Answer:
25, 36, 49, 64, 81
Step-by-step explanation:
How many distinct angles from the vertical axis can the orbital angular momentum vector l make for an electron with = 4?
The orbital angular momentum vector, represented by l, can make nine distinct angles from the vertical axis for an electron with l = 4.
The orbital angular momentum vector, denoted by l, is a vector quantity that describes the rotational motion of an electron around an atomic nucleus. The magnitude of the orbital angular momentum is given by the quantum number l.
The orbital angular momentum vector can point in different directions relative to the vertical axis. To determine the number of distinct angles it can make, we need to consider the possible values of the quantum number l.
For a given value of l, the orbital angular momentum vector can have 2l + 1 orientations. These orientations correspond to the magnetic quantum number ml, which can take integer values ranging from -l to +l.
In this case, the given value of l is 4. Therefore, the orbital angular momentum vector can have 2(4) + 1 = 9 distinct angles from the vertical axis.
These angles are determined by the values of ml, which range from -4 to +4 in integer steps. Each value of ml corresponds to a specific orientation of the orbital angular momentum vector relative to the vertical axis.
Hence, the orbital angular momentum vector l can make nine distinct angles from the vertical axis for an electron with l = 4.
Learn more about angular momentum here
https://brainly.com/question/4126751
#SPJ11
Find (a) the circumference and (b) the area of the circle. Use 3.14 or 22/7 for pi. Round your answer to the nearest whole number, if necessary.
A circle with a diameter of 70 inches.
(a) circumference: about ? in.
(b) area: about ? in.²
Answer:
a)219.8
b)3846.5
Step-by-step explanation:
a) circumference is pi*diameter, so 3.14*70 is 219.8
b) area is pir^2, and radius is 1/2 of diameter, it would be 3.14*35^2, so 3.14*1225, so 3,846.5 in^2.
Answer:
lol
Step-by-step explanation:
h
3.2 less than a number t is at most 7.5.
Answer:
10.7
Step-by-step explanation:
10.7-3.2 is at most 7.5
You grab your math teacher's standard number icosahedron (a die containing the numbers 1 through 20). You roll the die 10 times and get the following numbers: 5,12,1,9,20,14,13,8,11, and 20.
1. What is the theoretical probability (expressed as a fraction) of rolling an even number less than 12?
2. What is the experimental probability (expressed as a fraction) of rolling a 20?
3. What is the theoretical probability (expressed as a fraction) of rolling a number divisible by 3?
4. What is the experimental probability (expressed as a percent) of rolling a 1?
1. The theoretical probability of rolling an even number less than 12 is 5/10, or 1/2.
What is Probability?Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.
2. The experimental probability of rolling a 20 is 2/10, or 1/5.
3. The theoretical probability of rolling a number divisible by 3 is 4/10, or 2/5.
4. The experimental probability of rolling a 1 is 1/10, or 10%.
To know more about probability click-
brainly.com/question/24756209
#SPJ1
Dividend:
2x3 + 11x2 + 18x + 9
-6x3 - 15x - 9
2x2 + 5x + 3
Quotient:
2x4 + 11x3 + 18x + 9
2x3 + 5x2 + 3x
2x2 + 5x + 3
Answer:
Divisor-D Dividend- A Quotient-C
Step-by-step explanation:
It is to be noted that in the subtopic of Polynomials, a dividend is the factor or element being divided while the element that results from the division of one number using another is called the quotient.
What is a Divisor?In mathematics, a divisor is a factor or number that divides another leaving no remainder.
That is Dividend/Divisor = Quotient. It is important to note that in Polynomials, there is usually more than one similarity as far as the terms are concerned.
The full question is unavailable hence the general answer.
Learn more about dividends at:
https://brainly.com/question/2960815
#SPJ2
Gabrielle is 14 years younger than Mikhail. The sum of their age is 58. What is Mikhail’s age? __ years old
Kayla's father throws Kayla a graduation party that costs $775. He pays the DJ $250, $75 for the cake, and $5 per party guest for food. How many people were at the party?
Answer:
90 people
Step-by-step explanation:
Total: $775
DJ: $250
Cake: $75
Unknown party guests each getting $5
Let the unknown be x
We can form an equation; DJ + Cake + x number of party guests = $775
250 + 75 + 5x = 775
325 + 5x = 775
Subtract 325 from both sides of the equals sign.
