Answer:
See below.
Step-by-step explanation:
[tex]-2x+x=-x[/tex]
because we combine like terms. You will essentially ignore the x and just do -2 + 1, which is -1. So, the answer would be -1x which is simply just -x.
To see why we can combine like terms, use the distributive property. So we have:
[tex]-2x+x[/tex]
This is the same thing as saying:
[tex]=(-2)x+(1)x[/tex]
Factor out the x:
[tex]=x(-2+1)[/tex]
Add:
[tex]=x(-1)[/tex]
And simplify:
[tex]=-1x\\=-x[/tex]
Answer:
Step-by-step explanation:
-2x + x could also be written as x - 2x, which is x(1 - 2), or -x. Here we can rearrange the terms as we wish (commutative property).
If m/_a is 155º, what is m/_c?
Pls help ASAP
Angle Terminology with Equations
Answer:
∠ B = 54°
Step-by-step explanation:
Supplementary angles sum to 180°.
Sum A and B and equate to 180, that is
7x + 14 + 5x - 26 = 180, that is
12x - 12 = 180 ( add 12 to both sides )
12x = 192 ( divide both sides by 12 )
x = 16
Thus
∠ B = 5x - 26 = 5(16) - 26 = 80 - 26 = 54°
Round each number to three significant figures.a. 3.14159 b. 6.12356c. 4.56787
Answer:
The round off values are- 3.14, 6.12, and 4.57 respectively.
Step-by-step explanation:
The given value to which we have to round off is a. 3.14159 b. 6.12356 c. 4.56787
In order to round off the number we must keep in mind that there should be three digits in total and we will increase the value by one if the right-hand side value is more than 5.
Thus round off figure of 3.14159 is 3.14.
The round off figure of 6.12356 is 6.12.
The round off figure of 4.56787 is 4.57.
Let p be a prime number. The following exercises lead to a proof of Fermat's Little Theorem, which we prove by another method in the next chapter. a) For any integer k with 0 ≤ k ≤ p, let (p k) = p!/k!(p - k)! denote the binomial coefficient. Prove that (p k) 0 mod p if 1 ≤ k ≤ p - 1. b) Prove that for all integers x, y, (x + y)^p x^? + y^p mod p.c) Prove that for all integers x, x^p x mod p.
Hello,
a) We know the binomial coefficients are all integers, so
[tex]\dfrac{p!}{k!(p-k)!}[/tex]
is an integer.
And we can notice that the numerator p! is divisible by p.
If we take [tex]1\leq k\leq (p-1)[/tex]
It means that k! does not contain p, and we can say the same for (p-k)!
So, we have no p at the denominator so the binomial coefficient is divisible by p, meaning this is 0 modulo p.
b) We can write that
[tex]\displaystyle (x+y)^p=\sum_{i=0}^{p} \ {\dfrac{p!}{i!(p-i)!}x^{p-i}y^i[/tex]
We use the result from question a) and the binomial coefficients are 0 modulo p for i=1,2 , ... p-1 so there are only two terms left and then,
[tex](x+y)^p=x^p+y^p \text{ modulo p}[/tex]
c) Let's prove it by induction.
step 1 - for x = 0
This is trivial to notice that
[tex]0^p=0 \text{ modulo p}[/tex]
Step 2 - we assume that this is true for k
meaning [tex]k^p=k \text{ modulo p}[/tex]
and we need to prove that this is true for the k+1
We use the results of b)
[tex](k+1)^p=k^p+1^p=k^p+1 \text{ modulo p}[/tex]
and we use the induction hypothesis to say
[tex](k+1)^p=k^p+1^p=k^p+1=k+1 \text{ modulo p}[/tex]
And it means that this is true for k+1
Step 3 - conclusion
We have just proved by induction the Fermat's little theorem.
p a prime number, for for all x integers
[tex]\Large \boxed{\sf \bf x^p=x \textbf{ modulo p}}[/tex]
Thank you
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 33 mm and standard deviation 7.9 mm. (a) What is the probability that defect length is at most 20 mm
Answer:
0.49926
Step-by-step explanation:
We solve for this using z score formula
z-score is
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation
The probability that defect length is at most 20 mm is calculated as:
x = 20mm, μ = 33 mm, σ = 7.9mm
z = 20 - 33/7.9
= -13/7.9
= -1.64557
Obtaining the Probability value from Z-Table:
Probability (At most 20mm) = P(x ≤ 20mm) P(z = -1.64557)
P(x ≤ 20) = 0.049926
Therefore, the probability that defect length is at most 20 mm is 0.049926
Answer:
The probability that defect length is at most 20 mm is 0.0495.
