Answer:
-2
Step-by-step explanation:
We can find the slope for two points
m = ( y2-y1)/(x2-x1)
= ( 12 - 4)/(-6- -2)
= 8/( -6+2)
= 8/-4
= -2
Integral- Volumes by Slicing and Rotation About an Axis..Volume of a Pyramid... Could you help me solving this question, please?
Answer: volume is 9 cubic units
===================================================
Explanation:
Each cross section is a square with side length x, so the area of this cross section is x^2
We're integrating from x = 0 to x = 3
So we have
[tex]\displaystyle f(x) = x^2\\\\\\\displaystyle g(x) = \int x^2 dx = \frac{1}{3}x^3+C\\\\\\\displaystyle \int_{a}^{b} f(x) dx = g(b) - g(a)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = g(3) - g(0)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = \left(\frac{1}{3}(3)^3+C\right) - \left(\frac{1}{3}(0)^3+C\right)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = 9\\\\\\[/tex]
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
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]
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.
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!
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.
5(x - 10) = 30 - 15x
Answer:
x = 4
Step-by-step explanation:
We can first expand 5(x-10), getting 5x - 50.
Thus, 5x - 50 = 30 - 15x
We can then isolate x, getting (5+15) x = 30 + 50
20 x = 80
x = 4.
Answer:
5(x - 10) = 30 - 15x
We distribute 5 (x-10)
So 5x-50 = 30 -15x
5x+15x=50+30
(-15x became 15x because we brought it back to the other side and -50 became 50 because we brought it back to the other side to put the x's with the x's and the digits with the digits.)
So 20x=80
x= 50/20
We simplify 80/20
So x=4
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 :)
Rounding whole number which number could round to 80,600 80,532 80,549 80,617 80, ,651
Answer:
80,617
Step-by-step explanation:
the 1 in the tens place puts the number back down to 600
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:
Represent the following expression using an exponent.
12 x 12 x 12 x 12
Answer:
12<4 (12 to the power of 4)
Step-by-step explanation:
an exponet is used when a number is repeated multiplied against itself. sinec 12 is being multiplied against itself 4 times, we can use the exponent of 4
Answer: [tex]12^4[/tex]
Step-by-step explanation:
Concept to know: for exponents, the amount of same number that is multiplied together will be the number of exponents
--------------------------------------
12×12×12×12
There are in total 4 [12]'s multiplied together, so we will get [tex]12^4[/tex]
Hope this helps!! :)
Please let me know if you have any question or need further explanation
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
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
The measure of ZAOC is 90 degrees. Find the value of x.
Answer:
14 + 3x + 46 = 90
3x + 60 =90
3x = 30
x = 10
Answer:
Step-by-step explanation:
If u see it is right angle so 90 - 14 u will get an or bc 76
3x+46=76
3x=76-46
3x=30
X=30/3
10
14. Line AD is parallel to line EG. If
m<3 is 70°, what is m 24?
F 10°
H 110°
G 20°
| 290°
15. Which angle is congruent to Z 3?
H 22
C 26
B 24
D 28
Answer:
14. H. 110°
15. D. <8
Step-by-step explanation:
14. Given that line AD and line EG are parallel as shown above, m<3 and m<4 are linear pairs and are supplementary. That is, m<3 + m<4 = 180°.
If m<3 = 70°, therefore, m<4 = 180° - 70°
m<4 = 110°
15. <3 corresponds with <8. Corresponding angles are congruent. Therefore, <3 = <8.
0 to 100 miles per hour in a mere 0.8 seconds. Calculate its acceleration. Show your work and include units.
Answer:
Answer: so the answer is 80 miles per 0.8 Step-by-step explanation: consistence
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
find sum of series: 1+2+3+...+n
Answer:
the sum of the this series is Sn = [n(n+1)] / 2
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
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°
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
#SPJ2
(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]
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-
Simplify 55/66 to lowest terms ?
Answer:
5/6
Step-by-step explanation:
To simplify this fraction, we need to find the GCF (greatest common factor) of the numerator and denominator. In this case, the GCF of 55 and 66 is 11. Now, all we have to do is divide both the numerator and denominator by the GCF. The numerator will become 55 / 11 = 5 and the denominator will become 66 / 11 = 6 so the simplified fraction is 5 / 6.
Someone help!! Need answer fast!
Answer:
the area of the triangle is 20 units, and the answer to the expression is also 20, so its equal to each other. 20=20
the area of the trapezoid is 38.5 units
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]
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
Jessica always uses the same ratio of green beads to blue beads when she makes necklaces. The graph shows these equivalent ratios. Which table shows the same data?
Answer:
table 2
Step-by-step explanation:
see attached
Answer:
table no. 2
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 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
Solve x+9=7 show work
Answer: x = -2
x + 9 = 7, Move the constant to the right.
x =7 -9 now calculate that.
then you get x = -2
Hope that helps ya out :D
Answer:
x+9=7
So x= 7-9
( 9 became -9 because we brought it back to the other side to have the x alone and the digits alone )
So x= -2