5x = 450
Make x the subject and divide both sides by 5
x = 90
There were 90 party guests.
a fair coin is tossed 10 times in a row. what is the probability of getting at least 2 heads ? (hint: use combinatorics)
Answer:
Step-by-step explanation:
If you flip a fair coin 10 times, you can get 0 heads about 0.1% of the time, 1 head about 1% of the time, 2 heads about 4% of the time, 3 heads about 12% of the time, 4 heads about 21% of the time, and 5 heads about 25% of the time. Thus, the chances of getting 5 heads is about 1 in 4.
which points are solutions to the linear inequality y<0.5x+2 select three options. (-3,-2)(-2, 1)(-1, -2)(-1, 2)(1, -2)
The given inequality: y < 0.5x + 2
The coordinates of they satisfy the given inequality than they are the solutions of the inequality y < 0.5x + 2
Plot the given points on the given line, The points which are passes through the line is the solution of the given inequality:
The point (-1,2)
The points doenot pss through the line and lie in the shaded region
So, (-1,2) are not the solution of the given inequality:
Solution are :(-2, 1)
(1, -2)
Answer :
(-2, 1)
(1, -2)
The line plot represents data collected from a used bookstore.
Which of the following describes the spread and distribution of the data represented?
The data is almost symmetric, with a range of 9. This might happen because the bookstore offers a sale price for all books over $6.
The data is skewed, with a range of 9. This might happen because the bookstore gives away a free tote bag when you buy a book over $7.
The data is bimodal, with a range of 4. This might happen because the bookstore sells most books for either $3 or $6.
The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4.
The information that describes the line plot is
The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4.When is a line plot said to be symmetricA line plot is said to be symmetric when the data points on one side of the center line (usually the median) mirror the data points on the other side. In other words, if you fold the line plot in half at the center line, the two halves would overlap perfectly.
Symmetry can be determined visually by looking at the line plot and assessing whether the data points appear to be evenly distributed on either side of the center line.
If the line plot is symmetric, it suggests that the data is evenly distributed around the center, and there are no significant outliers or biases in the data. If the line plot is not symmetric, it suggests that there may be some skewness or asymmetry in the data, and further analysis may be needed to understand the underlying patterns and trends.
Learn more about symmetric data at
https://brainly.com/question/30888145
#SPJ1
For a
1
,…,a
n
>0, the set E={x∈R
n
:
a
1
2
x
1
2
+⋯+
a
n
2
x
n
2
≤1} is called an ellipsoid. Find the interior, closure, and boundary of E. Exercise 6.43. For a
1
,…,a
n
>0, the set E={x∈R
n
:
a
1
2
x
1
2
+⋯+
a
n
2
x
n
2
≤1} is called an ellipsoid. Find the interior, closure, and boundary of E.
The interior, closure, and boundary of the ellipsoid E.
- The interior of E is the set of all x ∈ ℝⁿ such that a₁²x₁² + ... + aₙ²xₙ² < 1.
- The closure of E is the set of all x ∈ ℝⁿ such that a₁²x₁² + ... + aₙ²xₙ² ≤ 1.
- The boundary of E is the set of all x ∈ ℝⁿ such that a₁²x₁² + ... + aₙ²xₙ² = 1.
An ellipsoid is a set of points in n-dimensional space that satisfies a certain equation. In this case, the set E is defined as follows:
E = {x ∈ ℝⁿ : a₁²x₁² + ... + aₙ²xₙ² ≤ 1}
To find the interior of E, we need to identify the points within E that are not on its boundary. In other words, we need to find the points for which the inequality is strict. The interior of E is the set of all x ∈ ℝⁿ such that a₁²x₁² + ... + aₙ²xₙ² < 1.
The closure of E includes the interior of E as well as the boundary of E. In other words, the closure of E is the set of all x ∈ ℝⁿ such that a₁²x₁² + ... + aₙ²xₙ² ≤ 1.
The boundary of E consists of the points on the surface of the ellipsoid. These are the points for which a₁²x₁² + ... + aₙ²xₙ² = 1.
This completes the explanation of the interior, closure, and boundary of the ellipsoid E.
Learn more about ellipsoid from the following link:
https://brainly.com/question/32356250
#SPJ11
Directions: Write an equation for the circle shown on the graph in standard form. 15.