Step-by-step explanation:
We are given that the defect length of a corrosion defect in a pressurized steel pipe is normally distributed with a mean value of 33 mm and a standard deviation of 7.9 mm.
Let X = the defect length of a corrosion defect in a pressurized steel pipe
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean defect length = 33 mm
[tex]\sigma[/tex] = standard deviation = 7.9 mm
So, X ~ Normal([tex]\mu=33 \text{ mm}, \sigma^{2} = 7.9^{2} \text{ mm}[/tex])
Now, the probability that defect length is at most 20 mm is given by = P(X [tex]\leq[/tex] 20 mm)
P(X [tex]\leq[/tex] 20 mm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{20-33}{7.9}[/tex] ) = P(Z [tex]\leq[/tex] -1.65) = 1 - P(Z < 1.65)
= 1 - 0.9505 = 0.0495
The above probability is calculated by looking at the value of x = 1.65 in the z table which has an area of 0.9505.
What is the solution of the equation below ?
Answer:
d = ±7i
Step-by-step explanation:
d^2 -1 = -50
Add 1 to each side
d^2 -1 = -50
d^2 = -49
Take the square root of each side
sqrt(d^2) = sqrt(-49)
d = sqrt(-1) sqrt(49)
d = i( ±7)
d = ±7i
Answer:
A.
Step-by-step explanation:
d^2-1= -50
First, add 1 to both sides.
d^2= -49
Take the square root of both sides:
d=√-49
Since i^2=-1
d=i√49
d= ±7i
Hope this helps!
What is the constant of proportionality
Answer:
The equation for constant of proportionality is:
y = kx
K = Constant of proportionality
An example:
4y = 8x
=> 4y/4 = 8x/4
=> y = 2x
In the answer, y = 2x; 2 is the constant of proportionality
Answer:
it is ratio of the amount s y and x:k = y/x. put another way: y = Kx.
Example:- you are paid 20 rupaye an hour the constant of proportionality is 20
because pay = 20 hours worked
Solve 3x – 1.1 = 0.7
Answer:
x = 0.6
Step-by-step explanation:
3x - 1.1 = 0.7
3x = 1.8
x = 0.6
Answer:
x = .6
Step-by-step explanation:
3x – 1.1 = 0.7
Add 1.1 to each side
3x – 1.1+1.1 = 0.7+1.1
3x = 1.8
Divide each side by 3
3x/3 = 1.8/3
x = .6
True or false? For any two integers x and y, |x+y| = |x| + |y|
Answer:
False
Step-by-step explanation:
|x+y| = |x| + |y|
To show this is false, all we have to do is find one example where it is false
Let x = -1 and y = 4
|-1+4| = |-1| + |4|
|3| = |1| + |4|
3 = 5
This is false so we have a set of integers where the statement is not true
The last digit of the heights of 39 statistics students were obtained as part of an experiment conducted for a class. Use the frequency distribution below to construct a histogram. Choose the correct histogram below. Answer
Answer: 32
Step-by-step explanation:
Simplify ten to the eighth divided by ten to the negative third.
Answer:
[tex]10^{11}[/tex]
Step-by-step explanation:
A statement is given i.e. "ten to the eighth divided by ten to the negative third."
It means that 10 to power 8 divided by 10 to the power -3.
Mathematically,
[tex]\dfrac{10^8}{10^{-3}}[/tex]
We know that, [tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]
Here, x = 10, a = 8 and b = -3
So,
[tex]\dfrac{10^8}{10^{-3}}=10^{8-(-3)}\\\\=10^{8+3}\\\\=10^{11}[/tex]
So, the answer is [tex]10^{11}[/tex]
Write an inequality for the graph shown below.
Use x for your variable.
Answer:
x ≤ 3
Step-by-step explanation:
In the graph given, values of variable x is represented.
From the plot, we note that a small circle is at point 3 on the numberline. This small "o" is shaded, which indicates that the values of x includes 3.
