $3 plus $2.50 per mile. write and graph an equation in two variables that represents the total cost of a taxi ride.
Answers
the 2 variables in the equation are as follows;
y = total cost of taxi ride
x = number of miles travelled per taxi ride
we need to write the equation in slope- intercept form
y = mx + c
m = gradient /slope
mx = cost per mile travelled x number of miles travelled
c= intercept. a fixed cost for every taxi ride
m = $2.50 per mile
c = $3
the graph equation is as follows;
y = 2.50x + 3
how much water do you add  to make 12% sugar syrup using 5g sugar?
Answers
so the syrup is just water and sugar, we know that the sugar percent is just 12%, and that happens to be 5grams.
now 100% - 12% is 88%, so the 88% leftover will just be water.
if 12% is 5g, how much is 88%?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 5&12\\ x&88 \end{array}\implies \cfrac{5}{x}=\cfrac{12}{88}\implies \cfrac{5}{x}=\cfrac{3}{22}\implies 110=3x \\\\\\ \cfrac{110}{3}=x\implies 36\frac{2}{3}=x[/tex]
Answer:
[tex]36\dfrac{2}{3}[/tex] g of water.
Step-by-step explanation:
You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then
5 g - 12%,
x+5 g - 100%.
Mathematically, you can write a proportion:
[tex]\dfrac{5}{x+5}=\dfrac{12}{100}\Rightarrow 500=12(x+5),\ 500=12x+60,\ 12x=440, \\ \\x=\dfrac{440}{12}=\dfrac{110}{3}=36\dfrac{2}{3}.[/tex]
if f(x) varies directly with x2, and f(x) = 96 when x = 4, find the value of f(6).
Answers
96=k(4)
k=24
f(x)=kx
f(6)=24(6)
f(6)=144