Answer: x(squared) + (y + 2)(squared) = 36
Step-by-step explanation:
The center of the circle is at (0 , -2), so we will eliminate the x value by just writing x(squared), and then we will write the y value as (y + 2)(squared) because the standard form for a circle is
(x - h)(squared) + (y + 2)(squared) = r(squared)
And if we count from the center to the top point of the circle, the number would be 6, so we would square 6 which would be 36.
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.) (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = x + 2y subject to x + 6y < = 15 3x + y < = 11 X > = 0, y > = 0. p = x= y=
The feasibility area is empty. The solution of the LP-problem is not possible (does not exists).
With the constraint that x and y are both non-negative, the second constraint has only one point in common with each of the first and third constraints; and those two points are different.
The feasibility region is empty; so nothing can be optimized.
Plots x + 2y = 30 (red), 2x + 2y = 30 (green) and 2x+y = 30 (blue)
The feasibility area, according to the condition, is the area of the first quadrant
- above the red line,
- below the green line,
- above the blue line.
It can be seen from the plot that this set is empty.
Therefore, the feasibility area is empty. The solution of the LP-problem is not possible (does not exists).
To learn more about linear inequations refer here
https://brainly.com/question/25799000
#SPJ4
Disclaimer
The question given by you is incomplete, so the above solution is of a similar question, and the question is
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT
Maximize p = x + y subject to
x + 2y ≥ 30
2x + 2y ≤ 30
2x + y ≥ 30
x ≥ 0, y ≥ 0.
p=
(x, y)=
a=zm+z solve for m please help!!!!!
Answer:
(a-z)/z = m
Step-by-step explanation:
a = zm+z
Subtract z from each side
a-z = mz+z-z
a-z = mz
Divide by z
(a-z) /z = mz/z
(a-z)/z = m
What is 7t + 2 = -12
1. An unknown number of liters of mixture containing 6% boric acid is to be mixed with 2 liters of
a mixture which is 15% boric acid. The new solution created is to be at a concentration of 12%
boric acid. How much of the 6% solution must be used? Show all work.
Answer:
0.4
Step-by-step explanation
2/0.15+x/0.06=x+2/0.12
30=x/0.12+2/0.12
1.6+2x=x+2
x=0.4
OK so I need help on this trigonometry problem, I need it by June 3rd HELP ME PLZ!
I asked my teacher and he said it's not a right triangle at all,
You must create a triangular Animal pen that covers 40 square yards however it has to contain a 30-degree angle. Give the lengths of two sides of a triangle that include the angle but has an area of 40 sq yards.
Answer:
a=16 b =10 or any other combination that gives 160
a = 20 b=8
a = 32 b = 5
Step-by-step explanation:
The area of a triangle using the lengths of two sides and the sine of the included angle is ½ ab sin C where a and b are sides and C is the angle.
A =40 = 1/2 ab sin 30°
sin 30° = 1/2 so
40 = 1/2*ab*1/2
40 =1/4 ab multiply each side by 4
160 = ab
any combination of sides that gives you 160 will work
Let's check if a=16 b =10
A = 1/2*16*10 sin 30°
A = 1/2*160*1/2
A = 40
Evaluate the surface integral ∫SF⋅ dS∫SF⋅ dS where F=〈5x,−4z,4y〉F=〈5x,−4z,4y〉 and SS is the part of the sphere x2+y2+z2=9x2+y2+z2=9 in the first octant, with orientation toward the origin.
The surface integral ∫SF⋅ dS∫SF⋅ dS where F=〈5x,−4z,4y〉F=〈5x,−4z,4y〉 and SS is the part of the sphere x² +y² +z² =9x² + y² +z² = 9 in the first octant, with orientation toward the origin is 45π / 2.
How to calculate the surface integralIt should be noted that a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field over the surface, or a vector field
The integral will be:
45∫π/2 0 (-cos)|π/2 d
= 45( π/2 - 0)
= 45π / 2
Learn more about integral on:
https://brainly.com/question/27419605
#SPJ1
Exponential function f is represented by the table.
X
f(x)
-2
-46
-1
-22
D.
0
-10
1
-4
2
-1
Function g is represented by the equation.
g(x) = -18()* + 2
Which statement correctly compares the two functions on the interval [-1, 2]?