The arrow which starts at 3 on the numberline, points towards our left. This means that the values of x are less than or equal to 3. No value of x is greater than 3.
Therefore, the following inequality can be written for the graph:
x ≤ 3
please help me in this question!
Answer:
n = 5
Step-by-step explanation:
All of the other choices are true except for n = 5, which is a counterexample. [tex]4^{5}[/tex] = 1024, which is greater than the other side as the other side is:
and [tex]4^{2}[/tex] = 16, 16 + 250 = 266
1024 < 266 is definitely false.
Therefore, the counterexample is n = 5.
The within-subjects F is the non-independent groups equivalent of the one-way ANOVA. True or False?
Answer:
Step-by-step explanation:
True
can y’all help me i keep posting this question and people keep guessing and i keep getting it wrong :/
Answer:
C
Step-by-step explanation:
So we have:
[tex]\frac{6^{\frac{3}{10}}}{6^\frac{1}{5}}[/tex]
To simplify, we can use the quotient rule of exponents, which says that if we have:
[tex]\frac{x^a}{x^b}[/tex]
Then this equals:
[tex]=x^{a-b}[/tex]
So, our equation will be:
[tex]\frac{6^{\frac{3}{10}}}{6^\frac{1}{5}}\\=6^{\frac{3}{10}-\frac{1}{5}}[/tex]
Subtract the exponents. Turn 1/5 into 2/10 by multiplying both layers be 2. Thus:
[tex]6^{\frac{3}{10}-\frac{1}{5}}\\=6^{\frac{3}{10}-\frac{2}{10}}[/tex]
Subtract in the exponent:
[tex]=6^{\frac{1}{10}}[/tex]
So, our answer is C :)
Calculate the perimeter of the segment of a circle of radius 8cm. If chord subtemds angle 98 degree at the center
Answer:
If radius = 8 cm and we needed perimeter of complete circle then
circumference (or perimeter) = 2*PI * 8 = 50.2654824574 cm
or 50.27 cm (rounded)
Step-by-step explanation:
Use the drop-down menus to identify the GCF of each pair of numbers.
The GCF of 12 and 16 is
The GCF of 15 and 60 is
The GCF of 24 and 30 is
The GCF of 18 and 72 is
Answer:
4, 15, 6, 18.
Step-by-step explanation:
12 = 1, 2, 3, 4, 6, 12 16 = 1, 2, 4, 8, 16 The GCF of 12 and 16 is 4 because when you compare the numbers that go into 12 and 16, 4 is the highest number that they both are multiples of.Try the others by yourself and if you have any questions ask me in the comments
find sum of series: 1+2+3+...+n
Answer:
the sum of the this series is Sn = [n(n+1)] / 2
Find the sum of -6x^2-1−6x 2 −1 and x+9x+9.
Answer:-6x^2+10x-5.
Step-by-step explanation: -6x^2-1−6x 2−1+x+9x+9 -6x^2-1−6x 2−1+10x+9 -6x^2-1-12−1+10x+9 -6x^2+10x-1-12-1+9 6x^2+10x-5
The sum of the two expressions are -6x²+22x+9
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here the expressions here as -6x²+1+6x ×2-1, x+9x+9
The sum is -6x²+1+6x ×2-1 +x+9x+9=-6x²+22x+9
Hence, The sum of the two expressions are -6x²+22x+9
Learn more about like and unlike terms here:
https://brainly.com/question/29078851
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math help on this question!
Answer:
none
Step-by-step explanation:
110 + 60 = 170
but 170 is obviously not 180 sooo none will be 60 degrees
Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. for any minutes over 200, andrew is charged $0.39 per minute. which of the following piece-wise functions represents charges based on andrews cell phone plan?
Answer:
f (x) = { 19 + 0.39(x - 300), x > 300
Step-by-step explanation:
Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. For any minutes over 300, Andrew is charged $0.39 per minute. Let x be the number of minutes Andrew uses per month and f(x) be the charges based on Andrew's cell phone plan. If then If then first 300 minutes are free and each minute of next (x-300) minutes costs $0.39, therefore Hence, { 19 + 0.39(x - 300), x > 300
Hoped I helped
A publisher sells either digital copies of their new book, paperback copies or hardback copies. For every 4 digital sales they make, they make 5 paperback sales and 1 hardback sale. In the first week of sales, the company sells 308 more paperback copies of the book than hardback copies.
