Answer and Step-by-step explanation:
Solution:
The equation is given by:
z – z0 = a(x – x0) + b(y – y0).
The point (1, 2, 3) is given , substitute them for x0, y0 and z0:
Z – 3 = a (x – 1) + b(y-2)
Both a and b should be negative, because normal vector to point in the negative x and y direction so that plane will enclose a tetrahedron with finite area in the first octant.
This will only happen if z becomes smaller as we move towards the positive x and y directions.
To find expressions for V, firstly find expression for x, y and z intercepts.
X – Intercepts (y and z = 0) : 2b +a -3 / a
y- Intercepts (x, z = 0): 2b + a- 3 / b
z – Intercepts( x, y = 0): 3 – a – 2b
The base is = (2b+a-3)2/ 2ab
Volume is 1/3 base x height, so
V (a, b) = - (2b+a-3)3 / 6ab
The gradient vector:
ΔV (a, b) = |- (3(2b+a-3)2 ab-b (2b+a-3)3)/6a2b2, (6(2b+a-3)2 ab-a(2b+a-3)3)/6a2b2| = 0
b (2b+a-3)2 [ (2b+a-3) -3a] = 0
a (ab + a-3)2 [(2b +a -3) – 6b] = 0
Where a, b not equal to 0.
We cannot solve for 2b +a-3 = 0 because, that will lead to V = 0, which is impossible.
Therefore, we only solve for second halves equations, which are system of linear equations:
-2a + 2b = 3 and a – 4b = 3
Which gives a = -3 and b = -3/2
Put in equation:
Z – 3 = -3 (x-1) – 3/2 (y-2)
3x +3/2 y +z = 9
Multiplying by 2:
6x + 3y + 2z = 18.
Two professors teach two sections A and B of the same class. Thecourse scores in section A follow a Gaussian random variable of mean 76 and variance64. The course scores in section B follow a Gaussian random variable of mean 67 andvariance 36. What is the probability that the scores of two students, one in sectionA and one in section B, differ by no more than 1 point in absolute value
Answer:
Step-by-step explanation:
Let A denote the score for students of section A.
Let B denote the score for students of section B.
It is provided that:
[tex]A\sim N(76,64)\\B\sim N(67,36)[/tex]
The scores of the students of the two section are independent.
Compute the mean and variance of A - B as follows:
[tex]E(A-B)=E(A)-E(B)=76-67=9\\\\V(A-B)=V(A)+V(B)-2Cov(A,B)=64+36-0=100[/tex]
Compute the probability that the scores of two students, one in section A and one in section B, differ by no more than 1 point in absolute value as follows:
[tex]P(|A-B|\leq 1)=P(-1\leq X-Y\leq 1)[/tex]
[tex]=P(\frac{-1}{10}\leq \frac{(X-Y)-E(X-Y)}{\sqrt{V(X-Y)}}\leq \frac{1}{10})\\\\=P(-0.10<Z<0.10)\\\\=P(Z<0.10)-P(Z<-0.10)\\\\=0.53983-0.46017\\\\=0.07966\\\\\approx 0.08[/tex]
Thus, the probability that the scores of two students, one in section A and one in section B, differ by no more than 1 point in absolute value is 0.08.
WhWhat is the equation of the line in slope-intercept form?
Line on a coordinate plane. The line runs through points begin ordered pair negative 5 comma 0 end ordered pair and begin ordered pair 0 comma 3 end ordered pair.
Enter your answer in the boxes.
y =
x +
Answer: y=3/5x+3
Step-by-step explanation:
I put both points into a graphing calculator (-5,0) (0,3) and found the difference between both and calculated slope using y2-y1/x2-x1 and plugged in each value.
NEED HELP FAST HURRY FAST 30 POINT PLZZZZZZZ
The map shows the locations of skirmishes and battles during the Atlanta Campaign of the Civil War.
John has measured some distances on the map. Atlanta and Kingston are 2.5 cm apart, and Kingston and Ringgold are 3.5 cm apart. If the actual distance from Atlanta to Kingston is 60 miles, what is the actual distance from Kingston to Ringgold?
A) 78 miles
B) 84 miles
C) 92 miles
D) 106 miles
Answer:
The actual distance is 78 miles.
Step-by-step explanation:
HELP MEEEEEEEEHHH pls
Answer:
whole, 5 containers
Step-by-step explanation:
i think this is the answer
Which equation is equivalent to 7 + 3 ( x+4 ) = 10 x -2
Answer:
X=3
Step-by-step explanation:
First, the 3 spread to the x and the 4 because of distribution property. Then, 3x is moved to the right, and the left turns into 19. The X's turn into 7x, and the -2 is moved to the left which makes it positive. The equation is simplified to 21=7x which means that x=3.
Hope this helps!
Help me plz :((((( helpsssbme tyyy
Answer:
jody is 11
Step-by-step explanation:
11x2=22.