O A. Only function f is increasing, and only function is negative.
B.
Only function f is increasing, but both functions are negative.
O C.
Both functions are increasing, but function / increases at a faster average rate.
Both functions are increasing, but function g increases at a faster average rate.
The correct statement is:
A. Only function f is increasing, and only function g is negative.
To compare the two functions on the interval [-1, 2], let's examine their properties.
For function f, we can observe that as x increases from -2 to 2, the corresponding values of f(x) are also increasing. Therefore, function f is increasing on the interval [-1, 2].
From the table, we can see that all values of f(x) are negative, indicating that function f is negative on the interval [-1, 2].
Now let's analyze function g, which is represented by the equation g(x) = \(-18(x^2) + 2\). This function is a quadratic function with a negative coefficient for the \(x^2\) term.
Since the coefficient of the \(x^2\) term is negative, the parabola representing function g opens downward. Therefore, function g is decreasing.
Comparing the properties of the two functions on the interval [-1, 2], we can conclude that:
A. Only function f is increasing, and only function g is negative.
So the correct statement is:
A. Only function f is increasing, and only function g is negative.
For such more questions on Comparing f and g.
https://brainly.com/question/30987074
#SPJ8
Let P=(0,0,1),Q=(1,−1,2),R=(−1,1,1). Find (a) The area of the triangle PQR. (b) The equation for a plane that contains P,Q, and R.
a) The area of triangle PQR is:
Area = √(6)/2
b) The equation of the plane that contains P, Q, and R is:
x + y + 2z = 2
a) For the area of the triangle PQR, we can use the formula:
Area = 1/2 |PQ x PR|
where PQ and PR are the vectors from P to Q and R, respectively, and x denotes the cross product.
So, we have:
PQ = <1-0, -1-0, 2-1> = <1, -1, 1>
PR = <-1-0, 1-0, 1-1> = <-1, 1, 0>
Taking the cross product:
PQ x PR = <1, -1, 1> x <-1, 1, 0> = <-1, -1, -2>
Taking the magnitude:
|PQ x PR| = √((-1)² + (-1)² + (-2)²) = √(6)
So, the area of triangle PQR is:
Area = 1/2 × √(6) = √(6)/2
b) To find the equation of the plane that contains P, Q, and R, we can use the point-normal form of the equation:
n · (r - P) = 0
where n is the normal vector of the plane (which is perpendicular to the plane), r is any point on the plane, and · denotes the dot product.
To find the normal vector, we can take the cross product of PQ and PR:
n = PQ x PR = <-1, -1, -2>
Now, we can use any of the three points to find the equation of the plane. Let's use P:
n · (r - P) = 0
Substituting n and P:
<-1, -1, -2> · (r - <0, 0, 1>) = 0
Expanding the dot product:
-1(r_x - 0) - 1(r_y - 0) - 2(r_z - 1) = 0
Simplifying:
-r_x - r_y - 2r_z + 2 = 0
So, the equation of the plane that contains P, Q, and R is:
x + y + 2z = 2
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ4
What is the modal number in points
Answer:
you look at which number comes up the most mode means the number tt comes up the most
Step-by-step explanation:
The Quik-Clean Car Wash charges $15 for a car wash plus $2.50 per gallon for unleaded gasoline. The Mighty Clean Car Wash charges $10 for a carwash plus $2.75 per gallon for unleaded gasoline. Josh is comparing the cost of having his car wash plus filling up his tank with gas at each business. How many gallons of gas would he need to purchase for the cost to be the same at each car wash?
Answer:
Josh would need to purchase 20 gallons of gas for the cost to be the same at each car wash
Step-by-step explanation:
We need to model both car wash's costs. The Quik-Clean Car Wash charges $15 for a car wash plus $2.50 per gallon for unleaded gasoline. If x is the number of gallons of unleaded gasoline. the total charges of this store are:
C1=15+2.5*x
The Mighty Clean Car Wash charges $10 for a carwash plus $2.75 per gallon for unleaded gasoline. Following the same procedure, their costs are:
C2=10+2.75*x
Josh wants to know how many gallons of gas will make both businesses charge the same. Equating both equations:
15+2.5*x=10+2.75*x
Simplifying:
-0.25x=-5
Solving:
x=-5/(-0.25)=20
Josh would need to purchase 20 gallons of gas for the cost to be the same at each car wash
Write each ratio using the given figure. If necessary, find the missing side.Cos R = __________
ANSWER :
9/41
EXPLANATION :
Using Pythagorean Theorem to find the other side of the triangle :
\(\begin{gathered} PR^2=QP^2+QR^2 \\ 41^2=40^2+QR^2 \\ 1681=1600+QR^2 \\ QR^2=81 \\ QR=\sqrt{81} \\ QR=9 \end{gathered}\)Recall that cos angle is adjacent over hypotenuse
The adjacent side to angle R is QR and the hypotenuse is RP
That will be :
\(\cos R=\frac{QR}{RP}=\frac{9}{41}\)If Scott’s monthly sales stay relatively the same, can he hire an employee with an average monthly salary of $1,000?