Answer:
This means in the first week the number sells of digital copies is 308, paperback sells was 385 copies and hardback sell was 77 copies
Step-by-step explanation:
Let the number of digital copies be x, the number of paperback copies be y and the number of hardback copies be z.
4 digital sales is equal to 5 paperback sales and 1 hardback sale.
5x = 4y, x = 4z, y = 5z
The company sells 308 more paperback copies of the book than hardback copies
y = 308 + z
But y = 5z
5z = 308 + z
4z = 308
z = 77
y = 5z = 5(77) = 385
x = 4z = 4(77) = 308
This means in the first week the number sells of digital copies is 308, paperback sells was 385 copies and hardback sell was 77 copies
Un guardia forestal divisa, desde un punto de observación A, un incendio en la dirección N27° 10’ E. Otro guardia, que se encuentra en el punto de observación B, a 6 millas al este de A, ve el mismo fuego en la dirección N52° 40’ W. Calcula, al décimo de milla más cercano la distancia de cada uno de los puntos de observación al incendio
Answer:
la distancia del punto de observación A al incendio = 5.5 millas
la distancia del punto de observación B al incendio = 3.8 millas
Step-by-step explanation:
La expresión esquemática de la pregunta se puede ver en la imagen adjunta a continuación :
Del siguiente diagrama;
Usando la sine regla:
[tex]\dfrac{sin \ F}{f} = \dfrac{sin \ A }{a}[/tex]
[tex]\dfrac{sIn \ 79}{6} = \dfrac{sin \ 63}{a}[/tex]
a sin 79 = 6 sin 63
[tex]a =\dfrac{6 \times sin \ 63}{sin \ 79}[/tex]
[tex]a =\dfrac{6 \times 0.8910}{0.9816}[/tex]
a = 5.446 millas
la distancia del punto de observación A al incendio = 5.5 millas (a la décima más cercana)
[tex]\dfrac{sin \ F}{f} = \dfrac{sin \ B}{b}[/tex]
[tex]\dfrac{sin \ 79}{6} = \dfrac{sin \ 38}{b}[/tex]
b sin 79 = 6 sin 38
[tex]b = \dfrac{6 \times sin \ 38}{sin \ 79}[/tex]
[tex]b = \dfrac{6 \times0.6157 }{0.9816}[/tex]
b = 3.7635 millas
la distancia del punto de observación B al incendio = 3.8 millas (a la décima más cercana)
Express the set x≥2x≥2 using interval notation. Use "oo" (two lower case o's) for ∞∞.
Answer: [x/2 , 1]
Step-by-step explanation: Convert the inequality to interval notation.
The union consists of all of the elements that are contained in each interval. There is No Solution.
I hope this helps you out. If not, my apologizes.
-Leif Jonsi-
What is 4.56 x 105in standard form? a.0.00000456 b.0.0000456 c.0.000456 d.456,000
Answer:
the answer is b
Step-by-step explanation:
5/8 + 7/12
A 1/2
B 5/24
C 1 5/24
Step-by-step explanation:
The answer is not in the option.
The answer is 29/24.
if you have driven 225 miles in 3 hours, then how long would it take you to drive 300 miles?
Answer:How many miles can a car be driven in 3 hours at 50 miles per hour? Under normal circumstances and the generally assumed conditions, the answer is of course (3 hours) * (50 miles / hour) = 150 miles.
3.5 hours
It will take you 3.5 hours to go 280 miles at 80 miles an hour.It travels at constant speed for the remaining time. Let x be the time traveled at the unknown constant speed. The total itme for the trip was 6 hours so: 6 = time traveled at 50 mph + time traveled at 60 mph + time traveled at x mph.