22-3=19
19+11=30
Answer:
jody is (2)11 and jody's brother is 19
Step-by-step explanation:
2x -3 + x = 30
3x = 33
x = 11
Why is the payroll calculator helpful in determining the effect of a 401k contribution on net pay?
a. 401k contribution can reduce gross pay
b. 401k contributes reduce the federal tax owned
c. 401k contributions reduce the employee share of social security
d. 401k contributes can be used to reduce the cost of insurance premiums
Answer: 401k contributions reduce the federal tax owed
Step-by-step explanation:
Simplify.
2(1-3) -4v
[tex]\tt Step-by-step~explanation:[/tex]
[tex]\tt Step~1:[/tex]
Whenever you see parentheses, you have to distribute, Here, 2 is next to (1 - 3), so we have to multiply 2 by 1 and -3.
[tex]\tt 2(1-3)-4v\\2*1=2.~~2*-3=-6.\\2-6-4v[/tex]
[tex]\tt Step~2:[/tex]
Simplify by combining like terms.
[tex]\tt 2-6-4v\\2-6=-4\\-4-4v[/tex]
[tex]\Large\boxed{\tt Our~final~answer:~-4v-4}\\\\\tt *Teachers~usually~prefer~having~the~variable~in~front~of~the~expression.[/tex]
Answer:
1. Subtract the numbers
2(1-3)=- 4v
2(2)- 4
2.Multiply the numbers
2(2)- 4v
-4- 4v
3. Rearrange terms
-4-4v
-4v-4
Solution
− 4v-4
Destiny needs a new coat for the winter and she found one at Old Navy for $48.88. The sales tax is 8%. How much will she pay for the sales tax?
Answer:
$52.79
Step-by-step explanation:
$48.88 + 8% = $52.79
Using the formula A = lw , evaluate if l = 3 and w = 9.
A = 27
A = 3
A = 6
A = 12
Answer:
A = 27
Step-by-step explanation:
plug in the numbers so A = (3)(9). you multiply 3 and 9 to get 27
Answer the following questions and round your answers to 2 decimal places. 31% of all college students major in STEM (Science, Technology, Engineering, and Math). If 36 students are randomly selected, find the probability that
Answer:
[tex]\mathbf{P(X =11 ) \simeq 0.1429}[/tex]
Step-by-step explanation:
The objective of this question is to find the probability that:
Exactly 11 of them major in STEM
So, Let assume X to be the random variable that follows a binomial distribution:
Then [tex]X \simeq Bin ( 36, 0.31)[/tex]
The probability that exactly 11 of them major in STEM can be computed as:
[tex]P(X =11 ) = ^{36} C_{11} (0.31)^{11} (1-0.31) ^{36-11}[/tex]
[tex]P(X =11 ) = \dfrac{36!}{11!(36-11)!} \times (0.31)^{11} \times (0.69) ^{25}[/tex]
[tex]P(X =11 ) = \dfrac{36!}{11!(36-11)!} \times (0.31)^{11} \times (0.69) ^{25}[/tex]
[tex]P(X =11 ) =600805296 \times (0.31)^{11} \times (0.69) ^{25}[/tex]
[tex]\mathbf{P(X =11 ) \simeq 0.1429}[/tex]
Thus; the probability that exactly 11 of them major in STEM is 0.1429
PLEASE HELP DUE NOW (10 PTS)
how to multiply inverse matrices
Answer:
Step-by-step explanation:
take 4a okay
so you take the first box and multiply it with the one that is in its spot in the other box.
so -6/7 times 0
-1/7 times -1
-1 times -7
0 times 6
so next you would write the answers to those problems in the spots you multiplied
soooo....
-6/7 times 0
that answer goes in the top left
-1/7 times -1
goes in the top right and so on
Point C is the image of A after a translation two units to the right, then a reflection using the x-axis.
The coordinates of point C are (
,
).
Using translation concepts, the coordinates of point C, considering A(x,y), are given as follows:
C(x + 2, - y).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, we have that:
The translation two units right is represented by x -> x + 2.The reflection over the x-axis is represented by y -> -y.Hence the coordinates of point C, considering A(x,y), are given as follows:
C(x + 2, - y).
More can be learned about translations at https://brainly.com/question/4521517
#SPJ1
Find the largest ratio from the following 3:7, 5:9, 11:3?
What is the coefficient of the term with a degree of two in the product of (2m-9) and (m^2+3m-4)
Answer:
-3
Step-by-step explanation:
First, identify the different possible ways to multiply 2 monomials and get an m^2 term: we can multiply a constant by an m^2 term, or we can multiply an m term by an m term.
Now, we can identify all the combinations of the products that will give a m^2 term:
m^2*-9=-9m^2
3m*2m=6m^2
Now, we just combine the 2 m^2 terms:
-9m^2+6m^2=-3m^2
Therefore, the coefficient of the term with a degree of 2 is -3.
Someone help please xxx
Answer:
Angle A is congruent to angle Z
Angle B is congruent to angle Y
Angle C is congruent to angle X
Line AB is congruent to line ZY
Line AC is congruent to line ZX
Line BC is congruent to line YX
Angle CBA is congruent to Angle XYZ
Two high schools, Jefferson Hills East and Jefferson Hills West are taking field trips to the state capital. A total of 408
students from Jefferson Hills East will be going in 3 vans and 6 buses. A total of 516 students from Jefferson Hills West
will be going in 6 vans and 7 buses. Each van has the same number of passengers and each bus has the same number of
passengers.