Answer:
yes
Step-by-step explanation:
bob says so he works at Scott
21y(y+3) please i need the answer
Answer:
21y^2+63y
Step-by-step explanation:
21y(y+3)
21y^2+63y
A rectangle has a height of 4x^3 and a width of x3 + 3x^2 + 2x.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.
Answer:
4x^6+12x^5+8x^4
Step-by-step explanation:
Can you please help me do that?
Answer:
v=8
Step-by-step explanation:
35=3v+11
subtract 11 from both sides
35-11=3v
24=3v
divide both sides by 3
8=v
Answer:
V=8.
Step-by-step explanation:
To get the answer you first subtract 11 from both sides of the equation
35=3v+11
-11 -11
The two 11's on the right side would cancel out leaving
24=3v
Then you divide both sides by 3
24/3=3/3
the two 3's would cancel out leaving
24/3 or 24 divided by 3.
24/3 equals 8.
so in conclusion v=8.
Hope this helps! :D
If Alfie designs the wheels to have a diameter of 67. 5mm and a width of 29. 3mm, what volume of plastic will be required to make the cylinder, to the nearest mm3?
To make wheels of a diameter of 67.5 mm and a width of 29.3 mm, Alfie requires 104891.38 cubic mm volume of plastic.
A cylinder is a 3-Dimensional shape with 3 faces that are one curved face and 2 flat ends. The volume of a cylinder is given by the expression:
V = π\(r^2h\)
r is the radius
h is the height
Given, diameter = 67.5 mm
radius = d ÷ 2 = 67.5 ÷ 2
= 33.75 mm
height = width = 29.3 mm
Volume = \(\frac{22}{7}*33.75*33.75*29.3\)
= 104891.38 cubic mm
Therefore, the volume of the cylindrical wheel that Alfie designed is 104891.38 cubic mm.
Learn more about volume:
https://brainly.com/question/27535498
#SPJ4
a fifth-degree polynomial can have a maximum of how many relative extrema and points of inflection? explain. a fifth-degree polynomial can have at most critical numbers, and hence relative extrema. it can have at most points of inflection.
A fifth-degree polynomial can have at most 4 critical numbers, and hence 4 relative extrema. It can have at most 3 points of inflection.
Explanation:
1. A polynomial function of degree n has (n-1) critical numbers, which are points where the derivative is either zero or undefined. Since a fifth-degree polynomial has a degree of 5, it can have at most (5-1)=4 critical numbers.
2. Relative extrema are local maximum or minimum points of the function. A relative extrema occurs at a critical number where there is a change in the sign of the first derivative (going from positive to negative or negative to positive). Since we have at most 4 critical numbers, there can be at most 4 relative extrema for a fifth-degree polynomial.
3. Points of inflection are points on the graph where the function changes its concavity (from concave up to concave down or vice versa). This occurs when the second derivative of the function changes sign. To find the points of inflection, we need to find the critical numbers of the first derivative, which is a fourth-degree polynomial (one degree less than the original polynomial). A fourth-degree polynomial has at most (4-1)=3 critical numbers.
4. Therefore, a fifth-degree polynomial can have at most 4 relative extrema and 3 points of inflection.
For more questions on polynomial
https://brainly.com/question/2833285
#SPJ11
The sum of two integers is 31. The larger of the two integers is 4 more than 2 times the smaller integer. What are the integers? 9 and 22 -22 and 53 allo -9 and 40 14 and 17
Answer:
x = 22 y = 9
Step-by-step explanation:
Let me know if you need an explanation! Hope this helped :)