Step-by-step explanation:So you drive 25 miles / hour. then 25 miles/ 1 hour = 225 miles / nb of hours.2 minutes
However, traveling at 30 MPH for 1 mile (1 lap) takes 2 minutes, which means that your average will never be 60MPH.approximately 0.6818 miles per hour.
roll two standard dice and add the numbers. what is the probability of getting a number larger than 8 for the first time on the third roll
Answer:
[tex]Probability = \frac{845}{5832}[/tex]
Step-by-step explanation:
Given
Two standard dice
Required
Probability that the outcome will be greater than 8 for the first time on the third roll
First, we need to list out the sample space of both dice
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
[tex]S_2 = \{1,2,3,4,5,6\}[/tex]
Next, is to list out the sample when outcome of both dice are added together[tex]S = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]
Next, is to get the probability that an outcome will be greater than 8
Represent this with P(E)
[tex]P(E) = \frac{Number\ of\ outcomes\ greater\ than\ 8}{Total}[/tex]
[tex]P(E) = \frac{10}{36}[/tex]
[tex]P(E) = \frac{5}{18}[/tex]
Next, is to get the probability that an outcome will noy be greater than 8
Represent this with P(E')
[tex]P(E) + P(E') = 1[/tex]
[tex]P(E') = 1 - P(E)[/tex]
[tex]P(E') = 1 - \frac{5}{18}[/tex]
[tex]P(E') = \frac{18 - 5}{18}[/tex]
[tex]P(E') = \frac{13}{18}[/tex]
Now, we can calculate the required probability;
Probability of a number greater than 8 first on the third attempt is:
Probability of outcome not greater than 8 on the first attempt * Probability of outcome not greater than 8 on the second attempt * Probability of outcome greater than 8 on the third attempt
Mathematically;
[tex]Probability = P(E') * P(E') * P(E)[/tex]
Substitute values for P(E) and P(E')
[tex]Probability = \frac{13}{18} * \frac{13}{18} * \frac{5}{18}[/tex]
[tex]Probability = \frac{13 * 13 * 5}{18 * 18 * 18}[/tex]
[tex]Probability = \frac{845}{5832}[/tex]
(6^2)^x =1 I need to now ASAP
Answer:
x =0
Step-by-step explanation:
[tex]\left(6^2\right)^x=1\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(6^2\right)^x=6^{2x}\\\\6^{2x}=1\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(6^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\ln \left(6^{2x}\right)=2x\ln \left(6\right)\\2x\ln \left(6\right)=\ln \left(1\right)\\[/tex]
[tex]\mathrm{Solve\:}\:2x\ln \left(6\right)=\ln \left(1\right):\\\quad x=0[/tex]
An 14-meter-tall cylindrical tank with a 2-meter radius holds water and is half full. Find the work (in mega-joules) needed to pump all of the water to the top of the tank. (The mass density of water is 1000 kg/m3. Let g = 9.8 m/s2. Round your answer to two decimal places.)
Answer:
to two decimal places
= 6.04 mega joules
Step-by-step explanation:
The volume of the half tank
= πr²h
r= 2 m
h= 14/2= 7 m
Volume= 22/7 *2² *7
Volume= 88 m³
work (in mega-joules) needed to pump all of the water to the top of the tank
= Volume*mass density *acceleration*distance
= 88*1000*9.8*7
= 6036800 joules
In mega joules
= 6.036800 mega Joules
to two decimal places
= 6.04 mega joules
The work needed to pump all of the water to the top of the tank is 6.03 MJ
What is work?
Work is said to be done whenever a force move a body through a certain distance.
To calculate the work needed to pump the water to the tank, first we need to find the volume of the water in the tank half full.
Formula:
V = πr²h/2................ Equation 1Where:
V = Volume of half full water in the tankh = height of the tankr = radius of the base of the tankπ = pieFrom the question,
Given:
r = 2 mh = 14 mπ = 3.14Substitute these values into equation 1
V = 3.14(2²)(14)/2V = 87.92 m³.Finally, to get the work needed to pump all the water to the top of the tank, we use the formula below.
W = ρVhg/2................. Equation 2Where:
W = Work needed to pump all the water to the of the tankρ = Density of the tankh = height of the tankV = Volume of halfull water in the tankg = acceleration due to gravityFrom the question.
Given:
ρ = 1000 kg/m³h = 14g = 9.8 m/s²V = 87.92 m³Substitute these values into equation 2
W = 1000(14)(9.8)(87.92)/2W = 6031312 JW = 6.03 MJ.Hence, The work needed to pump all of the water to the top of the tank is 6.03 MJ.
Learn more about work here: https://brainly.com/question/8119756