Answer:
see explanation!
Step-by-step explanation:
If Jefferson Hills East takes 3 vans and each van has xx students, then 3x3x students will ride in vans. If the school takes 6 buses and each bus has yy students, then 6y6y students will ride in buses. The total number of students is then 3x+6y3x+6y. It is given that the school has 408 students so 3x+6y=4083x+6y=408.
If Jefferson Hills West takes 6 vans and each van has xx students, then 6x6x students will ride in vans. If the school takes 7 buses and each bus has yy students, then 7y7y students will ride in buses. The total number of students is then 6x+7y6x+7y. It is given that the school has 516 students so 6x+7y=5166x+7y=516.
The system of equations is then { 3x+6y=408 6x+7y=516
{
3x+6y=408
6x+7y=516
.
HELP ME PLEASE will give brainliest
Answer:
a
Step-by-step explanation:
Find the area of the shaded region
Answer:
If you multiply it is 44,800 ft
If you add it is 64 ft
Step-by-step explanation:
If you multiply 28 x 16 x 10 x 10 = 44,800 ft
If you add 28 + 16 + 10 + 10 = 64 ft
(I really hope this helps, if you don't mind can you mark me brainiest?)
One bag of broccoli has 300 calories and you ate 3/4 of the bag; how many calories
did you consume?
Answer:
225 calories
Step-by-step explanation:
300 divided by 4= 75
75x3=225
Let s ( t ) = 6 t 3 − 9 t 2 − 360 t be the equation of motion for a particle. Find a function for the velocity.
Answer:
V(t) = 18t²-18t-360
Step-by-step explanation:
Given the equation of motion of particle expressed as:
s(t) = 6t³-9t²-360t
Velocity is the change in displacement of a body with respect to time.
V(t) = ds(t)/dt
V(t) = 3(6)t²-2(9)t¹-360
V(t) = 18t²-18t-360
Hence the function of the velocity is V(t) = 18t²-18t-360
You have a 7-by-5-inch photo of the math club that must be reduced to a size of 4.2 inches by 3 inches for the school yearbook. What percent does the photo need to be reduced to in order for it to fit in the allotted space?
Answer: 64%
Step-by-step explanation:
Given: Size of photo = 7-by-5-inch
Area of photo = 7 x 5 = 35 sq. inches [ Area = Length x width]
Required size = 4.2 inches by 3 inches
Area of required size = 4.2 x 3 =12.6 sq. inches
Area reduced =Area of photo - Area of required size = 35-12.6 =22.4 sq. inches
Percentage of the photo need to be reduced to in order for it to fit in the allotted space
[tex]=\dfrac{22.4}{35}\times100=64\%[/tex]
Percentage of the photo need to be reduced to in order for it to fit in the allotted space = 64%
H
what is the slop of the line shown below
Step-by-step explanation:
Answer:
j
Step-by-step explanation:
332/10 as an mixed number
Answer:
27 2/3
Step-by-step explanation:
Hope this helps :)
Answer: 33 & 1/5
Step-by-step explanation:
Step 1 - Find Whole Number
Calculate out how many times the denominator goes into the numerator. To do that, divide 332 by 10 and keep only what is to the left of the decimal point:
332 / 10 = 33.2000 = 33
Step 2 - Find New Numerator
Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.
332 - (10 x 33) = 2
Step 3 - Put Together
Keep the original denominator and use the answers from Step 1 and Step 2
Step 4 - Minimize
Minimize the fraction part from Step 3 by dividing the numerator and denominator by 2, which is the greatest common factor, to get the final answer. 332/10 as a Mixed Number.
You buy 3 apples at the quick market for 1.05. You can buy 5 of the same apples at the stop and save for 1.20. Which place is better?
Answer:
The stop
Step-by-step explanation:
3 apples = 1.05
5=1.20
Yes you will spend more at the stop but you get more apples
I hope this isn't a goofy answer please don't laugh i was trying to help :(
What is the answer to this complex math question? 1+1=
3
2
4
7
Answer: hMmMmMm..
Step-by-step explanation: bruh it’s gotta be 7, I mean it totally makes the most sense.
(Ello m8) :3
pls help !!!!! i do not understand this at all !??
Plzzz help this is a quick question
4.) Cellular phone company A has 86,000,000 customers and cellular phone company B has
83,200,000 customers. How many more customers does cellular phone company A have than
cellular phone company B? Express your answer in standard form and scientific notation.
Answer:
They have 2,8000,00 more customers. 2.8x10^6
Step-by-step explanation:
b) The area of a rectangular window is 7980 cm 2 If the width of the window is 84 cm, what is its length?
Answer:
The answer is 74 cm
Step-by-step explanation:
The area of a rectangle = length × width
Since we are finding the width
We have
From the question
area = 6216 cm²
length = 84 cm
The width is
We have the final answer as
74 cm
Step-by-step explanation: